Protostars, stars in the process of formation, are embedded deep inside molecular clouds. These clouds absorb radiation and heat up, emitting infrared light. Thus, while protostars cannot be observed directly, the infrared radiation is very bright and can be observed.

Observationallly, type Ia supernovae do not have hydrogen line in their spectra and type II supernovae do display these lines. Physically, type II supernovae are caused by the collapse of a massive star. Type Ia supernovae are driven by a white dwarf which accretes enough mass to exceed the Chandrasekhar limit and collapses into a neutron star.

Problem #2, page 325) If the stars at the turnoff point in a star cluster have masses of about how old is the cluster?

Since more massive stars have a shorter lifetime, we know that the most massive stars left on the Main Sequence give us an estimate for the age of the cluster. To do this problem, we need a relationship between the age of a star and its mass. This can be found in By the Numbers 12-1 (page 296) in the textbook. The relation is: . To eliminate the proportionality, we need to set up a ratio using the Sun as a standard:

M = 4 times the mass of the sun, so

The mass of the sun cancels out, leaving us with 4^-2.5 power. This equals: . We know the sun's lifetime is about 10 billion years (10 ¹⁰ years). Thus, . So the age of the cluster is approximately 300 million years.

The short length of pulsar pulses tells us that the object emitting the radio pulses must be very compact. If the object were large, light from the near side would arrive sooner than from the rest of the object. This would tend to smear out the signal into a longer pulse. Since we do not observe this, the object, a neutron star, must be very compact.

There are two reasons. First, gas and dust in the galaxy tends to redden and dim far away objects. Thus, distant stars appear very faint and cannot be easily seen. Since they could only see a small part of the galaxy, this led earlier astronomers to conclude it must be small.

Secondly, Shapley was the first astronomer to calibrate a distance scale for Cepheid variable stars. Applying this technique to globular clusters, he determined how far away they were and concluded, based on their distribution in the sky, the galaxy must be big.