A theoretical model of Fanaroff-Riley I jets

A fluid model of the jets in Fanaroff-Riley I class radio sources based on the idea that they are supersonic turbulent pressure confined flows consisting of relativistic and non-relativistic gases is described. Numerical simulations are used to investigate the properties of such flows propagating through typical atmospheres of an elliptical. The models whose parameters agree with the observational constraints on FR-I jets power, density, velocity, Mach number, spreading rate and pressure of relativistic particles are calculated. Natural assumptions such as a conservation of relativistic particles an equipartition of energy between magnetic field and turbulent motions are used to estimate the intensity evolution along simulated jets. It is concluded that an effective acceleration of relativistic particles is required to account for the observed FR-I jet brightness distribution.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain     

A model for GRB jets

By using relativistic, axisymmetric, ideal MHD, we examine the motion of the baryon/e^±/ photon fluid that emanates from a stellar-mass compact object/debris-disk system (a common outcome of many progenitor models). We prove that the motion can be described as a frozen pulse, which permits the study of each shell of the pancake-shaped outflow using steady-state equations. The ejected energy flux is dominated by the electromagnetic (Poynting) contribution, but it can also have a non negligible e^±/radiation (thermal fireball)component. We demonstrate, through exact self-similar solutions, that the flow is first thermally and subsequently magnetically accelerated up to equipartition between kinetic and Poynting fluxes, i.e., ～ 50% of the total energy is converted into baryonic kinetic energy. The electromagnetic forces also collimate the flow, reaching a cylindrical structure asymptotically.     

A magnetohydrodynamical model for the formation of episodic jets

Episodic ejection of plasma blobs has been observed in many black hole systems. While steady, continuous jets are believed to be associated with large-scale open magnetic fields, what causes the episodic ejection of blobs remains unclear. Here by analogy with the coronal mass ejection on the Sun, we propose a magnetohydrodynamical model for episodic ejections from black holes associated with the closed magnetic fields in an accretion flow. Shear and turbulence of the accretion flow deform the field and result in the formation of a flux rope in the disc corona. Energy and helicity are accumulated and stored until a threshold is reached. The system then loses its equilibrium and the flux rope is thrust outward by the magnetic compression force in a catastrophic way. Our calculations show that for parameters appropriate for the black hole in our Galactic centre, the plasmoid can attain relativistic speeds in about 35 min.     

A theoretical model of atmospheric ozone depletion

A critical study on different ozone depletion and formation processes has been made and following important results are obtained:(i) From analysis it is shown that O₃ concentration will decrease very minutely with time for normal atmosphere when [O], [O₂] and UV-radiation remain constant. (ii) An empirical equation is established theoretically between the variation of ozone concentration and time. (iii) Special ozone depletion processes are responsible for the dramatic decrease of O₃-concentration at Antarctica.     

A relativistic mixing-layer model for jets in low-luminosity radio galaxies

We present an analytical model for jets in Fanaroff & Riley Class I (FR I) radio galaxies, in which an initially laminar, relativistic flow is surrounded by a shear layer. We apply the appropriate conservation laws to constrain the jet parameters, starting the model where the radio emission is observed to brighten abruptly. We assume that the laminar flow fills the jet there and that pressure balance with the surroundings is maintained from that point outwards. Entrainment continuously injects new material into the jet and forms a shear layer, which contains material from both the environment and the laminar core. The shear layer expands rapidly with distance until finally the core disappears, and all of the material is mixed into the shear layer. Beyond this point, the shear layer expands in a cone and decelerates smoothly. We apply our model to the well-observed FR I source 3C 31 and show that there is a self-consistent solution. We derive the jet power, together with the variations of mass flux and entrainment rate with distance from the nucleus. The predicted variation of bulk velocity with distance in the outer parts of the jets is in good agreement with model fits to Very Large Array observations. Our prediction for the shape of the laminar core can be tested with higher-resolution imaging.     

A preliminary theoretical line-blanketed model solar photosphere

Solar Physics - A preliminary theoretical solar model is presented that produces closer agreement with observation than has been heretofore possible. The qualitative advantages and shortcomings of...     

A quantitative model of coherent,stimulated emission in astrophysical jets

On the basis of issues raised by observations of BL Lac objects and the qualitative jet model proposed by Bakeret al. in 1988, we have been led to consider the quantitative role of coherent, stimulated emission in jets and construct a new jet model of blazars in which a relativistic electron beam with an axial symmetric, power-law distribution is injected from the central engine into the jet plasma. We study quantitatively the synchrotron emission of the relativistic electron beams. Using the weak turbulent theory of plasma, we discuss the interaction between relativistic electron beams and jet plasma, and the roles of stimulated emission. The main results are:

1. The synchrotron emission increases sensitively with the increase of the angle between the direction of the beam and the magnetic field. When the direction of the beam is vertical to the magnetic field, the synchrotron emission reaches its maximum, i.e. the emitted waves are beamed in the direction of the jet axis. We suggest that radio selected BL Lac objects belong to this extreme classification.
2. The synchrotron emission of the relativistic beam increases rapidly with the increase of the Lorentz factor of the relativistic electron,γ, whenγ ≤ 22.5, then decreases rapidly with increase ofγ.
3. The stimulated emission also increases with increasing Lorentz factorγ of the relativistic electrons whenγ ≤ 35 and then decreases with the increasingγ. The maximum stimulated emission and the maximum synchrotron emission occur at different frequencies. Stimulated emission is probably very important and reasonable flare mechanism in blazars.
4. The rapid polarization position angle (PA) swings may arise from the interaction between the relativistic electron beam and the turbulent plasma.

     

A theoretical model of altitudinal distribution of sodium atom

It has been well accepted that sodium is a minor constituent in the upper atmosphere. The possible formation and destruction processes of sodium has been considered and the following results are obtained:(i) An empirical equation has been established for calculation of the concentration of sodium for different altitude and time.(ii) It is confirmed that the rate constant for the reaction NaO + O₂ Na + O₃ is temperature dependent. The activation energy for this reaction is 70.88 Kcals/mole.     

Turbulence in planetary occultations: I. A theoretical formulation

First- and second-order effects of turbulance on radio propagation through an atmosphere with uniformly varying average refractive index combined with a random component due to turbulence are calculated both from the Eikonal equation of geometrical optics and from a weak scattering wave-optical formulation. To second order in the strength of the turbulence, the average phase path is reduced relative to that in a nonturbulent atmosphere with the same average refractivity, implying a higher average phase velocity of the radiowave when turbulence is present. Also, the magnitude of the phase offset is controlled by the size of the principal Fresnel zone, implying that the medium becomes slightly dispersive by the addition of turbulence. Turbulence effects on the Doppler frequency separate into three distinct types involving: (1) zero-mean terms having the form of a coupling between the average and turbulent refractive field components; (2) terms of second order in the turbulence, modified by the average refractive field and consistent with an average bias in Doppler frequency when the rms turbulent intensity has a spatial variation normal to the raypath; and (3) additional second-order terms, again modified by the average refractive field, having a nozeroo average even for homogeneous turbulence. Under plausible conditions (1) produces the largest mean-square effects, while (2) represents the largest contribution to the average bias in Doppler frequency. For a turbulence power spectrum proportional to the (?p) power of the wave-number, the bias in Doppler frequency, like the average bias in phase path, depends on the radiation wavelength as $\text{λ}{}^{\mathrm{<mtext>p</mtext><mtext>2-2</mtext>}}$, or as $\text{λ}{}^{\mathrm{<mtext>?1</mtext><mtext>6</mtext>}}$ for Kolmogorov turbulence.     

A theoretical model of distribution of atmospheric ozone with altitude

A critical study of distribution of ozone with altitude of about 91 Km and above has been made and following important results are obtained:(i) An empirical equation is fitted theoretically between the variation of ozone concentration and altitude at a definite time.(ii) The rate of change of O₃ concentration with respect to altitude is directly proportional to the O₃ concentration at that altitude.(iii) From analysis it is shown that ozone concentration decreases with the increase of altitude.     

Estimation of solar illumination on the Moon: A theoretical model

The solar illumination conditions on the lunar surface represent a key resource with respect to returning to the Moon. As a supplement to mapping the solar illumination by exploring data, lighting simulations using high-resolution topography could produce quantitative illumination maps. In this study, a theoretical model is proposed for estimating the solar illumination conditions. It depends only on the solar altitude and topographical factors. Besides the selenographic longitude and latitude, the former is determined by the selenographic longitude and latitude at the subsolar site, the geocentric ecliptical latitude, and the dimensionless distance of the Sun–Moon relative to 1 AU, which are function of time. The latter is determined by comparing the elevations in solar irradiance direction within 210 km in which the topography might shadow the behind sites to the critical elevations determining whether the behind sites are shadowed or not. Compared to Zuber's model, the model proposed in this study is simpler and easier for computing. It is parameterized with selenographic coordinates, elevations, and time. With high-resolution topography data, the solar illumination conditions at any selenographic coordination could be estimated by this model at any date and time. The lunar surface is illuminated when the solar altitude is non-zero and all the elevations within 210 km in solar irradiance direction are lower than the critical elevations. Otherwise it would be shadowed.     

