Cataclysmic Variable Eclipse Photometry

   By Dennis Ritz

Cataclysmic variable (CV) stars consist of evolved binary stars, a red dwarf (RD) and a white dwarf (WD) in very close orbits with orbital times of 1-10 hours. White dwarf stars consist principally of the remaining core of carbon with some helium, nitrogen, and oxygen. The red dwarf star has evolved to fill its Roche lobe and the red dwarf’s atmosphere, principally of hydrogen, is overflowing into an accretion disk surrounding the white dwarf. Where the hydrogen flows into the accretion disk, an impact hot spot rotates with the disk as material spirals onto the surface of the white dwarf. After sufficient hydrogen accumulates on the surface, the WD hydrogen explosively ignites in what is known as a nova. Accretion disk instabilities also cause outbursts known as dwarf nova. Where the binary star orbits are planer to our line of sight, the larger red dwarf may eclipse the white dwarf and hot spot providing a glimpse at the dynamics of these stars and the accretion disk. Click here for a UCSD Astronomy review of stellar evolution.

            Using a Meade 16” LX200 equatorially mounted telescope, I attached a Santa Barbara Instruments Group (SBIG) 9E CCD camera. The CCD is a Kodak 1602 chip 512x512 pixel array of 20x20 micron detectors. It is cooled by a two stage Peltier cooler augmented by circulating water to a working temperature of –20 C. Cooling the chip reduces thermal emission of electrons which would cause a background current. Readout of the chip is via a parallel cable interface to a Pentium II computer. The LX200 is controlled by The Sky software (Software Bisque). The use of this software greatly simplifies acquisition of the target star by accurately slewing to a nearby bright star, syncing to known Right Ascension and Declination and slewing to the target CV coordinates. Computer time was set by listening to WWV time reference short wave broadcast.

The CCD camera was controlled by MaxIm DL software, (Cyanogen Productions). The image was focused using the focus mode of rapid acquisition and downloading for computer display of a star of relatively low magnitude, and finally focused using the target CV star field to produce as sharp an image as possible. Star charts of target CV fields were downloaded from the AAVSO (American Association of Variable Star Observers http://www.aavso.org/), The Catalog and Atlas of Cataclysmic Variables (Space Telescope Institute http://archive.stsci.edu/cgi-bin/dss_form), and The Center for Backyard Astrophysics (CBA http://cba.phys.columbia.edu/charts/) Comparison of the target field with the CCD field allowed verification that the target field was in the telescope field of view. Target CV’s were selected by comparison with a list of Right Ascension sorted CV’s from CBA and the book “Cataclysmic Variable Stars, How and Why the Vary” by Coel Hellier (see references).

Exposures using 1x1 binning were taken using automatic dark field subtraction performed by the MaxIm DL software. Dark field exposures were taken with the CCD shutter closed for an exposure time identical to the light field exposure time and dark (thermal) current noise and bias subtracted from the light image. Exposures varied, generally from 10-60 seconds depending on the target star magnitude and focal reducer on the telescope Guiding during exposures was performed by the guider CCD chip in the SBIG 9E camera, a separate chip that acquires a guiding star, images the star and periodically sends corrections to the telescope mounting stepper motors. Guiding is necessary to reduce drift due to imperfectly aligned equatorial axes, flexure in the telescope/camera, imperfect driving gears, etc. Once the focused image of the target CV was found and guiding initiated, a sequence of up to 500 exposures was made. Each image was saved to hard disk and transferred to a Zip drive for later photometric data reduction. The web site has images and data reduction, when the process worked- Click on the underlined links.

DY Peg (Pegasi)

I acquired target DY Peg and took a long series of images, only to find the f3.3 focal reducer produced some stars with nice images, while others had a weird coma. I placed an f6.6 focal reducer on the telescope and obtained images of WZ Sge.

WZ Sge (Sagittae)

WZ Sge is representative of a class of short period (1.36 hours) cataclysmic variables that undergo accretion disk instabilities resulting in ‘superhumps’. From magnitude 14 it undergoes disk outbursts over times much longer than its’ orbital cycle as accretion material slowly fills the elliptical accretion disk.

