Stellar Spectra

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Stellar Spectra

• Brightness of stars
• Colors/spectra of stars
• Classifying stars H-R diagram
• Measuring star masses
• Mass-luminosity relation

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Brightness of stars

• The brightness of a star is a measure of its
  flux.
• Ptolemy (150 A.D.) grouped stars into 6
  magnitude groups according to how bright they
  looked to his eye.
• Herschel (1800s) first measured the brightness of
  stars quantitatively and matched his measurements
  onto Ptolemys magnitude groups and assigned a
  number for the magnitude of each star.

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Brightness of stars

• In Herschels system, if a star is 1/100 as
  bright as another then the dimmer star has a
  magnitude 5 higher than the brighter one.
• Note that dimmer objects have higher magnitudes

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Apparent Magnitude
Consider two stars, 1 and 2, with apparent
magnitudes m1 and m2 and fluxes F1 and F2. The
relation between apparent magnitude and flux is
For m2 - m1 5, F1/F2 100.
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Flux, luminosity, and magnitude
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Distance-Luminosity relationWhich star appears
brighter to the observer?
Star 1
10L
L
Star 2
d
10d
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Flux and luminosity
Star 2 is dimmer and has a higher magnitude.
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Absolute magnitude

• The magnitude of a star gives it brightness or
  flux when observed from Earth.
• To talk about the properties of star, independent
  of how far they happen to be from Earth, we use
  absolute magnitude.
• Absolute magnitude is the magnitude that a star
  would have viewed from a distance of 10 parsecs.
• Absolute magnitude is directly related to the
  luminosity of the star.

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Absolute Magnitude
Absolute magnitude, M, is defined as
where D is the distance to the star measured in
parsecs. For a star at D 10 parsecs, 5log10
5, so M m.
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Absolute Magnitude and Luminosity
The absolute magnitude of the Sun is M
4.83. The luminosity of the Sun is L?
Note the M includes only light in the visible
band, so this is accurate only for stars with the
same spectrum as the Sun.
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Absolute Bolometric Magnitude and Luminosity
The bolometric magnitude includes radiation at
all wavelengths. The absolute bolometric
magnitude of the Sun is Mbol 4.74.
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• Is Sirius brighter or fainter than Spica
• as observed from Earth apparent magnitude
• Intrinsically luminosity?

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Sun
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Little Dipper (Ursa Minor) Guide to naked-eye
magnitudes
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Which star would have the highest magnitude?

• Star A - 10 pc away, 1 solar luminosity
• Star B - 30 pc away, 3 solar luminosities
• Star C - 5 pc away, 0.5 solar luminosities
• Charlize Theron

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What can we learn from a stars color?

• The color indicates the temperature of the
  surface of the star.

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Observationally, we measure colors by comparing
the brightness of the star in two (or more)
wavelength bands.
U
B
V
This is the same way your eye determines color,
but the bands are different.
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Use UVRI filters to determine apparent magnitude
at each color
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Stars are assigned a spectral type based on
their spectra

• The spectral classification essentially sorts
  stars according to their surface temperature.
• The spectral classification can also use spectral
  lines.

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Spectral type

• Sequence is O B A F G K M
• O type is hottest (25,000K), M type is coolest
  (2500K)
• Star Colors O blue to M red
• Sequence subdivided by attaching one numerical
  digit, for example F0, F1, F2, F3 F9 where F1
  is hotter than F3 . Sequence is O O9, B0, B1,
  , B9, A0, A1, A9, F0,
• Useful mnemonics to remember OBAFGKM
• Our Best Astronomers Feel Good Knowing More
• Oh Boy, An F Grade Kills Me
• (Traditional) Oh, Be a Fine Girl (or Guy), Kiss Me

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Very faint
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The spectrum of a star is primarily determined by

• The temperature of the stars surface
• The stars distance from Earth
• The density of the stars core
• The luminosity of the star

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Classifying stars

• We now have two properties of stars that we can
  measure
• Luminosity
• Color/surface temperature
• Using these two characteristics has proved
  extraordinarily effective in understanding the
  properties of stars the Hertzsprung-Russell
  (HR) diagram

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HR diagram
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HR diagram

• Originally, the HR diagram was made by plotting
  absolute magnitude versus spectral type
• But, its better to think of the HR diagram in
  terms of physical quantities luminosity and
  surface temperature

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If we plot lots of stars on the HR diagram, they
fall into groups
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These groups indicate types of stars, or stages
in the evolution of stars
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Stars come in a variety of sizes

• Recall the Stefan-Boltzmann law relates
  luminosity, temperature, and size
• L 4pR2sT4
• Small stars will have low luminosities unless
  they are very hot.
• Stars with low surface temperatures must be very
  large in order to have large luminosities.