Bipolar jets in planetary nebulae: An analytical model

The various and hitherto partially unsolved problems relative to the origin of bipolar jets or highly collimated fast outflows in planetary nebulae are reviewed within the framework of a stationary magnetohydrodynamic model. In order to explain the observations of high polar velocities and the presence of polar blobs or knots in planetary nebulae, theoretical models are proposed taking into account both a large scale azimuthal magnetic field and an anisotropic turbulent velocity field. The models predict equatorial-to-polar density ratios which are rather small, in the range 2 to 3. Conversely, the polar-to-equatorial velocity contrasts are higher, with typical values upto 10. Thus thead hoc hypothesis implicit in the literature that the density contrast is varying in inverse ratio to the velocity one, does not seem well adapted to the bipolar jet phenomenon in planetary nebulae. We point out, therefore, that the bipolar jets have to be considered as a transient aspect of a very complex phenomenon. The model can be applied to objects such as He 2–104 or Mz3, M2–9.     

A theoretical model of the bow shock and the magnetosphere of Jupiter

Using the data obtained from the Pioneer 10 and 11 observations, a theoretical model is proposed for the bow shock and the magentosphere of Jupiter. This indicates that the distance of the magnetopause from Jupiter on the sunlit side is (50–55) × r_J (r_J: Jupiter radius, = 7 × 10⁹ cm) and that the ratio of the stand-off distance to this distance is about equal to or slightly larger than unity. Hence the Mach number of the solar wind seems to be less than 1.5 at Jupiter's orbit. This result necessarily leads to a blunt body model of the Jovian magnetosphere, the tail region of which is not as extended as observed in the Earth's case.     

Observations of molecular jets in Orion A

We report on the results of a wide field near infrared survey for protostellar jets identified via their emission in the 2.12μm line of shock heated molecular hydrogen, done over a 1.2 square degree area in Orion A. We derive an evolutionary sequence for protostellar jets, based on the observed lenghts and H₂ luminosities as well as the evolutionary stage and bolometric luminosity of their driving sources. Protostellar jets start from zero length, evolve quickly to parsec scale extents during the Class 0 phase, and shrink during the Class I and Class II phase. They are first very bright in H₂ emission, and fade later on. This is indicative of strongly time-variably mass accretion onto the driving protostar, with a peak early on, and a subsequent continous decay of accretion activity. Finally, we present evidence for a molecular CO jet from a Class 0 object, supporting the idea that a very efficient outflow phase at very early evolutionary stages should produce very dense, molecular jets.     

iShocks: X-ray binary jets with an internal shocks model

In the following paper, we present an internal shocks model, iShocks, for simulating a variety of relativistic jet scenarios; these scenarios can range from a single ejection event to an almost continuous jet, and are highly user configurable. Although the primary focus in the following paper is black hole X-ray binary jets, the model is scale and source independent and could be used for supermassive black holes in active galactic nuclei or other flows such as jets from neutron stars. Discrete packets of plasma (or 'shells') are used to simulate the jet volume. A two-shell collision gives rise to an internal shock, which acts as an electron re-energization mechanism. Using a pseudo-random distribution of the shell properties, the results show how for the first time it is possible to reproduce a flat/inverted spectrum (associated with compact radio jets) in a conical jet whilst taking the adiabatic energy losses into account. Previous models have shown that electron re-acceleration is essential in order to obtain a flat spectrum from an adiabatic conical jet: multiple internal shocks prove to be efficient in providing this re-energization. We also show how the high-frequency turnover/break in the spectrum is correlated with the jet power,  ν _b ∝ L ^∼0.6_W  , and the flat-spectrum synchrotron flux is correlated with the total jet power,   F _ν∝ L ^∼1.4_W  . Both the correlations are in agreement with previous analytical predictions.     

A composite stellar model of geostrophic flows I

This paper has been presented the geometric study and solutions of the electromagnetogeostrophic flows, and spatially the geometry of magnetic and current lines are discussed.