Variable Stars and Their Light Curves

Arne Henden

Director, AAVSO

arne@aavso.org

Photometry Basics

• Brightness as a function of time• Possible color information if you use more

than one filter (visual is always one filter, no color vision at night). Wide-band photometry is “poor man’s spectroscopy”.

• Almost always “differential”; comparing brightness of target vs. constant stars

• If combining estimates from more than one person/system, need to use same comparison stars and/or possibly “transform” data to same system

Light Curve Basics

• Morphology: shape and structure • General Catalog of Variable Stars (GCVS)

classifications almost always morphology-based

• Rule: plotting light curves is easy; understanding the underlying physics is hard

• Rule: light curves only tell part of the story; use ancillary information whenever possible

• Time-series light curves• Phased light curves

W Virginis coverage from SRO - one season

W Vir phased light curve, BVRI

Dips, Bumps and Wiggles• General morphological classifications• Stars can exhibit one or more of these

features• Features can be transitory• No two stars are alike• Rule: to determine if a feature is periodic, you

need to see it replicated at least twice, and preferably 3-5 times

• Rule: use two or more comparison stars, as any dip/bump might be in the comp rather than the target

Dips

• Momentary decrease in brightness of star

• Can be caused by extrinsic obscuration by another object (eclipsing binary, exoplanet transit)

• Can be intrinsic decrease (R CrB, VY Scl)

More dips

• Rule: Never trust an individual measurement (lots of equipment/sky problems can make one point bright or faint)

• Rule: Never trust a dip that occurs at the beginning or end of a time series (airmass changes cause systematic changes; twilight does the same)

• Rule: Eclipsing systems often have periods twice what you think (equal-depth minima)

Z UMi - a circumpolar RCB

Note near complete BVRI coverage (dropouts due to summer monsoon) of this circumpolar object at SRO. 15:02:01.3 +83:03:49 Nearly “grey”

Eclipsing binaries

• Contact (K) - the two stars are in contact, usually no clean start/stop of eclipse

• Semidetached (SD) - the two stars are near one another, often ellipsoidal in shape, with perhaps Roche lobe overflow

• Detached (D) - no influence by one star on the other, usually flat between eclipses

• Period is helpful in determining category, but primary classifier is light curve shape

Modelling binaries

• Binary Maker 3 http://www.binarymaker.com Windows only

• PHOEBE/Wilson-DeVinney, primarily Linux http://phoebe.fiz.uni-lj.si/

• Usually require standardized filter photometry• Multiple filters improve results as it gives

temperature as well as geometry• Gives orbit size, inclination, relative sizes of

two stars

DU Leo 1.37d EA 13ks = 0.15d

These and similar plots are from VGUIDE

Example of total eclipse in LD 282. Note flatness. USNO 1.0m data

V477 Cyg 2.35d 14ks =0.16d

Rule: period often about 10x width of eclipse

IM Aur

IM Aur (EA, period=1.247296)

LD355 (note temp of secondary star)

Observations of HD126080 with 6cm telescope and CCDGomez-Forrellad & Garcia-Melendo 1997

3 year period; eclipse was a month longTerrell et al. 2003

Beta Lyr (Terrell)

BV 1005

FT UMa EW 0.655d

BV1004

DSct + EA

Transiting exoplanets

• Similar to detached light curves, with very small dip (planet is small compared to star)

• With high precision, eclipse has D-shape• Eclipse gives size of planet; radial velocity

wobble gives mass• Excellent probe of stellar surface (limb

darkening, star spots)

TrES-1

Bumps

• Momentary increase in brightness of star

• Almost always intrinsic (star gets brighter)

• Wide range of physics, from flare (M dwarf) to stellar disruption (SNe)

• Differentiate by luminosity, as outbursts look very similar

V344 Lyr (Still et al. ApJ)

SS Cyg, 1896-2004

Z Cam

Obtaining light curves of microlensing candidates

Planet Mass

~13 ME

Credit: J. Skowron

Note: amateurs discovered closest microlensed star (Casseopeia) November 2006; 8th magnitude at peak

Credit: NASA

Recent Novae

V838 Mon light curve

Two type Ia light curves (Hicken 2009)SN2007af SN2006X

SN 1987A

Light curve for a bright GRB afterglow, observed by amateurs

Wiggles

• Light curve that contains both bumps and dips• Irregular when no obvious period can be determined

(semiregular variables)• Periodic include most pulsating stars, such as RR

Lyr, Cepheid, Mira• Periodic wiggles give information about stellar

structure. Multiple periods probe the interior of the star. Can be radial or non-radial pulsation.

• Rule: don’t trust catalog periods• Rule: primary classification by period

DX Cet 0.104d

GG UMa 0.135d

V703 Sco 0.115 0.150

AQ Leo

RRd0.550 0.410

W Vir phased light curve, BVRI

SU Cyg

Classical Cepheid

Period 3.84 days

Note phase shift, amplitude and shape change with wavelength

(Madore & Freedman, 1991

You can observe single pulsation cycles…

…or follow decades-long trends

V Hya

Resources

• AAVSO Variable Star of the Season archive: http://www.aavso.org/vsots_archive

• GCVS web site: http://www.sai.msu.su/gcvs/gcvs/index.htm

• J.R. Percy, "Understanding Variable Stars”• D. Terrell, J.D. Mukherjee & R.E. Wilson,

"Binary Stars: A Pictorial Atlas”• C. Sterken & C. Jaschek, "Light Curves of

Variable Stars: A Pictorial Atlas”• J. Kallrath & E.F. Milone, "Eclipsing Binary

Stars: Modeling and Analysis"

Resources

• Chandra Variable Guide Star Catalog: http://cxc.harvard.edu/vguide/index.php

• G. Foster, “Analyzing Light Curves”