Properties of Stars

Properties of Stars

• Distance• Luminosity (intrinsic brightness)• Temperature (at the surface)• Radius• Mass

The Distances of StarsAs the Earth orbits the Sun, nearby stars appear to shift relative to more distant stars. The size of this parallax shift is larger for stars at smaller distances. Therefore, we can use parallax to measure the distances of stars.

The Distances of StarsThe parallax shift of a star is measured as an angle in units of arcseconds (abbreviated as ”) where 1”=1 degree/3600. The largest parallax angles (for the nearest stars) are <1”. For perspective, the angular size of the Moon as seen from the Earth is 1800” (0.5 degree). Such tiny parallax shifts can be detected only with telescopes, which is why Aristotle couldn’t see them.

The distance of a star can be computed from its parallax angle with the following equation:

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d(light years) =3.26

p(")

Distance to the nearest star to our solar system: 4 light years = 40 trillion km = 250,000 AU

The Luminosities of Stars

The luminosity of a star is the amount of light or energy that it produces per second, like the number of watts produced by a light bulb. But astronomers don’t use watts for the units of a star’s luminosity. Instead, they refer to the luminosities of stars in terms of the luminosity of the Sun, which is called a solar luminosity and is abbreviated as L.

The Luminosities of Stars

If you measure the distance (d) to a star via parallax and the star’s brightness as seen from the Earth (b), then you can compute the star’s luminosity (L) from the inverse square law of light.

Lb =

d2

The Temperatures of Stars: Colors

One way to estimate a star’s temperature is by its color. Red stars are cool, blue stars are hot.

However, if there’s a lot of dust in space between us and a star, the light we receive will appear red because the blue photons are scattered out of the beam of light (like the Sun at sunset).

In hydrogen, optical absorption lines begin in the n=2 level. So some of the atoms must have electrons in n=2 for these

lines to be produced.

The Temperatures of Stars:Absorption Lines

But at cold temperatures, the electron is in the ground state.So optical absorption lines cannot appear.

The Temperatures of Stars:Absorption Lines

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

The Temperatures of Stars:Absorption Lines

The Temperatures of StarsEach element has a “favorite” temperature range in which it produces absorption lines. By identifying which absorption lines appear in the spectrum of a star, one can measure its temperature.

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Astronomers assign a letter called a spectral type to a star based on which absorption lines appear in its spectrum. Hence, a spectral type is just another term for a star’s temperature.

Sun

The Radii of StarsOnly a few stars are large enough and close enough that telescopes can directly measure their radii.

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:

Luminosity is also proportional to a star’s surface area, which is πR2:

Combining those 2 relations:

, or

So we can estimate R by measuring L and T.

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R=L

T2

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L=R2T4

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L∝T4

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L∝R2

The Radii of Stars

Stars have a large range of radii, 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 masses) P is the orbital period (in years) a is the semi-major axis of the orbit (in A.U.)

The relative velocities of 2 stars in a binary system are related to their relative masses. If 2 stars have different masses, then the less massive one moves faster in its orbit.

The Masses of Stars

The velocities of the stars in a binary system can be measured from the Doppler shifts of their absorption lines as they repeatedly move towards and away from the observer during their obit.

The Masses of Stars

If a star’s 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 in order to be that bright. They are red giants.

Some stars are faint, but very hot. For a hot star to be faint, it must 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.