Reddening and Extinction

The discovery of the dust is relatively recent. In 1930 R.J. Trumpler (lived 1886--1956) plotted the angular diameter of star clusters vs. the distance to the clusters.

He derived the distances from inverse square law of brightness: clusters farther away should appear dimmer. IF clusters all have roughly the same linear diameter L, then the angular diameter should equal a (constant L) / distance. But he found a systematic increase of the linear size of the clusters with distance. This seemed unreasonable! It would mean that nature had put the Sun at a special place where the size of the clusters was the smallest. A more reasonable explanation uses the Copernican principle: the Sun is in a typical spot in the Galaxy. It is simply that more distant clusters have more stuff between us and cluster so that they appear fainter (farther away) than they really are. Trumpler had shown that there is dust material between the stars! The extinction of starlight is caused by the scattering of the light out of the line of sight, so less light reaches us.

Discovery of Dust by Trumpler

If the Sun is in a typical spot in the Galaxy, then Trumpler's observation means that more distant stars have more dust between us and them.

Dust Scattering is also well known on Earth!

There is some material between the stars composed of gas and dust. This material is called the interstellar medium. The interstellar medium makes up between 10 to 15% of the visible mass of the Milky Way. About 99% of the material is gas and the rest is ``dust''. The interstellar medium affects starlight and stars (and planets) form from clouds in the interstellar medium, so it is worthy of study.

Review

Hey! What is Interstellar Dust?

You have seen this before. A dark cloud, Barnard 86, is silhouetted against a starry background. Stars form in the dark clouds. A young cluster, NGC 6520, probably associated with Barnard 86 is seen just to

the left of it.

“Our galaxy probably closely resembles the galaxy NGC 891 as seen edge-on. Note the prominent dust lanes going through the disk mid-plane and how flat the galaxy is. “

“In the 1540's Nicolaus Copernicus removed the Earth from the center of the universe. He put the Sun at the center. Copernicus' view held up against the observational evidence for hundreds of years. In the 1910's the Sun was removed from the center of the universe and relegated to a typical patch in the galactic disk far from the center of the Galaxy. Harlow Shapley (lived 1885--1972) made this discovery by determining the distances to very old star clusters. He used the inverse square law of light brightness on a particular type of variable star in those old star clusters. “

Some stars are very useful for finding distances to clusters and to other galaxies because they have a known luminosity that is large, so they can be seen from great distances away. Bright objects of a known luminosity are called standard candles (though, in our modern day we should perhaps call them ``standard bulbs''). Standard candle objects are used to measure large distances. The particular standard candle stars Shapley used are in the last stages of their life and pulsate by changing size. They are trying to re-establish hydrostatic equilibrium but the thermal pressure is out of sync with the gravitational compression. The expanding star overshoots the equilibrium point. Then gravity catches up and contracts the star. But gravity contracts the star beyond the equilibrium point. The thermal pressure increases too much and the cycle continues.

In 1912 Henrietta Leavitt (lived 1868--1921) published the results of her study of variable stars in the Large and Small Magellanic Clouds. Leavitt found a very useful relationship for a certain type of variable star called a Cepheid variable (after the prototype in the constellation Cepheus. The fainter Cepheids in the Magellanic Clouds have shorter periods. Because all the Cepheids in a Magellanic Cloud are at the same distance from us, Leavitt reasoned that the more luminous Cepheids pulsated more slowly. This is the period-luminosity relation. Leavitt did not know the distances to the Magellanic Clouds, so she could not tell what the actual value of the luminosity part of the relation was.

Cephids

Astronomers had to wait a few years for Harlow Shapley to calibrate Leavitt's relation using Cepheids in our galaxy for which the distances could be determined. In the calibration process Shapley put actual values to the luminosity part of the period-luminosity relation. With a calibrated period-luminosity relation astronomers could use Cepheid variables as standard candles to determine the distances to distant clusters and even other galaxies. Cepheids have pulsation periods of 1 to 50 days. In the 1950's astronomers found that there are two types of Cepheids:

•Type I: classical Cepheids are from young high-metallicity stars and are about 4 times more luminous than Type II Cepheids. Below is the light curve (the plot of brightness vs. time) of a classical Cepheid from the Hipparcos database of variable stars.

