Radio synchrotron emission by protons and electrons in pulsars and the nuclei of quasars

Relations enabling estimation of the limiting brightness temperature of synchrotron radiation subject to self-absorption and inverse Compton scattering are presented for the case of relativistic electrons (positrons) and protons. Analogous expressions are presented for relativistic particles moving along curved magnetic lines of force (curvature radiation) and coherent radiation by relativistic particles. These relations can be used to determine the brightness temperatures expected for the central regions of active galactic nuclei, neutron stars, and other objects that produce relativistic particles. Radiation by relativistic protons yields higher intensities, and could be a source of the highest-energy cosmic rays.     

Method for Estimating the Doppler Factors of Relativistic Radio Jets

An expression for the intensity of synchrotron emission from a radio source (in the optically thin regime) in terms of the energy densities in the magnetic field and particles is obtained, based on a definition of a relativistic electron related to its rest energy. A relationship is obtained between the energy densities in particles E_e and the magnetic field E_H for a physical system containing a magnetic field and relativistic electrons in a minimum-energy state. A method for estimating the Doppler factors of the relativistic electrons has been developed. This method does not requires that all radio sources have the same radiation energies (brightness temperatures): it is sufficient that the energies of the magnetic fields and relativistic particles in the source be approximately equal. The method yields Doppler-factor estimates with reasonably good accuracy, even when there are modest deviations from energy equipartition in the radio source,making it applicable to many radio sources. The method is used to estimate the Doppler factor of the radio jet in CTA 21.

     

Study of the physical conditions in active galactic nuclei. A method for estimating the physical parameters of radio sources

A new method for estimating the physical parameters of active galactic nuclei involving the analysis of observations of the compact radio sources in them is proposed. The method is based on an inhomogeneous model for a synchrotron radio source. Theoretical spectra of the radio sources are obtained via numerical solution of the transfer equation. Due to the paucity of observational data, only interval estimates of the magnetic field strength and the energy densities of the magnetic field and relativistic particles can be obtained. A mechanism for the formation of flat radio spectra is proposed.     

The magnetic fields and density of relativistic electrons in the nucleus of NGC 1052

We analyze observations of the compact GHZ-peaked-spectrum radio source in the nucleus of the weakly active galaxy NGC 1052, assuming that the low-frequency turnover in its spectrum is due to synchrotron self-absorption. The analysis is based on a model for an inhomogeneous source of synchrotron radiation. It is shown that the magnetic field is not uniform, but the change in the field strength from the center to the edge of the compact radio source does not exceed an order of magnitude. The maximum magnetic-field strength in the nucleus of NGC 1052 is 20 G < H _⊥ < 200 G, and the density of relativistic electrons is 0.018 cm⁻³ < n _e < 0.18 cm⁻³ on scales of 0.1 pc; everywhere in the radio source, the energy density of the magnetic field exceeds the energy density of the relativistic electrons. The physical conditions are similar to those in the nuclei of the nearby radio galaxies 3C 111 and 3C 465, and differ strongly from those in the nucleus of the radio galaxy 0108+388, which is a compact GHz-peaked-spectrum source (these three galaxies were studied by the authors earlier using the same method).     

The theory of spontaneous emission by electrons during their motion along the quantizing magnetic field of a star

The quantum motion of non-relativistic and relativistic electrons in the presence of constant magnetic fields at the surfaces of magnetic stars, magnetic white dwarfs, and pulsars is considered. The quantizing magnetic-field strengths for charged particles with specified energies are determined. The quantum motion of these particles in a plane perpendicular to the magnetic field is accompanied by spontaneous radiation due to electron transitions from higher to lower discrete energy levels, right down to the ground state. In the non-relativistic case, this emission is monochromatic. In the non-relativistic case, various frequencies are emitted, but lie within an order of magnitude of each other. The electron kinetic energy along the magnetic field varies from zero to a maximum value, due to the one-dimensional character of the motion along the field, between each pair of potential barriers corresponding to the discrete energy levels. The results may be relevant to describing gamma-ray flares of pulsars.     

