Download 09astrophysics_2007Nov

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Intro to
Astrophysics
Dr. Bill Pezzaglia
Updated: Nov
2007
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III. Introduction To Astrophysics
A. Distances to Stars
B. Binary Stars
C. HR Diagrams
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A. Stellar Distances
1. Method of Parallax
2. Absolute Magnitudes
3. Magnitude-Distance Relation
1a. Measuring Distance to Stars
Parallax: the apparent change in position
of object (against distant background)
due to shift in position of observer
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1b. Parallax
As the earth
goes around
sun, the close
stars will
appear to move
relative to
background
stars.
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1c. Parallax
So over a year the close stars
would appear to move
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1d. The Parsec
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A star that has a parallax of 1 arcsecond is
defined to be 1 parsec away
Parsec is:
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3.26 light years
200,000 AU
3x1016 meters
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1e. Parallax
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1f. Parallax
Closer stars will have a bigger parallax
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1g. Parallax Formula
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Formula: Distance (pc)=1/parallax
Limiting Optical resolution of telescope
(due to wave nature of light) limits smallest
parallax we can measure
Parallax Distance Note
0.01”
100 pc
Hipparchos Limit
0.25”
4 pc
Smallest can measure from Earth
0.74”
1.35 pc
Closest Star
1”
1 pc
Definition of Parsec
2”
0.5 pc
1h. Bessel measures first parallax
(61 Cygni) in 1838
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1i. Bessel measures first parallax (61
Cygni) in 1838
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2a. Apparent Magnitude “m”
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•Apparent
Magnitude: how
bright the star appears
in the sky
•The sun appears very
bright only because its
very close
•Actually the sun is
one of the fainter stars
2b. Absolute Magnitude “M”
•Absolute Magnitude: how bright the would be if
viewed at standard distance
•Standard Distance: is 10 parsecs
•Sun is M=+4.83
•Star with 100 Solar Luminosities (100 x brighter
than sun) would be 5 magnitudes brighter, or have
absolute magnitude of M= -0.17
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3a. Inverse Square Law
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3b. Inverse Square Law
•Apparent Luminosity drops off inversely proportional
to squared distance.
•Sun at 100 parsecs away (10x standard) would
appear 1/100 as bright.
•A factor of 100 is 5
magnitudes.
•Sun’s apparent
magnitude at 100 pc
would be m=M+5,
where M=+4.83
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3c. Magnitude-Distance Relation
•M=Absolute Magnitude
•m=Apparent Magnitude
•(m-M) is called the “distance modulus”
(m-M)
D (pc)
-5
1 pc
0
10 pc
+5
100 pc
+10
1000 pc
+15
10,000 pc
Given Sun has M=+4.83
If the sun was near the
galactic core (10,000
parsecs away) it would
appear as apparent
magnitude: m=+19.83
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B. Binary Stars
1. Measure Mass of Stars
2. Eclipsing Binaries measure
size
3. Spectroscopic Binaries
1a. Binary Star
•Two stars orbit around each other
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1b. Center of Mass
The stars orbit about a common “center of mass”
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1c. Center of Mass
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•The stars orbit about a
common “center of mass”
•The distances of each
star to the center is
inversely proportional to
their masses: m1r1=m2r2
•The velocities of the stars
are proportional to their
orbital radii: v1/r1 = v2/r2
1d. Doppler Velocity
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1e. Doppler Velocity
•Doppler Effect: object moving away will have its
wavelengths redshifted (shifted to red)
•Amount of shift is proportional to speed: v/c = Dl/l
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2a. Solving the System
•“Spectroscopic Binaries” are so close together you
only see one star, but we can see the spectral lines
split and converge as the starts orbit.
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2b. Solving the System
•Product of period with velocity gives size of orbit
•Kepler-Newton Law gives stellar Mass: a3/P2
•From measuring angular separation can get
distance to binary star system.
•Hence the absolute luminosities can be determined
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2c. Mass Luminosity Relation
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•1913 H.N. Russell
studied binary star
systems and established
a relationship between
the masses of (main
sequence) stars and their
brightness. (check this)
•Approximately the
luminosity is proportional
to the (mass)4
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3a. Eclipsing Binaries
•The lengths of the eclipses give a measure of the
diameters of the stars.
•Only a small
fraction of stars
are oriented so
we see eclipses
•Algol is an
eclipsing binary
3b. Broadening of Spectral Lines
•If a star is rotating,
spectral lines will be
broadened due to
doppler effect
•Giant stars will
show more
broadening.
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3c. Indirectly Determining Sizes
•If you know the absolute magnitude of the star
(i.e. know the distance to the star) there is an
indirect way to determine the size of a star
•Determine the temperature (Wien’s law)
•Use the Stefan-Boltzmann law to determine the
size.
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3d. Stellar Sizes
•Smaller stars are 1/10 the size of the sun
•Red Giant stars are 10x the size of the sun
•Supergiant stars are perhaps 100x bigger
than the sun.
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C. Stellar Sequences
1. Spectral Classes
2. H-R Diagram
3. Stellar Sequences
1a. Color Indexing
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If we can measure the color of a star, we can
calculate its temperature (Wien’s Law)
Measure magnitude of star through color filters
Color Index=C.I. = B-V is measure of
temperature of star.
Standard Filters
U filter 370 nm
B filter 440 nm
V filter 550 nm
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1b. Color Ratio
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Recall that subtracting magnitudes is
equivalent to taking a ratio of luminosities
B-V = 2.5 Log(bv/bb)
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bv = luminosity in yellow
bb = luminosity in blue
B=magnitude in blue
V=magnitude in yellow
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1c. Hertzsprung’s Studies
•Not knowing distances to stars,
he didn’t know the absolute
magnitudes.
•But, a cluster of stars will all be
at the same distance
•So plot apparent magnitude vs
temperature
•1911 plotted Hyades and
Pleiades clusters, found
relationship between
temperature and luminosity
•1905 coined term “giant stars”
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2a. Persistence of Lines
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A more precise method is to look at the relative strengths of
various spectral lines to determine temperature.
2b. Spectral Classes
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Classes: (hot to cold): O B A F G K M
Subclasses: (hot to cold) B7 B8 B9 A0 A1 A2 etc.
Russell suggests Oh Be A Fine Girl Kiss Me
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2c. Spectral Classes
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2d. How we determine properties of stars
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3a. Hertzsprung-Russel Diagram
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•Combining their work,
they were able to calibrate
Hertzsprung’s diagram
•90% of stars fall on the
“main sequence”. They
are all burning hydrogen
into helium (like sun), and
obey the mass-luminosity
relation.
•The other 10% are giants
and white dwarfs.
3b. Luminosity Classes
•Sequence V is main
sequence. The sun is
hence a “G2 V”
•The other sequences
have different fuel cycles.
•Red giants are sequence
III and are burning helium
into carbon.
•Supergiants burn carbon
into heavier elements.
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3c. Spectroscopic Parallax
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•The distance to a
star can be
estimated if we can
guess which
sequence to which
the star belongs.
•From spectral
class, lookup
absolute
magnitude on HR
diagram.
•Use (m-M) to get
distance.
M=-10
M=-5
M=0
M=+5
M=+10
M=+15
Summary
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Summary
Most of the
stars visible
to naked eye
are giants
and
supergiants,
or the
brighter main
sequence
stars (B, A,
F).