Stellar Spectra - PowerPoint by TYSQIy76

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									              Stellar Spectra
•   Brightness of stars
•   Colors/spectra of stars
•   Classifying stars: H-R diagram
•   Measuring star masses
•   Mass-luminosity relation
           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 Ptolemy’s magnitude
  groups and assigned a number for the
  magnitude of each star.
         Brightness of stars
• In Herschel’s 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
          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:
                                 F1 
           m1  m2  2.5 log10  
                                F 
                                 2
               F1      m2  m1  / 2.5
                   10
               F2
             For m2 - m1 = 5, F1/F2 = 100.
Flux, luminosity, and magnitude
          L
     F
        4D 2


                           F1 
     m2  m1  2.5 log 10  
                          F 
                           2
                           L1 4D2     2

                           4D 2 L 
     m2  m1  2.5 log 10                 
                                1     2   
                            L2             D2
     m2  m1  2.5 log 10       5 log 10
                             L1            D1
 Distance-Luminosity relation:
Which star appears brighter to the
            observer?
                 Star 1
                                10L
                   L

           d                   Star 2

                       10d
     Flux and luminosity
 L2                          D2
     10                         10
 L1                          D1
                      L2            D2
m2  m1  2.5 log 10     5 log 10
                      L1            D1
m2  m1  2.5 log 10 10  5 log10 10
m2  m1  2.5  5  2.5

Star 2 is dimmer and has a higher magnitude.
        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.
           Absolute Magnitude
Absolute magnitude, M, is defined as

           M  m  5 log 10 D  5
where D is the distance to the star measured in parsecs.
For a star at D = 10 parsecs, 5log10 = 5, so M = m.
      Absolute Magnitude and
            Luminosity
The absolute magnitude of the Sun is M = 4.83.
The luminosity of the Sun is L
                               4.83 M  / 2.5
           L  L  10
                                    L 
           M  4.83  2.5  log 10  
                                   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.
Absolute Bolometric Magnitude
       and Luminosity
 The bolometric magnitude includes radiation at all
 wavelengths.
 The absolute bolometric magnitude of the Sun is
 Mbol = +4.74.


                                   L 
     M bol    4.74  2.5  log10  
                                  L 
                                   
Is Sirius brighter or fainter than Spica:

(a) as observed from Earth [apparent magnitude]
(b) Intrinsically [luminosity]?
Sun
   Little Dipper
   (Ursa Minor)


Guide to naked-eye
   magnitudes
     Which star would have the highest
                magnitude?
1.   Star A - 10 pc away, 1 solar luminosity
2.   Star B - 30 pc away, 3 solar luminosities
3.   Star C - 5 pc away, 0.5 solar luminosities
4.   Charlize Theron
    What can we learn from a
          star’s color?
The color indicates the temperature of the
             surface of the star.
  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.
  Use UVRI filters to
 determine apparent
magnitude at each color
 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.
                  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
Very
faint
       The spectrum of a star is
        primarily determined by
1.   The temperature of the star’s surface
2.   The star’s distance from Earth
3.   The density of the star’s core
4.   The luminosity of the star
          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
HR diagram
            HR diagram
• Originally, the HR diagram was made
  by plotting absolute magnitude versus
  spectral type
• But, it’s better to think of the HR
  diagram in terms of physical quantities:
  luminosity and surface temperature
If we plot lots of stars on the HR
  diagram, they fall into groups
These groups indicate types of stars,
 or stages in the evolution of stars
     Stars come in a variety of sizes
Recall the Stefan-Boltzmann law relates
 luminosity, temperature, and size:
                L = 4R2sT4

• 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.
         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.
    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)
        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
       ‘Spectroscopic Parallax’
   Measuring a star’s distance by
inferring its absolute magnitude (M)
         from the HR diagram
1.    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.
2.    Observe the apparent magnitude m.
3.    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:

     m  M  5 log 10 D  5  D  10 (5.55) / 5 pc  126 pc
            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.
       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.
        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.
      Kepler’s 3rd Law applied to Binary Stars

                       4       2
                                a P
                                 3   2

                    G(m1  m2 )
Where:
• G is gravitational constant
• G = 6.67·10-11 m3/kg-s2 in SI units
• m1, m2 are masses (kg)
• P is binary period (sec)
• A is semi-major axis (m)
  Simplified form of Kepler’s 3rd law
      using convenient units
                                   3
                        a
              M1  M 2  2
                        P
               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
Mizer-Alcor : A double-double-double system!


                        10 arcmin
                Alcor

                                                      Mizar A
                                Mizar A+B
                                                     Mizar B




                                                                Note: Mizar B is
                                                                 also a binary
                                                                with period of 6
                                                                    months!


                                       Mizar A
                                (Binary, P = 20.5 days)
    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)                    Alcor
    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",                                 Mizar
        remarked Castelli in letter to Galileo                                                A+B
                                                                          Sidus Ludoviciana
     –   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 (Ludwig’s 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)
     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
          Mizar observations using the NPOI
(Naval Prototype Optical Interferometer, near Flagstaff Arizona)
 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.) Θ = 0.008"

 3. Physical separation D = θ·d=0.19 AU

 4. Sum of masses (Kepler’s 3rd law)

                     a3    0.19 3
           M1  M 2  2         2
                                    2.2
                     P    0.056
 5. Orbit shows a1 ~ a2 (NPOI meas.) so:
           M1a1  M 2 a2
           M1  M 2  1.1M 
  Spectroscopy makes it possible to
study binary systems in which the two
    stars are very close together.
     Determining component masses of eclipsing
           binaries using velocity curves
1. Determine semi-major axis using
 observed velocity (V), period (P)
          2a1          2a2
     v1           v2 
            P            P
     a  a1  a2

2. Determine sum of masses using
Kepler’s 3rd law        3
                    a
          M1  M 2  2
                    P
3. Determine mass ratio using a1, a2
 M 1a1  M 2 a2 or M 1v1  M 2v2                   a1    a2
4. Use sum, ratio to determine component masses   a = a1 + a2
               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.
Light curves of eclipsing binaries provide
detailed information about the two stars.
Light curves of eclipsing binaries provide
detailed information about the two stars.
         Eclipsing Binary EQ Tau



 Light curve from
  Astronomical
Laboratory Course
    Fall 2003




    Java-animation of
       binary stars
Eclipse of an Exo-planet
      (HD209458)
     “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.
        “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.
Mass in
units of
Sun’s mass

             Mass - Luminosity
             relation for main-
              sequence stars
Mass-Luminosity relation on
   the main sequence

                                 3.5
                    L  M 
                           
                    L  M  
                            
          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

              M   M     1
           t    3.5  2.5
              L  M     M
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?

 1.   10 times as long
 2.   the same
 3.   1/300 as long
 4.   1/3000 as long
             M   10   1
          t       
             L 3000 300
  Mass-Lifetime relation
Mass/mass of Sun   Lifetime (years)
      60                     400,000
      10                  30,000,000
       3                600,000,000
       1             10,000,000,000
      0.3           200,000,000,000
      0.1          3,000,000,000,000
     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
(solar masses)
           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.
HW diagram for people
• 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.
HR diagram

								
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