Hello. We will now start talking about contents
of the universe and we'll begin with regular matter, the baryons.
First, let us recall what we learned from the cosmological tests.
What are the density parameters associated with different components we
see in the universe? We know largely from the precision
measurements of the cosmic microwave background that universe is very close to
flat, if not absolutely flat. That is that omega total is equal to one,
total matter energy density is exactly equal to critical, but with some very
small deviation. We also know from dynamical measurements
in microbe background, and to some extent supernovae, and other reasons that the
density parameter of all matter in the universe that exercises gravity, is about
0.27. And we know that the total density of
baryons expressed in units of critical density is only about four and half or 5%
of the critical density. As it turns out, luminous matter, stuff
that we actually see in galaxies as stars or gas,
only adds up to about half a percent. And so, therefore, looking at these
simple inequalities, there are implications,
because half a percent is less than 5%, there must be some sort of hidden or
missing baryonic matter. Because 5% is less than 27%,
there has to be some kind of non-baryonic dark matter,
and because 27% is less than 1, there has to be a dark energy.
So, let's look at the luminous bariums first,
those would be mostly in galaxies, and the way to do this is to integrate
them spatially. That is, what we need is a distribution
function of galaxy luminosities, also known as the luminosity function.
We obtained those from redshift surveys that measure distances to nearby
galaxies, and then we simply add up the light in the volume in which those
measurements that those are complete and average them over.
The results from different redshift surveys are all in very good agreement
and the amount of about couple 100 million solar luminosities per, per
comoving cubic megaparsecs locally here now for Hubble constant of 70, which is
close enough. But we want to find out how much mass is
in those stars, and for that, we need the circled mass-to-light-ratios of stellar
populations. Stars of different mass and different
ages produce energy of different rates, and so, we have to integrate over all
production of light for stellar population of certain age or mixture of
ages and see. And so, here it is for a variety of
galaxies of different Hubble types, and by and large, it doesn't change a lot
for stellar populations we see in galaxies is of the order four, four or
five. That is, on average, stellar populations
are less efficient in producing light per unit mass, and the reason for that, is
that there is a lot of mass in very low mass stars which are not very good light
producers. You probably recall that more massive
stars are fare more efficient in producing ash.
Now, these measurements do include a little bit of dark matter, but it's not
really important at the level we're talking about,
because the more massive stars are far more luminous per unit of mass and
because they live shorter, the age of stellar population plays an important
role, and those that are dominated by younger stars will be more luminous per
unit mass. Also, this will depend on the bandpass,
because most of the light produced by luminous stars in ultraviolet, then bluer
[UNKNOWN] will be more affected by star formation than the red ones.
And the flip side of that, is that blue light is more susceptible to extinction
by dust, so the corrections for that have to be
made. So we added all up and we find out that
the density of the material we actually see in galaxies is little less than a
billion solar masses per comoving cubic megaparsec for favorite values of hubble
constant. Converting that into grams per cubic centimeter and dividing it by the
critical density gives us the omega in visible stellar populations and it's only
about half a percent of the total. This is quite the remarkable result
actually, that all the stuff that we see out there,
adds up to less than a percent, only to half a percent of all the matter energy
that there is in the universe that we know from [INAUDIBLE].
But how much should we see? And, the answer to that is in measuring of the
total baryonic density, which you probably recall, is done in two very
different ways. One is by measuring abundances of
deuterium or other like nulcei, in the intergalactic clouds of high redshifts,
the deterium is the most sensitive of those and that produces a result of the
order of 4, 4 1/2% of the critical density.
A completely different approach based on different measurements in different
physics, is from [UNKNOWN] constellations in the early universe from cosmic
microwave background, and that produces result which is in perfectly good
agreement. So because of that, two completely
different base of measuring yield the same result and is repeated again and
again. We believe that, indeed, we do not, that
the total baryonic density universe corresponds to density parameter or
megavariance of about 5% or a little less.
Where are the remaining 90% of the variance?
