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Interstellar reddening. More blue light is removed from the incoming beam than red.

— q can see the effect of reddening in the various wavelength images of the globule in Fig. 14.1. More stars shine through at longer wavelengths.

Suppose we measure the magnitude of a star in two different wavelength ranges, say those corresponding to the B and V filters. Then, from equation (14.4) we have mV = MV + 5 log (r/10 pc)+ Av mB = Mb + 5 log (r/10 pc) + AB

If we take the difference mB — mV, the distance r drops out, giving

In equation (14.9), the quantity on the left-hand side is directly observed. The first quantity on the right-hand side depends only on the spectral type of the star. It is simply the B — V color of the star. We know it because we can observe the star's absorption line spectrum to determine its spectral type. Since the spectral type determination depends on the presence of certain spectral lines, it is not greatly influenced by interstellar extinction. We can therefore determine the quantity (Ab - Av ).

Since both AB and AV are proportional to the total dust column density ND, their difference is also proportional to ND. If we define a quantity

it will not depend on ND since ND appears in both the numerator and denominator. We call this quantity the ratio of total-to-selective extinction. Extensive observational studies have shown that, in almost all regions, R has a value very close to 3.1. (There are a few special regions where R is as high as 6.) This has a very important consequence. It means that if we can measure (AB — AV), we need only multiply by 3.1 to give AV. We have already seen that the difference can be determined by knowing the spectral type of a star and measuring its B and V apparent magnitudes, and then using equation (14.9). Note that we have not made use of knowing the distance to the star r. We can still go back to equation (14.8a) to find the distance to the star. So, the method of spectroscopic parallax works even in the presence of interstellar extinction. We just need to do an extra observation at a different wavelength.

Example 14.2 Spectroscopic parallax with extinction

Suppose we observe a B5 star (MV = -0.9, B — V = -0.17) to have mB = 11.0 and mv = 10.0. What is the visual extinction between us and the star, and how far away is the star?

solution

From equation (14.9) we have

(Ab — AV) = (mB — mV) — (Mb — MV) = 1.00 + 0.17 = 1.17

We can now use the ratio of total-to-selective extinction to convert this to AV:

We can now find the distance from

This gives r = 280 pc

14.2.4 Extinction curves

If we study how extinction varies with wavelength, we can learn something about the properties of interstellar dust grains. We try to measure the A(A) in the directions of several stars, to see the degree to which grain properties are the same or different in different directions. Since the dust column densities are different in various directions, we do not directly compare values of A. Instead, we divide by AV or (AB — AV), to get a quantity that is independent of the column density. It is conventional to plot the following function to represent interstellar extinction curves:

A typical curve is shown in Fig. 14.6. One general feature is that in the visible part of the spectrum f(\) is roughly proportional to 1/A. In the ultraviolet there is a broad 'hump' in the curve. The size of this hump varies from one line of

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