Annu. Rev. Astron. Astrophys. 1980. 18: 321-361 Copyright © 1980 by Annual Reviews. All rights reserved

V. THEORETICAL MODELS AND THE ORIGIN OF POLARIZATION

Of all active extragalactic objects, the blazar class exhibits the most extreme behavior in variability and polarization and places the greatest burden on current theoretical models of the central powerhouse. In this section, we review current theories with an emphasis on those areas pertaining to optical polarization and rapid variability. We devote the majority of the section to discussing basic emission mechanisms and, in particular, the canonical incoherent synchrotron model. After reviewing its success at describing extragalactic radio sources, we examine the difficulties of extending the theory into the optical, in addition to the well-known problems with the low-frequency variables, superluminal expansion, and short particle lifetimes - all of which are associated with the blazar class. Although the incoherent synchrotron theory and the alternative emission mechanisms are intimately connected to specific models for the central source of energy, we postpone discussing models for the central power-house and their common features until later in this section. Finally, we briefly review the processes by which dust scattering can cause linear and circular polarization.

INCOHERENT SYNCHROTRON RADIATION     Because of its success in explaining the radio emission from the Crab Nebula, incoherent synchrotron emission was proposed by Shklovsky (1955) and others to be the source of the diffuse extragalactic radio emissions whose power-law spectra at high frequencies (optically thin regime) resembled that of the Crab. The synchrotron theory was soon extended to the compact sources, whose flat spectra are generally considered to be the superposition of many components of varying optical depth (see, for example, Kellermann & Pauliny-Toth 1968). One of the successes of this canonical theory of incoherent synchrotron theory was its "prediction" of the upper limit of observed brightness temperatures, implied by the observed flux and VLBI measurements or limits on angular size, T_b 10¹² K. Such temperatures indicate that relativistic electron energies, coherent plasma effects, or both must be present. In the canonical theory, the maximum brightness temperature of ~ 10¹² K corresponds to the onset of significant Compton upscattering of the synchrotron radiation by the relativistic electrons. At higher brightness temperatures, the upscattered photons are themselves upscattered in energy leading to a "Compton catastrophe" and rapid cooling of the relativistic electron distribution (Hoyle, Burbidge & Sargent 1966, Kellerman & Pauliny-Toth 1969, Jones, O'Dell & Stein 1974). In addition to explaining the observed power-law spectra and surface brightness limits, the canonical synchrotron theory also predicts high polarizations (60-80%; Korchakov & Syrovatskii 1962) in the optically thin regions. Although radio sources generally show much lower polarizations, these could be understood as resulting from chaotic field geometries and self-absorption effects (Jones & O'Dell 1977a).

Despite the success of the canonical theory in describing the compact- and steep-spectra radio emission, there is little evidence that the observed optical emission from the large majority of QSOs or Seyfert nuclei is a simple extension of the observed radio emission (Section IV) or is even nonthermal in origin. For the blazar class, however, their smooth spectra, high polarization, and rapid variability make the incoherent synchrotron theory look more promising (Section III). In particular, rather simple models for the source can explain the observed polarization properties. For example, the presence of many misoriented emission regions with equal strength magnetic fields and particle distributions will produce a reduced net polarization that is independent of wavelength. Another model was explored by Nordsieck (1976) in which the field is preferentially stronger in one direction. In this case, the polarization depends on the electron energy distribution with the result that strong polarization should be associated with steep optical spectra and a convex curved spectrum will show polarization increasing to the blue. While indeed the blazars do tend to have steep spectra, recent observations do not support these specific predictions. Simultaneous infrared and optical measurements, summarized above, show polarization that is usually wavelength independent, even in BL Lac which falls steeply in the optical. We also find that several of the sources in Table 1 that show strong polarization have relatively flat spectra (Sections II and III).

Beyond explaining the spectral and polarization properties of the optical emission, the extension of the incoherent synchrotron spectrum into the optical region places several severe constraints on the emission source. For rapidly varying (t_var ~ 1 day), luminous sources ( F ~ 10⁴⁶ ergs s^-1 or L₄₆ ~ 1) the corresponding brightness temperature in the optical ( ~ 10¹⁵) is T_b 1 × 10⁵ K. For a spectral index of 0.5-1, we would expect the corresponding radio spectrum to be self-absorbed (T_b ~ 10¹² K) in the frequency range 2-5 × 10¹² Hz or ~ 60 µm in the far infrared. Thus the variable optical-infrared sources must be smaller than the observed radio components. Although relativistic beaming or lower luminosities may weaken this argument, in general we would expect little or no correlation between the optical and radio spectral bands on time scales of a week or less. As well as being more compact, the optical region must also have stronger fields. To avoid the Compton catastrophe, the lower limit to the magnetic field is given by Blandford & Rees (1978) B_c ~ 125L₄₆^1/2 t_var^-1 gauss (here t_var is in units of one day). Blandford & Rees also derive a cooling time due to synchrotron radiation followed by mildly relativistic cyclotron radiation t_cyc L₄₆^-1 t_var² hr. Since t_cyc < t_var for the rapid variations observed in most blazars, the electrons must be reaccelerated many times on a variability time scale if the density of thermal electrons is not to exceed the number of relativistic electrons. To avoid any significant Faraday rotation, the reacceleration may need to be almost continuous in the most variable sources. In the radio emission regions, the absence of Faraday rotation places an even more stringent upper limit on the number of nonrelativistic electrons, n( < 100) << n( > 100) (Wardle 1977, Jones & O'Dell 1977b, see also Noerdlinger 1978).

BEAMING AND RELATIVISTIC JETS     Two types of behavior found among the blazars, low-frequency variability with brightness temperatures inferred from variability arguments far exceeding 10¹² K (Condon et al. 1979) and superluminal expansion (Cohen et al. 1979), present serious difficulties for the canonical incoherent synchrotron theory. Many remedies have been offered: non-cosmological distances (Hoyle, Burbidge & Sargent 1966); anisotropic electron distributions (Woltjer 1966); coherent emission processes (see below); and various phase and absorption effects (Rees & Sciama 1965, Jones, O'Dell & Stein 1974). One promising group of theories employs the relativistic Doppler effects present when a relativistic jet of plasma is viewed "end-on" (Lovelace 1976, Rees 1978b, Blandford & Konigl 1979, Scheuer & Readhead 1979, Marscher 1980). Not only can these effects explain apparent superluminal velocities but the forward-beaming and time-dilation effects can increase the apparent radio brightness temperatures by very large factors (T_obs ~ 10² - 10³ T_true for ~ 5 - 10; Blandford & Konigl 1979). Recent VLBI observations indicate that many radio doubles have well-collimated structures on scales of 1 pc - 1 Mpc (e.g. Readhead, Cohen & Blandford 1978). In addition, the lack of interstellar scintillation in the low-frequency variables provides indirect evidence for relativistic bulk motions (Condon & Dennison 1978). In the comoving frame of the relativistic jet, the dominant emission mechanism is still thought to be incoherent synchrotron emission. For observers essentially on axis ( ^-1), special relativistic effects will shift the spectrum blueward, enhance the luminosity, and decrease the observed time scales for variability (Rees & Simon 1968, Burbidge, Jones & O'Dell 1974). In addition, small variations in the beam direction may appear as quite large changes in the position angle of polarization, with 180^o variations expected for end-on views. Blandford & Konigl (1979) and Blandford & Rees (1978) suggest these relativistic effects may be responsible for the optical as well as radio properties of AO 0235 + 164 and other BL Lac objects.

COHERENT RADIATION     S.A. Colgate and collaborators have suggested a coherent emission process that is capable of describing the qualitative features of the radio, optical, and X-ray spectra and permits brightness temperatures far in excess of 10¹² K (e.g. Petschek, Colgate & Colvin 1976). Coherent emission at ~ 2^p is produced and frequency-scattered by nonthermal plasma oscillations in a mildly relativistic, thermal gas (kT_e ~ 1/2m_e c²). Coherent and incoherent Compton scattering then produce the low-frequency and high-frequency (optical) radiation. Thermal bremsstrahlung is chiefly responsible for the observed hard X-ray spectrum.

Because the optical photons are created through multiple Compton scatterings, this model has great difficulty explaining the high polarization and variability of polarization that characterizes the blazar class (as does the electron scattering model suggested by Katz 1976). An important constraint on these scattering models is the very low upper limit on the net magnetic field set by the lack of observed Faraday rotation in the radio, B 10^-7 G (Colgate & Petschek 1978). Jones, O'Dell & Stein (1974) review the energetic problems of other coherent emission models.

THERMAL PROCESSES     There is a great amount of evidence, especially in Seyfert galaxies and in the unpolarized QSOs, that the nonthermal optical-infrared radiation has been diluted by thermal emission or reprocessed. Infrared studies of the variability and 10 µ features of nearby Seyfert galaxies indicate that most of the luminosity in both Type 1 and 2 Seyferts is due to thermal reradiation by dust (Rieke & Lebofsky 1979). Polarimetric evidence in support of dust is discussed in Section IV and reviewed by Maza (1979) and the high hydrogen column densities derived from recent X-ray data (Mushotzky et al. 1980) also indicate that absorption and scattering by dust may be important in these objects. For most QSOs, the nature of the infrared emission is unclear. Recent infrared-optical observations by Neugebauer et al. (1979) indicate significant structure and changes in the spectral slope in those QSOs that are not known polarized variables (see Section III). The complex spectra may be due to either thermal continuum emission from the photoionized regions responsible for the strong line emission seen in the objects (see the recent review by Davidson & Netzer 1979), reradiation by dust, or optically thick radiation from an accretion disk (Shields 1978).

