Intro to Astrophysics

Dr. Bill Pezzaglia

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Updated: Nov 2007

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

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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. ParallaxSo over a year the close stars would appear to move

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1d. The Parsec• A star that has a parallax of 1 arcsecond is

defined to be 1 parsec away• Parsec is:

• 3.26 light years • 200,000 AU• 3x1016 meters

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1e. Parallax 8

1f. ParallaxCloser stars will have a bigger parallax

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1g. Parallax Formula• Formula: Distance (pc)=1/parallax• Limiting Optical resolution of telescope

(due to wave nature of light) limits smallest parallax we can measure

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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” 13

•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” 14

•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

3a. Inverse Square Law 15

3b. Inverse Square Law 16

•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

3c. Magnitude-Distance Relation 17

•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=+4.83If the sun was near the galactic core (10,000 parsecs away) it would appear as apparent magnitude: m=+19.83

B. Binary Stars

1. Measure Mass of Stars

2. Eclipsing Binaries measure size

3. Spectroscopic Binaries

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1a. Binary Star 19

•Two stars orbit around each other

1b. Center of Mass 20

The stars orbit about a common “center of mass”

1c. Center of Mass 21

•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 22

1e. Doppler Velocity 23

•Doppler Effect: object moving away will have its wavelengths redshifted (shifted to red)

•Amount of shift is proportional to speed: v/c =

2a. Solving the System 24

•“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.

2b. Solving the System 25

•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

2c. Mass Luminosity Relation 26

•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

3a. Eclipsing Binaries 27

•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 28

•If a star is rotating, spectral lines will be broadened due to doppler effect

•Giant stars will show more broadening.

3c. Indirectly Determining Sizes 29

•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.

3d. Stellar Sizes 30

•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.

C. Stellar Sequences

1. Spectral Classes

2. H-R Diagram

3. Stellar Sequences

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1a. Color Indexing

• 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

• Recall that subtracting magnitudes is equivalent to taking a ratio of luminosities

• B-V = 2.5 Log(bv/bb)

• bv = luminosity in yellow

• bb = luminosity in blue

• B=magnitude in blue• V=magnitude in yellow

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1c. Hertzsprung’s Studies 34

•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”

2a. Persistence of Lines• A more precise method is to look at the relative strengths of

various spectral lines to determine temperature.

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2b. Spectral Classes• 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 37

2d. How we determine properties of stars 38

3a. Hertzsprung-Russel Diagram 39

•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 40

•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.

3c. Spectroscopic Parallax 41

•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.

SummarySummary

Most of the stars visible to naked eye

are giants and

supergiants, or the

brighter main sequence

stars (B, A, F).

42M=-10

M=-5

M=0

M=+5

M=+10

M=+15