Contents of the interstellar medium

14.1l Overview

When we look at photographs of the Milky Way (see Fig. 16.1), we note large regions where no light is seen. We think that these are due to dust blocking the light between us and the stars. We can see the same effect on a smaller scale (Fig. 14.1). Note that there is a high density of stars near the edges of the image. As one moves close to the center, the density of stars declines sharply. Near the center, no stars can be seen. This apparent hole in the distribution of stars is really caused by a small dust cloud, called a globule. The more dust there is in the globule, the fewer background stars we can see through the globule. We can use images like this to trace out the interstellar dust. We find that it is not uniformly distributed. Rather, it is mostly confined to concentrations or interstellar clouds.

We detect the presence of the gas by observing absorption or emission lines from the gas. By tracing these lines, we find that the gas also has an irregular distribution. Often the gas appears along the same lines of sight as the dust clouds. From this apparent coincidence we form the idea that the gas and dust are generally well mixed, with the gas having about 99% of the mass in a given cloud. In this chapter, we will see how the masses of different types of clouds are determined.

One of the reasons that the interstellar medium is so interesting is that it is the birthplace of stars. How do we know that stars are still forming in our galaxy? We have seen that stars are dying, and we know that there is still a large number of stars in the galaxy. We therefore presume that stars are being created at a rate that approximately offsets the rate at which they are dying. This is not an airtight argument, because it could be that many stars were formed early in the history of the galaxy and we are just seeing the ones that haven't died yet. However, we know that O stars live only about 107 years or less on the main sequence. Since we see O stars today, there must have been O star formation in the last 107 years. We think that the galaxy is ten billion years old. Compared with this, ten million years is almost like yesterday. If the conditions were right for star formation in the last 107 years, they must be right for star formation now. The actual star formation process will be discussed in Chapter 15.

14.2 I Interstellar extinction

If we want to see direct emission from the dust, we have to look in the infrared, as we will discuss in the next section. In the visible part of the spectrum the dust is generally evidenced by its blocking of starlight. The blocking arises from two processes, scattering and absorption. In scattering, the incoming photon is not destroyed, but its direction is changed. In absorption, the incoming photon is destroyed, with its energy remaining in the dust grain. The combined effects of scattering and absorption are called interstellar extinction. In Fig. 14.2 these two processes are depicted schematically. A dark nebula, in which background light

An image of a globule at various wavelengths.The globule is the region with the fewest number of stars per unit area.The dust in the globule is blocking the light from the background stars. [ESO]

An image of a globule at various wavelengths.The globule is the region with the fewest number of stars per unit area.The dust in the globule is blocking the light from the background stars. [ESO]

is being blocked, and a reflection nebula, in which scattered starlight is being sent in our direction, are depicted in Fig. 14.3.

14.2.1 The effect of extinction

We quantify interstellar extinction as the number of magnitudes by which a cloud dims starlight passing through it. For example, if a particular

Scattered

Absorbed

Scattering and absorption. Light is incident from the right. Light rays that are absorbed stop inside the cloud. Light rays that are scattered change direction. Rays that are scattered or absorbed are color coded as indicated.

star would have an apparent magnitude m without extinction, but its light passes through a cloud with A magnitudes of extinction, then the star will be observed to have a magnitude m' = m + A. (Remember, extinction dims the starlight, so the magnitude increases.)

We can relate the extinction, in magnitudes, to the optical depth t of the dust. This is useful, since it is the extinction in magnitudes that will be directly measurable, but it is the optical depth that is directly related to the dust properties. If we have light of incident I0 passing through the cloud of optical depth t, and intensity I emerges, then these are related by (as we saw in equation 6.18)

From the definition of extinction and the magnitude scale

Using equation (14.1), this becomes A = 2.5 log1o (eT ) = 2.5 t log1o (e) = (2.5)(0.4343) t

This means that one magnitude of extinction corresponds approximately to an optical depth of one.

The Horsehead Nebula, in Orion's belt, is formed by the dust blocking the light from the glowing gas in the background. In this image, north is to the left. (a) A wider view. The fuzzy blue patch at the lower left of the Horsehead is a reflection nebula, where dust is scattering light from a hidden background star towards us. Just off the left (north) of the image is the southwestern most star in Orion's belt. (b) A closer view from HST. This shows the intricacy in the structure in both the glowing gas and the absorbing dust. [(a) NOAO/AURA/NSF; (b) STScI/NASA]

If we have a star of known distance and spectral type, we can determine the extinction between the star and us. The spectral type gives us the absolute magnitude M. We can measure the apparent magnitude m. In the presence of A magnitudes of extinction, the star will appear A magnitudes fainter than without extinction, so m = M + 5 log (r/10 pc) + A (14.4)

Since we know m, M and r, we can find A. Obviously the presence of interstellar extinction will affect distance measurements by spectro-scopic parallax. If we don't correct for extinction, then a star will appear to be farther away than it actually is. You can see that if both r and A are unknown, then equation (14.4) only gives us one equation with two unknowns. We will see below that there is a way of obtaining additional information by observing at different wavelengths.

