Lecture 14: Stellar Spectra & Distances
Astronomy 101/103
Terry Herter, Cornell University
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Lecture
Topics
  • Stellar Spectra
    • The classification of stars
  • The Distances to Stars
    • How far to the stars
    • Stellar Parallax
  • Stellar Magnitudes
    • Apparent, Absolute, and Bolometric

Spectral
Sequence = Temperature Sequence

The Spectral Sequence

  • A figure of the spectral sequence to be inserted here (when I find a good one - see your textbook for now) - see the link below from some sample spectra.

 

More pictures and information on spectral sequences can be found at:
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit1/sptypes.html

Absorption Line Information


Temperature
Absorption Lines
High
Ionized atoms
Intermediate
Neutral atoms
Low
Molecules


Strength of Lines vs.
Spectral Class

 

Stellar Spectral Sequence

 

Class
Temperature (K)
Features
Examples
O
28000-60000
He II, Si IV, O III
Orionis
B
10000-28000
He I, Si II, H I
Rigel, Spica
A
7500-10000
H I, Fe II, Mg II
Sirius, Vega
F
6000-7500
Neutral metals, Fe I,

weak H I and Ca II
Canopus,

Polarius
G
5000-6000
Ca II, Neutral metals
Sun, Capella
K
3500-5000
Neutral metal,

Mol. Bands, TiO
Arcturus, Aldebaran
M
<3500
Mol. Bands, TiO,

VO, Neutral Metals
Betelgeuse,

Antares

 

The Picture
is Not Yet
Complete
  • The spectral type (class) of a star gives us temperature information, but we don't know its luminosity.
  • To get the luminosity, we must know the distance!
  • Remember the inverse square law!

Stellar Distances
  • How do we measure distances to nearby stars?
  • Astronomers use the parallax method.
  • The method is similar to that used by surveyors.

Surveyor's
Method

Observing the object from points A and B, we can compute the distance to it from angles alpha and beta, and the length of the baseline.


Stellar
Parallax






A nearby star will change position on the sky relative to distant (background) stars.


Calculating
Distances

How Do We Calculate Distances?

We have a very skinny triangle on the sky.

 

Determining Distances

  • Parallax is measured in arcseconds.

Notes on
Parallax:
  • As stars get further away, their parallax becomes smaller.
  • Parallax can not be measured to better than ~0.02" from the ground (d < 50 pc).
  • Alpha Cen has the largest parallax (~0.8")
  • 1 pc = 3.26 ly (light-years)

Current
Status
  • The satellite Hipparcos has measured the parallax of 120,000 stars to better than 0.002".
  • => d < 500 pc
  • Data still being worked.


Parallax
Distances

Importance of Parallax Distances

  • Parallax is the key to knowing distances in the universe.
  • Nearby stars are the stepping stones to measuring the distances to everything else in the universe.
  • We can now compute the luminosity of stars!

 


L, f and d
  • The luminosity, brightness (flux) and distance are related by the inverse square law:
  • Knowing the brightness and the distance, we can compute L.

Example:

  • A star like the sun has an observed flux of 2.4x10-10 W/m2. If the flux of the sun at the Earth is 1 kW/m2, how many parsecs away is the star?

  • There are two ways to work it:

Method 1: Calculate Lsun directly

  • Lsun = 4 x 3.14 x (1.5 x 1011 m)2 x 1000 W/m2 = 3 x 1026 W

  • dstar = sqrt ( 3 x 1026 W / (4 x 3.14 x 2.4x10-10 W/m2 )) = 3 x 1017 m = 10 pc

    • Method 2: Proportions

     


    The Closest
    Stars

     


    Star
    Parallax (")
    Distance (pc)
    Luminosity (Lsun=1)
    Proxima Centauri
    0.763
    1.31
    5 x 10-5
    a Centauri A
    0.741
    1.35
    1.45
    a Centauri B
    0.741
    1.35
    0.40
    Barnards Star
    0.522
    1.81
    4 x 10-4
    Wolf 359
    0.426
    2.35
    2 x 10-5
    Lalande 21185
    0.397
    2.52
    5 x 10-3
    Sirius A
    0.377
    2.65
    23
    Sirius B
    0.377
    2.65
    5 x 10-3

     


    Comparing
    Stars

    • If all stars were at the same distance, it would be easy to compare their properties.
    • But we can:
      • Find stellar distance.
      • Use the inverse square law to find what it's brightness would be at a standard distance.

     

    Absolute
    Magnitude
    • Astronomers adopt 10 pc as the standard distance.
    • The brightness a star would have at this distance is its absolute magnitude (Mv).
    • This is an intrinsic property of the star!
    • This differs from apparent magnitude (mv) which is how bright a star appears in the sky.

     


    Apparent
    and
    Absolute
    Magnitude

    Relating Apparent (mv) and Absolute (Mv) Magnitude

    • Suppose a star has mv = 7.0 and is located 100 pc away.
    • It is 10 times the standard distance.
    • Thus, it would be 100 times brighter to us at the standard distance.
    • Or 5 magnitudes brighter
    • => Mv = 2.0

     


    The Distance Modulus
    Equation
    • The relation between mv and Mv is written in equation form as:
      • mv - Mv = - 5 + 5 log10( d )

        where d is in parsecs.
    • mv - Mv is called the distance modulus.

    Examples

    • Deneb: mv = 1.26 and is 490 pc away.
      • mv - Mv = - 5 + 5 log10( d )
        1.26 - Mv = - 5 + 5 log10( 490 ) = -8.5
        => Mv = -7.2
    • Sun: mv = -26.8, d = 1 AU
      • -26.8 - Mv = - 5 + 5 log10( 1/206265 )
        => Mv = 4.8

     

    Bolometric Magnitude

    • The absolute bolometric magnitude is the brightness at ALL wavelengths.
    • Usually represented by M.
    • Mv is the absolute visual magnitude.

    Magnitude
    Summary
    • mv = apparent magnitude
      • apparent visual brightness of a star in the sky
    • Mv = absolute magnitude
      • visual brightness the star would have if it were at 10 pc
    • M = bolometric magnitude
      • total brightness (over all wavelengths) a star would have if it were at 10 p
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