Download Stars

Astrophysics of Life :
Stars
Wave Characteristics:
•Wavelength - Distance between
successive wave peaks
•Period – Time between passing wave
peaks
•Frequency – Number of wave peaks
passing per unit time (1/Period)
•Wave Speed – wavelength x
frequency (follow a crest)
Light Speed is 3x108 m/s
2
Wavelength =
400nm
500nm
600nm
COLOR
700nm
Visible light ranges in wavelength from
~400 to ~700 nanometers.
3
Electromagnetic Spectrum
Microwav
es,
cooking
heat
communication
most
energetic
sunburn
detected by our
eyes
penetrate
tissue
4
Blackbodies with different temperatures look like this:
Hotter blackbodies are brighter and “bluer.”
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Wien’s Law
 “Hotter bodies radiate more
strongly at shorter wavelengths (i.e.
they’re bluer).”
max =
0.29 cm
T (K)
We can measure a star’s temperature from its spectrum!
6
max =
0.29 cm
T (K)
(Flux)
Wien math fun
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Stefan’s Law
 “Hotter blackbodies are brighter
overall (at every wavelength).”
F =  T4
where: F = total radiative flux
 = constant
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Emission Line Spectra
Each element produces its own unique pattern of lines
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Absorption Line Spectra
Spectrum of the Sun:
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Luminosity and Apparent Brightness
Star B is more
luminous, but
they have the
same brightness
as seen from
Earth.
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)
Flux =
Luminosity
4d2
To know a star’s luminosity we must measure its apparent
brightness (flux) and know its distance. Then,
Luminosity = Flux *4d2
The Magnitude Scale
2nd
century BC, Hipparchus
ranked all visible stars –
brightest = magnitude 1
faintest = magnitude 6.
Faintest
To our eyes, a change of one
magnitude = a factor of 2.5 in
flux.
Hence
The magnitudes scale is
logarithmic.
A change of 5 magnitudes
means the flux 100 x greater!
Brightest
Apparent Magnitude - star’s apparent brightness when
seen from its actual distance
Absolute Magnitude - apparent magnitude of a star as
measured from a distance of 10 pc.
Sun’s apparent
magnitude (if seen
from a distance of
10 pc) is 4.8.
This is then the
absolute magnitude
of the Sun.
Enhanced color picture of the sky
Notice the color differences among the stars
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)
Stellar Temperature: Color
•You don’t have to get
the entire spectrum of a
star to determine its
temperature.
•Measure flux at blue (B)
and yellow (“visual”=V)
wavelengths.
• Get temperature by
comparing B -V color to
theoretical blackbody
curve.
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.
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!
Cannon’s system officially adopted in
1910.
Spectral Classification
“Oh Be A Fine Girl/Guy Kiss Me”
“Oh Brother, Astronomers Frequently Give Killer Midterms”
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
Stellar Sizes: Indirect measurement
Stefan’s Law
Luminosity is the Flux
multiplied by entire spherical
surface
Area of sphere
A = 4R2
Luminosity = 4R2 T4
-orL  R2  T4
F = T4
Giants - more than 10 solar radii
Dwarfs less than 1
solar radii
Understanding Stefan’s Law: Radius
L  R2  T4
Understanding Stefan’s Law: Temperature
L  R2  T4
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.
From Stefan’s
law…...
L = 4R2 T4
 More luminous
stars at the same T
must be bigger!
 Cooler stars at
the same L must
be bigger!
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
Using The HR Diagram to Determine Distance:
Spectroscopic “Parallax”
Example:
1) Determine Temperature from color
Main Sequence
2) Determine Luminosity based on
Main Sequence position
3) Compare Luminosity with Flux
(apparent brightness)
4) Use inverse square law to
determine distance
Flux =
Luminosity
4d2
The HR Diagram: Luminosity & Spectroscopic Parallax
What if the star doesn’t happen to lie on the Main
Sequence - maybe it is a red giant or white dwarf???
We determine the star’s Luminosity Class based on its
spectral line widths:
A star
These lines get
broader when
the stellar gas
is at higher
densities –
indicating a
smaller star.
Supergiant
A star
Giant
A star Dwarf
(Main Sequence)
Wavelength

The HR Diagram: Luminosity Class
Bright Supergiants
Supergiants
Bright Giants
Giants
Sub-giants
Main-Sequence (Dwarfs)
 We get distances to
nearby planets from
radar ranging.
The Distance Ladder
 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).
Stellar Masses:
Visual Binary Stars
•With Newton’s modifications to Kepler’s 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.
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…
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.
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….
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!
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
Or, since Luminosity  Mass3
For main sequence stars
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….