To the infinite and Beyond! The Cosmic Distance Ladder
The cosmic distance ladder (also known as the extragalactic distance scale) is
the succession of methods by which astronomers determine the distances to celestial objects.
Let's suppose we are observing two stars in the night sky, and we are wondering
which one is the most distant from us. This is not a simple question to answer.
For example, if the two stars were lying at the same distance from us and had the
same intrinsic luminosity, we would see them showing the same brightness.
But...what if one of them was more distant from us than the other? We would expect to detect a
difference in brightness: the more distant a star is, the less bright it will appear in the sky.
And that's exactly what we observe: apparent brightness.
Since intrinsic luminosity provides us with a huge quantity of information about stars,
their atmosphere, their surface temperature, and their radius, it has been worth it to spent a lot
of effort in the computing of distances. Finally, when we observe the sky, we are
seeing a 2-dimension space, without no information about the 3rd one:
the stars that form constellations, they are in general separated in the depth dimension.
Follow me on this journey to learn more about this topic,
and to understand how astronomers are measuring the distances in the universe,
starting from the measure of Astronomic Unit until we get to the famous Hubble's Law!
So now we know that if we want to understand the physics behind an astronomical phenomenon,
we need to quantify the basic properties of the system under observation.
Many of these properties cannot be determined
unless we know the distance to the object in question.
Although we are not able to determine many of the absolute properties of astronomical
phenomena without distance information, we can compare their relative properties.
For example, the stars in any galaxy outside our own are all
at essentially the same distance from us. Thus, if observations of a nearby galaxy
reveal that all the stars of a particular type have the same apparent brightness,
then we know that this class of objects all have the same intrinsic luminosity.
We can use this property to measure the relative distances to other galaxies:
if we can identify the same type of star in these galaxies and measure their apparent brightness,
then the ratio distances follows directly from the ratio of apparent luminosity fluxes.
Sources with identical intrinsic luminosities which can be used
in this way are known as “standard candles”.
Think about the procedure once again: the distance to a nearby galaxy might
be determined by comparing the apparent brightness of its individual stars to those of similar stars
in the Milky Way, the distance to a more remote galaxy whose individual stars cannot
be resolved can then be measured by comparing the properties of the galaxy as a whole to the
properties of the nearby galaxies, and so on... This bootstrapping approach has been dubbed the
“cosmic distance ladder”, where each rung up the ladder takes us to a greater distance.
But how do we calibrate the cosmic distance ladder?
We first need absolute methods that give us absolute distance measurements.
So, first: Absolute distance estimators.
We use some simple geometric techniques as absolute distance estimators.
The available method includes, for example, the trigonometric parallax.
Let's see how the Trigonometric Parallax Method works.
As the Earth revolves around the sun, the point from which we see the stars continually changes.
Thus, their apparent directions also change a bit.
We can measure this changing in position and write: d (parsecs) = 1/w'',
where w is half of the angle variation of the star's position over the year,
measured in arcseconds. The w angle it's also called Parallax.
This method comes from geometric considerations, so it's an absolute calibrator.
If we can measure the w angle, we are able to determine the distance of our object.
Problems start to arise when we are considering very distant stars, for which we aren't able
to determine the Parallax because it is too slight and we don't have the right instruments
to measure that little shift in position. The larger known parallax is 0''.75 for Alpha
Centauri, which places it at a distance of 1.3 pc, making it our nearest star.
To make sense of our accuracy in calibrating the distance ladder,
we need some other Absolute Methods. If we know a star's radius, for example,
then we can estimate its distance from us. This is made possible by the Baade-Wesselink
Method: from its optical colour or spectral type, we can measure
the effective temperature of the star. Its intrinsic luminosity is then given by:
L=(C)(R^2)(T^4) By comparing the apparent magnitude
of the star to its absolute magnitude, we have a direct measurement of the star's distance from us.
Unfortunately, is not usually possible to measure stellar radii directly,
but we can overcome the problem studying variables stars such as Cepheids and RR Lyrae: second step!
