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Imaging the sun with the Drao synthesis telescope Burke, Ian E. 1993

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IMAGING THE SUN WITH THE DRAO SYNTHESIS TELESCOPEByIan Edward BurkeB.A.Sc., The University of British Columbia, 1991A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF PHYSICSWe accept this thesis as conformingto the required standard THE UNIVERSITY OF BRITISH COLUMBIAOctober 1993© Ian Edward Burke, 1993In presenting this thesis in partial fulfilment of the requirements for an advanced degree atthe University of British Columbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission for extensive copying of thisthesis for scholarly purposes may be granted by the head of my department or by hisor her representatives. It is understood that copying or publication of this thesis forfinancial gain shall not be allowed without my written permission.Department of PhysicsThe University of British Columbia2075 Wesbrook PlaceVancouver, CanadaV6T 1W5Date:0 C. t^I cic1AbstractThe Synthesis Telescope at the Dominion Radio Astrophysical Observatory in Penticton,British Columbia, has been modified to make full-disk continuum maps of the Sun at1420 MHz. The hardware and software systems of the telescope were augmented for thispurpose. The standard observing procedure was altered, and image-processing algorithmswere written to produce solar images.To reduce the solar signals to an acceptable level for the telescope electronics, 20dB attenuators were introduced in the 1420 MHz receivers. The tracking and fringe-controller software was modified to allow for the motion of the Sun in right ascension.Algorithms were created to remove the effects of declination motion and rotation of theSun during the observation; these corrections are combined in a user-friendly softwarepackage to be run at the data-processing stage.The large field of view (2.6°) and arcminute resolution of the DRAO Synthesis Tele-scope make it is suitable for producing full-disk solar maps for the purpose of studyingthe different sources of the slowly-varying (S-) component; the large field allows the entiresolar disk to be mapped with high sensitivity. Because of solar variability and rotation,each map had to be made in one day, using one configuration of the antennas. To maxi-mize this sparse u, v coverage, solar "observing" simulations were used to determine thebest configurations of the antennas for solar synthesis; these antenna configurations wereused in the summer observations of 1992 and 1993. With each 12-hour solar observation,a calibration source, such as 3C48, was observed for half-an-hour.The resulting images, in general, represent both the extended structure (quiet Sun)and the more localized emission (active regions) well. Comparisons between integrated11map fluxes, and cotemporal single-antenna flux measurements at 1420 MHz (21 cm-A),indicate that most of the solar brightness distribution was being recovered satisfactorily.The degree to which the solar disk was recovered appears somewhat sensitive to the leveland distribution of solar activity. The images have resolutions comparable with otherDRAO synthesis maps, and have a dynamic range of about 100:1.A widely-distributed background component, covering large areas of the Sun in anactive latitude belt centered about the equator, is also evident in the solar images; itscontribution to the S-component is comparable with that by active regions. Regionsof high radio emission in the solar images have a strong spatial correlation with en-hanced magnetic activity in magnetograms; in addition, a linear correlation was foundbetween the total disk magnetic flux and the total radio emission at 21 cm. These re-sults suggest that the majority of the S-component at 21 cm is due to thermal free-free(bremsstrahlung) emission coming from density enhancements in the corona, which aresupported by magnetic fields.111Table of ContentsAbstract^ iiList of Tables viiList of Figures^ viiiAcknowledgement x1 Introduction to Aperture Synthesis^ 11.1 Two-Element Radio Interferometer  ^21.2 Aperture Synthesis  ^51.3 Recovering the Brightness Distribution  ^92 Scientific Motivation: Measuring the S -component^ 112.1 Solar Radio Emission ^  112.2 Slowly-Varying Component  142.3 Widely-Distributed Background Emission ^  193 Solar Mapping with Synthesis Telescopes 213.1 Difficulties with Solar Synthesis  ^213.2 Imaging the Sun with Other Synthesis Telescopes ^ 213.3 Imaging the Sun with the DRAO Synthesis Telescope  234 Baseline Optimization and Solar Simulations^ 264.1 DRAO SST Dirty Beam Patterns ^  27iv5^4.2^Uniform u, v Coverage ^^4.3^Sampling the Solar Visibility Function ^4.4^Solar Simulations ^Solar Observations292931355.1 Hardware Modifications ^ 355.2 Software Modifications 365.3 Calibration Procedure ^ 375.4 Solar Observing Specifications ^ 385.5 Using the DRAO 26 m Antenna 406 DRAO SST Solar Map Corrections 416.1 Declination Drift ^ 436.2 Solar Rotation 476.3 Gain Variations Introduced by Attenuators ^ 547 Solar Data Reduction 607.1 DRAO Data Reduction Software ^ 607.2 SUNVIS: Solar Visibility Correction Program ^ 627.3 D econvolut ion Procedures ^ 637.3.1^DRAO CLEAN 637.3.2^AIPS MEM ^ 658 Properties of the Final Maps 698.1 Dynamic Range ^ 698.2 Map Resolution 728.3 Total Fluxes ^ 738.4 Brightness Distribution Reconstruction ^ 76V9 S-component Emission Budget^ 779.1 Budget Description ^  779.2 Flux Budget at 1420 MHz  7810 Solar Radio and Magnetic Activity^ 8110.1 Magnetic Fields in the Solar Atmosphere  8110.2 DRAO SST Solar Map and Magnetogram Similarities ^ 8210.3 Simulation of DRAO SST Maps Using Magnetograms  8410.4 Magnetic and Radio Flux Similarities ^  8610.5 Relationship between Magnetic and Radio Flux ^ 8711 Summary, Conclusions, and Recommendations^ 9111.1 Summary ^  9111.2 Conclusions  9311.3 Recommendations^  94Bibliography^ 96Appendices^ 100A DRAO SST 1420 MHz Attenuators^ 100B Solar Map Collection^ 101viList of Tables3.1 DRAO SST 1420 MHz Continuum System Parameters ^ 234.2 DRAO SST Antenna Positions ^ 275.3 Solar Observing Specifications 398.4 1420 MHz Total Fluxes (in sfu) ^ 739.5 1420 MHz Flux Budget Averages 78viiList of Figures1.1 Two-Element Interferometer (from Thompson 1989, [53], p. 13)  ^31.2 Radio Source Geometry (from Thompson 1989, [53], p. 14)   51.3 Aperture Synthesis Coordinate Systems (from Thompson 1989, [53], p. 20) 71.4 Earth Rotation Aperture Synthesis (from Fomalont 1974, [22], p. 258) . . 82.5 Temperature and Density Variations in the Solar Atmosphere (from Lang1992, [37], p. 105)  ^122.6 S-component Spectrum (from Kundu 1965, [33], p. 169) ^ 142.7 Monthly Means of the 10.7 cm Solar Flux ^  183.8 The DRAO Synthesis Telescope ^  254.9 DRAO SST Dirty Beam Patterns  284.10 Solar Visibility Function  ^304.11 Simulation Maps for Antenna Configuration 64 53 45 ^ 326.12 Uncorrected Dirty Solar Map ^  426.13 Uncorrected Solar Map and Declination Drift Artifact ^ 446.14 Declination Drift Corrected Solar Map and Solar Rotation Artifact^486.15 Coordinate Frames for Solar Rotation Correction ^ 516.16 Declination Drift and Solar Rotation Corrected Solar Map ^ 557.17 Final Solar Maps Determined by CLEAN and MEM^ 678.18 Montage of CLEAN Final Solar Maps ^  70viii8.19 Averaged Visibility Amplitude Vs. Baseline ^  759.20 Total, Active Region, and Background Flux Variations ^ 7910.21 Magnetogram[Grey Scale]/DRAO SST[Contour] Overlay Map^ 8310.22 Observed and Simulated (Using a Magnetogram) CLEAN Solar Maps^8510.23 Total Magnetic Flux Vs. 10.7 cm Solar Flux Density ^ 8810.24 Total Magnetic Flux Vs. 21 cm Solar Flux Density  89A.25 Location of 20 dB Attenuators in 1420 MHz Receivers^ 100B.26 Collection of CLEAN Final Solar Maps (Part 1)  101B.27 Collection of CLEAN Final Solar Maps (Part 2) ^ 102B.28 Collection of CLEAN Final Solar Maps (Part 3)  103ixAcknowledgementThis project was only possible due to the help and support of the staff at the DominionRadio Astrophysical Observatory; almost everybody at the observatory helped me in oneway or another during the course of my project. With regards to the preparation of theDRAO Synthesis Telescope for observing the Sun, I thank Jean Bastien and Rod Stuartfor constructing and inserting the 1420 MHz attenuators, and Gary Hovey and DaveKarpa for modifying the telescope software. I also thank Tony Willis, Natalie Prowse,and Diane Parchomchuk for their assistance with the DRAO computer network and soft-ware, and Tom Landecker, Peter Dewdney, Russ Taylor, and Rob Roger for informativediscussions on aperture synthesis. I am grateful to Bette Jones for her valuable servicesas the observatory librarian.Special thanks go to Lloyd Higgs, the Director of DRAO, for allowing me to do thisproject at the observatory, and John Galt, who modified and used the 26 m Antenna toobserve the Sun in conjunction with the Synthesis Telescope. I thank Carl Henney forproviding Mount Wilson magnetograms, Karen Harvey and Jack Harvey for providingKitt Peak magnetogram data, and James Dean for providing the 10.7 cm solar flux dataused in this thesis. I thank Walter Wyslouzil for the figure showing the attenuators in the1420 MHz receivers. I also thank Bill Shuter of the University of British Columbia for hissupervision and advice during the course of this project. I am grateful to the NationalEngineering and Science Research Council who funded my Master's Degree through agraduate scholarship. Finally, I thank Ken Tapping, my "observatory" supervisor, forhis support, encouragement, technical advice, and countless discussions throughout myproject; he is also responsible for the computer program that calculates "dirty beam"patterns.Chapter 1Introduction to Aperture SynthesisThe birth of radio astronomy occurred with the experiments of Karl Jansky in 1931.Jansky, a radio engineer with Bell Telephone Laboratories, had been assigned the taskof studying the arrival of sources of interference liable to affect long-distance short-wavecommunications. In 1935, he identified a steady hissing signal which originated in theMilky Way Galaxy. This sparked a number of continuum studies of the radio sky byradio astronomy pioneers such as Grote Reber (1944, [41]) and Hey et al. (1946, [28]);in 1944, Reber also published the first report on radio emission from the Sun. In 1951,Ewen and Purcell (1951, [18]) detected the hydrogen line emission predicted by van deHu1st in 1944; this spectral line has become one of the most important diagnostic toolsin radio astronomy, and has been used to produce spectacular maps of our galaxy.The early work in radio astronomy was done with single antennas. However, it be-came apparent that greater angular resolution was required than could be obtained withany feasible single-antenna system. The angular resolution of a radio telescope is propor-tional to the wavelength divided by the antenna diameter. Since radio wavelengths areorders of magnitude larger than optical wavelengths, a radio telescope would have to beunreasonably large to give a resolution comparable to an optical telescope; such a radiotelescope would be difficult to build, and very costly.The first attempt to solve this angular resolution problem was the two-element in-terferometer, which comprises two small, but widely-separated antennas, connected toa common receiver. Important discoveries with interferometers include the Bolton and1Chapter 1. Introduction to Aperture Synthesis^ 2Stanley (1948, [4]) observation of the Cygnus region with their sea interferometer' inAustralia, and the confirmation of this result by Ryle and Smith (1948, [45]) usinga two-element type of interferometer at Cambridge University. Two-element interfer-ometers proved highly effective for estimating the positions and mean angular sizes ofsources, but provided only limited information about source structure; the problem isthat two-element interferometers sample little of the information about a source. A bet-ter solution to the angular resolution problem is aperture synthesis, invented by Ryleand Hewish (1960, [44]), where an array of several small antennas is used to emulate, toa large extent, the angular resolution and sensitivity of a large single antenna.1.1 Two-Element Radio InterferometerThe following discussion on interferometers comes largely from Thompson (1989, [53]).Figure 1.1 shows a simple two-element interferometer. The two antennas are separated bythe distance g, called the baseline, and are observing the same distant radio source; thisbaseline vector is directed from left-to-right in figure 1.1. The wavefront arriving from thesource in the direction 0 is basically planar because of the large distance traveled by thesignal; the signal reaches the right-hand antenna at a time 79 = g • -gl C before it reachesthe left-hand one. 79 is the geometrical delay, . a unit vector in the source direction,and c is the speed of light. The signals from the antennas pass through amplifiers withfilters that select a frequency band A v centered on the frequency v. The signals arecombined in a correlator, which is a voltage multiplier followed by a time averaging orintegrating circuit; the integrating circuit filters out the rapidly-varying components.The received signals can be represented by quasi-monochromatic Fourier components of1This sea interferometer was made by mounting an antenna on a cliff overlooking the ocean nearSydney, Australia; the second "image" antenna was provided by the reflection of the radio signal by theocean, to the first antenna.Chapter 1. Introduction to Aperture Synthesis^ 3Figure 1.1: Two-Element Interferometer (from Thompson 1989, [53], p. 13)frequency v; the output voltages from the two antennas are then VI (t) = v1 cos 27ru(t — rfl)and 172(t) = v2 cos 27rvt, respectively. The output of the correlator isr(T2) oc v1v2 cos 27rvrg,^ (1.1)with v1v2 being proportional to the received power.The geometrical delay 79 varies slowly with time as the Earth rotates, and the resultingoscillations of r(r9) represent the relative motion of the source through the interferom-eter fringe pattern2. This correlator output can be expressed in terms of the observedradio brightness distribution, which is the intensity or brightness as a function of chosen2The radiation pattern of a two-element interferometer has nulls in some directions, where the con-tributions from the two antennas cancel; this happens along small circles on the celestial sphere. Thisstriated interference pattern is called the fringe pattern of the interferometer.Chapter 1. Introduction to Aperture Synthesis^ 4celestial coordinates. The signal power received in the bandwidth Au from the sourceelement A/ is A(g)/(g)AvdD, where A(ñ) is the effective collecting area in the directiong, and 1-(g) is the radio brightness in the direction gs' at the frequency v. The correlatoroutput for the signal from c/S2, within a constant gain factor, isdr = A(g)I(.^)AvelS2 cos 271- vrg. (1.2)The fringe pattern has a sinc-function envelope due to the broadband response of theinterferometer called the fringe washing function or delay beam. An instrumental delayis inserted in the right-hand system in figure 1.1 before the correlator to compensatefor Tg; this is the part of the fringe stopping system that causes the delay beam to followthe source across the sky. At this point, it is convenient to express the interferometerresponse as the real part of a complex expression. Integrating over the source, the totalresponse of the interferometer, in terms of the baseline i; and source position g, isr(g) = R{R,(g)} = pv I A ( 7,0\7-(g)e-i2irv(t.gl c-Ti) daS(1.3)It is assumed that the bandwidth is small enough, compared with the observingfrequency v, that variations in A and I with v can be ignored. S denotes that theintegration is over the surface of the celestial sphere, even though the integrand usuallyfalls to very low values outside a small angular field. The source being integrated over isusually quite small, so it is convenient to write g = o +5-, where go is the phase trackingcenter, and is a vector indicating the location of a brightness element relative to go.Figure 1.2 shows these position vectors and their orientation relative to the brightnessdistribution. The response equation now becomesTZ(g) = e-i2Irv(r''.4/c-T')Avf Arc1)1(6)e-i2"t'aledil..5(1.4)The exponential factor preceding the integral is defined as the phase of R.(g) for the mapChapter 1. Introduction to Aperture Synthesis^ 5Figure 1.2: Radio Source Geometry (from Thompson 1989, [53], p. 14)center. The remaining integral is defined as the complex visibility function,V(g) =^A(c7)1(6)e- i21"11" 'a I c dS2^ (1.5)1.2 Aperture SynthesisThe brightness distribution 1(1, m) can be expressed as a sum of Fourier components. Asingle antenna collects all the information having spatial frequencies smaller than aboutD/A, where D is the diameter of the antenna. A two-element interferometer, on theother hand, samples Fourier components of the brightness distribution having spatialfrequencies close to B/A, where B is the separation of the antennas, as seen from thedirection of the source.An array of N antennas comprises N(N — 1)/2 different two-element interferometers.If the antennas are distributed so that no baseline is duplicated, then by correlatingseparately each pair, we measure the relative amplitudes and phases of that numberof spatial-frequency components of the brightness distribution. Each baseline providesChapter 1. Introduction to Aperture Synthesis^ 6a measure of one of the Fourier components of the brightness distribution; if enoughcomponents are sampled, the brightness distribution can be estimated. If the numberof antennas is increased to the point where all the baselines are represented, all spatialfrequencies are sampled up to about D/A, where D is the length of the array, as seenfrom the direction of the source. Unfortunately, this may require a very large numberof antennas, so that it is not possible within the available resources. However, a so-lution is offered by the very slow variation with time of the brightness distributions ofcosmic sources. By moving the antennas and making further observations, one can, overwhatever length of time is needed, make measurements at all the antenna separationsnecessary to fully sample the brightness distribution.Mapping sources in this way requires precise positioning of antennas in a two-dimen-sional grid of antenna locations on the ground. An easier method uses a linear East-Westarray of antennas, movable on a precisely-aligned railway track; the Earth's rotation isused to reposition the antennas relative to the cosmic source. Earth rotation synthesis,developed in Cambridge by Ryle (1962, [43]), uses the rotation of the Earth to change theorientation of the antennas in the process of "filling" in the aperture. The resulting res-olution is proportional to the largest antenna spacing and the field of view is determinedby the diameter of the individual antennas. This technique is used at the DominionRadio Astrophysical Observatory.The following is an extension of the two-element interferometer discussion from theprevious section. For Earth rotation synthesis, it is common practice to define specialcoordinate systems as shown in figure 1.3. The projected baseline g - g has spatial-frequency components (u, v, w) in units of A, with the u axis measured towards the East,the v axis towards the North, and the w axis towards the phase tracking center. ThevectorJ.,- is now defined in terms of the direction cosines 1, m, n, with 1 and m beingmeasured with respect to the u and v axes, respectively. With these new coordinate(1.8)(1.9)Chapter 1. Introduction to Aperture Synthesis^ 7Figure 1.3: Aperture Synthesis Coordinate Systems (from Thompson 1989, [53], p. 20)systems, the visibility parameters becomevg • .;-'^ = u/ + vm + wn,CVg • SP = w,Cand^dl dm— ^dmdt2 = ^ =  n^1/1 _ 12 _ m2The complex visibility function can now be expressed asdl dinV1 — 12 — rn2For a small region of sky to be mapped, (V1 — 12 — rn2 — 1)w P.