Astronomy 100

Lectures

Table of Contents

Astro 100

Lecture 13
Properties of Stars

Outline

How far are the stars, and how do we know?
Brightness of stars: distance vs. luminosity

Terms to Know

parallax
parsec (pc)
absolute magnitude

1. How far are the stars, and how do we know?

The ancient Greeks (as well as more "recent" astronomers, such as Tycho Brahe) based major theories on the lack of observed parallax of the "fixed" stars; i.e., the stars didn't appear to wiggle back and forth as the Earth rotates on its axis and revolves in its orbit around the Sun. But as we now know, some stars do show that wiggle, or parallax, every year. You can use that parallax to measure the distance to the nearest stars:

Use the Earth's orbit around the sun as baseline for triangulation:: Baseline = 2 A.U. (Earth's orbit)
Formula (just simple geometry using the small-angle approximation):: distance (parsecs) = 1 / angle (arcseconds); the 'angle' is referred to as the 'parallax'; 1 parsec ("PARallax SECond") = 3.26 light-years; 1 arcminute (') = 1/60th of one degree; 1 arcsecond (") = 1/60th of one arcmin
Nearest star: Proxima Centauri 1.3 parsecs: - actually a 3-star system, one like the Sun; - visible to the eye
Next closest: Barnard's star 1.8 parsecs: - invisible to the naked eye
Inference:: Stars must come in a wide range of luminosity; Could space be filled with dim stars that we just can't see?

Limitation of parallax:: - difficult to measure parallax angle for objects more than a few parsecs away -- most stars in the Milky Way Galaxy (and all galaxies outside the Milky Way) are too far to use parallax for measuring distances.
But remember importance of parallax:

- primary measurement of distance in astronomy.

- the 'bottom rung' of the cosmic distance ladder.

- with parallax, we calibrate all other methods of determining distances to objects that are farther away.

2. Brightness of stars: distance vs. luminosity

The luminosity of a star is its intrinsic, or physical, brightness, independent of its distance. Even if you can't see the star, its luminosity remains the same.

Recall the Inverse Square law for light: I 1/r²

So the apparent brightness of a star depends on both its luminosity and its distance!

The absolute magnitude, M, of an object (star, galaxy,...) is the apparent magnitude, m, it would have if it were placed at a distance d = 10 parsecs from the observer.

Think of "absolute magnitude" as a standard of reference. It's just the intrinsic luminosity (physical units), like "100 watts," of an object expressed in magnitudes (historical units)

There is nothing magical about 10 pc --

-- just an arbitrary choice.