the physics of interstellar dust

[...]... susceptibility is equal to the ratio of the radii of the two circles, 1 = P/E, whereas the imaginary part gives the phase lag, 2 = 1 Only the real components of P and E have a physical meaning, the complex representation is for mathematical convenience The static value 1 (0) is positive because the polarization must point in the direction of the electric eld Obviously the real part 1 determines the maximum polarization... medium where the electron clouds oscillate about the atomic nuclei; a dielectric medium where the charge distribution in the atomic dipoles is xed but the dipoles themselves may rotate; and a metal where the electrons are free 1.1 Maxwells equations At the root of all phenomena of classical electrodynamics, such as the interaction of light with interstellar dust, are Maxwells formulae They can be written... depicted in gure 3.4 of chapter 3 With the help of this gure, we can explain the minus sign in equation (1.20) Going from left to right, the polarization jumps at the left edge of the grain from zero to its value inside The gradient there is positive and thus a negative charge appears on the surface In the case of nonuniform polarization within the grain, at a place where div P > 0, the electric eld pulls... Applying the operator div to (1.30) gives the expression for charge conservation: free + div Jfree = 0 (1.31) E denotes the electric and H the magnetic eld, D the electric displacement, B the magnetic induction, J the current density and c, of course, the velocity of light Our choice of mathematical symbols is summarized in appendix A together with some common relations of vector analysis 10 The dielectric... grains 7.4.1 Origin of the two major dust constituents 7.4.2 The bonding in carbon 7.4.3 Carbon compounds 7.4.4 Silicates 7.4.5 A standard set of optical constants Grain sizes and optical constants 7.5.1 The size distribution 7.5.2 Collisional fragmentation Dust radiation 8.1 Kirchhoffs law 8.1.1 The emissivity of dust 8.1.2 Thermal emission of grains 8.1.3 Absorption and emission in thermal equilibrium... and thus produces aligned dipoles If the polarization within the particle is uniform, pol is zero because the positive and negative charges of the neighboring dipoles exactly balance; the only exception is the surface of the particle where charges of one kind accumulate However, if the polarization P is spatially non-uniform, pol does not vanish Then the separation of charges is inhomogeneous and leads... relations complementing the set of Maxwells formulae = 1.1.2.2 The electric polarizability Another quantity we will need is the electric polarizability e If we place a small grain of volume V into a constant electric eld E, it acquires a dipole moment p = e V E (1.8) Because of the dipole moment, the eld in the vicinity of the grain becomes distorted It no has longer the value E but some other value, say... out of mathematical convenience, are written as one complex variable: () = 1 () + i 2 () () = 1 () + i 2 () (1.10) (1.11) 1.1.4 The physical meaning of the electric susceptibility We explain the physical meaning of in the case of a harmonically and slowly varying eld, E = E 0 eit We use scalar notation for the moment and let E 0 be real The vector representing the complex eld E then rotates in the. .. 2c When the integral extends over a unit volume, it is called the magnetization M, M= m V (1.14) For example, a charge q traveling with velocity v in a circular orbit of radius r constitutes a current I = qv/2r The magnetic moment of this moving charge is qvr AI m= = 2c c where A = r 2 signies the area of the loop If A is small, the accompanying eld is that of a dipole Without the motion of the macroscopic... macroscopic charge, the magnetization of matter comes, in the classical picture, from the atomic currents (electron orbits) The magnetic moment per unit volume M may be interpreted as the number density N of molecules in the substance multiplied by the total magnetic moment mmol per molecule: M = Nmmol The magnetic eld H is dened by H = B 4M (1.15) Similar to the situation of the electric eld, we . pressure 46 2.1.3 Efficiencies, mass and volume coefficients 47 2.2 The optical theorem 47 2.2.1 The intensity of forward scattered light 47 2.2.2 The refractive index of a dusty medium 50 2.3 Mie theory. 1 1.1 Maxwell’s equations 1 1.1.1 Electric field and magnetic induction 1 1.1.2 Electric polarization of the medium 2 1.1.3 The dependence of the dielectric permeability on direction and frequency. 438 14.3.1 General properties of the diffuse gas 438 14.3.2 The 21 cm line of atomic hydrogen 439 14.3.3 How the hyperfine levels of atomic hydrogen are excited 440 14.3.4 Gas density and temperature from