Download HW #8 Answers (Due 10/21)

HW #8 Answers (Due 10/21)
1) What is a large molecular cloud and how is it different from the normal interstellar
medium (normal material between stars).
Large molecular clouds are regions of in a galaxy where the density of gas is higher than
it is in the normal interstellar medium. The density in the clouds are not large but much
larger than in the rest of space. Typical density for the interstellar medium is about 1
atom/cubic centimeter. In a molecular cloud the density can be 10 times higher and even
up to 100 times higher. These clouds are called molecular clouds because various
molecules can be found to reside in them, most notably molecular hydrogen and carbon
monoxide. The clouds provide a region where potential star formation can occur if the
cloud is compressed in some manner, allowing gravity to become strong enough to start
to pull the gas together into clouds.
2) List four star formation mechanisms with a short description of how each cause star
formation and also which ones initiate star formation in a cloud and which are part of
self-sustained star formation.
Cloud collision with spiral arms – As molecular clouds orbit in a spiral galaxy they pass
they periodically pass through an over density of gas which is related to the spiral density wave
in the galaxy. When this happens, the interaction between the cloud and the spiral density wave
can compress a cloud and initiate star formation in the cloud. This is the primary mechanism for
star formation in most galaxies.
Cloud – Cloud collisions – This mechanism is most common in galaxies which are
merging together. As two galaxies collide, the large molecular clouds can collide as well and
this compresses both clouds and sets off a large amount of star formation within the merging
galaxies. This type of collision is also a way to initiate star formation.
Winds from hot O and B type stars – Once star formation is initiated in a molecular
cloud there are often high mass stars formed. These high mass stars give off large amounts of
electromagnetic radiation and charged particles (stellar wind). These effect drive the gas and
dust around the stars deeper into the molecular cloud, causing compression of the cloud and
setting off a new round of star formation. This method of stars helping to form new stars is
called self-sustained star formation
Shock waves from supernova explosions – The highest mass stars use their fuel very
rapidly and therefore die while still nearby the region in which they formed. They die as
supernova explosions which send out shock waves that run into the molecular cloud from which
they formed. This helps to compress the cloud and set off new star formation. This is also a selfsustaining process.
3) O-stars are rarely found in between the spiral arms of galaxies. There are plenty of other
lower mass stars in between the spiral arms, but not O-stars. Explain why this is.
This is because O stars use their fuel very rapidly, in order to hold the star up against the inward
force of gravity. Their lifetimes can be on the order of 1-10 million years. Since is takes a few
hundred million years to orbit the galaxy one time, these stars never move very far from the
spiral density wave where they formed. They die close to where they were born. This means that
O stars are found in the spiral arms of galaxies but seldom in between the spiral arms.
NOTE: There is a small number of O-stars in between the spiral arms, but these are the ones
that formed from self-sustained star formation and their numbers are much less than that of the
spiral arm O-stars.
4) Use angular momentum conservation to explain why a shrinking proto-star begins to spin
rapidly.
Conservation of angular momentum means that angular momentum is constant for a
system. The equation is L = mvr, where L is angular momentum, m is the mass, r is the radius
and v is the velocity of the spinning object. When a proto-star contracts due to gravity, the
radius shrinks. If the mass is about the same, and the radius is getting smaller, then there is no
choice but for v to get larger. Otherwise the angular momentum would not be conserved, L =
constant. The results is that a shrinking proto-star begins to spin more rapidly.
5) State the relation between luminosity and surface temperature and radius of the star.
(Write the equation). A proto-star that is just beginning to form has a luminosity. In this
very early stage, explain whether temperature or radius is most important for the amount
of luminosity.
The equation for luminosity, as a function of surface temperature and radius is
𝐿 = 𝜎𝑇 4 (4𝜋𝑅 2 )
If the proto-star is contracting (R getting smaller) and the Luminosity is increasing, then it must
be the case that T is increasing also. If this wasn’t the case, and T was decreasing and R was
decreasing, then the Luminosity would have to be going down. Since T must be increasing this
means that T must be controlling the Luminosity in the very early stages of a proto-star’s
formation.