Measuring the Masses of Stars Binary Star Systems

How Can the Mass of a Star be Measured? Knowing the mass of a star is important to astronomers. It’s the star’s mass that controls all the other characteristics of the star: it’s luminosity, temperature, color, size, even lifetime. BUT…it’s not possible to directly measure the mass of a single, isolated star. So what can we do?

Binary Star Systems If something, like a planet or a 2 nd star, is in orbit around the star whose mass we wish to know…we can use Newton’s form of Kepler’s 3 rd Law to find the total mass of the system: (Mass Star A + Mass Star B ) = 4π 2 a 3 G p 2 (a is the distance between the stars in meters, and p is the period of revolution of the stars in seconds.)

Doesn’t sound too hard! The good thing is that 50% to 75% of all stars are found in binary or multiple star systems. If we can watch 2 stars orbit each other and determine the period of revolution and the distance between the stars, we can calculate the total mass of the system and maybe even the individual masses of the two stars.

Extending to single stars Once we know the masses of many stars in binary star systems, we can infer the masses of single, isolated stars by comparing them to similar stars with known masses.

Types of Binary Star Systems Optical Doubles – the foolers Visual Binaries Spectroscopic Binaries Astrometric Binaries Eclipsing Binaries

Optical Doubles In a telescope, an optical double looks like a binary star system, 2 stars that are in orbit around a common center of mass. However, they’re really far apart from each other. They just happen to be in the same part of the sky. Mizar and Alcor are an optical double pair.

Mizar is 78 LY away. Alcor is 81 LY away Mizar and Alcor do not orbit each other.

Visual Binary Stars The 2 stars actually orbit a common center of mass. Both stars are visible either to the naked eye or through a telescope. We call the brighter star the primary, and the fainter star the secondary.

Albireo is the beak of Cygnus the Swan. domeofthesky.com/clicks/images/albireo.gif

Procyon, in the winter triangle is a class F subgiant with a white dwarf, only 11 LY away.

Sirius A is a class A star about 25 times brighter than our sun, with a tiny white dwarf companion, Sirius B.

Spectroscopic Binary Stars In a spectroscopic binary system, one of the two stars can’t be seen in a telescope. –The system may be too distant to resolve the two stars. –One of the stars may be too faint to see (a red dwarf). –The two stars may be very close to one another. How do we even know 2 stars are there?

It’s all in the Doppler Shift If the orbits of the two stars are edge-on to us, then one of the stars is moving towards us, while the other star is moving away. The light from the star moving towards us is blueshifted, while the light from the star moving away is redshifted.

It’s all in the Doppler Shift As we look in the spectrum of light from the stars, over time we see each spectral line split into two lines, then slowly come back together. We can get the stars’ orbital period from how long it takes the lines to split, come back, split, and come back together again.

Watch it here… ies/spectroscopic.html 01/java/binary/binary.htm

Dubhe, in Ursa Major, about 124 LY away, is a spectroscopic binary system, as is Capella in Auriga, 40 LY away.

The “star” that we call Castor, in Gemini, is actually 3 pairs of stars. Each pair is a spectroscopic binary pair. Pairs A & B orbit each other every 400 years. Pair C orbits A & B with a period of about 10,000 years.

Mizar in Ursa Major is also a spectroscopic binary star. In fact, it was the first one ever discovered, in Recent work has been able to resolve the two stars.

Astrometric Binary Stars An astrometric binary system is a spectroscopic binary where we can actually observe the primary star “wobble” as it moves across the sky (proper motion.) The star’s “wobble” lets us know that something massive, but unseen, is in orbit with the primary star.

Above is the proper motion of Sirius A (orange) as it moves across the sky. At right are the orbits of the two stars.

Eclipsing Binary Stars An eclipsing binary system is a special type of spectroscopic binary, where the orbit of the two stars is edge-on to our line of sight. We periodically see one star pass in front of or eclipse the other star. When this happens the total amount of light that we receive from the pair dims for a few hours.

education/senior/astrophysics/ images/binvar/svcamweba.jpg

Special Information Eclipsing binaries give us some very special information. If you plot the light curve of the stars, the total amount of light received over time, you can actually measure the diameters of the two stars. The plot on the previous page was a light curve.

Click here for an animation ofhere an eclipsing binary system. Scroll down to the bottom of the web page. Click here for a goodhere illustration of a light curve.

Algol The first eclipsing binary system studied was the “winking demon star” Algol, the knee of Perseus. Algol has a period of 2.87 days and is easily noticeable to the naked eye.

Algol The Algol system is about 96 LY away. The primary is a massive blue-white B8 star with 3.5 M sun and 100 L sun. The secondary is an orange K2 subgiant star with 0.8 M sun and 3 L sun. Click here for an animation of Algol.here

Algol’s Light Curve

Tomorrow… …you’ll have the opportunity to plot your own light curves for 2 different eclipsing binary star systems.