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Sizes of Stars on an HR Diagram

• We can calculate R from L and T.
• Main sequence stars are found in a band from the
  upper left to the lower right.
• Giant and supergiant stars are found in the upper
  right corner.
• Tiny white dwarf stars are found in the lower
  left corner of the HR diagram.

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Hertzsprung-Russell (H-R) diagram

• Main sequence stars
• Stable stars found on a line from the upper left
  to the lower right.
• Hotter is brighter
• Cooler is dimmer
• Red giant stars
• Upper right hand corner (big, bright, and cool)
• White dwarf stars
• Lower left hand corner (small, dim, and hot)

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Luminosity classes

• Class Ia,b Supergiant
• Class II Bright giant
• Class III Giant
• Class IV Sub-giant
• Class V Dwarf
• The Sun is a G2 V star

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Spectroscopic ParallaxMeasuring a stars
distance by inferring its absolute magnitude (M)
from the HR diagram

• If a star is on the main-sequence, there is a
  definite relationship between spectral type and
  absolute magnitude. Therefore, one can determine
  absolute magnitude by observing the spectral type
  M.
• Observe the apparent magnitude m.
• With m and M, calculate distance

Take spectrum of star, find it is F2V, absolute
magnitude is then M 4.0. Observe star
brightness, find apparent magnitude m
9.5. Calculate distance
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Masses of stars

• Spectral lines also allow us to measure the
  velocities of stars via the Doppler shift that we
  discussed in searching for extra-solar planets.
  Doppler shift measurements are usually done on
  spectral lines.
• Essentially all of the mass measurements that we
  have for stars are for stars in binary systems
  two stars orbiting each other.
• The mass of the stars can be measured from their
  velocities and the distance between the stars.

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Binary star systems Classifications

• Double star a pair of stars located at nearly
  the same position in the night sky.
• Optical double stars stars that appear close
  together, but are not physically conected.
• Binary stars, or binaries stars that are
  gravitationally bound and orbit one another.
• Visual binaries true binaries that can be
  observed as 2 distinct stars
• Spectroscopic binaries
• binaries that can only be detected by seeing two
  sets of lines in their spectra
• They appear as one star in telescopes (so close
  together)
• Eclipsing binaries binaries that cross one in
  front of the other.

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Visual Binary Star Krüger 60 (upper left hand
corner)
About half of the stars visible in the night sky
are part of multiple-star systems.
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Keplers 3rd Law applied to Binary Stars

• Where
• G is gravitational constant
• G 6.6710-11 m3/kg-s2 in SI units
• m1, m2 are masses (kg)
• P is binary period (sec)
• A is semi-major axis (m)

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Simplified form of Keplers 3rd law using
convenient units
Where M in solar masses a in AU P in Earth years
Example a 0.05 AU, P 1 day 1/365 yr, M1
M2 16.6 Msun
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Mizer-Alcor A double-double-double system!
10 arcmin
Alcor
Mizar A
Mizar AB
Mizar B
14"
Note Mizar B is also a binary with period of 6
months!
0.008"
Mizar A (Binary, P 20.5 days)
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Historical Notes on Mizar-Alcor discoveries

• Romans (c. 200BC) Used Mizar-Alcor (11 arcmin
  separation) as test of eyesight for soldiers
• Benedi Castelli (c. 1613, student and friend of
  Galileo) discovers Mizar is a double star
  (separation 15")
• "It's one of the beautiful things in the sky and
  I don't believe that in our pursuit one could
  desire better", remarked Castelli in letter to
  Galileo
• Both Galileo and Castelli were interested in
  optical doubles to prove the heliocentric view
  of solar system (nearer star would move w.r.t
  more distant star annually)
• Johann Liebknecht (1722) announced that the
  8thmag star SW of Mizar was a new planet!
  (Incorrect observation of motion)
• He named it Sidus Ludoviciana (Ludwigs Star) in
  honor of his local monarch King Ludwig.
• 1887 Pickering at Harvard announces Mizar A is a
  spectroscopic binary, 20.5 day period
• 1996 NPOI directly images the Mizar A binary
  (separation 0.008 arcsec)

