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Differential polarisation studies of the deffuse interstellar band and Be stars Dinshaw, Nadine 1992

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to the required standardDIFFERENTIAL POLARISATION STUDIES OF THE DIFFUSE INTERSTELLARBANDS AND Be STARSbyNADINE DINSHAWB.Sc., University of British Columbia, 1989A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of Geophysics and AstronomyWe accept this thesis as conformingTHE UNIVERSITY OF BRITISH COLUMBIADecember 1991© Nadine Dinshaw, 1991In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature) Department of GeoS/YS/ cS "iwf) #457-,peNeo4yThe University of British ColumbiaVancouver, CanadaDate ^DG-C /0 /91/ DE-6 (2/88)AbstractA microcomputer-controlled polarisation analyser has been designed and built at theDominion Astrophysical Observatory specifically for the 1.83-m telescope. It is mountedbefore the Cassegrain spectrograph entrance, and is capable of providing spectropolarime-try at the full (--, 0.15 A) resolution of the spectrograph-detector system. The device usesa polarising beamsplitter for selecting a plane of polarisation, and a quarter-wave plateto remove most 90%) of the effects of instrumental polarisation. The throughput ofthe analyser is --, 40%. The analyser may be rotated at a rate of up to 12.5° s'; positionangles of the analyser may be set to within +0.5°.We present the results of three studies carried out with the polarisation analyser: ifthe diffuse interstellar bands arise in the same grains which produce the optical continuumpolarisation, whereby the bands represent spectral regions of enhanced extinction, thena corresponding enhancement in the polarisation is expected. Differential polarisationmeasurements in four of the strongest diffuse features in the spectra of HD 183143, 55 Cygand Per revealed no polarisation structure through any of the bands at levels significantlylower than those predicted. From our results, we have established upper limits to thevariation of polarisation in the 5780, 5797, 6177 and 6284 A bands of 0.01, 0.01, 0.02 and0.03%, respectively. We conclude that the diffuse features are not associated with thegrains responsible for the continuum polarisation. Intermediate-sized grains (0.02 < a <0.1pm) which are poorly aligned or spherical are still consistent with our results as well asother observational properties of the bands. The absence of polarisation tends to favoura molecular origin for the diffuse bands.Attempts to measure differential polarisation associated with the line profile variationsof two OB stars are also described. Analysis of the travelling subfeatures in the H/3 lineof C Oph and the H/3 and He I \4921 lines of E Per failed to reveal polarisation structurewith upper limits of 0.08% and 0.1%, respectively.iiDifferential polarisation measurements in the 11,3 emission line of three intrinsicallypolarised Be stars are described. The stars Per and -y Cas exhibit significant polarisationchanges across the HO line. These changes are characterised by a decrease of polarisationtoward the center of the line and an increase at the line center itself. Our observations alsoshow strong evidence for variations in the plane of polarisation across the line. We arguethat unpolarised line emission cannot completely account for the observed polarisationchanges. Indeed, some of the polarisation structure especially in the line wings appearsto be caused by absorption processes in a rotating circumstellar envelope. No significantchange of polarisation was detected in the line of 28 Cyg.iiiContentsAbstractList of Tables^ viiList of Figures viiiAcknowledgements^ xi1 Introduction 11.1 Historical Background ^ 11.2 The Description and Measurement of Polarisation ^ 21.3 An Outline of this Thesis^ 42 The UBC/DAO Polarisation Analyser 52.1 Introduction ^ 52.2 Design of the Polarisation Analyser ^ 62.2.1^The Optics ^^Beamsplitter Cubes ^^Quarter-Wave Plate 82.2.2^The Mount ^ 82.2.3^The Controller 92.3 Data Acquisition and Analysis ^ 132.4 Performance    142.4.1^Design Evolution ^ 142.4.2^Testing the Analyser 17iv3 Differential Polarisation Studies of the Diffuse Interstellar Bands 203.1 Diffuse Interstellar Bands ^ 203.1.1^Introduction ^ 203.1.2^Possible Carriers of the DIBs ^ 213.1.3^Past Polarisation Studies of the DIBs ^ 243.2 Observations ^ 253.3 Data Reduction 303.4 Results ^ 323.5 Discussion 483.6 Interpretation ^ 554 Differential Polarisation Studies of Be Stars 584.1 Be Stars ^ 584.1.1^Introduction ^ 584.1.2^The Be Phenomenon ^ 594.1.3^Past Polarisation Studies of Be Stars ^ 624.2 Observations ^ 654.3 Data Reduction 694.4 Polarisation Analysis ^ 714.5 Results and Discussion 734.5.1^Differential Polarisation Associated with Line-ProfileVariations ^ 734.5.1.1^C Oph 734.5.1.2^€ Per^ 904.5.1.3^Interpretation ^ 944.5.2^Differential Polarisation Measurements Across the HP Lineof Be rements Across the 11/3 Lineof Be Stars ^ 944.5.2.1^Physical Interpretation ^ 1084.5.2.2^Individual Stars ^ 111Persei ^ 111ry Casssiopeiae 11328 Cygni ^ 1185 Summary and Conclusions^ 119References^ 122A Component Specifications for the UBC/DAO Polarisation Analyser 129viList of Tables3.1 Program Stars for DIB Polarisation Study ^ 273.2 Summary of DIB Observations ^ 313.3 Upper Limits to the Polarisation in the Diffuse Interstellar Bands ^ 474.1 Program Stars for Be Star Polarisation Study ^ 664.2 Summary of Be Star Observations ^ 684.3 Standard Unpolarised Stars for Be Star Polarisation Study ^ 704.4 Model Parameters for 0 Per and -y Cas ^ 115A.1 Optical Component Specifications 129A.2 Mount Components ^ 129viiList of Figures2.1 Optical Design of the UBC/DAO Polarisation Analyser^ 72.2 Top View of Analyser Mount^  102.3 Bottom View of Analyser Mount  112.4 Polarised Spectrum of the Standard Unpolarised Star 0 Ori ^ 152.5 Polarisation Curves of the Standard Polarised Star HD 183143  182.6 Polarisation Curves of the Standard Unpolarised Star a Cyg ^ 193.1 Representative Spectrum of HD 183143 ^  283.2 Representative Spectra of 55 Cyg and ( Per  293.3 (a) Residual Spectra of HD 183143 ^  333.3 (b) Residual Spectra of 55 Cyg  343.3 (c) Residual Spectra of ( Per ^  353.4 Typical Rectification of a Residual Spectrum ^  373.5 (a) Rectified Residual Spectra of HD 183143  383.5 (b) Rectified Residual Spectra of 55 Cyg ^  393.5 (c) Rectified Residual Spectra of ( Per  403.6 Mean Residual Spectrum of the Standard Unpolarised Star a Cyg ^ 423.7 (a) Mean Residual Spectrum of HD 183143^  433.7 (b) Mean Residual Spectrum of 55 Cyg  443.7 (c) Mean Residual Spectrum of C Per ^  453.8 Cancellation of S-shaped Structure from the Mean Residual Spectrum ofHD 183143^  463.9 Mean Residual Spectrum of HD 183143 and 55 Cyg ^ 493.10 (a) Predicted Differential Polarisation for HD 183143  523.10 (b) Predicted Differential Polarisation for 55 Cyg ^  53viii3.10 (c) Predicted Differential Polarisation for ( Per ^  544.1 Polarised Spectral Time Series of C Oph at H/3  754.2 Polarised Residual Time Series of C Oph at H/3 ^  764.3 Unpolarised Spectral Time Series of C Oph at He I A6678 ^ 774.4 Unpolarised Residual Time Series of C Oph at He I A6678  784.5 Superposition of Polarised and Unpolarised Residual Time Series of C Ophat H/3 and He I A6678 ^  '804.6 Superposition of Polarised and Unpolarised Residual Time Series of C Ophwith Subfeatures Aligned ^  814.7 (a) Polarisation Analysis of the First Five Polarised Residual Spectra ofOph ^  824.7 (b) Polarisation Analysis of the Last Five Polarised Residual Spectra ofOph ^  834.8 (a) Polarisation Analysis of the First Five Unpolarised Residual Spectra ofC Oph ^  844.8 (b) Polarisation Analysis of the Last Five Unpolarised Residual Spectra ofC Oph ^  854.9 Differenced Time Series of C Oph. ^  874.10 (a) Polarisation Analysis of the First Five Differenced Spectra of C Oph • 884.10 (b) Polarisation Analysis of the Last Five Differenced Spectra of C Oph . • 894.11 Spectral Time Series of c Per at IV and He I A4921 ^  924.12 Residual Time Series of c Per at HP and He I A4921  934.13 Mean Residual Spectra of c Per at Different Position Angles ^ 954.14 Polarisation Analysis of Mean Residual Spectra of c Per  964.15 Mean Residual Spectra of 0 Per at Different Analyser Position Angles .^974.16 (a) Mean Residual Spectra of y Cas at Different Analyser Position Angles(23 Sep 1990 UT) ^  984.16 (b) Mean Residual Spectra of -y Cas at Different Analyser Position Angles(24 Sep 1990 UT) ^  994.17 Mean Residual Spectra of 28 Cyg at Different Analyser Position Angles ^ 1004.18 Mean Residual Spectra of y Boo at Different Analyser Position Angles . ^ 1024.19 Polarisation Analysis of Mean Residual Spectra of 0 Per ^ 103ix4.20 (a) Polarisation Analysis of Mean Residual Spectra of -y Cas(23 Sep 1990 UT) ^  1044.20 (b) Polarisation Analysis of Mean Residual Spectra of -y Cas(24 Sep 1990 UT) ^  1054.21 Polarisation Analysis of Mean Residual Spectra of 28 Cyg ^ 1064.22 Explanation of Why the Measured Position Angles are Offset by ±90° from^the True Values.     1074.23 Effects of Line Absorption in a Rotating Circumstellar Envelope on theDegree and Position Angle of Polarisation ^  1104.24 Synthetic Spectrum of Per at H3 ^  1144.25 Synthetic Spectrum of y Cas at Hp  117AcknowledgementsI would like to thank my supervisor, Dr. Gordon Walker, for suggesting this study, pro-viding many valuable insights during the course of the work, and for allowing me thefreedom to pursue many of my own ideas. I am equally grateful to Dr. Anne Underhillfor reviewing several drafts of the thesis and providing help with the interpretation of theresults. Financial support through a grant to Dr. Underhill is gratefully acknowledged.The polarisation analyser used for all the observations presented in this thesis couldnot have been made without the support and contributions of a number of people atthe Dominion Astrophysical Observatory. Frank Younger kindly helped me with thedrafting of the analyser mount and allowed me the use of his wonderful drafting table.Les Saddlemyer developed the control system for the analyser and wrote most of thecontrol software. The mount was expertly built in the DAO instrumentation shop by JimCockrill. Doug Bond was always helpful during my observing runs and made up many ofmy data tapes. David Duncan took the photographs of the analyser shown in Figs. 2.2and 2.3.I have benefitted greatly from many discussions with various members of the astron-omy department, in particular, Drs. Dave Bohlender, Phil Bennett, Gerry Grieve andStephenson Yang. Thanks also go to Ted Kennelly for generating the synthetic spectrapresented in Figs 4.24 and 4.25, and for being a "decent kind of guy". I am indebted toJonathan Thornburg for reading several drafts of the thesis and providing many (!) usefulsuggestions.xiChapter 1Introduction1.1 Historical BackgroundMost of our knowledge of the universe comes from the analysis of starlight. Therefore it isto our advantage to exploit as many different properties of this radiation as possible. Oneproperty of light which has received attention only in the last 50 years is its polarisation.The probable reason can be found in the assumption that all stars are spher-ical. Any such object would be completely symmetric about the line of sightfrom the observer to the center of the apparent disk so if even local regionson the surface emitted 100 percent polarized light, the symmetric orientationof their planes would yield no net polarization to an observer viewing theintegrated light of the disk. However, many astronomical processes producepolarized light, and numerous stars are not spherical. (Collins 1989, p. 440)Early theoretical work by Chandrasekhar (1946a, 1946b) of the atmospheres of early-type stars (where the dominant opacity is electron scattering) implied that as much as11% of light emanating from a point at the stellar limb may be linearly polarised. Hesuggested that this polarisation might be observed when the early-type component of aneclipsing binary is occulted by its companion.Attempts to detect polarisation in the eclipsing binary CQ Cephei led instead tothe independent discovery by Hall (1949) and Hiltner (1949) of interstellar polarisation.Subsequent polarimetric observations showed that the light from a significant number ofstars in our galaxy is linearly polarised. The polarisation is now known to be caused byscattering of stellar light by elongated interstellar grains aligned by the galactic magneticfield.1Since then, many astrophysical processes have been found to produce polarisation (cf.Serkowski 1974a). For example:• scattering of light by molecules (Rayleigh scattering) in the atmospheres of Jupiterand other outer planets, and in the photosperes and circumstellar matter of late-typestars;• scattering of light by free electrons (Thomson scattering) in the solar corona andthe circumstellar envelopes of early-type stars;• scattering of light by grains in the interstellar medium of our galaxy and othergalaxies, as well as active galactic nuclei.Polarimetry, therefore, provides important additional information about the nature andgeometry of the source, which cannot be obtained from brightness measurements alone(McLean 1989).1.2 The Description and Measurement ofPolarisationAccording to Maxwell's classical theory of electromagnetism, light is a propagating trans-verse electromagnetic wave. Any collection of such waves travelling in the same directionwhose electric-field' vector displays a preferred plane of vibration is said to be linearlypolarised. More precisely, linearly polarised light is defined as light for which the electricfield vector is confined (at all times) to a single plane which also contains the propagationvector. The angle of polarisation, Op is a measure of the orientation of this plane. It isconventional to define 4a as the angle from celestial North to the plane, measured in thedirection from North through East (Walker 1987). Note that ii*, has a range of 0° to 180°,rather than 0° to 360°, because it is a measure of the orientation of a plane as opposedto that of a vector.We can resolve any light beam into two orthogonal linearly polarised components andclassify the light according to the components' relative amplitudes. 2 Unpolarised light'It is conventional to discuss polarisation entirely in terms of the electric-field component of light(Clarke 1974).2 111 this thesis, we always assume the case of incoherent superposition, so the question of the phaserelationship between the components does not arise.2is defined as light in which the two (orthogonal) components are of equal intensity. Incontrast, partially polarised light is defined as light in which the two components are ofdifferent intensities.We can consider a beam of partially polarised light of total intensity I to consist of twocomponents, one of intensity Ip which is completely polarised, and the other of intensity/up which is unpolarised. The contribution of the polarised component to the total beamdetermines the "degree" of linear polarisation of the total beam, defined by the ratioPAs we have seen in Section 1.1, the light from a variety astronomical sources is partiallypolarised and its measurement involves determining the quantities P and Op .The measurement of P and Op entails passing the light through a polarisation anal-yser, an optical component which divides the incident beam into its two orthogonally(linearly) polarised components, and measuring the intensities of the components leavingthe analyser. For the special case of linearly polarised incident light the transmission ofthe analyser is given by Malus' Law:-rout-rin^cos 2 1/2^(1.2)where = 0 — Op is the angle between the axis of the analyser (at an angle 0) and theplane of polarisation of the incident light (at an angle q5 p ). In the general case of partiallypolarised light, it is useful to consider the transmission of the polarised and unpolarisedcomponents separately. Because the polarised and unpolarised components of the incidentbeam are incoherent, the total intensity of the beam after passing through the analyseris simply given by the sum of the component intensities1(8) = 2lup + ipcos 2 (9 — op)^(1.3)where we have averaged Eqn. 1.2 over all possible values of Op to obtain the transmissionfor the unpolarised component.If the orientation, Op , of the source polarisation is already known, then it is easy toshow from Eqn. 1.3 that the degree of polarisation is given by-p 'max /min/max + -rmin(1.4)3where Imax and Im in are defined to be the maximum and minimum values of I(0).Alternatively, if the orientation is not known or if it varies, it is useful to write Eqn. 1.3in terms of PI(0) = Ia„{1 P cos[2(0 — OA}^ (1.5)where /a„9 =^/min). The parameters P and 0, may then be determined by aleast-squares fit to I measured at a number of different orientations, 0, of the analyser.1.3 An Outline of this ThesisIn this thesis we present differential spectropolarimetric studies at N 0.15 A resolution ofthe diffuse interstellar bands and of features in Be star spectra. The data were obtainedwith a new polarisation analyser; a detailed description of the design and performance ofthe instrument is provided in Chapter 2. In Chapter 3, we describe a search for differen-tial polarisation effects in four of the strongest diffuse interstellar bands and discuss theconstraints imposed on their possible origin by our results. In Chapter 4, we describe anattempt to measure the differential polarisation associated with the line profile variationsof two OB stars. In the same chapter, we describe the results of differential polarisationmeasurements of the H/3 emission line in three intrinsically polarised Be stars; these re-sults are explained in terms of the dynamics of the stars' circumstellar envelopes. In theselast two chapters, we also describe different techniques used to reduce and analyse ourdifferential polarisation measurements.4Chapter 2The UBC/DAO PolarisationAnalyser2.1 IntroductionPolarimetry has traditionally been carried out using single-channel detectors, such as pho-tomultipliers, and many of the first polarimetric observations were restricted to broad-band continuum measurements. Polarisation measurements in spectral lines usually em-ploy narrow-band interference filters which are either fixed or scanned in wavelength bytilting the filter to various discrete positions. Since both techniques exclude most of theincident light, the precision of the measurements are limited by low photon statistics. Butthe second method of observation, in particular, requires high accuracy because the mea-surements are made sequentially at various wavelength points across the spectral feature.Another drawback of the narrow-band measurements is that they are confined to spectralresolutions of the order of the full width at half maximum (FWHM) of the filter, at best— 2 A.In the past decade, the trend in polarimetry has been toward using multi-channel solid-state detectors. These detectors offer greater efficiency because data may be recordedsimultaneously at many wavelengths. In addition, used with a spectrograph, they alsoallow very high resolution spectropolarimetry.In this chapter, we describe the design and performance of a microcomputer-controlledpolarisation analyser which, when incorporated into the DAO 1.83-m telescope, allows5differential spectropolarimetry at the full spectral resolution of the spectrograph-detectorsystem.2.2 Design of the Polarisation AnalyserThe UBC/DAO polarisation analyser (hereinafter, analyser) was designed and built in1990 at the Dominion Astrophysical Observatory specifically for the 1.83-m telescope. Theinstrument comprises four main components: the optics, the mount, the controller andthe data analysis software. The hardware components are discussed in the following threesections; the data analysis software is discussed in Section 4.4. Technical specifications ofthe component parts are given in Appendix A.2.2.1 The OpticsThe analyser was designed for linear polarisation measurements. The optical design ofthe analyser is straightforward and is shown schematically in Fig. 2.1. It incorporates apolarising beamsplitter cube and a quarter-wave plate. The beamsplitter selects a plane ofpolarisation by separating unpolarised or partially-polarised light into two beams havingopposite (or orthogonal) polarisations. The two beams emerge from adjacent faces ofthe beamsplitter cube with an angular separation of 90°. The component of the incidentbeam whose plane of polarisation is aligned with the transmission axis of the beamsplitteris transmitted straight through the cube and emerges linearly polarised from the oppositeface (Fig. 2.1). The component whose plane of polarisation is oppositely oriented isreflected at right angles to the incident beam and is not used in our configuration. Thusthe efficiency of the analyser is at best 50%.For reasons that will become apparent in Section 2.4.1, the directly transmitted beamis then passed through a quarter-wave plate whose optical axis is oriented at a 45° angle tothe beamsplitter axis. At this orientation, the linearly polarised light from the beamsplit-ter is transformed to circularly