Measuring the Masses of Stars: Binary Stars Please press “1” to test your transmitter.
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Transcript of Measuring the Masses of Stars: Binary Stars Please press “1” to test your transmitter.
Measuring the Masses of Stars:
Binary Stars
Please press “1” to test your transmitter.
Binary StarsMore 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 Masscenter 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. Py = aAU
2. Py2 = aAU
3. Py = aAU2
4. Py2 = aAU
3
5. Py3 = aAU
2
Estimating Stellar MassesRewrite Kepler’s 3. Law as
1 = aAU3 / Py
2
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)
Examples: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.
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. 1 solar mass.
2. 2 solar masses.
3. 3 solar masses.
4. 4 solar masses.
5. 5 solar masses.
MA + MB = 53/52 = 5
MA + MB = 5 and MA = 3
=> MB = 2
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:
Approaching
Receding
Center of Mass
A B
Wavelength
Flu
x
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?
0
Spectroscopic Binaries
1. We will see one line exactly at wavelength .
2. We will see a blue shifted line from star A and a red shifted line from star B.
3. We will see a red shifted line from star A and a blue shifted line from star B.
4. We will see no absorption line.
5. We will see an emission line at wavelength.
What will we see in the spectrum?
Approaching
Receding
Center of Mass
A B
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
Hertzsprung-Russell Diagram
0.5
18
6
3
1.7
1.0
0.8
40
Masses in units of solar masses
Low m
asses
High masses
Mass
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 of Stars in the Hertzsprung-Russell Diagram
0.5
18
6
3
1.7
1.0
0.8
40
Low m
asses
High masses
Mass
What is the typical mass of the type of stars that show the strongest Balmer
lines in their spectra?
1. 0.5 solar masses.
2. 1 solar mass.
3. 3 solar masses.
4. 10 solar masses.
5. 40 solar masses.
Maximum Masses of Main-Sequence Stars
Carinae
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
Example: 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
At masses below 0.08 Msun, stellar progenitors do not get hot enouth to
ignite thermonuclear fusion.
→ Brown Dwarfs
Gliese 229B
1. Infrared.
2. Optical
3. Ultraviolet.
4. X-rays.
5. Gamma-rays.
Considering that brown dwarfs are much colder than main-sequence stars, in which wavelength band do you think they could be most easily observed?
Brown DwarfsHard 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.