Nomographs for relativistic velocity transformation.
Three nomographs for relativistic velocity transformation for teaching aids
RELATIVISTIC VELOCITY↗
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Results for “RELATIVISTIC VELOCITY”
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Ionization loss at relativistic velocities.
Grain density variation of relativistic protons and pions noting ionization loss
Jain, P. L.↗
Rapid acceleration of energetic particles in the 1982 February 8 solar flare
Hard X-ray and gamma-ray measurements of the February 8, 1982 (1250 UT) solar flare made with spectrometers aboard the ISEE 3 and SMM spacecraft show that bursts of photons from 40 keV to 40 MeV are coincident within + or - 1 s. This indicates that the acceleration of particles to relativistic velocities can occur promptly (within 1 s). As far as the energetic particles interacting at the sun are concerned, the 'two-phase' process, which requires several minutes for particle acceleration to relativistic velocities, cannot account for the present gamma-ray observations. Even the 'two-step' acceleration process, which is assumed to occur in a small magnetic loop, is severely constrained by the present observations.
Kane, S. R.↗
Speed Limits for Radiation-driven SMBH Winds
Context. Ultra-fast outflows (UFOs) have become an established feature in analyses of the X-ray spectra of active galactic nuclei (AGN). According to the standard picture, they are launched at accretion disc scales with relativistic velocities, up to 0.3-0.4 times the speed of light. Their high kinetic power is enough to induce an efficient feedback on a galactic scale, possibly contributing to the co-evolution between the central supermassive black hole (SMBH) and the host galaxy. It is, therefore, of paramount importance to gain a full understanding of UFO physics and, in particular, of the forces driving their acceleration and the relation to the accretion flow from which they originate. Aims. In this paper, we investigate the impact of special relativity effects on the radiative pressure exerted onto the outflow. The radiation received by the wind decreases for increasing outflow velocity, v, implying that the standard Eddington limit argument has to be corrected according to v. Due to the limited ability of the radiation to counteract the black hole gravitational attraction, we expect to find lower typical velocities with respect to the non-relativistic scenario. Methods. We integrated the relativistic-corrected outflow equation of motion for a realistic set of starting conditions. We concentrated on a range of ionisations, column densities, and launching radii consistent with those typically estimated for UFOs. We explore a one-dimensional, spherical geometry and a three-dimensional setting with a rotating, thin accretion disc. Results. We find that the inclusion of special relativity effects leads to sizeable differences in the wind dynamics and that v is reduced up to 50% with respect to the non-relativistic treatment. We compare our results with a sample of UFOs from the literature and we find that the relativistic-corrected velocities are systematically lower than the reported ones, indicating the need for an additional mechanism, such as magnetic driving, to explain the highest velocity components. Finally, we note that these conclusions, derived for AGN winds, are generally applicable.
A Luminari↗
Electron acceleration to high energies at quasi-parallel shock waves in the solar corona
In the solar corona shock waves are generated by flares and/or coronal mass ejections. They manifest themselves in solar type 2 radio bursts appearing as emission stripes with a slow drift from high to low frequencies in dynamic radio spectra. Their nonthermal radio emission indicates that electrons are accelerated to suprathermal and/or relativistic velocities at these shocks. As well known by extraterrestrial in-situ measurements supercritical, quasi-parallel, collisionless shocks are accompanied by so-called SLAMS (short large amplitude magnetic field structures). These SLAMS can act as strong magnetic mirrors, at which charged particles can be reflected and accelerated. Thus, thermal electrons gain energy due to multiple reflections between two SLAMS and reach suprathermal and relativistic velocities. This mechanism of accelerating electrons is discussed for circumstances in the solar corona and may be responsible for the so-called 'herringbones' observed in solar type 2 radio bursts.