-:, 0; consequently,this part of the complex exponential can be removed from the integrand. With thisV (u , v, w) = I I A(1, rn)I (i , no e-i2iqui+vm+w(v 1-12 -m2 -1))00Chapter 1. Introduction to Aperture Synthesis^ 8NFigure 1.4: Earth Rotation Aperture Synthesis (from Fomalont 1974, [22], p. 258)assumption, the three-dimensional problem has been reduced to two dimensions. Thetwo-dimensional complex visibility function isV(u,v) . if . A(1, n)iv, rn)e-iziqui+vm) dl dm.^(1.10)Measuring the complex visibility function at one point in u, v space, which is a func-tion of the projected baseline of one interferometer pair, is equivalent to measuring theamplitude and phase of one of the Fourier components of the brightness distribution. Asthe Earth rotates, the u, v components of the projected baselines are constantly changing,tracing out tracks in the u, v plane; figure 1.4, from Fomalont (1974, [22]), shows thiseffect from the perspective of the source being observed. As each antenna pair tracesout an elliptical u, v track with the minor and major axes determined by the antennaseparation and the source declination, multiple Fourier components of the brightness dis-tribution can be measured. The width of a track is determined by the spatial-frequencyresponse of an interferometer system. Only 12-hour observations are needed for eachChapter 1. Introduction to Aperture Synthesis^ 9u, v track because the visibility function is hermitian3, or more simply, in 12 hours, eachantenna pair has been interchanged. If the brightness distribution does not change withtime, the antennas can be moved so that different Fourier components of the bright-ness distribution can be measured on different days; the frequency-sampling theoremdefines the minimum sampling interval in u, v space required to completely determinethe weighted brightness distribution, A(1, rn)I (1 , m), in the deconvolution process. Lowspatial-frequency visibilities give information about the extended, broad structure of theobserved radio source, while high spatial-frequency visibilities give information about itsfine structure.1.3 Recovering the Brightness DistributionWith the aperture synthesis technique, the complex visibilities are measured directlyby the telescope. Determining the complex visibility function allows one to take theinverse two-dimensional Fourier transform in order to recover the observed brightnessdistribution, 1(1, m). In most cases, the u, v plane is undersampled, which is equivalentto having an unfilled aperture. This process then becomes more difficult because thecomplex visibility function is not completely determined for the inverse Fourier transform,according to the frequency-sampling theorem.This problem can be solved by introducing a weighting function g(u, v); for uniformweighting, the values are 1 or 0, depending on whether that particular u, v point wassampled or not. The Fourier transform of this weighting function gives the synthesizedor dirty beam asiqui+g(i,m). c ff°3 g(u, v) ei2^vm) du dv , (1.11) 3Since the brightness distribution is a real function, its Fourier transform must be hermitian; that is,V(—u, —v) = V*(u, v). This means that only 12-hour, rather than 24-hour, observations are required tofill in an elliptical track in the u, v plane.Chapter 1. Introduction to Aperture Synthesis^ 10with C being a constant. The "apparent" brightness distribution i*(/, m) can then beexpressed in the equation.1* (1, m) = {1(1, m)A(1, m)} * (l, m) cx g V (u, v)g(u, v)e'21r(ul+vni) du dv. .^(1.12)coThe "apparent" brightness distribution /*(/, m), called the dirty map, is the truebrightness distribution 1(1, m) weighted by the antenna pattern A(1, m), and convolvedwith the dirty beam g (l, in). Deconvolution procedures, such as CLEAN and the Maxi-mum Entropy Method (MEM), are used to extract the true brightness distribution fromthe dirty map.Chapter 2Scientific Motivation: Measuring the S-component2.1 Solar Radio EmissionThe Sun's close location to the Earth has given it a special role among cosmic radiosources; observations of the radio Sun have been ongoing since World War II when thesignals were first received and mistaken for a new kind of jamming device. The discoverywas made in 1942 by Hey, but he did not publish the results, for security reasons, until1946. Also in 1942, Southworth, of Bell Telephone Laboratories, discovered the steadythermal emission from the Sun at centimeter wavelengths. Despite these investigations,the first published report on radio emission from the Sun was made by Reber in 1944. In1946, the importance of continuous monitoring of the Sun's radio emission was recognized;the main progress at this time was made by centers in Australia, Great Britain, andCanada. The National Research Council of Canada's solar flux patrol has been measuringand distributing the 10.7 cm solar flux' since 1946; the 10.7 cm data used in this thesiswas taken from this database.The solar atmosphere can be divided into three main layers: the photosphere, thechromosphere, and the corona. Figure 2.5 (Lang 1992, [37]) shows the temperatureand density variations in these different layers. Almost all of the Sun's visible emissionoriginates in an optically-thick layer called the photosphere; the negative hydrogen ions'1The correct term is solar flux density, but the term solar flux is common usage among solar as-tronomers; in this thesis, radio flux densities are referred to as radio fluxes. All other uses of the termflux follow the standard definition of some quantity emitted from, or passing through, a surface per unittime.2A negative hydrogen ion is created when a hydrogen atom captures and temporarily holds a passingelectron; this negative hydrogen ion can absorb visible light and dissociate into a hydrogen atom and afree electron again.11Chapter 2. Scientific Motivation: Measuring the S-component^ 12Figure 2.5: Temperature and Density Variations in the Solar Atmosphere (from Lang1992, [37], p. 105)in this dense stratum give rise to the absorption spectrum that is characteristic of moststars. Within the photosphere, the temperature falls from around 6000 K just abovethe convective zone, to about 4000 K at the temperature minimum Tmin, at the heightwhere the photosphere merges with the chromosphere. The chromosphere is considerablyless dense than the photosphere and is characterized by an emission, rather than anabsorption, spectrum. At heights of about 2000 to 5000 km above the photosphere, thetemperature rises from 104 K in the chromosphere, to 106 K in the corona, while thedensity drops by more than two orders of magnitude. The majority of the temperatureincrease and density decrease occur within a thin "layer" between the chromosphere andthe corona called the transition region; there are intrusions of the chromospheric plasmaChapter 2. Scientific Motivation: Measuring the S-component^ 13into the corona, so the transition region is not a well-behaved horizontal interface. Thecorona is the outermost part of the Sun's atmosphere; it consists of a hot, thin plasmaat 106 K with no clear outer boundary.The majority of optical radiation from the Sun originates in the photosphere; radioemission, on the other hand, originates in the chromosphere and the corona. The prop-agation of radio waves depends basically on the index of refraction in these layers; eachvalue of the index of refraction is related to an electron density, and a critical frequencybelow which propagation is impossible. Since electron density falls off as height increases,measuring radio emission at different frequencies is equivalent to probing the structure ofthe solar atmosphere at different heights; we "see" to the level where the plasma becomesoptically thick.According to time scales of variability, solar radio emission can be separated into threemain components: the quiet Sun, the slowly-varying (S-) component, and various typesof burst. The quiet Sun is the steady radiation coming from the whole Sun; its value isdefined as the extrapolated flux that would be observed if no active regions were present.The bursts are transient phenomena occurring on the order of minutes to seconds; theyare intense increases in radiation associated with flares. The S-component is relatedto the emergence, evolution, and decay of active regions as well as the center-to-limbvariations due to solar rotation; it is the arithmetic difference between the active andinactive (or quiet) solar emissions.The S-component spectrum is represented by a solid line in figure 2.6 (Kundu 1965,[33]). The total emission, excluding transient phenomena such as bursts, is the sumof the S-component and quiet Sun curves. At millimeter wavelengths, the quiet Sunspectrum resembles the Planck curve at the chromospheric temperature of 104 K; at meterwavelengths, one is "looking" at the corona at 106 K. In between these two extremes, inthe cm-dm wavelength range, there is the transition between the chromosphere and theChapter 2. Scientific Motivation: Measuring the S-component^ 14Figure 2.6: S-component Spectrum (from Kundu 1965, [33], p. 169)corona. It is in this region that the S-component curve has its maximum value at around11 cm, the wavelength where the active and inactive solar emissions differ the most.2.2 Slowly-Varying ComponentThe S-component at centimeter wavelengths originates in the upper chromosphere andlower corona. It comprises contributions from three classes of source: bright sources a fewarcseconds in diameter having brightness temperatures of 106 K, diffuse, weaker sourcesat about 104 K, and a more widely-distributed background component, a thousand or sodegrees warmer than the quiet Sun. Through this "pool" of widely-distributed emission,covering large areas of the Sun in an active latitude belt +400 about the equator, theactive regions emerge, evolve and decay.Chapter 2. Scientific Motivation: Measuring the S-component^ 15The solar atmosphere is a hot, rarified plasma, with a considerable number of freeelectrons. The deflection of electrons with a Maxwellian (thermal) distribution, due totheir passage past "heavy" ions, gives rise to emission of radio waves termed free-free, orbremsstrahlung. Free-free emission indicates that the energy transitions of the electronsare due to "collisions" with heavy ions, where the electrons are not captured, rather thanby transitions to, or from, bound states. Bremsstrahlung by non-thermal electrons is alsoa possibility, but this process is not important in the absence of flares.Gyroresonance emission occurs when electrons are deflected by magnetic fields. Thisemission occurs at low harmonics of the gyrofrequency, which is given byv = 2.8 x B, (2.13)where v is in MHz and B is the magnetic field in Gauss (Kakinuma and Swarup 1962,[31]). For the Sun, with thermal electrons, only the first three harmonics are important(Zheleznyakov 1962, [57]). Higher-energy electrons give rise to gyrosynchrotron emission.When the radiating electrons are relativistic, the spectrum becomes a continuum, and themechanism becomes known as the synchrotron process. Gyroresonance, gyrosynchrotron,and synchrotron emissions are termed thermal or non-thermal depending upon whetheror not the radiating electrons have a thermal (Maxwellian) velocity distribution.Although there is a possibility of non-thermal emission occurring in non-flaring activeregions, the S-component can be assumed to be essentially thermal. Since most of theS-component originates in areas where the average magnetic field strength is not morethan 100 Gauss, radio emissions at frequencies higher than a few hundred megahertz areprobably dominated by the thermal free-free contribution.Kundu (1959, [32]) was the first to suggest a core-halo brightness distribution of activeregions, with measurements made at 3 cm. Further observations have found this compactcore and diffuse halo model at a number of different wavelengths (Pallavicini et al. (1979,Chapter 2. Scientific Motivation: Measuring the S-component^ 16[39]) at 2.8 cm, Felli et al. (1981, [19]) at 6 cm, and Chiuderi-Drago et al. (1982, [10])at 2, 6 and 20 cm); the very bright cores of small dimension (20") are imbedded inextended halos of lower brightness (Felli et al. (1975, [21]) at 10 GHz and 17 GHz).The centimetric emission from compact cores is usually due to gyroresonance, and has abrightness temperature of up to 106 K. The diffuse halo is believed to be due to free-freeemission, with a brightness temperature of the order of 104 K. The core and halo arecospatial with the core associated with the sunspot, and the halo associated with the morediffuse plage3. The compact cores have emissions that are highly variable and stronglypolarized, with the strong magnetic fields taking an active role in the emission mechanism.The ambient magnetic fields around the diffuse halos are too weak to cause significantcontributions from gyroresonance; they are, however, strong enough to create densityenhancements in the plasma. The thermal free-free emission is significantly increased bythese density enhancements which have been called coronal condensations. At 21 cm, thecore-halo brightness distribution becomes more suspect since the existence of the cores isquestionable at this wavelength. Chiuderi-Drago et al. (1977, [11]) found that the peaktemperatures at 21 cm do not seem to be correlated with sunspots, and that polarizationis negligible all over the active regions; they conclude that at 21 cm, the active regiondistribution is different from what is observed at shorter wavelengths.This core-halo brightness distribution of active regions is a bit of a misnomer since itimplies that the bright core is always spatially associated with the weaker halo, and thatthe emission mechanisms are the same. The core emission may be thermal as the haloemission is, but it will likely be gyroresonance, not bremsstrahlung. Compact sourceshave also been observed that are not spatially associated with the strong magnetic fieldsof sunspots (Gaizauskas and Tapping (1980, [23]), Felli et al. (1981, [19]), Webb et3Plages are bright patches in the solar chromosphere that are at a higher temperature than theirsurroundings; they occur in areas where there are enhancements of the relatively weak magnetic fields.Chapter 2. Scientific Motivation: Measuring the S-component^ 17al. (1983, [55]), Willson and Lang (1987, [56]), and Gaizauskas and Tapping (1988,[24])). For these sources, unreasonably high thermal temperatures are required to givethe observed radiation; non-thermal mechanisms are then required. For flaring activeregions, the disruptive action of the magnetic fields and plasma instabilities can acceleratethe electrons to very high speeds, so the intensities of these bright, compact sources canbe explained in terms of gyrosynchrotron emission. For non-flaring active regions, theproblem becomes more difficult since there seems to be no accelerating mechanism forthe electrons. Tapping (1993, [51]) has provided one solution involving potential dropswhich are amplified by associated flux tube' motions; these motions are able to producelarge enough potential differences to accelerate the electrons to the required speeds.Active regions are not independent but tend to coexist in associated groups calledcomplexes of activity (Bumba and Howard 1965, [8]). Gaizauskas et al. (1983, [25])reported the existence of large-scale patterns in the distribution of solar active regions inlongitude, latitude, and time, during cycle 215 by analyzing magnetograms. Castenmilleret al. (1986, [9]) also looked at large-scale magnetic structures and found sequences ofsunspot groups that appear within a small area on the solar sphere, and that last formany months; they found that at least three quarters of these groups of active regions, orsunspot nests, appeared in real, and not chance, clusters. Castenmiller and Gaizauskas'sunspot nests, or nests of activity, are defined by the restrictions on the proximity andcontinuity of the active regions within the nests.The nests of activity examined by Gaizauskas et al. (1983, [25]) were found to besituated in active latitude belts; these nests were regularly spaced around these activelatitude belts in bands of alternating magnetic polarity', indicating a wavelike pattern in4Solar magnetic fields are not uniformly distributed over the solar surface but, instead, are concen-trated into discrete flux tubes.5 Cycle 21 was the eleven-year solar cycle spanning 1975 to 1986.6The magnetic polarity is an indication of the direction of the magnetic field.Chapter 2. Scientific Motivation: Measuring the S-component^ 181945^1950^1955^1960^1965^1970^1975^1980^1985^1990^1995YEAR OF OBSERVATIONFigure 2.7: Monthly Means of the 10.7 cm Solar Fluxlongitude. The nests usually form within 1 month and live for 3 to 6 solar rotations, withnew injections of magnetic flux being manifest in a sequence of emerging active regionsin the same belt of activity. Castenmiller et al. (1986, [9]) estimated that at least 30%of sunspots are contained in nests of activity; within the nests, there is an equal balanceof positive and negative flux, and the total level of magnetic flux is sustained within afactor of 2 during its lifetime (Gaizauskas et al. 1983, [25]).The total amount of magnetic flux within a nest varies slowly compared with theevolution of its active region members; the variations due to the dynamics of individualactive regions are over-ridden by the large number of elements within the nest. Theresulting magnetic flux variations of the nest reflect the average level of activity of itsmembers. Due to the strong relationship between the magnetic fields and the coronalChapter 2. Scientific Motivation: Measuring the S-component^ 19emissions, the centimetric flux from a nest also varies over the evolutionary time scalesof the nest, rather than the individual active regions. (Tapping 1987, [49]).This "smoothing" effect produces an overall stable time variation of the S-component.The S-component solar cycle variation of 11 years is shown in figure 2.7; the solar fluxeswere measured at 10.7 cm and are given in solar flux units7. The solar cycle is closely as-sociated with the dynamics of these nests of activity. Despite all the emission mechanismscontributing to the S-component, at centimetric wavelengths, it is dominated by ther-mal free-free emission; Tapping and DeTracey (1990, [52]) reproduced the S-componentspectrum shown in figure 2.6 with a simple thermal free-free emission model for solaractivity.2.3 Widely-Distributed Background EmissionAs an active region disperses, part of the flux expands, weakens, and flows to formand contribute to the large-scale magnetic pattern (Howard and LaBonte 1981, [30]);the magnetic field elements break away from active regions and cluster at the edges ofthe chromospheric network8, probably due to supergranular9 flow (Bumba and Howard1965, [7] and Zirin 1988, [58]). These accumulated fields make up the enhanced magneticnetwork. This enhanced magnetic network exists in the active latitude belts and makesup the "pool" of magnetic flux in which active regions form and decay. High-resolutionstudies indicate that the supergranulation is observable at 6 cm (Kundu et al. 1979, [36]and Erskine and Kundu 1982, [17]). Since the supergranulation extends at least to theheight of the 6 cm emission, any emission chromospheric in origin will certainly have a71 solar flux unit (sfu) = 10-22Wm-2Hz-1.8The chromospherac network is a large-scale cellular pattern in the solar chromosphere that coincideswith the underlying supergranulation.9Supergranulation is a network of large-scale^30,000 km dimension) convective cells in the solarphotosphere.Chapter 2. Scientific Motivation: Measuring the S-component^ 20contribution to the S-component from these network elements (Tapping 1987, [49]). Thisenhanced magnetic network is probably the agent giving rise to the widely-distributedbackground alluded to earlier; these weak magnetic fields are only strong enough to causeincreased thermal free-free emission via density enhancements in the corona.The widely-distributed background has been identified in one-dimensional scans of thesolar disk made with the Algonquin Radio Observatory (ARO) 32-element interferometerat 10.7 cm (Tapping 1987, [49] and 1990, [52]). Tapping suggests that the backgroundcannot be explained by a "weak