Relativistic Aberration Research Articles

Mansouri-Sexl Test for Light Speed Anisotropy via Cosmic Aberration~!2010-02-11~!2010-02-26~!2010-06-30~!

The Mansouri-Sexl theory is a well known test theory of relativity. In the current paper we will derive the Man- souri-Sexl formalism for the light aberration and we will show how to improve on the theoretical and experimental basis by constraining both the Mansouri-Sexl parameter a(!) and the parameter b(!) . In the process of constraining the Man- souri parameters we devise a novel experiment for measuring and constraining light speed anisotropy as well. An over- whelming number of experiments dealing with light speed anisotropy are laboratory-bound and they are limited to con- straining only parameter a(!) ; we will also take the approach of setting up an astronomical experiment instead of a lab- based one as it befits the relativistic aberration effect. Our paper is organized as follows: in the first section we give a new and more complete derivation of the Mansouri-Sexl aberration effect. In the second part, we apply the newly expanded Mansouri-Sexl aberration formalism in order to devise an astronomical experiment used for constraining both the parame- ter a(!) and the parameter b(!) . This turns the Mansouri-Sexl aberration experiment into a very powerful tool for con- straining light speed anisotropy. 1. THE ROBERTSON-MANSOURI-SEXL TEST THEORY The test theories of special relativity differ in their as- sumptions about the form of the Lorentz transforms. The main test theories of special relativity (SR) are named after their authors, Robertson (1), Mansouri and Sexl (2-4) (RMS). These test theories can also be used to examine po- tential alternate theories to SR - such alternate theories pre- dict particular values of the parameters of the test theory, which can easily be compared to values determined by ex- periments analyzed with the test theory (5-20). The existing experiments put rather strong experimental constraints on any alternative theory. RMS starts by admitting by reduction to absurd that there is a preferential inertial frame Σ in which the light propagates isotropically with the speed c 0 . All other frames in motion with respect to Σ are considered non- preferential and the light speed is anisotropic. The light speed in the non-preferential frames can be deduced via sim- ple calculations described in (3). We start with the Mansouri- Sexl transforms: x=b(v)(X!vT) y=d(v)Y z=d(v)Z t=a(v)T+(v)x=(a!bv)T+bX

Relativistic Doppler-boosted emission in gamma-ray binaries

<i>Context. <i/>Gamma-ray binaries could be compact pulsar wind nebulae formed when a young pulsar orbits a massive star. The pulsar wind is contained by the stellar wind of the O or Be companion, creating a relativistic comet-like structure accompanying the pulsar along its orbit.<i>Aims. <i/>The X-ray and the very high energy (<i>><i/>100 GeV, VHE) gamma-ray emission from the binary LS 5039 are modulated on the orbital period of the system. Maximum and minimum flux occur at the conjunctions of the orbit, suggesting that the explanation is linked to the orbital geometry. The VHE modulation has been proposed to be due to the combined effect of Compton scattering and pair production on stellar photons, both of which depend on orbital phase. The X-ray modulation could be due to relativistic Doppler boosting in the comet tail where both the X-ray and VHE photons would be emitted.<i>Methods. <i/>Relativistic aberrations change the seed stellar photon flux in the comoving frame so Doppler boosting affects synchrotron and inverse Compton emission differently. The dependence with orbital phase of relativistic Doppler-boosted (isotropic) synchrotron and (anisotropic) inverse Compton emission is calculated, assuming that the flow is oriented radially away from the star (LS 5039) or tangentially to the orbit (LS I +61303, PSR B1259-63).<i>Results. <i/>Doppler boosting of the synchrotron emission in LS 5039 produces a lightcurve whose shape corresponds to the X-ray modulation. The observations imply an outflow velocity of 0.15–0.33<i>c<i/> consistent with the expected flow speed at the pulsar wind termination shock. In LS I +61303, the calculated Doppler boosted emission peaks in phase with the observed VHE and X-ray maximum.<i>Conclusions. <i/>Doppler boosting is not negligible in gamma-ray binaries, even for mildly relativistic speeds. The boosted modulation reproduces the X-ray modulation in LS 5039 and could also provide an explanation for the puzzling phasing of the VHE peak in LS I +61303.

