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HIRES Spectroscopy of Magnetic White Dwarfs McAnerin, Mark 2007-06-30

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HIRES Spectroscopy of MagneticWhite DwarfsbyMark McAnerinA THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFBachelor of ScienceinThe Faculty of Science(Physics and Astronomy)The University Of British ColumbiaJune, 2007c© Mark McAnerin 2007AbstractThe atmospheres of magnetic white dwarfs behave as theoretical analoguesto neutron stars. The magnetic fields strengths and effective temperaturesof the white dwarfs with the strongest magnetic fields are both two to threeorders of magnitude below neutron stars. So the expectation is that theiratmospheres and stellar enevelopes will be as difficult to model as neutronstars due to the high degree of anisotropy in the thermal conduction throughtheir atmospheres and envelopes. The construction of spectra and analyz-ing their absorption features with data taken with the HIRES instrumenton Keck-I, could better constrain the models for all magnetic stellar atmo-spheres. Using the response transfer method of reducing echelle spectra wehave created complete relative flux spectra of several magnetic white dwarftargets. Our reference in the reduction is Van Maanen 2, which behaves asa good blackbody and is devoid of spectral features above 4000˚A. Errorsbetween orders due to the limitations of our method have prevented assem-bly of complete continuous spectra, but spectral data seems to indicate thatthere ranges of spectra up to several hundred angstroms wide with low sys-tematic error, allowing analysis of the large spectral features of magneticwhite dwarfs.iiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . vi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Magnetic White Dwarfs . . . . . . . . . . . . . . . . . . . . . 11.2 HIRES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Data Reduction Methods . . . . . . . . . . . . . . . . . . . . . 52.1 Reference Spectra . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Theoretical Modelling . . . . . . . . . . . . . . . . . . . . . . 52.3 Response Transfer . . . . . . . . . . . . . . . . . . . . . . . . 63 Calculation and Results . . . . . . . . . . . . . . . . . . . . . . 84 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . 17Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18iiiList of Tables1.1 Magnetic White Dwarf Targets . . . . . . . . . . . . . . . . . 23.1 Day 1 Smoothed Conversion Ratio Coefficients . . . . . . . . 10ivList of Figures1.1 Light Path through the HIRES instrument . . . . . . . . . . 31.2 Example CCD image of a cross dispersed echelle spectrum . . 33.1 The 10th spectral order of Van Maanen 2 before reduction . . 113.2 The 10th spectral order of the reference spectra . . . . . . . . 123.3 The 10th spectral order of the unsmoothed conversion ratio . 133.4 The 10th spectral order of the conversion ratio . . . . . . . . 143.5 The 10th spectral order of Van Maanen 2 after data reduction 153.6 Spectral orders 20, 21, 22 of PG1015+014 . . . . . . . . . . . 16vAcknowledgementsMany thanks go to Dr. Jeremy Heyl, my supervisor, for always pointing mein the right direction whenever I lost my way with this project. Whether itwas help with the daily struggles with IDL and other pieces of software ora good reference book, he was always seemed to have an answer.I’d also like to thank the Theoretical High-Energy Astrophysics groupat UBC for the use of their Tabitha and even putting me on the webpage asa member.Myself, and I’m sure Dr. Heyl, wish to recognize and acknowledge thevery signifigant cultural role and reverence that the summit of Mauna Keahas always had within the indigenous Hawaiian community. We are mostfortunate to have been able to conduct observations from the mountain.viChapter 1Introduction1.1 Magnetic White DwarfsSince the late 30’s, magnetic white dwarfs have been studied due to theirunusual absorption features. The positions of the hydrogen absorption linesin the spectra are perturbed from their normal positions to positions dictatedby the stationary points of the wavelength of hydrogen atom transitions,which are dependant on magnetic field strength. [1]The white dwarfs that we studied are highly magnetized. Their mag-netic fields are measured by the position in their spectrum of absorption fea-tures, which are often signifigantly altered from their unperturbed positions.White dwarf magnetic