polarised light. The plate rotates with the beamsplitterso as to maintain this angle.645 deg41111111bPartially polarised lightPolarising beamsplitter cubeLinearly polarised lightQuarter-wave plateCircularly polarised lightFigure 2.1: The optical design of the UBC/DAO polarisation analyser. The polarisingbeamsplitter cube selects the plane of polarisation. Linearly polarised light is then con-verted to circularly polarised light by the quarter-wave plate whose fast axis is alwaysoriented at a 45° angle to the beamsplitter transmission axis. Beamsplitter CubesThe beamsplitter cubes are broad-band^60 nm) devices with peak transmittance atthe wavelengths 488 nm and 633 nm. The 25.4-mm cubes are constructed from two right-angle prisms cemented together with a multilayer dielectric film sandwiched in between.For unpolarised incident light of the specified wavelength, the emerging beams are linearlypolarised to a purity of 98%. Each entrance and exit face has also been coated with amultilayer antireflection coating such that less than 0.25% of the light is lost to reflection.The specifications of the beamsplitters are listed in Table A.1 of Appendix A. Quarter-Wave PlateThe quarter-wave plate is a broad-band device suitable for use in the visible spectrumfrom 400 nm to 700 nm. It is made of mica cemented between two protective glassdiscs. Unfortunately, mica retarders suffer from high absorption coefficients 20%) andpossible inhomogeneities in the mica. The latter should not seriously affect the uniformityof the telescope beam since, at the location of the analyser, the beam fills most 60%) ofthe retarder disc's area. Those disadvantages, however, are compensated by the retarder'srelatively low cost, typically, 5-6 times cheaper than their quartz counterparts. Thespecifications of the retarder are given in Table A.1 of Appendix A.2.2.2 The MountThe analyser mount was designed specifically for use on the DAO 1.83-m telescope. It ismounted in the telescope beam approximately 33 cm above the Cassegrain spectrographentrance. The mount supports the optical components of the analyser as well as a steppermotor. It is held in place by a support arm which screws onto a mirror cell located beneaththe primary mirror. [The mirror is free to move along an overhead track between twopositions. When in the path of the telescope beam, it directs the light onto a TV cameraallowing the observer to locate and set on a star within a wide field of view. Once thestar has been found, the mirror can be moved back along the track (out of the path ofthe telescope beam) so that the beam can be focussed onto the spectrograph slit. In thisposition, the beam is automatically centered on the analyser.]Photographs of the top and bottom of the assembled mount are shown, respectively, in8Figs. 2.2 and 2.3. The beamsplitter cube is housed in the cylindrical cell shown in Fig. 2.2,and the quarter-wave plate is held in place by the aluminum ring shown in Fig. 2.3. Boththe beamsplitter cube and the wave plate rotate together.The entire analyser housing is mounted onto the main plate, and is free to rotate on aflange fixed to the housing. Rotation of the analyser is acheived via a worm gear assemblyand stepper motor. This type of gear allows very precise rotation of the analyser. Thestepper motor sits in its own bracket which then mounts onto the main plate (Fig. 2.3).The position of the bracket may be adjusted to set the pressure between the worm andthe gear.The mount is slotted in two orthogonal directions so that it may be adjusted in boththe North-South and East-West directions. This allows positioning of the telescope beamat the center of the beamsplitter cube. Once the analyser has been aligned in this way,the entire mount may be removed from the solid mirror and replaced without requiringfurther adjustments. The analyser was originally aligned using a laser beam to define theoptical axis of the telescope. The laser was mounted at the location of the spectrographcollimator.The main components of the mount, including the main mounting plate, were madeat the DAO from 5 mm thick aluminum, except the cell bushing which was made 11 mmthick so that the analyser housing when rotating does not wobble or tilt from the stressapplied by the gear assembly. Flexure of the mount at different positions of the telescopeshould similarly be neglible.2.2.3 The ControllerDirect or low-level control of the analyser is provided by an Intel 80286-based single-boardcomputer operating under an iRMX 86 environment. The controller is interfaced to acustom-made motor driver dubbed the "DAO Instrumentation Crate" which respondsto signals from the CPU. In addition to controlling the power output to the steppermotor, the driver also returns status of a number of monitoring switches. Both thecontroller/CPU and motor-driver box are mounted on the spectrograph.The control-system software was written in PL/M-286, a high-level programming lan-guage designed by the Intel Corporation for microcomputer applications. The routinewhich controls the analyser is incorporated into a larger software package that will even-91. Main Plate^5. Stepper Motor2. Support Arm 6. Stepper Motor Bracket3. Cell Bushing^7. Worm Gear4. Beamsplitter Cube CellFigure 2.2: Top view of analyser mount.101. Main Plate^4. Reference Switch2. Support Arm 5. Limit Switch3. Quarter-Wave Plate Ring 6. Index SwitchFigure 2.3: Bottom view of analyser mount.11tually operate all the spectrograph and imaging devices using the same computer anddriver as described above. When a call to the analyser-control routine is made, the po-sition angle of the analyser is checked against the desired, or target, position. If thepresent position does not equal the target position, the analyser is rotated by the amountcorresponding to one step of the stepper motor, i.e., one sixteenth of a degree. Eachsubsequent call to the routine causes another step of the motor until the target positionis reached. The absolute position of the analyser is monitored by counting the number ofsteps of the stepper motor from a reference position (discussed below).A call to the analyser-control routine is made every 5 ms. This effectively determinesthe rotation rate of the analyser, i.e., 200 step s -1 , or 12.5° s -1 . Ideally, the positioningprecision should be limited by the step increment ( 71 -6 ° ); however, in practice, it is closerto 0.5° owing to slippage or imperfect meshing of the gears.At the start of each run, the analyser is automatically initialised to the zero-degreeposition (the north-south direction) from which all subsequent positioning of the deviceis made. This is achieved by stepping "down" (to smaller position angles of the analyser)until a zero-degree reference switch (Fig. 2.3) is sensed (i.e., the switch is turned on). Thedevice is then stepped "up" until the reference switch registers the off position. If thereference switch is not found after the number of steps (5760) corresponding to the fullrotation of the device, an error is returned. The analyser may be initialised to the zero-degree reference position periodically throughout the night to ensure proper zero-pointcalibration of the analyser position angle.To ensure that the analyser is rotating correctly, an index switch was mounted along-side a wheel which rotates with the analyser (Fig. 2.3) . The wheel has ridges every 20° at0°, 20°, 40°, etc., and, as it rotates, a ridge depresses the switch to reveal the orientationof the analyser; the switch is released as the ridge moves away. While the analyser isrotating, the software checks that at every odd multiple of 10° (i.e. 10°, 30°, 50°, etc.)the index switch is off and at every even multiple of 10° (i.e. 0°, 20°, 40°, etc.) the indexswitch is turned on. If this switching sequence is not followed at the correct intervals, anerror is returned.As a further precaution, an electrical limit switch which will shut down the device wasalso installed to protect the device from damage due to power surges. The limit switchis mounted just behind the zero-degree reference switch and cannot be reached in normal12operation.2.3 Data Acquisition and AnalysisOnly a general overview of some of the ideas and principles behind polarisation measure-ments with the analyser is given here. The data acquisition and analysis techniques arediscussed in greater detail in Sections 3.2, 3.3 and 4.2-4.4.Observations with the analyser were made with either the DAO Reticon or the RCACCD detector, employing standard spectroscopic techniques. For the measurement ofP and Op , spectra were obtained at a minimum of four equally-spaced position anglesof the analyser [as recommended by Serkowski (1962)] to ensure adequate sampling ofthe cosine function in Eqn. 1.5 (cf. Chapter 4). However, where the polarisation angleOp was known, measurements at only the two angles, corresponding to 0 1, and Op + 90°,were obtained (cf. Chapter 3). We found that measurements were best performed byalternating between clockwise and anticlockwise rotations of the analyser. In this way, itwas possible to reduce the effects of systematic changes in the spectra [e.g., wavelengthshifts due to spectrograph flexure (cf. Section 4.5.1) and variations in the strengths oftelluric lines caused by variable air mass (cf. Sections 3.2 and 3.4)] that could lead tospurious detections of polarisation.The procedure for processing the polarisation data departs from conventional tech-niques in one important way. Since the flat field lamps do not illuminate the detectorin the same way as the light from the star,' we have generally found cancellation of thediode-to-diode variations in flat-fielded spectra to be unsatisfactory. But, in astronomi-cal sources P is generally small (typically 1%), demanding high polarimetric accuracy.Therefore, no flat-flielding of the spectra was performed; instead, we analysed our data interms of the ratios of two spectra. The spectral ratios were formed by dividing a spectrumobtained at a given position angle by either another spectrum taken at the orthogonalposition angle or the mean of spectra taken over a range of angles. Besides normalisingthe different sensitivities of the diodes, this technique also revealed any polarisation effectsin the line profiles. The residual spectra were then rectified by dividing by polynomialfits to selected continuum points.'Proper facilities for dome flats were unavailable at DAO.13Following Fahlman and Walker (1975), if the polarisation in the line profile PL, iswritten= Pc + AP (2.1)where Pc is the continuum polarisation, then the rectification procedure removes Pc aswell as any instrumental polarisation. 2 Our analysis procedure is sensitive only to thechange in polarisation AP in the line profile.2.4 Performance2.4.1 Design EvolutionThe optical design of the analyser was tested at the focus of the 1.83-m telescope duringtwo observing runs in late 1989. A temporary mount was built for this purpose and theposition angles were set manually.The original design incorporated a half-wave plate' (in place of the quarter-wave plate)after the beamsplitter cube which rotated the plane of polarisation of the transmittedbeam such that the same (optimum) polarisation was delivered to the spectrograph re-gardless of the beamsplitter position angle. In this way, we had hoped to eliminate anypolarisation effects caused by the different efficiencies of the spectrograph grating to theplanes of polarisation parallel and perpendicular to the rulings (cf. Walker 1987; Fig. 5.5).At the same time, we thought we could to take advantage of the greater efficiency of thegrating to the latter orientation of polarisation. We encountered, however, an unexpectedproblem.Fig. 2.4 shows a polarised spectrum of the standard unpolarised star # Orionis (B8 Ia;V = 0.12). A third-order polynomial fit to selected continuum points has been dividedinto the spectrum to emphasise the obvious depression in the continuum. The size of thedepression is large, nearly 20% of the continuum Moreover, it was found to be highlyvariable, being largely a function of guiding and seeing quality. The problem was lesssevere for long-exposure data as the effects of guiding and seeing averaged out.2 Eqn. 2.1 assumes that the position angles Op of the continuum and line polarisations are the same.3 Linearly polarised light incident on a half-wave plate such that the plane of polarisation of the lightmakes an angle of 0 with the axis of the plate emerges with its plane of polarisation at —0 to the axis ofthe plate. Thus the effect of the half-wave plate is to rotate the plane of polarisation by the amount 20.1400•OCO0500^1 0 00^1500Pixel NumberFigure 2.4: Polarised spectrum of the standard unpolarised star [3 Ori showing the effectsof the different responses of the image slicer's aperture and slit mirrors to polarised light.The spectrum was obtained with only the beamsplitter in the path of the light. A third-order polynomial fit has been divided into the spectrum.15It is unlikely that this kind of structure could be caused by the differential responseof the spectrograph grating to polarised light. That would tend to introduce only large-scale gradients in the slopes of the spectra and would not be expected cause such highlyvariable structure. Rather, the structure in Fig. 2.4 was almost certainly caused by theRichardson image slicer (cf. Walker 1987; p. 155) used during the observations. It isplausible that different responses of the aperture and slit mirrors of the slicer to polarisedlight could cause variations in the intensities of the individual slices, introducing largeripples into the continuum of each spectrum.In order to minimise the undesirable polarisation effects from the image slicer, it wasnecessary to introduce a depolariser into the beam before the slicer. The simplest andleast expensive approach was to use a quarter-wave plate, whose fast axis is oriented 45°to the beamsplitter axis. The light incident on the image slicer is therefore circularlypolarised, which, as far as what the image slicer "sees", is indistinguishable from naturalor unpolarised light. 4The effectiveness of the quarter-wave plate is demonstrated by the residual spectra inFig. 2.5. The residuals were formed by dividing a spectrum of the standard polarised starHD 183143 (Serkowski 1974b) taken at the 179° orientation of the analyser by another atthe 89° orientation. The integration times for all spectra were one hour. The spectra usedto compute the residual spectrum in Fig. 2.5a were obtained with only the beamsplitterin the path of the light; those used to form the residual in Fig. 2.5b were obtained usingboth the beamsplitter and quarter-wave plate. In Figs. 2.5a' and b', we have plotted theresidual spectra in Fig. 2.5a and b, divided by a straight-line fit.The addition of the quarter-wave plate was effective in reducing two intrumental ef-fects: (1) small-scale structure or ripples in the residuals and (2) large-scale gradients intheir slopes. The small-scale structure, being of the order of a few percent 3-4%) with-out the quarter-wave plate (Fig. 2.5a') have been reduced to tenths of a percent 0.8%)with the wave plate in place (Fig. 2.5a'). Similarly the reduction in the slopes of bothresiduals (from es, 25% in Fig. 2.5a to 4% in Fig. 2.5b) represents an order of magnitudeimprovement. The remaining variations are probably due to imperfect "depolarisation"of the light entering the spectrograph as well as unavoidable guiding errors. The quarter-4 Recall that unpolarised and circularly polarised light are both composed of equal amounts of twoorthogonally-orientated linearly-polarised components of light.16wave plate was therefore ti 90% effective in eliminating the sensitivity dependence of theimage slicer and spectrograph to the plane of polarisation.The residual spectrum in Fig. 2.5b also contains a real component since the continuumlight from HD 183143 is highly polarised with Op = 179° (Hiltner 1956). Therefore, inorder to estimate the level of instrumental polarisation, we have plotted the residualspectra of the standard unpolarised star a Cyg in Fig 2.6. The residuals were obtained onfour different nights and were formed in an identical manner to the HD 183143 spectra ofFig 2.5. (In fact, they were obtained for the DIB polarisation study of Chapter 3 in orderto monitor instrumental polarisation effects in those data.) The integration times of thespectra ranged from 60-120 s. From Fig 2.6, it is clear that instrumental polarisationis present in the residuals at the very low level of ti 2-3%. But more importantly, thegeneral shape of the residual spectra did not vary significantly from night-to-night.2.4.2 Testing the AnalyserThe efficiency of the analyser was estimated from observations of a Cyg obtained with andwithout the analyser. It was found that the analyser caused a reduction in the light fromthe star of N 1 mag. (Of course, this is in addition to the requirement that measurementsbe taken at multiple position angles in order to derive the polarisation parameters.)In addition to observations of standard unpolarised stars, another important test ofany polarisation analyser is its ability to accurately measure the degree and position angleof polarisation in standard stars of known polarisation. Unfortunately, since our analysistechnique is not sensitive to continuum polarisation, there are few objects suitable forsuch a test. It is known that some emission-line stars exhibit reduced polarisation (fromthe continuum value) across their hydrogen Balmer lines. We have measured this changein the 10 A4861 line of two Be stars 4 Per and 7 Cas (cf. Figs 4.19 and 4.20a, b) forwhich reduced polarisation has previously been measured. Although most of these othermeasurements are of lower spectral resolution and therefore do not exhibit the level ofdetail of our data, our results compare favourably in both the degree and position angleof polarisation. Besides forming the basis of this test, these measurements are also ofastrophysical interest; therefore, more detailed discussions may be found in Section 8000 6200 6400(a')6000^ 6200Wavelength (A)a.)1.041.0210.980.961.00510.9950.9964001. 2.5: Polarisation curves of the standard polarised star HD 183143 showing theeffectiveness of the quarter-wave plate in reducing instrumental polarisation. The curveswere formed by dividing a spectrum of HD 183143 at the 179° orientation of the analyserby a similar spectrum at the 89° orientation.(a) Residual spectrum obtained with only the beamsplitter in the path of the light.(b) Residual spectrum obtained with the beamsplitter plus the quarterwave plate.(a') As a, rectified by a straight line fit.