UNCERTAINTIES OF MODELING GAMMA-RAY PULSAR LIGHT CURVES USING VACUUM DIPOLE MAGNETIC FIELD

Current models of pulsar gamma-ray emission use the magnetic field of a rotating dipole in vacuum as a first approximation to the shape of a plasma-filled pulsar magnetosphere. In this paper, we revisit the question of gamma-ray light curve formation in pulsars in order to ascertain the robustness of the "two-pole caustic (TPC)" and "outer gap (OG)" models based on the vacuum magnetic field. We point out an inconsistency in the literature on the use of the relativistic aberration formula, where in several works the shape of the vacuum field was treated as known in the instantaneous corotating frame, rather than in the laboratory frame. With the corrected formula, we find that the peaks in the light curves predicted from the TPC model using the vacuum field are less sharp. The sharpness of the peaks in the OG model is less affected by this change, but the range of magnetic inclination angles and viewing geometries resulting in double-peaked light curves is reduced. In a realistic magnetosphere, the modification of field structure near the light cylinder (LC) due to plasma effects may change the shape of the polar cap and the location of the emission zones. We study the sensitivity of the light curves to different shapes of the polar cap for static and retarded vacuum dipole fields. In particular, we consider polar caps traced by the last open field lines and compare them to circular polar caps. We find that the TPC model is very sensitive to the shape of the polar cap, and a circular polar cap can lead to four peaks of emission. The OG model is less affected by different polar cap shapes, but is subject to big uncertainties of applying the vacuum field near the LC. We conclude that deviations from the vacuum field can lead to large uncertainties in pulse shapes, and a more realistic force-free field should be applied to the study of pulsar high-energy emission.

Relativistic satellite astrometry atμarcsec precision and the measurement of the stellar aberration

Analysis and interpretation of the μarcsec precision astrometric data shortly to be provided by the ESA-GAIA satellite has prompted the development of a fully general-Relativistic Astrometric MODel (RAMOD), which is able to account for all the general-relativistic corrections up to the required order of precision O(c ―3 ). We obtain the covariant expression for the general relativistic aberration effect and provide the analytical module for determining the stellar aberration from the GAIA observables (the direction cosines of the incoming light-ray trajectory) at this same O(c ―3 ) order of precision.

Relativistic effects in radar detection of ionization fronts produced by ultra-high energy cosmic rays

We revisit the radar echo technique as an approach to detect ultra-high energy cosmic rays (UHECR). The UHECR extensive air showers generate disk-like ionization fronts propagating with a relativistic velocity and creating fast decaying plasma. We study the reflection of a radio wave, such as the one from a radar transmitter or commercial radio and TV station, from the relativistic ionization front. The reflected wave will be frequency upshifted due to the relativistic Doppler effect and propagate almost normally to the front due to relativistic aberration. The amplitude of the reflected wave depends strongly on the front velocity and parameters (density, collision frequency) of the plasma behind the front. We develop a theory that allows one to find the reflected wave. Using this theory and typical parameters of extensive air showers, we discuss the feasibility of UHECR detection.

Erratum: The structure of the jet in 3C 15 from multiband polarimetry

Our observations have constrained the differences in polarization position angle between the optically and radio bright regions of the jet. If these arise predominantly from regions of different velocity (as in a spine–sheath model), relativistic aberration of the polarization position angle may be large. In order to test such a model is not ruled out by the data, we attempt to model the jet as two components: a central high-velocity spine emitting optical synchrotron radiation, and an outer sheath of radio-emitting plasma. Our model has a magnetic field with components (B x, B ′ y, B ′ z) in the jet frame, where the z-axis is parallel to the jet direction, and the xy-plane is transverse to the jet. For a Lorentz factor γ in the z-direction, and an angle φ between the z-axis and the line of sight, the observer will see a projected magnetic field in the plane of the sky Bu = γB ′ x cosφ + B ′ z sinφ, (1)

