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Eclipsing Binaries
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If the binary stars are eclipsing, then it is
guaranteed that we are in the orbital plane.
This means that the maximum radial velocity on
the velocity plot gives us the orbital velocity.
Now we have “a” and we have “P”. We can get
rid of one of the “M”s because we know how
they are related.
Example
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(M1 + M2)P2 = (4π2/G)a3
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If v2 = 3v1 then M1 = 3M2 then we can write:
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(3M2 + M2)P2 = (4π2/G)a3
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(4M2) = (4π2/G)(a3/P2)
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Once we find M2 we know that M1 is three times
the mass
Masses of Stars
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Many such measurements show us that mass
increases on the Main Sequence as the temperature
and luminosity increase. As theory predicts.
Furthermore, Mass does not correlate with luminosity
for giant, evolved stars. Giants might have a large
mass, or they might have a small mass, but still they
are very luminous.
Also the mass of a white dwarf is not correlated to its
luminosity.
Something different is happening for these guys.
Well established relation on Main-Sequence
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L*/Lsun = (M*/Msun)4
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Example:
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If a star has M* = 5Msun then (M*/Msun) = 5
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But 54 = 625. So L*/Lsun = 625.
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The star has 5 times the fuel but is burning it 625
times as fast. Lifetime = 80 million years.
Spectral Typing of Stars
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Spectral typing involves comparison of the
absorption lines in stars in order to determine
temperature and the amount of various
elements in a star.
In particular, it is comparing the strength (how
dark) of the line.
Different stars have different absorption line
strengths
Early Spectral typing
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In the 1900s, scientists didn’t know why stars had different line
strengths. Not knowing the physical reason, they just classified
them from A to O. A-stars had the strongest hydrogen lines.
O-stars the weakest.
Later they found many classifications were actually the same
spectral type.
Finally they realized that the strength of the hydrogen line
correlated to the stars color, or temperature.
The spectral type order was changed to go from the hottest
stars to the coolest. O,B,A,F,G,K,M
They were later subdivided, A0, A1, A2, … A9 ; with A0 the
hottest
Cooler stars where added, L, T.
Different stars have different absorption line
strengths
Plot of Intensity versus wavelength (λ)
How strong a line appears depends primarily on
TWO PARAMETERS
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The surface temperature
Example: If an element is ionized then it can not form
an absorption line.
The amount of a particular element present in the
star.
Example: If there is no Iron in a star, how strong will
the absorption line for Iron appear to be?
If there is no Iron in a star, how strong will
the absorption line for Iron appear to be?
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4.
Very Weak
Strong
Can’t say, it depends on the
star’s temperature
Non-existent
No shortage of hydrogen in normal stars.
But, Balmer lines are transistion between
levels n=2 and n=3,4,5,6,etc.
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In order to have the hydrogen Balmer lines
appear, Hydrogen has to be in the first excited
state. (n = 2)
Which stars are the most likely to not have
enough energy to maintain the hydrogen
electrons at the first excited state?
Which stars are the most likely to not have enough
energy to maintain the hydrogen electrons at the first
excited state?
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2.
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4.
Cool stars (M-type)
Warm stars (G-type)
Hot stars (A-type)
Hottest stars (O-type)
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If a star is very hot, the electrons will be freed
from the hydrogen atom. (Ionized)
Once they are free, they act like particles and
emit a continuous spectrum.
If the star is hot enough that hydrogen is ionized
all the way to the surface, then there will be no
hydrogen Balmer lines.
Here is how line strength depends of
temperature
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Remember, the line strength depends primarily
on two parameters. (1) Surface Temperature
and (2) Number of absorbers.
If we want learn about the number of absorbers
for a given element (say, calcium, iron, gold,
etc) then we need to know the temperature of
the star. If we know the temperature we can
account for its effect and…
The line strength will only depend on the
Number of Absorbers.
Why doesn’t the spectrum of HD 161817 line
up with the model spectrum?
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4.
The model spectrum is
wrong
The star is very far away
It is caused by the
doppler effect
I f’ed up and plotted the
spectrum wrong
Spectral typing Summary
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Spectral typing can be used to find the surface
temperature of a star. (Along with color and Wien’s
Law)
Spectral typing can also be used to find out how much
of a given element is in a star.
HD 161817 has much less of all the elements, other
than Hydrogen and Helium, than the Sun.
In fact, it has about 0.03 the value of the Sun for all 90
elements. That is 3% the amount in the Sun. The
most deficient star known has about 0.001% the Sun.
There are also stars with up to 3 times the amount in
the Sun.