Transcript Measuring the Mass of Stars Physics 113 Goderya Chapter(s): 9 Learning Outcomes: Binary Stars More than 50 % of all stars in our Milky Way are not.

Measuring the Mass of Stars
Physics 113 Goderya
Chapter(s): 9
Learning Outcomes:
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.
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.
Estimating Stellar Masses
Recall Kepler’s 3rd Law:
Py2 = aAU3
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:
3
a
____
AU
MA + MB =
Py2
(MA and MB in units of solar masses)
Examples: Estimating Mass
a) Binary system with period of P = 32 years
and separation of a = 16 AU:
163
____
MA + MB =
= 4 solar masses.
2
32
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.
Visual Binaries
The ideal case:
Both stars can be
seen directly, and
their separation and
relative motion can
be followed directly.
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
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
Spectroscopic Binaries (3)
Typical sequence of spectra from a
spectroscopic binary system
Time
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!
Eclipsing Binaries (2)
Peculiar “double-dip” light curve
Example: VW Cephei
Eclipsing Binaries (3)
Example:
Algol in the constellation
of Perseus
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.
The Light Curve of Algol
Masses of Stars in the HertzsprungRussell Diagram
The higher a star’s mass,
the more luminous
(brighter) it is:
40
L ~ M3.5
High-mass stars have
much shorter lives than
low-mass stars:
tlife ~
M-2.5
Sun: ~ 10 billion yr.
10 Msun: ~ 30 million yr.
0.1 Msun: ~ 3 trillion yr.
Masses in units of
solar masses
18
6
3
1.7
1.0
0.8
0.5
Maximum Masses of Main-Sequence Stars
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
h Carinae
Example: h Carinae: Binary system of a 60 Msun and 70 Msun star.
Dramatic mass loss; major eruption in 1843 created double lobes.
Minimum Mass of Main-Sequence Stars
Mmin = 0.08 Msun
Gliese 229B
At masses below
0.08 Msun, stellar
progenitors do not
get hot enough to
ignite thermonuclear
fusion.
 Brown
Dwarfs