Measuringstellarmasses

We measure mass using gravity.

Direct mass measurements are possible only for stars in binary star systems.

P = orbital period

a = orbital semimajor axis

P2 = a34π2

G (M1 + M2)

Need2outof3observablestomeasuremass:

1) OrbitalPeriod(T)2) OrbitalSeparation(a orr=radiusof

circularorbit)3) OrbitalVelocity(v)

Forcircularorbits,v =2pr /Tr

M

v

VisualBinary

We can directly observe the orbital motions of these stars.

α1α2

=r2r1=a2a1=m1m2

SpectroscopicBinary

We determine the orbit by measuring Doppler shifts.

SpectroscopicBinary:CircularOrbits

SpectroscopicBinary:EllipticalOrbits

Most massive stars:

~100 MSun

Least massive (hydrogen-burning) stars:

0.08 MSun

Firstexoplanet detectedaroundaSun-likestar,discoveredindependently in1995byMayor&Queloz (Switzerland)andMarcy&Butler(SanFranciscoStateU.)

EclipsingBinary

We can measure periodic eclipses.

Eclipsin

gBinarie

s—Lig

htCurves

Totaleclipses

Partialeclipses

Credit: P. Zasche, Astronomical Institute, Prague, Czech Republic

OrbitModelsFittoLightCurvesofEclipsingBinaries

Figure 5: The points show the masses versus semimajor axis in units of the snow linedistance for the exoplanets that have been discovered by various methods as of Dec. 2011.See the Extrasolar Planets Encyclopedia (http://exoplanet.eu/) and the Exoplanet DataExplorer (http://exoplanets.org/). Here we have taken the snow line distance to be asl =2.7 AU(M∗/M⊙). Radial velocity detections (here what is actually plotted is Mp sin i) areindicated by red circles (blue for those also known to be transiting), transit detections areindicated by blue triangles if detected from the ground and as purple diamonds if detectedfrom space, microlensing detections are indicated by green pentagons, direct detections areindicated by magenta squares, and detections from pulsar timing are indicated by yellowstars. The letters indicate the locations of the Solar System planets. The shaded regions showrough estimates of the sensitivity of various surveys using various methods, demonstratingtheir complementarity.

29

Wright&Gaudi(2012)Exop

lanetD

etectio

nsaso

fDecem

ber2

011

https://exoplanetarchive.ipac.caltech.edu

3,529confirmedexoplanetsasofOctober5,2017