(b') As b, rectified by a straight line fit.185800^6000^6200^6400WAVELENGTH ( A )Figure 2.6: Polarisation curves of the standard unpolarised star a Cyg, formed by divid-ing a spectrum of a Cyg at the 179° orientation of the analyser by a similar spectrum atthe 89° orientation. Instrumental polarisation is present in the residuals at the -, 2-3%level of the continuum.19Chapter 3Differential Polarisation Studies ofthe Diffuse Interstellar Bands3.1 Diffuse Interstellar Bands3.1.1 IntroductionBesides producing the general extinction and reddening of the light from stars and cer-tain atomic and molecular resonance lines in their spectra, the interstellar medium (ISM)is also responsible for a series of unexplained absorption features known as the diffuseinterstellar bands (DIBs). There are more than 60 such features scattered over approx-imately 4000 A of the visible spectrum, with no obvious pattern in wavelength (Herbig1988). They display a range of full widths at half intensity from about 1 A to 40 A. Thestrongest bands are at 4430 A and at 6177 A, with equivalent widths of 3.4 A and 2.0 A,respectively, in the heavily reddened star HD 183143 (Greenberg 1978). The strengthsof the bands depend largely on the amount of interstellar matter in the line-of-sight tothe star. Despite their large numbers, the DIBs make only a small contribution to thetotal energy absorption of starlight (Puget and Leger 1989). However, they potentiallyharbour important information about the composition and physical nature of the ISM.Reviews of the observational aspects of DIBs may be found in Krelowski (1988).Since their discovery by Merrill in 1934, the diffuse bands have inspired a great deal ofspeculation as to their origin. However, no definitive picture of the agents responsible forthe DIBs has yet emerged. One fundamental question is whether the DIBs arise from the20grain or gas component of the ISM. Polarisation studies present an ideal opportunityto distinguish between the two possibilities. If the interstellar grains responsible forthe optical continuum extinction and polarisation are also the cause of the DIBs, suchthat the bands represent spectral regions of enhanced extinction, then a correspondingenhancement in the polarisation might also be present (cf. Martin and Angel 1974;Fahlman and Walker 1975). On the other hand, no polarisation of the stellar light isexpected if the DIBs are formed by the interstellar gases (atoms and/or molecules) [cf.Smith, Snow and York 1977; van der Zwet 1986].3.1.2 Possible Carriers of the DIBsAlmost all current research on the diffuse interstellar bands is devoted to understandingthe origins of these enigmatic features. Many carriers for the bands have been proposed;they may be grouped according to the two main components of the interstellar medium:solid grains and gas-phase molecules. At present, the arguments for molecular and grainorigins of the DIBs are equally strong. Excellent reviews may be found in the articles byHerbig (1975), Smith et al. (1977), Chlewicki et al. (1986) and van der Zwet (1986).Prior to the mid-1970's, the favoured explanation for the DIBs was that they arosefrom impurities embedded in the solid grains responsible for interstellar reddening [cf.Aannestad and Purcell (1973); Herbig (1975); Smith et al. (1977)]. This was motivatedby the generally good correlation between the band strengths and E(B — V) colour excess(Herbig 1975) and by the absence of detectable fine structure in the band profiles whichmight be expected if the DIBs are caused by free molecules (Smith et al. 1977; Josafatssonand Snow 1987).The possible link between DIBs and interstellar grains was first suggested by Merrilland Wilson (1938) because of the strength-reddening correlation. Since then, furtherstudies of the correlations between DIB strengths and various extinction parameters havebeen made in efforts to identify the particular grain population responsible for the bands.Some of the earliest studies by Greenstein and Aller (1950), Duke (1951) and Underhill(1955) showed correlations between the 4430 A band and the then photometric index forextinction, El . Walker (1963) and Wampler (1966) found positive correlations betweenthe 4430 A band and E(B — V). Their results were confirmed by Wu (1972) whose studyalso included DIBs at 5780 and 5797 A. Herbig (1975) also conducted correlation studies21of all the stronger DIBs in his Table I and reported reasonable correlations betweenthose DIBs and E(B — V). Better correlations were found when the band strengths werecompared with red and near-IR colour excesses (Herbig 1975; Sneden et al. 1978). Thoseobservations would seem to suggest that the grains which produce the visible and IRextinction are also responsible for the diffuse interstellar bands.As noted originally by van de Hulst (1949), extinction profiles produced by large grains0.1pm, such as those responsible for the extinction in the visible) would be stronglyasymmetric with steeper edges and obvious emission wings blueward of the absorption (seealso Greenberg and Hong 1976; Chlewicki et al. 1986; van der Zwet 1986). Observationsobtained with modern detectors provide no evidence for an emission component in anyof the DIBs (cf. Chlewicki et al. 1986; Krelowski and Walker 1987; Krelowski 1988).Moreover, the intrinsic profiles of the DIBs show a high degree of symmetry (e.g. 4430,5778, 6177, 6284 A), although a number of the narrow DIBs do possess slight asymmetry(e.g. 5780, 5797 A ; Chlewicki et al. 1986; Krelowski and Walker 1987; Krelowski 1988).Using similar arguments, Herbig (1975) concluded that the DIBs probably arise fromimpurities in very small grains (a ti 0.01pm), which are also required to explain thefar-UV extinction (Greenberg and Chlewicki 1983).If the small grains are responsible for the DIBs, then there might be a correlationbetween band strength and UV colour excess. Although a weak correlation exists betweenthe 4430 A band and the extinction bump at 2175 A (Witt, Bohlin and Stecher 1983; Seaband Snow 1984; Josafatsson and Snow 1987), no correlations between the strengths of the4430 A band and E(1500 — 1800) [Krelowski et al. 1987] and between the 4430, 5780,6284 A bands and E(1800 —V) [Wu, York and Snow 1981] have been found (see also Nandy,Morgan and Houziaux 1982; Witt et al. 1983; Seab and Snow 1984). 1 Nevertheless, itis worth noting that Savage (1976) and Welter and Savage (1977) were able to obtaingood fits to the asymmetric profiles of 5780 and 6614 A assuming the lines are caused byimpurities in small (aa,0.075 pm) cold grains.Another problem with the grain-based hypothesis, and perhaps the most serious, isthat the bands do not show the significant variations in central wavelength expected if theyarise from impurity sites in grains (Chlewicki et a/. 1986). Laboratory studies indicateshifts in wavelength as large as 100 A can occur depending on the chemical composition'The 2175 A bump does not appear to correlate with the far-UV extinction (Bless and Savage 1972).22and temperature of the grains (Smith et al. 1977; Chlewicki et al. 1986; van der Zwet1986). The observed lack of variability in the band wavelengths would require the grainsto have very similar formation histories and physical environments toward all lines-of-sight(Smith et al. 1977).Partly because of such problems, there has been a definite shift, in the last decade,towards molecular theories of the diffuse interstellar bands. In fact, some of the earliercriticisms of the molecular hypothesis may not be entirely valid in light of new observa-tional and theoretical evidence.The presence of rotational fine structure within an interstellar band would be strongevidence that the bands are formed by free molecules (Smith et al. 1977). Attempts toresolve the narrowest of the diffuse interstellar bands into discrete structure have beenmade by several authors (e.g. Savage 1976; Danks and Lambert 1976; Welter and Savage1977; Snell and Vanden Bout 1981; Herbig and Soderblom 1982). No structure at thelevel of 0.05 A resolution was detected in any of the features studied. However, accordingto Danks and Lambert (1976), the absence of structure may be understood if the diffusebands are the result of electronic transitions in large molecules. The rotational structureof the bands from such electronic transitions might be compressed below the observationalresolution limit.One of the major criticisms of a molecular origin for the bands has been the percep-tion that gas-phase molecules would not be able to survive the harsh ultraviolet radiationfield of the ISM in sufficient numbers to account for the DIBs. Recently, van der Zwetand Allamandola (1985), Leger and d'Hendecourt (1985) and Crawford, Tielens and Alla-mandola (1985) have proposed that polycyclic aromatic hydrocarbons (PAHs) [which areused to explain the unidentified infrared emission bands (UIB)] could also be the carriersof the DIBs. PAHs are attractive molecular candidates because they are thought to beextremely stable to UV radiation and their abundance, calculated from the UIBs, is suffi-cient to produce the observed equivalent widths of DIBs. Although they look promising,there remain a number of problems with PAHs as the carriers of the DIBs. Because ofthe large variety of PAH species, any model which tries to explain the DIBs using PAHmolecules must account for the existence in the ISM of only those species which cause theDIBs (Puget and Leger 1989). Moreover, no laboratory spectra of PAHs in the visible areavailable to compare with the DIB spectra.23It is now becoming apparent that all DIBs may not even arise from the same carrier.Although Herbig (1975) reported that all the bands correlated well with each other andtherefore must share a common origin, recent correlation studies do not bear this out(Chlewicki et al. 1986; Krewlowski and Walker 1987; Josafatsson and Snow 1987). Byanalysing the anomalous strengths of some DIBs and the absence of others in the lightlyreddened star C Per whose diffuse bands are thought to be caused by a single cloud,Krelowski and Walker (1987) concluded that there are at least three DIB carriers. Asimilar conclusion was reached by Josafatsson and Snow (1987), based on the degree ofcorrelation between individual DIBs.3.1.3 Past Polarisation Studies of the DIBsThere have been numerous attempts to detect polarisation changes within the diffusebands. Walker (1963) searched for polarisation excess associated with the 4430 A band ofHD 183143. His observations were made using a photoelectric photometer and polaroidfilter at five position-angle settings. A narrow-band filter was used to isolate the band.He was not able to detect any polarisation to within the uncertainty of his measure-ments. Another null result was obtained two years later by Wampler (1966) using similarphotoelectric techniques at considerably higher resolution.A'Hearn (1972) also looked for excess polarisation in the 4430 A feature of five starsincluding 55 Cyg and HD 183143. He employed a variety of photopolarimeters at threedifferent observing sites and compared the intensity within a 20 A bandpass centred onthe feature with the intensities in two similar bandpasses in the neighbouring continuum.A'Hearn found no evidence of polarisation excess for any of the stars and established alow upper limit to the change in polarisation in the 4430 A band of about 0.05-0.1%. Hisresults represent the most accurate polarimetric measurements of the DIBs, prior to thisthesis.Later efforts by Martin and Angel (1974, 1975) and Fahlman and Walker (1974) con-firmed the results of A'Hearn. Besides the 4430 A band, Martin and Angel also inves-tigated the 5780 A feature in HD 183143 and the 6284 A feature in HD 21389, using ascanning polarimeter. Their observations revealed no significant polarisation change ex-ceeding the standard error (0.1%) of their measurements. Fahlman and Walker (1975)also looked for polarisation changes in one of the strongest features at 6284 A in the spec-24trum of HD 183143. They employed a spectrograph and Isocon television camera in orderto resolve the line; they set an upper limit of 0.4% to the polarisation change.Amidst those null results, there have been two reports of positive detections. The firstwas made by Nandy and Seddon (1970) who claimed to have found polarisation structurein the 4430 A band of 55 Cyg. Their photographic data suggested an incredible doublingof the polarisation from 2.7% in the continuum to 5% in the band. That report was neverconfirmed. This was followed by Gammelgaard and Rudkjobing's (1973) report (alsounconfirmed) of differential polarisation within the broad 6177 A band. An interestingpoint about their result is that the angle of polarisation they measured within the banddoes not match the continuum polarisation angle, but is nearly orthogonal to it.The most recent polarimetric observations of DIBs were made roughly 15 years ago,before the introduction of solid-state detectors. These new detectors are ideally suited toinvestigating the polarisation structure in the diffuse bands given the small levels expected.For example, one of the most favourable cases, the 6284 A feature in HD 183143, waspredicted by Fahlman and Walker (1974) to have an excess polarisation no greater than0.8%. Until now, only A'Hearn's work has had a precision capable of showing an effect ofthe predicted size. However, his broadband measurements were incapable of showing thechange with wavelength of the polarisation within the profiles of the bands.By using a Reticon detector and our polarisation analyser, we can acheive order-of-magnitude improvements in both precision and wavelength resolution over the earlierstudies. In addition, spectropolarimetric measurements over a moderate wavelength band(840 A) allow us to investigate the polarisation structure across a number of DIBs sus-pected of having different origins, to test the multiple carrier hypothesis.3.2 ObservationsTable 3.1 lists the stars observed for this program, their spectral type, visual magnitudes(V), E(B — V) colour excess, wavelength A max at which their polarisation P(A max ) is amaximum, and position angle Op of the continuum polarisation. The first two, HD 183143and 55 Cyg, were the main focus of our observations, both having been the object of earliersearches for polarisation structure in their DIBs. Krelowski and Walker (1987) have arguedthat the last star in Table 3.1, C Per, lacks one family of DIBs and is probably obscured25by only one cloud. Thus, observations of ( Per present the possibility of studying DIBpolarisation effects from a single cloud.'Spectropolarimetry of the three stars in Table 3.1 was carried out at the DAO 1.8 mtelescope using the UBC/DAO polarisation analyser (described in Chapter 2) and 633 nmbeamsplitter cube. The observations of C Per were made on one night in November1989 and those of HD 183143 and 55 Cyg during two observing runs in August 1990.The detector was a liquid-nitrogen-cooled RL1872 F/30 EG&G Reticon, described indetail by Walker, Johnson and Yang (1985). All of the observations were taken with the600 lines mm -1 grating blazed at 5000 A which give a reciprocal dispersion of 30 A mm-1 .On the Reticon array, this corresponds to a resolution of 0.45 A diode' and a spectralcoverage of 840 A.The polarised spectra were taken in pairs with the beamsplitter transmission axisorientated in the two orthogonal positions corresponding to the position angle (0 p) of thecontinuum polarisation and perpendicular to it (Op 90°). By sampling only these twoposition angles, it was assumed that the agent responsible for the enhanced extinction ofthe diffuse features is distributed in the same grains that produce the adjacent continuumpolarisation.Observations were confined to the yellow-red region of the spectrum where a significantnumber of prominent diffuse features are found, including one of the strongest at 6284 A.They are identified along with some of the weaker DIBs in Fig. 3.1 which shows therich interstellar spectrum of HD 183143. By convention, the DIBs are named accordingto their approximate central wavelengths listed in Herbig's (1975) Table I. The stellarHe I A5875 and Si II )\6347, 6371 lines and interstellar Na D lines are also indicated.Representative spectra of 55 Cyg and C Per are also provided in Figs. 3.2a and b forcomparison. Notice that the broad 6177 A band is very weak in the spectrum of C Per.The spectra are contaminated by the rotational bands of atmospheric H2O in thewavelength interval from 5880-6000 A. The 6284 A feature is strongly affected by the a-band of 02 , which has its bandhead at 6276 A. Since we intended to analyse the data interms of the ratios between the spectra at the two angles of polarisation, if the individualspectra were obtained at different air masses, the absorption lines from water vapour and2 If the absorption bands arise from several clouds along the line-of-sight and the alignment of the grainsvaries from cloud-to-cloud, the net amount of polarisation is reduced. Studying polarisation effects inDIBs produced by a single cloud, however, ensures preferential grain alignment.26Table 3.1: Program Stars for DIB Polarisation StudySpectral Xmax P(Amax) OpHD Star Type V E(B — V) (pm) (%) (degrees)24398^ ( Per B1 Ma 2.83a 0.31b 0.54b 1.2b 145'183143^ B7 Ia 6.87 1.28 0.56 6.1 179198478^ 55 Cyg B3 Ia 4.83 0.52 0.53 2.8 2a) Hoffleit and Jaschek 1982.b) Serkowski, Matthewson and Ford 1973.c) Hiltner 1956.27DIB 5778   1120  ^ DIB 6177^— 02 —Wavelength (A)1to0A mCVcotop.\towtotoz0totoz0.65800 6000 6200 6400Figure 3.1: Representative spectrum of HD 183143. The strongest DIBs are identifiedalong with the interstellar Na D and stellar lines. The telluric a-band of 0 2 and therotational bands of H2 O are also marked.280.90.8›-,0"d 0.7a)as0(a)0.90.8(b)0.75800^ 6000^ 6200^ 6400Wavelength (A)Figure 3.2: Representative spectra of (a) 55 Cyg and (b) C Per.29the a-band of oxygen would not completely cancel in the ratio. This was recognised asa possible source of confusion at the times of the observations. Therefore, when mul-tiple pairs of spectra were obtained on a given night, they were taken in the sequence:'max Imin Im in Imax• If the air mass varied monotonically over the sequence of obser-vations, then the ratios Lmax //„, i,, from the first and last pair in each sequence, shouldshow residual effects within the telluric bands that are similar in strength but opposite insense. That is, one should show residual emission and the other residual absorption. Inthe mean, the spurious structure is expected to cancel out. When only one pair of spectracould be obtained, especially in the case of HD 183143 which required long integrationtimes, attempts were made to observe the star near the meridian.Table 3.2 summarises of the observations, including the number of pairs of spectrataken per night, the mean exposure time of each pair and the average S/N per diode ofeach spectrum.Polarised spectra of the relatively unreddened star, a Cyg, were obtained in the sameway as the program star spectra to monitor possible instrumental polarisation effects.3.3 Data ReductionThe data were reduced using the UBC version of the program RETICENT (Pritchet,Mochnacki and Yang 1982). The preprocessing techiques described by Walker et al. (1985)for extracting optimal S/N from Reticon data were employed. Each stellar spectrum wascorrected for the fixed pattern in its baseline by subtracting the average of 10-12 ten-second dark exposures, taken immediately following readout of every stellar spectrum.The differential offsets between the four video-line amplifier zero-points were calibratedusing the outputs of the pre- and post-scan diodes and the appropriate normalisationsmade to each spectrum.Ratios of the spectra within each set (defined as two consecutive spectra taken at or-thogonal orientations of the analyser) were then formed for all the program stars. Besidesenhancing the visibility of any polarisation structure in the bands, this step effectivelyremoved diode-to-diode variations in sensitivity, as well as the four-point fixed patternarising from the differential gains of the amplifiers. Also, the small variations in thelinearity of the amplifiers were automatically normalised in the ratio since the exposure30Table 3.2: Summary of DIB ObservationsStarDate(UT) NaExposure Time(s) S/NHD 183143^ 06 Aug 1990 1 7200 45007 Aug 1990 2 3600 60024 Aug 1990 2 3600 54025 Aug 1990 1 3600 55055 Cyg^ 06 Aug 1990 1 1800 50007 Aug 1990 1 1340 95024 Aug 1990 2 1200 74025 Aug 1990 2 1800 850C Per^ 07 Nov 1989 3 900 1400a) Number of pairs of spectra.31levels between the spectra in a set are nearly equal. Finally, an eight-point multiplicativenormalisation was applied to the ratios to remove any persistent fixed pattern.Prior to forming the ratios, the spectra in each set were aligned with respect to eachother. This was done in order to correct for shifts in the spectral line positions caused byspectrograph flexure which could, in the ratio, lead to spurious S-shape structure withinthe diffuse bands. To calculate the shifts, each spectrum was divided by a continuouslamp spectrum and rectified by a second-order cubic-spline fit to selected continuumpoints. The relative shifts between spectra were determined using the Fahlman-Glaspeydifference-function technique (Fahlman and Glaspey 1973). This technique evaluates, fora range of trial shifts, the relative shift needed to minimise the difference between twospectra. Only the sharp interstellar Na D doublet at )36890, 5896 and the stellar Si IIlines at AA6371, 6347 were used in the calculations in order not to bias the results. Thecomputed shifts amounted to no more than one-tenth of a pixel for HD 183143 and weremuch smaller for the other stars. Because the shifts were so small, effective cancellationof the diode-to-diode variations in the ratios was still acheived. In each set, the spectrumcorresponding to ./„„„ was chosen as the reference spectrum.The calculated shifts were used to align the original spectra which had not beendivided by a flat-field spectrum nor rectified, from which ratios were then formed.The final step in the reductions involved aligning the ratios for each program star toallow later averaging of all the ratios of a given star. Since all the ratios were alignedwith respect to the spectra at the Op orientation, the amount of shift required to alignthe ratios was evaluated from those same spectra relative to a mean spectrum for eachstar. The mean spectra for HD 183143 and 55 Cyg were formed from the average of theirrespective 24th Aug 1990 UT observations; for C Per the average of the 7th Nov 1989 UTobservations was used.3.4 ResultsSpectral ratios in the sense i„,,„ x//„,i„ are plotted in Figs. 3.3a, b and c for all the programstars. In order to improve the S/N ratio, the ratios have been smoothed by a Gaussiantransfer function with a a value of 0.90 A. (This assumes that no significant wavelengthdependent change of polarisation occurs in the wavelength range 2o - = 1.80 A.)325800^6000^6200^6400WAVELENGTH ( A )Figure 3.3: (a) The complete set of residual spectra of HD 183143. The residuals wereformed by forming the spectral ratios in the sense: Imax/Imin.33tiviitimmks 6 Au g 907 Aug 9024 Au g 9024 Aug 9025 Aug 9025 Au g 90I 0 . 