Chapter 9

Basic Properties of Stars


    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.


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
G - (our sun)
M cool
L new class
T new class

Each class subdivided into 10 subclasses (0 - 9)
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