Measuring Rod Hierarchy

kw: parallax, cepheids, cosmology

Reading of Henrietta Leavitt and her work with Cepheid variables nearly a century ago, got me thinking of stellar and galactic distance measurement. The "hierarchy" of measurement methods is really a set of parallel ladders, at least in places.

1. The scale of the Solar system.

The earth-moon distance, being about thirty times the Earth's diameter (or about 10x the circumference), was measured centuries ago. Measure the moons' position in early evening, then just prior to sunrise for a few successive days around full moon. This allows you to back out the effect of the moon's motion. Then you just need to know the size of Earth. Eratosthenes's measurement of 23,000 miles (this is approximate, because we don't know for sure how long his σταδιου was) for Earth's circumference thus yielded nearly 230,000 miles. The modern average (it varies, of course) is 240,000 miles or 385,000 km.

But, try as they might, nobody could determine a parallax for the sun until the telescope was put to use (though not discovered) by Galileo. It comes out to about 400 times the moon's distance, and today most of us learn 93 million miles, or 149 million km.

Much later, 28th Century, secular variation in the timing of the eclipses of Jupiter's moons coupled with early measurements of the speed of light yielded a parallel measurement of the distance to the sun. This distance, the Astronomical Unit, or AU, is our beginning baseline for measuring larger distances.

Within the Solar system, we often state distances in AUs: 5.2 for Jupiter, 19 for Uranus, and so forth.

2. Direct parallax of the nearer stars.

Alpha Centauri was not the first star to be 'parallaxed.' Stars known to have large proper motions (apparent sideways motion, year to year) were checked, and the first to be determined was found to be at a distance of about 9 light years. That is about 600,000 AUs. That means the long, skinny triangle they had to measure had an acute angle of 1/10,000th of a degree or about a third of a second of arc. Alpha Centauri, which came later, has a parallax of about 0.8 arc second. The smallest distance between two points that the human eye can see is about one arc minute, or 60 arc seconds. It takes a pretty good telescope to reliably measure angles smaller than an arc second.

The stirring of the atmosphere prevented accurate measurement of stellar distances beyond about 100 light years. In the past twenty years, orbiting telescopes, most notably the Hipparcos observatory, being above the atmosphere, have been able to provide accurate parallaxes within about 1000 light years.

So how to measure farther?

One idea was to measure star positions over many years, letting the motion of the Sun through the galaxy provide a longer baseline. This is called Secular parallax. Trouble is, you don't know the relative motions of the Sun and the stars you want to measure. Using a star cluster, such as the Pleiades or Hyades, you can use perspective to back out the needed relative motion. Such measurements have allowed the distance to a few clusters within 2,000 light years to be determined. This method is called statistical parallax.

This was enough to get the distance to a Cepheid or two...

3. The rôle of Cepheid variables

Henrietta Leavitt measured the light curves for hundreds of Cepheids in the Magellanic Clouds. Once she discovered the Period-Luminosity relationship, she had a 'law' of sufficient accuracy to determine that the Large and Small 'clouds' (LMC and SMC) were at different, but similar, distances. At the time, no Cepheid's parallax was known, so it wasn't known just how far away the Clouds were. Now they are known to be about 185,000 and 165,000 light years from here.

Shapley's first use of statistical parallax gleaned a couple of Cepheids, and they were found to be among the brightest stars in their clusters. This was good news. In fact, it is very good news, because Cepheids are bright enough to give us reliable information to a distance of about 50 million light years. So in my earlier post about Miss Leavitt's biography, the "joint" in the intergalactic yardstick provided by "her stars" fills the gap between modest intragalactic distances and rather great intergalactic, though intracluster, distances. A range of between 1,000 light years and distances 50,000 times as great.

4. Beyond the Local Group of galaxies

Going farther than that, we get into the "Realm of the Nebulae," to borrow the title of Edwin Hubble's book on galaxies (He never used the term 'galaxy' himself). He measured the spectrum of many galaxies, starting of course with the brighter ones. Before long, he realized something akin to Leavitt's realization: there was a something-versus-distance rule at work here. In her case, the period-luminosity relation uncovered a way to determine distance using Cepheids' brighnesses. In his, redshift and distance were correlated.

What is redshift? Oddly enough, it seems almost everything that can happen to starlight as it makes its way to an observer is one or another kind of reddening. Thin gas clouds scatter blue light away from the path between us and the source, leaving more green, yellow and red. Dust clouds absorb light pretty evenly across the spectrum, but also scatter blue and green more than yellow and red. So a star that you would classify as a very white type A based on its spectrum—which lines are present or absent—looks more like a type F or G based on its visibly yellow color, if its light has passed through some gas or dust.

Motion of a star toward or away from us causes a blueshift or redshift, but these don't change the visible color much. Rather, lines in the spectrum appear to be misplaced. For example, there is prominent red Hydrogen line in stars cooler than type F. If the star is moving toward us, the line will be shifted to a shorter wavelength; it is blueshifted. If the star is moving away, the line will be at a longer wavelength, redshifted.

Hubble found that the spectra of the galaxies were nearly all redshifted, and the farther away a galaxy was, the greater the shift. As mentioned, the overall color didn't seem much different; even though a speed of 10% the speed of light only shifts a yellow 580nm line to the orange-yellow 640nm, there is plenty of light that began around 530nm that is now at 580nm. Yet such a red shift, we now know, implies a distance of 1/10th the way to the edge of the visible universe, or more than a billion light years.

Since the time of Hubble, other distance measures have provided parallel checks on the redshift-distance relation. Type Ia supernovae, for example, have been studied in sufficient detail that we know they all have the same brightness (within a small measure of variation). The more things we discover, the better we are able to determine the distances of objects throughout the visible universe.