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Figure 10.3. Measured extinctions in magnitudes versus photon frequency. The ordinate is the extinction coefficient A(v) at frequency v normalized to the extinction at the visual band, AV. The effective frequencies of the V and B bands are indicated. The absorption increases approximately linearly with frequency in the optical region. The large bump in the ultraviolet at X « 0.22 |m (1.4 x 1015 Hz) may be due to enhanced scattering by small graphite particles. [Adapted from A. Savage and B. Mathis, Ann. Rev. Astron. Astrophys. 17, 75 (1979), with permission]

Dust-hydrogen association

The grains in the Galaxy are quite closely clumped with the hydrogen in the interstellar medium. We now describe how this was determined.

Studies from satellites of individual hot stars at ultraviolet frequencies provide information about the interstellar hydrogen. The ultraviolet photons en route to the earth from the star being studied can excite neutral hydrogen and also molecular hydrogen and hence be absorbed. Thus, the stellar spectra of bright hot stars show absorption lines from these constituents of the interstellar medium. The strength of these features permits one to estimate the amount of hydrogen summed over the distance from the star to the earth.

The data yield a column density (atoms/m2) of neutral hydrogen atoms (H I), including those in H2 molecules, along the line of sight to the star at distance r, f jo

density)

This is the total number of hydrogen atoms in a column 1 m2 in cross sectional area and of length r (see Fig. 8.9). It would be more precise to call NH the number column density.

Eb-V magnitudes

Figure 10.4. Correlation between hydrogen column density (atoms/m2) and color excess EB-V due to interstellar grains (dust) along the line of sight to ~100 stars. Each point represents a given star. The reddening (abscissa) due to interstellar grains was obtained from studies of the reddening of the same stars in optical light. It is expressed as the color excess EB-V. The hydrogen values (ordinate) are from studies with the Copernicus satellite of ultraviolet absorption lines in the light from hot stars. The clustering of points along a line indicates that hydrogen and dust cluster together in the clumpy interstellar medium. [Adapted from A. Savage and B. Mathis, Ann. Rev. Astron. Astrophys. 17, 86 (1979), with permission]

Eb-V magnitudes

Figure 10.4. Correlation between hydrogen column density (atoms/m2) and color excess EB-V due to interstellar grains (dust) along the line of sight to ~100 stars. Each point represents a given star. The reddening (abscissa) due to interstellar grains was obtained from studies of the reddening of the same stars in optical light. It is expressed as the color excess EB-V. The hydrogen values (ordinate) are from studies with the Copernicus satellite of ultraviolet absorption lines in the light from hot stars. The clustering of points along a line indicates that hydrogen and dust cluster together in the clumpy interstellar medium. [Adapted from A. Savage and B. Mathis, Ann. Rev. Astron. Astrophys. 17, 86 (1979), with permission]

The dust content along the same line of sight may be obtained from the degree of reddening of optical light from the star. This is possible because the star can be spectroscopically classified, and the intrinsic spectral distribution (or color) of each type of star is presumed to be well known. This and the measured spectral distribution (or color) yield the amount of extinction, or equivalently the color excess EB-V, for the star in question.

The color excess and hydrogen column densities are obtained for a number of independent stars over a large range of distances and directions. The values for each star may be plotted as points on an NH vs. EB-V plot (Fig. 4). The two quantities are found to be reasonably well correlated; the data points tend to follow more or less a straight line. The best fit to the points in the figure gives the correlation:

N(H I + 2H2)/EB-v = 6 x 1025 atoms m-2 mag-1 (10.14)

where N(HI + 2H2) is the column density of hydrogen atoms (one for each neutral atom and two for each molecule). If the color excess EB-V equals 1.0, the column density will be about 6 x 1025 hydrogen atoms/m2 according to (14).

This correlation suggests that the diffuse interstellar clouds that contain the dust also contain the hydrogen in approximately proportional amounts. Directions that happen to have lots of dust also have lots of hydrogen. The ratio of mass in grains relative to that in hydrogen quoted above, >1%, derives from these measurements. Keep in mind that this result applies to our region of the Galaxy, in the solar neighborhood; it could differ elsewhere.

The ultraviolet absorption lines used for these measurements can be measured only for the brighter (and hence closer) stars. Radio astronomers, in contrast, detect emission from low-lying states of neutral hydrogen and can derive values of NH out to very large distances. X-ray astronomers can derive values of NH from x-ray spectra of x-ray emitting compact stars (neutron stars and black holes) throughout the Galaxy (see below). Molecular hydrogen, a very important component of the interstellar medium, unfortunately does not emit a radio signal, but as we have seen, it is detected in absorption by ultraviolet astronomers.

X-ray astronomers often make use of the correlation of Fig. 4. If they derive a value of Nh from their x-ray data for a particular source, they can find EB—V from Fig. 4. This gives the extinction AV, from (11), expected in the optical counterpart star of the x-ray source. Sometimes the source is in the galactic plane behind so much dust that it is too faint to be detected at optical wavelengths. In such cases, the source can sometimes be located in the infrared for which the extinction is less.

Heretofore we have noted the correlation between NH and EB—V but we have not commented on the linearity of the correlation, namely the straight-line character on the linear-linear plot of Fig. 4. We will demonstrate below that the definition of the color excess EB—V implies that it is proportional to the grain column density, Ng a Eb—v . Thus, if the grain and hydrogen number densities are everywhere in a constant ratio, we would expect to find the linear relation, NH a EB—V, as we do.

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