Basic Properties of Stars
Measure of brightness (Hipparchus)
By agreement, absolute magnitude is apparent magnitude at a standard distance - 10 parsecs
Parsec = 3.26 light years
Absolute mag. of sun = +4.8
Range in absolute magnitude for stars
~ -10 to +17 mag.
Basic, difficult problem.
Geometric methods basic and most reliable - for nearby stars only.
Used to calibrate secondary methods.
Parsec: distance at which star has a parallax of 1 arcsec.
d (distance) in parsecs.
ex.: p = 0.10 second of arc (arcsec):
From earth, measure only parallax greater than 0.01 arcsec (distance less than 100 pc).
Hipparcos - parallax ~ 0.001 arcsec (distance to 1000 pc)
Spectroscopic parallax - derive absolute magnitude from spectrum, measure apparent magnitude
Magnitude - distance relation:
mv - Mv = -5 + 5(log10d)
Luminosity: Amount of energy emitted in one second at all wavelengths.
Use Mv, correct for non-visible wavelengths.
Absolute bolometric magnitude:
Mbol: Absolute magnitude including all wavelengths.
Compare Mbol star to Mbol sun (star = observed star) to get stellar luminosity.
ex.: Luminosity of sun, Lsun = 4x1026joules/sec
Color and Temperature
Color and temperature of stars related
Black body: absorbs and re-emits all radiation that falls on it. Spectrum depends only on temperature. Idealized, does not really exist.
Stars can be represented as black bodies.
Hot stars bluer than cool stars.
λ in micrometers (microns, Ám) = 10-6 meter
T temperature in Kelvin
Estimate star's temperature by measuring color:
Luminosity, Size, Temperature
Luminosity of a star depends on temperature and size (surface area)
Amount radiated from every square meter equals σ x T4
The hotter the star, the more energy radiated per square meter
Total amount radiated (luminosity)
L = 4πR2σT4
R is star's radius, T is temperature
If measure L, T can estimate R
Strength of lines determined by temperature, as well as chemical abundance
Group spectra according to strength of various lines
Line strengths define temperature sequence:
Stars of the same spectral type may be at different stages of evolution, vary greatly in brightness, density of atmosphere.
Plot temperature against luminosity (or equivalent parameters)
Stars found in certain parts of H-R diagram
Main sequence - class V stars - converting H -> He in their centers
Red giants - class III, cool and big, evolved stars
Supergiants - evolved, class I, very bright
White dwarfs - small, hot stars. End of stellar evolution for most stars.
Mass range in stars: 0.08 - 100 M (solar masses)
Space velocity - motion relative to the sun ~ tens of km/sec
Radial velocity, transverse velocity
Proper motion - angular shift in star's position on sky due to transverse velocity.
Binary and Multiple Stars
Binary star - 2 stars bound by mutual gravitational attraction. More than half of stars are in binary or multiple systems
Binaries only way to directly measure masses of stars
Visual binary - can resolve both stars in binary
Observe period, average distance between stars, distance of each star from center of mass
Calculate masses using Kepler's Third Law
Astrometric binaries - identify by 'wobble' in proper motion
Spectroscopic binaries - identify by combined spectrum. Two sets of absorption lines - shift due to orbital motion. (Single-line binaries.)
Eclipsing binaries - orbit nearly edge-on, stars pass in front of each other. Periodic changes in brightness of the system.
Eclipses can be used to estimate stellar radii
Roche lobes - define volume controlled by individual stars in binaries
If star overflows Roche lobe, matter can be transferred to other star
Contact binary - both stars fill Roche lobes, surfaces in contact
Change in brightness
Pulsating variables - expand and contract regularly.
Cepheid variables : 1 - 80 day periods.
Brighter Cepheids have longer periods.
Used to get distances to nearby galaxies
Cataclysmic Variables - sudden increases in brightness - flare stars, novae, supernovae
Prof. Donna Weistrop
University of Nevada, Las Vegas