fields above 105 are found to be evenly distributedin strength up to 109G, far stronger than most white dwarfs. [7][6] Thesewhite dwarfs with strong magnetic fields can be thought of as analogues toneutron stars, in that their effective (surface) temperatures and magneticfield strength are both two orders of magnitude less than neutron stars. Thismeans the ratio of these two values is approximatley the same for these twoclasses of compact objects. [3]The magnetic field-temperature ratio represents the degree of anisotropyin electron phase space. In natural units for magnetic field and temperature,β/τ ≈ 134B/T (B and T in units of MG and K). For neutron stars, this isB ≈1011−12G and T ≈106−7K. So the ratio for neutron stars β/τ ≈10. [3]With the ratio being approximately the same between neutron stars andstrongly magnetic white dwarfs, we expect the thermal conduction throughmagnetic white dwarf atmospheres to be as complicated and challenging tomodel as neutron stars. So studying magnetic white dwarfs can give usinsight in the modelling of neutron star atmospheres and envelopes. Ourmagnetic dwarf targets and some of their properties are given in Table 1.1.Some of our target stars also have noted periodicities in their luminosity,as noted in the Table 1.1. These may be linked to changes in their magneticfield strength as well which if true would correspond to shifts in absorptionfeatures in their spectra. Several exposures were taken of these targets andhigh resolution spectra would allow the construction of precise time-resolved1Chapter 1. IntroductionName Period Teff (K) B (MG) β/τPG 1031+234 3.4h 15000 1000 8.96SBS 1349+5434 − 11000 760 9.28LB 11146 − 15000 670 6.00LP 790-29 − 8600 200 3.12PG 1015+014 1.7h 14000 120 1.15G 195-19 1.3d 8000 100 1.68Table 1.1: Magnetic White Dwarf Targets [7] [3]spectra of these targets.1.2 HIRESOur observations were taken on HIRES, the high resolution echelle spec-trometer, a cross-dispersed echelle spectrograph mounted on the nasymthplatform of the Keck-I telescope at Mauna Kea, Hawaii. This instrument isdesigned to use the Keck telescope’s ten-meter diameter to take very highsignal-to-noise ratio measurements across a wide range of wavelengths in-cluding the entire visual spectrum and portions of the near-infrared andultraviolet. [10] [9] [5]The instrument provides such high resoultion by using an echelle grating,a diffraction grating with a steep step-profile. The grating produces a seriesof overlapping high resolution spectral orders about 60˚Along. A second,low-dispersion grating, called a cross disperser, with grooves perpendicularto the echelle grating is used to separate the overlapping spectral ordersout onto a single CCD. A cartoon of the lightpath is given in Fig. 1.1 Anexample of a cross dispersed echelle CCD image is Fig. 1.2. [5]These CCD images are preprocessed (debiased, flatfielded, and wave-length calibrated) into a more accessible format by a piece of software de-veloped by the Keck observatory called MAKEE. This program reduces theCCD image into relative flux and wavelength information across each spec-tral order. The data is binned into ≈ 0.03˚Apieces, giving 2046 data points,per spectral order. Our data set contains information from 28 spectral or-ders, and a total range of about 2000˚A. [10]The trade-off for is the large non-linear response of the instrument onseveral scales. Both within each spectral order as well as across each gapof orders there are up to 10% errors which must be removed by calibration.2Chapter 1. IntroductionFigure 1.1: The light path through the HIRES instrument. [5]Figure 1.2: An example CCD image of cross dispersed echelle spectrumseperated out into spectral orders with the range of wavelengths displayed.[5]3Chapter 1. IntroductionFortunately there is a small overlap of wavelengths at the beginning andend of each order, which are used to match orders together by setting theseoverlaps equal and shifting the neighbouring orders to match them up. [8]4Chapter 2Data Reduction Methods2.1 Reference SpectraThe normal method for reducing HIRES echelle spectra was developped bySuzuki et al [8]. It uses a well calibrated reference spectrum combined withthe HIRES data to develop a continuous spectra with the overall shape ofthe reference spectra while including the high resolution detail of HIRESinformation.The method relies on reducing the HIRES data’s resolution to matchthe reference spectra, and rebinning the data to compare