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DISTANCES
• Parallax is an object's apparent
shift relative to some more
distant background as the
observer's point of view changes
• As the distance to the
object increases, the
parallax becomes smaller and
therefore harder to measure.
• Astronomers measure parallax in
arc seconds rather than in degrees.
• At what distance must a star lie in
order for its observed parallax to be
exactly 1 arc-sec?
• We get an answer of 206,265 A.U.
• Astronomers call this distance 1
parsec (1 pc), from "parallax in arc
seconds."
• Calculating Parallax:
• Sirius displays a large known stellar
parallax, 0.377”. Calculate its distance
in parsecs and in light years
d = 1/p
d = 1/0.377
d = 2.65 pc away
• 1 pc = 3.26 light years, so d = 8.65
light years
• Astronomers measure the apparent
brightness
• This is compared to the star’s luminosity
(actual brightness)
• Distance is calculated by comparing the
two values
• Distances to galaxies can be measured
via:
• Redshift
• Brightness of supernovae
Temperature
• The color of a star indicates its relative
temperature – blue stars are hotter than red stars
• More precisely, a star’s surface temperature is
given by Wien’s law
3x106
λm
T = star’s surface temperature in Kelvin
λ m = strongest wavelength in nanometers (nm)
LUMINOSITY &
APPARENT BRIGHTNESS
Luminosity
• The amount of energy a star emits
each second is its luminosity
(usually abbreviated as L)
• A typical unit of measurement for
luminosity is the watt
• Compare a 100-watt bulb to the
Sun’s luminosity, 4x1026 watts
Luminosity
• Luminosity is a measure of a star’s
energy production (or hydrogen
fuel consumption)
• Luminosity is determined by
diameter and temperature
• The inverse–square law relates an
object’s luminosity to its distance
(apparent brightness)
• As the distance to a star increases, the
apparent brightness decrease with the
SQUARE of the distance
• About 150 B.C., the Greek astronomer
Hipparchus measured apparent
brightness of stars using units called
magnitudes
• Brightest stars had magnitude 1 and
dimmest had magnitude 6
• A star’s apparent magnitude depends
on the star’s luminosity and distance.
Magnitude differences equate to
brightness ratios:
• A difference of 5 magnitudes =
a brightness ratio of 100
• 1 magnitude difference =
brightness ratio of 1001/5=2.512
“Absolute magnitude” is a measure a
star’s luminosity
–The absolute magnitude of a star is the
apparent magnitude that same star
would have at 10 parsecs
–An absolute magnitude of 0
approximately equates to a luminosity
of 100L¤
Spectral
Types
Spectra of Stars
Introduction
• A star’s spectrum typically depicts
the energy it emits at each
wavelength
• A spectrum also can reveal a star’s
composition, temperature,
luminosity, velocity in space, rotation
speed, and it may reveal mass and
radius
Spectra of Stars
Measuring a Star’s Composition
–A star’s spectrum = absorption
spectrum
–Every atom creates its own unique
set of absorption lines
–Match a star’s absorption lines with
known spectra to determine surface
composition
Classification of Stellar Spectra
• Historically, stars were first classified into
four groups based on color (white, yellow,
red, and deep red), then into classes using
the letters A through N
• Annie Jump Cannon: classes were more
orderly if arranged by temperature – Her
new sequence became O, B, A, F, G, K, M (O
being the hottest and M the coolest) and are
today known as spectral classes
Spectral
Class
O
B
A
Surface
Temp
Absorption Example
Lines
Ionized He
30,000 K Weak H
He, H
20,000 K moderate
Rigel
Vega
10,000 K Strong H
Sirius
Spectral Surface
Class
Temp
F
7,000 K
G
6,000 K
K
4,000 K
M
3,000 K
Absorption Example
Lines
Mod. H,
Canopus
Metals
Mod. H,
Sun
Metals
Metals
Arcturus
strong
Metals
Betelgeuse
strong
Measuring a Star’s Motion
• A star’s radial motion is determined from
the Doppler shift of its spectral lines
• The amount of shift depends on the star’s
radial velocity
• Δλ = the shift in wavelength of an
absorption line
• λ = resting wavelength, the radial speed v is
given by:
V = Δλ/ λ • c
where c is the speed of light
• Surface temperature and luminosity
can be plotted to make the single
most important graph for the study
of stars, the Hertzsprung-Russell
Diagram
• Luminosity (y-axis) increases
upwards, and temperature (x-axis)
increases to the left
• The majority of stars lie along a
band (not a sharp line) from top
left to bottom right called the
main sequence.
• On the main sequence, hot stars
are the most luminous, (top left)
and cool stars are the least
luminous (bottom right).
• We now know that the main
sequence comprises all the stars
that are converting hydrogen to
helium in their cores.
• Stars that are not on the main
sequence are doing something
else
• The Mass-Luminosity Relation
– Main-sequence stars obey a massluminosity relation, approximately given
by:
L = M3
where L and M are measured in solar units
– Consequence: Stars at top of mainsequence are more massive than stars
lower down
Another look
• Dwarf stars are comparable in
size (or smaller) to the Sun
• Giants range from 10 to 100
times the radius of the Sun
• Supergiants range from 100 to
1000 solar radii
 The range in sizes of Main
Sequence stars is about 0.1 to 100
solar radii.
 Supergiants can be enormous.
Betelgeuse would reach out to the
orbit of Mars.
• White dwarfs stars are around the
size of the Earth
• Visual binaries
– actually see the stars moving around each other
• Spectroscopic binaries
– make use of the Doppler shift of the spectral
lines of the stars
• Eclipsing binaries
– binaries may be orbiting in such a way that
one star moves in front of the other as in an
eclipse
Shape:
Irregular, no
specific shape
Where:
Types
Galactic disk
of Stars:
Population I
Age
of Stars:
Young!
Shape:
Spherical
Where
found:
Galactic Halo
Types
of Stars:
Population II
Age
of Stars:
Old
http://www.astrographics.com/GalleryPrints/Display/GP0046.jpg
http://images.astronet.ru/pubd/2008/05/07/0001227653/OmegaCen_spitzer_c800.jpg
• Stellar motion has two components:
• The transverse component measures a
star's motion perpendicular to our line
of sight—in other words, its motion
across the sky.
• The radial component measures a star's
movement along our line of sight—
toward us or away from us.
• The annual movement of a star
across the sky, as seen from
Earth (and corrected for
parallax), is called proper
motion.
• It describes the transverse
component of a star's velocity