Dust layer h

' Plane of galaxy

Figure 10.2. (a) Starlight passing through interstellar grains toward observer #1 is fainter and redder because the blue light is preferentially scattered by the grains toward, for example, observer #2. (b) Simple model for absorption of optical light by interstellar grains in the Galaxy. The grains are assumed to occupy a horizontal slab that varies in density only in the vertical direction.

features they generate in stellar spectra. The conclusions are that grains must be solid with sizes of order 200 nm, somewhat smaller than the wavelength of visible light, and that they consist of graphite, ice (water), silicates, etc.

Among the many wavelengths in the impinging light, the smaller (blue) wavelengths are closest to the grain size and hence experience the most scattering. Thus the blue light is preferentially scattered out of the beam en route to the earth. Stated differently, the red light penetrates the dust clouds more efficiently. Infrared radiation is even more penetrating.

Interstellar grains are a significant fraction of the interstellar medium, >1% by mass. The interstellar medium in turn makes up roughly 10% of the —6 x 1010 M© of normal (baryonic) matter in the disk of the Galaxy. The dust grains in the disk thus have a total mass in excess of 107 M©. That is a lot of mass tied up in grains.

A dust grain is very much larger and more massive than a hydrogen atom. Thus even though the mass in grains constitutes a full ~ 1% of the interstellar mass density, their number density is manyfold times less than for hydrogen. Typical numbers for the Galaxy are —500000 hydrogen atoms/m3 and only —100 dust grains per cubic kilometer! The small number densities of grains interfere with starlight much more than the numerous hydrogen atoms because of their extremely high efficiency for scattering optical photons. It is this large effect that makes us so aware of their existence. The interstellar medium is very clumpy; extinction per unit path length along various lines of sight can vary by factors up to ~10.

Interstellar grains are believed to originate from the huge stellar winds of ionized gas (plasma) flowing out from M-giant stars, and also from mass ejections by other types of stars: carbon stars, planetary nebulae and probably novae and supernovae. These plasmas contain some heavy elements which then condense to grains of iron and silicates. Subsequently atoms of lighter elements strike the grain and are accreted onto it, possibly forming an ice coating.

The light removed by grains from starlight should appear as diffuse blue radiation from the sky, and one might expect it to appear as a diffuse halo surrounding individual stars. However, for most ordinary stars, this light is too faint to be detectable. Reflection nebulae such as the Pleiades are a special case. They are regions of recent star formation wherein the stars are especially bright and the quantities of dust especially high. The bluish scattered light is highly visible and dramatic in the regions between stars in both black and white and color photos of the Pleiades (Fig 1.7). Most stars in the Galaxy are older and in less dense regions of the interstellar medium.

The information about the grains provided by a single star is an average of the conditions all along the path traveled by the photons en route to the earth. Studies of numerous stars that lie at different distances and directions from us provide more detailed information about the distribution of the dust. Its clumpiness leads to the term dust clouds.

A very important effect of the interstellar grains is that they slightly polarize the starlight passing through them. This is an indicator of interstellar magnetic fields that tend to align the (non-spherical) grains. It is this alignment and the dependence of the scattering probability on grain size (in the direction of the electric field vector of the electromagnetic wave) that gives rise to the polarization. Maps of the sky showing polarization direction as a function of celestial position trace the magnetic field directions.

Extinction parameters

Extinction coefficient

The extinction AV is the number of magnitudes by which light in the visual V band (Section 8.3) is dimmed by the intervening dust. The average or typical amount of extinction of visible light (V band) in the plane of the Galaxy (within ~500 LY of the plane) is about 0.6 magnitudes for each 1000 LY of distance along the line of sight. For galactic latitudes b < 2°, where r is the distance to a source given in LY. One must use this expression only as a rough approximation because of the clumpiness of the grains.

The extinction Av is measured in magnitudes; it is the observed magnitude mv less the magnitude mv,o that would be measured if the intervening dust were not present.

Note that Av is positive since always mv > mv 0.

The 0.6-mag decrease in light in 1000 LY of travel in the galactic plane (4) amounts to a 58% decrease of the v -band light. This percentage follows from (8.14) where m2 — m 1 = 0.6. Thus, in optical light, one sees only the closer portions of the Galaxy; the galactic center, 25 000 LY distant, can not be seen. The expected brightening of the Milky Way in the direction of the galactic center (in Sagittarius) is much diminished for the observer who sees, for the most part, only the local region of several thousand light years. (There are lines of sight between dust clouds that permit longer views.) If the extinction were significantly greater, the Milky Way would not even be apparent. Only the very closest stars would be visible, and they are isotropically distributed about the sun.

Extragalactic sources It is fortunate that this extinction is sufficiently low to let us see out of the Galaxy in directions away from the galactic plane. In this way we can study and learn about other galaxies. In the direction of the galactic pole, perpendicular to the plane of the Galaxy, the visual-band extinction is about 0.2 magnitudes. It is possible to construct a simple model that will predict the amount of extinction at other galactic latitudes, but excluding the galactic plane.

Consider the geometry of Fig. 2b. The dust is assumed to occupy a horizontal slab of uniform density and height z0. The line-of-sight distance at angle b through the dust is:

z(b) = z0/(sin b) = z0 csc b (m; path length in slab) (10.6)

What is the relation between path length z and extinction Av ? The extinction Av (in magnitudes) describes how many factors of 2.51 the radiation flux is reduced; an extinction of Av = 1 .0 mag corresponds to a reduction in flux by a factor of r

100 4 = 2.51. Assume that a path length z = 1.0 z1 causes such a reduction. Now if the path is doubled to z = 2.0 z1, the radiation that survived in the first case will be further reduced by a factor of 2.51, or an additional 1.0 mag, for a total of AV = 2.0. Similarly, a third unit of path so z = 3.0 z1 would result in a total of AV = 3.0. It is apparent from these examples that z and AV are proportional to one another,

for the uniform-density model. This relationship was assumed implicitly in (4) and is demonstrated more formally below; see (35). Now introduce (6) into (7),

The proportionality factor is obtained by direct measurement of AV at the galactic pole, b = 90°, because csc 90° = 1.0. One obtains ~0.18 mag. Thus the approximate visual extinction AV along a line of sight at galactic latitude b is

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