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ASTR 200 : Lecture 13
Basic Properties of Stars
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Once you get past the Oort cloud,
we reach empty interstellar space
Scales
1 au : Earth-Sun semimajor axis
5 au : Jupiter's semimajor axis, start of outer Solar System
30 au : Neptune's semimajor axis, end of planetary system
30-1000 au : The Kuiper Belt
1000 au – 50,000 au : The Oort cloud
How far away are the stars?
How can one measure it???
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How can one measure the distance to,
or size of, a point of light???
• What can we directly observe about a star?
– It's position on the sky
• Maybe parallax, if close enough
• Proper motion, if star is close and moving fast
– The radiation we receive
• Incident flux
• Spectrum
– Allows measurement of radial motion
– Allows surface T to be estimated
– Provides compositional information
– Even provides rotational information
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Direct distances to stars (parallax)
Recall that a nearby star's distance is related to the parallactic angle  due to the annual
motion of the Earth:
('') = 1 / d(pc)
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Stars within about 10 pc ~ 30 light years from the Sun
Hipparcos satellite
Measured good parallaxes out to ~100 pc
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Gaia space mission
Will measure parallaxes 'this half of the galaxy'
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Stellar motions
The star's true motion (or star's velocity VS) can be decomposed
Into two perpendicular components:
­ The radial velocity VR (>0 if away)
­ the tangential velocity VT, when
observed at distance d generates
a `proper motion' (angular rate) μ = VT/d
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(typically given in ''/year)
A close star will appear to slowly shift
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Barnard's Star
Close by, AND fast moving
Proper motion is roughly
North by 20 ''/year
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Barnard's Star
Close by, AND fast moving
Proper motion is roughly
North by 20 ''/year
Notice the annual parallax
superposed here! (left­right motion)
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Stars within about 10 pc = 30 light years from the Sun
Radial motion: from the Doppler effect
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The Doppler Effect
The (non­relativistic) doppler effect relates the observed wavelength λo of a wave (in this case a spectral line) to
that emitted λe in the lab, and the radial speed vr of the emitter relative to the observer λ
−λ
v
o
e
r
Δλ =
=
λe
λe
c
SIGNS note: vr> 0 is for motion APART, giving λo > λe
UNITS note: Need v and c in the same units; if one uses consistent units for wavelengths, all will be OK.
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So, can measure speeds of CARS!
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The Doppler Effect
1. Light emitted from an object moving towards you will have its wavelength shortened.
BLUESHIFT
2. Light emitted from an object moving away from you will have its wavelength lengthened.
REDSHIFT
3. Light emitted from an object moving perpendicular to your line­of­sight will not
change its wavelength (unless v~c, in which
case use relativistic).
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The Doppler shift for light

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So, can measure speeds of STARS!
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Measuring Radial Velocity
We can measure the Doppler shift of emission or absorption lines in the spectrum of
an astronomical object.
Can calculate the velocity of the object in the direction either towards or away from
Earth. (radial velocity)
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Measuring Rotational Velocity

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Called 'rotational broadening' of spectral lines

The Doppler shift for light

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The relativistic Doppler effect
Once the emitter/observer distances are changing by speeds that become
a non­negligible fraction of the speed of light, the previous formulation is only a first­order approximation
Derivation requires special relativity, due to time dilation. We will just use
the result, for a light emitter moving a speed v away from an observer, that:
1+ v / c
√
λ o =λ e
√ 1−v / c
Notice that as v approaches c, the observed wavelength o goes to infinity.
The `redshift' z is defined as : 25
λ o −λ e
z≡
λe
Stellar Temperatures, from spectra
Can match full stellar spectrum
to a 'best fit' blackbody.
­ eg: Sun's spectrum (red)
Inverse wavelength (cm­1)
Sometimes, this fitting is
complicated by the many
spectral lines present.
­ so a 'best' match is
a bit of an art...
­ stars are not perfect blackbodies in any case.
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Example of estimating stellar radii
The nearby star 'Sirius A' has a surface temperature T~10,000 K and
a flux of arriving radiation at Earth (integrated over all wavelengths) of :
F = 1.2 x 10­7 W/m2
From measurement of parallax, the distance is r = 2.64 pc = 8.1x1016 m
The energy output of the star, as it washes over the Earth, is spread out
over a sphere of surface area 4r2, so the total intrinsic luminosity is
L = 4 r2 F = 1.0 x 1028 W = 26 solar luminosities
This then allows us to get the stellar radius R, because under the assumption
that the star radiates like a black body, L = 4 R2 T 4 so solving for
R and plugging in gives:
R = 1.7 solar radii
So Sirius A is a star about twice as hot and twice as big as the Sun. Note
that because L varies as the 4th power of T, this makes the 26x luminosity
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size or smaller
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But some are MUCH larger than the Sun
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