5%I^,^1^i^1^ 1 5800 6000 6200 6400WAVELENGTH ( A )Figure 3.3: (b) As Fig. 3.3a for 55 Cyg.345800^6000^6200^6400WAVELENGTH ( A )Figure 3.3: (c) As Fig. 3.3a for ( Per.35Any polarisation effects within the diffuse bands should appear as enhancements inthe continuum polarisation curve at the locations of the features (Martin and Angel 1974;Fahlman and Walker 1975). The curvature evident in some residuals near the broad6177 A band deserves comment since it could be misinterpreted as polarisation excesswithin the band. A gradual downturn in the residual intensities at the bandhead of thetelluric a-band of oxygen appears in the ratios of HD 183143 and 55 Cyg indicated by theasterices in Figs. 3.3a and b. Those ratios all show significant residual absorption at theoxygen band since the spectra were taken at increasingly larger air masses. The depressionis rather broad, spanning the extent of the band, ti 60 A, and tends to draw the intensitylevel of the residual spectrum downward, giving the appearance of enhanced polarisationshortward of the bandhead. Notice similar curvature on the short-wavelength side of thewater-vapour and Na D lines. We therefore conclude that this effect is an artifact ofimperfect cancellation of the telluric bands in the ratio. Also, in light of the fact thatsimilar structure is not present in all the residual spectra, we are certain that the curvatureevident in the residuals marked in Figs. 3.3a and b do not represent polarisation excessin the 6177 A band.To emphasise any enhancements in continuum polarisation curve, polynomial fits wereused to normalise the residuals to zero slope. Care was exercised in carrying out the fitssince it was conceivable that improper removal of the curve could introduce false structureor remove real effects. This is especially critical near the broad diffuse feature at 6177 A.For this reason, only low order polynomial fits, usually third- or fifth-order, were used inthe normalisation. Fig. 3.4 shows a typical fit to a residual spectrum. Clearly, no structureof the width of the DIBs is present in the fit. Therefore, we are confident that, in carryingout this step, we have removed only the smooth curve associated with the continuumand residual instrumental polarisation while retaining the small-scale (< 50 A) structureexpected if the diffuse bands are indeed polarised. The rectified residual spectra are shownin Figs. 3.5a, b and c.The residuals show significant structure in the regions of the telluric lines. Becausethese lines are relatively narrow, even small displacements in the line positions betweenthe spectra will produced S-shaped structure in the ratio. However, this effect is notexpected to be quite as severe in the diffuse bands of interest since the widths of thebands 5-40 A) are larger than those of the telluric lines (r- 2-3 A).360I^,^I^i^I 5800 6000 6200Wave length (A)Figure 3.4: Typical rectification of the (7 Aug 1990 UT) residual spectrum of HD 183143.A fifth-order polynomial has been fitted to selected continuum points.376 Au g 907 Au g 907 Au g 9024 Au g 9024 Au g 9025 Au g 90sea)^6000^6200^6400WAVELENGTH ( A )Figure 3.5: (a) Rectified residual spectra of HD 183143, formed by dividing polynomialfits into the residual spectra of Fig. 3.3a.38riNth 24 Aug  9025 Aug  9025 Aug  90Aug 90Aug 90Au g 90VAlity"NithAPAIWITWAS4 67141\i‘rovivelAk4fArAsteMINAM"bsettiottirtLytVeirAt 245800^6000^6200^6400WAVELENGTH (A)Figure 3.5: (b) Rectified residual spectra of 55 Cyg, formed by dividing polynomial fitsinto the residual spectra of Fig. 3.3b.395800^6000^6200^6400WAVELENGTH ( A )Figure 3.5: (c) Rectified residual spectra of C Per, formed by dividing polynomial fits intothe residual spectra of Fig. 3.3c.40Figs. 3.5a, b and c also show residual effects resulting from the spectra being obtainedthrough different air masses. Due to the combination of this effect and the sequencein which the measurements were taken (cf. Section 3.2), on nights when multiple pairswere obtained, the first pair shows residual absorption whereas the second shows residualemission. This effect should cancel by taking the mean of all the residuals.(We used the spectra of a Cyg to check for polarisation structure within the water-vapour and oxygen bands themselves. Ratios were computed in the same way as for theprogram stars and the mean of those ratios is shown in Fig. 3.6. No polarisation structurewithin the telluric bands is evident.)To improve the S/N of the spectral ratios and cancel the residual effects in the telluricbands caused by the variable air mass, the ratios of each star were averaged. The meanspectral ratios for HD 183143, 55 Cyg and C Per are shown together with representativespectra in Figs. 3.7a, b and c. The formal standard deviation of the ratios are 0.07, 0.03and 0.03%, respectively.The apparent S-shape profile appearing in the region of the narrow 5780 A band inthe mean ratio of HD 183143 (Fig. 3.7a) is not a polarisation effect; it is caused by smalldiplacements in the line positions despite the attempts to align the spectra before formingthe individual spectral ratios. Similar effects occur in the sharper stellar and telluric linesof the spectrum. In fact, the nearby He I A5875 line shows nearly identical S-shapedstructure and we have used it to try to remove the effect in the 5780 A band. The residualin the vicinity of the He I line was scaled according to the ratio of the band and the stellarline intensities and then subtracted from the residual effect at the DIB. Fig. 3.8 showsgood cancellation of the effect from the 5780 A DIB.Note that the S-shaped structure in the region of the 6284 A DIB in the mean residualspectrum of HD 183143 (Fig. 3.7a) is also caused by small misalignments between thespectra used to form the individual ratios. This structure is associated with the bandheadof telluric 0 2 and not with the 6284 A DIB.No obvious polarisation structure associated with the DIBs is present in any of themean residual spectra. Upper limits to the differential polarisation in the four strongestbands at 5780, 5797, 6177 and 6284 A are given in Table 3.3 for each of the program stars.The upper limits represent the standard deviation across the entire band.Our final result was obtained by combining the mean residual spectra of HD 183143410ODal•0 siI0. 1 %^IpI^ I^ 1000•,-15800 6000 6200Wavelength (A)Figure 3.6: Mean residual spectrum of the standard unpolarised star a Cyg. A represen-tative spectrum (not to scale) is shown below. The error bar indicates the intensity scalewith respect to the continuum level.426000^62005800/ANI 0 . 1%vYWave length (A)Figure 3.7: (a) Mean residual spectrum of HD 183143. A representative spectrum (notto scale) is shown below. The error bar indicates the intensity scale with respect to thecontinuum level.43000a)a)•00coa)05800^6000^6200Wave length (A)Figure 3.7: (b) Mean residual spectrum of 55 Cyg. A representative spectrum (not toscale) is shown below. The error bar indicates the intensity scale with respect to thecontinuum level.4400005800I^ I 6000 6200Wave length (A)Figure 3.7: (c) Mean residual spectrum of C Per. A representative spectrum (not to scale)is shown below. The error bar indicates the intensity scale with respect to the continuumlevel.45•stOO‘-4CuOOI11 I11/F/II^II II—5775^5780^5785Wave length (A)Figure 3.8: S-shaped structure (dashed line) is apparent in the mean residual spectrum ofHD 183143 in the region of the 5780 A band. The He I A5875 line shows nearly identicalstructure (Fig. 3.7). The effects were caused by small displacements in the line positions.In order to remove the effect from the band, the residual in the vicinity of the stellar linewas scaled according to the ratio of the band and He I line intensities and subtractedfrom the residual structure at the DIB. The result is shown by the solid line.46Table 3.3: Upper Limits (±1o) to the Polarisation in the Diffuse Interstellar BandsStar5780A(%)5797 A(%)6177 A(%)6284 A(%)HD 183143 0.01 0.01 0.04 0.0755 Cyg 0.02 0.02 0.03 0.01C Per 0.04 0.01 0.01Meana 0.01 0.01 0.02 0.03a) Mean residual spectrum of HD183143 and 55 Cyg.47and 55 Cyg and is shown in Fig. 3.9. Upper limits to the change of polarisation througheach band were then estimated by the standard deviation within each profile. (The meanresidual spectrum of C Per was not used in the calculation because the strengths of thebands in its spectrum are much weaker than in the others.) As listed in Table 3.3, theupper limits are 0.02, 0.01, 0.01, 0.02 and 0.03% in the 5780, 5797, 6177 and 6284 A bands,respectively.3.5 DiscussionWe may better understand our results by comparing them with model predictions, follow-ing the approaches of Martin and Angel (1974, 1975) and Fahlman and Walker (1974).If we make the assumption that the diffuse interstellar bands, extinction and continuumpolarisation all arise from the same aligned grains, then we may make specific predictionsas to the size of the polarisation effect within the features.Martin and Angel (1974) have modelled the wavelength dependence of polarisationacross the diffuse bands assuming the interstellar grains causing the continuum polar-isation are infinitely long circular cylinders aligned by the "perfect" Davis-Greensteinmechanism.3 The diffuse features were assumed to arise from impurities, i.e., atoms ormolecules, dispersed through those same grains The impurities produced specific wave-length dependent changes in the index of refraction related to the profile of the DIB.Without knowing the precise nature of the impurities, the index of refraction over an ab-sorption feature were determined by the observed width, central wavelength and depth ofthe feature. It was also dependent on the index of refraction assumed outside the absorp-tion features. Martin and Angel (1974) assumed the index of refraction of the interstellargrains producing the continuum polarisation to be purely or almost purely dielectric.They computed models for the range of continuum refractive indices from m = 1.5 — Oito 1.5 — 0.1i.Their primary result was that, in general, the polarisation profile of a diffuse bandhas the same shape as its extinction profile. Quantitatively, they expressed this in the31n the theory of Davis and Greenstein, the interstellar grains are assumed to be aligned by theGalactic magnetic field and spin about their short axes. Details of the Davis-Greenstein mechanism maybe found in Davis and Greenstein (1951), Davis (1958) and Jones and Spitzer (1967). -48I0.1%1 I^i^IOOO0)0)•OOW0)•O05800^6000 6200Wave length (A)Figure 3.9: Mean residual spectrum formed from the average of all the residual spectra ofHD 183143 (Fig. 3.7a) and 55 Cyg (Fig. 3.7b). A representative spectrum (not to scale)of HD 183143 is shown below. The error bar indicates the intensity scale with respect tothe continuum level.49following way:AP(A)^fA-7- (A)(3.1)P(A) r(A)(from Martin and Angel 1974) where AP is the change of polarisation from the adjacentcontinuum polarisation P, AT is the change in optical depth from the adjacent continuumoptical depth T and f is a model-dependent parameter.We have used their result to predict the size of the polarisation effect in the diffusebands of our data. For f , we adopted a value of 1.4, in agreement with Martin and Angel(1974, 1975) and Fahlman and Walker (1974). The continuum polarisation, P (A), wascalculated using the empirical formula describing the wavelength dependence of opticalpolarisation from Serkowski, Matthewson and Ford (1975):P (A A) ) e— xp [—K1n2 (--A )1 (3.2)where 'max is the wavelength of maximum polarisation, P() niar), and K = —0.10 +1.86Amaz from the improved fit of Wilking, Lebofsky and Rieke (1982). We used thevalues of Amax and P(Amax ) given by Serkowski et al. (1975) and listed in Table 3.1.The optical depth, 7-(A), over the wavelength range of our spectra was computed fromthe relation Av = 1.0867-v (Mihalas and Binney 1981) and the 1/A extinction law. Weassumed a ratio, Rv, of total to selective extinction of 3.2 which is suitable for all theprogram stars (Johnson 1968) and used the colour excesses listed in Table 3.1. The changein optical depth A-7- (A) across a band from the continuum optical depth was calculatedfrom the following equation:A7-(A) = In ( ) (3.3)where /), is simply the intensity at each point in the band profile and is the continuumintensity. For IA, we used the mean of all our spectra rectified to a continuum value ofunity, so that = 1. -In calculating the predicted AP, we did not attempt to divide out the telluric a-bandof oxygen from any of the spectra. Since the telluric band dominates the spectrum of ( Perin the region of the 62841, we have used the mean spectrum of HD 183143 to calculateAP and then scaled the computed value of AP to the level appropriate for C Per.In Figs. 3.10a, b and c, we have plotted the differential polarisation (AP) profilepredicted using Eqn. 3.1 in the region of the 5780 and 5797 A bands, the 6177 A band and50the 6284 A band. The observed residual spectra of Figs. 3.7a, b and c are plotted on thesame figures for the purpose of comparison. Those figures show no polarisation structurewithin the 5780, 5797 and 6284 A DIBs at a level significantly smaller that the predictedeffect. In the case of HD 183143, the observed AP in those bands is at least an order ofmagnitude less than that predicted.Similarly, in the 6177 A band of HD 183143, there is no statistically significant po-larisation structure, the magnitude of the predicted AP being four times the standarddeviation of the observed AP in the band. We cannot make the same claim in the 6177 Aband of 55 Cyg since there the noise level of our results is similar in magnitude to thepredicted polarisation effect.Have we overestimated the expected amount of polarisation in the DIBs due to grains?Since the degree of polarisation predicted by the model depends on the assumed compo-sition of the grains and would be largest for dielectric grains (Greenberg 1978), it isimportant to establish whether the dielectric assumption is valid. According to Chlewickiand Greenberg (1990), the strong linear polarisation observed in the 3.08-pm ice bandand the 9.7-pm silicate feature (Lonsdale et al. 1980) demonstrates convincingly thatthe polarising grains are most likely dielectric. In addition, Mie theory calculations showthat conducting grains, with refractive indices that are strongly a function of wavelength,tend to produce more structure in the wavelength dependence of the polarisation thanis observed (cf. Martin 1975; Greenberg 1978; Chlewicki and Greenberg 1990). Indeedaccording to Chlewicki and Greenberg (1990), the interstellar polarisation curve is wellmatched using a simple size distribution of dielectric grains.The model of Martin and Angel (1974) produces results that are consistent with thoseof others. Greenberg and Stoeckly (1971), Kelly (1971), Bromage (1972), and Greenbergand Hong (1974, 1976) have computed the wavelength dependence of polarisation acrossthe 4430 A band. Their models were similarly computed by treating the DIBs as finestructure in the general extinction curve. Despite the different optical properties, align-ment mechanisms and shapes of the grains assumed in the computations, the results areremarkably consistent. Of note is the general agreement that the polarisation profilestend to mimic the extinction profiles of the bands. One exception is given by Greenbergand Hong (1974) who predicted anomalous dispersion 4 through the polarisation profile.4 Dispersion is defined by Greenberg and Hong (1974) as apparent "emission" at shorter wavelengths515800Wavelength (A)Figure 3.10: (a) Differential polarisation AP in the AA5780, 5797 (left panel), A6177(middle panel) and A6284 (right panel) bands of HD 183143. The predicted AP wasobtained by Eqn. 3.1 and is indicated by the dashed curve; the observed AP is given bythe solid curve.6150^62000.05%1^1^I^1^1^1^1^1^1^1 .^I 6300,62500.05%^11 11III11111 \ 111—^I 0 . 01%IIII0.05% rI I1 11I14 ■OMII 5800 6150^6200Wave length  (A)I , 6250^6300Figure 3.10: (b) As Fig. 3.10a for 55 Cyg. ,0.01%0.01%1 iI111^11^11^11^11I 58001 I1111I 6300Wavelength (A)Figure 3.10: (c) As Fig. 3.10a for C Per. The predicted AP in the 6177A band is notshown because the band is very weak in this star.54However, as pointed out by Fahlman and Walker (1974), the magnitude of the polarisationpredicted by the model of Greenberg and Hong (1974) is of the same order of magnitudeas that computed by Eqn. 3.1. In any case, we feel that Eqn. 3.1 gives a reasonable esti-mate of the size of the polarisation effect if the diffuse bands are caused by the interstellargrains responsible for the visible continuum polarisation.Our results support those of A'Hearn (1972), Martin and Angel (1974, 1975) andFahlman and Walker (1975), and represent an order of magnitude improvement in theupper limit to the polarisation change set by those authors. We find no evidence for thedifferential polarisation effect reported by Gammelgaard and Rudkjobing (1973) in the6177 A band in any of the stars observed in this program. We would have observed thiseffect as a dimunition of the polarisation in the 6177 A band.3.6 InterpretationA straightforward interpretation of the results of Sections 3.4 and 3.5 is that the DIBs donot originate in the solid grains which produce the visible continuum polarisation. Thatpolarisation is produced by a population of partially-aligned elongated grains, which arealso responsible for the visible extinction (cf. Smith et al. 1977).There are two plausible explanations for the lack of polarisation structure in the DIBs.The first explanation is simply that the DIBs have a non-grain origin, presumably molec-ular. (This is because there is no known mechanism which could efficiently align themolecules (Chlewicki et al. 1986; van der Zwet 1986).) A further discussion of themolecular-hypothesis is beyond the scope of this thesis. Recent articles by Chlewicki etal. (1986) and van der Zwet (1986) outline the arguments in favour of a molecular originfor the bands.The second explanation (for the lack of polarisation structure in DIBs) is that thebands arise from a population of grains distinct from those producing the visible contin-uum polarisation (Martin and Angel 1974; Chlewicki et al. 1986). Obviously, the grainsresponsible for the DIBs would have to be inefficient at polarising the stellar light. Twopossibilities that would suit this requirement are spherical or unaligned grains.Existing observational data place rather stringent constraints on the optical propertiesand absorption at longer wavelengths about the center of the band.55and sizes of these grains. Although some show very slight asymmetry, the intrinsic profilesof many of the DIBs are highly symmetric (cf. Section 3.1.2). Therefore, large grains(a 0.1pm) can be excluded as the possible carriers of the bands since they would producestrong asymmetry in the band profiles. Since small particles are relatively inefficientscatterers in the visible, dispersion effects in the line profiles should be small (Chlewickiet al. 1986); hence the bands produced in such grains could have symmetric profiles.However, Greenberg and Hong (1974) have computed the DIBs produced by modelgrains of various sizes whose shapes resemble spheres, spheroids and infinite cylinders. 5Using the usual Clausius-Mosotti equation to introduce the impurities into the host mate-rial, they found that the only way to symmetrize the profiles was to put the the impuritiesinto the very small particles (i.e., a < A). Even under that condition, some asymmetryof the profiles persists so long as the impurity centers are located in non-spherical grains.Chlewicki et al. (1986) computed similar models using the more accurate Purcell-Shapiro equation which better takes into account the interaction between the electricfield produced in the impurity centre and the external field. They remark that in thesmall-grain limit, the lines tend to be asymmetric with a steeper redward edge.Moreover, if the DIBs are formed in the very small grains then one would expectthe strengths of the bands to correlate with the far-UV extinction, which appears to beproduced by a population of N 0.01pm grain. However, as described in Section 3.1.2,several statistical studies show poor correlations of the 4430, 5780 and 6284 A DIBs withfar-UV extinction.As Chlewicki et al. (1986) conclude,Insofar as particles are concerned, the only remaining sizes to be considered aspotential diffuse line carriers are in the intermediate range (0.02 < a < 0.1pm).The typical size of "diffuse line" particles indicated by the observed profiles[see their Fig. 5] is r•-• 0.05pm. However, using absorbers embedded in theintermediate-size particles, it is difficult to explain both the details of theindividual profiles, such as the lack of broad wings in A5780, and the largevariety of observed line shapes.The strength of the 4430 A band does correlate with the 2175 A extinction bump.5They assumed the optical properties of "dirty ice" in their models. They also performed model calcu-lations for core-mantle grains with the intention of determining whether the placement of the impurities,either in the cores or the mantles, have any affect on the symmetry of the resulting interstellar absorptionbands (Greenberg and Hong 1976; Greenberg 1978).56(The positive correlation between these features does not contradict the lack of correlationbetween the 4430 A band and far-UV extinction, since the 2175 A feature also does notcorrelate with with far-UV extinction.) The 2175 A extinction bump is often attributed toa population of small 0.01pm) graphite grains or "platelets" (Draine 1988). Recently,Clayton et al. (1991) have measured the polarisation across the 2175 A bump of thesupergiant a Cam. They found no statistically significant enhancement of polarisation inthe bump. Therefore, the results of Clayton et al. and of this chapter do not contradictthe possibility that the two features share a common origin.In conclusion, it would seem that our results suggest that the bands are either molec-ular in origin, or are due to intermediate-sized (0.02 < a < 0.1pm) grains which arespherical or unaligned.57Chapter 4Differential Polarisation Studies ofBe Stars4.1 Be Stars4.1.1 IntroductionThe most striking characteristic of Be stars, and that which distinguishes them fromnormal B stars, is the presence of emission in the Balmer series of hydrogen. For historicalreasons, the term Be has been reserved only for the B stars of luminosity classes III, IVand V that have emisson lines, although emission in (predominantly) Ha is common in thesupergiants. The underlying absorption spectra of Be stars are typical of normal B-typespectra in which the absorption lines have been broadened by rotation. The emissionlines are usually superimposed on the broad absorption lines and most commonly occurat Ha and 11/3. If present at all, the emission decreases for the higher members of theBalmer series and disappears toward 1120. Emission is also sometimes present in the singlyionized metallic lines such as Fe II. The presence of emission is not a rare anomaly in thespectra of B-type stars; in fact, the Be stars make up a significant (, 20%) proportion ofB stars. There are many excellent reviews of Be stars; some include the proceedings ofIAU Symposium No. 70 (Slettebak 1976), Underhill and Doazan (1982), the proceedings ofIAU Symposium No. 98 (Jaschek and Groth 1982) and the proceedings of IAU ColloquiumNo. 