From Point of Light to Astrophysical Model The Research Reach of the Modern Amateur Illustrated with a study of NSV 1000 (Hyi) by Tom Richards & Col Bembrick Southern Eclipsing Binaries Research Group of Variable Stars South (VSS-SEBRG) www.eclipsingbinaries.prettyhill.org This presentation is online at www.variablestarssouth.org/vss-community/events/ MOTIVATION Encourage CCD/digital camera photometric research on variable stars PIPELINE Will illustrate by showing the pipeline for Eclipsing Binary research That pipeline applies with changes to many other areas of variable star research RESEARCH VALUES Vitally important astrophysical laboratory Common in the sky but mostly poorly studied Each one can add something significant to our understanding Excellent for amateur research

The Research Pipeline Observatory Setup Imaging Calibration, Photometry Light Curve Time of Minimum Curve Fitting with astrophysical parameters Orbital Period Astrophysical Model Period Change Publication

Observatory Setup – can you handle these? Computer Telescope with CCD camera, or telephoto digital camera Driven mount to track a target all night Continuous imaging all night All-night imaging needs needs camera control software

Target for the night What magnitude can you image with 15-120 second exposures? In the Ephemerides app find a target binary which: Has an eclipse with >2h astronomical darkness either side Eclipses near meridian Is in your mag range URLs for all software in the last slide. signal/noise ratio > 1000 It may be a target you’ve followed before, or in the VSS-SEBRG list.

Colour Imaging? Digital cameras automatically take colour Astro CCD cameras are greyscale, but can add photometric filters --------------------- Now take your night’s images – while sound asleep in bed. I use Astrodon Johnson B and V, Sloan r’ and i’; Be consistent in filter choice for multi-night work on a given target. No photometric filter necessary for minima-timing work, red cuts moonlight. Must use a photometric filter for astrophysical modelling.

Processing your night’s images You may have many hundreds of images of same star field Your processing software will do the following Calibration (bias-removal, dark-subtraction, flat-fielding) Photometry (raw measurement of star image intensities) Star matching (across all your frames) (I use MuniWin, a front-end to Daophot routines)

Preparing for light curve analysis Find in your field a Comparison star (C): You use C to obtain the difference V-C in raw mags across all your night’s images. And find one or two checK stars (K) K is used to test the stability (C-K) of C. C should be: About same colour index as your target star V (important) About the same mag as V (quite important) Near to V in the field (flat-fielding is never perfect!) Some people use several C’s (ensemble) but this has problems The raw mags are too unstable to use by themselves. K Same criteria as for C, but they’re less important C-K should stay constant in all your night’s images. Stdev of C-K gives your mag error for V-C

Producing a light curve Tell software to find V- C mag across all your night’s images (from one filter!) And to measure C-K mag similarly V-C mag process will output a light curve plot and mag data Is the C-K plot flat? What’s its standard deviation? V-C vertical range 0.4 mag. C-K vertical range 0.04 mag, stdev 0.00465 mag And a table of <HJD, V-C mag, mag error> for all images standard deviation in C-K as a realistic measure of the V-C error.

Finding the Time of Minimum aka Epoch, E There’s special software that uses statistical or Fourier routines, etc. Enter your output photometric data for V and ask it to find the time of minimum. I use PERANSO and Minima25 It outputs HJD of minimum plus error. The VSS-SEBRG explains what to do with it; we collect & publish these annually in a refereed international journal.

Get the orbital period P Take time-series over several well-spaced nights & find several minima Go to AAVSO’s VSX portal to find (approximate) period P www.aavso.org That’s a guide to finding your P from your minima But it may be a bit different! Catalogued period P (usually near enough to reality for point 3 below) Catalogued zero epoch T0 (HJD of one minimum, usually near enough) Also collected in VSS-SEBRG. P is a publishable result. A year’s work folded on the period of NSV 1000 (PERANSO) P = 0.337 +/- 0.001 days

Obtain from VSX an historic time of minimum or epoch E0. Calculate the time one of your minima should have occurred But the minimum you Observed might be different So plot O-C against cycle number for all your minima (and any others) Has the period changed? En = E0 + nP (time of min. after n orbital cycles) O-C and hence P Increasing, decreasing or constant, this is publishable! O times getting behind C times at increasing rate, so P is steadily decreasing (Erdem et al 2001A&A...379..878E)