Mann, G.↗
Realizability-preserving discontinuous Galerkin method for spectral two-moment radiation transport in special relativity
Here we present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady background material moving with relativistic velocities. The model is obtained as the special relativistic limit of a four-momentum-conservative general relativistic two-moment model. Using a maximum-entropy closure, we solve for the Eulerian-frame energy and momentum. The proposed numerical method is designed to preserve moment realizability, which corresponds to moments defined by a nonnegative phase-space density. The realizability-preserving method is achieved with the following key components: (i) a discontinuous Galerkin phase-space discretization with specially constructed numerical fluxes in the spatial and energy dimensions; (ii) a strong stability-preserving implicit-explicit time-integration method; (iii) a realizability-preserving conserved to primitive moment solver; (iv) a realizability-preserving implicit collision solver; and (v) a realizability-enforcing limiter. Component (iii) is necessitated by the closure procedure, which closes higher order moments nonlinearly in terms of primitive moments. The nonlinear conserved to primitive and the implicit collision solves are formulated as fixed-point problems, which are solved with custom iterative solvers designed to preserve the realizability of each iterate. With a series of numerical tests, we demonstrate the accuracy and robustness of this discontinuous-Galerkin-implicit-explicit method.
79 ASTRONOMY AND ASTROPHYSICS↗
Acceleration of isolated atoms by radiation pressure
A model is considered of a point source of radiation with a power-law spectrum in which atoms are both accelerated and photoionized by the radiation pressure, and the resulting spectrum of escape velocities is calculated. It is found that the velocity spectrum will depend only on the power-law index and will be independent of the radiation intensity. It is shown that relativistic velocities are not possible for power-law indices typical of astrophysical objects.
Gordon, R. H.↗
AT2018cow: A Luminous Millimeter Transient
We present detailed submillimeter- through centimeter-wave observations of the extraordinary extragalactic transient AT2018cow. The apparent characteristics—the high radio luminosity, the rise and long-lived emission plateau at millimeter bands, and the sub-relativistic velocity—have no precedent. A basic interpretation of the data suggests E(k) ≳ 4 X 10^(48) erg coupled to a fast but sub-relativistic (v ≈ 0.13c) shock in a dense (n(e) ≈ 3 X 10^(5) per cu. cm) medium. We find that the X-ray emission is not naturally explained by an extension of the radio-submm synchrotron spectrum, nor by inverse Compton scattering of the dominant blackbody UV/optical/IR photons by energetic electrons within the forward shock. By ∆t ≈ 20 days, the X-ray emission shows spectral softening and erratic inter-day variability. Taken together, we are led to invoke an additional source of X-ray emission: the central engine of the event. Regardless of the nature of this central engine, this source heralds a new class of energetic transients shocking a dense medium, which at early times are most readily observed at millimeter wavelengths
Anna Y. Q. Ho↗
Measurements on a shock wave generated by a solar flare
Shock waves generated by intense solar flares may be driven by a large amount of ejected mass, about 5 x 10 to the 16th g, and the total energy involved may be of the order of 10 to the 32nd erg. The shocks may have initial velocities of the order of 2,000 km/s and, in their exodus through the corona, may be accompanied by fast-moving optical transients, the emission of highly characteristic radio signatures and the acceleration of particles to quasi-relativistic velocities. Here, a review is presented of data on a high-velocity shock generated by a flare on 18 August 1979, 1400 UT, and comments are provided on some previously deduced velocities for the shock. Attention is given to a model, based on current computer programs to account for the overall characteristics of the shock as it propagated through the corona and the interplanetary plasma.
Maxwell, A.↗
The Fast, Luminous Ultraviolet Transient AT2018cow: Extreme Supernova, or Disruption of a Star by an Intermediate-Mass Black Hole?