source" tail to the strong source distribution. Thisrelatively weak emission, which covers a large area of the solar surface, is comparable inmagnitude to the active region contribution to the total integrated flux at 10.7 cm.Single-antenna measurements of the Sun's total radio emission at a wide range ofwavelengths have been ongoing since the late 1940's; the Solar-Geophysical Data promptreports currently catalogue this data in a monthly manual. This data is useful forstudying the S-component variations on different time scales and frequencies. Unfor-tunately, single-antenna data cannot be used effectively to study the widely-distributedbackground, since this extended component is combined with the compact and diffusesource contributions. The one-dimensional 10.7 cm ARO scans can be used, but theseparation of the emission into background and sources is still difficult. Full-disk mapsof the Sun are the best way of studying this widely-distributed background.The DRAO Synthesis Telescope is very suitable for these studies; its wide field andgood resolution allow full-disk solar maps of the Sun at 21 cm to be made, that showthe active regions, widely-distributed background, and quiet Sun. Observations done byTapping (Tapping 1987, [49], 1990, [52], and 1993, [50]) at 2.8 and 10.7 cm indicate thatthe widely-distributed background should be quite strong at 21 cm. Full-disk maps wouldprovide new insight into the origin, evolution, and distribution of this widely-distributedbackground.Chapter 3Solar Mapping with Synthesis Telescopes3.1 Difficulties with Solar SynthesisThere are many problems associated with imaging the Sun with aperture synthesis tele-scopes, unless they have been designed with solar observations in mind. The receiversand data logging systems are generally designed for imaging weak sources, and the con-trol and imaging systems are designed for tracking sources fixed to the celestial sphere.The Sun, on the other hand, is a high intensity radio source which moves significantlyagainst the celestial sphere during the course of a 12-hour observation, and it rotates.The aperture synthesis technique assumes that the source being imaged has a constantbrightness distribution over the course of the observation. Solar rotation and the evo-lution of the solar brightness distribution restrict synthesis observations to one day; theresulting u, v coverage is sparse. The severity of this problem depends on which synthesistelescope is being used; telescopes with a large number of antennas, or telescopes withantennas distributed in both East-West and North-South lines, can obtain sufficient u, vcoverage in less than day, while other smaller telescopes cannot.3.2 Imaging the Sun with Other Synthesis TelescopesSynthesis telescopes have been used for high-resolution studies of the Sun at a widerange of wavelengths. Studies of active regions and solar bursts have been numerouswhile the study of the widely-distributed background has been relatively ignored. This21Chapter 3. Solar Mapping with Synthesis Telescopes^ 22section is an overview of two important synthesis telescopes that have been used for solarimaging, the Very Large Array (VLA) and the Westerbork Synthesis Radio Telescope(WSRT), and their potential for full-disk solar mapping for the purpose of studying thewidely-distributed background.The VLA is able to produce undisputably the best synthesis images of the Sun atcentimeter wavelengths. The large number of antennas (27) operating at multiple fre-quency bands, combined with the technique of bandwidth synthesis', allows the telescopeto obtain considerable u, v coverage in a short period of time; this is ideal for a variablesource such as the Sun. Bastian (1989, [3]) has produced high-resolution solar images at21 cm with a dynamic range exceeding 300:1 in just 4 hrs using these techniques; thisdynamic range is extremely high by solar standards. Unfortunately, the field of view ofthe VLA at 21 cm, to half power, is only 30', which is approximately the size of the solardisk; consequently, the solar disk cannot be imaged without significant attenuation at thelimb. Also, in order to measure the quiet Sun and the widely-distributed background,single-antenna measurements are needed to "fill in the hole" in the u, v plane where VLAmeasurements cannot be made. This adds the constraint that a suitable single antennabe available at the chosen observing time; for a single map of the Sun, this is not aproblem, but for a long-term study it could be.The WSRT has also been modified to image the Sun (Bregman and Felli 1976, [5]).The twelve-antenna East-West interferometer can make full-disk solar maps at 21 cmwith a resolution better than 0.5'. This telescope produces good images of active regionsin a 12-hour synthesis (Bregman and Felli 1976, [5] and Chiuderi-Drago et al. 1977, [11]).The WSRT suffers from the same problem as the VLA in that its field of view is about 36'to half power, which is only slightly larger than the size of the solar disk; consequently,'Since the baseline coordinates u, v are proportional to the observing frequency v, one can effectivelychange the baseline by changing v; this technique is called bandwidth synthesis.PolarizationContinuum BandwidthSystem TemperatureField Size (to 20% response)Synthesized beam (E/W x N/S)rms noise level, map center:brightness temperatureflux densityleft + right circular (Stokes I)30 MHz80K2.6°1.0' x 1.0' csc 560 sin 8 mK0.28 mJy/beamChapter 3. Solar Mapping with Synthesis Telescopes^ 23Table 3.1: DRAO SST 1420 MHz Continuum System Parametersemission originating near the solar limb is suppressed by the antenna pattern, makingany study of the widely-distributed background difficult.3.3 Imaging the Sun with the DRAO Synthesis TelescopeThe Dominion Radio Astrophysical Observatory (DRAO) Spectroscopic Synthesis Tele-scope (SST) (Roger et al. 1973, [42]) is located in Penticton, British Columbia, Canada;figure 3.8 shows a side-view of this telescope. The DRAO SST is a wide-field aperturesynthesis telescope which operates simultaneously in continuum bands at 408 MHz (74cm-A) and 1420 MHz (21 cm-A), and in 128 channels on the spectral line of atomic hy-drogen at 21 cm. The solar imaging discussed in this thesis used only the 1420 MHzcontinuum capability. Table 3.1 shows the 1420 MHz parameters for this telescope. At1420 MHz, this telescope has a resolution of 1.0' x 1.0' csc S (E/W x N/S), where 6 isthe declination of the source being imaged, and a field of view of 2.6° to 20% responseof the bore-sight sensitivity.This telescope uses the Earth's rotation to trace out elliptical tracks in u, v space.It consists of seven 9 m paraboloids on a 600 m East-West track; four of the antennasare stationary and three are movable along this precision rail track to stations spaced4.3 m apart. This allows visibilities to be made for 140 baselines, from 12.9 m to 604.3Chapter 3. Solar Mapping with Synthesis Telescopes^ 24m, with twelve moves of these three antennas. In the normal mode of operation, thesource is observed for 12 hours at each of these antenna configurations to produce a fullysampled u, v plane. The interferometer signals are measured in four different frequencybands, (A,B,C,D), each of bandwidth 7.5 MHz, and four different polarization combina-tions, (RR,LL,RL,LR). R denotes right-circular polarization and L denotes left-circularpolarization; LR and RL are the cross-hand products. Total intensity maps, Stokes I,use only the RR and LL polarization products.The DRAO SST solves some of the problems associated with imaging the Sun witha synthesis telescope; it is unique in its ability to map a large region of sky with highresolution at 1420 MHz. It is well suited for studying the distribution and evolution of thewidely-distributed background; the large field of view allows the whole Sun to be mappedwith no significant attenuation of any parts of the solar disk. The arcminute resolutionis adequate since it is comparable with the size of the active regions; besides, any higherresolution could be degraded to this value because of solar rotation effects (Alissandrakiset al. 1992, [2]). Even though the DRAO SST has a relatively small number of antennas,it does have antenna configurations that will give a reasonable combination of high andlow spatial-frequency information in a one-day observation. Consequently, data from theDRAO SST can be used to make solar maps without the addition of data from othertelescopes; this is convenient for long-term studies of the widely-distributed background.Chapter 3. Solar Mapping with Synthesis Telescopes^ 25Figure 3.8: The DRAO Synthesis TelescopeChapter 4Baseline Optimization and Solar SimulationsAt the initial stages of the project, it was not known whether usable solar images couldbe made with the DRAO SST. In order to evaluate the feasibility of doing actual solarobservations, software was used to simulate observing the Sun with this telescope; theDRAO programs ptsrcs and ph2 were modified for this purpose. The u, v coverage result-ing from a 12-hour observation with one configuration of the DRAO antennas is sparse;this configuration, which corresponds to 21 baselines, must be chosen carefully in orderto optimize this sparse u, v coverage. For this telescope, some baselines are repeated andu, v coverage is lost. With only 21 baselines available for a solar observation, any extraredundancy in the baselines would be unacceptable.Table 4.2 indicates the possible station locations of each of the seven antennas, withasterisks marking the three movable antennas whose positions are to be optimized. Theantenna stations are measured relative to an arbitrary, but consistent position near thecenter of the array. There are many closely related criteria that can be used to determinewhich configuration of the SST antennas is optimum for solar observations. A well-placed set of baseline sample points on the solar visibility function is the most importantconsideration. Antenna configurations that sample the solar visibility function well tendto produce "good" dirty beams and uniform u, v coverage; these two criteria are used as aguide to find antenna configurations that adequately sample the solar visibility function.These two tests are not conclusive in finding appropriate antenna configurations sincethey contain no information about the structure of the Sun. Computer programs were26Chapter 4. Baseline Optimization and Solar Simulations^ 27Antenna Number Possible Stationsin units of 4.29 m1 732 58-70*3 46-58*4 34-46*5 16 —357 —71Table 4.2: DRAO SST Antenna Positionswritten to find the antenna configurations with the "best" dirty beam and the mostuniform u, v coverage, with the added constraint of minimum redundancy; these antennaconfigurations were then tested for how well they sample the solar visibility function.The simulation software was used as a final test to confirm that these SST antennaconfigurations were suitable for solar imaging.4.1 DRAO SST Dirty Beam PatternsThe configuration of the seven antennas determines the dirty beam of the telescope.The dirty map produced by the SST is the solar brightness distribution, weighted bythe antenna pattern, and convolved with this dirty beam; the CLEANing process canonly partially separate the brightness distribution from the dirty map, so optimizing the"shape" of the dirty beam is desirable. A "good" dirty beam will have a sharp, or thin,main lobe, and small sidelobes. An antenna configuration with such a dirty beam wouldprobably sample the solar visibility function well.The width of the main lobe is determined by the largest baseline of the telescope,which is fixed by the Antenna 1 and 7 positions; the sizes of the sidelobes, on the otherhand, vary from configuration to configuration. A criterion for "minimizing" the sidelobesof the dirty beam must be chosen. Since the main lobe for different antenna configurationsChapter 4. Baseline Optimization and Solar Simulations^ 28Figure 4.9: DRAO SST Dirty Beam Patternsis approximately the same, the relative values of the integral over the dirty beam is anindicator of the sidelobe level. The smaller the integral, the smaller the sidelobes, andthe better the dirty beam. The integral is taken from —0.25° to 0.25'; the solar disk is0.5° in diameter, so this is the angle over which the dirty beam will effect the solar image.A simple computer program simulating seven isotropic radiators on a East-West linewas used to calculate dirty beam patterns; the program cycles through all the possi-ble antenna configurations to find those with the smallest integrals. These dirty beampatterns are equivalent to East-West cross-sections of two-dimensional DRAO SST dirtybeams for the same antenna configurations. The best stations for the three movableantennas according to this criterion are 6.4 54 45; with an added constraint of minimumredundancy, a good set of antenna stations would be 64 53 45. Figure 4.9 shows the dirtyChapter 4. Baseline Optimization and Solar Simulations^ 29beam pattern for this configuration, calculated by the computer program; notice that thesidelobes are quite small compared with the main lobe. Superimposed on the same figure,for comparison purposes, is another dirty beam pattern for antenna configuration 65 4934. Even though its two sidelobes adjacent to the main lobe are slightly smaller than the64 53 45 sidelobes, the third sidelobe is much larger, making the 64 53 45 configurationmore desirable.4.2 Uniform u, v CoverageSince only one configuration of the seven antennas can be used for solar imaging, abalance must be made between which parts of the u, v plane are to be sampled. The shortbaselines give information about the extended structure (quiet Sun and widely-distributedbackground), while the longer baselines give information about the fine details on thesolar disk (active regions). In studying the S-component, recovering all this informationis important; consequently, uniform u, v coverage is probably optimum.The most uniform u, v coverage is found by minimizing the expression20E(baselinei+i — baselinei)2.^ (4.14)i=iThe optimum stations for the three movable antennas according to this criterion, withthe added constraint of minimum redundancy, are 62 53 45.4.3 Sampling the Solar Visibility FunctionThe antenna configurations determined by the uniform u, v coverage (62 53 45) and thedirty beam pattern (64 53 45) tests are quite similar, which shows that the tests areconsistent with each other. These antenna configurations were then checked to see howwell they sample the solar visibility function, which is the Fourier transform of the solar0.90.8En0.7• 0.6•_0.50▪ 0.4• 0.3CA•^0.20.1000—0.1—0 264,53,4565,49,34Zero Spacing *FluxMain LobeFirst Negative SidelobeChapter 4. Baseline Optimization and Solar Simulations^ 3010^20^30^40^50^60BASELINE in 4.29 m incrementsFigure 4.10: Solar Visibility Functiondisk; the active regions and the widely-distributed background are not included in thismodel. The quiet solar disk is extended emission at low intensity, so it is the hardestcomponent of the solar radio brightness distribution to recover; if the solar visibilityfunction is sampled well enough, the solar disk will be "measured", and represented in theresulting solar image. The solar visibility function and the sample points for configuration64 53 45 are shown in figure 4.10; the visibility sample points for configuration 65 49 34are also shown in the figure, for comparison. The 64 53 45 configuration does an adequatejob of sampling the solar visibility function whereas the 65 49 34 configuration leaves theimportant lower baselines of the solar visibility function undersampled. Note that bothconfigurations have at least one sample point on the first negative sidelobe of the solarvisibility function, but the main lobe is left unsampled. The zero spacing flux or totalChapter 4. Baseline Optimization and Solar Simulations^ 31power, marked with the star in the figure, can be included through the imaging software;this is discussed in chapter 7. The 64 53.45 and 62 53.45 configurations similarly samplethe solar visibility function; since the dirty beam will be better for the CLEAN processwith the 64 53 45 configuration, it is favored.4.4 Solar SimulationsThe next stage in the baseline optimization process was to use simulation software to testthe antenna configurations recommended in the previous sections; this helped confirmwhether an antenna configuration would actually produce a good image when observingthe Sun. The DRAO programs ptsrcs and ph2 were modified for use with model solardata.The ptsrcs program creates a set of "observed" visibilities from an input model solarbrightness distribution and set of baselines for SST. The generated visibilities are thosethat would have been observed with the DRAO Synthesis Telescope if the solar modelwere the only source of emission in the field of view. For these simulations, the Sunis assumed to be stationary with respect to the celestial sphere, and have a constantbrightness distribution.The files from ptsrcs are then processed through ph2, the map-making portion of thestandard DRAO data reduction software. The program ph2 takes the visibility files andthe set of baselines used, and creates a dirty map and beam. The dirty map and beam arethen processed through a deconvolution algorithm, such as CLEAN or MEM, to obtainthe model solar brightness distribution.Figure 4.11 shows the model solar map, dirty simulation map, and CLEAN simulationmap for the 64 53 45 configuration. The solar model was "observed" for 12 hours at thedeclination 16° 58' 34.99", which is the average declination of the Sun during the AugustZ 16° 58' 35"0017° 18 35"16° 38' 35"MODEL Solar Map0Z 16° 58' 35"C.)16° 38' 35"17° 18' 35"DIRTY Simulation Map-3■■Z 16° 58' 35"0C.)16° 38' 35"17° 18' 35"CLEAN Simulation MapChapter 4. Baseline Optimization and Solar Simulations^ 329h 01" 21°^9" 00" 01°^Eth 58" 41°RIGHT ASCENSION (J2000)9h 01" 21'^9" 00" 01'^81' 58" 41°RIGHT ASCENSION (J2000)9' 01" 21'^9h Or^ 8h 58" 41°RIGHT ASCENSION (J2000)Figure 4.11: Simulation Maps for Antenna Configuration 64 53 45Chapter 4. Baseline Optimization and Solar Simulations^ 334, 1992 observation (shown in table 5.3). The model solar map consists of a variety ofpoint sources and extended structure superimposed on a uniform disk with a Gaussiandecay at the limb. This combination represents the quiet Sun, active regions, and widely-distributed background. All these components of the model solar brightness distributionare represented well in the CLEAN map; the standard deviation in the pixel to pixelvariations between the CLEAN and model maps is about 2%.Many different antenna configurations were tried in the simulation process. Generally,if the solar visibility function was adequately sampled, the "observed" image would re-produce the model solar brightness distribution well. If an antenna configuration yieldednon-uniform u, v coverage, the simulated solar image would show a poor reproductionof the model map with the CLEAN process never adequately removing the effects ofthe dirty beam. The simulation process also served as a test-bed for investigating theperformance of the deconvolution procedures CLEAN and MEM, on extracting the solarbrightness distribution from a dirty map; chapter 7 discusses these programs in detail.All the antenna configurations discussed in the previous sections, 64 53 45, 62 5345 and 65 49 34, produced good images in the simulation process. When the antennaconfiguration for July 16, 1992 was chosen, some of the tests discussed in this chapterwere still being developed, but the simulation software was already available; the 65 4934 configuration produced good simulation results, so it was chosen for the first observingday. It was later discovered through tests concerning how well the solar visibility functionis sampled, that this configuration was not the best for solar imaging. The 64 53 45configuration, which has a similar distribution of sample points on the solar visibilityfunction to the 62 53 45 configuration, but a "better" dirty beam, was used for ten of theeleven observing days discussed in this thesis. In fact, there is no