92 (Slettebak and Snow 1987).58The emission is thought to be produced in a flattened circumstellar envelope' of ionisedgas extending to some 5-15 stellar radii. Much effort has gone into trying to understandhow the extended circumstellar envelope is formed and how it is maintained (Plavec 1976).An important way of studying the envelopes around Be stars is by measuring the degree towhich the light from these stars is polarised. Indeed, the presence of intrinsic polarisationin Be stars has provided compelling evidence for the disk-like nature of the circumstellarenvelopes (Coyne 1976a). Furthermore, our understanding of the physical conditionsinside the envelopes has been enhanced by studying the wavelength dependence of thecontinuum polarisation (Coyne 1976a; Coyne and McLean 1982). Since the mid-1970's,studies of the variations of polarisation across spectral features have proven particularlyvaluable in probing the dynamics, expecially the rotational and expansion velocities, ofthe gas in Be star envelopes (Coyne and McLean 1982).4.1.2 The Be PhenomenonThe Be phenomenon represents one of a number of transient phases exhibited by stars ofthis type (Underhill and Doazan 1982; Dachs 1987). A Be star may undergo, in any order,transitions between the normal B, shell and Be phases. Each phase is distinguished by itsown characteristic line spectrum The Be phase is usually characterised by emission lineswith (and sometimes without) shallow central depressions. The shell phase is identifiedby the presence of very deep, sharp absorption cores in the lines of hydrogen and ionisedmetals (e.g. Fe II, Ti II, Cr II) where usually the lowest Balmer and some metallic linesare also bordered by emission wings. (Such stars are normally referred to as shell starsin the literature.) It is also not uncommon for Be or shell stars to lose their emission orshell features completely and assume normal B phase characteristics. Transitions fromone phase to another are gradual and can take anywhere from a few days to decades(Underhill and Doazan 1982). Following the example of Kitchin (1982), in this thesis, wedo not distinguish between Be and shell phases but consider them to be different aspectsof the same phenomenon.The origin of the emission lines is attributed to recombination processes in a coolcircumstellar envelope, the gas in which is ionised by the UV radiation of the star. Typical'In this thesis, we use the term envelope to denote the outer regions of Be stars where the emissionlines are produced.59electron densities of the envelopes are on the order of 10 11 -10 13 cm' (Underhill andDoazan 1982), and the masses of the envelopes range from 10'o_its-su Me (Baade 1987).The presence of Fe II implies electron temperatures of 10 4 K. The intensities of theemission lines suggest that the envelopes in which they are formed must be extensive(— 5-15 R„); the small displacements of the lines in the visible spectrum indicate lowexpansion velocities of the gas.In contrast, far-UV observations indicate the presence of superionized regions withelectron temperatures of ti 105 K (Underhill and Doazan 1982). These superionized re-gions exhibit high expansion velocities which generally exceed the escape velocity at thestar's photosphere and seem to imply the existence of a mass flux from the star (Doazan1987; Dachs 1987). The mass flux in Be stars is highly variable; the strong variabil-ity might be a condition for the formation of the circumstellar envelopes (Underhill andDoazan 1982).Besides B-Be phase transitions, Be stars frequently exhibit irregular or quasi-periodicvariations in their emission-line profiles. Variations of V1 R, the ratio of the strengths ofthe violet and red emission peaks, are common in Be stars with double-peaked emissionlines. The timescales for VI R variations are of the order of years to decades (Dachs 1987).Be stars may also display rapid periodic variations in the profiles of some of theirunderlying absorption lines. There is growing evidence that these variations are verycommon, and perhaps universal, among the early to mid B-type stars (Penrod 1986,1987; Baade 1987). The variations can take either one or both of the following forms: (1)changes in the width and asymmetry of the absorption line; (2) several quasi-emission orabsorption bumps travelling from blue to red across the line profile. Several -models havebeen suggested to explain the line-profile variations such as nonradial pulsation (NRP),"spots" or "spokes" carried across the stellar disk by rotation, and binarity. The favouredexplanation is NRP. Conceptually, NRP can be thought of as waves travelling around theequator of a star; the form of these waves is described by spherical harmonics. The modeof oscillation is specified by the quantum numbers, and m. In practice, sectorial modes(1 = Im1), which divide the star into longitudinal strips each strip moving out of phasewith its neighbours, have been found to best reproduce the line-profile variations (Walker1991). A review of the theoretical aspects of NRP can be found in the book by Unno etal. (1989; and references therein).60In addition to line variability, many Be stars exhibit rapid photometric variations withperiods of the order of fractions of a day or days; the amplitudes of the variations aresmall, typically 0TO1 to 0•1 (Percy 1987). These rapid photometric variations have alsobeen attributed to NRP (Percy 1987). Longer-term variations are also observed in Bestars and usually accompany high-amplitude changes in the line spectrum as well as phasetransitions (Underhill and Doazan 1982).Struve (1931) was the first to suggest a model for the Be phenomenon. In this model,the emission lines arise in a gaseous equatorial ring formed by the ejection of matterfrom a rapidly rotating star. It was implicitly assumed that all Be stars are rotating attheir critical velocity. Although in general Be stars rotate faster than normal B stars, therotational velocities of most Be stars do not approach the critical velocities required formass ejection. In fact the largest observed v sin i is 400 km s -1 . Moreover, rotation aloneis incapable of ejecting matter to large enough distances for the formation of the envelope(Underhill and Doazan 1982). Thus, later models have usually incorporated a mechanismfor producing a mass flux from the star in addition to stellar rotation.Recently, it has been suggested that NRP could provide the additional energy requiredto power a Be outburst (Penrod 1986, 1987). In this interpretation, low-i pulsation modesproduce shock waves which dramatically increase the scale height of the atmosphere suchthat, combined with the forces due to radiation pressure and rotation, material is thrownoff the outer photosphere into a circumstellar disk. Wilson (1986) and Osaki (1986) havealso discussed possible mechanisms for a generating a Be outburst from NRP.Other models of note are the stellar wind model (Marlborough 1987; and referencestherein) in which the circumstellar envelope is formed by a radiation-driven rotationallydistorted wind; the binary model (Kriz and Harmanec 1975; Harmanec 1982, 1987) inwhich the envelope is the result of mass accretion from a close companion filling its innerLagrangian surface; and the magnetic-loop model (Underhill and Fahey 1984; Underhill1987) in which the disk arises from "plumes" of plasma supported by closed magneticstructures located around the equatorial regions of the star, while plasma streams, alongopen magnetic field lines, form an expanding spiral as a result of rotation of the star.614.1.3 Past Polarisation Studies of Be StarsPolarisation studies of Be stars have contributed significantly to our understanding ofthe extended envelopes about these stars. The intrinsic polarisation of Be stars was firstdiscovered by Behr (1959) because of temporal polarisation variations in the star 7 Cas.This was followed by similar detections in x Oph (Shakhovskoj 1962) and other Be stars(Shakhovskoj 1964; Coyne and Gehrels 1967). Subsequent polarimetric surveys haveshown that about 50% of Be stars are intrinsically polarised (Serkowski 1970; Poeckert,Bastien and Landstreet 1979). The degree of continuum polarisation in the visible regionof the spectrum of most Be stars is about 1% and never exceeds 2% (Underhill and Doazan1982).The intrinsic polarisation of the light from Be stars has a characteristic wavelengthdependence which is distinct from that observed for interstellar polarisation. Serkowski(1968) first noticed that the polarisation in the emission-line stars decreases much morestrongly (in the UV spectrum) across the Balmer limit than is the case with the interstel-lar polarisation. Coyne and Kruczewski (1969) later showed that the polarisation riseslongward of the Paschen limit in a manner that is also unlike interstellar polarisation. 2The wavelength dependence of the polarisation has provided valuable insight into theprocesses occuring in the Be star envelopes.It is generally accepted that the intrinsic polarisation in Be stars is caused by thescattering of stellar radiation from free electrons in an extended envelope which is notspherically symmetric with respect to the observer. 3 This interpretation was first putforward by Shakhovskoj (1964) and Rucinski (1966, 1967) to explain the intrinsic polar-isation of the eclipsing binary /3 Lyrae and later independently proposed by Coyne andKruszewski (1969) to explain the polarisation of Be stars. In order to account for thewavelength dependence of the polarisation, Coyne and Kruszewski (1969) also proposedthat the otherwise wavelength-independent polarisation produced by electron scatteringcould be modified by continuous absorption (before and after scattering) by partly ionisedhydrogen in the envelope. In their model, hydrogen absorption and electron scattering are2 Examples of polarisation curves for Be stars may be found in Coyne and Kruczewski (1968) andPoeckert et al. (1979).3The photosphere of a rotationally distorted star does not produce polarisation greater than 0.1% andtherefore cannot be entirely responsible for the polarisation observed in Be stars (Nagirner 1962; Collins1970; Rucitiski 1970).62important sources of opacity, but at some wavelengths absorption is the dominant opac-ity while at other wavelengths electron scattering opacity dominates. Shortward of theBalmer limit, absorption dominates the electron scattering opacity such that the decreasein polarisation across the Balmer limit to shorter wavelengths is an inverse function ofthe bound-free hydrogen opacity at those wavelengths (Underhill and Doazan 1982).More complex models of the intrinsic polarisation of Be stars have since been developed(Haisch and Cassinelli 1976; Capps, Coyne and Dyck 1973; Coyne and McLean 1975;Coyne and Vrba 1976; Poeckert and Marlborough 1977, 1978a, 1978b; Jones 1979). Suchmodels usually assume a disk-shaped geometry' and include both bound-free and free-free processes.' In these models, the direction of the net polarisation is parallel to thepolar axis of the star. Reviews of the various models may be found in Coyne (1976a) andUnderhill and Doazan (1982).Emission and absorption processes in the Balmer lines of Be stars modify the wave-length dependence of polarisation inside the lines; thus the polarisation profiles of theemission lines serve as further (independent) constraints on the models of Be stars (Coyneand McLean 1982). A decrease in polarisation across the Hp emission feature in C Tauwas first discovered by Serkowski as reported in Zellner and Serkowski (1972). Similardetections were announced by Clarke and McLean (1974a) at the IAU colloquium onphotopolarimetry in 1972. Numerous studies have since verified those preliminary re-sults. They are reviewed in Coyne (1976a), Coyne and McLean (1982) and only citedhere: Clarke and McLean (1974b, 1975, 1976); Hayes and Illing (1974); Hayes (1975);Coyne (1974, 1976b); Coyne and McLean (1975); Poeckert (1975); Poeckert and Marl-borough (1976, 1977, 1978a); McLean et al. (1979); McLean and Clarke (1976, 1979);and Clarke and Brooks (1984). With the exception of McLean et al. (1979), all of themeasurements have been made using narrow-band (typically, 2-26 A) photopolarimetrictechniques.From the early observations, the decrease in polarisation observed in the lower Balmeremission lines was found, to a first approximation, to vary inversely with the total intensityI of the emission line [i.e., PL = Pc' I, where Pi, and Pc are, respectively, the line4Haisch and Cassinelli (1976) found that very flattened, disk-shaped envelopes are required to producethe observed levels of continuum polarisation when absorption is taken into account.5 Capps et at. (1973) showed that unpolarised free-free emission from the disk is required to accountfor the rapid decrease in polarisation between 0.9 and 2.2 pm.63polarisation and adjacent continuum polarisation] (cf. Coyne 1976a; McLean and Clarke1976). This decrease was attributed to dilution of the continuum polarisation by theaddition of unpolarised emission in the lines (Clarke and McLean 1974; Poeckert 1975).This interpretation however appears to be too simplistic for some stars. For example,polarimetric measurements across the Ha line of 7 Cas have shown that the polarisationin the blue wing of the line was smaller (Poeckert 1975; Mclean and Clarke 1976) thanexpected if the reduced polarisation was caused solely by the addition of unpolarisedemission flux. Anomalous polarisation changes have also been reported for cb. Per wherethe emission flux in Ha has been estimated to be about 0.5% polarised (Coyne and McLean1975), and for C Tau where an increase in polarisation from the continuum value has beendetected (McLean and Clarke 1976).The highest resolution (0.45 A) polarimetric observations (prior to this thesis) havebeen made by McLean et al. (1979) with a Digicon echelle spectropolarimeter. Theymeasured the polarisation across the 1-1# line of Be stars -y Cas and 0 Per. Their datarevealed variations in the line polarisation which had previously gone undetected due tothe poor resolution of the earlier studies. The line polarisation was generally charac-terised by a systematic decrease in the polarisation (from the continuum value) towardthe center of the line accompanied by an increase at the line center. There was also slightevidence in their data for changes in the position angle of the polarisation. McLean et al.(1979) pointed out that their results could not be explained solely in terms of dilution byunpolarised line emission, and suggested that absorption also plays an important role indetermining the polarisation in the line profiles of Be stars.Polarisation studies also offer an independent way of investigating the possible sourcesof the line profile variations observed in many Be stars (cf. Section 4.1.2). If NRPs are thesource of these variations, then it should be possible to observe changes in the intrinsic po-larisation of the star and these changes should correlate with the periods of the line profilevariations' (Odell 1979; Stamford and Watson 1980). Short-term polarimetric variations,of the order of days or fractions of a day, have been reported by a number of authors (e.g.6The continuum polarisation is produced in the denser regions closer to the star GS 3 14; Poeckertand Marlborough 1978a); the emission flux is produced in the outer regions where it is less scattered andtherefore less polarised.7NRPs distort the star from its spherical shape. Therefore, in the integrated light of the star, thereshould be a net polarisation.64Poeckert 1975; Clarke and McLean 1976; Poeckert and Marlborough 1978a; Poeckert et al.1979). However, most attempts to find a correlation between the polarisation variationsof Be stars (and other stars suspected of being nonradial pulsators) and their line-profilevariations have thus far either failed or been inconclusive (e.g. Clarke 1986; Gies andMcDavid 1987). Polarimetric variations consistent with a nonradial (i = 2) mode havebeen reported by Odell and Tapia (1981) and Odell (1981). All of these studies relied onwide-band (UBV) polarimetry.In fact, with the exception of McLean et al. (1979), none of the studies of Be starsmentioned above has employed spectropolarimetry. Therefore, using our polarisation anal-yser and a CCD detector, we obtained moderate resolution (0.15 A), high S/N (500-1000)spectra to investigate polarisation effects associated with two phenomena observed in Bestars:1. We present a first attempt using spectroscopic techniques to measure excess polari-sation associated with the line profile variations of OB stars. The prime candidatesfor this program were C Oph and e Per, which display the largest amplitude varia-tions^1%) known among the OB stars.2. We also observed three intrinsically polarised stars -y Cas, 0 Per and 28 Cyg toinvestigate the polarisation effects across their IP emission lines in order to studyingthe nature of the extended circumstellar envelopes about these stars.4.2 ObservationsTable 4.1 lists the line profile variables and emission-line stars observed, their spectraltypes, visual magnitudes, v sin i, NRP mode, the time separation between individualsubfeatures (At),8 intrinsic polarisation in the B band and the angle of polarisation. Forthe line profile variables, information regarding the mode and At were obtained fromthe given reference. We have also provided the reference from which the polarisationparameters were obtained.All of the polarised spectra presented in this chapter were obtained with the UBC/DAOpolarisation analyser described in Chapter 2 and the 488 nm beamsplitter cube. The ob-8Zit has alternatively been refered to as the "period" of the variations by Gies and Kullavanijaya(1988). In this thesis, we use the notation of Walker et a/. (1987).65Table 4.1: Program Stars for Be Star Polarisation StudySpectral^v sin i^StHD^Star^Type^V^(km s-1 )^i^(hrs)Line-profile VariablesPBc(%) Op Reference ^149757^ C Oph 09.5Vea 2.56a^3906^8^2-3^•••^...^Vogt and Penrod24760 ^c Per^B0.5V^2.89^153^3,4,5,6 4.5,3.8,3.0,2.3^...^...