Wednesday 9 March 2011

Stellar parallax One way to measure the distance to some stars is to use the stellar parallax method. This works much like the way a surveyor can measure distances using trigonometry. If you look at an object from two different places (the distance between them is called the baseline), it will appear to shift relative to more distant background. From the angle of the shift, and a little trig, you can calculate the distances to the object. For stars, we need to move a long way from one measurement to another, because the stars are very far away, so we use the diameter of the Earth's orbit around the Sun as our baseline, or separation of the two observing sites.

In the two pictures of the sky, one taken in June and the other in December, note the shift of the nearby star relative to the background (more distant) stars.

Although this diagram shows the idea behind parallax, it is VERY misleading. The distance to the nearest star is about 300,000 times the distance from the Earth to the Sun, rather than the 4 or 5 as shown in graph. Showing the distance to the nearest star to scale with the Earth-Sun distance on this scale would require a graph several MILES long!

We often talk about distances to stars in units of light-years, which is the distance that light (or other EMR) travels in one year. One light-year is about 6 trillion miles. The Sun is 8 light-MINUTES from Earth. The nearest star other than the Sun is about 4 light-YEARS from us. Most of the stars you see in the night sky are 100s or 1000s of light years away.

***********Binary (or double) stars************

The majority of stars are in binary systems. A binary star consists of two stars that orbit each other. Our Sun is a lonesome single star- it does not have a companion- how sad! (But the Sun has us!)

Most binary stars are so close (compared to their distance from us) that we just see them as a single point of light. (There are some stars, like the one shown next, that *are* seen as two separate stars).

If two stars are so close that they look like one, how do we know there are 2 stars? The two most important ways are: eclipsing binaries and spectroscopic binaries.

Binary stars are of extreme importance to us as they provide us the only way to find the masses of stars (or "weigh" the stars). By combining the size and period of the orbit of a binary star with Keplers/Newtons Laws, we can find the masses of the two stars. So we can "weigh" stars that are trillions of miles away from us! Pretty amazing! But true!

Orbiting center of mass When two stars orbit in a binary system, they both go around a point between them called the center of mass (COM). The position of the COM is related to the relative masses of the two stars. If they have equal mass, the COM is halfway between the stars.

In this little animation, the bigger star is also the more massive, so the COM is closer to the bigger "star".

A colorful double star This nice binary or double star (named Albireo) shows a nice color contrast between a cool, red star and a hot blue star. This star is a favorite of amateur astronomers, as it can been easily seen with a small telescope.

Eclipsing binary star This is a cartoon of a binary star (double star) consisting of a bigger star (blue) and a smaller star (white). The graph shows the brightness of the star (axis labled "m" for magnitude) as a function of time (t). In the top frame, we can see both stars. In the next frame, the small star goes in front of the big star, blocking some of the light from the big star. The brightness we see goes down, as indicated on the graph. In the 3rd frame, the little star has passed by the big star, and we again see the light from both stars. In the 4th frame, the little star goes behind the big star, and we can't see the light from the little star, so the brightness we see again drops. In the last frame, we again see both stars, and the process starts over from the top. WE CAN SEE THE DIPS IN BRIGHTNESS EVEN THOUGH THE WE CAN'T SEPARATE THE TWO STARS- we SEE A SINGLE POINT OF LIGHT THAT CHANGES BRIGHTNESS.

As far back as 2000 years ago, the ancient Greeks noted several stars that appeared to brighten and dim in a predictable fashion. The most famous of these is a star called Algol. If you carefully watch Algol with your naked eye and compare its brightness to stars near it in the sky, you would see it dim for a few hours every 3 days or so. Algol is an eclipsing binary. Not all binary stars are eclipsing binaries as seen from Earth- the orbit of the binary star has to be oriented so that the Earth is near the plane of the orbit. If the orbit is tilted much, we don't get to see the stars eclipse each other.

Eclipsing binary: The Movie This little animation shows two stars orbiting each other. The bottom line is a plot of brightnes (the combined light of both stars) we would see versus time. Note that when one star goes in front of the other, some of the background star light is blocked so the total amount of light we would see goes down- there is a "dip" in the curve. Analysis of the spacing, duration, and depth of these dips can tell us lots about a binary star system: the period of the system, the sizes of the stars, the temperature of the stars, and more.

Spectroscopic binary star.. Some binary stars can be detected by the periodic changes in the Doppler shift of the spectra of one or both stars, as the stars orbit their common center of mass. In the top frame, star A is moving towards us, and B is moving away, so that the spectral lines of star A are blueshifted and those of star B are redshifted. As the stars go around each other, the spectral lines shift. In the middle frame, both stars are moving across our line of sight (not moving either towards or away from us) and their is temporarily no Doppler shift for either star.

By measuring the Doppler shifts of the stars as they orbit each other, we can find the orbital period of the system, the size of the orbit, even the relative masses of the two stars. Putting all this info together with Kepler's Laws and Newtons Law of gravity allows us to find the mass of each star. Thus, we can "weigh" the stars in a binary system, even though they are trillions of miles from us!

Hertzsprung-Russell diagram with masses

This HR diagram shows some stars labeled with their masses, in terms of solar masses. Note that the masses of stars on the main sequence increase monotonically as you go from cool to hot stars (from right to left on the diagram).

The lowest mass main sequence stars (those of spectral class M, in the lower righthand corner of the HR diagram) have masses of about 1/10 the Sun. The heaviest main sequence stars (the O main sequnce stars in the upper left) have a mass about 100 times that of the Sun.

Hertzsprung-Russell diagram

This is a HR diagram. Note that the temperature scale appears to run "backwards"- higher temperatures are on the left. Also shown are lines of constant star size (radius, expressed in terms of Suns radius). These slope upward (to increasing luminosity) with increasing temperature. If you compare two stars of the same size, the hotter one will be more luminous, as each square meter of the hotter star's surface will emit more EMR than for the cooler star.