clear optimum antennaconfiguration of the SST for doing solar observations, but instead a class of antennaconfigurations that have a "good" distribution of sample points on the solar visibilityChapter 4. Baseline Optimization and Solar Simulations^ 34function.The main lobe of the solar visibility function is unsampled for the antenna config-urations discussed; since most of the Sun's power is located in the extended structure,sampling the main lobe and first negative sidelobe is very important. The present viewis that the best configurations of the antennas for solar synthesis would be configurationswith at least one sample on the main lobe, and a uniform distribution of sample pointson the rest of the solar visibility function; these configurations would probably give goodresults in both the dirty beam pattern test, and the uniform u, v coverage test.Chapter 5Solar ObservationsThis chapter discusses the hardware and software modifications of the DRAO SST thatwere required for solar observing, and the specifications for the observing runs in thesummers of 1992 and 1993.5.1 Hardware ModificationsThe only hardware modification necessary to prepare the SST for solar observations wasthe introduction of 20 dB attenuators, and their corresponding switches, into the 1420MHz receivers, just after the pre-amplifiers; figure A.25 shows the location of two of theattenuators, one for each circular polarization channel of the antenna. The solar signalsreceived by the SST are on the order of 105 Janskysl; the average signal received by theSST from other radio sources is on the order of mJy to Jy. The Automatic Gain Control(AGC) circuits are designed to maintain a constant signal level input to the processingelectronics; unfortunately, the AGC circuits are not constructed to handle the very strongsolar signals. Consequently, 20 dB attenuators are needed to reduce the signals to anacceptable level. The attenuators and their associated switches have been constructed tobe phase constant; that is, the phase shifts introduced by all attenuator-switch systemsare the same. This means that the correlated signal for each antenna pair is the same asif there were no attenuators present.11 Jansky (Jy) = 10 - 26Wm -2Hz- 1.35Chapter 5. Solar Observations^ 365.2 Software ModificationsThe DRAO SST normally observes sources that are fixed to the celestial sphere; sincethe Sun moves significantly in right ascension and declination during the observation,a new observing technique utilizing the existing system was used. There are effectivelythree beams to be steered by the SST control system: the physical antenna beam, thefringe pattern, and the delay beam. The DRAO SST antennas have equatorial mounts,which have one axis (polar axis) parallel to the Earth's rotation axis, and a second axis(declination axis) at right angles to it.The antennas usually track a source at the sidereal rate; the hour angle (HA) motor,driven about the polar axis, simply compensates for the Earth's rotation during theobservation. To get the physical antenna beam to track the Sun in HA, the HA tosidereal (tracking rate) ratio on the antenna-control-system computer was changed from1.0 to 0.9972696; this takes into account the fact that the solar day is 3 minutes and 56seconds longer than the sidereal day. The measured visibilities describe the motion of theSun against the fringe pattern. The faster this relative motion, the greater the requiredsampling speed; tracking the Sun with the fringe pattern reduces this sampling speedsignificantly. This fringe pattern also has a sinc-function envelope, due to the broadbandresponse of the telescope, called the delay beam. It is desirable to observe the fringes inthe vicinity of the maximum of this envelope, where the fringe amplitudes are the greatest;this is done by tracking the Sun with the delay beam. The fringe pattern and delay beamtracking are both implemented by the SST fringe-controller computer. The ODELAYand OPHASE parameters specify the delay beam and fringe pattern tracking rates; theyare changed from 4.1666667 x 10-6 deg/millisecond to 4.1552899 x 10-6 deg/millisecond.Again, the conversion factor between these two rates is simply the ratio of the durationof solar and sidereal days.Chapter 5. Solar Observations^ 37The declination (DEC) motors usually do not run during the observation; they areonly used for an initial pointing at the beginning of the run. There is no easy way ofadding a slow DEC scan during the observation. Two different options were consideredto deal with this problem; both are discussed by Bregman and Felli (1976, [5]) regardingthe use of the WSRT as a solar instrument. The first is to break up the observationinto many short segments, perhaps 1 hour, over which the Sun's declination will nothave changed significantly. The data from these different mini-observations would thenbe combined to form a complete 12-hour synthesis. This option has many drawbacksbecause it is computationally difficult within the structure of the existing data reductionsoftware, and because time would be lost between each of these mini-observations whilethe telescope was preparing for the next one. The option we have chosen is to trackthe Sun in HA, point the antennas at the average declination of the Sun during theobservation, and let the Sun drift in the field of view; the effects of the declinationsmearing could then be eliminated later in software. Since the field of view of the SSTat 1420 MHz is 2.6° to 20% response, and the Sun's average change in declination in 12hours, over the summer months, is about 5', all of the solar disk will remain close to thepeak of the main lobe of the antenna pattern.5.3 Calibration ProcedureThe calibration of the DRAO SST is obtained by observing a known radio source for ashort time before and/or after the main observation; this data is used to gain and phasecalibrate the visibilities. With the introduction of the attenuators, the calibration for thesolar observations becomes difficult. It was originally thought that Cygnus A would beused as the calibrator, and that it could be observed with the attenuators switched in,since it is a strong source of 1500 Jy. The attenuators have an accuracy of ±0.3 dB; if theChapter 5. Solar Observations^ 38calibrator was observed with attenuators switched in, the effects of any gain deviationsof the attenuators from their specified value of 20 dB2, on the solar visibilities, wouldbe taken care of in the standard calibration procedure. Unfortunately, the attenuatorsdecreased the Cygnus A signal too much and the AGC circuits could not operate on thevery small input signal.The only other alternative was to observe a calibrator with the attenuators switchedout, and then observe the Sun with the attenuators switched in. The gain deviationsof the attenuators would then be dealt with in software, at a later stage; with all theattenuator-switch systems having the same phase introduced, the standard phase cali-bration is valid whether the attenuators are used for the calibrator observation or not.The calibrator used for June 29, 1993 was 3C147; all the other observations used 3C48.The calibrator was observed for half-an-hour, usually preceding the solar observation.5.4 Solar Observing SpecificationsTable 5.3 shows the parameters for the 1992 and 1993 solar observing sessions. Theantenna configurations are those that were discussed in chapter 4; they were chosento produce adequate sampling of the solar visibility function in a one-day synthesis.Note that the first (A) band of the 1420 MHz continuum correlator was not workingfor three days in August, and that the observations for two days in 1992, July 23 andAugust 3, were less than 12 hours due to technical problems. Since the switching of theattenuators is at present done manually, the observer is required to be on-site when thesolar observation begins and ends.Each time an observing day approached in the summer of 1993, the question arose as2The gain of one of these attenuators should technically be referred to as -20 dB, not 20 dB; in thisthesis, the minus sign is left out, because it is implied, since the electrical component being discussed isan attenuator.Chapter 5. Solar Observations^ 39Day ObservationDuration (hrs)AntennaPositionsSunDeclination'CommentsJuly 16, 1992 12.00 65 49 34 21° 12' 02.79" NoneJuly 23, 1992 11.10 64 53 45 19° 50' 41.42" NoneAugust 1,1992 12.00 64 53 45 17° 46' 01.74" No A bandAugust 2,1992 12.00 64 53 45 17° 30' 29.70" No A bandAugust 3,1992 11.15 64 53 45 17° 14' 00.77" No A bandAugust 4,1992 12.00 64 53 45 16° 58' 34.99" NoneJune 22, 1993 12.00 64 53 45 23° 25' 50.70" NoneJune 23, 1993 12.00 64 53 45 23° 24' 59.97" NoneJune 24, 1993 12.00 64 53 45 23° 23' 44.56" NoneJune 29, 1993 12.00 64 53 45 23° 11' 20.23" NoneJune 30, 1993 12.00 64 53 45 23° 07' 36.86" NoneTable 5.3: Solar Observing Specificationsto whether to use the antenna configuration that was known to be good from 1992 maps,or to try out a new antenna configuration. It was decided that for the observing sessionin the summer of 1993, the same 64 53 45 configuration would be used, so comparablesolar images could be obtained and used in the scientific portion of this thesis. There isno clear optimum configuration of the antennas for solar observing, but instead a class ofantenna configurations that produce good solar images. The solar observing sessions arecurrently limited to the summer months; only during this period is the Sun high enoughin declination to obtain adequate resolution, and the days long enough to get a full 12-hour synthesis. The Sun's declination motion over a 12-hour synthesis is also smallestaround June 21, the summer solstice; this minimizes the declination drift correction thatmust be applied after the observation. Also, when the Sun is too low in declination,geometrical "shadowing" of the antennas can occur, when one antenna physically blocksthe solar signal from another antenna.3The Sun's declination changes with time, so the values in the table are the average declinations of theSun during the observations; they are also the declinations that the antennas are pointed at throughouteach solar observation. To be consistent with the figures in this thesis, the declinations are given inJ(Julian year)2000 coordinates.Chapter 5. Solar Observations^ 405.5 Using the DRAO 26 m AntennaThe DRAO 26 m Antenna was used for the solar observations in both 1992 and 1993 as asolar burst monitor; the Sun was observed simultaneously with the DRAO SST for each12-hour observing period. 20 dB attenuators were required in the front-end of the 26meter antenna to bring the solar signals down to an acceptable level for the electronics.The Sun was tracked and the total power was logged in left- and right-linear polarizations;the resolution of the 26 meter Antenna at 1420 MHz is about 0.5°, so most of the solarpower was measured. This data was used, along with DRAO solar flux patrol total powermeasurements at 10.7 cm for the same period, to edit the SST solar visibilities of anyshort-lived bursts that occurred during the observation.Chapter 6DRAO SST Solar Map CorrectionsThe solar visibility files produced by the observations were processed through the stan-dard DRAO software to produce a dirty solar map; figure 6.12 shows the uncorrecteddirty map for August 4, 1992. The image has been gain and phase calibrated using itscalibrator data; chapter 7 describes the software used for this image processing.The right ascension (RA) and declination (DEC) coordinates have a special meaningin these maps; the DEC of the map center is the average declination of the Sun overthe 12-hour observation, and the RA of the map center is the right ascension of theSun at the start of the observation. After the solar motion corrections discussed in thischapter, the solar disk center will coincide with the map center'. The distances fromthese central RA and DEC coordinates will be the offsets of different solar features fromthe solar disk center, averaged to the middle of the observation. The "size" of the Sunin RA coordinates changes with its declination; the figures in this thesis compensate forthis effect, so circular brightness distributions will appear circular in the figures with aRA/DEC grid.The dirty image looks like the Sun, but is affected strongly by artifacts; before anyscience can be done with this solar image, the artifacts must be removed. Synthesizingthe Sun while it is in motion in the field of view is equivalent to taking a picture of amoving object with a camera: the resulting image is smeared. The simulation software,1 An error in the original modification of the fringe pattern and delay beam tracking for solar obser-vations produced an offset of the solar disk center from the map center for the 1992 images; hence, forthese maps, the RA of the solar disk center is not actually equal to the RA of the Sun at the start ofthe observation.41Chapter 6. DRAO SST Solar Map Corrections^ 42Figure 6.12: Uncorrected Dirty Solar Mapdescribed in chapter 4, was used to simulate observing a source moving in the field ofview. Different motions produced different artifacts in the simulation map. In this way,the artifacts due to declination drift and solar rotation were identified. Algorithms basedon the shift theorem of Fourier analysis were then used to correct the visibilities for thesemotions. The visibilities were also corrected for the gain deviations of the attenuatorsfrom their listed value. This chapter outlines how the solar imaging problems wereidentified, and how they were corrected.Chapter 6. DRAO SST Solar Map Corrections^ 436.1 Declination DriftThe declination motion of the solar disk produces the most significant artifact that mustbe corrected. The solar tracking is done only in hour angle, not declination. Con-sequently, the Sun is effectively in motion through the field of view of the telescopethroughout the observation. The distance the Sun drifts in declination during the ob-servation depends on what part of the year the observing is done. For the observingsession in 1992, the average declination change over 12 hours was about 7'; for the 1993observing session in June, containing the summer solstice, the average declination changeover 12 hours was only 1'. With a resolution of 1', this motion will be noticeable in theSST maps for the 1992 observing session, and might be noticeable in SST maps for daysin the 1993 observing session.Figure 6.13 shows a contour representation of an uncorrected CLEAN solar map forAugust 4, 1992; the circle is the optical solar disk, shown for reference. The lowest contouris set at the zero level and the highest contour is set at the maximum image value; theother contours represent levels linearly interpolated between these two extremes. Allthe contour plots in this thesis have their contour levels chosen in this way. The Sunmoved about 8' in declination during this observation. The image is very distorted bywhat looks to be a "half ellipse" artifact; all the active regions are smeared out in thisartifact shape. The size of this artifact is about 10'; this roughly agrees with the expectedsize of the declination drift artifact. To confirm that this is indeed due to the drift ofthe Sun in declination during the 12-hour synthesis, the simulation software, ptsrcs andph2, was used to simulate observing a source drifting across the observational field indeclination. The calculated declination drift artifact is also shown in figure 6.13. Theartifact is exaggerated and not to the same scale as the solar map, but it is still identifiedas the "half ellipse" shape that appears in the solar map.Chapter 6. DRAO SST Solar Map Corrections^ 44RIGHT ASCENSION (J2000)Figure 6.13: Uncorrected Solar Map and Declination Drift ArtifactChapter 6. DRAO SST Solar Map Corrections^ 45Once the artifact had been identified as being due to declination drift, a scheme forremoving the artifact was created. The declination of the phase center of the map is theaverage declination of the Sun during the 12-hour observation. During the 12 hours, theSun's disk center has drifted through this point. The declination correction applied tothe complex solar visibilities consists of shifting the solar disk center to the phase centerat all the sampled times; computationally, this is achieved by changing the visibilityphase of the solar disk center to the phase of the map center at each of these times. Thisproduces a set of visibilities that would have been measured if the solar disk had beentracked in both HA and DEC throughout the observation.The shift in the phase of the solar disk center is most easily executed in the frequencydomain on the complex visibility files. The shift theorem gives a relationship betweenspatial locations and Fourier transform phases. The shift theorem of Fourier analysis intwo dimensions states that•F[f(i _ l*, m _ m.)] = if. f(1 l*, m _ mle_i2iqui+.) dl dm = e-i27,-(ui*+.*) F(u, v),-. j ' (6.15)where F(u, v) = ,F[f (1, m)]. Therefore, if the function f (1, m) is located at (/*, m*) atsome time, its Fourier transform has a phase relative to F(u, v), the Fourier transformof the same function located at the map center (1 = 0, m = 0), of —271-(u/* + vm*). Thevisibility function, from chapter 1, isV (u, v) = if Au, mg(i ,  dl dm, (6.16)where u, v are the spatial frequencies in the East and North directions, A(/, m) is theantenna pattern, and 1(1, m) is the brightness distribution.If one assumes that the antenna pattern is approximately constant over the artifactdistance, that is A(/, m);:-..,' A(/ — /*, m — m*), then the shift theorem in equation 6.15 canbe used. This assumption is justified since the antenna pattern only reduces to aboutChapter 6. DRAO SST Solar Map Corrections^ 4699% of its bore-sight sensitivity at a 4' (half of the 8' declination drift) shift away fromthe field center. At the time when the solar brightness distribution 1(1, m) is centered at(1*, m*), the measured visibility becomesV (u , v)* = j. coo A(1, m)I (1 — r,m — m _i2iqui+vm) dl dm (6.17)fro  A(1 — r,m —^— l, in — re)e-121qui+vm) dl dm^(6.18)= e -i21r(u0A-umlv(u, v)^ (6.19)= e-ig5V(u, v).^ (6.20)Therefore, to produce a set of visibilities with the solar disk center always located atthe map center, as if it was properly tracked in HA and DEC, each visibility must becorrected for this extra phase factor 0. From Brouw (1971, [6]), the phase shift 0 canbe expressed in terms of the coordinates of the map phase center (ao, 60) and the solardisk center (asun, &sun); a is the HA and S is the DEC. The phase shift 0 can now beexpressed as271-B= 27(u • 1* + v • m*) = ^ (sin asun cos 6sun — sin a, cos 60),A(6.21)where all the variables, except the declination of the map phase center °to, are a functionof time. B is the baseline being considered and A is the wavelength of the observation.The hour angle of the map phase center a() changes at the solar rate while its dec-lination 60 stays constant at the average declination of the Sun during the observation.The solar disk center hour angle as also changes at the solar rate for the declinationdrift correction. The Sun's declination &sun during the observation can be found accu-rately via a simple ephemeris program; the ephemeris program used is the U.S. NavalObservatory Nautical Almanac Office Interactive Computer Ephemeris (Version 0.50).All coordinates used in the phase shifts are taken in the observational epoch.Chapter 6. DRAO SST Solar Map Corrections^ 47Therefore, to remove the declination drift artifact, the phase correction to be appliediscp = ei2r 14 sin a (cos Ssurt —cos 80 ) (6.22)where a denotes the hour angle for both the solar disk center and the map phase center.Multiplying the visibility function V(u, v) by this correction factor produces a set ofconsistent visibilities, all "measured" with respect to one brightness distribution location.These corrected visibilities produce an unsmeared solar map.Since the field of view of the SST is large, 2.6° to 20% response, the declination driftof 8' centered about the field center did not take the Sun out of the high-sensitivityportion of the field. With the solar limb displaced to about 20' from the field center, the16' solar radius with a 4' declination offset, the antenna pattern was only reduced to 92%of its bore-sight sensitivity.6.2 Solar RotationThere is another solar motion that smears the image, and therefore must be correctedfor: solar rotation. The Sun rotates once about every 27 days, with the rotation ratebeing largest at the equator and decreasing towards the poles; the rotation axis is tiltedperpendicular to the observer by an angle x1i, and "leans" toward the observer with anangle Bo. 4i is the position angle, and B0 is the heliographic latitude of the projectedsolar disk center. The average rotational displacement over 12 hours at the true solardisk center, where the heliographic latitude and longitude are zero, is about 2'. This istwice the East-West resolution of the SST and is noticeable on the DRAO maps.Figure 6.14 shows a contour representation of a CLEAN solar image for August 4, 1992that has been corrected for declination drift in the field. The declination drift correctionhas unsmeared the image, and the disk and active regions are much more recognizable.Chapter 6. DRAO SST Solar Map Corrections^ 48SimulatedSolar RotationArtifact17° 08 35"000CV—).._..,Z 16° 58' 35"0E—.