Observational Appearance of Luminous Relativistic Movers

Abstract We examine the observational appearance of optically thick luminous gaseous objects that move or rotate at a relativistic speed. In relativistic objects traveling at about the speed of light, Doppler and aberration effects influence their observational appearance. In gaseous objects with a hotter interior, furthermore, there exists a usual limb-darkening effect, which has a direction-dependency, and is therefore affected by the relativistic aberration. In addition, the emitted radiation suffers from a relativistic Doppler boost. Hence, the apparent photosphere of relativistic gaseous objects depends on their velocity and direction as well as the temperature distribution. We have derived the optical depth of the apparent photosphere of such relativistic movers under the plane-parallel approximation, and calculated several typical cases. When the velocity is almost parallel to the line of sight, the relativistic effect on the optical depth becomes important; otherwise, the limb-darkening effect dominates. In the case of a rotating sphere, except for some small fraction in the equatorial direction, the optical depth of the apparent photosphere becomes small due to the relativistic aberration. In the case of a geometrically thin disk, the optical depth becomes large in the left approaching part, whereas it becomes small in the right receding part. In the case of a geometrically thick disk, the projection effect becomes important, and the optical depth is large at the far side, while it is small at the near side. We have also examined light curves of luminous orbiters around a black hole and luminosities and spectra of accretion disks under special relativity, as applications. The light curve of the relativistic orbiter does deviate from a sinusoidal pattern due to the transverse Doppler effect. The pole-on luminosity of accretion disks is enhanced by the limb-dakening effect and reduced by the relativistic one, while the luminosity observed from the inclined direction is reduced by the limb-darkening effect.

Radiation hazard of relativistic interstellar flight

From the point of view of radiation safety, interstellar space is not an empty void. Interstellar gas and cosmic rays, which consist of hydrogen and helium nucleons, present a severe radiation hazard to crew and electronics aboard a relativistic interstellar ship. Of the two, the oncoming relativistic flow of interstellar gas produces the most intense radiation. A protection shield will be needed to block relativistic interstellar gas that can also absorb most of the cosmic rays which, as a result of relativistic aberration, forms into a beamed flow propagating toward the front of the spaceship.

Relativistic aberrations in quantum phase space

A phase space treatment of special relativity of quantum systems is developed. In this approach a quantum particle remains localized if subject to inertial transformations, the localization occurring in a finite phase space area. Unlike in the non-relativistic case, relativistic transformations generally distort the phase space distribution function, being equivalent to aberrations in optics. The relativistic aberrations of massive particles are in general different from those of optical images.

Linear wave propagation in relativistic magnetohydrodynamics

The properties of linear Alfvén, slow, and fast magnetoacoustic waves for uniform plasmas in relativistic magnetohydrodynamics (MHD) are discussed, augmenting the well-known expressions for their phase speeds with knowledge on the group speed. A 3+1 formalism is purposely adopted to make direct comparison with the Newtonian MHD limits easier and to stress the graphical representation of their anisotropic linear wave properties using the phase and group speed diagrams. By drawing these for both the fluid rest frame and for a laboratory Lorentzian frame which sees the plasma move with a three-velocity having an arbitrary orientation with respect to the magnetic field, a graphical view of the relativistic aberration effects is obtained for all three MHD wave families. Moreover, it is confirmed that the classical Huygens construction relates the phase and group speed diagram in the usual way, even for the lab frame viewpoint. Since the group speed diagrams correspond to exact solutions for initial conditions corresponding to a localized point perturbation, their formulae and geometrical construction can serve to benchmark current high-resolution algorithms for numerical relativistic MHD.

Relativistic aberration for accelerating observers

We investigate the effects of the aberration of light for a uniformly accelerating observer. The observer is initially at rest with respect to a luminous spherical object and then starts to move away with constant acceleration. Our main results are the following: (i) The observer sees an initial increase of the apparent size of the object, (ii) the apparent size of the object approaches a nonzero value as the proper time of the observer goes to infinity, and (iii) there exists a critical value of the acceleration such that the apparent size of the object is monotonically increasing when the acceleration is supercritical. Although the first effect is purely nonrelativistic, the others are the result of the relativistic aberration of light and are intimately connected with the Lorentzian geometry of Minkowksi spacetime. The examples we present illustrate that the three effects are more or less negligible in everyday life, but significant in the context of space flight.

Visualizing flat spacetime: Viewing optical versus special relativistic effects

A visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean four-space to yield accurate visualizations as predicted by special relativity. The contributions of relativistic aberration as compared to classical prerelativistic aberration to the geometry are discussed in the context of its visual representation.

