Lecture #1-- The Importance of the ISM
Astrophysics is literally translated as the study of stars, but it has grown to
quite a few other aspects of space, obviously.
For one thing, to understand stars and what their significance is, we need to
understand where they come from and where they go when they die.
That is the fundamental importance of the ISM, along with the fact that
everything we see in space that is outside our solar system is seen through
the screen of the ISM.
In this course, we will often consider the importance of scaling laws.
Scaling laws can be thought of as a constraint on the "outer scale" of some
object of phenomenon, where by outer scale I mean how the object or
phenomenon varies if its gross global scale is altered.
This requires imagining that the object or phenomenon is part of a sequence
of homologous (structurally similar) versions of the same thing, just with
a different overall scale-- a different "outer" scale but a similar "inner-scale"
structure.
Let us consider one example of this right now-- a cluster of stars, or even a whole
galaxy, that has recently formed and exhibits a distribution of stars over mass.
If this distribution is homologous, then it won't matter the size of the cluster,
and we can get information about the stellar distribution over mass (how many stars
are in each mass bin) independently of the total number of stars or total mass of
the cluster.
Such a homologous distribution is called an "initial mass function", where the term
"initial" refers both to the fact that the mass referred to is the initial mass that
each star had when it formed, and to the fact that the distribution itself refers
to the formation of stars, not their subsequent evolution (which can include things
like supernovae or white-dwarf creation, or binary mass transfer).
The simplest, and most widely used, version of an initial mass function is the
Salpeter IMF, which asserts that dN/dM is proportional to M to the -2.3 power.
Note several things here.
I am only interested in the proportionality here, how dN/dM (the number of stars dN per bin
width dM as a function of M) depends on M, because the overall constant out in front
will just tell me how many stars there are, or what the total mass is, but I'm interested
in the scaling law only-- I want to know how each mass bin in the stellar population contributes to the
overall attributes of the cluster, so I need to know only the relative number of stars in each
bin, not the actual number of stars in each bin.
Also, note that all power laws require an upper and a lower cutoff, or else they would not be
physically possible.
Often, the things we are interested in depend on either the upper or lower cutoff, but a given
attribute is rarely sensitive to both, so it behooves us to track which attributes of the cluster
depend on the upper-mass cutoff of the power-law distribution, and which ones depend on the
lower-mass cutoff.
In class, I demonstrated two limiting assumptions about the stellar population: (1) that it was a
newly-formed cluster, and (2) that it was a whole galaxy in a constant state of star formation
and evolution, such that the galaxy is not changing over the lifetime of the stars.
Note that both of these assumptions are physically impossible-- a newly-formed cluster will have
its massive stars go supernova in the time it takes the lowest mass stars to finish forming, and
a galaxy in a steady state is still creating more and more metals, so the younger stars should
generally have more metals than the older, breaking the homology of all the different clusters
that make up the galaxy. But we have to start somewhere!
See if you can recover my findings.
I got that in case (1), the number of stars in a cluster, and the mass of the cluster, both depend
primarily on the lower-mass cutoff, but the luminosity of the cluster, using L proportional to
M to the 3.5 power, depends quite strongly on the upper mass cutoff.
I also found that the fraction of the luminosity that comes above some M_o is essentially unity unless
M_o gets pretty close to the upper cutoff.
In case (2), however, I found that even the luminosity comes somewhat more from the lower-mass stars,
so the fraction of the luminosity that comes from above M_o gets pretty small if M_o is large.
So if we want to understand the luminosity of a collection of stars, which is often used to infer how
much (baryonic) mass is present there, it makes a huge difference between case (1) and case (2).
But the difference between case (1) and case (2) is all about what the ISM is doing-- did it make a
whole bunch of stars at some early point (relevant to case 1), or is it continuously making stars
(relevant to case 2)? Note that a starburst galaxy sounds more like case (1), and even an elliptical
galaxy (we just have to let the upper-mass cutoff evolve down the main sequence as the elliptical ages),
but a normal spiral galaxy like the Milky Way sounds more like case (2).
Understanding these differences, and also the metallicity issues I alluded to above, requires understanding
what the ISM is doing in a starburst, a spiral, and an elliptical
galaxy.
its outer sca