Binary stars and clusters

Chapter 11

Review• Properties of stars

– apparent brightness (apparent magnitude)• measure energy/area/second

– luminosity (absolute magnitude)• calculate distance, use inverse-square law

– distance to the star• parallax

– temperature• blackbody curve (color, wavelength of max. energy)

– spectral class (OBAFGKM)• absorption spectrum, temperature

– radius• for two stars of same T, star of larger radius has greater luminosity• for two stars of same luminosity, star of smaller T has greater radius

H-R Diagram

What else would we like to know?

• mass?

• part of a binary (or triple) system?

• part of a cluster?

• age?

• evolution?

Why do we want to know the mass of stars?

• the total mass of the universe has implications for its ultimate fate (the Big Crunch?)

• mass is related to the age of the star

• mass is the single most important characteristic that determines the life and fate of a star

How can we calculate the mass of a star?

• The same way we calculate the mass of the Sun, the mass of Jupiter, the mass of ...

• Kepler’s Third Law (corrected by Newton of course)

• But we need to analyze something orbiting the star!

• Use a binary system (i.e. system of two stars orbiting each other)

• simulation

Important points to consider

• Both stars orbit about the center of mass of the system.

• We must consider how we are viewing the binary stars (top view, side view, at an angle?)

• How can we analyze the orbit?

Mass related to luminosity

• For binary stars, that we can reliably measure their masses and luminosities, graph luminosity vs. mass

• HUGE changes in luminosity correspond to small changes in mass -- power relationship!

• L ~ M4

• this is only true for main sequence stars

Mass-Luminosity diagram

How do we find binary stars?• visual binaries

– viewed with a telescope

• spectroscopic binaries– stars are too close together to be resolved with a telescope– measure period shifting of two sets of aborption lines in a single spectrum

• astrometric binaries– stars are too close together to be resolved with a telescope– one set of absorption lines are too faint to be seen– analyze doppler shift in the aborption lines of one star, thus measuring its

“wobble” and then calculate the properties of the other star.– similar to how we discover extrasolar planets

• eclipsing binaries– one star eclipses the other causes a change in its brightness

Star Clusters

• Most stars in the Milky Way are in multiple systems but far from other stars.

• Some stars group together to form clusters

• Types of clusters: open and globular

Open Clusters

• Example: Pleides• ~100-1000 stars• ~10-100 ly across• few stars/ly3

• HR diagram tells us something about stellar evolution--more massive stars are red giants

Notice that the more luminous stars in the Pleiades are off the main sequence.

These are red giants.

Evidently, the higher mass stars have evolved into red giants.

This is a typical characteristic of open clusters.

What does this tell us about the age of a cluster?

The more stars that are on the main sequence, the younger the cluster.

The more stars that are off the main sequence, the older the cluster.

Globular Clusters

• more dense– 1000-1,000,000 stars

– ~100 stars/ly3

– up to 1 million stars jammed into a sphere of diameter ~ 100 ly

HR diagrams look similar for all globular clusters.

They are similar in age, probably formed early in the universe (11-14 billion y).

The horizontal branch is “signature” of globular clusters.

The horizontal branch may indicate fewer heavy metals in the star, as would be the case for very old stars.