<z-ziciLi.,016° 48' 35"16° 38' 35"9h 00m 41s 9h Or OiS^8h 59m 21s^8h 58m 41sRIGHT ASCENSION (J2000)Figure 6.14: Declination Drift Corrected Solar Map and Solar Rotation ArtifactChapter 6. DRAO SST Solar Map Corrections^ 49The solar disk seems to be reasonably shaped (roughly circular) but the active regions arestill distorted by a "Y" shaped artifact. The simulation software was used to simulateobserving a source moving in the field in both RA and DEC in a manner similar tosolar rotation. The calculated solar rotation artifact is also displayed in figure 6.14. Theartifact is exaggerated and not to the same scale as the solar map; nevertheless, it isidentified as the "Y" shape that is distorting the active regions.The next step was to develop a scheme for removing this artifact. The solar rotationrate is described by the equationdl52 = —dt = A — B sin2 b — C sin4 b deg/day, (6.23)where 1 is the solar longitude and b is the solar latitude. Values of the constants A,B,Chave been found from analyzing the motions of sunspots, coronal holes2, filaments', andmagnetic structures; they are discussed by Zirin (1988, [58]). The values determined frommagnetograms seem to remove the solar rotation artifact the best; this is not surprisingconsidering that the coronal condensations, where the 21 cm emission originates, aredetermined predominately by the magnetic fields branching out of the photosphere. Thevalues for the constants A, B, and C used in the solar rotation corrections are 14.37, 2.30and 1.62, respectively (Snodgrass 1983, [47]).Since the observed solar rotation is equivalent to projected motion on a RA/DECgrid, rotational motion near the solar limb corresponds to smaller RA and DEC changesthan near the solar disk center; every latitude and longitude on the Sun has a differentprojected rotation rate, except for those that are symmetric about the solar equatorand the line of zero heliographic longitude. This makes the task of correcting for solar2 Coronal holes are regions of low density and temperature compared with the surrounding corona;they overlie regions of divergent magnetic fields, and are major contributors to the solar wind.3 Filarnents are regions located in the the upper chromosphere and inner corona, with a higher densityand lower temperature than their surroundings; they are visible as dark absorption features (in certainFraunhofer lines) against the brighter solar disk.Chapter 6. DRAO SST Solar Map Corrections^ 50rotation very difficult. Essentially, any phase factors applied to correct for the rotationmovements of one region will not be appropriate for most others. Doing a rigorous full-disk solar rotation correction would require a complicated iterative scheme that modelsthe sources being corrected. Because the resolution of the DRAO SST is on the order of1', a one-point solar rotation correction works quite well if the reference point is chosento be in the midst of all the regions of interest. The regions closest to this reference pointwill be corrected very well, while regions distant from this reference point will be slightlyover- or under-corrected.In order to correct for the rotational motions of the reference point on the solar disk,its calculatable solar latitude and longitude motion must be transformed to changes ona RA/DEC grid (standard DRAO format). The Sun's "size" in RA coordinates dependson its declination; nevertheless, since the solar rotation corrections are quite small, andthe Sun's declination is not very high (less than 24°), the assumption that the Sun hasthe same diameter in both RA and DEC will not produce any significant errors in thecorrection process. Integration along the motion of the reference point, at a particularlatitude for the observation duration, will be easiest in a coordinate frame in which thesolar equator and the solar rotation axis correspond to coordinate axes; figure 6.15 showsthe required coordinate transformations.The first reference frame P(X, Y, Z) is the apparent coordinate system for solar ro-tation in which Z DEC and Y —RA. The second reference frame P'(X',Y',Z') isthe one in which Z' coincides with the solar rotation axis; this is obtained by a rotationof W about the X axis in the P frame. In the third reference frame P"(X",Y", Z"), theZ" axis coincides with the solar rotation axis and the X" axis coincides with the solarequator; this is obtained by a rotation of Bo about the Y' axis in the P' frame. In theP" frame, solar rotation is simply a displacement along the Y" and X" axes. The knownmotions in the P" frame must be converted to RA and DEC motions in the P frame.Bo = Heliographic.A;^tr,^Latitude of ProjectedSolar CenterX"Chapter 6. DRAO SST Solar Map Corrections^ 51Coordinate Transformation:P to P by arotation of^about XIn P (X,Y,Z) Frame:Z = DECY = —RA^›Y= Position Angleof Rotation AxisCoordinate Transformation:P to P by arotation of Bo about Y'In P" (X",Y",1) Frame:dl/dt =0 where I isthe solar latitudeFigure 6.15: Coordinate Frames for Solar Rotation Correction( X"yl,Z"anddY (6.29)dt = r cos b(cos III cos — sin sin / sin /30)52.Chapter 6. DRAO SST Solar Map Corrections^ 52The coordinate transformation from P to P" iscos Bo sin tif sin Bo — sin Bo cos kli^X=^0^cos tlf^sin 'I'^Ysin Bo — sin Ilf cos Bo cos klf cos Bo^Z 3.^(6.24)The position angle of the rotation axis 111 and the heliographic latitude of the solardisk center Bo are found in the Astronomical Almanac (Hagen and Boksenberg 1991, [26]and 1992, [27]). In the P" frame, Z" = r sin b, Y" = r cos b sin 1, and X" = r cos b cos 1,where b is the solar latitude, 1 is the solar longitude, and r is the solar radius. Thedifferentials in the P" frame are thendZ"dt== o,^ (6.25)dY"^dlr cos b cos /—dtdt (6.26)anddX"^dldt = —r cos b sin lk (6.27)Inverting the 3 by 3 coordinate transformation matrix in equation 6.24, and using thefact that d//dt = Cl in the P" frame, the differentials in the P frame are—dZ r cos b(sin cosl + cos 111 sinlsin B0)11dt(6.28)Integrating the motion throughout the observation, assuming a constant rotation rateSi, and using the middle of the observation as t=0, the RA and DEC differentials arecalculated asdRA(t) = —r cos b cos 111(sin(10 + fit) — sin(10)) — r cos b sin W sin B0(cos(10 + fit) — cos(10))(6.30)Chapter 6. DRAO SST Solar Map Corrections^ 53anddDEC(t) = r cos b sin kli(sin(1, + SR) — sin(10)) — r cos b cos xlf sin Bo(cos(/, + SU) — cos(/o))•(6.31)The phase shifts applied to the visibilities to correct for solar rotation are similar tothe declination drift correction factors; equation 6.21 is used again, in a modified form.This time, the reference point for the solar rotation correction is being shifted relative tothe map phase center, (ao, 80). The phase correction iscio = ei21r 21 (sin(0 e 0 + da) cos(80+d6)—sin ao cos So), (6.32)where da = —dRA and db =dDEC. All the variables in the equation are functions oftime except the map phase center declination 80. The differential displacements of thereference point over the course of the observation are used in the phase correction formulato shift the reference point, at the sampled times, to its location at the middle of theobservation; in this way, a consistent set of visibilities is generated as if solar rotationnever occurred for this point. Multiplying the visibilities by cio effectively shifts the wholeSun by the differentials listed above, relative to the map phase center. Consequently,the quiet solar disk will be compressed in a direction perpendicular to tIf by one or twoarcminutes; this small distortion of the solar disk is overshadowed by the improvementof the shape of the active regions after the correction procedure. The solar image afterthe declination drift and solar rotation corrections represents an "average" solar radiobrightness distribution for the observation.The solar rotation smearing is a maximum at the center of the "true" solar disk,where the heliographic longitude and latitude are zero, and is usually about 2'. If thecenter of the solar disk is chosen as the reference point, the regions on the solar limb,which have no projected smearing, will be overcorrected by 2'. On the other hand, if thereference point is chosen as being halfway between the solar disk center and the solarChapter 6. DRAO SST Solar Map Corrections^ 54limb, the error at that particular latitude will be at most 1', which is the resolution of theSST; this is the standard practice. The errors produced at other latitudes are still lessthan the resolution of the SST. The regions which rotate in and out of the field duringthe observation can never be corrected properly; the reconstruction of the regions on thesolar limb is always questionable.This integration assumes that the tilt angle 'If and the heliographic latitude B0 areconstant during the integration; in fact, both 41 and Bo are changing throughout theobservation. They are taken as the values at the middle of the observation. For theobservational period of 1992, the average Atif over a 12-hour synthesis was approximately0.21°, and the average AB, was approximately 0.04°. The largest errors in RA and DECthat could be produced from assuming that both IF and Bo are constant for a 12-hourobservation during this period, are less than 0.5"; this is much less than the both theresolution of the SST (1') and the DRAO default pixel resolution (20").6.3 Gain Variations Introduced by AttenuatorsFigure 6.16 shows the declination drift and solar rotation corrected CLEAN solar imagefor August 4, 1992. The solar rotation correction has produced an image with roughly-elliptically-shaped active regions; the "Y" shaped artifact has been removed. The finalcorrection to be made to the solar maps does not consist of the removal of an imagingartifact, but instead, a refinement of the gain calibration procedure. The solar complexvisibilities are gain and phase calibrated in phi with the data obtained from observinga calibrator. Since the calibrator was observed without the 20 dB attenuators, the cal-ibration coefficients do not adjust the solar visibilities for any phase or gain variationsintroduced by the attenuators. The attenuators were carefully constructed and testedChapter 6. DRAO SST Solar Map Corrections^ 55Figure 6.16: Declination Drift and Solar Rotation Corrected Solar Mapto ensure that the phases introduced through each attenuator-switch system, on all an-tennas, were the same. Assuming that the phase shift is constant for all antennas, thesignals correlate as if there were no attenuators present, and the phase calibration in phiis still valid.The gains of the attenuators used are 20 ± 0.3 dB. Although stable with time, theattenuators differ slightly from the specified value of 20 dB (1/100), and this can changethe measured flux significantly. A procedure was devised, that uses the autocorrelationvalues from the solar observation and the amplitude calibration coefficients from thecalibrator observation, to eliminate this effect. It produces a set of unbiased complexvisibilities with consistent gain factors on all baselines.For the correlation process, the signals received at each antenna are split into in-phaseChapter 6. DRAO SST Solar Map Corrections^ 56and quadrature channels; the quadrature channel has a 900 phase delay introduced. Thereare four autocorrelation values for each antenna: right- and left-circular polarization forthe in-phase channel, and right- and left-circular polarization for the quadrature channelFor a given polarization, the in-phase and quadrature values differ slightly because ofinequalities in the signal paths, and the different electrical components they pass throughafter the signal is split.The autocorrelation values discussed in this chapter are the average values for the solarobservation. Since the Sun's signal is so strong, it is the only significant contribution tothe system temperature during a solar observation. Hence, the autocorrelation values,for all seven antennas logged during the observation, can be taken as a measure of thetotal power of the Sun at 1420 MHz. The following discussion applies to both right- andleft-circular polarizations. The in-phase autocorrelation value for antenna i is denotedAl„ whereas the quadrature autocorrelation value for antenna i is denoted A. Theseautocorrelation values can be expressed in terms of the uncalibrated total solar powerT, an antenna voltage gain, either gi for the in-phase channel, or gQt for the quadraturechannel, and the attenuator voltage gain a..,atten, • The antenna voltage gains are the gainsof the in-phase and quadrature paths in the antenna system, including the signal pathbefore the signal was split, except for the attenuators. The autocorrelation values can bewritten asT(glig0tteni)2 (6.33)andAQi T(gQi gatteni )2. (6.34)Let us define a new variable A as=^AQi^ (6.35 )Tga2tteniga2ntt^ (6. 36)Chapter 6. DRAO SST Solar Map Corrections^ 57with2^2^2gants = gh gQI (6.37)The variable gant, is defined as the total voltage gain of the antenna system, except forthe attenuators. In phi, the baseline-based coefficients, used to gain and phase calibratethe uncalibrated solar visibilities, are calculated from the antenna-based calibration co-efficients. These values are derived from the calibrator observations with the attenuatorsswitched out. For antenna i, the amplitude component of the antenna-based calibrationcoefficient Ci can be expressed in terms of a voltage calibration factor Rv, and the totalantenna voltage gain gant, asCi = Rvganti • (6.38)The voltage calibration factor Rv is used to change the correlator values from low-levelvoltages to standard DRAO SST units; this factor is independent of which antenna isbeing considered.The autocorrelation factor ..11I is the correlation of the antenna i voltage with itself;the visibility Vixi, on the other hand, is the correlation of the antenna i voltage withthe antenna j voltage. The magnitude of this visibility can be expressed in terms ofthe uncalibrated total solar power T, the antenna i and j total voltage gains, and theantenna i and j attenuator voltage gains as= (6.39)= ganttgant gattenigattenj • (6.40)The phi program scales these visibilities by the calibration coefficients. After phi, themagnitude of the calibrated visibility can be written as1Vixi Ica' =^c, 1 (6.41))2t\—s7gatten,gatten3 L■n=1 gantn )2(E7n=1 gantngattenn(6.48)Chapter 6. DRAO SST Solar Map Corrections^ 58Tgantsgant3gatten,gatten3Rvgantsgant3= Tgatten,gatteniRvThese calibrated visibilities would be the values used to make maps in ph2 if noextra gain calibration was required. The problem is that the attenuator power gainsmay differ from their listed value of 20 dB; this would produce visibilities that are afunction of which attenuators are being used. This dependence can be eliminated from thecalibrated visibilities by an appropriate choice of scaling factor, which is a function of theautocorrelation values and the amplitude components of the phi calibration coefficients.The scaling factor for IV,xj,l,„/ iswith the definitionssixi = V^A; c„fC„f ()(^),A;1/4-.efAef =^(6.44)(6.45)(6.42)(6.43)andEn7--1 Cn Cref =^—^•7(6.46)Substituting values into the Sixi expression yields)2Tgantigattenigantigatten3-Rv2(E: ,-1 gantn) SZX3 -^Ri2santtgant, (ELI. gantngattenn )2(6.47)Applying the scaling factor Six.; to,IVixj1./ givesvi xi ic°a/ = T gattenigattenjRS= gatten gatten (En-7 —1 gantngantn)2T ^3 ^7It'vgattenigatteni(En=i gantj2(6.49)(6.50)Chapter 6. DRAO SST Solar Map Corrections^ 59T / V=^i.1 gantrigatten.  \ 2^ (6.51) - X ) .11,2,^E7n =1 gantnThe T/R2, ratio is the uncalibrated total solar power scaled to standard DRAO units(mJy/beam), and the ratio multiplying it in equation 6.51, consisting of a number ofdifferent gain expressions, is a weighted average of attenuator voltage gains for all anten-nas. This weighted average is assumed to be approximately 1/100 (20dB); any deviationsin the attenuators should be "smoothed out" in this averaging process. After this gaincalibration is done, the magnitudes of the visibilities depend only on the intensity of theSun, and the weighted average of the attenuator gains; they no longer depend on whichattenuators, and hence, which antennas, were being used in the correlation process.This gain calibration procedure increases the dynamic range of the solar images byabout 5%; the accuracy of this correction depends on how close the weighted average ofthe attenuator gains is to 20 dB. Constantly calculating the correction factors for theattenuators assures that if one of the attenuator switches begins to wear out, it can bedetected. Even though this is not very likely, it is an advantage over applying somepredetermined constant correction factor.Chapter 7Solar Data ReductionDRAO has a complete set of data-processing routines to take the raw data from the SSTand produce a calibrated image. When solar observational data was processed throughthese standard programs, an image (such as figure 6.12) was produced that containedmany artifacts specific to solar synthesis. These artifacts and their respective correctionprocedures were discussed in chapter 6. These correction algorithms are combined in auser-friendly program, SUNVIS, that has been integrated into the standard DRAO datareduction software.7.1 DRAO Data Reduction SoftwareThis section describes some of the DRAO programs used in the reduction of SST 1420MHz continuum data, and the format of the data files used at each stage of the processing.This gives the reader an idea of where the SUN VIS program fits in the image-processingprocedure, and what information is used in the correction algorithms. The DRAO com-puting system runs on two types of operating system: UNIX and VMS. The telescopecontrol software and data logging facilities are run on the VMS system, whereas theimage processing and data reduction is done mostly on the UNIX system.The DRAO software consists of a sequence of different programs, run in a varietyof environments, that produce a calibrated radio image from raw SST data. The datais collected, averaged, and partially processed on the VMS system; the data is thentransferred to the UNIX system for the rest of the processing. The main routines on60Chapter 7. Solar Data Reduction^ 61the UNIX system for image processing are dove, phi, ph2, CLEAN, and polarcorr. Theprogram dove (Display Observational Visibilities and Edit program) is used to edit solarbursts and "bad" data out of the visibility files. The program phi takes visibility filesand calibrates them with data from the 3C48 or 3C147 observation. The program ph2takes the calibrated visibility files produced by phi, and creates a dirty map and beam.At this stage, the dirty map and beam can be run through a deconvolution procedure,such as CLEAN or MEM (Maximum Entropy method), to extract the solar brightnessdistribution from the dirty map. Finally, the solar image is processed through polarcorrto correct for the SST antenna pattern.SST DATA ON VMS: The SST 1420 MHz continuum data from the telescope is col-lected and streamed