Measuring the Masses of Stars:

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Measuring the Masses of Stars
Binary Stars
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Binary Stars
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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
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center of mass balance point of the system.
Both masses equal gt 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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Remember What was Keplers 3rd law?(Py
orbital period in years aAU average distance
in AU)

• Py aAU
• Py2 aAU
• Py aAU2
• Py2 aAU3
• Py3 aAU2

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Estimating Stellar Masses
Rewrite Keplers 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
aAU3
____
MA MB
Py2
(MA and MB in units of solar masses)
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Examples
a) Binary system with period of P 32 years and
separation of a 16 AU
163
____
MA MB 4 solar masses.
322
b) Any binary system with a combination of period
P and separation a that obeys Keplers 3. Law
must have a total mass of 1 solar mass.
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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?

• 1 solar mass.
• 2 solar masses.
• 3 solar masses.
• 4 solar masses.
• 5 solar masses.

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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
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Approaching
Center of Mass
A
B
Receding
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?
Flux
l0
Wavelength l
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What will we see in the spectrum?

• 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.

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Spectroscopic Binaries (II)
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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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Masses of Stars in the Hertzsprung-Russell Diagram
Masses in units of solar masses
40
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High masses
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The higher a stars mass, the more luminous it is.
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1.7
1.0
High-mass stars have much shorter lives than
low-mass stars
Mass
0.8
0.5
Sun 10 billion yr.
Low masses
10 Msun 30 million yr.
0.1 Msun 3 trillion yr.
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Masses of Stars in the Hertzsprung-Russell Diagram
40
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High masses
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3
1.7
1.0
What is the typical mass of the type of stars
that show the strongest Balmer lines in their
spectra?
Mass
0.8
0.5
Low masses
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What is the typical mass of the type of stars
that show the strongest Balmer lines in their
spectrum?

• 0.5 solar masses.
• 1 solar mass.
• 3 solar masses.
• 10 solar masses.
• 40 solar masses.

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Masses of Stars in the Hertzsprung-Russell Diagram
40
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High masses
6
3
1.7
1.0
What is the typical mass of the type of stars
that show the strongest Balmer lines in their
spectra?
Mass
0.8
0.5
Low masses
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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.
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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 enouth to ignite thermonuclear fusion.
Gliese 229B
? Brown Dwarfs
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Considering that brown dwarfs are much colder
than main-sequence stars, in which wavelength
band do you think they could be most easily
observed?

• Infrared.
• Optical
• Ultraviolet.
• X-rays.
• Gamma-rays.

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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.