Astrophysics of Life:

1
Astrophysics of Life Stars
2
Luminosity and Apparent Brightness
Star B is more luminous, but they have the same
brightness as seen from Earth.
3
Apparent Brightness and Inverse Square Law

• Light appears fainter with increasing distance.
• If we increase our distance from the light
  source by 2, the light energy is spread out over
  four times the area.
• (area of sphere 4?d2)

To know a stars luminosity we must measure its
apparent brightness (flux) and know its distance.
Then, Luminosity Flux 4?d2
4
The Magnitude Scale
2nd century BC, Hipparchus ranked all visible
stars brightest magnitude 1 faintest
magnitude 6. To our eyes, a change of one
magnitude a factor of 2.5 in flux. The
magnitudes scale is logarithmic. A change of 5
magnitudes means the flux 100 x greater!
Hence
5
Apparent Magnitude - stars apparent brightness
when seen from its actual distance Absolute
Magnitude - apparent magnitude of a star as
measured from a distance of 10 pc.
Suns apparent magnitude (if seen from a distance
of 10 pc) is 4.8. This is then the absolute
magnitude of the Sun.
6
Enhanced color picture of the sky Notice the
color differences among the stars
7
Starlight Who Cares?

• We do!
• Primary source of life energy on Earth
• Many living things convert sunlight to energy
• Most other living things eat them (or eat things
  that eat them, or )
• Also, heat/temperature
• Living things want liquid phase (remember)
• Need the right star/distance combination for
  this
• Also, want STABLE temperatures for long time
  (i.e. millions, or better yet, BILLIONS of years)

8
Stellar Temperature Color

• You dont have to get the entire spectrum of a
  star to determine its temperature.
• Measure flux at blue (B) and yellow (visualV)
  wavelengths.
• Get temperature by comparing B -V color to
  theoretical blackbody curve.

9
Stellar Temperature Spectra

• 7 stars with same chemical composition
• Temperature affects strength of absorption lines

Example Hydrogen lines are relatively weak in
the hottest star because it is mostly ionized.
Conversely, hotter temperatures are needed to
excite and ionize Helium so these lines are
strongest in the hottest star.
10
Spectral Classification
Before astronomers knew much about stars, they
classified them based on the strength of observed
absorption lines.
Annie Jump Cannon
Classification by line strength started as A, B,
C, D, ., but became O, B, A, F, G, K, M,
(L) A temperature sequence! Cannons system
officially adopted in 1910.
11
Spectral Classification
Oh Be A Fine Girl/Guy Kiss Me
Oh Brother, Astronomers Frequently Give Killer
Midterms
12
Stellar Sizes

• Almost all stars are so small they appear only as
  a point of light in the largest telescopes
• A small number are big and close enough to
  determine their sizes directly through geometry

13
Stellar Sizes Indirect measurement
Stefans Law F ?T4
Luminosity is the Flux multiplied by entire
spherical surface
Giants - more than 10 solar radii
Dwarfs - less than 1 solar radii
Area of sphere A 4?R2
14
Understanding Stefans Law Radius
L ? R2 ? T4
15
Understanding Stefans Law Temperature
L ? R2 ? T4
16
Hertzsprung-Russell (HR) Diagram
HR diagrams plot stars as a function of their
Luminosity Temperature
About 90 of all stars (including the Sun) lie on
the Main Sequence. where stars reside during
their core Hydrogen-burning phase.
17
From Stefans law...
L 4?R2 ?T4

• More luminous stars at the same T must be
  bigger!
• Cooler stars at the same L must be bigger!

18
The HR Diagram 100 Brightest Stars

• Most of these luminous stars are somewhat rare
  they lie beyond 5pc.
• We see almost no red dwarfs (even though they are
  very abundant in the universe) because they are
  too faint.
• Several non-Main Sequence stars are seen in the
  Red Giant region

19
Using The HR Diagram to Determine Distance
Spectroscopic Parallax
Example
1) Determine Temperature from color
2) Determine Luminosity based on Main Sequence
position
Main Sequence
3) Compare Luminosity with Flux (apparent
brightness)
4) Use inverse square law to determine distance
20
The HR Diagram Luminosity Spectroscopic
Parallax
What if the star doesnt happen to lie on the
Main Sequence - maybe it is a red giant or white
dwarf??? We determine the stars Luminosity
Class based on its spectral line widths
These lines get broader when the stellar gas is
at higher densities indicating a smaller star.
21
The HR Diagram Luminosity Class
22

• We get distances to nearby planets from radar
  ranging.
• That sets the scale for the whole solar system
  (1 AU).
• Given 1 AU plus stellar parallax, we find
  distances to nearby stars.

• Use these nearby stars, with known Distances,
  Fluxes and Luminosities, to calibrate Luminosity
  classes in HR diagram.
• Then spectral class Flux yields Luminosity
  Distance for farther stars (Spectroscopic
  Parallax).

23
Stellar Masses Visual Binary Stars

• With Newtons modifications to Keplers laws, the
  period and size of the orbits yield the sum of
  the masses, while the relative distance of each
  star from the center of mass yields the ratio of
  the masses.
• The ratio and sum provide each mass individually.

24
Stellar Masses Spectroscopic Binary Stars
Many binaries are too far away to be resolved,
but they can be discovered from periodic spectral
line shifts.
In this example, only the yellow (brighter) star
is visible
25
Stellar Masses Eclipsing Binary Stars
How do we identify eclipsing binaries?
The system must be observed edge on. Also tells
us something about the stellar radii.
26
The HR Diagram Stellar Masses
Why is mass so important? Together with the
initial composition, mass defines the entire
life cycle and all other properties of the
star! Luminosity, Radius, Surface Temperature,
Lifetime, Evolutionary phases, end result.
27
Example On the Main Sequence Luminosity ?
Mass3 Why?

• More mass means
• more gravity,
• more pressure on core,
• higher core temperatures,
• faster nuclear reaction rates,
• higher Luminosities!

28
How does Mass effect how long a star will live
Lifetime ? Fuel available / How fast fuel is
burned
So for a star
Lifetime ? Mass / Luminosity
Lifetime ? Mass / Mass3 1 / Mass2
How long a star lives is directly related to the
mass!
Big stars live shorter lives, burn their fuel
faster.