Figure 2.13 Polarization by dichroic extinction. Radiation propagating in direction n impacts an elongated grain rotating about the magnetic field B. The transmitted radiation is polarized in the direction of B.

to the field. The observation of polarized light from background stars is a powerful method for mapping the magnetic field throughout the Galaxy.

2.4.4 PAHs

Returning to the reflection nebulae around massive stars, we often find that such regions emit copiously at far-infrared wavelengths, in addition to the optical and ultraviolet. This radiation represents the thermal emission from the grains themselves. For a star at distance r, the flux on the grain falls as r-2. With Qx,abs varying as A-2, the thermal emission is proportional to T^ (see Chapter 7). Hence, the grain temperature falls as r-1/3. For a representative distance of 0.1 pc from a B star, Td is about 100 K. The temperature is somewhat higher for smaller grains, for which the efficiency factor governing emission is lower. However, the high temperature-sensitivity of the emission implies that this effect is not strong.

A number of reflection nebulae display a quantitatively small, but significant, anomaly in their emission. While the lion's share of the luminosity is in the ultraviolet, visual and far infrared, about one percent is emitted at near-infrared wavelengths. Figure 2.14 gives one example. Here, the observed near-infrared flux is well matched by a blackbody at a temperature of about 1500 K, along with a narrower emission feature near 3 pm. The broadband emission could not possibly be reflected starlight, since the radiation of the illuminating B star is predominantly in the visible and ultraviolet. Furthermore, the derived temperature is an order of magnitude higher than the value for heated dust, even at the smallest sizes posited in the Mathis, Rumpl, and Nordsiek distribution. Most intriguingly, the temperature does not decline with distance from the star.

The solution to this puzzle is to consider grains so tiny that their total thermal energy content is much less than the energy of a single stellar photon. Since the energy of a photon, unlike the stellar flux Fv, does not decrease with distance, the peak temperature Td could also be distance-independent. Under such circumstances the very concept of an equilibrium dust temperature loses significance. The temperature of each grain would undergo stochastic jumps with every photon impact and then rapidly fall as the grain cools. Because of the steep temperature-dependence of the emissivity, the observed Td would be heavily weighted toward the peak values.

How small does such a grain have to be? If ATd is the temperature jump, then the grain lattice gains energy 3NkB ATd, where N is the number of atoms. We equate this energy to the photon value hv and solve for N:

Figure 2.14 Near-infrared radiation from the reflection nebula NGC 7023. The specific flux Fv is displayed as a function of wavelength. The solid curve shows the flux from a blackbody at 1500 K. Note the excess emission between 3 and 4 |m.

For a representative photon energy of 10 eV and temperature jump of 1000 K, we find that N = 40. If At is the lattice spacing between atoms, this number can be packed into a sphere with radius R « N1/3 At = 10 Â, assuming a typical At of 3 Â.

The 3 |m emission spike seen in Figure 2.14 is actually one of several that were unexplained in the standard grain models. Since the 1980s, much effort has been devoted to the laboratory study of tiny grains (or macromolecules) that can reproduce these features. The most promising are known chemically as polycyclic aromatic hydrocarbons, or PAHs. These consist of linked carbon rings lying in a single plane. Figure 2.15 shows a representative PAH together with its emission spectrum in the near infrared. Here, the peaks arise from vibration of the C-H and C-C bonds.

Despite their small cross section, PAHs within clouds are important as heating agents, facilitating the transfer of the energy in starlight to the interstellar gas. In this role, their planar structure helps, allowing electrons to be readily liberated by ultraviolet photons. Theoretical studies which include PAHs in order to match observed cloud temperatures find that their population relative to ordinary grains can still be found by extrapolation of the standard size distribution. This fact lends support to the view that the distribution itself has a universal character, reflecting essential aspects of the origin and dissemination of interstellar grains.

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