Cal Poly Pomona - Measuring stellar massesalrudolph/classes/phy424/PDF/MP...Partial eclipses Credit:...
Transcript of Cal Poly Pomona - Measuring stellar massesalrudolph/classes/phy424/PDF/MP...Partial eclipses Credit:...
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.
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Wright&Gaudi(2012)Exop
lanetD
etectio
nsaso
fDecem
ber2
011
https://exoplanetarchive.ipac.caltech.edu
3,529confirmedexoplanetsasofOctober5,2017