Lines in the spectrum of such a variable star show Doppler shifts that vary cyclically with the same
period as the star's brightness variations. These variations arise because the atmosphere of the
star is unstable and undergoes global expansion and contraction, changing the size of the star.
Studies conducted us to a well-defined relationship between the star's period and its
intrinsic luminosity (P is proportional to L, that is, the brighter the star, the longer the period).
So, know that we know the star's intrinsic luminosity,
we can use the so-called “distance module” that will give us the distance of the star.
A similar approach is used with RR Lyrae stars,
old-population stars with a smaller period and fainter than Cepheids.
Thank the Cepheids, we are able to estimate the distance of about
Cepheids and RR Lyrae are called “primary estimators”,
in order to distinguish them from the absolute estimators.
Now we are ready to do one more step.
Where were we? Oh, sure... Third step: secondary distance estimators.
There are a lot of secondary estimators that astronomers use to estimate the
distance of faraway objects, but the most efficient one is the Type Ia Supernovae.
What's a Type Ia Supernova?
A Type-one-a supernova is a type of supernova that occurs in binary
systems (two stars orbiting one another) in which one of the stars is a white dwarf.
The other star can be anything from a giant star to an even smaller white dwarf.
Physically, carbon-oxygen white dwarfs with a low rate of rotation are limited to below 1.44 solar
masses. Beyond this "critical mass”, they reignite and in some cases trigger a supernova explosion.
The type Ia category of supernova produces a fairly consistent peak luminosity because of
this fixed critical mass at which a white dwarf will explode. Their consistent peak
luminosity allows these explosions to be used as standard candles to measure the distance to
their host galaxies: the visual magnitude of a Type Ia supernova, as observed from Earth,
indicates its distance from Earth. But how do we do that?
Studying Type Ia supernovae at a known distance, astronomers found that the luminosity peak is
the same for almost all of them so that, from the distance module, we can estimate their distance.
Type Ia Supernovae provide us with the distances for objects that reach 100 Mpc,
which makes them one of the most powerful distance estimators.
Of course, we are not done with all the secondary distance estimators, for example,
we can say that some empiric laws (Tully Fisher relation, Faber Jackson Relation) exist that
can give us the distance for distant objects. But we needed to talk about Type Ia Supernovae
because they are very bright and help astronomers calculating the Hubble constant.
In fact, when we reach the top of the distance ladder, we understand that there
is a connection between the shift in spectral lines of an object and its distance from us.
This crucial cosmological result was originally obtained without
good absolute distance calibration. The first one who makes an attempt
to understand how things work was Edwin Hubble, an American astronomer.
Following on from the discovery that the characteristic lines in
the spectra of almost all galaxies are shifted systematically toward the red by Slipher in 1914,
Hubble investigated the relationship between the distance D, to a galaxy
and the amount that a line of intrinsic wavelength is shifted in its spectrum.
Hubble provided evidence that the recessional velocity of a galaxy
increases with its distance from the Earth, a property now known as "Hubble's law”,
despite the fact that it had been both proposed and demonstrated observationally two years earlier
by Georges Lemaître. The Hubble–Lemaître law implies that the universe is expanding,
and the recession of the galaxies gives rise to their redshift via the usual Doppler formula.
Let's write down the Hubble's Law: v = H0 D
where v is the speed of separation and H0 is the Hubble's Constant.
Running the clock backwards, we can see that one Hubble Time ( (H0)^-1 = D/v) ago, all the
galaxies must have started from the same place. This is how we set the cosmology introducing a
Big Bang at a finite time in the past, when all the universe was concentrated in a small volume.
That's why is so important to determine a reliable value of the Hubble Constant:
it gives us an estimate of the age of the universe.
We made a huge effort to estimate H0, and the accepted value for it is today
somewhere between 65 and 75 km/s/Mpc, although its estimate is still uncertain.
Type Ia Supernovae, with their brightness, are very well visible and can help us covering very
long distances and thus have a better estimate of the Hubble's constant.
Also, it should be said that the more distant we go, the less error we have on the v value.
That's why Type Ia Supernovae are important to astronomers.
We made a long way through the universe today, and we are happy of that.
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