Transcript Slide 1

Binary Stars
Measuring the
Masses of Stars:
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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.
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.
Remember: What is Kepler’s 3rd law?
(Py = orbital period in years; aAU =
average distance in AU)
1.
2.
3.
4.
5.
Py = aAU
Py2 = aAU
Py = aAU2
Py2 = aAU3
Py3 = aAU2
Estimating Stellar Masses
Rewrite Kepler’s 3. Law as
1 = aAU3 / Py2
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:
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.
If we know that two stars are orbiting each other
once every 5 years, at an average separation of 5
AU, and we know that one of the stars has a mass of
3 solar masses, what is the mass of the second star?
3/52 = 5
M
+
M
=
5
1. 1 solar
mass.
A
B
2. 2 solar masses.
MA + MB = 5 and MA = 3
3. 3 solar masses.
4. 4 solar masses.
=>masses.
MB = 2
5. 5 solar
Spectroscopic Binaries
Usually, binary separation a
can not be measured directly
because the stars are too
close to each other.
But a lower limit (i.e. smallest possible
value) on the masses can still be
estimated in the most common case:
Spectroscopic Binaries:
Spectroscopic Binaries
Approaching
Center
of Mass
Assume the two stars A and B
have the same absorption line in
their spectra. They are so close to
one another that we can only see
them as one star, and we can
only measure their combined
spectrum. What will we see in the
combined spectrum at the instant
illustrated above?
B
Receding
Flux
A
l0
Wavelength l
What will we see in the spectrum?
Approaching
A
1.
2.
3.
4.
5.
Center
of Mass
B
Receding
We will see one line exactly at wavelength l0.
We will see a blue shifted line from star A and a
red shifted line from star B.
We will see a red shifted line from star A and a
blue shifted line from star B.
We will see no absorption line.
We will see an emission line at wavelength l0.
Spectroscopic
Binaries
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
Masses of Stars
in the
HertzsprungRussell Diagram
The higher a star’s
mass, the more
luminous 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.
Masses in units
of solar masses
40
18
6
3
1.7
1.0
0.8
0.5
Masses of Stars in
the HertzsprungRussell Diagram
40
18
What is the typical
mass of the type of
stars that show the
strongest Balmer
lines in their spectra?
6
3
1.7
1.0
1.
2.
3.
4.
5.
0.5 solar masses.
1 solar mass.
3 solar masses.
10 solar masses.
40 solar masses.
0.8
0.5
Maximum Masses of
Main-Sequence Stars
Mmax ~ 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 enouth to
ignite thermonuclear
fusion.
→ Brown Dwarfs
Considering that brown dwarfs are much
colder than main-sequence stars, in
which wavelength band do you think
they could be most easily observed?
1.
2.
3.
4.
5.
Infrared.
Optical
Ultraviolet.
X-rays.
Gamma-rays.
Brown Dwarfs
Hard to find because they are very faint
and cool; emit mostly in the infrared.
Many have been detected in star forming
regions like the Orion Nebula.