into direct-access files; the data is sampled and stored se-quentially at 5.26 s intervals. These files contain the following: solar visibilities,calibrator data, and autocorrelation values from the solar observation. This datais collected in four frequency bands (A,B,C,D) and four polarization combinations(RR,LL,RL,LR). Other files include the observational spacings and parameters,and an error log. Only the RR and LL polarization products are used to make theintensity, Stokes I, maps discussed in this thesis.SST DATA ON UNIX: When the files are transferred to the UNIX system, the solarvisibility data is transposed to the —6 hours to 6 hours time window in HA, andaveraged to 90 s intervals. Calibration coefficients are calculated from the calibra-tor observation during the transfer process. The transferred autocorrelation filescontain averages over the whole solar observation. A survey database of all theobservational parameters is also created.Chapter 7. Solar Data Reduction^ 627.2 SUNVIS: Solar Visibility Correction ProgramThe SUNVIS program has three main subroutines to correct for declination drift, solarrotation, and attenuator gain variations; the correction algorithms are discussed in detailin chapter 6. For consistency, all calculated sidereal times and hour angles are taken fromthe DRAO survey database, and all coordinates are taken in the observational epoch.The corrections are executed on the uncalibrated visibility files just prior to phi, onthe UNIX system. It would be more "accurate" to correct the unaveraged visibility fileson the VMS system but this was not done for two reasons. Firstly, all the data processingis likely to be done on the UNIX system in the future, so the solar correction softwareshould be consistent with this progression. Secondly, and most importantly, the errorsproduced by doing the corrections on the averaged, rather than the unaveraged, visibilityfiles are much smaller than the resolution of the SST. For a total declination change of10', and a total solar rotational displacement of the reference point of 2', over a 12-hourobservation, the maximum averaging errors for the declination drift and solar rotationcorrections are about 1.2" and 0.2", respectively. The SUN VIS program is very effectiveat removing the solar synthesis artifacts, as can be seen from the figures in chapter 6.The code was written in FORCE, a variation of FORTRAN 77, in order to be consis-tent with the other DRAO data-processing software, which is written in this language.The SUNVIS program also follows the standard DRAO conventions in terms of formatand documentation. The software accesses the standard DRAO library of functions, andthe survey database, which contains information that is needed for the corrections. TheSUNVIS program operates in a user-friendly fashion and creates a detailed history file ofall the solar corrections performed on a set of observational data. This history file canbe accessed within SUNVIS, and a log of past solar corrections can be produced.Chapter 7. Solar Data Reduction^ 637.3 Deconvolution ProceduresThe Sun's bright, disk-shaped brightness distribution is very different from most radiosources mapped with the SST; consequently, special consideration had to be given tothe type of deconvolution procedure used. This a priori knowledge provides a power-ful boundary condition for selecting appropriate brightness distribution solutions; this isparticularly valuable for the sparse u, v data obtained. The two main deconvolution pro-cedures used in radio astronomy today are CLEAN and MEM; both of these procedureswere used with SST solar data.7.3.1 DRAO CLEANThe CLEAN algorithm is a solution to the problem of deconvolving a synthesis telescopedirty beam from its dirty image; it is an iterative procedure used to determine the solarbrightness distribution, by assuming that the region being mapped consists of pointsources in an otherwise empty field of view (118gbom 1974, [29]). Mathematically, it isequivalent to a least-squares fit of sine functions to the visibility data (Schwarz 1978,[46]). For solar imaging, the point source assumption is very poor because of the Sun'sextended structure; the standard CLEAN algorithm does not work well on extendedstructure and tends to produce stripes or corrugations in the map-making process. TheDRAO CLEAN algorithm is a modified version that works well on extended structureby removing source components in groups, rather than individually; it is a hybrid of theSTEER algorithm (Steer, Dewdney, and Ito 1984, [48]), which works well on extendedstructure, and the CLARK algorithm (Clark 1980, [12]), which works well on strong pointsources. The a priori knowledge about the shape of the solar brightness distribution alsoallows a powerful limited support constraint to be imposed in the CLEAN process byrestricting the CLEAN program to finding components inside a small window whichChapter 7. Solar Data Reduction^ 64surrounds the solar disk. A careful selection of the DRAO CLEAN parameters allowsthe program to converge on a map with a good representation of the solar disk, activeregions, and widely-distributed background.The DRAO CLEAN parameters suitable for solar data were found partly by commonsense, and partly by trial-and-error in the simulation process. The CLEAN parametersused for the maps included in this thesis are listed below; the parameters not mentionedhave their standard default values within the program. When the listed parametersare specified as shown below, the DRAO CLEAN algorithm consistently converges on areasonable solar map.DRAO CLEAN Parameters for Solar Data: L Maximum number of iterations: 1000The standard default is 100 but the Sun's extended emission requires a significantincrease of this value to ensure convergence. The average number of iterations fora solar image is around 400.2.Fraction of initial peak to switch to STEER CLEAN: 1.00This starts the CLEAN algorithm in STEER mode right away, bypassing theCLARK algorithm The CLARK algorithm is good with strong point sources whilethe STEER algorithm is good with extended structure.3. CLEAN gain for STEER algorithm: 0.1The standard default is 0.25 but a value of 0.1 is more suitable for extended struc-ture.4. Badly-conditioned data check parameter: 5Convergence check parameter: 8These parameters establish the maximum number of iterations that will executedChapter 7. Solar Data Reduction^ 65while the CLEAN program tries, unsuccessfully, to determine critical values tobe used in the iterative process. These parameters are both increased from 2, tothe values listed, to allow more flexibility in the program execution; because ofthe sparse u, v obtained, the dirty image is quite poor, and the extra flexibility isneeded if the program is going to find a good solution.5.Maximum number of components: 20000The standard value of 10000 is increased to 20000 to take into account the extendedstructure in the dirty image.6.Negative additions to components will be allowedNegative CLEAN components will not be allowedNot allowing negative CLEAN components causes the number of iterations to in-crease, but it also allows a better solution to be found.7. CLEAN window: small box around solar diskSpecifying a small CLEAN window around the solar disk restricts the program tofind CLEAN components within this area; this limited support constraint worksvery well in reconstructing the solar brightness distribution.7.3.2 AIPS MEMThe Maximum Entropy Method (MEM) treats the deconvolution problem differently;it selects the map that has the maximum entropy, but is still consistent with the givenincomplete u, v data. The MEM is derived from the basic axioms of Bayesian statistics.The MEM enables the user to introduce a priori information about the sky brightnessdistribution very effectively as the default model in the entropy expression. The defaultmodel is taken to be a uniform solar disk on a "zero" background level, having the sameChapter 7. Solar Data Reduction^ 66integrated flux as single-antenna data from the Solar-Geophysical Data prompt reports(Coffey 1992, [13], 1992, [14] and 1993, [15]); this constraint is quite powerful in "bringingout" the solar disk. The AIPS (Astronomical Image Processing System) MEM programVTESS uses a simple Newton-Raphson approach to optimize the relative entropy of theimage, subject to constraints upon the rms error and total integrated flux of the image(Cornwell and Evans 1985, [16]). The relative entropy expression used isS = - bi ln( 2), (7.52)where bi is the value at pixel i in the reconstructed MEM map, and rni is the value atpixel i in the default map; the sum is taken over all the map pixels. The rms error is afunction of the deviations between the MEM map and the default map. The resultingMEM image is the map that is most noncommittal about data that is not present.Figure 7.17 shows the DRAO CLEAN and AIPS MEM final solar maps for August4, 1992 and June 23, 1993. For August 4, the structure is nearly identical in bothmaps; both CLEAN and MEM have reconstructed the solar disk, active regions, andwidely-distributed background well. The fluxes in the two maps are slightly differentbecause the flux chosen for the total flux constraint in the MEM was taken from theSolar-Geophysical Data prompt reports (Coffey 1992, [13], 1992, [14] and 1993, [15]),rather than the integrated flux from the DRAO CLEAN map for the same day; table 8.4shows that these fluxes are slightly different. Obtaining such similar maps from differentmethods instills confidence in their validity.The DRAO CLEAN map for June 23 has a "patchy" solar disk. The AIPS MEMroutine was used to "include" the solar disk via the default solar map and a constrainton the total power. As the AIPS MEM algorithm tried to match the map flux to thespecified total flux, the default uniform disk was used to "fill" in areas of weak emissionaround the North and South poles; the resulting MEM map looks like the CLEAN mapChapter 7. Solar Data Reduction^ 67DRAO CLEAN Solar Mapfor August 4, 1992AIPS MEM Solar Mapfor August 4, 1992 ,-, 17° 08 35"CNI16° 58 35"00 16° 48' 35"16° 38' 35"17° 08' 35"cDCN16° 58' 35"0.7]0 16° 48' 35"16° 38 35"9h Or 41° 9" 00" 01° 8h 59" 21° 8" 58r" 41°RIGHT ASCENSION (J2000)DRAO CLEAN Solar Mapfor June 23, 19939" Or 41° 9" 00" 01° 8h 59r" 21' Elh 58r" 41°RIGHT ASCENSION (J2000)AIPS MEM Solar Mapfor June 23, 1993,-, 23° 35'Z 23° 25'01-=23° 15'23° 35(Z 23° 2501710 23° 1523°05,-^ -^23°05,-^ -6" 10" 55° 6" 10" 15° 6" Or 35° 6" 08" 55° 6" 08" 15° 6" 10r" 55° 6" 10" 15° 6" Or 35' 6" 08r" 55° 6" 08" 15°RIGHT ASCENSION (J2000) RIGHT ASCENSION (J2000)Figure 7.17: Final Solar Maps Determined by CLEAN and MEMChapter 7. Solar Data Reduction^ 68with the missing parts of the solar disk added in. This is a way of including the zerospacing flux, shown in the solar visibility function plot of figure 4.10. The CLEAN mapsare probably more reliable than the MEM maps since the MEM uniform disk defaultmaps are reasonable, but not very accurate, approximations of the actual solar brightnessdistributions.Chapter 8Properties of the Final MapsThis thesis includes eleven DRAO solar synthesis maps: six from the summer of 1992,and five from the summer of 1993; all the solar maps are displayed in appendix B. Amontage of solar maps is shown in figure 8.18. These maps were created by the standardDRAO image-processing software and the solar correction program, SUNVIS. Because ofthe unique nature of observing the Sun with a synthesis telescope, solar map propertiesdiffer from those maps of other radio sources made using the same instrument.8.1 Dynamic RangeThe dynamic range of an image is defined as "the ratio of the highest to the lowestbrightness levels of reliable detail" (Thompson 1986, [54]); in other words, the peak levelto artifact level ratio. The dynamic range of a standard 1420 MHz synthesis image madewith the DRAO SST is of the order 300-400:1; the dynamic range of a SST solar image istypically 100:1. The difference between the intensity of the "quiet" portions of the Sunand the active regions can be very significant, so a large dynamic range is needed to avoidsuppressing the solar disk; this problem will vary with the level of solar activity. Thefactors that usually limit dynamic range in SST maps are sensitivity, calibration errors,and system noise. In the solar case, these are overshadowed by problems associated withsource variability and sparse u, v coverage.The whole process of aperture synthesis is built on the assumption that the sourcebeing imaged has a constant brightness distribution over the course of the observation;69,—, 17° 40' 30—)Z 17° 30' 300LL.117° 20' 3017° 10' 30August 2, 1992August 1, 199217° 56 02"Z 17a 46' 02"0-7JuJ oCI 17- 36' 02'17° 26' 0223° 35' 51"CNIZ 23° 25' 51"0-7JLU0 23° 15' 51"23° 35C•J23° 250LUo 23° 15Chapter 8. Properties of the Final Maps^ 70Bh 49' 06° Bh 48m 26° 8" 47m 46° Eih 47r° 06°^8h 52m 58° Bh 52' 18° Eih 51r° 38° Bh 50m 58°RIGHT ASCENSION (32000) RIGHT ASCENSION (32000)June 22, 1993^June 23, 199323° 05' 51" ^I^I^I^I^I^—6" Or 46° 6" Or 06' 6" 05r° 26' foh 04r° 46° 6" 04r° 06'RIGHT ASCENSION (32000)23° 05^I —6" 10r° 55° 6" 10r° 15° 6" 09' 35° 6h Or 55° 6" Or 15°RIGHT ASCENSION (J2000)Figure 8.18: Montage of CLEAN Final Solar MapsChapter 8. Properties of the Final Maps^ 71this is not true of the Sun. The active regions vary in intensity on the order of monthsto days; more transient phenomenon such as solar bursts vary on the order of minutesto seconds. These bursts can be edited out of the visibility files, but the evolution ofthe active regions and the widely-distributed background cannot This evolution of thebrightness distribution over the 12-hour synthesis causes a discontinuity in the visibilitiesat the beginning and end of the run; for a source of constant strength, the visibilities 12hours apart are complex conjugates. This discontinuity is equivalent to a small "spike" ofinterference in the u, v plane at one particular hour angle; it creates a set of parallel low-level grating lines, which raise the artifact level, and reduce the dynamic range. Simplescaling factors have been used to match up the visibilities; unfortunately, this produceserrors in the resulting image because only the variable portion of the solar brightnessdistribution in the visibilities should be scaled, and this is difficult to do. The mapsincluded in this thesis do not have a visibility discontinuity correction applied.Solar variability also poses a problem for the solar motion corrections implemented bySUNVIS. If the solar brightness distribution is varying in intensity during the synthesis,the corrections will not "unsmear" the image properly; portions of the artifacts willremain. This problem applies especially to the regions on the solar limb, that rotate inand out of view during the synthesis; the intensity levels for these regions are not veryreliably known, and represent some average value for the observation.The sparse u, v coverage obtained from a 12-hour synthesis, with one configurationof the seven antennas, also limits the dynamic range. The "hole" at the center of theu, v plane means that some of the power emitted by the Sun at large angular scalescould be lost. The standard DRAO observations have a large number of redundantbaselines which increase the dynamic range of the resulting images; for the solar maps,only a minimum amount of redundancy is obtained. The DRAO SST solar images endup having a dynamic range < 100:1. Under "good" imaging conditions, with only a fewChapter 8. Properties of the Final Maps^ 72short-lived bursts, and fairly constant active region and background emission, this shouldbe enough to recover all the components of the solar brightness distribution.8.2 Map ResolutionThe resolution of the SST under normal operating conditions is 1.0' x 1.0' csc (E/Wx N/S), where 6 is the declination of the radio source being observed. In the summer,the Sun reaches its highest declination of about 23.5° on June 21, the summer solstice;consequently, the resolution for solar mapping is always less than or equal to 1.0' x 2.51'.The average size of an active region is a couple of arcminutes, so the resolution undergood declination conditions is quite acceptable.The declination drift and solar rotation corrections only leave spatial errors that aresmaller than the SST resolution; unfortunately, this is only true if the solar brightnessdistribution is constant during the synthesis. If it is not, the "smearing" artifacts leftbehind after the corrections can reduce this resolution; this reduction will depend on theevolutionary time scales of the brightness distribution compared with the extent of thespatial corrections. This problem would be more severe for the declination drift correctionbecause it operates over a larger distance than the solar rotation correction. The regionson the solar limb that rotate in and out of view during the synthesis cannot be accuratelycorrected for declination drift or solar rotation; the resolution of these regions is degradedsomewhat. The good representations of the solar brightness distributions shown in themaps of figure 8.18 suggest that no significant degradation in resolution is occurring,except, perhaps, on the solar limb.Chapter 8. Properties of the Final Maps^ 73Day Prompt Report DRAO Observation Percentage Missing FluxJuly 16, 1992 103 96 7%July 23, 1992 69 61 12%August 1,1992 72 76 —5%August 2,1992 79 82 —3%August 3,1992 88 85 4%August 4,1992 86 87 —1%June 22, 1993 72 64 11%June 23, 1993 73 63 14%June 24, 1993 85 74 13%June 29, 1993 91 89 2%June 30, 1993 90 76 16%Table 8.4: 1420 MHz Total Fluxes (in sfu)8.3 Total FluxesThe total integrated fluxes for the DRAO CLEAN maps are listed in table 8.4; these fluxeshave been corrected for the SST antenna pattern, and adjusted to 1 Astronomical Unit.A SUNVIS corrected solar map and its total flux represent an "average" solar brightnessdistribution and total power for the observation. These fluxes are calculated using theDRAO program view; the error in an integrated flux is predominately determined byhow this value was calculated. Repeating the measurement process about ten times foreach map in view yields an average standard deviation of about 2% of the total flux.The view program integrates the flux above a fitted background level; consequently, thiscalculation takes into account the fact that the solar brightness distribution in a SSTsolar map is located in a negative bowl'. An indicator of the extent to which the solarbrightness distribution has been recovered is provided by the difference between the totalflux in the map, and the flux measured at the same wavelength by a small, single-antennaradiometer, which is given by the Solar-Geophysical Data prompt reports (Coffey 1992,'Since each DRAO SST map is missing the zero spacing flux, the sum of all its map values mustequal zero; this produces a negative bowl in the map to balance the positive solar emission.Chapter 8. Properties of the Final Maps^ 74[13], 1992, [14] and 1993, [15]). The percentage missing flux seems to have a wide spreadin values from 16% on June 30, 1993 to —5% on August 1, 1992; this negative missing fluxindicates that the combined errors of the solar map-making process, and the integratedflux calculations, can reach at least 5% of the total flux.The solar image for July 16, 1992 was obtained with the 65 49 34 configuration, whichis not as good as the 64 53 45 configuration used for the other solar observations, accord-ing to the criteria discussed in chapter 4; consequently, its "patchy" solar disk, shownin figure B.26, and the 7% missing flux are expected. There seems to be a systematicdifference between the other 1992 and 1993 missing fluxes, even though the observationshad the same 64 53 45 configuration. The 1992 images appear to have recovered mostof the flux while the 1993 images have not, even though the declination of the Sun washigher during this period.The 1993 maps suggest that the recovery of the solar disk is probably dependent onthe level and distribution of solar activity; the configuration of antennas that was able togive a good reconstruction of the quiet Sun in 1992, was unable to in 