Astrophysical Modelling (Richards & Bembrick, “A Photometric Study Of The Eclipsing Binary NSV 1000”, JAAVSO 2018) What sort of binary can cause your (phased) light curve? You will characterise the 2 stars by 3 sets of parameters (Assumed + Adjustable  Output) Assumed (look them up) T1, temp of brighter star Gravity brightening, Limb darkening, Reflection coefficient Adjustable (by you) T2, temp of fainter star Inclination of orbit, i Fillout, f (“fatness”of light curve) Mass ratio, q = m2/m1 Output (by modelling software) Calculated light curve 3-D model of binary system Shape size separation & luminosity parameters (relative!) Light curve diagram is of your light curve Assumed: T1 from colour index, rest from tables given T1. They affect uniformity of surface brightness of the 2 stars. Adjustable: I is angle between axis of orbit and line of sight. 90deg when orbit edge-on (best eclipses) F is actually a measure of gravitational potential (Lagrange points, Roche surfaces, etc.) Output Assumed + adjustable params enable calculation of shape & LC of binary system. Calculated LC is overlaid on your LC, with residuals

Adjust the Easier Parameters In software – we used BinaryMaker 3 (www.binarymaker.com/) Starting point: look up similar light curve in CALEB (http://caleb.eastern.edu/) Effect of adjustments seen in calculated (“synthetic”) light curve. Temperature, T2 Adjust temperature to match relative eclipse depths (too hot here) Fillout, f Try to to match “fatness” of light curve (too high here) Inclination, i Adjust to match eclipse depths (i too high here) From CALEB get starting parameters Temperature is of fainter star – it’s only temp diff that matters. Fillouts same for contact binaries, so need only one. In 3rd diagram, we had the eclipse depths right then changing the fillout changed the depths. So the 3 params are not independent. Adjust them jointly.

That leaves the mass ratio (q) Step 4, Mass ratio, q Work through a range of values to find one that minimized the residuals (q-search) Mass ratio wrong – overall poor fit Residuals are sum of squares of point-by-point differences between calculated (synthetic) and observed LCs Note minima fit too shallow, but had it right at Step 1. Explain repeat & idea of convergence Then repeat steps 1,2,3 & even 4 as often as needed (gasp!)

Visualising the Results Red ellipses how orbits of mass centres of stars around the mass centre of the system (+ sign) Publish!

How to make output parameters absolute Photometric analysis only gives mass ratios and relative sizes & luminosities 2 ways to make absolute: Doppler spectroscopy to measure orbital velocities (needs vastly bigger telescopes). (not as reliable) Place the (brighter) star in the H-R diagram and then use mass-luminosity laws Spectroscopy: Orbital velocities + inclination I + period P fixes absolute size of orbit, hence absolute masses & sizes. Using H-R: Place on main sequence (reasonable assumption, & luminosity class probably known) then tables based on many star measurements give absolute masses & sizes. Then tables then give absolute luminosities, & hence distance.

Getting going on this research Review this presentation at http://www.variablestarssouth.org/vss-community/events/ Read the VSS-SEBRG website http://www.eclipsingbinaries.prettyhill.org/ Contact Tom Richards to join the group & get data access etc. Contact Tom for CCD mentoring & advice Contact Mark Blackford for digital-camera mentoring and advice tomprettyhill@gmail.com, markgblackford@outlook.com

That’s the end – of the beginning Here’s a list of the equipment and software used for the NSV 1000 project Tom’s Equipment at Pretty Hill Observatory, Kangaroo Ground, Victoria, AU RCOS 0.41 m Ritchey-Chretien OTA with automated instrument rotator, cooling, heating, focusing Astro-Physics 1200GTO German equatorial mount SBIG STXL-6303e CCD camera with Astrodon B, V, r’, i’ filters Automated AstroDome Boltwood Cloud Sensor II Software on Windows PC Ephemerides to select target http://www.motl.cz/dmotl/predpovedi/ ACP to automate observatory http://acpx.dc3.com/ Clarity for sky monitoring http://diffractionlimited.com/ MaxIm-DL for camera control http://diffractionlimited.com/ MuniWin to process & measure images http://c-munipack.sourceforge.net PERANSO to analyse light curves http://www.cbabelgium.com/peranso/ BinaryMaker 3 to model eclipsing binaries http://www.binarymaker.com/ CALEB to explore eclipsing binary light curves and models http://caleb.eastern.edu/ EXCEL calculation and database spreadsheets supplied by VSS-SEBRG Can’t read? Never mind. Presentation available on VSS website (previous slide) Equipment listed is rather high-end. Don’t worry, a driveway C8 can do the job.