^Gies and Kullavanijaya (1988)Emission-line Stars10516^ 4 Per^B2Vep^4.07^450^•••^•••^2.0^26° Poeckert et al. (1979)5394^ 7 Cas^BOIVe^2.47^300^••• •••^0.8 105° McLean et al. (1979)191610^ 28 Cyg B2.5Ve^4.93^310^•••^•••^0.5 180° Coyne (1975)a Hofileit and Jaschek 1982b Hutching and Stoeckley 1977c Continuum polarisation measured with Johnson B filterservations were made using the DAO 1.83-m telescope and Cassegrain spectrograph in sixobserving runs between June 1990 and July 1991. The 1800 lines mm-1 grating, blazedat 5000 A, was used in the first order and gave a reciprocal dispersion of 10 A mm-i . Thespectra were centred at 1113 A4861 and some included He II )4921.Each star was monitored in a continuous series of integrations with the analyser ro-tated in position angle between each integration. Spectra of C Oph obtained in the June1990 observing run were recorded with the Reticon detector. The integration time foreach spectrum was 20 min; the mean S/N per diode was 600. The resolution of thedata was 0.15 A diode'. An RCA CCD (620x 1024) detector was employed during thesubsequent observing runs in September 1990 and January 1991. It gave a resolution of0.15 A diode". Because of the low noise penalty per read out of the CCD, the integrationtimes of the spectra were reduced, ranging from 20s-40s. We took advantage of on-chipbinning to improve the signal in each spectral element without increasing the read outnoise. The spectra were aligned along the columns of the CCD and were binned onlyin the direction cross-wise to the dispersion into one (September data) or three or more(subsequent data) columns.A complete journal of the observations is presented in Table 4.2, listing typical inte-gration times, mean S/N per diode, the number of spectra and the length (in hours) ofeach time series.Spectra obtained in 1990 were taken with the temporary analyser mount mentioned inSection 2.4.1. Position angles were selected manually using five detents located every 40°at 180°, 140°, 100°, 60°, 20°. Rotation of the analyser was alternated between clockwiseand counter-clockwise directions (as seen projected onto the sky), with exception of theSeptember 1990 run. This was done in order to minimise spurious polarisation detectionscaused by systematic zero-point drifts in wavelength due to spectrograph flexure and theredward movement of the travelling subfeatures across the line profiles of the programstars (see Section 4.5.1). In September 1990, the analyser was always rotated in theclockwise direction. Also, three spectra at each rotation of the analyser were obtained inorder to limit the amount of time spent in overhead [i.e. in reading out the CCD (20 s perread out) and rotating the analyser]. The median was taken of each set of three spectrato improve the S/N and reduce the effects of cosmic-ray spikes. The observing sequencefinally adopted for the observing run in January 1991 was as follows: (1) one polarised67Table 4.2: Summary of Be Star ObservationsStarDate(UT)to(hr) Detector NE'ExposureTime (s) S/NSpectralRegion 9C Oph^ 15 Jun 1990 3 DAO Reticon 9 1200 600 I113 )4861 20°, 60°, 100°, 140°, 180°15 Jun 1990` 3 UBC Reticon 14 900 600 HO, He I A6678e Per^ 05 Jan 1991 7 RCA CCD 336 30 300 HO, He I A4921 0°, 45°, 90°, 135°4) Per^ 25 Sep 1990 22 RCA CCD 105 40 280 HO A4861 20°, 60°, 100°, 140°, 180°-y Cas^ 23 Sep 1990 41- RCA CCD 225 20 500 HO A4861 20°, 60°, 100°, 140°, 180°24 Sep 1990 5 RCA CCD 255 20 500 11/3 A4861 20°, 60°, 100°, 140°, 180°28 Cyg^ 24 Sep 1990 4 RCA CCD 165 40 200 HO M861 20°, 60°, 100°, 140°, 180°a) Total time coverage of time series.b) Number of spectra in time series.c) Unpolarised data set taken with DA0 1.22-m telescope.spectrum at each of 0°, 45°, 90°, 135°, was obtained, and (2) the process was repeated inthe reverse order, i.e., 135°, 90°, 45°, 0°. The polarisation analyser was operated remotelyfor these runs.On one night (15 June 1990 UT), a times series of Reticon spectra was obtained ofOph in natural light using the coude spectrograph of the DAO 1.22-m telescope withthe 1200 lines mrn -1 grating, blazed at 6000 A. These observations were timed to coincidewith the polarimetric observations at the 1.83-m telescope. The reciprocal dispersion wasthe same as that used at the 1.83-m telescope, namely, 10 A mm-1 The spectra werecentred at about 6650 A and included both Ha A6563 and He I A6678.In addition to the program stars, standard stars known to be unpolarised were observedin an identical manner on each night of the observations. These stars are listed in Table 4.3along with their visual magnitudes, spectral type and the source from which they weretaken.Iron-Argon comparison spectra were recorded approximately every 1/2 hour to 45 minin order to monitor possible wavelength shifts due to spectrograph flexure.4.3 Data ReductionThe Reticon data were processed following the procedures described in Section 3.3. Re-ductions of the CCD data were carried out using routines in the software package IRAF(Image Reduction and Analysis Facility). The first task in the reductions was to sub-tract a bias frame from each data frame. The bias frame was formed from the medianof all (usually 9-10) zero-second exposures taken throughout the night. Because the biaslevel or offset in each frame tends to fluctuate from one exposure to another, individualbias levels, calculated from the overclock pixels and recorded in the image header, werefirst subtracted from all the frames including the bias frames using the DAO-written tasksubocpm.No flat-flielding of the data was done, avoiding the unnecessary addition of noise whichcould undermine the precision of our results. Instead we followed a procedure of formingresidual spectra similar to the one carried out in Chapter 3. In this case, however, residualspectra were computed by dividing each spectrum by a mean spectrum (cf. Section 4.5).Besides cancelling the variations in sensitivity between the individual diodes, this method69Table 4.3: Standard Unpolarised Stars for Be Star Polarisation StudyHD StarSpectralType V References127762^ y Boo A7 III 3.03 Appenzeller (1966)172167^ a Lyr AO Va 0.03 Appenzeller (1966)432^ Cas F2 III 2.27 Serkowski (1974)197345^ a Cyg A2 Iae 1.25 Clarke and Brooks (1984)70reveals the presence of wavelength-dependent polarisaton in the line profiles.The spectra were extracted from the two-dimensional CCD spectrum images in one oftwo ways. Where the spectra had been binned (on-chip) into a single column, onlythat column was extracted from each spectrum using the IRAF task toonedspec innoao .prot o. The data in three or more column bins were extracted individually using thetask apsum in noao.twodspec.apextract. This task displays the cross-sectional profileof the 2D spectrum and allows the user to define the width of the aperture used in theextraction. The aperture widths, taken to be the width of the profile at half-maximum,were typically 3-4 pixels. The spectra were traced along the center of the profile at vari-ous positions on the dispersion axis in order to account for any distortions in the spectraor misalignments of their dispersion axes. The spectra were then extracted by summing(unit weights) the pixels within the apertures at each point along the dispersion axis.The extraction parameters, such as the aperture width and the tracing information, werestored in a database directory. No sky-background subtraction was performed on thedata since the spectra were obtained with an image slicer and therefore contain negligiblecontributions from the sky.In the case where the data were binned in three or more columns, the residual spectrawere formed from the 2D spectrum images before being extracted. Because the taskapsum had difficulty tracing the poorly defined profiles of the residual spectra, the sameparameter values defined in the extraction of the spectra corresponding to those residualswere used as defaults in the residual extraction.The residual spectra formed from the CCD were then rectified using a second-orderLegendre polynomial so that their mean intensity levels were equal to one. Second-ordercubic splines were used to rectify the Reticon residual spectra.4.4 Polarisation AnalysisThe polarisation data for this analysis consisted of a set (or sets) of residual spectrafor each star (each spectrum having been divided by an average spectrum and rectified)obtained at (4-5) different rotations of the analyser (cf. Section 4.2). The analysis of theobservations involved computing the differential polarisation AP and the position angleOp at wavelengths A i , where i = 1, 2, ... , N across a given spectral feature. We have71defined AP and Op by Eqn. 1.5 of Section 1.2 to beI,„(0) = 1 + AP icos[2(0 i — Cbp i )]^ (4.1)where we have written /(0)//avg (in Eqn. 1.5) as /res (0) to denote the rectified residualspectra and P (in Eqn. 1.5) as AP to denote the differential measurements (cf. Sec-tion 2.3). Here 0 takes the values of the position angles of the analyser for which eachseries of Iles was obtained.From Eqn. 4.1, we were able to determine the wavelength dependence of polarisationacross a spectral feature and investigate possible changes in the position angle throughthe line profile. We introduce the terms "differential polarisation (AP) spectrum" and"position angle (Op) spectrum" to describe the wavelength dependence of AP and Op.Since the number of wavelength points N was in general large (ranging from 500to 2000), a FORTRAN program was written by the author to calculate AP and (Ap byleast-squares fits to /rie3 (0) at each point in the given wavelength region. Because thefunction /, depends nonlinearly on 0, the Levenberg-Marquardt least-squares fittingroutine MFtQMIN from Numerical Recipes (Press, Flannery, Teukolsky and Vettering 1986)was used. The intensities I,i.e,(0) were weighted according to cri 2 in the fit where cri is thestandard deviation of the i th data point. In our analysis, we assumed that all data pointshad the same standard deviation, ai = a, and set a to be the standard deviation measuredin the continuum regions of the residual spectra. The uncertainties associated with thefitted parameters were also provided by the least-squares fitting routine (cf. NumericalRecipes).Like most nonlinear least-squares fitting algorithms, the Levenberg-Marquardt methodrequires a good intial guess. We calculated the initial parameters using a Fourier seriestruncated to the first harmonic. Thus,AP = [a? +^ (4.2)= arctan(—b1)^ (4.3)2^alwhereal = —2 fr Ires (0) cos 20 d0^ (4.4)obl = —2 f  IT s(9) sin 20 d0 (4.5)Ir 072and we used the trapezoidal rule to do the numerical integrations.' Using these initialparameters, the Levenberg-Marquardt algorithm typically converged in 3-4 iterations.4.5 Results and Discussion4.5.1 Differential Linear Polarisation Associated withLine-Profile Variations4.5.1.1 ( OphThe bright 09.5 Ve star, C Oph, was the first object investigated for excess polarisationassociated with the line-profile variations of the star. It is the prototype of a class ofnonradially pulsating stars with rapid rotation (v sin i > 170 km s -1 ; Unno et al. 1989). Itwas the first star in which travelling subfeatures within the absorption lines were detected(Walker, Yang and Fahlman 1979) and displays some of the largest variations known(,1%) among the OB stars. Since one might expect the size of any polarisation excessto be correlated with the strength of the variations, C Oph is probably one of the bestcandidates for this program.The time series of polarised spectra of C Oph at 11,8 is shown in Fig. 4.1. The cor-responding analyser position angle is given above and to the left of each spectrum. Thespectra have been smoothed by a Gaussian transfer function with a o- value of 0.23 A.Small variations are just noticeable in the line profiles. These variations are best seen inthe residual spectra shown in Fig. 4.2, formed by dividing the individual spectra by themean of all the spectra in the series. The "bumps" moving across the line profiles are muchlike those observed by Walker, Yang and Fahlman (1979) and Vogt and Penrod (1983)9 The reader may wonder why we did not use a more sophisticated numerical integration algorithm.Initially our choice was for the sake of convenience. Since then, we have become aware that the trapeziodalrule is extremely accurate for periodic data at equally spaced points (modulo the periodicity). This isdiscussed in more detail by Kahaner, Moler and Nash (1989; p. 162). Because of this requirement forequally spaced points modulo the periodicity, this exceptionally high accuracy is obtained only for thecase of c Per and not for any of our other observations.73and are most consistent with the = = 8 mode of pulsation.'As a check that any apparent polarisation effect seen in the polarised spectra did notarise from another (time-dependent) variation, we carried out an identical analysis on theunpolarised spectra. The corresponding times series at He I 6678 is shown in Fig. 4.3. Onlythose spectra whose mid-exposure times coincided with those of the polarised spectra arepresented. In some cases, adjacent spectra were averaged in order that their mid-exposuretimes match more closely the times of the polarised spectra. The residual spectra formedin the same way described above are shown in Fig. 4.4. Despite the striking differencesbetween the two line profiles in Figs. 4.1 and 4.3, their residuals (Figs. 4.2 and 4.4) areremarkably similar.To compare directly the variations in both lines, the residual spectra were interpolatedwith a sine function onto the same velocity scale. Rest wavelengths were taken from(Moore 1959). The result of the transformation is shown in Fig. 4.5 where the residualswithin a pair of polarised and unpolarised residuals (with corresponding mid-exposuretimes) are shown superimposed. Some show slight velocity shifts with respect to eachother which is due to the fact that the mid-exposure times of the spectra within a pairwere not always the same. (The time difference never exceeded five minutes.) Alsobecause the He I line is weaker than 10, it is not unexpected that the amplitudes ofthe subfeatures in the He I line should be correspondingly smaller Despite the smalleramplitudes, the visibility of the subfeatures is better in the He I line, most probablybecause of the inverse correlation between the resolution of the bumps and the intrinsicwidths of the lines (Kennelly, Walker and Hubeny 1990). Nevertheless, in general, thematch between the bump patterns within each pair is very good.In order to analyse the subfeatures for polarisation using the method of Section 4.4, itwas necessary to shift the residual spectra so that the subfeatures were aligned. We usedthe unpolarised residual spectra for this purpose. To calulate the shifts, the displacementsloAn approximate value of imj was calculated from the formulaimi 2r(v sin 0 Ata.(4.6)(Walker et al. 1987) where a o is the acceleration of the subfeature at line center and At is the average timeseparation between successive subfeatures. The values of a. and At were measured from the unpolarisedresidual spectra in Fig. 4.2 to be 3197 km s -1 4:1-1 and 0.1309 d, respectively, and v sin i = 379 km s -1from Unno et al. (1989). We obtained Imi 6.744860^ 4880WAVELENGTH ( A )Figure 4.1: Polarised spectral time series of Oph at the 11/9 A4861 line. The analyserposition angle is shown above and to the left of each spectrum. The corresponding mid-exposure time in fractions of a day from the barycentric JD 2,448,057 is given to the rightof each spectrum. The intensity scale with respect to the continuum is indicated by theerror bar.754860^4880WAVELENGTH ( A )Figure 4.2: Polarised residual time series of C Oph at the HQ A4861 line formed by dividingthe individual spectra in Fig. 4.1 by their mean spectrum.766680^ 6700WAVELENGTH ( A )Figure 4.3: Unpolarised spectral time series of C Oph at the He I A6678 line. The cor-responding midexposure time in fractions of a day from the barycentric JD 2,448,057 isgiven to the right of each spectrum. The intensity scale with respect to the continuum isindicated by the error bar.776660^6680^6700WAVELENGTH (A)Figure 4.4: Unpolarised residual time series of C Oph at the He I A6678 line formed bydividing the individual spectra in Fig. 4.3 by the their mean spectrum.78(in velocity) of the bumps from the line center were measured as a function of time and aline fitted to the points corresponding to each bump. Taking the average shift derived fromthe two fits, the residuals were then shifted according to their respective mid-exposuretimes. As shown in Fig. 4.6, besides aligning the bumps within each series of polarisedand unpolarised residuals, this step also improved the alignment within the residual pairswhose mid-exposure times did not exactly coincide.We applied the polarisation analysis outlined in Section 4.4 to the both polarisedand unpolarised datasets. In both cases, the data were divided into two subsets, onecontaining the first five residual spectra and the other containing the last five, so thatthe middle spectrum was included in both sets. In this way the subset containing thepolarised data comprised one complete sequence of residuals taken at the five positionangles of the analyser.The results for the polarised and unpolarised datasets are compiled in Figs. 4.7 and4.8, respectively. The results of the first subsets are plotted in Figs. 4.7a and 4.8a andthose of the second subsets are shown in Figs. 4.7b and 4.8b. In the middle and upperpanels of each of those figures are plotted the differential polarisation (AP) spectrum andthe position angle (Op) spectrum in the region of the line profile. Typical 2o - errors in APand Op from the least-squares fit, at each wavelength point are given by the error bars inthe respective panels. The middle residual spectrum from each subset (corresponding to100°) is also plotted in the lower panel of each figure for comparison.There is evidence for pronounced structure in the AP spectra of Figs. 4.7a and b thatappears to be strongly correlated with the bump pattern in the IV profile. However, wefeel, in view of the significant scatter in both AP and O p in the region of the line profile,that it is unlikely that this structure represents an actual polarisation effect. In fact, thestructure in AP is almost certainly caused by systematic (time-dependent) variations inthe subfeatures of the line profile.Besides their systematic movement across the line profiles, the subfeatures also displayother variations which could complicate the polarisation analysis. As a bump emergesfrom, or disappears into, a line wing, there is a systematic increase, or decrease, in itsamplitude (cf. Unno et al. 1989). An example of type of behaviour is shown by sub-feature b in Fig. 4.2. Furthermore, it is not unusual for individual subfeatures to decayin amplitude or suddenly disappear as they traverse the line profile (Yang, Ninkov and79-500^0^500^1000VELOCITY (k mss )Figure 4.5: Superposition of polarised and unpolarised residual time series of Oph atHQ (Fig. 4.2) and He I A6678 (Fig. 4.4). The residual spectra have been interpolatedonto the same velocity scale. The analyser position angle corresponding to the polarisedresiduals is given to the right of each pair of residual spectra.80-500^0^500^1 0 00VELOCITY (km/s)Figure 4.6: As Fig. 4.5, but with the subfeatures aligned.81cpr.005I^I •AP2r •^NJ ^-•• •.^.^.ITI III^IIIV I^1^If^I . 1. i I^I^"%I^1:^I^I 'III-^III.^• .150150100—.011.01:^ .....I .... •• . •^ _IN. ■•.,^ _".^re/ %. ■^1. % .^ •••^01. .. "VI ‘1f -t. ....,. ft —./Nr- -,....,.,-- ./.... -.... ..„-...-^...-^.... -- ,-....; -r^.. . ..„...-^...c.•—.005I arI.99 ^I^I^III^1^I^I^I^I^1^I^I^1^I^I^1^[III!^111111111^—800 —600 —400 —200^0^200^400^600Velocity (km/s)Figure 4.7: (a) Results of the polarisation analysis of the first five (first subset) polarisedresidual spectra of Fig. 4.6 for C Oph. The differential polarisation (AP) spectrum andposition angle (4) spectrum are plotted in the middle and upper panels respectively. Themiddle residual spectrum from the first subset (corresponding to 100°) is shown in thelower panel for comparison.80082J^1^1^J^1^-1^.1'•1.. 1►1^1^r^i^1^T^I^1^1^1^1•.005—.005150100• •^•^. •g• •^•• • •■•• • • •^• ••• .^••^•••••^ • eimi.•1 I I I^1.1. I I I^I rAP -'"••woo.^•••.,^ d'‘•^Nor . •••^ a•tr••••• •50I 2a— .01 I I^^I1.01I.99- 1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1 -^-800 -600 -400 -200^0^200^400^600^800Velocity (km/s)Figure 4.7: (b) Results of the polarisation analysis of the last five (second subset) polarisedresidual spectra of Fig. 4.6 for C Oph. The differential polarisation (AP) spectrum andposition angle ( Op ) spectrum are plotted in the middle and upper panels respectively. Themiddle residual spectrum from the second subset (corresponding to 100°) is shown in thelower panel for comparison.83.99 - I^1^1^1^1^  -800 -600 400-400 600^800-200^0^200Velocity (km/s)I 2crI.995150I^I I^I^I .1^I ••••I^1 . f'I I100_ .500.005••^•.• • •^"ft^• -^ • ••• •1-1-1 -I rem- [1 II fi^111-1 11• 1'1.•ri -AP -.^-^•.^...^ —_^„......, ..^. • -•^ —0 rt.=^..••••"1"\ = % ••*"..••^- I:^--",,,, p.a.% ...N.^ ..-ar. %1%."... •^...f.^ til:,•• JO?^■^: '^'''''....^.^I%.,'—',..."........' ."..^"••• I ^'VI ...„ .• Se.• / .—-.005Figure 4.8: (a) Results of the polarisation analysis of the first five (first subset) unpolarisedresidual spectra of Fig. 4.6 for C Oph. The differential polarisation (AP) spectrum andposition angle (Op ) spectrum are plotted in the middle and upper panels respectively. Themiddle residual spectrum from the first subset (corresponding to 100°) is shown in thelower panel for comparison.84t.- :••.1."‘:^I. I 1^I^I ^1^I^I^I^tf..r.•••••1.0;-150100•• •.^.• ow^•^• • • •i•^-I I ill I^i^I i^I I^- 1 -1.^.I-^ .....••• •^ . % "-^ -4" • • %N. I%^...-N,^.... ^ .:. %••• e -.^..-.. -N.^-• v.: .• 1, .^#^„els. 1e°,614%,..N. . .k.^.r",„.....#1/41‘..^ • ••••' l'....^ %.:.. % •_,_^'••^"i^•sor^..,. -^• e .