Download Hubble`s Law is the relation between the recession velocity of a

Astronomy 301
Fall 2004
Dr. Frank Bash
Exam #2 Answers
1. How do we use Hubble’s Law to determine the age of the universe?
Hubble's Law is the relation between the recession velocity of a galaxy and its
distance: Vr = H d, that is, the velocity of recession Vr equals the distance d times
the Hubble constant H.
Assuming the galaxies have receded at a constant velocity since the big bang
and all galaxies expanded from the same spot, we can divide distance by velocity
to find out how long the expansion has taken to separate the galaxies to their
present distances. That is the age of the universe.
From Hubble's Law, we know the Hubble constant is just velocity divided by
distance. Thus the reciprocal of Hubble constant (1/H) must be proportional to
the age of the universe.
(In other words, if you know the velocity and the distance of a far away galaxy, you can
figure out how long ago our galaxy and that galaxy were in the same place, which must
have been when the big bang occurred)
2. Is a hot white dwarf star in thermal equilibrium?
Thermal equilibrium is a state in which the energy radiated from the surface of a
star per unit time, or the luminosity, is equal to the energy generation rate at the
core of the star.
A white dwarf has used up its fuel for nuclear reaction. It generates no energy
inside of it, and is cooling. Thus a hot white dwarf is not in thermal equilibrium.
(A white dwarf may be hot, but the high temperature just makes them cool more
quickly.)
Note: A white dwarf is still in hydrostatic equilibrium. In a white dwarf, the gravity is
supported not by energy flowing outward but by the pressure from the dense degenerate
matter.
On this problem, many people confused thermal equilibrium—which is essentially means
the temperature isn’t changing—with hydrostatic equilibrium—which essentially means
that the size isn’t changing.
3. Explain why there is less carbon in very distant stars than in nearby Population I stars.
Very distant stars are seen by us as they were a long time ago. The Universe
was born composed of Hydrogen, Helium, and a bit of Lithium. Carbon is
“pollution” produced by stars. A long time ago there was little Carbon since only
a small number of stars had been born. Nearby (recently) we see much more
Carbon in gas clouds from which the Population I stars are born.
4. What is the cause of the “main-sequence” on the Hertzsprung-Russell Diagram?
In order to be a star, the gas blob must be able to ignite the H → He nuclear
reaction. The main-sequence is a stage in the life of a star where it burns
Hydrogen. The main-sequence stars are in thermal and hydrostatic equilibrium.
5. What is the evidence that the spiral arms in spiral galaxies are the birthplaces for stars?
In the spiral arms of galaxies, we see bright, blue, highly luminous O and B stars.
Since these stars have very short lifetimes, we know that they can not have
moved far from where they were born. We also see, strung out like beads along
the arms, regions of ionized hydrogen, which are lit up from the inside by bright
new stars pouring out ultraviolet radiation.
Some common mistakes:
The density wave theory is not evidence that spiral arms form stars. Rather, it is a theory that
may explain why stars form there. The fact that we see star formation in spiral arms is evidence
for the density wave theory, not the other way around. Similarly, the fact that we see star
formation implies that elliptical galaxies were once more efficient then spirals, not the other way
around.
Also, while population I stars are younger than population II stars, not all (or even most)
population I stars are bright blue O stars. Most (like our sun) are plain old mid or low mass stars
that formed relatively recently (compared to pop. II stars in the halo), but are a still a long way
from the spiral arms they were born in.
And finally, it is true that there is plenty of gas and dust in spiral arms, and that these are needed
to form stars. However, there is gas and dust throughout the whole disk, and stars are not
forming everywhere in the disk, just the arms. Just because there's Bisquick in my kitchen
doesn't mean I'm making pancakes.
6. Why does the main-sequence turnoff point on the H-R diagram of a star cluster tell you
that cluster’s age?
Stars on the main sequence are lined up according to luminosity. But the more
luminous a star is, the more massive it is. And the more massive a star is, the
quicker it burns its hydrogen, and therefore the shorter its lifetime. The stars in a
cluster are all formed at the same time. Since the more massive stars have
shorter lifetimes, they die first. A star at the turnoff point is just about to die, and
therefore its age is equal to its lifetime. So since we know lifetime of that star
(since we know its luminosity and hence its mass) we know the age of the entire
cluster.