First note the 20-second exposure with labeled calibration and target stars (page WZ1). The image is a mirror image and reversed from the AAVSO identification chart. This is due to the optical characteristics of Schmidt-Cassegrain telescopes, but MaxIm DL easily allows the re-orientation of the field for identification. Once identified, the ‘raw’ FITS fields obtained from the CCD are used for photometry data reduction. Thus the screen shot (bottom of page) illustrating the calibration reference (Ref 1), check star (Chk 1) and target object (Obj 1) WZ Sge is a reversed mirror image of the Field image. Once the stars are identified, it is not difficult to view the raw images and identify the correct stars. AAVSO charts are provided in regular and reversed view. Based on the AAVSO charts, the reference and calibration stars are identified before data photometry. The WZ Sge series consists of 318 images that are presented as a graph on WZ2 and WZ3. The upper black trace plots the magnitude of the Chk 1 star as a reference point as calculated from the Ref1 star. The Chk star provides an ‘error’ estimate of the readings obtained from image to image. The lower red line shows the image magnitudes of WZ Sge. There is a short scale point-to-point fluctuation probably representing measurement error or CV ‘flickering’, as well as a longer period of about 1 hour probably generated by the orbital eclipse. However the data is very noisy, due to the short exposure. The left box on WX2 shows a Maximum count of only 190 electrons/photons. This is a very low value and the short 20-second exposure was insufficient to obtain sufficient counts for decent light curves. So I needed to increase the exposures and next observed TT Ari.

TT Ari (Arietis)

TT Ari field was located, focused and tracking initiated, taking 61 CCD images. Regretfully the TT Ari CV image was saturated, i.e. the CCD pixels maximized their ability to record photons at 64,000 counts. The CV image was basically overexposed with an exposure of 40 seconds. This was the exact opposite of the problem with WZ Sge. While the ‘noise’ in the Check star is very low, a flat line, the lower TT Ari plot is not useful.

IP Peg (Pegasi)

            IP Peg was discovered to be an eclipsing binary in 1985 and is a premier cataclysmic binary of the U Gem dwarf nova type seen nearly edge on from Earth (80 deg inclination), allowing the red dwarf to deeply eclipse the white dwarf, the hot spot, and the accretion disk. It has a 1.02 solar mass white dwarf and a 0.5 solar mass red dwarf feeding the accretion disk. It undergoes disk instabilities causing dwarf nova disk outbursts approximately every 3 months. It is one of the brighter deeply eclipsing CV’s with an orbital period of about 3.8 hours. Thus in one night a complete orbital cycle can be recorded. The animation of a few images shows the eclipse- can you see IP Peg eclipsing?

            As soon as darkness arrived I began aligning and focusing the CCD. I adjusted the Peltier cooler to –20 C, and acquired the target field, shown as IP Peg Finder. A 40 second exposure produced only about 1000 photon/electron counts. Wind gusts streaked some images that were discarded from photometry. Exposures began about 8:55 pm at a rate of about 1 every 50 seconds until 4:04 am, totaling nearly 500 exposures. The early morning exposures lost focus and some were discarded. However using MaxIm DL photometry plotting software, a light curve (see bottom of page) was obtained comparing very favorably with that shown on page 2 of the AAVSO ‘Variable Star of the Month’ taken with the 2.1 meter telescope at McDonald Observatory.

Analysis of IP Peg Results

            First consider this illustration of IP Peg and compare to the following image of labeled photometry:

Illustration 1 shows the red dwarf emerging from behind the accretion disk. Note the hot spot is not directly between the WD and RD, but forms ahead of the RD as the accreting material enters the gravitational orbit of the WD. White dwarfs commonly have masses from 0.3-1.4 solar masses, below the Chandrasekhar limit of 1.4 solar masses, with a diameter about that of Earth. Above 1.4 solar masses the WD will collapse into a neutron star about 10 km in diameter. Neutron star binaries are X-ray emitters, while ordinary WD have surface temperatures as high as 60,000 K and emit white-hot light of spectral class O. White dwarf stars are generally the carbon core of sun sized stars which have exhausted their hydrogen and helium fuels and released their outer atmospheres as planetary nebula. The carbon cores emerge from the planetary nebula as white-hot remnants unable to support further nuclear fusion and slowly cool over billions of years. The red dwarf companion is lighter than the WD. In the case of IP Peg the WD is about 1.02 solar masses and the RD about 0.5 solar masses. The more massive the star, the faster it evolves through the hydrogen burning main sequence, into a red giant with a core containing carbon, helium, and hydrogen concentric shells, and through the planetary nebula ejection of the outer atmosphere to the white dwarf carbon core. In the common envelope phase of a binary system when the first heavier star reaches the planetary nebula stage, both are enveloped in a common envelope ejecting/transferring mass and reducing the angular momentum/orbits until the WD is heavier than the RD. The only stable binary systems that have Roche lobe contact, that region of equal gravitational potential where the inner Lagrangian point (L1) allows mass transfer, are where the WD is heavier than the RD. As binaries evolve, they may become ‘detached’ binaries where the Roche lobe is not filled by the red giant and mass transfer does not occur. IP Peg is that rare case where the RD Roche lobe is filled and mass transfer occurs stably in a ‘semi-detached’ binary, and the stars orbit one another in a plane from our view where the RD eclipses the WD and hot spot. The rate of material transferred through the L1 point is dependent on the evolution of the RD and closeness of the orbits. As the stars closely and rapidly orbit, magnetic braking and gravitational radiation (relativistic) reduce angular momentum and orbits. Magnetic braking dominates from orbital periods of 10-3 hours. Orbital times above (>10hrs) have no Roche lobe contact, and below 2 hours gravitational radiation dominates. Between 2-3 hours is the ‘orbital gap’, an instability in mass transfer between magnetic braking and gravitational braking. These mechanisms reduce the orbits and providing a ‘steady’ flow of approximately 10 ¹³ Kg/sec to the accretion disk.

