Chapter 9

Basic Properties of Stars


Magnitudes:

    Measure of brightness (Hipparchus)

1st - 6th class stars:

1st - brightest

6th - faintest


1st magnitude is 2.5 x brighter (more intense) than 2nd magnitude.


2nd magnitude is 2.5 x more intense than 3rd magnitude


5 magnitudes - factor 100 in intensity


Sun's magnitude: -26.5


Hubble Space Telescope measures about 30th magnitude.


Magnitude range:


-26.5 to +30


2.5 x 2.5 x 2.5 .........


Sun is 4x1022 times brighter (more intense) than faintest thing observable from Hubble Space Telescope.


Apparent (visual) magnitude (m) - measure of how bright object appears on earth. Due to intrinsic brightness and distance.


Absolute magnitude (M) - due to intrinsic brightness only.

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.


Distances


Basic, difficult problem.


Geometric methods basic and most reliable - for nearby stars only.


Used to calibrate secondary methods.


Trigonometric parallaxes




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.

(Bolometric correction)

Absolute bolometric magnitude:


Mbol: Absolute magnitude including all wavelengths.

ex.: Mbol sun = 4.7 magnitude


Compare Mbol star to Mbol sun (star = observed star) to get stellar luminosity.


ex.: Luminosity of sun, Lsun = 4x1026joules/sec

Range of stellar luminosities:
10-4 Lsun to 105 Lsun

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.


Wein's Law:
λ ( maximum intensity) = 2900/T

λ in micrometers (microns, Ám) = 10-6 meter


T temperature in Kelvin



Estimate star's temperature by measuring color:


B: 400 - 480 nm


V: 500 - 600 nm


B - V color:


Hot, blue stars: B - V = -0.4


Cool, red stars: B - V = +2.0


Sun: B - V = +0.5


Luminosity, Size, Temperature


Luminosity of a star depends on temperature and size (surface area)


Amount radiated from every square meter equals σ x T4

{Stefan-Boltzmann Law}


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



Spectral Classification


Strength of lines determined by temperature, as well as chemical abundance


Group spectra according to strength of various lines


Line strengths define temperature sequence:

O hot
B
A
F
G - (our sun)
K
M cool
L new class
T new class


Each class subdivided into 10 subclasses (0 - 9)
ex.:
Sun - G2
Vega - A0



Stars of the same spectral type may be at different stages of evolution, vary greatly in brightness, density of atmosphere.


Principal Luminosity classes:


I - supergiants


III - Giants


V - Dwarfs
ex.: Sun - G2V


Hertzsprung-Russell Diagram


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)



Stellar Motions


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



Unresolved Binaries


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




Variable stars


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