Alcor
Mizar AB
Sidus Ludoviciana
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Mizar A A Spectroscopic Binary

• 1887 Spectroscopy of Mizar A shows periodic
  doubling of spectral lines, with 20.5 day period

Note Asymmetric light curves indicated ellipical
orbits
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Mizar observations using the NPOI (Naval
Prototype Optical Interferometer, near Flagstaff
Arizona)
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Determining masses of Mizar-A binary stars from
observations of period, angular separation,
distance
1. Distance (from parallax) d 24 pc (88ly)
2. Max. angular separation (NPOI meas.) T 0.008"
3. Physical separation D ?d0.19 AU
4. Sum of masses (Keplers 3rd law)
5. Orbit shows a1 a2 (NPOI meas.) so
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Spectroscopy makes it possible to study binary
systems in which the two stars are very close
together.
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1. Determine semi-major axis using observed
velocity (V), period (P)
Determining component masses of eclipsing
binaries using velocity curves
2. Determine sum of masses using Keplers 3rd law
3. Determine mass ratio using a1, a2
a1
a2
a a1 a2
4. Use sum, ratio to determine component masses
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Tilt of Binary Orbits
We have been assuming that we see the binary
system face on when imaging the orbit and edge-on
when measuring the velocity. In general, the
orbit is tilted relative to our line of sight.
The tilt, or inclination i, will affect the
observed orbit trajectory and the observed
velocities. In general, one needs both the
trajectory and the velocity to completely
determine the orbit or some independent means of
determining the inclination.
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Light curves of eclipsing binaries provide
detailed information about the two stars.
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Light curves of eclipsing binaries provide
detailed information about the two stars.
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Eclipsing Binary EQ Tau
Light curve from Astronomical Laboratory Course
Fall 2003
Java-animation of binary stars
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Eclipse of an Exo-planet (HD209458)
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Vogt-Russell theorem for spheres of water

• Spheres of water have several properties mass,
  volume, radius, surface area
• We can make a Vogt-Russell theorem for balls of
  water that says that all of the other properties
  of a ball of water are determined by just the
  mass and even write down equations, i.e.
  volume mass/(density of water).
• The basic idea is that there is only one way to
  make a sphere of water with a given mass.

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Vogt-Russell theorem

• The idea of the Vogt-Russell theorem for stars
  is that there is only one way to make a star with
  a given mass and chemical composition if we
  start with a just formed protostar of a given
  mass and chemical composition, we can calculate
  how that star will evolve over its entire life.
• This is extremely useful because it greatly
  simplifies the study of stars and is the basic
  reason why the HR diagram is useful.

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Mass - Luminosity relation for main-sequence
stars
Mass in units of Suns mass
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Mass-Luminosity relation on the main sequence
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Mass-Lifetime relation

• The lifetime of a star (on the main sequence) is
  longer if more fuel is available and shorter if
  that fuel is burned more rapidly
• The available fuel is (roughly) proportional to
  the mass of the star
• From the previous, we known that luminosity is
  much higher for higher masses
• We conclude that higher mass star live shorter
  lives

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A ten solar mass star has about ten times the
sun's supply of nuclear energy. Its luminosity is
3000 times that of the sun. How does the lifetime
of the star compare with that of the sun?

• 10 times as long
• the same
• 1/300 as long
• 1/3000 as long

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Mass-Lifetime relation
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Stellar properties on main sequence

• Other properties of stars can be calculated such
  as radius (we already did this).
• The mass of a star also affects its internal
  structure

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(solar masses)
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Evolution of stars

• We have been focusing on the properties of stars
  on the main sequence, but the chemical
  composition of stars change with time as the star
  burns hydrogen into helium.
• This causes the other properties to change with
  time and we can track these changes via motion of
  the star in the HR diagram.

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HW diagram for people
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• The Height-Weight diagram was for one person who
  we followed over their entire life.
• How could we study the height-weight evolution of
  people if we had to acquire all of the data from
  people living right now (no questions about the
  past)?

• We could fill in a single HW diagram using lots
  of different people. We should see a similar
  path.
• We can also estimate how long people spend on
  particular parts of the path by how many people
  we find on each part of the path.

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HR diagram