them. A lowresolution conversion ratio between the reference and HIRES spectra can becreated to both relate the reference spectra fluxes and the HIRES fluxes aswell as force the HIRES data to follow the overall shape of the light curveof the reference. This conversion ratio is then fitted with a polynomial fitto remove low resolution spectral features that may remain from reference.Depending on the amount of structure in the spectrum, different types ofpolynomials or different degrees polynomial may be appropriate for differentspectral orders. [8]That conversion ratio is then binned back to HIRES resolution usingthe polynomial coefficients and divided from the full HIRES spectra. Thisresults in the HIRES spectra matching the light curve of the reference, butwith the absorption features of the HIRES data.This method is highly successful but dependant on a well-calibrated ref-erence spectra to match the HIRES data for every target. Unfortunately,we lack reference spectra to apply this method to any of our target stars soalternatives must be explored.2.2 Theoretical ModellingAnother method of analyzing echelle data is to compare the data to a knownstellar model. This method can be successful over short wavelength rangesif the features being studied are small compared to the size of a spectral5Chapter 2. Data Reduction Methodsorder and the features exhibit large flux differences from the surroundinghigh area. This method may be appropriate for analyzing such things as thewidths and profiles of prominant spectral lines.For a small area of interest, possibly as large as a few angstroms, the non-linearity in that area can be considered a small perturbation. This allowsa theoretical model to be used as a reference level for the feature with thestudied spectral feature being much larger than local non-linearities in theresponse. Something as simple as a fitted low order curve could be usedas a baseline for an spectral feature due to the extremely short range ofwavelengths under consideration. [9]This method is feasible only over very short wavelength spans and witha specific feature that you wish to be studied. While our targets spectrawere observed over a range of 2000˚A, there are absorption features whichspan tens of angstroms making this method inappropriate for our use.2.3 Response TransferDue to a lack of reference spectra, we elected to use a combination of thesetwo methods to achieve the goal of spectral construction. A non-magneticwhite dwarf, Van Maanen 2 (vMA2), was observed both nights that ourdata was taken. Van Maanen 2 is notable for it’s lack of spectral featuresabove 4000˚A, especially its lack of hydrogen or helium lines. This makesthis white dwarf an excellent blackbody in this spectral range. [2] [11]Since Van Maanen 2’s light curve behaves approximately as a blackbody,we can generate a set of reference fluxes using Planck’s Law (Eq. 2.1) above4000˚A. Below 4000˚Athere are multiple absorption features in the spectra,including two very strong carbon absorption lines in the near ultraviolet,because they are not included in our reference we must trim out the rangebelow 4000˚A. Unfortunately this is almost 25% of our data. [11]I(λ,T) = 2hc2λ51exp hcλkT −1 (2.1)Using extracted wavelength information for vMA2 and knowing it’s ef-fective temperature to be 6750 K, we apply Planck’s Law and built an ap-propriately binned reference spectrum. Only the relative overall shape ofthe curve is necessary due to our interest being a relative flux calibration,a spectrum that is only an overall normalization factor away from being acalibrated absolute flux spectra. Our theoretical reference light curve is then6Chapter 2. Data Reduction Methodsused to build a conversion ratio using the reference spectra method outlinedabove. [2]Smoothing across each spectral order with a low order polynomial fitand trimming the data below 4000˚Aremoves any artifacts in the vMA2 datafrom short scale non-linearity in response. This is conversion ratio is thenapplied to our magnetic white dwarf targets spectra taken the same eveningto get a relative flux calibrated reference.The validity of using a conversion ratio from a different star for ourscience targets is questionable. The reason echelle spectra are so difficultto calibrate is that the non-linearities can change on time scales that maybe short compared to an evening’s observations, especially when observingmultiple targets. This method is well known for magnifying relative