We now turn to Measurement of Cosmological Parameters.
The first one of which, is Hubble Constant, or Hubble Parameter.
It sets, both the spatial and temporal scales for the whole universe.
In a given cosmological model, specified by values of different, omegas, or little
w as well. All distances and all times scale
linearly with Hubble's constant. And thus, its importance.
So, the inverse of the Hubble constant is the characteristic time unit of
cosmology. The Hubble time.
Multiplied by the speed of light, it gives Hubble length.
Which is commensurate with the size of the observable universe.
Note that, Hubble's constant, is independent of all other cosmological
parameters. We have this neat separation, between
Hubble constant that sets the scale, and all under parameters that Describe the
qualitative behavior of the universe. So distances to anything, galaxies,
quasars, anything cosmology. Scale with Humboldt's constant and it's
importance. Moreover.
Physical parameters of, objects like galaxies or anything else, such as their
total luminosity, or their masses or physical sizes, all scale, with the
distance, with the appropriate power. And in order to understand these objects
better, and how they form, how they evolve, we need, distances to them.
However, measuring the distances in cosmology is, a very difficult thing to
do. Because galaxies are very far away.
And, in fact, the only distances in astronomy that are measured cleanly,
without recourse 20 models or statistics, are trigonometric paralexes to stars.
Everything else requires some sort of physical modeling or assumptions or
statistics. Because we have a concept of the distance
ladder. Which means, that we first measure,
distances to objects that, where we're sure how to do it, such as nearby stars.
Then we use that, to calibrate distances to some objects further away, star
clusters say, and, so on and so on. So we calibrate the distance indicators
relevant to each other. And this is what's known as the distance
ladder. Locally, those will be various stellar
types of indicators, say, based on pulsating stars or star clusters and
things like that, then properties of nearby galaxies, using their scaling
relations And sun, until we reach what is called pure Hubble flow, where only the
recession of velocities matter. And that is where the expansion of the
universe, unperturbed by local non-infirmities really sets in.
Now the age of the universe, can be actually estimated Independent of
Hubble's constant.The look back times, objects cannot, but the total age of the
universe can. We can, for example, estimate ages of
stars or clusters, or chemical elements and that gives a lower limit to the age
of the universe. Independent of any measurements or
distances. This is a hard thing to do, and thus,
measurements of Hubble constant have somewhat disreputable history.
Hubble's own estimate of it was an order of magnitude off from what we know today
is more or less the correct value. And through the history, people always
thought they knew it to about 10% accuracy.
Even though its value changed by a whole order of magnitude.
The reason for this is that they didn't really account properly for errors of
measurement. And especially for the systematic errors.
So, for example, when Hubble first measured value of Hubble's Constant.
One over that was a couple billion years, and already then people knew that there
were rocks on planet Earth that are three or four billion years old.
So planet Earth was older than the universe, and that was a problem.
Ever since then, the value of the Hubble constant was revised, usually downward.
The first major revision was due to Walter Baddey who recognized that there
are really two very different kinds of pulsating stars, one of which is confused
for the other, and he came up with the concept of stellar populations.
That immediately halved the value of Hubble's constant.
Then improved measurements. Pushed it further down, and down.
And in 1970's, it go down to the range of, between roughly 50 and 100 kilometers
per second, per mega-parsec. There were two prominent schools of
thought on this. One, led by Allen Sandage, the.
The disciple of Hubble, pushed for the lower values, around 50 kilometers per
second per megaparsec. The other one, led by Gerard de
Vaucouleurs and his collaborators in Texas and elsewhere, pushed for twice
that much, about 100 kilometers per second per megaparsec.
And the 2 just could not just get into an agreement.
The reasons for this were the. They made different assumptions, they
used different calibrations, and things went like that until 1980's.
But even in the modern days, the spread continued.
People started being more careful about the error bars, and yet still the actual
spread of quoted values in the literature was always larger error bars.
That persisted until roughly, 1990's. There are two kinds of methods to measure
distances. There are methods that obstensibly give
absolute distances to particular kind of objects, like trigonometric parallax for
stars, or using physical models to derive distances to supernovae or clusters of
galaxies Galaxies. Parallax is the only safe one.
The geometry is well-understood, and there are no problems.
However, we cannot measure parallaxes of stars more than about kiloparsec from us
now, well within sight of our own galaxy. There is so-called moving cluster method,
but that relies on statistics and certain assumptions.
There is so-called Baade-Wesselink method that uses pulsating stars.
That too makes assumptions about stellar atmospheres and thing, things like that.
A very simliar to it, is so called expanding photosphere method for
supernova. They are one also has to make some,
non-trivial assumptions, about physics, of what's really an exploding star.
Pushing further into Hubble flow, there are 2 important methods.
One is based on so called Sunyaev-Zeldovich effect, which measures
Distances to clusters of galaxies using observations of cosmic microbackground.
And of the x ray mission from clusters. We will talk about those in more detail.
And the other one is using gravitational lens time delays.
We will also address that one in due time.
The other kind of distance indicators is the secondary ones.
Which require callibration from somewhere else.
They can be used to measure relative distances say things there are objects
which may be further away but there zero point has to be obtained from something
else. And there are many of those, both using
stars and galaxies and we will address them all.
So here is schematically what the distance ladder is like Each method,
operates in certain range of possible, plausible distances.
And hopefully it overlaps in part, at least, with another method, which then
can reach deeper, and so on. That is what we call the distance ladder.
Nearest to us, trigonometric parallaxes, can be used to measure distances.
Proper motions of stars, can also be used.
Looking at statistical sense. Then we can measure distances to some of
the nearby star clusters. And use properties of star clusters to
measure distances to even more distant ones.
In particular, this leads to measurement to distances to pulsating stars.
Cephids and so called RR-Lyrae Stars, which are key step in the measurements of
the Hubble Constant. But notice that several steps precede.
With those, we can measure distances to a number of nearby galaxies.
And then we can calibrate distance indicator relations for galaxies
themselves. Those are correlations between 2
quantities. One of which does not depend on distance.
Say, rotational speed of a galaxy. And the other one of which does, like
luminosity. So these important distance relations can
be used to measure distances to galaxies far away, but they have to be calibrated
locally, with something else. Then super novae come in, and those are
currently favorite ways of measuring distances in cosmology.
From near to far. We will cover them in some detail.
Once we go beyond the regime where it's easy to do galaxy distance indicators,
two other methods come in, on really cosmological scales.
The Sunyaev–Zel'dovich effect, and the Gravitational Lensing.
In principle, they do not depend on the distance ladder, however they are
model-dependent. And therefore, previous calibrations are
important as a check. So, here is a schematic flow chart.
It's not there to confuse you, it's just to show you, a little bit, how complex
the network of measurments has to be, with mutual checks to find out how far
things are in the universe. It starts.
With nearer stars and goes all the way to supernovean and cosmological, truely
cosmological scale. Well that's it for now, next time we will
actually talk about stellar distance indicators.