            Examining the labeled IP Peg photometry curve, the top green line is the magnitude plot of the Reference star (selected from the AAVSO chart as a non-variable labeled C1, the blue line is the Check star 2 (AAVSO 4) and Black line Check star 1 (AAVSO 7). As expected brighter Check star 2 shows lower variation, due to more photon/electron counts, while Check star 1 shows somewhat more noise, but is very similar in magnitude to the baseline of IP Peg and fairly represents the variation in measurement at the magnitude of IP Peg. (One Standard Deviation of Check star 2 is 0.029, 95% confidence level is 15.53-15.65 magnitude variations. The label shows ‘V’ above the light curve corresponding to the eclipse event. First, before the deep eclipse is the ‘orbital hump’, corresponding to figure 2 above, where all the components are visible and the hot spot rotates into our view along with the RD. As the RD covers the hot spot and WD, the photometry shows a rapid decline to minimum, occurring in only about 6 minutes! Careful photometry allows the diameters of the WD and RD to be determined, the orbital period and velocity, RD and WD masses, and other parameters calculated.

            Coming out of the eclipse there are two evident ‘steps’, corresponding to the emergence of the WD and then hot spot. The accretion disk is larger than either the WD or hot spot and also emerges. IP Peg is known as a dwarf nova, where over a somewhat irregular schedule on the order of every few months, the accretion disk outbursts, rapidly heating and dumping material onto the WD. This thermal instability of the disk is known as the Balbus-Hawley instability, and requires a strong coupling between the magnetic field of the WD and disk material. Cool disk hydrogen is neutral, not highly ionized nor coupled to the WD magnetic field. But as disk material accumulates and the disk heats up, at critical temperature (7,000K) the disk ionizes, couples with the magnetic field, and rapidly absorbs energy, resulting in more ionization and hotter temperatures. It is this disk instability that creates the ‘dwarf nova’. This is not evident in my photometry, occurring on irregular several month schedule depending on the rate of accretion. The study of the eclipse of the accretion disk allows determination of the dynamics of the disk. In IP Peg the disk instability begins on the disk inside and travels outward; an ‘inside out burst’. Disk tomography, utilizing Doppler shift of the accretion disk, has demonstrated that spiral waves are present in the accretion disk. These waves are caused by the RD pulling the disk material into elliptical orbits while the WD strongly circularizes the orbits, creating spiral shock waves. This is likely the same mechanism as causes spiral arms in galaxies where galactic orbits are disturbed by neighboring galaxies. (References 2)

            In relatively short learning curve, excellent light curves were obtained for IP Peg, providing a fascinating glimpse at stellar evolution. However as an old astronomer asked; “ Very good, but have you considered the effect of magnetic fields?”   Ah well, back to the telescope! Tune in for next months’ article on Magnetic Cataclysmic Variables –The Polars

References---

Books

1. E. Chaison and S. McMillan, Astronomy Today 4^th Ed, Ch 19, 20, 21, Prentice Hall 2002, ISBN 0-13-091542-4
2. C. Hellier, Cataclysmic Variable Stars, How and Why They Vary, Springer Praxis, 2001, ISBN 1-85233-211-5
3. D. Prialnik, An Introduction to the Theory of Stellar Structure and Evolution, Cambridge University Press 2000, ISBN 0-521-65065-8

Articles

            1.Variable Star of the Month, IP Pegasi, December 2001, AAVSO URL: http://www.aavso.org/vstar/vsotm/1201.stm

Web Sites

            1. American Association of Variable Star Observers (AAVSO): http://www.aavso.org/

            2. Center for Backyard Astrophysics, Columbia University: http://cba.phys.columbia.edu/charts/

  3. A Catalog and Atlas of CVs at STScI: http://archive.stsci.edu/prepds/cvcat/

5. General Catalog of Variable Stars, Sternberg Astronomical Institute, Moscow, Russia: http://www.sai.msu.su/groups/cluster/gcvs/gcvs/

IP Peg Screen Shot showing light curve and labels from text: