Abstract
The light of normal galaxies in the optical and near infrared part of the spectrum is dominated by stars, with small contributions by gas and dust. This is thermal radiation since the emitting plasma in stellar atmospheres is basically in thermodynamical equilibrium. To a first approximation, the spectral properties of a star can be described by a Planck spectrum whose temperature depends on the stellar mass and the evolutionary state of the star.
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- 1.
The complete optical identification of the 3CR catalog, which was made possible by the enormously increased angular resolution of interferometric radio observations and thus by a considerably improved positional accuracy, was finalized only in the 1990s—some of these luminous radio sources are very faint optically.
- 2.
For this reason, radio surveys for gravitational lens systems, which were mentioned in Sect. 3.11.3, concentrate on sources with a flat spectral index because these are dominated by the compact nucleus. Multiple image systems are thus more easily recognized as such.
- 3.
The ionization stages of an element are distinguished by Roman numbers. A neutral atom is denoted by ‘I’, a singly ionized atom by ‘II’, and so on. So, Civ is three times ionized carbon.
- 4.
The physical mechanism that is responsible for the viscosity is unknown. The molecular viscosity is far too small to be considered as the primary process. Rather, the viscosity is probably produced by turbulent flows in the disk or by magnetic fields, which become spun up by differential rotation and thus amplified, so that these fields may act as an effective friction. In addition, hydrodynamic instabilities may act as a source of viscosity. Although the properties of the accretion disk presented here—luminosity and temperature profile—are independent of the specific mechanism of the viscosity, other disk properties definitely depend on it. For example, the temporal behavior of a disk in the presence of a perturbation, which is responsible for the variability in some binary systems, depends on the magnitude of the viscosity, which therefore can be estimated from observations of such systems.
- 5.
When a photon scatters off an electron at rest, this process is called Thomson scattering. To a first approximation, the energy of the photon is unchanged in this process, only its direction is different after scattering. This is not really true, though. Due to the fact that a photon with energy E γ carries a momentum E γ ∕c, scattering will impose a recoil on the electron. After the scattering event the electron will thus have a non-zero velocity and a corresponding kinetic energy. Owing to energy conservation the photon energy after scattering is therefore slightly smaller than before. This energy loss of the photon is very small as long as E γ ≪ m e c 2. When this energy loss becomes appreciable, this scattering process is then called Compton scattering. If the electron is not at rest, the scattering can also lead to net energy transfer to the photon, such as it happens when low-frequency photons propagate through a hot gas (as we will discuss in Sect. 5.4.4 for the case of AGNs, and in Sect. 6.4.4 for galaxy clusters) or through a distribution of relativistic electrons. In this case one calls it the inverse Compton effect. The physics of all these effects is the same, only their kinematics are different.
- 6.
The classification into allowed, semi-forbidden, and forbidden transitions is done by means of quantum-mechanical transition probabilities, or the resulting mean time for a spontaneous radiational transition. Allowed transitions correspond to electric dipole radiation, which has a large transition probability, and the lifetime of the excited state is then typically only 10−8 s. For forbidden transitions, the time-scales are considerably larger, typically 1 s, because their quantum-mechanical transition probability is substantially lower. Semi-forbidden transitions have a lifetime between these two values. To mark the different kinds of transitions, a double square bracket is used for forbidden transitions, like in [Oiii], while semi-forbidden lines are marked by a single square bracket, like in Ciii].
- 7.
To make forbidden transitions visible, the gas density needs to be very low. Such low densities cannot be produced in the laboratory. Forbidden lines are in fact not observed in laboratory spectra; they are ‘forbidden’.
- 8.
Note, however, that this argument essentially pictures the clouds as having some random velocities. It is not unlikely that the picture of ‘clouds’ is somewhat misleading; instead, the BLR could consist of a turbulent gas, with a large-scale velocity field, in which condensations are present. These condensations then take the roles of the ‘clouds’ in the simple picture.
- 9.