The radio sources CTA 21 and OF+247: The hot spots of radio galaxies

The physical conditions in the radio sources CTA 21 and OF+247 are studied assuming that the low-frequency spectral turnovers are due to synchrotron self-absorption. The physical parameters of the radio sources are estimated using a technique based on a nonuniform synchrotron source model. It is shown that the magnetic-field distributions in the dominant compact components of these radio sources are strongly inhomogeneous. The magnetic fields at the center of the sources are B ～ 10^?1 G, and the fields are two to three orders of magnitude weaker at the periphery. The magnetic field averaged over the compact component is B ～ 10^?3 G, and the density of relativistic electrons is n _e ～ 10^?3 cm^?3. Assuming that there is equipartition of the energies of the magnetic field and relativistic particles, averaged over the source, 〈E _H 〉 = 〈E _e 〉 ～ 10^?7–10^?6 erg cm^?3. The energy density of the magnetic field exceeds that of the relativistic electrons at the centers of the radio sources. The derived parameters of CTA 21 and OF+247 are close to those of the hot spots in the radio galaxy Cygnus A. On this basis, it is suggested that CTA 21 and OF+247 are radio galaxies at an early stage of their evolution, when the hot spots (dominant compact radio components) have appeared, and the radio lobes (weak extended components) are still being formed.     

Synchrotron spectra of short-period pulsars

A model with synchrotron radiation near the light cylinder is proposed to explain the observed spectra of short-period pulsars (P≤0.1 s). These spectra can be described if a power-law energy distribution of the emitting electrons with exponent γ=2–8 is assumed. For most pulsars, the peak frequency ν_m is below 10 MHz. The ν_m(γ) dependence is derived, and shows that the peak frequencies for pulsars with spectral indices α<1.5 may fall in the observable range. In particular, ν_m may be ν_m ～ 100 MHz for PSR J0751 + 1807 and PSR J1640 + 2224. The observed radio spectrum of Geminga (PSR J0633 + 1746) can be described by a synchrotron model with a monoenergetic or Maxwellian distribution of relativistic electrons and a small angle β between the spin axis and magnetic moment (β ～ 10°).     

Relative variations of the physical parameters of variable extragalactic radio sources

A method for studying the physical conditions in compact components of extragalactic radio sources displaying variability on time scales of hundreds of days is proposed. The method can be used to estimate the relative variations of the magnetic-field strength and number density of relativistic electrons in superluminal jets from the cores of quasars and radio galaxies. Results are presented for the jets of the quasars 3C 120, 3C 273, 3C 279, and 3C 345. The energies of the magnetic field and relativistic particles in these objects are not in equipartition. As a rule, the magnetic-field strength decreases appreciably during the evolution of an expanding jet, while the number of relativistic electrons grows.     

Physical conditions in the nucleus of the radio galaxy 3C 274

Interplanetary scintillation observations of the compact nucleus of 3C 274 have been carried out at 111 MHz on on the Large Phased Array radio telescope. We have derived an upper limit for the flux density of the compact radio source, and determined the parameters of the low-frequency cutoff of the spectrum of this source. We have analyzed the observational data assuming that the low-frequency spectral cutoff is due to synchrotron self-absorption. In this case, the magnetic field in the nucleus of 3C 274 must be very nonuniform. At the center, on scales of < 0.01 pc, the magnetic field varies in the range 0.4 G < H < 40 G, while its mean value over the entire radio source is 〈H〉 ～ 10^?3 ? 10^?4 G. The energy density of the relativistic electrons exceeds the energy density of the magnetic field everywhere within the nucleus, though energy equipartition is also possible near the center.     