•Type II: W Virginis Cepheids are from older low-metallicity stars and are about 4 times less luminous than Type I. Below is the light curve of a W Virginis Cepheid from the Hipparcos database of variable stars. Note the differences in the shape of the light curve. The two types of Cepheids are distinguished from each other by the shape of the light curve profile. In order to compare the shapes without having to worry about the pulsation periods, the time axis is divided by the total pulation period to get the ``phase'': one pulsation period = one ``phase''.

Because the luminosity of Cepheids can be easily found from the pulsation period, they are very useful in finding distances to the galaxies in which they reside. By comparing a Cepheid's apparent brightness with its luminosity, you can determine the star's distance from the inverse square law of light brightness. The inverse square law of light brightness says the distance to the Cepheid = (calibration distance) × Sqrt[(calibration brightness)/(apparent brightness)]. Recall that brightnesses are specified in the magnitude system, so the calibration brightness (absolute magnitude) is the brightness you would measure if the Cepheid was at the calibration distance of 10 parsecs (33 light years). In some cases the calibration distance may be the already-known distance to another Cepheid with the same period you are interested in.

Early measurements of the distances to galaxies did not take into account the two types of Cepheids and astronomers underestimated the distances to the galaxies. Edwin Hubble measured the distance to the Andromeda Galaxy in 1923 using the period-luminosity relation for Type II Cepheids. He found it was about 90,000 light years away. However, the Cepheids he observed were Type I (classical) Cepheids that are about four times more luminous. Later, when the distinction was made between the two types, the distance to the Andromeda Galaxy was increased by about two times to about 2.3 million light years. Recent results from the Hipparcos satellite have given a larger distance of between 2.5 to 3 million light years to the Andromeda Galaxy.

Another type of pulsating star similar to the Cepheids are the RR Lyrae variable stars (named after the prototype star RR Lyrae). They are smaller than Cepheids and, therefore, have shorter periods and lower luminosities. They pulsate with a period between 5 and 15 hours (Cepheid pulsation periods are greater than 24 hours). Low-mass stars will go through a RR Lyrae pulsation stage while the high-mass stars will go through a Cepheid stage. Because low-mass stars live longer than high-mass stars, the Cepheid stars as a group are younger than the RR Lyrae stars. RR Lyrae are found in old star clusters called globular clusters and in the stellar halo part of our galaxy. All of the RR Lyrae stars in a cluster have the same average apparent magnitude. In different clusters, the average apparent magnitude was different. This is because all RR Lyrae have about the same average absolute magnitude (=+0.6, or 49 solar luminosities). If the cluster is more distant from us, the RR Lyrae in it will have greater apparent magnitudes (remember fainter objects have greater magnitudes!).

RR Lyrae stars can be used as standard candles to measure distances out to about 760,000 parsecs (about 2.5 million light years). The more luminous Cepheid variables can be used to measure distances out to 40 million parsecs (about 130 million light years). These distances are many thousands of times greater than the distances to the nearest stars found with the trigonometric parallax method. The method of standard candles (inverse square law) provides a crucial link between the geometric methods of trigonometric parallax and the method of the Hubble Law for very far away galaxies.

The Hubble Law explained further

In 1914 Vesto Slipher (lived 1870--1963) announced his results from the spectra of over 40 spiral galaxies (at his time people thought the ``spiral nebulae'' were inside the Milky Way). He found that over 90% of the spectra showed redshifts which meant that they were moving away from us. Edwin Hubble and Milton Humason found distances to the spiral nebulae. When Hubble plotted the redshift vs. the distance of the galaxies, he found a surprising relation: more distant galaxies are moving faster away from us. Hubble and Humason announced their result in 1931: the recession speed = H × distance, where H is a number now called the Hubble constant. This relation is called the Hubble Law and the Hubble constant is the slope of the line.

The Hubble Law

Left: Red Shift for a galaxy nearer; Right Red Shift for a more distant Galaxy

The Hubble Law as applied to the recession of galaxies

In 1918 Harlow Shapley used his calibrated variable star period-luminosity relation to find distances to 93 globular clusters. Globular clusters are spherical clusters of 100,000's to several million stars (looking like a glob of stars) in very elliptical orbits around the center of the galaxy. Two globular clusters are shown below: Messier 5 (in Serpens Caput constellation) and 47 Tucanae (in the southern constellation Tucana).

Shapley found a strong concentration of globular clusters in the direction of the constellation Sagittarius. In a continuation of the process started by Copernicus almost 500 years before, Shapley announced that our solar system is not at the center of the Galaxy!