What Are They, and How Far Are They?

• History: Around 1600, Thomas Digges suggested that stars are distributed in 3D space, and Giordano Bruno that they are like distant suns, but only in the 1800s were astronomers finally able to see the first stellar parallax and spectra.
• What we now know: A star is a body that (at least for some time in its life) generates light and heat by nuclear reactions that fuse hydrogen into helium, under conditions of enormous temperature and density. Our knowledge of the Sun can help us understand other stars.
• Parallax: Remember its importance for the issue of whether the Earth moves; Using the diameter of Earth's orbit as baseline, it now works for stars out to a few hundred ly, with angles that are always less than 1"!
• New distance unit: 1 parsec (pc) = 3.3 ly [= 206,000 AU = 33 trillion km], the distance at which the parallax of an object would be 1"; For other objects,

• Nearest stars: Proxima Centauri [p = 0.77"], d = 1.3 pc = 4.3 ly; Barnard's star [p = 0.54", d = 1.8 pc]; There are about 300 within 30 ly, mostly small and dim (no O and B stars, a few A and F stars, a few dozen sunlike G stars and K dwarfs, a whopping 236 cool, orange-red M dwarfs like Proxima Centauri, some white dwarfs and L and T dwarfs – but there could be many more, and newly discovered ones were reported even in 2006), a million within 1000 ly (with even a modest amateur telescope, millions of stars can be seen).

  Luminosity and Brightness

• Apparent brightness and magnitude: Indicated by the power received per unit area (measured with CCD's at specific wavelengths) or the apparent magnitude m (introduced by Hipparchus in the 2nd cy BC)
• Luminosity and absolute magnitude: From the apparent brightness and distance using the inverse square law; the absolute magnitude M is the apparent magnitude they would have if they were at 10 pc from us.
• Examples: Brightest is Sirius [a Canis Majoris, m = –1.5, M = 1.4], second Canopus [a Carinae, m = –0.72, M = –3.1]; [the Sun has m = –27 but M = 4.8!].
• A twist: Many stars change luminosity over time! Why does this happen?

Motion and Rotation

• Fact: Stars move, but extremely slowly; The first who noticed this was Edmund Halley, by comparing his star charts to the ancient ones drawn by the Greeks.
• Proper motion: The transverse movement, in arcsec/year. Fast ones move by a few arcsec/year; fastest is Barnard's star [10.3"/year].
• Actual velocity: Sideways one from proper motion (if distance is known). Radial one measured from Doppler shift; some stars move back and forth!). Typical speeds are in the tens of thousands of mph, or tens of km/s!
• Rotation: From broadening of spectral lines, or high-resolution imaging (differential, like the Sun). [For example, Altair and Regulus spin fast and bulge at the equator.]

  Star Sizes

• Size, directly? Only for very few stars we can get an angular size from an image and use their distance to find the true radius [Polaris is 46 times the Sun, Betelgeuse much larger].
• Size, indirectly: Use absolute brightness + temperature to get surface area and radius [using Stefan's law], but again we need to know the distance.
• Supergiant stars: Their radius is hundreds of times the Sun's; For example, Betelgeuse [650 R_sun, at 150 pc] is a red supergiant, Rigel [at 250 pc] a blue supergiant; The very largest know ones are about 1500 R_sun, or 15 AU across (why is there an upper limit to size?).
• Giant stars: They have R between 10 and 100 times the Sun's [Polaris is 46 times as large as the Sun]; Can be red or blue (why the difference?).
• Medium size stars: R like the Sun's, or a little larger.
• Dwarfs: Down to 8% of the Sun's mass (why not lighter?); "Normal" ones are red and brown dwarfs, but there are white dwarfs too; The smallest known one is almost 100 times as massive as Jupiter, but only 16% larger!

Summary - Things We Can Measure and Things Beyond Our Reach

• If we don't know the distance: Radial velocity, proper motion (not transverse velocity), color, temperature.
• So how do we find the distance to more stars? First we need to understand them and classify them better.
• Mass? We must see the star's gravitational effect on something else, such as another star in a binary system or a planet (or a passing beam of light, or light coming from its surface...), and know the distance.
• Surface details? We know that some (maybe all?) stars have flares and starspots, and the study of vibrations (astroseismology) is important [but to have enough resolution to even see the surface of a Centauri the telescope would need to be at least 14 m wide, and 150 to see starspots!]; So other stars also have magnetic fields.
• How many stars have we actually mapped? Between 1989 and 1993, the Hipparcos spacecraft mapped over two and a half million; Gaia (due for launch around 2012) will extend this work to about a thousand million.

Note: One reason for the rapid development in astronomy during recent decades is "the gradual erosion of the gentlemanly agreement not to observe someone else's star" ...