Wide-field optical surveys have begun to uncover large samples of fast (trise <~ 5 d), luminous (Mpeak < −18), blue transients. While commonly attributed to the breakout of a supernova shock into a dense wind, the great distances to the transients of this class found so far have hampered detailed investigation of their properties. We present photometry and spectroscopy from a comprehensive worldwide campaign to observe AT 2018cow (ATLAS 18qqn), the first fast-luminous optical transient to be found in real time at low redshift. Our first spectra (<2 days after discovery) are entirely featureless. A very broad absorption feature suggestive of near relativistic velocities develops between 3 and 8 days, then disappears. Broad emission features of H and He develop after >10 days. The spectrum remains extremely hot throughout its evolution, and the photospheric radius contracts with time (receding below R < 1014 cm after 1 month). This behaviour does not match that of any known supernova, although a relativistic jet within a fallback supernova could explain some of the observed features. Alternatively, the transient could originate from the disruption of a star by an intermediate-mass black hole, although this would require long-lasting emission of highly super-Eddington thermal radiation. In either case, AT 2018cow suggests that the population of fast luminous transients represents a new class of astrophysical event. Intensive follow-up of this event in its late phases, and of any future events found at comparable distance, will be essential to better constrain their origins.
Black-hole↗
A current generation by Compton scattering in a relativistic plasma with velocity shear and temperature gradient
Current generation by Thomson scattering in a non-relativistic plasma with the velocity shear and the temperature gradient (Hinata and Daneshvar, 1983) is extended to a relativistic plasma by replacing Thomson cross section by the Klein-Nishina formula. Because of the energy dependence of the cross-section, a numerical rather than analytic result is presented. The present calculation may be applied to a supernova implosion where the temperature may reach several MeV and a strong differential rotation is expected. It may also find applications in the early universe, and laser-pellet interaction.
Hinata, S.↗
VLBI observations of the jet in Cygnus A
The luminous radio galaxy Cyg A was observed with a five-station US VLBI array at 5 GHz at epoch 1983.25. The jet can be followed from the core to a distance of 9 milliarcsec (mas). Within the limited dynamic range of these observations, it is one-sided (jet:counterjet ratio greater than 12:1). If this one-sidedness is due to Doppler boosting, then (1) the jet must decelerate to a mildly relativistic velocity on a kiloparsec scale, (2) the source cannot lie with 30 deg of the plane of the sky. The jet points directly at the base of the kpc-scale jet seen by Perley, Dreher, and Cowan (1984); the curvature occurs primarily or entirely on a scale of 10-100 kpc. The jet brightness falls off more slowly inside 1 kpc than in other powerful sources. A search for compact structure in the three bright hot spots revealed no structure lower than 3 mas in size with flux greater than 6 mJy.
Linfield, R.↗
Cosmic-ray propagation in the Galaxy and in the heliosphere - The path-length distribution at low energy
The energy dependence of the path-length distribution of cosmic rays at low energies, below relativistic velocities, is studied, and its implications for models of cosmic-ray confinement and propagation in the Galaxy and Galactic halo, including the effects of a possible Galactic wind, are studied. It is found that the mean free path in Galactic propagation must be fully energy-dependent, with the mean of an exponential path-length distribution increasing with increasing energy below 1 GeV per nucleon and decreasing with increasing energy above 1 GeV per nucleon. This indicates that, at low energies, diffusion is not the controlling process. The path-length distribution is not purely exponential but is depleted in short path lengths at low energies. This depletion is energy-dependent, being largest at low energies and decreasing with increasing energy.
Garcia-Munoz, M.↗
Cosmic Ray Nuclei (CRN) detector investigation
The Cosmic Ray Nuclei (CRN) detector was designed to measure elemental composition and energy spectra of cosmic radiation nuclei ranging from lithium to iron. CRN was flown as part of Spacelab 2 in 1985, and consisted of three basic components: a gas Cerenkov counter, a transition radiation detector, and plastic scintillators. The results of the experiment indicate that the relative abundance of elements in this range, traveling at near relativistic velocities, is similar to those reported at lower energy.