Scattering of cyclotron radiation in a moving plasma

We consider the scattering of cyclotron radiation in a plasma moving along a homogeneous magnetic field. The equation of radiation transfer in a co-moving frame is derived and two limiting cases are pointed out. In the first case of a “small” velocity gradient, the total Doppler frequency shift due to variations in the plasma velocity over the flow is much smaller than the width of the line. The second, opposite, case of a “large” velocity gradient is analogous to the Sobolev approximation in the theory of moving stellar envelopes. The solution of the transfer equation for a wind-type flow illuminated by radiation of a given intensity is obtained in the latter case, when the influence of the plasma motion on cyclotron scattering is most important. It is shown that cyclotron scattering in a moving plasma differs from the known (and qualitatively similar) problems of resonance scattering in moving stellar envelopes and cyclotron scattering in a motionless plasma permeated by an inhomogeneous magnetic field. In particular, a symmetric absorption band with residual intensity proportional to the velocity gradient appears in the spectrum of the outgoing radiation, while in these two other problems, the depth of the corresponding spectral features cannot exceed half the continuum level. Detailed qualitative analysis reveals that this difference is due to the particular form of the frequency redistribution for cyclotron scattering.     

The electric fields of radio pulsars with asymmetric nondipolar magnetic fields

The effect of the curvature of open magnetic field lines on the generation of electric fields in radio pulsars is considered in the framework of a Goldreich-Julian model, for both a regime with a free outflow of electrons from the neutron-star surface and the case of a small thermoemission current. An expression for the electron thermoemission current in a strong magnetic field is derived. The electric field associated with the curvature of the magnetic flux tubes is comparable to the field generated by the relativistic dragging of the inertial frames.     

The magnetic fields and angular sizes of radio sources displaying synchrotron self-absorption

A method for estimating the magnetic-field strengths and angular sizes of radio sources displaying synchrotron self-absorption based on their observed radio spectra is considered. The method is used to derive the angular sizes of compact radio sources (components) and the magnetic fields in these regions, as well as the energy and number of relativistic electrons and the radiative power of a number of quasars and radio galaxies.     

Radiative transfer in relativistic plasma outflows and comptonization of photons near the photosphere

We study radiative transfer in plasma by numerical solution of kinetic Boltzmann equations for all particles. We are interested in the thermalization of photons. We considered three cases: 1. The calculations of the timescales of the thermalization in the uniform isotropic plasma. 2. The expansion of the mildly relativistic pair plasma for the mini fireball in the frame of the kinetic approach. 3. The case of ultra relativistically expanding outflow from the surface of the compact object with the Fokker-Planck approximation to the Boltzmann equation for photons. The last case gives the generalized Kompaneets equation which takes into account anisotropic distribution of photons developed near the photosphere. For the electron temperature dependence from radius T ∝ r ^?2 and thermal electrons spectrum we found the low-energy photon index can be ?0.5 as typically observed in GRB.     

Study of the physical conditions in active galactic nuclei. Physical conditions in the cores of two nearby radio galaxies

We have carried out a search for compact radio sources in the cores of 16 nearby radio galaxies. We detected compact components in four radio galaxies, and found upper limits for the flux density in compact components in ten radio galaxies. VLBI observations enabled the detection of a turnover in the spectra of the two nearby radio galaxies 3C 111 and 3C 465. Using a method based on an inhomogeneous model for a synchrotron source, we estimate the magnetic-field strength and the energy densities in the magnetic field and relativistic electrons in the cores of these radio galaxies. Strong inhomogeneity in the distribution of the magnetic fields in the cores of 3C 111 and 3C 465 is implied by our analysis. The magnetic-field strengths in the central regions of these galactic nuclei, on scales of ～0.1 pc, exceed the mean strength by four to five orders of magnitude, and lie in the range 10² G < H < 10⁴ G.     

The physical conditions in the core of the quasar 3C 273 on parsec scales

VLBI observations of the quasar 3C 273 are analyzed. The physical parameters of the components in the parsec-scale jet of the quasar are estimated using amethod based on an inhomogeneous synchrotron sourcemodel. All the jet components (on scales of??0.1 pc) have magnetic fields that are either uniform or close to uniform, with magnitudes B ?? 0.1 G. The core component, which is probably associated with the central engine, differs from the remaining components in its unusually high density of relativistic electrons.     