Example 14.1 Interstellar extinction Suppose we observe a B5 (M = —0.9) star to have an apparent magnitude of 9.2. The star is in a cluster whose distance is known to be 400 pc. What is the extinction between us and the star?

solution

We solve equation (14.4) for A to give A = m — M — 5 log (r/10 pc) = 9.2 + 0.9 — 5 log(40) = 2.1 mag

14.2.2 Star counting

If we record an image of a field which has some interstellar extinction, fewer stars will appear than if the extinction were not present. This is because the light from each star is dimmed by the extinction. Some stars that would have appeared on the image if there were no extinction are now too dim to appear with extinction. We can estimate the extinction in a cloud by comparing the number of stars we can see through the cloud with the number we can see in an unobscured region of the same size. Suppose an image is exposed to a threshold magnitude m0. All stars with apparent magnitude less than m0 (that is, stars that are brighter than m0) will appear on the image. If the light from each star is dimmed by A magnitudes, only stars that have undimmed magnitudes of m0 — A will appear.

There are two ways of applying this idea. In one, we measure the number of stars per unit area

The Horsehead Nebula, in Orion's belt, is formed by the dust blocking the light from the glowing gas in the background. In this image, north is to the left. (a) A wider view. The fuzzy blue patch at the lower left of the Horsehead is a reflection nebula, where dust is scattering light from a hidden background star towards us. Just off the left (north) of the image is the southwestern most star in Orion's belt. (b) A closer view from HST. This shows the intricacy in the structure in both the glowing gas and the absorbing dust. [(a) NOAO/AURA/NSF; (b) STScI/NASA]

Effect of extinction on star counts.The plot gives the number of stars per magnitude interval, as a function of magnitude m.The distribution is such that when the vertical axis is logarithmic, the curve is close to a straight line.The effect of a cloud with A magnitudes of extinction is to make each star A magnitudes fainter, shifting the curve to the right by A magnitudes.

Effect of extinction on star counts.The plot gives the number of stars per magnitude interval, as a function of magnitude m.The distribution is such that when the vertical axis is logarithmic, the curve is close to a straight line.The effect of a cloud with A magnitudes of extinction is to make each star A magnitudes fainter, shifting the curve to the right by A magnitudes.

If a photographic plate has a limiting magnitude m0, then the number of stars per unit area, without extinction, is

If we now look at a region with extinction A, only the stars that would have had magnitude m0 — A without extinction will show up. We therefore count m0- A

in each magnitude range. In the more common way, we measure just the total number of stars per unit area. We define the function N'(m) such that N'(m) dm is the number of stars per unit area with magnitudes between m and m + dm in the absence of extinction. We measure N'(m) for a region we think is partially obscured by dust and for a nearby region we think is unobscured. If we plot graphs of these two quantities, as shown in Fig. 14.4, we see that the two curves look like each other, except that one is shifted by a certain number of magnitudes. The amount of the shift is the extinction in the partially obscured region.

Often we don't have enough stars in each magnitude range to obtain a good measure of N'(m), In that case we must use integrated star counts. We let N(m) be the number of stars per unit area brighter than magnitude m. This is related to N'(m) by

Therefore, if we know N'(m), we can predict N(m0 — A) for various values of A. If we use plates with a limiting magnitude of 20, then we can generally obtain good star count data for A in the range 1 to 6 mag. For A much less than 1 mag, the difference between an obscured and an unob-scured region is hard to detect. For A much greater than 6 mag, there are very few stars bright enough to shine through, and the obscured region will appear blank, a situation in which 6 mag of extinction is indistinguishable from 20 mag.

14.2.3 Reddening

If we measure interstellar extinction we find that it is not the same at all wavelengths. In general, the shorter the wavelength is, the higher is the extinction. This means that blue light from a star is more efficiently blocked than red light. In the presence of extinction, the images of stars will therefore appear redder than normal, as shown in Fig. 14.5. This is called interstellar reddening. You

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