1993. This can beexplained by figure 4.10, which shows that how well the first negative sidelobe is sampled,varies strongly with small changes in the solar brightness distribution. Different levels ofsolar activity may be able "shift" the solar visibility function, leaving the first negativesidelobe badly sampled; this is believed to be the explanation of this difference betweenthe 1992 and 1993 maps.Figure 8.19 shows a plot of two visibility amplitude curves as a function of baseline.These curves are the RR and LL polarization product visibilities on each baseline, av-eraged over their respective observing period, and added to obtained a measure of thevisibility "power" or amplitude. The curves show a smooth, exponential-like decrease inamplitude with increasing baseline; there do not appear to be any calibration problemsfor the relative amplitudes of the visibilities, except perhaps, at baseline 36. There seemsAugust 1-4.1992June 22-24,1993 - - -Chapter 8. Properties of the Final Maps^ 75110000100000900008000070000600005000040000 -30000 -20000 -10000 ---- - _ -010^20^30^40^50^60^70^80^90^100 110 120 130 140BASELINE in 4.29 m incrementsFigure 8.19: Averaged Visibility Amplitude Vs. Baselineto be a small "kink" in the June 1993 visibility curve at baseline 36, which correspondsto an angular scale of 2.3'; this is the approximate size of both the active regions, andthe North-South resolution of the SST for this observing period. Figure 8.19 also showshow most of the solar power is located in the lower baselines, at large spatial scales;Alissandrakis et al. (1992, [2]) produced a similar plot for observations made with theSiberian Solar Radio Telescope. The August 1992 and June 1993 solar maps, some ofwhich are displayed in figure 8.18, show that the Sun's activity level and intensity weresimilar for both time periods. The visibility curves for these two periods show simi-lar variations except at the lower baselines, when the June 1993 observations "missed"measuring portions of the Sun's extended structure.The visibility amplitude curves in figure 8.19 would have the same "shape" as theChapter 8. Properties of the Final Maps^ 76square of the solar visibility function (visibility amplitude) shown in figure 4.10, if the"true" solar brightness distribution consisted of only the quiet solar disk; the actual solarbrightness distribution also has active regions and the widely-distributed background,which cover a wide range of spatial scales, so the observed visibility amplitude curves aresmooth and exponential-like, as shown in figure 8.19.8.4 Brightness Distribution ReconstructionThe Sun was quite active during the observations of 1992 and 1993; the maps in figure 8.18show around 6 active regions on the solar disk on any day. The SUNVIS program hasdone a good job of "unsmearing" the active regions; they have a shape resembling thesynthesized beam, indicating that the sources are not quite resolved. The active regionson the solar limb are distorted due to projection and uncorrectable solar rotation effects.The DRAO SST solar maps show that there is a lot of structure in the widely-distributed background that is superimposed on the solar disk. This background emissionis intimately associated with active regions and is almost exclusively located in the +40°active latitude belt centered around the solar equator. The success of the reconstructionof the solar disk for the 1992 and 1993 maps was partially dependent on the observingperiod, with 1992 maps displaying a better solar disk than the 1993 maps. There issignificant limb brightening on the East and West limbs for all the solar maps; conversely,there does not seem to be much activity at the North and South poles, which is expectedfor this stage of the solar cycle.Chapter 9S-component Emission Budget9.1 Budget DescriptionSolar radio emission can be separated into the quiet Sun, S-component, and various typesof burst; the S-component can be further be separated into diffuse and compact sources,and the widely-distributed background. This "budget" procedure, if done quantitatively,reveals the percentage of flux that is coming from each of these components and hence,their relative importance to the solar radio emission.Since the solar bursts are edited out of the visibility data before the SST maps aremade, the emission exceeding the quiet Sun is the S-component. With the arcminute res-olution of the SST, the arcsecond-diameter compact bright sources cannot be separatedfrom the diffuse sources, and they are combined under the label of "active region emis-sion"; the widely-distributed background is then the difference between the S-componentand the active region contribution.To budget the fluxes, the SST maps must be separated into their various emission con-tributions. The active region emission originates from the compact and diffuse sources,while the background emission originates in the widely-distributed structure superim-posed on the quiet solar disk in the active latitude belt, centered on the equator. TheDRAO program view was used to integrate over all the active regions on each solar map,above a fitted background level; the sum of these contributions, for each solar map, isthe active region flux. The remaining flux is the background and the quiet Sun. Defining77Percentage of Total FluxQuiet 56S-component 44Background 28Active Regions 16Percentage of S-component FluxBackgroundActive Regions6238Chapter 9. S-component Emission Budget^ 78Table 9.5: 1420 MHz Flux Budget Averagesthe active region boundaries for the flux calculation is quite subjective, so only a "rough"budget can be produced. Table 9.5 shows the budget numbers averaged for the 1992 and1993 DRAO solar maps.9.2 Flux Budget at 1420 MHzAs table 8.4 indicates, most of the solar observations have "missed" some of the solar fluxbecause of incomplete spatial-frequency sampling. Undersampling the lower baselines re-sults in low-level extended structure being missed; some of the DRAO SST images shownin appendix A, with "patchy" solar disks, support this hypothesis. The S-componentbudget assumes that all the missing flux comes from an incomplete recovery of the quietSun. In fact, some of the missing flux almost certainly comes from the background, andperhaps even the active regions. Nevertheless, this assumption is quite good since thequiet Sun is the extended structure at the lowest emission level. The quiet sun at 21 cmwas found, by interpolation over the solar minima in 1964 and 1976, to be 46 sfu; thedata used comes from the Aeronomica Acta (Nicolet and Bossy 1984, [38]).The S-component at 21 cm contributes, on average, slightly less than half (44%) ofthe total emission for the days observed. This percentage is dependent on the part of thesolar cycle in which the observations are taken. Near solar maximum, the S-componentChapter 9. S-component Emission Budget^ 79 110105100959085807570656055504540353025201510iOBSERVATIONAL DAYFigure 9.20: Total, Active Region, and Background Flux Variationsmakes a significant contribution to the total flux; at solar minimum, there is little orno S-component contribution and the total flux will be essentially the quiet Sun. Solarmaximum occurred in 1991, so both 1992 and 1993 are still quite high on the descentdown from this peak, as can be seen by the large number of active regions in both the1992 and 1993 maps. The average active region and background contributions to thetotal flux are 16% and 28%, respectively; their average contributions to the S-componentare 38% and 62%, respectively. Since the S-component budget is quite sensitive to theidentification of active region boundaries, the only conclusion that can be drawn is thatthe active region and background contributions are both significant at 21 cm.Figure 9.20 shows the variation of the total, active region, and background flux forthe observational days. Note that the observational days in figure 9.20 are sequential,Chapter 9. S-component Emission Budget^ 80but not consecutive; the 1992 observations span a nineteen-day period, and the 1993observations span an eight-day period. From this limited data set, there seems to be afairly strong correlation between the active region and background activity. The activeregion and background contributions seem to vary with time in a similar manner; this isnot surprising since groups of active regions, or nests of activity, live, evolve, and decayin this background "pool" of flux. Tapping (1987, [49]) produced a similar plot at 10.7cm; again, the total, active region, and background emissions had similar behaviors withtime. Analyzing the active region and background variations over a solar cycle will allowone to start to derive conclusions about the flux transfer mechanisms between activeregions and the widely-distributed background.A S-component budget done at 10.7 cm (Tapping 1987, [49] and 1990, [52]) and 2.8cm (Tapping 1993, [50]) for days in November, 1981, indicates that the background andactive region contributions are approximately equal at these wavelengths. This result,combined with the budget done in this chapter, suggests that for wavelengths between2.8 and 21 cm, which is the range over which the S-component has its largest values,the background and active region contributions are comparable. This shows that whenstudying the S-component at centimeter wavelengths, it is important to consider thewidely-distributed background, as well as the active regions.Chapter 10Solar Radio and Magnetic ActivitySolar magnetic fields have a strong influence on the intensity of radio emission at centime-ter wavelengths; they support density enhancements, or coronal condensations, that giverise to the majority of the S-component by thermal free-free (bremsstrahlung) emission.It is tempting to speculate whether there is a simple relationship between the magneticflux and the radio flux, and if a magnetic field map, such as a magnetogram, could beused to predict the "radio structures" in the corona.10.1 Magnetic Fields in the Solar AtmosphereMost activity on the Sun can be linked to the presence of magnetic fields. Since theplasma in the outer solar atmosphere generally has a large conductivity, because of itshigh degree of ionization, magnetic flux is transported along with material motion withinthe plasma; the field lines behave as if they were "frozen" to the moving fluid. Thisvery close association between the magnetic fields and the fluid properties extends fromthe photosphere, where the magnetic fields are usually measured, to the corona, wherethe radio emission originates. In the corona, the plasma-magnetic field association isdominated by the magnetic field behavior.Magnetic fields are important for the emission mechanisms associated with all thedifferent S-component contributions. In compact sources, thermal gyroresonance is usu-ally produced when electrons gyrate about the magnetic field lines; in diffuse sources andthe widely-distributed background, magnetic fields act to create coronal condensations,81Chapter 10. Solar Radio and Magnetic Activity^ 82which significantly increase the observed thermal free-free emission. The flux budget inchapter 9 indicates that the contributions to the S-component from active regions andthe widely-distributed background are comparable. With all the background emissionand part of the active region emission being thermal bremsstrahlung, one concludes thatthe S-component is predominately thermal free-free emission at 21 cm.Felli et al. (1977, [20]) compared photospheric magnetic fields from Kitt Peak mag-netograms with 2.8 cm emission, and found many relationships between the differentstructures. Active regions are all magnetic bipoles, with the two areas of opposite mag-netic polarity usually being of different size and strength. The compact, high brightnesstemperature sources correspond to the magnetic polarity where the field is strongest andmost concentrated, while the diffuse sources, with lower brightness temperatures, overlayneutral lines' of the magnetic field. A third component is only rarely present over the lesslocalized and opposite polarity. Kundu and Alissandrakis (1984, [35]) observed strongsources associated with neutral lines which were characterized by having their oppositepolarities close to each other, implying a high magnetic field gradient.10.2 DRAO SST Solar Map and Magnetogram SimilaritiesFigure 10.21 shows a Mount Wilson magnetogram with a DRAO SST overlay. Mag-netograms are maps of the line-of-sight (LOS) photospheric magnetic fields measuredfrom the Zeeman splitting of a spectral line; the positive (white) polarity means thatthe field is directed towards the observer, while the negative (dark) polarity means thatthe field is directed away from the observer. The regions with strong magnetic fields(white and black patches in the magnetogram) seem to correspond to regions of highradio emission. The chromospheric network can be seen at least to the height of the 61-A. neutral line denotes the separation of areas of opposite polarity, usually on a magnetogram; hence,they mark where the line-of-sight (LOS) magnetic field is zero.Chapter 10. Solar Radio and Magnetic Activity^ 838' 13' 58' 81' 13' 18'^8h 12' 38^8h 11" SeRIGHT ASCENSION (J2000)8h 11" 18'Figure 10.21: Magnetogram[Grey Scale]/DRAO SST[Contour] Overlay Mapcm emission (Kundu et al. 1979, [36] and Erskine and Kundu 1982, [17]). Since at 21cm, some of the emission is still chromospheric in origin, one would expect that theremight be some correspondence between the enhanced magnetic network, which is re-lated to the chromospheric network, and the widely-distributed background. In fact, thewidely-distributed background contours in figure 10.21 do seem to trace out the generalstructure of the weak magnetic fields making up this network. The spatial relationshipbetween the radio and magnetic structures is not exact because they are not measuredat the same height in the solar atmosphere; the magnetic fields are photospheric and theradio emission is coronal. This spatial relationship will be strongest at the map centerbecause of projection effects.Chapter 10. Solar Radio and Magnetic Activity^ 8410.3 Simulation of DRAO SST Maps Using MagnetogramsTo further verify the strong relationship between the magnetic fields and the "radio struc-tures", an algorithm for producing a pseudo-synthesized radio map from a magnetogramwas developed. Alissandrakis (1980, [1]) was able to reproduce the shape and intensityof a sunspot observed at 6 cm by modelling the emission using a magnetogram.The Mount Wilson magnetogram LOS magnetic fields are first changed to radialfields; this can be done only if one assumes that these magnetic fields branching out of thephotosphere are completely radial, with no transverse component. Because the magneticpressure is much larger than the kinetic pressure in the solar atmosphere, magneticfields in the corona can be approximated by a simple magnetic monopole diffusion ofphotospheric magnetic fields; this simple model is justified because in the far field, twomagnetic monopoles appear to radiate like a magnetic dipole. In fact, only the LOS fieldsbetween ±70° solar latitude and longitude have been converted to radial fields; outsidethis range, the amplification of the noise due to the LOS-to-radial field conversion getsto be unreasonable. This calculation makes assumptions about where the magnetic fieldsare originating and being measured. The magnetic fields are assumed to originate at thebase of the photosphere, and the magnetograms are assumed to measure the magneticfields at the center of photosphere; the 21 cm emission is assumed to originate at thebase of the corona, so this is the reference height for the computed magnetic fields. Thediffusion process produces a reasonable coronal magnetic field map with the features atthe photosphere broadened as the magnetic field lines spread apart in their travel intothe corona.Because of the strong spatial correlation between magnetic field intensity and coronalradio emission shown in figure 10.21, the coronal magnetic field "structures" are assumedto approximate, in shape and relative intensity, the actual features of the solar radio00O 16° 48' 35"160 38' 35"Observation:1420 MHz ContinuumSolar Map forAugust 4, 199217° 18' 35"17° 08' 35"Z 160 58' 35"Chapter 10. Solar Radio and Magnetic Activity^ 85170 08' 35"•—■Z 16° 58 35"012116° 48' 35"16° 38' 35"Simulation:1420 MHz ContinuumSolar Map forAugust 4, 19929h 00m 41' gh 00m 01'^8h 59r0 ^8b 58m 41'RIGHT ASCENSION (J2000)9h 00m 41° gh 00m 01° 8h 59m 21' 8h 58m 41° 8h 58m 01'RIGHT ASCENSION (J2000)Figure 10.22: Observed and Simulated (Using a Magnetogram) CLEAN Solar MapsChapter 10. Solar Radio and Magnetic Activity^ 86brightness distribution at 21 cm. The numbers are, of course, incorrect, but the radiomap features should be close to that predicted by these magnetic fields. Also, in orderto reproduce a reasonable radio brightness distribution for the solar disk, the coronalmagnetic field map has a Gaussian weighting factor applied to it to smooth out thedisk at the edges. This map is used as the model map in the ptsrcs and ph2 simulationsoftware; the simulated map can then be directly compared with the observed 21 cm SSTmap.The simulated and observed maps, shown in figure 10.22, resemble each other strongly.The active regions match quite well in the two maps, and even the background emission isadequately reproduced in the simulated map. Since the LOS-to-radial field conversion isonly done between ±700 solar latitude and longitude, the solar limb on the simulated radiomap is questionable. The exact size of the simulated solar radio brightness distributionon the RA/DEC grid will be different than the observed map because the magnetogramwas taken to be the size of the optical solar disk, which is slightly smaller than the radiosolar disk; also, the different size of the solar disk in RA and DEC coordinates was nottaken into account in this simulation process. Nevertheless, the magnetic fields from thephotosphere do seem to be the main agents determining the radio emission at 21 cm.10.4 Magnetic and Radio Flux SimilaritiesWe can the separate the magnetic flux into components in a way analogous to the iden-tification of different S-component contributions, discussed in chapter 2. Rabin et al.(1991, [40]) describes how the total magnetic flux can be decomposed into weak- andstrong-field components. The magnetic fields above the 25 Gauss threshold are definedas the strong-field component, and are associated with active regions; the magnetic fieldsbelow this threshold are defined as the weak-field component, and are associated withChapter 10. Solar Radio and Magnetic Activity^ 87the quiet magnetic Sun and the enhanced magnetic network. Most of the magnetic fluxin the weak-field component comes from dispersing active regions. Rabin et al. (1991,[40]) show how the weak- and strong-field components of the magnetic flux have similarvariations with time, as do the background and active region radio fluxes at 21 cm, shownin figure 9.20.The amplitude of the strong-field variations are large compared with the weak-fieldvariations, indicating that only a fraction of the flux that emerges in an active region,actually leaves it; instead, a significant fraction of the magnetic flux within active regionsdisappears within the boundaries of their associated nests of activity (Rabin et al. 1991,[40] and Gaizauskas et al. 1983, [25]). Not enough DRAO SST data is available to see ifthis result also applies radio fluxes; long-term studies of the S-component with the SSTwould be needed.10.5 Relationship between Magnetic and Radio FluxThe total magnetic flux is the surface integral of the absolute values of the radial magneticfields over the solar disk (or sphere). Since there is a strong correlation between plagearea and radio flux (Kundu 1971, [34]), one might expect a similar correlation betweenmagnetic flux and radio flux. In fact, there is a very strong correlation between the10.7 cm solar flux (density) and the total magnetic flux; figure 10.23 shows this "tight"linear correlation (Tapping 1993, [50]). The 10.7 cm solar fluxes come from the NationalResearch Council of Canada solar flux patrol database, and the total magnetic fluxescome from Kitt Peak magnetograms. The 10.7 cm solar fluxes are rotational means,while the total magnetic fluxes are calculated over the entire solar sphere. Felli et al.