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Analyzing Starlight
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Chapter 11
Analyzing Starlight
• Starlight is only information we have
– Take picture
• Measure brightness
• Determine color
• Measure position
– Take spectrum
• Measure spectral lines
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Stellar Positions
• Stars move (slowly)
– Proper Motion (sideways motion)
• Determined by measuring position
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Brightness of Stars
• Luminosity
– amount of energy emitted per second
– not the same as how much we observe!
• We observe a star’s apparent brightness
– Depends on:
• luminosity
• distance
– Brightness decreases as 1/r2
(as distance r increases)
• other dimming effects
– dust between us & star
Measuring Brightness: History
• Photometry - the measure of brightness
• Hipparchus (150 B.C.)
– catalog of 1000 stars
– included position & brightness
– Magnitude = brightness
• brightest stars were first magnitude
• faintest stars were sixth magnitude
• estimated by eye
(logarithmic response)
Modern Magnitude System
• Refined scale of Hipparchus
– 5 magnitude difference = brightness factor of 100
• 6th mag. star is 100x fainter than 1st mag. star
• 1 magnitude difference is 2.5 times brighter/fainter
Star Colors
• Measure brightness at different wavelengths
• U = ultraviolet magnitude
• B = blue magnitude
• V = visual (yellow) magnitude
– Color = magnitude difference
• (B-V) or (U-B)
• Measures stellar temperature (recall blackbody)
Stellar Spectra
• Cool atmosphere in front of star
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Spectra of Stars
• Fraunhofer measured solar spectrum
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• Spectra of other stars not same
– hydrogen (and other) lines:
• Sometimes strong
• Sometimes weak
• not always present
– because stars have different temperatures
Stellar Spectra
Hot
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Cool
Stellar Spectra
Hot Star
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Cool Star
Classification of Stars
• Classified by absorption lines in
their spectra
• Annie Jump Cannon at Harvard
(1863-1941)
– classified large numbers of stars (over
400,000!)
– HD catalog (still used today)
– From hottest to coolest stars:
O, B, A, F, G, K, M
Hot
Oh be a fine guy/girl kiss me!
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Cool
Oh, brother, astronomers
frequently give killer midterms!
What We Learn from Spectra
• Stellar Temperature
– Which lines are present and their strength
Hot
Cool
What We Learn from Spectra
• Abundances of elements
– From strength of absorption lines
• Radial Velocity
– From Doppler shift
– velocity toward (blueshift) or away (redshift) from us
• Stellar Size
– indirectly from atmospheric pressure
• Low pressure: lines are narrow
– giant & supergiant stars
• High pressure: lines are wide
– normal stars
– Luminosity Class: I, II, …, V
• I = narrow lines = supergiant = large radius
• V = broad lines = normal star = small radius
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Homework for today was
WORKBOOK EXERCISES:
“Analyzing Spectra”
(pages 43-46 in workbook)
Parallax and Distances
• Parallax
– angle by which object shifts when viewed from
different places
• Triangulation
– calculating distance from parallax angle
Distances to Stars
• Use Earth’s orbit as baseline
– measure parallax of nearby stars
– triangulation gives distance
• Parallax angle
– extremely small (stars very far)
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The Parsec
• If star at distance of 206,265 AU
– parallax = 1 arc second (1/3600 degrees)
– defines new distance unit, the parsec (pc)
• 1 pc = 206,265 AU = 3.26 light-years
• distance of star
distance = 1/parallax
(distance in pc; parallax in arcseconds)
Which of the following stars is closest to us?
A.
B.
C.
D.
Procyon (parallax angle = 0.29”)
Ross 780 (parallax angle = 0.21”)
Regulus (parallax angle = 0.04”)
Sirius (parallax angle = 0.38”)
Below are two star photos taken six months apart and laid
atop one another so the background stars (circles) line up.
There are two nearby stars also shown. Which of these
nearby stars is closer?
Brightness
• Two kinds:
– Absolute (or intrinsic) brightness
• Same as luminosity
– Apparent brightness
• depends on luminosity and distance
Recall:
Apparent Bright ~ L/d2
• Magnitudes measure brightness
– Apparent magnitude
• Measures apparent brightness
– Absolute magnitude
• Measures luminosity
• When observer at standard distance (10 pc) from star:
apparent magnitude = absolute magnitude
WORKBOOK EXERCISES:
“Apparent and Absolute Magnitudes of Stars”
(pages 67-68 in workbook)
Results for Luminosities
Sun
• Luminous stars are rare
• More low luminosity stars than high
• Most stars less luminous than sun
The H-R Diagram
Bright
• Plot of
Luminosity vs. Temperature
– by Einar Hertzsprung and
Henry Norris Russell
(hence H-R diagram)
• Reveals relationships between
stellar parameters
• THE fundamental tool of stellar
astronomy
Faint
Hot
Cool
H-R Diagram
Measuring Stellar Size
• Indirect from Luminosity and Temperature
– L ~ R2T4
Small
Large
HOMEWORK WORKBOOK EXERCISE:
“H-R Diagram”
(pages 77-78 in workbook)
Stellar Masses
• Mass is the primary characteristic
– determines luminosity, temperature, lifetime
• How to measure mass?
– Use binary stars (orbiting pair)
• Measure orbital period, P, and orbital size, a
• Kepler’s Law gives sum of masses
(M1+M2)P2 = a3
Binary Stars
• First binary star discovered in 1650
– Mizar (in handle of Big Dipper)
• Double Star (not same as binary)
– pair of stars (close together in sky), but not orbiting each other
• Visual Binary
– both stars seen in telescope
– stars orbit each other
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• Spectroscopic Binary
– only one star seen in telescope
– other inferred from spectroscopy
• Doppler shift measures orbital motion
Visual Binary
Binary Star Orbits
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• Stars orbit around each other
– each star orbits around Center
of Mass
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Spectroscopic
Binaries
• As each star orbits, spectral lines
Doppler-shifted back and forth
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Range of Stellar Masses
• Smallest mass
– about 0.08 Msun
– smaller objects never hot enough to fuse
hydrogen
• Largest mass
– about 100 Msun (very rare)
– larger stars unable to maintain hydrostatic
equilibrium
• would blow themselves apart!
H-R Diagram
High Mass
Low Mass
Brightness and Distances
• If we:
– know absolute magnitude (luminosity)
– measure apparent magnitude
 can calculate distance.
• need “STANDARD CANDLES”
– objects whose luminosity is known
Distances from Spectral Types
• Find luminosity class (from
spectrum)
– place on H-R diagram
– gives luminosity
• Luminosity + apparent
magnitude gives distance
• Method called spectroscopic
parallax
Pulsating Variables
• Stars that pulsate (expand and contract)
• Two special types:
– Cepheid variables
– RR Lyrae variables
• Pulsation period depends on luminosity
– Can be used as standard candles
Period-Luminosity Relation
• Discovered by
Henrietta Leavitt
• Measure period of
brightness variation
– place on plot at right
– find luminosity
• Luminosity +
apparent magnitude
gives distance