Properties of Stars

"There are countless suns and countless earths all rotating around their suns in exactly the same way as the seven planets of our system. We see only the suns because they are the largest bodies and are luminous, but their planets remain invisible to us because they are smaller and non- luminous. The countless worlds in the universe are no worse and no less inhabited than our Earth” Giordano Bruno (1584) in De L'infinito Universo E Mondi

Properties of Stars Distance Luminosity (intrinsic brightness) Temperature (at the surface) Radius Mass

Parallax is the apparent motion of a nearby object relative to a distant object due to the changing position of the observer. The Distances of Stars

As 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 Stars The 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:

The light year Rather than kilometers, astronomers use a larger unit of distance when referring to the distances to stars and galaxies. One light year is the distance that light travels in 1 year, corresponding to 9.5 trillion km. 1 light sec 8 light min 5.5 light hours to Pluto 4 light years to nearest star

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

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. L b =  d2d2

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 Stars Each 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.

Oh Be A Fine Girl Kiss Me. 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 Stars Only 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 πR 2 : Combining those 2 relations:, or So we can estimate R by measuring L and T.

The Radii of Stars Stars have a large range of radii, from 0.01 R  to 1000 R 

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: (M 1 + M 2 ) P 2 = a 3 where  M 1 and M 2 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.