-; ‘‘,1•%., 1—.005—.011.011.0051.995.99- I 2o-_500.0050.985-8001^I^1^I^I^I^I^1^I^I^1^1^1^1^I^1^1^1^1^1^I^1^I^I^1^1^1^1 I^1^I —-600 -400 -200^0^200Velocity (km/s)400^600^800Figure 4.8: (b) Results of the polarisation analysis of the last five (second subset) unpo-larised residual spectra of Fig. 4.6 for C Oph. The differential polarisation (6.P) spectrumand position angle (0 p) spectrum are plotted in the middle and upper panels respectively.The middle residual spectrum from the second subset (corresponding to 100°) is shownin the lower panel for comparison.dP85Walker 1988). In fact, the amplitude of subfeature a appears to diminish as it approachesthe line center. It is clear from Eqn. 4.1 that the magnitude of these variations will bereflected in AP and Op, producing spurious structure in the both spectra.Figs. 4.8a and b were generated using the unpolarised dataset and are therefore mea-sures of the systematic variations in the line profile. The same general structure in theAP spectrum of Figs 4.7a, b (polarised dataset) was found in Figs. 4.8a, b (unpolariseddataset). The similarity between both figures strongly indicates that the structure ob-served in Figs 4.7a, b is spurious and arose from systematic changes in the line profile ofOph. This would also explain the significant scatter in both AP and Op.In an effort to minimise the sytematic effects in the polarised residuals, we subtractedthe unpolarised residual spectra from their corresponding polarised residual spectra andrepeated the analysis of Section 4.4 on the dzffereneed spectra. As shown in Fig. 4.9, somebump pattern remained in those spectra because (as mentioned above) the amplitudesof the bumps were not the same in both line profiles. Analysis of the first and last fivedifferenced spectra revealed no significant structure in the AP spectrum of either subset.The results of the analysis are shown in Figs 4.10a and b. The standard deviation fromthe mean of all the points in AP for the first subset is 0.07% and for the second subsetis 0.08%. As our final result we combined the AP spectra for both subsets. The meanspectrum shows no evidence for polarisation structure associated with the line profilevariations of Oph, exceeding the standard deviation of 0.05%.Notes: A curious feature of the AP spectra of Figs. 4.7, 4.8 and 4.10 is the ripple-like structure present (particularly) in the regions outside the line profile. If the analysisof Section. 4.4 is of random noise, then one might expect this scatter to be reflected inAP spectrum at the same level. The "ripple" pattern hints at the presence of periodicvariations in the residual spectra which is reproduced in AP. These variations are mostprobably artifacts of the geometrical arrangement of the diodes in the Reticon array.Each diode in the array is read out by one of four video lines; every fourth diode in thearray is read out by the same video line. Differences between the gains and zero-points ofthe video-line amplifiers combine to produce a variety of patterns which repeat every n thdiode in the array where n is an integral multiple of four (Walker et al. 1985). Althoughthe processing procedures outlined in Section 3.3 were designed to remove such patterns,some low-level pattern usually persists especially if the diode-to-diode variations are not86-500^0^500^1000VELOCITY (km/s)Figure 4.9: Differenced time series formed by subtracting the unpolarised residual spectrafrom the corresponding polarised residual spectra in Fig. 4.6.87r.^• I^. 1 .-%1^r; i1^I^1 111ZAP -01^1^1 1^1^1^1^1^1^1^I^1^I re 1I A- ... J-11I^I^I.'20. '.-• •:.• :^:^Irri1H1^1 1 1 1 1 1150100500.005—.005I 20-^—.01 - 111111111111111^111^11111111111 -_I1.011.99^I^I^I^1^1^I^I^1^1^1^1^1^1^1^1^1^1^1^1^1^1^I^I^1^1^1^1^1^1^1^1^—800 —600 —400 —200^0^200 400 600 800Velocity (km/s)Figure 4.10: (a) Results of the polarisation analysis of the first five (first subset) dif-ferenced spectra of Fig. 4.9 for Oph. The differential polarisation (AP) spectrum andposition angle (Op) spectrum are plotted in the middle and upper panels respectively. Themiddle residual spectrum from the first subset (corresponding to 100°) is shown in thelower panel for comparison.881^1".,..,k^i^1^1^1 .4. 1^j^1^1 . 1 -. 1^1^i^1^1^1 ...1^1^1^1^41 1 ■ i 1 i "- : I' . -...- -^N.:^. ^.^- e. ' -. :I.N... :150^^ -^gyp:... • . . . .-■^ .. ..100titi•502o-0 if - }^1111111^fv: 1^I^1 . 1^I^I^I^I^1 - 1^I^I-^I - 1AP -....^ _-,,-.^ -r.. •■--/ ..: • /N.-% :•\ .4-.^r•-1. ..., -^1"*. •"*-^..4.."6"^:sr^%. : .. : . i Nor : : -, • • ". "^-- _—.005 I 2o-i I^I^I^I^I^I^I^I^I^I^I^I^1^1^I^I^I^I—.01 1 1 1 11 1 1 11 1i :1.01I.99-( 1111 1 (111 1 1 1 1111 1 11 11111111,11--800 -600 -400 -200^0^200^400^600^800Velocity (km/s)Figure 4.10: (b) Results of the polarisation analysis of the last five (second subset) dif-ferenced spectra of Fig. 4.9 for C Oph. The differential polarisation (AP) spectrum andposition angle (Op ) spectrum are plotted in the middle and upper panels respectively. Themiddle residual spectrum from the second subset (corresponding to 100°) is shown in thelower panel for comparison..00589perfectly removed. Thus the intensity is a periodic function of diode number and thisperiodicity is reproduced in the polarisation measurements. Even though the residualshave been shifted with respect to each other, a periodic effect remains and would still bereflected in the polarisation. In contrast, CCDs generally do not suffer from this "ripple"effect (see for example Figs. 4.20a, b).The 0.1, spectra of Figs. 4.7, 4.8 and, in particular, 4.10 also show evidence for system-atic effects. In the absence of polarisation, we would expect Op to exhibit random scatter(with amplitude 1/I API; as is evident in Fig. 4.19) as a function of wavelength. Wesuspect that the sytematic changes in Op are caused by time-dependent variations in theline profile. At a particular wavelength A i , the least-squares fit of Eqn. 4.1 to /„s (0) willyield a certain value of Op. At the next wavelength point A2, Op will take a different value.Since the amplitude of the bumps varies continuously with wavelength (i.e., Ai and A2 arecorrelated), Op will also vary in a continuous manner. Further study of this effect wouldbe of interest. e PerWe also looked for polarisation associated with the line profile variations of the brightB star e Per. Like ( Oph, e Per also exhibits exceptionally large line profile variations,with the amplitudes of the travelling subfeatures approaching 1% in this star.In an effort to reduce the systematic errors encountered in the analysis of the C Ophdata (see Section, we decided to take a different approach for our polarimetricobservations of e Per. Recall from the last section that a major problem with the previousobservations was the fact that the positions and shapes of the subfeatures in the lineprofile had changed significantly between spectra at the different position angles of theanalyser. The systematic differences in the spectra produced spurious structure in thepolarisation spectrum which could have been mistakenly interpreted as a real effect. Themost practical solution to the problem was to use a CCD detector which, because of itslow read out noise 50e- for the RCA CCD compared with N 500e- for the Reticon),permitted rapid switching between position angles of the analyser. An integration time ofas little as 30 s was used for the c Per observations; thus, one sequence of position angles(corresponding to 0°, 45°, 90° and 135°) took approximately 3 min, and very little shiftof the subfeatures occurred over the sequence.90Drifts in the zero-point of the detector array from spectrograph flexure were estimatedfrom the line positions in the Fe-Ar arc spectra obtained every half hour during thenight. The zero-point shifts amounted to no more than one pixel for the entire nightand were therefore negligible between spectra of any given set. Displacements of themoving bumps in the lines between those spectra were also small. Gies and Kullavanijaya(1988) calculated the time for a single bump of the most dominant mode (1 = 4) totraverse the entire line profile to be hrs. If Hp is roughly 15 A wide (measured at thecontinuum) then the rate at which the subfeature crosses the line profile is approximately0.04 A min'. At that rate, the subfeature has travelled 0.1 A in the time it takes tocomplete one sequence of position angles. This shift is small compared to the widthA) of the subfeature.Spectral time series of c Per at HP and He I 4921 are shown in Figs. 4.11a and b,respectively. The corresponding residual time series at H,Q and He I 4921 are presentedin Figs. 4.12a and b. The spectra have been averaged in 1/2-hour bins in order to clearlydisplay the line profile variations of this star. Each binned spectrum is the compositeof 24 spectra obtained at all the different position angles of the analyser and thereforecontains no polarisation information. The residual spectra were computed by dividingthe spectra in Figs. 4.11 a and b by the mean of all the spectra in the time series. Giesand Kullavanijaya (1988) attributed the line profile variations of c Per to sectorial NRPmodes with = Irni = 3, 4, 5 and 6.In order to carry out the analysis of Section 4.4, residual spectra were again computedbut in a slightly different way from those in Fig 4.12a, b: Each spectrum within a set(considered to be one complete sequence of position angles) was divided by the mean ofthe spectra in that set. This would reveal any polarisation effects in the line profile byremoving the component of the profile that is independent of position angle. In orderto improve the S/N ratio, the residuals at each position angle were then combined in1/2-hour bins, resulting in 14 binned residuals at each position angle. Since each binnedresidual was the average of six residual spectra, each spectrum having been taken withthe analyser alternated between clockwise and counterclockwise rotations, the effects ofwavelength shifts due to spectrograph flexure and the movement of the subfeatures acrossthe line profile were expected to average out.No obvious polarisation structure above the level of the noise was apparent in any of910.64080.66110.68410.70260.72160.74000.77440.79120.80890.82680.84710.86670.89830.9178(b)^^^ I^111it l,i,iI 4915 4920 4925 49301 1^1^1^1^1^1^' 1^1^1^1^1^1^1^10Wavelength (A)Figure 4.11: (a) Spectral time series of E Per at 11/3. Each spectrum is the average of 24spectra. The corresponding midexposure time in fractions of a day from the barycentricJD 2,448,261 is given to the right of each spectrum.(b) Spectral time series at He I A4921. The corresponding midexposure time in fractionsof a day from the barycentric JD 2,448,261 is given to the left of each spectrum.92I 111^1^1 1^1^1^1^1 1 1 1 1 ^  (b)^4864^4916^4920^4924^4928Wavelength (A)Figure 4.12: (a) Residual time series of c Per at Hfl formed by dividing the mean spectruminto the individual spectra in Fig. 4.11a.(b) Residual time series at He I A4921 formed by dividing the mean spectrum into theindividual spectra in Fig. 4.11 b.93the sets of residual spectra. As an example, we present only one of these sets in Fig. 4.13.The residuals have been smoothed by a Gaussian function with a a of 0.27 A and the S/Nratio of each of the residuals is 150. Analysis of all the sets of residual spectra by themethod outlined in Section 4.4 revealed no polarisation structure across either the HO orHe I 4921 profile, and an upper limit (1u) of 0.15% was established by the results. Wepresent in Fig. 4.14 only the result of the polarisation analysis on the residual spectra ofFig. InterpretationOur observations of C Oph and f Per represent the first spectroscopic polarisation mea-surements of the line profile variations of OB stars. We are not aware of any theoreticalpredictions of polarisation in the travelling subfeatures for any of the three models in-voked to explain these variations. However, the upper limits obtained in this study shouldprovide additional constraints on the possible sources of the line profile variations.4.5.2 Differential Polarisation Measurements Across theHO Line of Be StarsWe investigated the wavelength dependence of polarisation across the Hfl emission line ofthe Be stars -y Cas, 4' Per and 28 Cyg. Polarimetric observations of -y Cas were made ontwo consecutive nights to investigate reports in the literature of variable polarisation.Residual spectra were formed in the manner outlined above for f Per. Since we wereonly interested in the polarisation variation across the entire line profile rather than indiscrete moving subfeatures within the profile (as in Section, nightly averagesof all the residuals at each position angle were formed for all the stars. Thus the datawere reduced to a single set of residual spectra per night of observations fOr each star.The residual spectra of 0 Per, 7 Cas and 28 Cyg are shown, respectively, in Figs. 4.15,4.16a, b, 4.17. The residuals have been smoothed by a Gaussian function with a a valueof 0.27A. The S/N of each of these spectra is typically between 1000 (for 0 Per) and4000 (for y Cas). With the exception of 28 Cyg, all the residual plots show well-definedstructure at 10. Moreover, the degree of structure clearly varies as a function of theanalyser position angle.940 .98 ^111111111111111111111"^11111111111111111111111 4850 4855 4860 4865 4870 4910 4915 4920 4925 4930Wavelength (A)Figure 4.13: (a) Mean residual spectra of E Per corresponding to barycentric JD2,448,261.6841 at HP. Residual spectra were calculated by dividing the individual spectrawithin a set (considered to be one complete sequence of position angles) by the mean ofthe spectra in that set. Six of these residual spectra at each position angle were averagedto form the mean residual spectra shown in the upper panel. The corresponding analyserposition angle is shown to the right of each mean residual spectra. The residual spectrumof Fig. 4.12 corresponding to the above BJD is shown for comparison in the lower panel.(b) Mean residual spectra corresponding to barycentric JD 2,448,261.6841 at He I A4921.. 9511111111111111111.1111•••■.^.^• ..—.^.^. ..• • .^•. •• ,..1 gr^/ • . 11, •• 1r • • V^•^• J• ._II •^■• %^• .^• V" ^• •J.. •••••• a e". • . ••^. • • • a 4* • • ..".,...^• •.^...• a^• •^• a--• • • '. 4.. -A^•^0•^• • •.1.141^I^1^1^1^I^1111• •^• .• •• • ••^• 11111/4. r";^111—■• -• •^• •• % ••• • • •^• • •^•• •• • • •• • •III IIIIIIIIIIII . 111111 1AP1. •• • •• •.14^•- • •• %. •—0.0051.02 Iiiii ji mjiit tl iiiil1111111111111111111_1.0110.990.98150100500.0050- .• 4. pgh^a, 4 to'll," "^..^v .:_ -., . .^•Ir • •^-. . 1,...^:,..•^•At % 'A. •0.if: v^1: • •sri. • .^-...e-:44V •• ••IF"nr• • .4^••.fr.••^•• .01,_ 4 N"^ ■ • •.• ^-VeV^I IIII IIII III II I^I(b)11111111111111111111111 ..4850 4855 4860 4865 4870 4910 4915 4920 4925 4930Wavelength (A)Figure 4.14: (a) Results of the polarisation analysis of the mean residual spectra ofFig. 4.13 at 1113 fore Per. The differential polarisation (AP) spectrum and position angle( Op ) spectrum are plotted in the middle and upper panels respectively. The residual spec-trum of Fig. 4.12 corresponding to barycentric JD 2,448,261.6841 is shown for comparisonin the lower panel.(b) Results of the polarisation analysis of the mean residual spectra of Fig. 4.13 at He IX4921 fore Per.96100°140°180°^I^I^I^I^I^4820 4840Figure 4.15: Mean residual spectra of 4 Per at H/3. Residual spectra were calculatedby dividing the individual spectra within a set (considered to be one complete sequenceof position angles) by the mean of the spectra in that set. All of the night's residualspectra at each position angle were averaged to form the mean residual spectra shown inthe upper panel. The corresponding analyser position angle is shown to the right of eachmean residual spectrum. The average spectrum of all the night's observations normalisedto the continuum is shown for comparison in the lower panel.4860^4880^ 4920Wavelength (A)I^I490097120°1 0 o°I^I^I I^I^I I^I^I I^I^I I^I^II^i14820^4840^4860^4880^4900^4920Wavelength (A)Figure 4.16: (a) As Fig. 4.15 for y Cas. The observations were taken on 23 Sep 1990 UT.^I^,^,^I4820 4840I^I^I^I^I^i^486 4880Wavelength (A)1.0260°1.01140°1.41.2 ,^I 4900^4920Figure 4.16: (b) As Fig. 4.15 for 7 Cas. The observations were taken on 24 Sep 1990 UT.994840^4860^4880Wavelength (A)4920Figure 4.17: As Fig. 4.15 for 28 Cyg.100To ensure that the structure seen in the residual spectra did not originate in theinstrument, we computed (in the same manner as for the program stars) residual spectraof unpolarised standard stars obtained on each night of the observations. They weregenerally very similar; as a sample we present only Fig. 4.18. No structure across Hp isevident in the residual plots.The residual spectra for all the program stars were analysed using the method de-scribed in Section 4.4. The normalised intensity profile I (lower panel), differential po-larisation (AP) spectrum (middle panel) and the position angle (Op) spectrum (upperpanel) in the region of Hp are plotted in Figs. 4.19, 4.20a, b and 4.21 for Per, 7 Cas,and 28 Cyg, respectively. The normalised intensity I in each figure represents the nightlymean of all the spectra for each star. The dashed line in the figures denotes the "pre-dicted" change in polarisation if the effect is caused only by the addition of unpolarisedflux to the line (see discussion below). The error bars in the respective panels representthe formal 2a errors in AP and Op from the least-squares fit, at each wavelength pointinside the 1-1# profile. Outside lig, the error in Op tended to be larger (±20°). This simplyreflects the fact that outside the line profile the least-squares fits of Eqn. 4.1 are largelyto noise.Before discussing the results presented in Figs. 4.19 and 4.20a, b, it is important torealise that, as a consequence of measuring AP (instead of absolute P), the measuredposition angles Op are offset by ±90° from the true or absolute values. The reason for thisis as follows: Suppose (as shown in part (a) of Fig. 4.22) we have measurements of thecontinuum polarisation at the two orthogonal position angles O p and Op ± 90°, where theintensities are /max and 'min respectively. The emission lines of Be stars are represented,in part (b) of Fig. 4.22, by an additional component of unpolarised radiation which isadded to 'maz and Imin in the same absolute amount. Our data reduction procedure isequivalent to normalising the intensities, /max and Imi„, to the same continuum value,which amplifies the /min emission component. This is illustrated in part (c) of Fig. 4.22.Our analysis procedure is sensitive only to the difference between the two intensities. But,as shown in part (d) of Fig. 4.22, the measured intensity is a maximum at an angle of± 90°, which contradicts the definition of Imax set out in Section 1.2.1014820^4840^4860^4880^4900Wavelength (1.)Figure 4.18: As Fig. 4.15 for 7 Boo.10215010050.—.0021.4 I1 1^1^I1^1^1^1I_I^I I I1 i^ 1^1^1 1^1^11^1^1^1• •^.- I 2cr -7 I 2 ff -. "Ned,.^•AP/IN\VA.11ft `..^• •\•1.21^I ^I^1^1^I^I^1^1^1^I^I^I4840^4850^4860 4870 4880Wavelength (A)Figure 4.19: Results of the polarisation analysis of the mean residual spectra of Fig. 4.15at H/3 for 0 Per. The differential polarisation (AP) spectrum and position angle (q5 p)spectrum are plotted in the middle and upper panels respectively. The average spectrumof all the night's observations normalised to the continuum is shown for comparison inthe lower panel. Note that the measured position angles Op are offset by +90 from thetrue values. To obtain the true AP and 4, the following transformation must be made:AP • —APOp^Op + 90°1031^1^I 1^1^1^1- 2o--50.004 I I^ I^I^I I^I^I^I I^••• •••• •50 —A 1,‘'l'%\s \• /AP.6^ utb•../^-..--.• ......-.°^ ,.........-- ...■• .10^_...." ...... V , _.....^%.7 .^—^■-..- —".* ft^...—, 1........";...^.. Ir.....10..—%—. 00 1: I^I1.4 —I1.2 —ti4840I^I4850I^I I^I^i^III 4860^4870 4880Wavelength (A) Figure 4.20: (a) As Fig. 4.19 for -y Cas. The observations were taken on 23 Sep 1990 UT..003 —.002I 2o-.001 • /. .^.• Viet,• 1%1I I I^III I^I -_104•••^••••^• A... •••• ••■•••• • 1E1 ••••.003.002I 2a• ear.^"‘• • j•^„el"^4"Sli"4.31..X ••37/..‘—‘•■.„• •Ir•• eft.0010; A\--‘4.• •1^1^I^1^ 1^1^1^I^I^I^I- 1 I^ I I II I I II 11 1 1 1111^I I^1^1^I 1^1^1^I I^I^I^I 1^1^1^1 1^IopV •"".^1•••••",,: • . • ••.1"•••••••••■^—^••• ••11.^•^".- 2cI^ I^I^I^1 I^1^I^I 1^I^1^1 IIII500-50.004-.001AP1.41.214840^4850 4860 4870Wavelength (A)4880Figure 4.20: (b) As Fig. 4.19 for -y Cas. The observations were taken on 24 Sep 1990 UT.1051^1^I^• I^Li .91.% 1 -^. I^1^1^1••• •^.20-'^••••. :• '^• I •I • I* -^-•• •.^ :-.1 'i -.I. T-'^i ..r .1.95.9• I^I^J^•1^.1^I^.1^I.r.150'Op100AP -^r• .^1.^• • lq"^Lajt,^ 1 • • • • • • J. • • i. •• •• • , • • °%r •^• •^• le 0‘.^•^•• • • •^• ••• • -^IN.; • .1171,.- ,"^we,^•:""^pa.% • ••• • •• • •l• •• le •50.004.0020-.002-.0041.05^1^111111111111111111111.85^I^I 1^1^I^I^I^1^1 -4840 4850 4860Wavelength (A)4870 4880Figure 4.21: As Fig. 4.19 for 28 Cyg.106(a)op(b)Op+ 90 °' Mat&^op11711010^Op-4-90°Ilni4b^ ,+90°\\\\^0p(c)(d) Imo. Op+ 9 0 °Figure 4.22: Explanation of why the measured position angles Op are offset by ±90° fromthe true values.(a) Continuum polarisation measurements at the two orthogonal position angles q5p andOp + 90° corresponding to intensities 'max and Imin .(6) Addition of unpolarised (emission) component in the same absolute amount.(c) Our reduction procedure normalises Imax and /,„i„ to the same continuum value, whichamplifies the Imin emission component.