Properties of StarsProperties of Stars

Basic Properties of Stars

• Distance

• Luminosity (intrinsic brightness)

• Temperature (at the surface)

• Size

• Mass

The Distances of StarsStellar distances can be determined via parallax – the larger the distance, the smaller the parallax angle ()

QuickTime™ and aVideo decompressor

are needed to see this picture.

The Distances of Stars

Stellar distances can be determined via parallax – the larger the distance, the smaller the parallax angle ()

The nearest stars have parallax angles of less than 1 arcsecond (1”=1 degree/3600). For perspective, the angular size of the Moon as seen from the Earth is 0.5 degree. No wonder Aristotle couldn’t see this shift!

Astronomers define a parsec as the distance a star would have if its parallax angle were 1". From geometry: D(pc) = 1 / 1 pc = 30,860,000,000,000 km = 206,265 A.U. = 3.26 light years

The Stars Closest to the Sun

Measuring Stellar Luminosities

If you know the distance to a star (via parallax), then you know the star’s luminosity from the inverse square law of light, i.e., l = L / r2, where

l is the apparent luminosity, L is the absolute luminosity, andr is the distance.

Astronomers don’t use watts (or gigawatts) for the units of a star’s luminosity. Instead they use the solar luminosity (i.e., a star that is equal in brightness to the Sun has 1 L).

Measuring Stellar Temperatures: Colors

One method of taking a star’s temperature is to look at its color. Red stars are cool; blue stars are hot.

But watch out – dust may redden a star by scattering away the blue light.

In hydrogen, all optical absorption lines come from the n=2 level.

Measuring Stellar Temperatures:Absorption Lines

But at cold temperatures, the electron is in the ground state.So no optical absorption lines.

Measuring Stellar Temperatures:Absorption Lines

And at hot temperatures, the electron is in high levels.Again, no optical absorption lines.

Measuring Stellar Temperatures:Absorption Lines

Measuring Stellar TemperaturesEach element works the same way; each has a “favorite” temperature range for absorption. By carefully identifying absorption lines, one can fix the temperature of a star precisely.

Oh

Be

A

Fine

Girl

Kiss

Me.

A star is assigned a letter called a spectral type that refers to the type of lines in its spectrum, and hence its temperature. In other words, spectral type is just another term for a star’s temperature.

Sun

The Sizes of Stars

Telescopes can directly measure the sizes of only the largest and closest stars.

All other stars appear as unresolved points of light. We must estimate their sizes from T and L.

Like any blackbody source of radiation, a star’s luminosity is related to its temperature:

L T4

Luminosity is also proportional to a star’s surface area (and radius):

L R2

Combining those 2 relations:

L R2T4

So we can get R by measuring L and T.

The Sizes of Stars

The sizes of stars can be anywhere from 0.01 R to 1000 R !

• http://www.youtube.com/watch?v=k7hsQA3wo3Q

The Masses of Stars

Using Kepler’s and Newton’s laws, the mass of a star can be measured if it is orbiting with another star in a binary system:

(M1 + M2) P2 = a3

where M1 and M2 are the stellar masses (in solar units)

P is the orbital period (in years) a is the semi-major axis of the orbit (in A.U.)

Visual BinariesWhen both stars can be seen, it’s called a Visual Binary. By measuring separation and period of their orbit, we can measure the masses of the stars.

Castor

If two stars in a binary system are too close to be resolved as separate points of light and their light is blended together, we can still measure their orbits by watching how their velocities relative to the Earth change via the Doppler shift in their absorption lines.

Spectroscopic Binaries

Determining Masses from Binaries

• The relative speeds of the stars gives you their relative masses.

QuickTime™ and aCinepak decompressor

are needed to see this picture.

Determining Masses from Binaries

• The absolute velocities of the stars (times the period) gives you the circumference of their orbits. From that, you can derive the orbits’ semi-major axes. In other words,

Circumference = v · t = 2 a (at least for circular orbits)

• From the semi-major axis and the period, you can derive the total mass of the system through

(M1 + M2) P2 = a3

• Since you already know the relative masses, you now know everything!

• The relative speeds of the stars gives you their relative masses.

If a star’s absolute luminosity and temperature are both measured, they can be plotted versus each other. This is called the Hertzprung-Russel (H-R) diagram. Stars appear in distinct locations on this diagram.

The H-R Diagram

Red Giants and White Dwarfs

Some stars are very cool, but also very bright. Since cool objects don’t emit much light, these stars must be huge. They are red giants.

Some stars are faint, but very hot. These must therefore be very small – they are white dwarfs.

how size changes with T and L

The Main Sequence

Most stars (including the Sun) appear within the middle band from high temperatures and luminosities to low temperatures and luminosities. This is called the main sequence. Main sequence stars are larger (in diameter) than white dwarfs but smaller than giants.

Masses on the H-R diagram

1) All stars have masses between 0.1 M and 100 M

2) Brighter stars on the main sequence have higher masses

3) All white dwarfs have masses <1.4 M

4) There is no pattern to the masses of red giants.

3) All white dwarfs have masses <1.4 M

4) There is no pattern to the masses of red giants.