Measuring Stars

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Measuring Stars
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What Stellar Properties do we want to measure?

• Distances
• Intrinsic Brightnesses (Luminosities)
• Motions
• Temperatures
• Diameters
• Masses

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Measuring Distances
The most important measurement we can make of a
star is its Distance. Once we know the
distance to a star, we can determine its
luminosity, its diameter, and many other things
of interest. The only direct way to measure the
distance of a star is through the method of
Trigonometric Parallax.
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Trigonometric Parallaxes
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Trigonometric Parallax
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Trigonometric Parallaxes are measured in
seconds of arc. Recall that 1 second of arc
1/60 minute of arc 1 minute of arc 1/60
degree. A star with a parallax of 1" has a
distance of 206265 A.U. Therefore, we define
1 Parsec 206265
A.U. Then, Distance in Parsecs 1/(parallax in
seconds of arc) d
1/p 1 Parsec 3.26 light years.
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Parallax Example Vega has a parallax of 0.133".
What is its distance in parsecs? d 1/p
1/0.133 7.52 pc Distance in light years? 1
parsec 3.26 lightyears, so, d 7.52pc X 3.26
lightyears/pc 24.5 ly.
Try this one The parallax of
Sirius is 0.378", what is its distance in parsecs
and lightyears?
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• Answer?
• 3.78 pc, 12.33 lyr
• 2.65 pc, 8.62 lyr
• 77968 pc, 23917 lyr

d 1/p 1/0.378 2.65 pc 2.65pc 8.62
lightyears
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The Brightness of Stars
We measure the brightness of stars using the
Magnitude system. Recall that most of the
brightest stars in the sky are 1st magnitude.
The faintest stars visible to the naked eye are
6th magnitude. The magnitude system is defined
so that
A difference of 5 magnitudes a factor of 100
in the brightness of the stars. Thus, a 1st
magnitude star is 100 times brighter than a 6th
magnitude star.
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Really bright objects actually have
negative magnitudes on the magnitude system.
Thus, Sirius, the brightest star in the sky has a
magnitude of mv 1.46.
Venus (at brightest) mv -4 Full Moon mv
-12.6 Sun mv -26
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Intrinsic Brightness of Stars

• What we really want to measure is the actual
• or intrinsic brightness of a star, which is a
  measure
• of the luminosity (or wattage) of the star. The
• Apparent brightness (or magnitude) of a star is
• due to two things
• The distance to the star
• The intrinsic brightness of a star.

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Absolute Magnitude
We define the Absolute Magnitude of a star to
be the apparent magnitude the star would have
if it were located at a distance of 10
parsecs. Mv Absolute Magnitude
Mv mv 5 log(d/10)
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Absolute Magnitude Example
Vega parallax 0.133", mv 0.03 d 1/0.133
7.52pc Mv mv 5 log(d/10) Mv 0.03 5
log(7.52/10) 0.03 5 (-.124) Mv 0.65
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Calculate the absolute magnitude of Sirius. We
have d 2.65pc, mV -1.47. What is MV?
MV mv 5log(d/10) -1.47 5log(0.265)
-1.47 2.88 1.41
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Absolute Magnitudes (continued)
The absolute magnitudes of stars range from -8
(for supergiants) to 16 (faint white
dwarfs). The absolute magnitude of the sun is
4.83
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Stellar Velocities

• Stellar velocities must be measured
• Along the line of sight (Radial Velocities)
• Perpendicular to the line of sight (Tangential
  velocities, yielding Proper Motions)