(d) Our analysis prcedure is sensitive only to the difference between the two intensities.The measured intensity is a maximum at an angle of Op ± 90°, contradicting the definitionof 'mar in Section 1.2.107Therefore, to obtain the true AP and Op we must make the transformation'AP^--AP^(4.7)Op ± 90° (4.8)In this thesis, however, we have elected to present our data in terms of the measuredAP and Op in order to allow straightforward comparison between the AP and emissionprofiles of Figs. 4.19 and 4.20a, b. Physical InterpretationWe interpret our results in terms of the stellar wind model of Poeckert and Marlborough(1978a).' Although their model is — by their own admission — ad hoc (as are all Be starmodels), it nevertheless provides a conceptual framework for understanding the complexwavelength dependence of the polarisation and position angle across the HP profile inFigs. 4.19, 4.20a, b. It is also the only detailed radiative transfer model which attemptsto account for the polarisation changes observed in the emission lines of Be stars. Anequally valuable analytical discussion is given by McLean (1979).Both absorption and emission processes in the envelopes of Be stars influence thewavelength dependence of the degree and position angle of the polarisation across the lineprofile. A significant result of the computations of Poeckert and Marlborough (1978a) isthat line absorption plays an important and perhaps a dominant role in determining thedetailed polarisation structure of Be-star line profiles. However, the general characteristicsof this structure may be interpreted in terms of simpler qualitative arguments. In thefollowing, we first examine the effects of line absorption on the degree and position angleof polarisation across a (rotationally-broadened) profile before looking at the effects ofline emission.Consider the simple case of a differentially rotating axisymmetric disk-like envelopeinclined at some arbitrary angle to the observer, shown in Fig. 4.23. The stellar flux ispolarised by scattering in the envelope. The degree and direction of polarisation projectedonto the sky are indicated by the bold vectors in Fig. 4.23. The net polarisation is11 We point out that if the polarisation increases through the line then the transformation is unnecessaryby the same arguments given in the text.12The details of Poeckert and Marlborough's model are described in Marlborough (1969) and Poeckertand Marlborough (1977, 1978a, 1978b).108simply the vector integral of the individual polarisations over the disk. Because thedegree of polarisation is larger (smaller) for scattering matter in the 3 and 7 (1 and 5)orientations, 13 the net plane of polarisation lies along the projected rotation axis (the3 and 7 orientations).Absorbing matter within the disk along the line of sight to positions 1 and 5 in Fig. 4.23increases the net polarisation by preferentially absorbing direct (unpolarised) light andscattered light which is polarised in the direction perpendicular to the net polarisation.Because this matter has a relatively small Doppler shift, it has the largest effect at thecenter of the line profile (as shown in part (a) of Fig. 4.23).On the other hand, absorbing matter within the disk along the line of sight to positions3 and 7 in Fig. 4.23 preferentially absorbs light which is strongly polarised in the samedirection as the net polarisation. In a rotating disk, this matter has the most effect in theline wings and produces polarisation minima in the blue and red wings of the line profile.If the rotational velocity of the envelope decreases with radius (as in a Keplerian disk),absorption at larger radii occurs at smaller Doppler shifts, so the resulting polarisationminima move towards the line center (as shown in part (a) of Fig. 4.23). If the envelopeis rotating only (i.e., there is no expansion or contraction), these minima should similarlybe symmetric with respect to the line center.The explanation for the position-angle changes across the line profiles is slightly morecomplicated. Consider a rotationally broadened spectral line produced by the disk shownschematically in Fig. 4.23. In (say) the blue wing, the scattered flux in the approachinghalf of the disk (positions 2, 3 and 4) is affected by line absorption whereas the fluxin the receding half of the disk (positions 6, 7 and 8) is affected only by continuumabsorption. Therefore, the scattered flux at wavelengths in the blue wing of the line ismore attentuated for the approaching half of the envelope and less attenuated for thereceding half. Of course, the opposite is true for wavelengths in the red wing. Becausefor each wing the integration of the scattered light is not symmetrical with respect to therotation axis, the net plane of polarisation varies systematically across the line profile (as13 Radiation scattered through a large angle with respect to the direction of the incident radiation will bestrongly polarised. If the unpolarised incident wave is represented by the superposition of two orthogonallinearly polarised waves with equal electric field strengths Es = Ei , then the scattered components (Es)are related to the incident components (Ei ) by El oc Ei and Erg oc Eti cos where the symbols and Idenote the parallel and perpendicular planes of polarisation with respect to the plane of scattering.1095-4--111.-(a)Pc X.(b)Figure 4.23: Schematic representation of the effects of absorption in a rotating axisym-metric circumstellar envelope on the degree and position angle of polarisation across astellar line profile. The ellipse represents the envelope inclined at some arbitrary angleto the observer. The bold vectors represent the degree and direction of polarisation pro-jected onto the sky. The rotational velocities of the envelope are indicated by the lightarrows. The expected polarisation structure and position angle changes across the lineprofile are shown in (a) and (b), respectively.110shown in part (b) of Fig. 4.23).In the case of an envelope undergoing pure rotation, these position-angle changes areantisymmetric with respect to the line center. That is, the variation in Op will have thesame amplitude but opposite sense for both wings, as shown in part (b) of Fig. 4.23. Ad-ditional random motions, expansion or contraction will tend to produce more complicatedposition-angle changes.The position-angle changes depend on the inclination of the disk, the magnitude of thechanges decreasing with inclination (cf. Poeckert and Marlborough 1978b). For example,Poeckert and Marlborough (1978b; see their Fig. 3) show that at an inclination i 89°the position angle changes by less than 0.5°, while at i 30° the change can approach30°. Thus, for a disk viewed edge-on, there is little rotation of the position angle. Incontrast, the degree of line polarisation is highest for a disk viewed edge-on.The principal effect of line emission is to dilute the polarisation in the profile. In theidealised case where the emission line flux is completely unpolarised, the line polarisationis given by (McLean and Clarke 1976)(A) PL(A) — PE()^ (4.9)where Pc is the continuum polarisation and /E is the total intensity of the additionalunpolarised emission flux (with the continuum normalised to unity). Note that here thedegree of polarisation in the absorption line is assumed to be same as that in the adjacentcontinuum. In this (idealised) case, the line emission has no effect on Op. It should bepointed out, however, that there is no particular reason to believe the emission flux to beunpolarised. In fact, the line emission may itself be partially polarised either by furtherelectron scattering, or by flourescence or resonance scattering 14 (McLean 1979). In thiscase, if the net plane of polarisation of the emission flux is not the same as that of thecontinuum flux, there is a rotation of op through the line profile. Individual StarsPersei This bright (V = 4.07) Be star is a member of a double-lined spectroscopicbinary (Abt and Cardona 1984); the underlying star has a spectral type of B2 Vep (Hoffleit14For resonance scattering where an upward transition is followed by a downward transition, the re-emission of the photon is not isotropic, but follows a phase-angle distribution similar to that of Rayleighscattering (Collins 1979; p. 467).111and Jaschek 1982) and a v sin i = 450 km s -1 (Hutchings and Stoeckley 1977). Variationsin the linear polarisation of the continuum light from Per have been reported by Coyne(1976), but were not found to correlate with either the radial-velocity or light curves ofthe binary orbit (Coyne 1975; Gies and McDavid 1987). Polarisation changes across thelower Balmer emission lines Ha and HP have been reported by McLean et al. (1979) and,at considerably lower resolution 10 A), by Coyne and McLean (1975), McLean andClarke (1976) and Clarke and Brooks (1984). The general appearance of the AP profileof Fig. 4.19 agrees with that of McLean et al. (1979); however, the greater precision ofour results allows us draw stronger conclusions.As shown in Fig. 4.19, there is a strong 0.85%) decrease' s of the polarisation towardthe center of the 11 /3 profile, accompanied by a smaller (", 0.25%) increase at the linecenter. The AP profile is symmetric with respect to the line center which, accordingto the discussion in Section, suggests that the velocity field of the circumstellarenvelope of q Per is dominated by rotation. There is only slight evidence for a changein Op with wavelength. This is consistent with a circumstellar envelope of Per viewedequator-on (cf. Section According to McLean and Clarke (1976), the equator-onaspect is also consistent with its high value of v sin i.We see no evidence in our data of the oscillatory behaviour of AP in the line wingsreported by McLean et aL (1979). Given that the error level of our results is 4 x smallerthan that of McLean et al. (1979), we believe it is unlikely that these variations are agenuine polarisation effect. However, it is not improbable that there has been a change inthe line polarisation since their 1977 observations. (Changes in line polarisation are notuncommon in Be stars. We discuss a notable example in the next section.)In Fig. 4.19, we have indicated (by the dashed line) the predicted AP if the reducedpolarisation in Ht/ is caused solely by unpolarised emission. The predicted effect wasestimated from Eqn. 4.9. In order to obtain a good estimate of the total emission fluxIE, a synthetic (rotationally-broadened) absorption spectrum 'ABS was subtracted fromthe observed (normalised) intensity profile IoBS (i.e., IE = JOBS — IABS)• The syntheticspectrum was generated using the non-LTE model atmosphere program of Hubeny (1988).The model parameters used are those given by Poeckert and Marlborough (1979) andI5 Recall that the AP plotted in Fig. 4.19 equal to —AP and that AP lies at the continuum polarisation.112listed in Table 4.4. We assumed a continuum polarisation of 2.0% near 11 /3 (Poeckert etal. 1979).The predicted AP shows excellent agreement with the observed AP at the centerof the line profile, as shown in Fig. 4.19. However, as apparent in the line wings, theobserved AP profile is significantly broader than the AP profile predicted by Eqn. 4.9.This suggests that dilution by unpolarised line emission cannot completely account forthe decrease in the line polarisation observed in q Per. There is some indication in thelower panel of Fig. 4.19 that the width of AP profile is comparable to the width of theunderlying absorption profile 30 A) of the star. (Better evidence for this is shownin the model absorption spectrum in Fig. 4.24.) The positive correlation between thewidth of AP and the absorption spectrum tends to favour the suggestion of Poeckert andMarlborough (1978a) that absorption in a rotating circumstellar envelope also contributesto the decrease of polarisation in the line profiles of Be stars.Our results tend to reinforce the conclusions of Poeckert and Marlborough based ontheir model calculations (cf. Section and should provide important additionalconstraints for their model.Casssiopeiae This bright (V = 2.47) Be star was the first in which emission lineswere discovered in its spectrum (Secchi 1867); the underlying star has a spectral type ofBO IVe (Hoffleit and Jaschek 1982) and a v sin i-2300 km s -1 (Hutchings and Stoeckley1977). It is one of the most intensely studied of the emission-line stars for polarisationeffects across its hydrogen Balmer lines (see Coyne 1976a; Coyne and McLean 1982; andreferences therein). Most of these studies have concentrated on the Ha and 11/3 emissionlines, where polarisation changes of 0.2% and 0.3 — 0.4% respectively from thecontinuum values have been measured. Reduced polarisation has also been detected inHry by Hayes and Illing (1974).As shown in Figs. 4.20a, b, there is a steep drop in the polarisation in both wings of11/3; the largest decrease occurred in the red wing. There is evidence for a small increase inthe polarisation at the centre of the line. The total change in AP corresponded to about0.3%. There also appears to be evidence for variations in Op across the line profile. Theresults for the second night Fig. 4.20b show changes of about 20°. This agrees reasonablywell with the position-angle changes predicted by the model of Poeckert and Marlborough(1978a; see their Fig. 9). They assumed an inclination of 45° for the envelope of 7 Cas.1130.90.8I^I^I^I^I^t^I^I^I^I^I^I^I^I^I4820 4840 4860 4880 4900Wavelength (A)Figure 4.24: Synthetic spectrum of 95 Per at 1 -1,3. The spectrum was generated using thenon-LTE model atmosphere program of Hubeny (1988) with Teff = 21, 000K, log g = 3.5and v sin i = 450 km s-1.114Table 4.4: Model Parameters for 0 Per and 7 CasTe f f^vsiniStar^(K) log g (km s -1 )0 Per^ 21,000 3.5 450Cas^ 25,000 3.5 300115Our data do not show any evidence for the secondary polarisation minimum in theblue wing of HP near !I? 4850 A reported by McLean et al. (1979). The data of McLean etal. suggest a decrease in the polarisation comparable to that in the line, i.e. AP 0.4%.The fact that we do not see this effect suggests that the polarisation profile may havechanged since their observations.We have computed the predicted AP for -y Cas in the same manner as for 0 Per, usingEqn. 4.9. The synthetic (rotationally-broadened) absorption spectrum of -y Cas, shown inFig. 4.25, was used in the calculations. We used the model parameters given by Poeckertand Marlborough (1978b) and listed in Table 4.4 to generate the synthetic spectrum.Within the uncertainties of our measurements, the predicted AP profiles show goodagreement with the observed AP profiles at the center of the 11/3 line, as shown inFigs. 4.20. However, the observed AP profiles are significantly broader than the theircorresponding predicted AP profiles. We interpret this in the same way as we did for0 Per; that is, at least part of the reduced polarisation in the line wings is caused by ab-sorption processes in the circumstellar envelope of the star. This is supported by Fig. 4.25,which shows that the width of the absorption profile 25 A) is comparable to the widthof the AP profile.Comparing Figs. 4.20a and b, there is some suggestion that there has been a changein the AP profiles from the first night to the next. Although the general shape of the APprofiles is the same, there is slight evidence for an overall increase in the polarisation fromthe first night. However, it is possible that the difference is an artifact of the rectificationof the residual spectra, although the rectification procedure would not be expected toaffect the measurement of AP by more than ±1o.Assuming that the change in AP is in fact genuine, then some of it may be attributableto variable line emission. We found that the emission flux in the line decreased by about1%, which according to Eqn. 4.9 corresponds to an increase in the line polarisation of about0.005% assuming Pa = 0.8%. Since the change in AP between nights appears to be anorder of magnitude larger, rs 0.05%, it is possible that there may be an additional sourcecontributing to the observed variations. Since the line emission arises from a much largervolume than the polarised flux, polarisation changes do not necessarily have to accompanychanges in the emission lines (Piirola 1979). It has also been suggested by Poeckert etal. (1979) that polarimetric changes may precede spectroscopic changes on timescales of1161174820 4840 4860Wavelength (A)Figure 4.25: Synthetic spectrum of 7 Cas at 11 /3. The spectrum was generated using thenon-LTE model atmosphere program of Hubeny (1988) with T eff = 21,000K, log g = 3.5and v sin i = 300 km s -1 .4880 490010.90.80.7the order of months. Alternatively, it not unlikely is that our measurement of the changein the intensity profile is in error because of problems in defining the continuum of theintensity profiles in a consistent way. Therefore, we do not feel that any firm conclusionscan be drawn without further observations.28 Cygni We found only one reference in the literature of polarisation measurementsacross the emission lines of this star. Coyne (1975) reported a decrease in the polarisationat H/3 of AP = 0.4%. At the time of our observations, no significant change in polarisationwas apparent across the HP feature of this star despite the presence of appreciable emissionin the line. We can place an upper limit to AP in 28 Cyg of 0.1% from our data.118Chapter 5Summary and ConclusionsWe have described in Chapter 2 the design and performance of the UBC/DAO polar-isation analyser. The analyser was developed specifically for use at the DAO 1.83-mtelescope; it is mounted before the Cassegrain spectrograph entrance slit, and is capableof providing polarisation data at the resolution of the spectrograph-detector system. Thedevice incorporates a polarising beamsplitter for selecting a plane of polarisation, and aquarter-wave plate. We have shown that the quarter-wave plate is highly (rs , 90%) effec-tive in minimising effects of instrumental polarisation. Using observations of a standardunpolarised star, the overall efficiency of the analyser was estimated to be N 40%. Theanalyser is microcomputer-controlled and may be rotated at a rate of 12.5° s -1 . Positionangles of the analyser may be set to within ±0.5°.In Chapters 3 and 4, we have presented the results of three studies carried out withthe polarisation analyser. Our results may be summarised as follows:1. We have investigated differential polarisation in four of the strongest diffuse inter-stellar features in the spectra of HD 183143, 55 Cyg and C Per. No evidence forpolarisation structure through any of the bands was found. From our results, wehave established upper limits to the variation with wavelength of polarisation in the5780, 5797, 6177 and 6284 A DIBs of 0.01, 0.01, 0.02 and 0.03%, respectively. Theselimits are significantly lower than the predicted levels if the agent (agents) respon-sible for the DIBs resides (reside) in the same interstellar grains which produce theoptical continuum polarisation. Thus, we concluded that the diffuse features are notassociated with the grains responsible for the continuum polarisation. However, our119results do not allow us to eliminate all grains as possible carriers. Intermediate-sizedgrains (0.02 < a < 0.1,um) which are poorly aligned or spherical are consistent withour results as well as other observational properties of the DIBs. Our results arealso consistent with (and would tend to favour) a molecular origin for the diffusebands.2. We have attempted to measure differential polarisation associated with the lineprofile variations of two OB stars. Analysis (by the methods described in Section 4.4)of the travelling subfeatures in the 11/3 line of ( Oph and the Hi3 and He I A4921 linesof f Per failed to reveal polarisation structure related to the travelling subfeatureswith upper limits of 0.08% and 0.1%, respectively. Theoretical estimates of thepolarisation levels expected if the line profile variations arise from either NRP, spotsor circumstellar spokes will be required before the limits placed by this study canbe used to constrain the possible sources of the line profile variations.3. We have presented differential polarisation measurements in the 11/3 emission line ofthree intrinsically polarised Be stars: q Per, -y Cas and 28 Cyg. No significant changeof polarisation has been detected for 28 Cyg despite the presence of appreciableemission. However, Per and y Cas exhibit significant polarisation changes acrossthe^line. These changes are characterised by a decrease of polarisation towardthe center of the line and an increase at the line center itself. Our observations alsoshow evidence for variations in the plane of polarisation across the line.We have argued that unpolarised line emission cannot completely account forthe observed polarisation changes. The width of the polarisation structure is com-parable to the width of the underlying rotationally-broadened absorption feature; itis significantly greater than the width of the expected polarisation structure if theeffect is solely caused by dilution of the continuum polarisation by unpolarised lineemission. 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