Issue 5.05

The Astrophysics Spectator

March 19, 2008

The mass of a star is among the most difficult stellar properties to measure.  We cannot simply point an instrument at a star and read its mass from a gauge.  Mass manifests itself only through its interactions.  Inertial mass manifests itself by constraining how an object accelerates when subjected to a force; if you know the force exerted by a rocket's thrust, you can infer the rocket's mass by measuring the rocket's rate of acceleration.  Gravitational mass manifests itself through the gravitational force an object exerts on other bodies; if you can measure the influence of a planet's gravitational field on the motions of satellites, you can infer that planet's gravitational mass.  As far as anyone can tell, the inertial mass and the gravitational mass of an object are identical.

We can only measure the gravitational mass of a star, and this measurement is only available for a small fraction of the stars we see stars.  The Sun is the star with the best-determined mass.  By precisely tracking the motions of the planets, asteroids, and spacecraft around the Sun, the gravitational mass of the Sun—or more accurately, the gravitational constant times mass of the Sun—is known to better than 1 part in 1 billion.  The only other stars for which we can derive masses are those in binary star system or in triplet star systems.  The masses of these stars can be know to better than 1%.  The masses of all other stars are unmeasurable, and can only be estimated from a star's luminosity and spectrum.

The key bit of information astronomers derive from binary star systems is how the luminosity and spectrum of a star is related to the star's mass.  This knowledge guides the development of stellar evolution computer codes, and it enables astronomers to derive the mass density of the Galactic disk and the distribution of mass among the stars by simply counting stars.

Next Issue:  The next issue of The Astrophysics Spectator is scheduled for April 2.

Stars

Binary Stars and Stellar Mass.  Binary star systems provide us with our only opportunity to measure the masses of stars, the Sun excepted.  Astronomers measure the positions of the stars of a binary on the sky and the Doppler shift of the emission lines in each star's spectrum to derive the characteristics of each star's orbit.  Under Newtonian mechanics, the masses these stars are directly related to the sizes and period of the orbits.  With the latest instrumentation, astronomers are able to derive the stellar masses of angularly-resolved binary stars with errors of less than 5%, and in some cases of less than 1%.  Binary stars that cannot be resolved—the spectroscopic binaries—can have the masses of their individual stars determined to better than 1% if the stars eclipse each-other.  (continue)