1. Credit: University of California Santa Cruz

2. Introduction – Astrophysics from Light Curves The Big Players have: Big telescope Liquid N2 cooled CCD camera Multiple filters High dispersion spectrograph Research assistants Fancy software You have Little telescope DSLR or lightly cooled CCD camera No filters (or just V) Amateur-level software Multi-bandpass transformed light curves. Spectrum determining Harvard (OBAFGKM) and Morgan-Keenan (giant, dwarf etc) classes of the two stars, very accurately. Doppler spectra yielding radial (orbital) velocities. What can you do with it? Thoroughgoing astrophysical characterization of the binary system. A light curve But remind me to tell you a little secret about this!

3. Introduction – Astrophysics from Light Curves CU Hya, from Richards 2013, JBAA 123:3 What can you extract by looking and thinking? Without software, or maths Just play the amateur detective Just use logical deduction from what you see. What’s the value in doing so? 1.You learn to read light curves. 2.You amaze yourself at your powers of deduction. 3.Vital for deeper analysis – starting point and major parameter space constraint for modelling. 4.Publishable results – refereed or informal.

4. Geometry of Detached Binaries – circular orbit, spherical stars GET RELATIVE DIAMETERS Period (P) is time for one complete orbit. Two eclipses, always of same duration. In this diagram primary is smaller, brighter.  Relative to P, diameter of secondary = time to move from t1 to t3.  Relative to P, primary diam = time from t1 to t2. Flux 100% 0%

5. At each minimum the same area of the back star is occulted.  So relative depths = relative brightnesses.  In a primary eclipse, the brighter star is always occulted. ?How do you tell from the light curve these are partial eclipses? Geometry of Detached Binaries – circular orbit, spherical stars

6. Credit: Catalog & Atlas of Eclipsing Binaries, http://ebola.eastern.edu/ GZ CMa Geometry of Detached Binaries – circular orbit, spherical stars HS Aur Note vertical axis!

7. AZ Cam Geometry of Detached Binaries – circular orbit, spherical (?) stars Plainly very close. ?Why the hump at quadratures (stars sideways)?  Must present a bigger area, so tidally distorted.

8. Here, primary depth = 3.5 x secondary.  So primary is 3.5 x brighter  And hotter ?But is it bigger or smaller? More or less luminous? Can’t tell. Geometry of Detached Binaries – circular orbit, spherical stars BH Dra Or this could. This could be the primary. Brightness is energy emitted per unit area. Luminosity is total energy emitted. Luminosity = brightness x area

9. Geometry of Detached Binaries – circular orbit, spherical (?) stars Flat secondary min, so...  Must be a total eclipse,  The eclipsed star is smaller & less bright,  Primary eclipse must be annular,  Primary is deep, so quite a bit of the brighter bigger star must be covered ?Why is primary min rounded?  There must be limb darkening. Total secondary eclipse Annular primary eclipse IQ Per

10. Minima completely sharp, & Eclipse depths = 0.5; so…  Eclipses total (for an instant)  Radii equal  i = 90°  Each star contributes half the total luminosity  Temperatures equal Geometry of Detached Binaries – circular orbit, spherical stars DM Vir No Yes Primary eclipse Secondary eclipse

11. Geometry of Detached Binaries – circular orbit, spherical stars Why the volcano shape?  Can’t be because of ellipsoids side on.  The side of the secondary facing the primary must be much brighter  So it’s being heated by the much hotter primary. V477 Lyr What can we learn from the eclipse depths?  Eclipses are partial (why?)  Primary eclipse very deep (~0.15 flux) so occulted star must nearly disappear  Secondary eclipse much shallower (but same area of star occulted), so it must be far less bright (cooler).

12. Geometry of Detached Binaries – circular orbit, spherical stars Eclipse type: Total + annular, or two partials Measure star radii Relative to orbital radius (easy only for total + annular) Detect tidal distortion Measure relative brightnesses (Not luminosity!) Explain the special case of two equal, 50% depth, eclipses Detect limb darkening Detect heating of one star by another

13. Detached Binaries – astrophysical clues Star colour tells temperature and spectral type.  Measure mags through B and V filters to get B-V colour index. (Or look it up). Go to SIMBAD http://simbad.u- strasbg.fr/simbad/http://simbad.u- strasbg.fr/simbad/ Click “Queries > by identifier” Enter e.g. “V* HS Aur” & stand back!! HS Aur HS Aur: B-V = 0.8. Take that as for the more luminous star. Then (from Allen):  spectrum = G5, T1 = 5500 K, radius & luminosity = Sun (actually T1 = 5346K).  Use depths + arithmetic to get the secondary. Allen’s Astrophysical Quantities 4 th edn, edited A.N. Cox, Springer 1999. Good result!

14. Detached Binaries – astrophysical clues Colour Index: From SIMBAD, (B-V) = 0.60 (star 1 really)  So from Allen, Sp1 = A2, T1 = 9000K IQ Per Depth at totality ÷ what’s left = luminosity ratio 0.0 flux 87% 13% Arithmetic + Allen  From relative eclipse depths: L1/L2 = 87/13 = 6.7  T2 = ~6500K, Sp2 = F5  … and so, get absolute luminosities, radii, orbit radius, distance, don’t we? That’s all assuming these are normal Zero Age Main Sequence stars!

15. Detached Binaries – astrophysical clues Schafly, E.F. & Finkbeiner, D.P., 2011. Astrophysical Journal 737, 103. Lacy & Frueh (1985): B-V at mid-secondary eclipse: (B-V)1 = 0.03. They determined an interstellar reddening correction (B-V) = -0.14. So they got: (B-V)1 = -0.11, Spectral class = B7.5, temp1 = 12300K  You had obtained A2 and 9000K. Phooey! The culprit is interstellar reddening Lacy, Claud H. and Frueh, Marian L., 1985. Astrophysical Journal, 295, 569-579 IQ Per

16. ×You CAN’T reliably infer temperature or spectrum from observed B-V colour, so you’re stuck. ×So how do you get around interstellar reddening? You ask a friend with a spectrograph to get a spectrum. YY Gru – Terry Bohlsen

17. Detached Binaries – astrophysical clues Suppose your friend tells you the spectral class for IQ Per is B8. Arithmetic + Allen You + light curve + spectrum + Allen + arithmetic Lacy & Frueh + McDonald 2.7m + really fancy spectrograph + radial velocity Doppler data Spectrum 1B8B7.5 Temperature 113000K12302K Temperature 28912K7674K Spectrum 2A2A6 But you’re still assuming your stars are main- sequence! Friend’s gear Lacy & Frueh’s gear

18. Thoughtful inspection of a light curve yields much information: Partial or total eclipse (so some idea of inclination) Star sizes relative to orbit (sort of) Tidal distortion (ovoid stars) Heating of cooler star’s near face by hotter star Eclipse depth ratio is brightness ratio. A good spectrum can tell you the spectral class (don’t rely on apparent B-V colour). Assume both stars are on main sequence & your spectrum is of the brighter: Then (Allen + arithmetic) derive temperatures, absolute luminosities & masses, distance…. All of these can STRONGLY CONSTRAIN any modelling work you take up (since you have to start with guesses). But recognize your assumptions and the limitations of your data. You may be quite wrong! The road to hell is paved with assumptions. - C.I.A.