The Family of Stars

Chapter 8:

Organizing the Family of Stars: The Hertzsprung-Russell Diagram

We know:

Stars have different temperatures, different luminosities, and different sizes.

To bring some order into that zoo of different types of stars: organize them in a diagram of:

Luminosity versus Temperature (or spectral type)

Lum

inos

ity

Temperature

Spectral type: O B A F G K M

Hertzsprung-Russell Diagram

orA

bsol

ute

mag

.

The Hertzsprung Russell Diagram

Most stars are found along the

Main Sequence

The Hertzsprung-Russell Diagram

Stars spend most of their active

life time on the M

ain Sequence.

Same temperature,

but much brighter than

MS stars

→ Must be much larger

→ Giant Stars

Same temp., but

fainter → Dwarfs

Radii of Stars in the Hertzsprung-Russell Diagram

10,000 times the

sun’s radius

100 times the

sun’s radius

As large as the sun100 times smaller than the sun

Rigel Betelgeuze

Sun

Polaris

Luminosity ClassesIa Bright Supergiants

Ib: Supergiants

II: Bright Giants

III: Giants

IV: Subgiants

V: Main-Sequence Stars

IaIb

II

III

IVV

Luminosity effects on the width of spectral lines

Same spectral type, but different luminosity

Lower gravity near the surfaces of giants

smaller pressure

smaller effect of pressure broadening

narrower lines

Binary StarsMore than 50 % of all stars in our Milky Way

are not single stars, but belong to binaries:

Pairs or multiple systems of stars which

orbit their common center of mass

If we can measure and understand their orbital

motion, we can

estimate the stellar masses.

The Center of Masscenter of mass =

balance point of the system

Both masses equal => center of mass is in the middle, rA = rB.

The more unequal the masses are, the more

it shifts toward the more massive star.

Estimating Stellar MassesRecall Kepler’s 3. Law:

Py2 = aAU

3

Valid for the Solar system: star with 1 solar mass in the center

We find almost the same law for binary stars with masses MA and MB different from 1 solar mass:

MA + MB = aAU

3 ____ Py

2

(MA and MB in units of solar masses)

Visual Binaries

The ideal case:

Both stars can be seen directly, and

their separation and relative motion can be followed directly.

Spectroscopic Binaries

Usually, the binary separation a can not be measured

directly because the stars are too close to each other.

A limit on the separation and thus the masses can

be inferred in the most common case:

Spectroscopic Binaries

Spectroscopic Binaries

The approaching star produces blue shifted lines;

the receding star produces red shifted lines in the spectrum.

Doppler shift → Measurement of radial velocities

→ Estimate of separation a

→ Estimate of masses

Spectroscopic Binaries

Tim

e

Typical sequence of spectra from a spectroscopic binary system

Eclipsing BinariesUsually, the inclination

angle of binary systems is unknown →

uncertainty in mass estimates.

Special case:

Eclipsing Binaries

Here, we know that we are looking at the

system edge-on!

Eclipsing Binaries

Peculiar “double-dip” light curve

Example: VW Cephei

Eclipsing Binaries

From the light curve of Algol,

we can infer that the system

contains two stars of very

different surface temperature, orbiting in a

slightly inclined plane.

Example:

Algol in the constellation of Perseus

The Mass-Luminosity Relation

More massive stars are more

luminous.

L ~ M3.5

Masses of Stars in the Hertzsprung-Russell Diagram

Masses in units of solar masses

Low m

asses

High masses

Mass

The higher a star’s mass, the more

luminous (brighter) it is:

High-mass stars have much shorter lives than

low-mass stars:

Sun: ~ 10 billion yr.

10 Msun: ~ 30 million yr.

0.1 Msun: ~ 3 trillion yr.

L ~ M3.5

tlife ~ M-2.5

Surveys of Stars

Ideal situation:

Determine properties of all stars within a

certain volume

Problem:

Fainter stars are hard to observe; we

might be biased towards the more luminous stars.

A Census of the StarsFaint, red

dwarfs (low mass) are the most common

stars.

Giants and supergiants

are extremely rare.

Bright, hot, blue main-sequence

stars (high-mass) are very rare.