Measuring the Mass of Stars Physics 113 Goderya Chapter(s): 9 Learning Outcomes:
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Transcript of Measuring the Mass of Stars Physics 113 Goderya Chapter(s): 9 Learning Outcomes:
![Page 1: Measuring the Mass of Stars Physics 113 Goderya Chapter(s): 9 Learning Outcomes:](https://reader031.fdocuments.us/reader031/viewer/2022032006/56649eec5503460f94bfdd3a/html5/thumbnails/1.jpg)
Measuring the Mass of StarsPhysics 113 Goderya
Chapter(s): 9Learning Outcomes:
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Binary Stars
More than 50 % of all stars in our Milky Way
are not single stars, but belong to binaries:
Pairs or multiple systems of stars which
orbit their common center of mass.
If we can measure and understand their orbital
motion, we can
estimate the stellar masses.
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The Center of Mass
center of mass = balance point of the system.Both masses equal => center of mass is in the middle, rA = rB.
The more unequal the masses are, the more it shifts toward the more massive star.
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Estimating Stellar Masses
Recall Kepler’s 3rd Law:
Py2 = aAU
3
Valid for the Solar system: star with 1 solar mass in the center.
We find almost the same law for binary stars with masses MA and MB different
from 1 solar mass:
MA + MB = aAU
3 ____ Py
2
(MA and MB in units of solar masses)
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Examples: Estimating Mass
a) Binary system with period of P = 32 years and separation of a = 16 AU:
MA + MB = = 4 solar masses.163____322
b) Any binary system with a combination of period P and separation a that obeys Kepler’s
3. Law must have a total mass of 1 solar mass.
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Visual Binaries
The ideal case:
Both stars can be seen directly, and
their separation and relative motion can be followed directly.
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Spectroscopic Binaries
Usually, binary separation a can not be measured directly
because the stars are too close to each other.
A limit on the separation and thus the masses can
be inferred in the most common case:
Spectroscopic Binaries
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Spectroscopic Binaries (2)The approaching star produces blue shifted lines; the receding star produces red shifted lines in the spectrum.
Doppler shift Measurement of radial velocities
Estimate of separation a
Estimate of masses
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Spectroscopic Binaries (3)T
ime
Typical sequence of spectra from a spectroscopic binary system
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Eclipsing Binaries
Usually, inclination angle of binary systems is
unknown uncertainty in mass estimates.
Special case:
Eclipsing Binaries
Here, we know that we are looking at the
system edge-on!
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Eclipsing Binaries (2)
Peculiar “double-dip” light curve
Example: VW Cephei
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Eclipsing Binaries (3)
From the light curve of Algol, we can infer that the system contains two stars of very different surface temperature, orbiting in a slightly inclined plane.
Example:
Algol in the constellation of Perseus
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The Light Curve of Algol
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Masses of Stars in the Hertzsprung-Russell Diagram
The higher a star’s mass, the more luminous
(brighter) it is:
High-mass stars have much shorter lives than
low-mass stars:
Sun: ~ 10 billion yr.10 Msun: ~ 30 million yr.0.1 Msun: ~ 3 trillion yr.
0.5
18
6
31.7
1.00.8
40
Masses in units of solar masses
Low
masses
High masses
Mass
L ~ M3.5
tlife ~ M-2.5
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Maximum Masses of Main-Sequence Stars
Carinae
Mmax ~ 50 - 100 solar masses
a) More massive clouds fragment into smaller pieces during star formation.
b) Very massive stars lose mass in strong stellar winds
Example: Carinae: Binary system of a 60 Msun and 70 Msun star. Dramatic mass loss; major eruption in 1843 created double lobes.
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Minimum Mass of Main-Sequence Stars
Mmin = 0.08 Msun
At masses below 0.08 Msun, stellar progenitors do not get hot enough to ignite thermonuclear fusion.
Brown Dwarfs
Gliese 229B