The emissivity of the gas in the BLR reacts very quickly to a change of the ionizing radiation: if the ionizing flux onto a cloud in the BLR decreases, the corresponding line emission from the cloud decreases on the recombination time scale. For a gas density of n ∼ 1011 cm−3, this time scale is about a minute—that is, almost instantaneously. Thus, the line emission from a cloud depends on the instantaneous ionizing flux at the cloud.
- 10.
The virial temperature of the protons is much higher, but it is not clear how well electrons and protons are coupled in this hot, thin plasma.
- 11.
The absorption of X-rays is due to ionization of metals. Whereas the photoelectric effect is also present for hydrogen, the corresponding cross section for X-rays is small, due to their high energy and the strong frequency dependence of the cross section, ∝ ν −3 above the energy threshold. Despite the fact that metals have a much smaller abundance than hydrogen and helium, they dominate the optical depth for X-ray absorption. Nevertheless, the absorber is characterized in terms of a hydrogen column density, implicitly assuming that the gas has Solar metallicity.
- 12.
There might be a trend that radio-loud QSOs have a somewhat larger λ Edd, but these correlations are controversial and might be based on selection effects. On the other hand, radio galaxies have a lower value of λ Edd than QSOs.
- 13.
Not all Seyfert 2 galaxies show broad emission lines in polarized flux, which may be either due to the fact that there is no appropriate scattering medium which makes the BLR visible for us, or that some of the sources intrinsically lack a BLR. The discussion about the possible existence of such ‘true Seyfert 2’ objects has not yet come to a clear conclusion.
- 14.
This dependence of the cooling time \(t_{\mathrm{cool}} = E/\dot{E}\) on the magnetic field strength follows from (5.3), which at a fixed frequency yields \(\gamma = E/(m_{\mathrm{e}}c^{2}) \propto B^{-1/2}\), and the energy loss (5.5), which reads \(\dot{E} \propto \gamma ^{2}B^{2} \propto B\) at fixed frequency.
- 15.
Compare the mass estimate in Sect. 5.3.1 where, instead of 107 yr, the lifetime to be inserted here is the age of the Universe, ∼ 1010 yr.
- 16.
The Voigt profile ϕ(ν) of a line, which specifies the spectral energy distribution of the photons around the central frequency ν 0 of the line, is the convolution of the intrinsic line profile, described by a Lorentz profile,
$$\displaystyle\begin{array}{rcl} \phi _{\mathrm{L}}(\nu ) = \frac{\varGamma /4\pi ^{2}} {(\nu -\nu _{0})^{2} + (\varGamma /4\pi )^{2}}\;,& & {}\\ \end{array}$$and the Maxwellian velocity distribution of atoms in a thermal gas of temperature T. From this, the Voigt profile follows,
$$\displaystyle{ \phi (\nu ) = \frac{\varGamma } {4\pi ^{2}}\int _{-\infty }^{\infty }\mathrm{d}v\;\frac{\sqrt{m/2\pi k_{\mathrm{B} } T}\,\exp \left (-mv^{2}/2k_{\mathrm{B}}T\right )} {(\nu -\nu _{0} -\nu _{0}v/c)^{2} + (\varGamma /4\pi )^{2}} \;, }$$(5.46)where the integral extends over the velocity component along the line-of-sight. In these equations, Γ is the intrinsic line width which results from the natural line width (related to the lifetime of the atomic states) and pressure broadening. m is the mass of the atom, which defines, together with the temperature T of the gas, the Maxwellian velocity distribution. If the natural line width is small compared to the thermal width, the Doppler profile dominates in the center of the line, that is for frequencies close to ν 0. The line profile is then well approximated by a Gaussian. In the wings of the line, the Lorentz profile dominates. For the wings of the line, where ϕ(ν) is small, to become observable the optical depth needs to be high. This is the case in damped Lyα systems.
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Schneider, P. (2015). Active galactic nuclei. In: Extragalactic Astronomy and Cosmology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54083-7_5
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DOI: https://doi.org/10.1007/978-3-642-54083-7_5
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