The X-ray emission of magnetars

It is shown that cyclotron radiation by electrons near the surface of a neutron star with a magnetic field of ～10¹² G can easily provide the observed quiescent radiation of magnetars (Anomalous X-ray Pulsars and Soft Gamma-ray Repeaters). Pulsed emission is generated by the synchrotron mechanism at the periphery of the magnetosphere. Short-time-scale cataclysms on the neutron star could lead to flares of gamma-ray radiation with powers exceeding the power of the X-ray emission by a factor of 2γ², where γ is the Lorentz factor of the radiating particles. It is shown that an electron cyclotron line with an energy of roughly 1 MeV should be generated in the magnetar model. The detection of this line would serve as confirmation of the correctness of this model.     

The radio emission of anomalous pulsars

Previously developed methods for estimating the angle β between the spin axis of a neutron star and its magnetic moment together with observational data for anomalous X-ray pulsars (AXPs) indicate that these objects are nearly aligned rotators, and that the drift model can be applied to them. The magnetospheres of aligned rotators are appreciably more extended than in pulsars with large values of β. With such extents for the magnetosphere, the conditions for the generation of transverse waves via the cyclotron instability are satisfied. The expected spectrum of the resulting radiation is very steep (its spectral index is α > 3), consistent with the observed radio spectra of known AXPs (α > 2). A large magnetosphere also favors the appearance of appreciable pitch angles for relativistic electrons, and therefore the generation of synchrotron emission. The maximum of this emission falls in the microwave range. This mechanism provides appreciable fluxes at frequencies of tens of gigahertz and can explain the observed enhanced AXP radiation in this range.     

Physical conditions in the hot spots of the radio galaxy Cygnus A

It is shown that composite radio spectra of the hot spots of the radio galaxy Cygnus A can be fully explained by assuming a nonuniform distribution of the magnetic fields inside the hot spots, without invoking any physical mechanisms other than synchrotron radiation. The magnetic fields are strong (B ?? 10^?2?10^?1 G) at the center of the hot spots, and decreases at the hot-spot edges to the level of the magnetic field of the radio lobes in which the hot spots are embedded (B ?? 10^?4?10^?5 G). The difference in the magnetic field between the hot-spot center and edge decreases during the evolution, while the average magnetic-field intensity increases.     

Determining the Inclination of the Kiloparsec-Scale Jet of the Quasar 3C 273 Based on Competition of Mechanisms for the Knot X-ray Emission

Based on the idea that the X-ray emission of the knots in the kiloparsec-scale jet of 3C 273 located closest to the active nucleus is due to inverse Compton scattering on the quasar radiation, while the X-ray emission of knots further from the nucleus is due to inverse Compton scattering on the cosmic microwave background, we find that the angle of the jet to the line of sight is θ ≈ 30°. The magnetic field and electron density in the knots are estimated. It is concluded that there is a break in the electron-energy spectrum at a Lorentz factor of г ∼ 10⁶. It is shown that the energy density of the relativistic electrons in the knots appreciably exceeds the energy density in the magnetic field.     

Returning positron flux in the polar-cap regions of a radio pulsar

An approximate method for calculating the returning positron flux in the polar-cap regions of a radio pulsar is proposed. The pulsar is considered in the Goldreich-Julian model for a regime of free-electron emission from the neutron-star surface in the region of open lines of the dipolar magnetic field. Calculations have been done for the case when the dipolar magnetic moment is aligned with the star's rotational axis. The acceleration of primary electrons is assumed to occur near the neutron-star surface on scales comparable to the transverse radius of the tube of open field lines. The generation of electron-positron pairs by curvature radiation of the primary electrons is taken into account. A considerable contribution to the returning flux is made by the region where the electric field is screened by the electron-positron plasma.