fluxerrors by compounding the small flux errors multiple times into the finalresults. [8]Joining spectral orders into a continuous spectra from this method isalso suspect. This method also tends to bias the removal of instrumentalresponse in the middle of each spectral order over the edges. Unfortunatelythe largest non-linear areas are the near the edges of each spectral order,and the jumps between them. This method can leave 5-10% errors towardsthe edges of each spectral order and as much as 10% errors for the jumpsbetween spectral orders, where discontinuities may occur in the worst cases.Thankfully the the relative flux is calibrated well in the middle of each order,so studying some spectral properties is still possible. [8]7Chapter 3Calculation and ResultsWe used the above described response transfer method to our reduce ourdata. We have constructed, order by order, complete yet uncombined spec-tra of our target white dwarfs. Across individual orders, we were successfulin removing the non-linear nature of the echelle spectrometer. Unfortu-nately, due to the polynomial fit’s equal weighting (as we have no errorinformation other than photon noise which is equal point to point), thepolynomial fit has preferentially removed instrumental response at the cen-ter of spectral orders. This has caused large errors to develop at the edges ofsome spectral orders depending on the amount of structure contained withineach order.Although we were able to match the relative flux order to order, thespectra is not smooth as it should be. There are clear errors order to orderas the polynomial fits naturally diverge from the conversion ratio at eitherend of the spectral order. The polynomial fits of neighbouring orders oftendiverge in opposite directions, this causes the first derivative of the lightcurve with respect to wavelength to be different order to order in the smallregions of overlapping wavelength. Even the polynomial coefficients orderto order change enough to be same magnitude but with the opposite signin some cases. While a full spectrum could not be constructed, there areregions where the spectral orders can be joined in a well behaved manner.An outline of the involved calculation follows, with illustrative figures ofthe various intermediate steps following:1. The raw data is extracted within from a standard echelle .FITS (CCDimage) file, flux information is pulled from the image itself while thewavelength information is stored in the header of the fits file and ex-tracted seperately. (Fig. 3.1)2. From the wavelength information, we construct the reference spectrausing Planck’s Law (Eqn. 2.1). This creates a reference flux, for everydata point. (Fig. 3.2)3. Individually dividing each reference data point by the raw fluxes at8Chapter 3. Calculation and Resultstheir associated wavelengths produces the unsmoothed conversion ra-tio.(Fig. 3.3)4. Fitting a polynomial to the unsmoothed conversion factor for eachspectral order creates the smooth conversion factor for that spectralorder. We decided on a 3rd order polynomial because it appears tobe a working middle ground between the large scale and small scaleresponse of the instrument. The polynomial fit results in an array of112 coefficients, 4 per spectral order. The first night of observationspolynomial coefficients are given in Table. 3.1. These coefficients arethen evaluated in simple polynomial form (Eqn. 3.1) to create the finalsmoothed conversion ratio. (Fig. 3.4)5. Multiplying the raw data by the conversion ratio idealy removes allinstrument response and produces a relative flux spectral order whichcan then be joined to its neighbours to create a continuous relativeflux spectra. If necessary the spectra can then be renormalized to anabsolute flux spectra simply by a multiplicative factor. (Fig. 3.5)CR(λ) = C[0]+ C[1]λ + C[2]λ2 + C[3]λ3 (3.1)Due to the sheer amount of data involved in the results of even a singleHIRES integration it is impractical to display a full spectrum in any formother than digital. Below are three orders joined together from PG1015+014(Fig. 3.6), one of our magnetic white dwarf targets. Centered on order 21 anabsorption line displaying the characteristic spreading that occurs in strongmagnetic fields is apparant.9Chapter 3. Calculation and ResultsSpectral Order C[0] C[1] C[2] C[3]0 7899.73 -13.3958 0.00688 0.01 -5.23320e+08 425719. -115.430 0.010432 -8.76186e+09 6.91739e+06 -1820.38 0.159683 -1.74316e+09 1.35794e+06 -352.593 0.030524 5.44198e+10 -4.21197e+07 10866.3 -0.934435 1.52410e+11 -1.16648e+08 29759.1 -2.530686 1.36550e+10 -1.03290e+07 2604.39 -0.218907 1.29829e+09 -979660. 