Meyer, Peter↗
Relativistic motion in gamma-ray bursts
Three fundamental problems affect models of gamma-ray bursts, i.e., the energy source, the ability of high-energy photons to escape the radiation region, and the comparative weakness of X-ray emission. It is indicated that relativistic bulk motion of the gamma-ray-emitting plasma generically provides a solution to all three of these problems. Results show that, if the plasma that produces gamma-ray bursts has a bulk relativistic velocity with Lorentz factor gamma of about 10, several of the most troubling problems having to do with gamma-ray bursts are solved.
Krolik, Julian H.↗
Project Longshot
Project Longshot is an unmanned probe to our nearest star system, Alpha Centauri, 4.3 light years away. The Centauri system is a trinary system consisting of two central stars (A and B) orbiting a barycenter, and a third (Proxima Centauri) orbiting the two. The system is a declination of -67 degrees. The goal is to reach the Centauri system in 50 years. This time space was chosen because any shorter time would be impossible of the relativistic velocities involved, and any greater time would be impossible because of the difficulty of creating a spacecraft with such a long lifetime. Therefore, the following mission profile is proposed: (1) spacecraft is assembled in Earth orbit; (2) spacecraft escapes Earth and Sun in the ecliptic with a single impulse maneuver; (3) spacecraft changed declination to point toward Centauri system; (4) spacecraft accelerates to 0.1c; (5) spacecraft coasts at 0.1c for 41 years; (6) spacecraft decelerates upon reaching Centauri system; and (7) spacecraft orbits Centauri system, conducts investigations, and relays data to Earth. The total time to reach the Centauri system, taking into consideration acceleration and deceleration, will be approximately 50 years.
West, J. Curtis↗
(abstract) A Relativistically Expanding Radio Source Associated with GRO J1655-40
GRO J1655-40 was discovered as a new, bright X-ray source with the BATSE detector of the Gamma Ray Observatory (GRO) on July 27, 1994. During the subsequent radio outburst we completed VLBI synthesis imaging observations at a frequency of 2.29 GHz. An unprecedented angular motion of 65+/- mas per day was reported between two components of complex and disparate morphology ?? The separation rate indicates that the two components were at zero separation near the onset of the radio flare. Similar to the recently reported GRS 1915+105, it seems that the motion of material ejected from a stellar mass compact object with at least a mildly relativistic velocity may explain the observed radio structural changes in GRO J1655-40. The two-week delay between the X-ray outburst and the production of radio components may indicate that the X-rays were produced by a super-critical accretion process onto the compact member of this stellar binary system. This process inhibited or smothered the ejection of radio components until the accretion disk stabilized.
X-ray sources Gamma Ray Observatory GRO radio outb↗
A Compton-thick Wind in the High Luminosity Quasar, PDS 456
PDS 456 is a nearby (z=0.184), luminous (L(sub bol) approximately equal to 10(exp 47) ergs(exp -1) type I quasar. A deep 190 ks Suzaku observation in February 2007 revealed the complex, broad band X-ray spectrum of PDS 456. The Suzaku spectrum exhibits highly statistically significant absorption features near 9 keV in the quasar rest-frame. We show that the most plausible origin of the absorption is from blue-shifted resonance (1s-2p) transitions of hydrogen-like iron (at 6.97 keV in the rest frame). This indicates that a highly ionized outflow may be present moving at near relativistic velocities (0.26-0.31c). A possible hard X-ray excess is detected above 15 keV with HXD (at 99.8% confidence), which may arise from high column density gas (N(sub H) greater than 10(exp 24)cm(exp -2) partially covering the X-ray emission, or through strong Compton reflection. Here we propose that the iron K-shell absorption in PDS 456 is associated with a thick, possibly clumpy outflow, covering about 20% of 4(pi) steradian solid angle. The outflow is likely launched from the inner accretion disk, within 15-100 gravitational radii of the black hole. The kinetic power of the outflow may be similar to the bolometric luminosity of PDS 456. Such a powerful wind could have a significant effect on the co-evolution of the host galaxy and its supermassive black hole, through feedback.
Reeves, J. N.↗