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Radial Velocities
If a star is moving away from or toward
the Earth, its spectral lines will show either a
red shift or a blue shift (Doppler effect). The
velocity can be calculated from this shift
(??) Vr c (??/?) Vr Radial velocity
positive ? red shift (receding) negative ? blue
shift (approaching)
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Radial Velocity Example
In the laboratory, the wavelength of H?? is
measured to be 656.3nm. In a distant galaxy,
this same line has a wavelength of 706.5nm. What
is the velocity of the galaxy?
Vr c(???/?), where ?? ?obs - ?rest 706.5
656.3
50.2nm
c 3.0 X 105 km/s Vr 3.0 X 105
km/s(50.2nm/656.3nm) 22950km/s
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Proper Motions
If a star moves perpendicular to our line of
sight, we say it shows a Tangential Velocity,
which leads to Proper Motion (µ).
The proper motion of Barnards star.
VT 4.74µd
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Proper Motion and the Big Dipper
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Space Velocities
The Radial Velocity (VR) and the Tangential
Velocity (VT) represent two components of the
stars Space Velocity, VS
VS (VR2 VT2)1/2
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Temperatures
How do we measure the temperature of a
star? Recall that a star is approximately a Black
Body Radiator. As the temperature of a Black
Body Radiator increases, its color changes from
red to orange, to yellow, white and finally
bluish. Therefore, the color of a star is
correlated with its temperature.
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The Color Index
If we measure the brightness of a star through
a Blue (B) filter and a yellow-green (V) filter,
a hot star will look brighter through the B
filter than through the V filter
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The Color Index (continued)
With a photometer on our telescope, we
can measure the B magnitude of the star and the
V magnitude, and then form the difference, B
V, which is called the B-V index. This index
is correlated with temperature B-V
Temperature -0.30
30,000K 0.00 10,000K
(Vega) 0.60 5,800K
(Sun) 1.80 3,000K
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The Hertzsprung-Russell Diagram Plot the
temperature of the star versus the absolute
magnitude (or luminosity)
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Temperature (continued)
However, the B-V color index can be fooled
by Interstellar reddening, caused by dust in
interstellar space.
This can lead us to think that a hot (blue) star
is actually a cool (red) star.
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Temperature, continued
The appearance of the Spectrum of a star is
not changed by interstellar reddening
Hot
Cool
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Features in the spectrum can be used to
determine the temperature. Note the behavior of
the Hydrogen lines
Hydrogen Lines
?
?
Hot
Cool
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The Balmer (Hydrogen) Thermometer
Temperature
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Why do the Balmer lines come to a
maximum at an intermediate temperature?
Recall the energy level diagram of the Hydrogen
atom
For a Balmer absorption line to form, the
electron must first be excited up to the second
(n2) energy level. Cool stars Not enough
Hydrogen atoms excited to n2, thus Balmer lines
weak.
Hot stars Most of the Hydrogen atoms have been
ionized (electron lost), again giving weak Balmer
lines.
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The problem with the Balmer thermometer is
that it gives two different temperatures for the
star.
What this means is that we must consider
other absorption lines in the spectrum of the
star to determine the correct temperature.
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Hot stars show lines of Helium in their spectra,
whereas cooler stars show spectral lines due to
different metals, such as Iron and Calcium.
Using these lines, which come to maxima at
different temperatures allows us to determine the
correct temperature.
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A side note on how stellar spectra are displayed
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Hot
Luke Warm
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Luke Warm
Cool
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The Spectral Classification System
Spectral T(K) Spectral Features
class O 20-30,000K Weak
Hydrogen, lines of Ionized Helium B
10-20,000K Stronger Hydrogen, lines of
neutral helium A 8 10,000K
Hydrogen lines at max, weak lines of metals
F 6 8000K Hydrogen lines weaker,
metals stronger G 5 6000K
Hydrogen lines very weak, metals strong,
features due to molecules make appearance K
4 5000K Hydrogen lines very very
weak, metals very strong, molecules
strong M 2 4000K Spectrum
dominated by molecules
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OBAFGKM
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The Hertzsprung-Russell Diagram Plot the
temperature of the star versus the absolute
magnitude (or luminosity)
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The Spectral Classification system also
includes a Luminosity Dimension Ia Bright
Supergiant Ib Supergiant II Bright
Giant III Giant IV Subgiant V Dwarf (Main
Sequence)
Sun G2 V Vega A0 V Betelgeuse M2 Ia Rigel
B8 Ia
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Notice in the HR diagram that we can have
two stars with the same temperature, but
different luminosities (dwarf giant, for
instance). If these two stars have the same
temperature, the only way they can have different
luminosities is
if they have different sizes. Recall
the Stefan-Boltzman law L 4??R2T4
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Relative sizes of the sun, and a typical giant
and supergiant
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A Form of the Stefan-Boltzmann Law Useful
to Astronomers
L Luminosity of the Star R Radius of
Star T Temperature of Star So,
For a star
L? 4psR?2T?4
For the sun
Dividing the two equations,
And canceling common factors ,
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Example
A star has a radius twice that of the Sun
But its temperature is three times the suns
How does its luminosity compare?
(324 times more luminous than the sun.)
Thus
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Try this
Find R
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Which means