A series of authors have suggested that Compton scattering from a hot gas (kT_e ~ 5 - 100 keV) may play an important role in reprocessing the nonthermal synchrotron spectrum (Katz 1976, Stockman 1978, Eardley et al. 1978). The scattering will tend to destroy any intrinsic polarization and variability and will harden the emergent spectrum. Thus these models are also more relevant for the nonpolarized sources.

MODELS OF THE CENTRAL POWERHOUSE     The tremendous luminosities of bright QSOs, L ~ 10⁴⁶ - 10⁴⁸ ergs s^-1, are generally thought to be gravitational in origin. Models that invoke thermonuclear burning are usually inefficient and are incompatible with the high polarizations and rapid variability displayed by the blazar class. These blazar properties, the observed radio jets, and Eddington luminosity arguments suggest a central aligned supermassive object, M ~ 10⁸ - 10¹⁰ M, either a magnetically and rotationally supported "spinar" (Pacini & Salvati 1978) or accretion onto a black hole (Rees 1978a).

Estimates of the ages for the double radio lobes and their alignments with the central VLBI sources and the optically polarized QSOs (Stockman, Angel & Miley 1979) require alignment of the central source over time scales of 10⁷ years. For accretion onto black holes, the required accretion rate is 2^-1 L₄₇ M / year where is the efficiency. For steady luminosities less than the Eddington limit, the lower limit on the mass of the black hole is M L₄₇10⁹ M. The alignment of the rotation/jet/polarization axis will be maintained for time scales of ~ M/ 4 × 10⁸ years (Rees 1978b). It is interesting to note that an upper limit on the mass of the central source can be obtained from equating the variability time scale (t_var (days) ~ 1) with the light travel time across a Schwarzschild radius, M t_var10¹⁰ M (Elliot & Shapiro 1974, Moore et al. 1980). Relativistic beaming effects can raise this upper limit by approximately the Lorentz factor.

The relativistic particles required to explain the observed nonthermal radiation are generated by strong electromagnetic fields in spinar or some accretion disk models (e.g. Lovelace 1976) or by nonequilibrium processes (turbulence, relativistic shocks, Fermi acceleration, etc.) in the region near the black hole where v_infall ~ 1/2c (E ~ 100-200 MeV/nucleon). In this regime, the emission is likely to be dominated by nonthermal processes rather than bremsstrahlung.

Details of the accretion process and the formation of a relativistic jet are extremely uncertain. Disk models have been suggested by Lynden-Bell & Pringle (1974), Blandford (1976), Eardley et al. (1978) and others. Electromagnetic and hydrodynamic models for the formation of relativistic jets are discussed by Blandford & Rees (1974), Lovelace (1976), and Blandford (1976).

POLARIZATION BY DUST SCATTERING     The production of polarization by dust scattering is a well-known phenomenon that has been well studied in our own galaxy and is recently discussed by Martin (1978). Light transmitted through grains aligned by a magnetic field becomes linearly polarized, the effect responsible for the interstellar polarization of reddened stars. As in our own galaxy, the magnetic field of external galaxies appears to be in the direction of orbital motion (Elvius 1972). If light from a galactic nucleus were polarized by transmission through aligned grains in a spiral host galaxy, viewed nearly equatorially, we would expect the polarization to be parallel to the galaxy's major axis. If the grains are of a similar size to those causing polarization in the Milky Way, then polarization peaking in the visible part of the spectrum is a characteristic signature.

Polarization is also produced in the light that is scattered off small grains, regardless of their orientation. In some nuclei the very strong thermal radiation in the infrared shows the presence of optically thick dust, and most of the visible light must be scattered before leaving. Any departure from spherical symmetry will then result in net polarization of the source. This process is likely responsible for most of the polarization of Seyfert nuclei, including the strongly polarized ones where emission lines and continuum all share the same polarization. The very strong increase of polarization to the ultraviolet in most of these is probably indicative of scattering by very small particles (i.e. Rayleigh scattering).

When the scattering optical depth exceeds unity, multiple scattering in a skew geometry can produce significant circular polarization if the grains are not too small. In NGC 1068, the observed ellipticity, amounting to nearly 5% in the red, is probably due to this mechanism (Angel et al. 1976). For most active extragalactic objects with low linear polarization, circular polarization due either to scattering or synchrotron self-compton effects (Sciama & Rees 1967) is expected to be very small in the optical, 0.1%. This is consistent with current observational limits (Landstreet & Angel 1972, Kemp, Wolstencroft & Swedlund 1972, Maza 1979).