246.420 -0.020668 1.69294e+09 -1.25814e+06 311.679 -0.025749 5.65796e+08 -418109. 102.994 -0.0084610 3.39148e+08 -248023. 60.4630 -0.0049111 -9.96050e+08 709953. -168.665 0.0133612 -2.75957e+08 193144. -45.0496 0.0035013 -2.91256e+08 201940. -46.6648 0.0035914 -9.63505e+08 662994. -152.065 0.0116315 -7.87600e+08 534907. -121.092 0.0091416 -8.37957e+08 561800. -125.546 0.0093517 -9.94092e+08 658668. -145.467 0.0107118 -7.94577e+08 519164. -113.062 0.0082119 -8.56270e+08 552633. -118.878 0.0085220 -3.53654e+08 224345. -47.4282 0.0033421 8.68006e+07 -57232.5 12.5619 -0.0009222 5.12323e+08 -321613. 67.2995 -0.0046923 3.06929e+08 -190939. 39.5954 -0.0027424 4.87957e+08 -296510. 60.0649 -0.0040625 2.69026e+08 -161758. 32.4253 -0.0021726 2.42011e+08 -143325. 28.2988 -0.0018627 1.16727e+08 -67807.1 13.1335 -0.00085Table 3.1: Day 1 Conversion Ratio Coefficients10Chapter 3. Calculation and ResultsFigure3.1:The10thspectralorderofVanMaanen2,beforeanydatareduction.11Chapter 3. Calculation and ResultsFigure3.2:The10thspectralorderthetheoreticalreferencespectra,builtoffofthewavelengthsofthe10thspectraorderofvMA2usingPlanck’sLaw.12Chapter 3. Calculation and ResultsFigure3.3:The10thspectralorderoftheunsmoothedconversionratio.13Chapter 3. Calculation and ResultsFigure3.4:The10thspectralorderoftheconversionratioafterbeingsmoothedbytheapplicationofa3rdorderpolynomial.Thepatternintheimageistheperiodicityofthewavelengthbins,whicharenotallexactlyequalinsizebutveryontheorderof0.01˚A.14Chapter 3. Calculation and ResultsFigure3.5:The10thspectralorderofVanMaanen2,beforeanydatareduction.Thelargescatterofpointsisnotindicativeofhighinstrumentnoise,butofnoiseintroducedbythedatareductionmethodandrepresentsanerrorofabout5%inthecenterofthespectralorderand8%intheouter5−10˚A.Theseerrorsaretypicalforthismethodofechelledatareduction.15Chapter 3. Calculation and ResultsFigure3.6:Spectralorders20,21,and22joinedfromPG1015+014fromthefirstnightofobservations.Notetheshapeoftheabsorptionfeatureat4740˚Ashowingthecharacteristicspreadingofthespectrallineduetothepresenceofastrongmagneticfields.16Chapter 4Discussion and ConclusionsThe response transfer method of reducing echelle data has produced results,which while not as accurate across many spectral orders as those generatedwith the reference spectra method, seem promising. Several absorption fea-tures have been highlighted in the mangetic targets and the identificationprocess has begun, albeit complicated by the varied effects of the magneticfield.Van Maanen 2 has been demonstrated to be a good calibration toolfor observations at wavelegths ≥ 4000˚A. Although there are several waysto improve the quality of the output data. Taking reference spectra forvMA2 and the magnetic white dwarf targets could be used to bench markthe quality of the data by comparing this method to the reference spectramethod.In terms of future work on this project, it is likely that better resultscould be obtained by indiviually treating each spectral order and determin-ing an appropriate degree of polynomial to fit. Also, using a different style ofpolynomial rather than just a basic may be appropriate to avoid the problemof diverging rapidly from the conversion ratio at the tails.Intensive examination of the produced spectra could result in identifi-cation of more absorption features for analysis. Analysis of those featuressuch as by studying the width and profile of absorption lines to characterizethe magnetic field structure could lead to better constraints on the modelsfor magnetic stellar atmospheres. [4] [3]17Bibliography[1] Angel, J. R. P., Liebert, J., and Stockman, H. S., 1985, ApJ, 292[2] Farihi, J. et al., 2004, ApJ, 608[3] Heyl, J.S., Reid, N., 1998, Keck Observing Proposal: HIRES Spec-troscopy of Magnetic White Dwarf Stars[4] Heyl, J.S., Hernquist, L., 1998, Phys. Rev. A, 58, 3567[5] Hill, G. (site accessed Apr. 19-23th, 2007), High Res-olution Echelle Spectrometer, W.M. Keck Observatory.(http://www2.keck.hawaii.edu/inst/hires/hires.html).[6] Putney, A., 1996, ApJS, 112[7] Schmidt, G.D. & Smith, P.S., 1995, ApJ, 448[8] Suzuki, N., et al., 2003, PASP, 115, 1050[9] Vogt, S. S. et al., 1987, PASP, 99, 1214[10] Vogt, S. S. et al., 1994, Proc. SPIE, 2198, 362[11] Weidemann, V. & Koester, D., 1989, A&A, 21018


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