Chapter 15 Surveying the Stars

Most massive stars are 100 MSun Least massive stars are 0.08 MSun (MSun is the mass of the Sun)

Amount of energy a star radiates each second Luminosity: Amount of energy a star radiates each second Apparent brightness: Amount of starlight that reaches Earth (energy per second per square meter) Energy / second = watt, measures power of star

Inverse Square Law Sun is very bright, but is the Sun really a “bright” star? The amount of light received from a star decreases with distance from the star. Example: 10 ly = 100 photons 20 ly = ? photons 2 x farther = 22 or 4 times dimmer, so only 100/4 = 25 photons Clearly, a star that is very bright in our sky could be bright primarily because it is very close to us (the Sun, for example), or because it is rather distant but is intrinsically very bright (Betelgeuse, for example). It is the “true” brightness, with the distance dependence factored out, that is of most interest to us as astronomers. Therefore, it is useful to establish a convention whereby we can compare two stars on the same footing, without variations in brightness due to differing distances complicating the issue.

(LSun is luminosity of Sun) Most luminous stars: 106 Lsun Least luminous stars: 10-4 LSun (LSun is luminosity of Sun) Stars come in a wide variety of luminosities

Apparent magnitude measures apparent brightness 2nd century BC Hipparchus 6 categories of brightness ( 1st mag. = the brightest, 6th mag. = the faintest) backward scale: brighter = lower the magnitude.

How it works: There is a 100:1 ratio of brightness over magnitudes 1 → 6 So each magnitude difference is 5√100 = 2.5 brightness

Apparent magnitude depends on distance luminosity

Absolute Magnitude Measures the true brightness of a star To find the absolute magnitude, M, of a star we need to know: -Apparent magnitude, m -Distance from us, d Absolute magnitude is given by: m – M = 5 log (d – 5) Astronomers define the absolute magnitude to be the apparent magnitude that a star would have if it were (in our imagination) placed at a distance of 10 parsecs (which is 32.6 light years) from the Earth. I can do this if I know the true distance to the star because I can then use the inverse square law to determine how its apparent brightness would change if I moved it from its true position to a standard distance of 10 parsecs. There is nothing magic about the standard distance of 10 parsecs. We could as well use any other distance as a standard, but 10 parsecs is the distance astronomers have chosen for this standard. A common convention, and one that we will mostly follow, is to use a lower-case "m" to denote an apparent magnitude and an upper-case "M" to denote an absolute magnitude.

Parallax and distance Parallax: the apparent shift in position of a nearby object against a background of more distant objects Intro_to_parllax.swf

Parallax measurements are the foundation for other methods to determine the distance to other objects so they must be accurate Apparent positions of nearest stars shift by about an arcsecond as Earth orbits Sun

How do we measure stellar temperatures? Every object emits thermal radiation with a spectrum that depends on its temperature An object of fixed size grows more luminous as its temperature rises

Properties of Thermal Radiation Hotter objects emit more light per unit area at all frequencies. Hotter objects emit photons with a higher average energy. Remind students that the intensity is per area; larger objects can emit more total light even if they are cooler.

Wien’s Law Wien’s Law:   1/T higher temperature  The Wien Law gives the wavelength of the peak of the radiation distribution, while the Stefan-Boltzmann Law gives the total energy being emitted at all wavelengths by the blackbody (which is the area under the Planck Law curve). Thus, the Wien Law explains the shift of the peak to shorter wavelengths as the temperature increases, while the Stefan-Boltzmann Law explains the growth in the height of the curve as the temperature increases. Notice that this growth is very abrupt, since it varies as the fourth power of the temperature. For convenience in plotting these distributions have been normalized to unity at the respective peaks; by the Stefan-Boltzmann Law, the area under the peak for the hot star Spica is in reality 2094 times the area under the peak for the cool star Antares. Wien’s Law:   1/T higher temperature  shorter wavelengths  “bluer” star.

Hottest stars are 50,000 K Coolest stars are 3,000 K (Sun’s surface is 5,800 K)

Absorption lines in star’s spectrum tell us ionization level

Level of ionization also reveals a star’s temperature 106 K 105 K Ionized Gas (Plasma) 104 K Level of ionization also reveals a star’s temperature 103 K Neutral Gas Molecules 102 K 10 K Solid

Absorption lines in a star’s spectrum correspond to a spectral type that reveals its temperature. O B A F G K M (Hottest) (Coolest) Also each spectral class is divided into 10: Sun  G2

Why no green stars?

All stars are made of the same “stuff” Remember, the spectra of stars differ because of differences in surface temperature. All stars are made of the same “stuff” 75% Hydrogen 21-24% Helium 4% or less of heavy elements like Neon, Oxygen, Sulfur, Iron and Chlorine.