(1977, [20]) also found a linear relationship between radio flux and magnetic flux at 2.8cm, and Zwaan (1987, [59]) notes a linear relationship between coronal emissions and120110100908070605040302010060 80^100^120^140^160^180^200^220^240^260Chapter 10. Solar Radio and Magnetic Activity^ 8810.7 cm SOLAR ROTATIONAL MEAN FLUX DENSITY in sf uFigure 10.23: Total Magnetic Flux Vs. 10.7 cm Solar Flux Densitymagnetic flux within active regions.This linear relationship also exists at 21 cm, as figure 10.24 shows. The 21 cm fluxesare total flux measurements from the Solar-Geophysical Data prompt reports (Coffey1992, [13], 1992, [14] and 1993, [15]), and the total magnetic fluxes are calculated fromMount Wilson magnetograms, by integrating the radial fields over the projected solardisk. The total magnetic flux is calculated from the radial photospheric fields withoutdiffusing them into the corona, since a simple dipole diffusion of the fields through thesolar atmosphere will conserve the total magnetic flux anyway. Only the LOS magneticfields between +70° solar latitude and longitude have been converted to radial fields forthis calculation.This linear relationship seems to exist at least from 2.8 to 21 cm, the interval overChapter 10. Solar Radio and Magnetic Activity^ 89Figure 10.24: Total Magnetic Flux Vs. 21 cm Solar Flux Densitywhich the S-component has its largest values. As the wavelength moves out of thisrange, it is likely that this strong correlation will be degraded because sources at shortwavelengths will be optically thick in the chromosphere at 104 K, and sources at longwavelengths will be optically thick in the corona at 106 K. Centimeter-wavelength emis-sions have their greatest optical thicknesses in the upper chromosphere and lower corona;in this region, the magnetic fields have their largest effect on radio emission.The best-fit linear equation for figure 10.23 at 10.7 cm isOB --= 5.26 x 1021.F10.7c. — 9.77 x 1022,^(10.53)Chapter 10. Solar Radio and Magnetic Activity^ 90with a correlation coefficient of 0.98. The best-fit linear equation for figure 10.24 at 21cm is— 2.70 x 1022,(DB = 1.09 x 1021F2i.^ (10.54)with a correlation coefficient of 0.93. The variable .7* is the solar radio flux (density) insfu; the variable toB is the total magnetic flux in Maxwells (Gauss•cm2), calculated overthe solar sphere at 10.7 cm, and over the projected solar disk at 21 cm.Chapter 11Summary, Conclusions, and Recommendations11.1 SummaryThe Synthesis Telescope at the Dominion Radio Astrophysical Observatory has beenmodified to observe the Sun, in continuum, at 1420 MHz. This thesis describes thetelescope hardware and software modifications, solar observing procedure, solar image-processing software, and resulting map properties. Chapters are also devoted to dis-cussing the different contributions to the slowly-varying (S-) component, and how theyrelate to each other, and the relationship between the solar radio flux and the solarmagnetic flux.A 20 dB attenuator was placed in each 1420 MHz receiver after the pre-amplifier; eachof the seven antennas has two attenuators, one for each circular polarization channel. Allthe attenuator-switch systems introduce the same phase shift, so the signals correlate asif there are no attenuators present. These attenuators reduce the solar signals to a levelthat can be processed by the telescope electronics.The antenna-control-system and fringe-controller software was modified to track theSun in right ascension with the physical antenna beam, fringe pattern, and delay beam.The Sun's declination drift and rotation during the observation are corrected in software,at the data-processing stage. These correction algorithms, along with a routine thatreduces the effects of any attenuator gain deviations from their listed value, are combinedin a user-friendly program called SUNVIS; this program is now integrated into the DRAO91Chapter 11. Summary, Conclusions, and Recommendations^ 92data reduction software.This thesis discusses solar observations made with the DRAO SST for six days inthe summer of 1992, and for five days in the summer 1993. Because of solar variabilityand rotation, each solar observation was restricted to one day, with one configurationof the antennas. A calibration source, such as 3C48, was observed for half-an-hourwith the attenuators switched out, usually preceding each solar observation. Observinga calibration source with the attenuators switched in reduces its signal too much forthe signal-processing electronics. Solar "observing" simulations were used to determinethe best antenna configurations for the 1992 and 1993 solar observations; these antennaconfigurations were carefully chosen to maximize the sparse u, v coverage obtained in a12-hour synthesis. These configurations provide adequate spatial-frequency sampling ofthe solar visibility function, which is the Fourier transform of the solar disk (quiet Sun).With a large field of view (2.6° to 20% response of the bore-sight sensitivity) andarcminute resolution at 1420 MHz, the DRAO SST produced solar images that show allthe different sources of the S-component, with high sensitivity over the entire solar disk.Before the map-making process, the solar visibilities were edited for "bad" data and solarbursts; the DRAO 26 m Antenna was used as a solar burst monitor for each solar obser-vation. The solar visibilities were also corrected for declination drift and rotation of theSun during the observation, and any gain deviations of the attenuators from their listedvalue. Images were then made from these corrected visibilities with the standard DRAOdata reduction software. The DRAO CLEAN and the AIPS Maximum Entropy Method(MEM) were both successful in extracting the solar brightness distribution from the dirtymap; in both programs, a priori knowledge about the solar brightness distribution wasused to help select a plausible solution.Chapter 11. Summary, Conclusions, and Recommendations^ 9311.2 ConclusionsThe resulting images, in general, show good representations of the active regions, widely-distributed background, and quiet Sun. To find out if any flux was "missing", the in-tegrated map fluxes were compared with single-antenna flux measurements made at thesame time; it appears that most of the solar brightness distribution was being recovered.Any missing flux is predominately due to an incomplete recovery of the solar disk. The1993 solar images have more missing flux, and a more "patchy" solar disk, than the 1992solar images; the degree to which the quiet Sun is recovered could be partially sensitiveto the level and distribution of solar activity. The images have resolutions comparablewith other DRAO synthesis maps; the solar motion corrections seem to have successfullyremoved the artifacts due to declination drift and solar rotation. The dynamic range ofthe solar images is about 100:1, and can be reduced by solar variability. The solar obser-vations are currently limited to the summer months, when the Sun's declination is highenough to give adequate resolution; the Sun's declination motion over a 12-hour synthesisis also the smallest around the summer solstice, which minimizes the declination driftcorrection that must be applied after the observation.For the limited data set discussed in this thesis, there seems to be a strong correlationbetween active region and background activity, with their flux contributions varyingwith time in a similar manner; long-term studies of the distribution of flux between theactive regions and the background would give valuable clues concerning the flux transfermechanisms between these components. The widely-distributed background and activeregion contributions to the S-component are comparable at 1420 MHz (21 cm-A). Whenstudying the S-component at centimeter wavelengths, it is important to consider thewidely-distributed background, as well as the active region contribution. These resultssuggest that the majority of the S-component at 21 cm is free-free (bremsstrahlung)Chapter 11. Summary, Conclusions, and Recommendations^ 94coming from density enhancements in the corona, which are supported by weak magneticfields.A strong spatial correlation has been found between regions of high radio emission inDRAO SST solar maps, and enhanced magnetic activity in magnetograms. In fact, witha simple simulation procedure, a magnetogram was used to reproduce, to a large extent,the different "radio features" present in a DRAO SST solar map for the same day. A tightlinear relationship has also been found between total magnetic fluxes, calculated over thesolar disk, and total solar fluxes at 21 cm. These results identify photospheric magneticactivity, measured by magnetograms, as an important diagnostic for radio emission levelsat 21 cm, and vice versa; the magnetic fields seem to be the main agents producing radioemission at this wavelength.11.3 RecommendationsTo minimize the cost of this project, software was used to correct hardware and controlsystem problems, but this is not really a desirable solution. The necessary telescopemodifications should be made so the Sun can be tracked properly in both right ascensionand declination. This is especially important for year-round observations, where thedeclination motion over a 12-hour synthesis can get quite large. Careful measurementsof the attenuator characteristics, in the frequency bands being used for the observations,would eliminate the need for a complicated correction for the attenuator gain deviationsfrom their specified value of 20 dB.The dynamic range of the solar images can be improved by two methods: reductionof the effects of solar variability, and improvement of u, v coverage. Solar variabilityproduces a visibility discontinuity at the beginning and end of the run; the visibilityvalues at these points, 12 hours apart, would be complex conjugates if the solar brightnessChapter 11. Summary, Conclusions, and Recommendations^ 95distribution was of constant strength. This visibility discontinuity produces low-levelgrating lines that reduce the dynamic range. A procedure to match up these points byscaling the variable portions of the solar brightness distribution is needed; the resultingsolar image would represent an average solar brightness distribution over the observation,and would have an improved dynamic range.The u, v coverage could be improved by a variety of methods. The DRAO 26 mAntenna could be used to make raster scans of the Sun at 1420 MHz to provide some ofthe low spatial-frequency information that is missing in the DRAO SST maps. A moreeffective solution would involve the introduction of an "eighth" antenna to the pre-existingseven-element array. If this eighth antenna was placed at a suitable distance in a North-South line from the SST array, a considerable improvement of the u, v coverage wouldbe obtained in a 12-hour synthesis. This would also allow the Sun to be imaged at lowerdeclinations without an unreasonable reduction in resolution; consequently, solar imagescould be made year-round, rather than just in the summer months. The configurationsof the existing seven antennas used in future solar observations should have at least acouple of baselines measuring low spatial frequencies, where most of the solar poweris represented; this would improve the chances of consistently recovering the quiet Suncomponent.The scientific motivation for this project is the investigation of the Sun as a star. TheDRAO Synthesis Telescope has demonstrated its utility as a solar mapping tool at 1420MHz. Long-term statistical studies of full-disk solar maps at 1420 MHz with the DRAOSST, combined with magnetograms and solar maps made at other frequencies, will leadto a better understanding of the global properties of the Sun, and how they vary andrelate to each other.Bibliography[1] Alissandrakis, C. E.: 1980, in M. ft. Kundu and T. E. Gergely (eds.), 'Radio Physicsof the Sun', Proceedings of IAU Symposium 86, 101.[2] Alissandrakis, C. E., Lubyshev, B. I., Smolkov, G. Ya., Krissinel, B. B., Treskov, T.A., Miller, V. G., and Kardapolova, N. N.: 1992, Solar Physics 142, 341.[3] Bastian, T.: 1989, in R. A. Perley, F. R. Schwab, and A. H. Bridle (eds.), SynthesisImaging in Radio Astronomy, Proceedings of NRAO Workshop No. 21, AstronomicalSociety of the Pacific Conference Series, Vol. 6, p. 395.[4] Bolton, J. G. and Stanley, G. J.: 1948, Australian Journal of Scientific Research,Series A 1, 58.[5] Bregman, J. D. and Felli, M.: 1976, Astronomy and Astrophysics 46, 41.[6] Brouw, W. N.: 1971, 'Data Processing for the Westerbork Synthesis Radio Tele-scope', Ph.D. Thesis, University of Leiden.[7] Bumba, V. and Howard, R.: 1965, Astrophysical Journal 141, 1492.[8] Bumba, V. and Howard, R.: 1965, Astrophysical Journal 141, 1502.[9] Castenmiller, M. J. M., Zwaan, C. S., Van Der Zalm, E. B. J.: 1986, Solar Physics105, 237.[10] Chiuderi-Drago, F., Bandiera, R., Falciani, R., Antonucci, E., Lang, K. R., Willson,R. F., Shibasaki, K., and Slottje, C.: 1982, Solar Physics 80, 71.[11] Chiuderi-Drago, F., Felli, M., and Tofani, G.: 1977, Astronomy and Astrophysics61, 79.[12] Clark, B. G.: 1980, Astronomy and Astrophysics 89, 377.[13] Coffey, H. E. (ed.): 1992, Solar-Geophysical Data, National Oceanic and Atmo-spheric Administration, No. 576, Part 1.[14] Coffey, H. E. (ed.): 1992, Solar-Geophysical Data, National Oceanic and Atmo-spheric Administration, No. 577, Part 1.96Bibliography^ 97[15] Coffey, H. E. (ed.): 1993, Solar- Geophysical Data, National Oceanic and Atmo-spheric Administration, No. 588, Part 1.[16] Cornwell, T. J. and Evans, K. F.: 1985, Astronomy and Astrophysics 143, 77.[17] Erskine, F. T. and Kundu, M. R.: 1982, Solar Physics 76, 221.[18] Ewen, H. I. and Purcell, E. M.: 1951, Nature 168, 356.[19] Felli, M., Lang, K. R., and Willson, R. F.: 1981, Astrophysical Journal 247, 325.[20] FeIli, M., Poletto, G., and Tofani, G.: 1977, Solar Physics 51, 65.[21] FeIli, M., Tofani, G., First, E., and Hirth, W.: 1975, Solar Physics 42, 377.[22] Fomalont, E. B. and Wright, M. C. H.: 1974, in G. L. Verschuur and K. I. Kellermann(eds.), Galactic and Extra - Galactic Radio Astronomy, Springer-Verlag, New York,p. 256.[23] Gaizauskas, V. and Tapping, K. F.: 1980, Astrophysical Journal 241, 804.[24] Gaizauskas, V. and Tapping, K. F.: 1988, Astrophysical Journal 325, 912.[25] Gaizauskas, V., Harvey, K. L., Harvey, J. W., and Zwaan, C. S.: 1983, AstrophysicalJournal 265, 1056.[26] Hagen, J. B. and Boksenberg, A. (eds.): 1991, The Astronomical Almanac for theyear 1992, Her Majesty's Stationary Office, London.[27] Hagen, J. B. and Boksenberg, A. (eds.): 1992, The Astronomical Almanac for theyear 1993, Her Majesty's Stationary Office, London.[28] Hey, J. S., Parsons, S. J., and Phillips, J. W.: 1946, Nature 158, 234.[29] HOgbom, J. A.: 1974, Astronomy and Astrophysics Supplement Series 15, 417.[30] Howard, R. F. and LaBonte, B. J.: 1981, Solar Physics 74, 131.[31] Kakinuma, T. and Swarup, G.: 1962, Astrophysical Journal 136, 975.[32] Kundu, M. R.: 1959, Annales D'Astrophysique 22, 1.[33] Kundu, M. R.: 1965, Solar Radio Astronomy, Interscience, New York.[34] Kundu, M. R.: 1971, in R. Howard (ed.), 'Solar Magnetic Fields', Proceedings ofIAU Symposium 43, 642.Bibliography^ 98[35] Kundu, M. R. and Alissandrakis, C. E.: 1984, Solar Physics 94, 249.[36] Kundu, M. R., Rao, A. P., Erskine, F. T., and Bregman, J. D.: 1979, AstrophysicalJournal 234, 1122.[37] Lang, K. R.: 1992, Astrophysical Data: Planets and Stars, Springer-Verlag, NewYork.[38] Nicolet, M. and Bossy, L. (eds.): 1984, Aeronomica Acta - A, Belgian Space Aeron-omy Institute, No. 282.[39] Pallavicini, R., Vaiana, G. S., Tofani, G., and Felli, M.: 1979, Astrophysical Journal229, 375.[40] Rabin, D. M., DeVore, C. R., Sheeley Jr., N. R., Harvey, K. L., and Hoeksema, J.T.: 1991, in A. N. Cox, W. C. Livingston, and M. S. Matthews (eds.), Solar Interiorand Atmosphere, University of Arizona Press, Tucson, p. 781.[41] Reber, G: 1944, Astrophysical Journal 100, 279.[42] Roger, R. S., Costain, C. H., Lacey, J. D., Landecker, T. L., and Bowers, F. K.:1973, Proceedings of the IEEE, Vol. 61, No. 9, p. 1270.[43] Ryle, M.: 1962, Nature 194, 517.[44] Ryle, M. and Hewish, A.: 1960, Monthly Notices of the Royal Astronomical Society120, 220.[45] Ryle, M. and Smith, F. G.: 1948, Nature 162, 462.[46] Schwarz, U. J.: 1978, Astronomy and Astrophysics 65, 345.[47] Snodgrass, H. B.: 1983, Astrophysical Journal 270, 288.[48] Steer, D. G., Dewdney, P. E., and Ito, M. R.: 1984, Astronomy and Astrophysics137, 159.[49] Tapping, K. F.: 1987, Journal of Geophysical Research 92, 829.[50] Tapping, K. F.: 1993, Proceedings of IAU Symposium 143 (in press).[51] Tapping, K. F.: 1993, Solar Physics (in press).[52] Tapping, K. F. and DeTracey, B.: 1990, Solar Physics 127, 321.Bibliography^ 99[53] Thompson, A. R.: 1989, in R. A. Perley, F. R. Schwab, and A. H. Bridle (eds.),Synthesis Imaging in Radio Astronomy, Proceedings of NRAO Workshop No. 21,Astronomical Society of the Pacific Conference Series, Vol. 6, p. 11.[54] Thompson, A. R., Moran, J. M., and Swenson Jr., G. W.: 1986, Interferometry andSynthesis in Radio Astronomy, John Wiley and Sons, New York.[55] Webb, D. F., Davis, J. M., Kundu, M. R., and Velusamy, T.: 1983, Solar Physics85, 267.[56] Willson, R. F. and Lang, K. R.: 1987, Solar Physics 114, 93.[57] Zheleznyakov, V. V.: 1962, Soviet Astronomy (English Translation) 6, 3.[58] Zirin, H.: 1988, Astrophysics of the Sun, Cambridge University Press, Cambridge.[59] Zwaan, C. S.: 1987, Annual Review of Astronomy and Astrophysics 25, 83.Appendix ADRAO SST 1420 MHz AttenuatorsFigure A.25: Location of 20 dB Attenuators in 1420 MHz ReceiversThe attenuators are made by HEX BODY MINIPAD, Model 294; their attenuationrating is 20 + 0.3 dB. There are two attenuators for each antenna, one for each circularpolarization channel. They are located in the 1420 MHz receivers, just after the pre-amplifiers. In figure A.25, SW denotes the switch for an attenuator. Each attenuator-switch system introduces a phase shift of 110.6° at 1420 MHz.1008h 49' 06' 0 48' 26' 8h 47'° 46° Elh 47' 06'RIGHT ASCENSION (J2000)17° 10' 30"-^I 0 52m 50 0 52" 18°^51" 30 0 50m 58'RIGHT ASCENSION (J2000)17° 40' 3006 17° 30' 301.00 17- 20' 3017° 56' 0206 17° 46' 020UJto 17° 36 0217° 26' 02Appendix BSolar Map CollectionJuly 16, 1992 July 23, 1992210 22' 03"006 21° 12' 03''R-<LI!0 21-n 02' 03"200 52' 03'45^, 4• 71 40" 00 7° 44" 29' 7" 43, 49°RIGHT ASCENSION (J2000)190 30' 41 ^I 81 13'" se 0 13" 10 8h 12" 38° 0 11' se 0 11'" 18'RIGHT ASCENSION (J2000)20° 00' 41"z 19. 50' 410 19- 40 41"August 1, 1992 August 2, 1992Figure B.26: Collection of CLEAN Final Solar Maps (Part 1)101,-, 17° 08 35"00LLI0 16- 48' 35"Z 16° 58' 35"June 22, 199323° 35' 5123° 25' 51LUo023° 15' 51"June 23, 1993,-, 23° 35'Z 23° 25'0HL0 23° 15Appendix B. Solar Map Collection^ 102August 3, 1992^August 4, 199216° 38' 35"16° 54' 01",- I^I^I^I^I -^El" 56" 59° 8° 56h° 19° 8h 55°' 39' 8h 54m^ 8h 54' 19'RIGHT ASCENSION (J2000)9" Or 41° 9" Or 01° 8" 59" 21° 8° 5e 41°RIGHT ASCENSION (J2000)„,-, 17° 24' 01a-36 17° 14' 01_7]LLJ0 17° 04' 0123° 05' 51 ^I -^23° 05' ^I^I^I^I^-Or 46' 6° 06`" 06' 6" Or 26' 6" 04' 46' 6" 04' 06' 6" 1e 55' 6° 10`n 15' 6" Or 35' 6" Or 55' 6" 08" 15'RIGHT ASCENSION (J2000)^RIGHT ASCENSION (J2000)Figure B.27: Collection of CLEAN Final Solar Maps (Part 2)23° 21' 20"CZ 23° 11' 20"011.123° 01' 20"June 24, 199323° 33' 45"Z 23° 23 45'0L1.123° 13' 45'June 30, 199323° 17' 37"CV—3Z 23° 07' 3T0:71uJ22° 57' 37Appendix B. Solar Map Collection^ 103June 29, 1993RIGHT ASCENSION (J2000)^RIGHT ASCENSION (J2000)22° 47' 37" ,—^1 1^1^1^1 6" 39' 55° 6" 39r" 15° 6" 38" 35° 6" 37' 55° 6" 37r" 15°RIGHT ASCENSION (J2000)23° 03' 45" ^1 I^1^1 —^22° 51' 20"^6" 15" 04° 6h 14' 24° 6" 13r" 44° 6h 13" 04° 6" 12' 24' 6" 35rn 45° 6" 35' 05° 6" 34' 25° 6" 33' 45° 6" 33' 05°Figure B.28: Collection of CLEAN Final Solar Maps (Part 3)

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