Many suggestions have been made, but essentially bounce down to three
different counts. One possibility is the varying form of
some optically dark objects called MACHOs or Massive Compact Halo Objects, which
could be of different physical nature, it could be ground words that is the
substellar objects, could be planets, could be even gigantic comets, could be
black holes. This is not known,
but there are ways in which we can test that.
As we will learn later in the class, this turns out not to be the viable
possibility with that measurement and we know that.
The second possibility is that these missing variants are in the form of very
dense cold molecular clouds. This is a little bit ad hoc because we do
know about molecular gas in the galaxy. This would have to be a completely new
component, because these clouds would be very small, they'd be very hard to
detect, it's cold,
they will not emit much light. It's a legitimate possibility and people
look for it, and so far, there doesn't seem to be any evidence for such a, the
final possibility and most likely the correct one, is that these baryons are in
form of hot gas bound to galaxy groups simply corresponding to the large scale
structure, because, of the virial temperature equilibrium, it has to be
balanced against whatever the gravitational potential is.
The expected temperature of those gas is of the order of a million degrees Kelvin.
So that is not as hot as x-ray gas in clusters of galaxies.
The predictions are made by numerical simulation and structure formation,
and, it is perfectly a reasonable thing to expect.
Now, the problem is, that the gas, at that temperature emits primarily in hard
ultraviolet to very soft x-rays and those wavelengths are very effectively absorbed
by interstellar hydrogen. Our galaxy has an atmosphere,
interstellar gas, mostly neutral hydrogen, and because that
absorbs light in these wavelengths, we cannot see this gas.
This is same as looking through earth's atmosphere that absorbs UV radiation
through the ozone layer or in, infrared [UNKNOWN] bands of molecular water
absorption. So we, since we cannot get outside milky
way's atmosphere, we are doomed not to see this gas,
which is a little bit of joke of nature that most of the barriers in the universe
are hidden from us by hydrogen fog. However, there is a way to discover it
and that is by absorption. Let's now take a quick look at some of
these possibilities in turn. First, the possibility of MACHOs, Massive
Compact Halo Objects. If we look at distribution of stellar
masses, it is a very steep power load. There are many more low mass stars than
there are high mass stars and because stellar luminosity scales roughly, as the
fourth power of stellar mass, that means that the faint end of the luminosity
function would contribute least amount of light, but most of the mass,
and the critical issues is where is the cutoff if any, at the low mass end.
We know that stars with masses less than about 8% of solar cannot fuse hydrogen
into helium in their cores and those are the brown dwarfs.
So you can pack a lot of mass in these substellar objects without them producing
any observable physical signatures. You can go as far as you want down to
mass function or there could be additional peaks,
there may be interstellar planets or interstellar/balls and comets.
They'd very hard to detect, but there are ways in which we can test some of these
possibilities. Well, first of all, good thing is that we
know that brown dwarfs do exist. They've been discovered almost two
decades ago, and by now, we have thousands of them from various [UNKNOWN]
surveys so we know fairly well what that population is like.
And the answer is, there isn't enough of them to account for the missing baryonic
matter let alone the rest of the dark matter.
So the most viable possibility today, the one which most astronomers believe,
is that most of the baryons are in the form of this hot,
but not too hot gas, which emits radiation that's effectively
absorbed by intergalactic by interstellar medium in our galaxy.
But we can detect it in absorption, because of its physical state absorption
lines of elements like oxygen or they're ionized multiple times, should be present
and from the atomic physics, we can figure out if we observe some of these
lines, and their strengths, and ratios, what is the temperature, and the density
or Coulomb density of the [INAUDIBLE] gas.
And that turns out to be exactly what was needed.
these measurements have been on both with Hubble Space Telescope in ultraviolet and
also with Chandra X-Ray emission, x-Rays, and this hot gas has been unambiguously
detected in exactly the right amounts, and so, this is probably where all those
missing bariums really are. But that doesn't tell us where the
remaining matter density is, and so, next time we will talk about dark
non-baryonic matter.