Star distances beyond 500 million light years
 Q: We measure star distances up to about 100 light years using the parallax method. How do we measure
distances beyond 100 light years? - Terry B., Albuquerque, New Mexico
A: Last week we discussed how to measure star distances up to 500 million light years away. In this, the final part of a
three part answer, we consider stars beyond 500 million light years.
[Stephen Kent, SDSS Collaboration] Quasar (redshift of 5.8) 4 billion light years away
First, let's discuss techniques that work for distances not so remote: From 40 to 300 million light years, we estimate
distances by comparing distant unknown galaxies with ones we know. The features we use for comparison are the size of a
galaxy's luminous gaseous region, the brightness of its global clusters, and the rotation of a galaxy.
Here's how it works:
- A luminous gaseous region-called, planetary nebula-is an expanding cloud of gas that a dying star (usually a red giant)
has ejected. The compact, hot, burnt-out star core remains at the center of the cloud and ionizes the gas cloud. These
nebulae are useful for measuring distances because they are extremely bright and emit large amounts of light with the
light spectra of ionized oxygen. Thus, they are easy to find. Moreover, the brightest planetary nebulae apparently have
the same brightness in many galaxies. Therefore, since we know the intrinsic brightness of nearer planetary nebulae, we
also know that in more remote galaxies. We can measure the apparent brightness of a remote galaxy, which allows us to calculate the distance to the remote
galaxy because, we know that the intrinsic brightness dims with the square of distance.
- A galaxy's global cluster is a spherically symmetrical cluster of stars, containing from several tens of thousands to a million stars that probably share a
common origin. That profusion of stars is visible a long ways off. One hundred and fifty globular clusters (e.g., the Big Dipper) occur in our own Milky Way
galaxy. Thus, we have compiled a Hertzsprung-Russell diagram (see H-R diagram discussion in last week's column) for global clusters, which gives intrinsic
brightness of stars in a cluster as a function of the stars' colors. We can measure the apparent brightness and color of a remote global cluster and then find its
intrinsic brightness on the global cluster H-R diagram. Once again, solving for distance, knowing both intrinsic and apparent brightness, we calculate the
distance to the remote galaxy. This method assumes that remote systems are the same in age, constitution, and number as globular clusters around our
Galaxy.
- Spiral and elliptical galaxies
are galaxies whose names describe their shape. Most galaxies (i.e., giant assemblies of stars, gas, and dust where most of the
Universe's matter dwells) have both a central spheroidal bulge and a flattened disc. Spiral galaxies are those with both bulge and disc; our Milky Way galaxy
is a spiral galaxy. Elliptical galaxies lack the disc. The vast numbers of stars in a galaxy make them visible for millions of light years away. We can estimate
their distance by capitalizing on a feature of their rotational velocity.
The brightness of a spiral galaxy is directly related to its rotational velocity, raised to the fourth power. The faster a spiral galaxy spins the brighter it glows.
This function (called the Tully-Fisher Relation) is the most accurate technique at present for estimating distances to remote spiral galaxies. We can measure the
rotational velocity (with a radio telescope) and we can measure the apparent brightness. We plug the rotational velocity into the Tully-Fisher relation to get the
intrinsic brightness. Once again, knowing the intrinsic and apparent brightness, we calculate the distance to the remote spiral galaxy. In 1977, R.B. Tully and
J.R. Fisher discovered the rotation velocity and luminosity relation. We use an analogous technique, called the Faber-Jackson relation (determined in 1976), to
measure distances to elliptical galaxies.
These methods provide distances out to at least 300 million light years. We can, however, see more remote galaxies and quasars. (A quasar is a compact
extragalactic object that looks like a point of light but emits more energy than a hundred supergiant galaxies).
Here's the catch: Beyond 300 million light years we must include the expansion of the Universe in our calculations. We're OK, however, because we know how
to describe the space expansion--that's the standard "Big-Bang" cosmological model, which is expressed using Einstein's general theory of relativity equations.
Thus, we use Hubble's expansion law and Einstein's equations to calculate truly remote distances.
The procedure is a two-step operation. First, we evaluate Hubble's constant (the expansion rate of the Universe), which is a part of the expansion law. Then we
use the expansion law again to calculate the distance to the remote object. The Hubble's constant is a number that relates a galaxy's apparent speed of recession
to its distance from the Milky Way galaxy. It's normally expressed in units of "kilometers per second per megaparsec" where a megaparsec is about 3.26 million
light years.
Step 1. To evaluate Hubble's constant we target a distant galaxy whose distance we know and calculate how fast it is receding from us by measuring its redshift.
(A redshift is the shift of a star's spectral lines toward longer wavelength values-i.e., toward the red-because light waves lengthen as they speed through
expanding space. See WonderQuest article, "Expanding Universe", given in Further Surfing below.) Calculating redshift is a snap, given the simple relationship:
received wavelength = (emitted wavelength)
x (1 + z) where z is the redshift.
All quasars have a prominent feature in their spectrum: the Lyman alpha line of hydrogen, whose wavelength is 1216 Angstroms. Suppose we examine the light
from a distant quasar and determine that the Lyman hydrogen line is about 8300 A. Then, plugging these values in the equation above, we get a redshift, z =
5.82
Now, Hubble's Law says the velocity of recession is related directly to the distance (d) of a galaxy from our Milky Way galaxy:
The recession velocity (v) is a function of the redshift (z) that is expressed using Einstein's general theory of relativity equations, which is beyond the scope of
this article. But the task is straight forward: we measure z and then evaluate the function.
So, Hubble's constant = v / d .
We pick a somewhat nearby galaxy, whose distance we know and whose redshift we can measure. This then gives us Hubble's constant.
In actual practice, Hubble's constant is difficult to determine. Our best present estimate is about 65 or 70 kilometers per second per megaparsec.
Step 2. To estimate the distance to a remote galaxy or quasar, we measure its redshift. We then plug the redshift value and Hubble's constant into Einstein's
equations to get the recession velocity. Then we use that result in Hubble's expansion law again, this time solving for distance:
d = v / (Hubble's constant)
The farthest quasar discovered so far (and this changes often) is now about 27 billion light years away. The light we see now was emitted when the quasar was
about 4 billion light years away and the Universe was about 0.95 billion years old. The Universe today is about 14 billion years old.
(Answered by April Holladay, science correspondent, October 10, 2001)
Further Surfing:
WonderQuest, USATODAY.com: Expanding Universe
Royal Observatory at Greenwich: Galaxies
Harvard-Smithsonian: Hubble's constant
U of California at Los Angeles: ABCs of distances
U of California at Los Angeles: Cosmology tutorial
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