A relativistic model of the radio jets in 3C 296

We present new, deep 8.5-GHz VLA observations of the nearby, low-luminosity radio galaxy 3C 296 at resolutions from 0.25 to 5.5 arcsec. These show the intensity and polarization structures of the twin radio jets in detail. We also derive the spectral-index and rotation-measure distributions. We apply our intrinsically symmetrical, decelerating relativistic jet model to the new observations. An optimized model accurately fits the data in both total intensity and linear polarization. We infer that the jets are inclined by 58 deg to the line of sight. On-axis, they decelerate from a (poorly-constrained) initial velocity of 0.8c to approximately 0.4c around 5 kpc from the nucleus, the velocity thereafter remaining constant. The speed at the edge of the jet is low everywhere. The longitudinal profile of proper emissivity has three principal power-law sections and the emission is centre-brightened. Our observations rule out a globally-ordered, helical magnetic-field configuration. Instead, we model the field as random on small scales but anisotropic, with toroidal and longitudinal components only. The ratio of longitudinal to toroidal field falls with distance along the jet, qualitatively but not quantitatively as expected from flux freezing, so that the field is predominantly toroidal far from the nucleus. The toroidal component is relatively stronger at the edges of the jet. A simple adiabatic model fits the emissivity evolution only in the outer region after the jets have decelerated and recollimated; closer to the nucleus, it predicts far too steep an emissivity decline with distance. We also interpret the morphological differences between brightness enhancements (arcs) in the main and counter-jets as an effect of relativistic aberration. (Abridged)

A colorful relativity problem

Borchers comments: The image on the Physics Today cover depicts the geometric distortion only, so it is not what one would actually see when falling at 90% the speed of light. In addition to the shift in colors due to the Doppler effect, the appearance would be dominated by the searchlight effect. When looking in the direction of motion at 90%, the wavelengths would be shorter by a factor of 4.35, while the intensity would increase by a factor of more than 1500 (Doppler factor to the fifth power); the exact value depends on the spectral distribution in the infrared. To accurately render the color distortion, we would need the spectral distribution of the scene in the infrared. Unfortunately, we don’t know this distribution for the market square.© 2006 American Institute of Physics.

Spectra of the spreading layers on the neutron star surface and constraints on the neutron star equation of state

Spectra of the spreading layers on the neutron star surface are calculated on the basis of the Inogamov-Sunyaev model taking into account general relativity correction to the surface grav- ity and considering various chemical composition of the accreting matter. Local (at a given latitude) spectra are similar to the X-ray burst spectra and are described by a diluted blackbody. Total spreading layer spectra are integrated accounting for the light bending, gravitational red- shift and the relativistic Doppler effect and aberration. They depend slightly on the inclination angle and on the luminosity. These spectra also can be fitted by a diluted blackbody with the colour temperature depending mainly on a neutron star compactness. Owing to the fact that the flux from the spreading layer is close to the critical Eddington, we can put constraints on a neutron star radius without the need to know precisely the emitting region area or the distance to the source. The boundary layer spectra observed in the luminous low-mass X-ray binaries, and described by a blackbody of colour temperature T c = 2.4 ± 0.1 keV, restrict the neutron star radii to R = 14.8 ± 1.5 km (for a 1.4-M ⊙ star and solar composition of the accreting matter), which corresponds to the hard equation of state.

Relativistic aberration of light as a corollary of the relativity of simultaneity

A new derivation of the relativistic aberration formula for a plane-polarized lightwave is presented that does not require any use of the Lorentz transformation. The method is based on a modification of the Huygens–Fresnel principle to include the relativistic effects introduced by the relative motion between the observer and the emitter. The derivation clearly shows that the aberration formula is a direct consequence of the relative simultaneity.

Effects of Pulsar Rotation on Timing Measurements of the Double Pulsar System J0737−3039

We study the effect of pulsar rotation on the timing of binary pulsars, with particular emphasis on the double pulsar system J0737-3039. Special relativistic aberration due to the orbital motion of a pulsar changes both the longitude and latitude of the emission direction with respect to the pulsar spin axis. The former gives rise to a shift of the arrival time of the pulse centroid (this is the conventional aberration delay), and the latter results in a distortion (contraction or dilation) of the pulse profile on the orbital timescale. In the framework of the rotating vector model of pulsar emission, the amplitude of pulse distortion depends inversely on the variation of the polarization position angle across the pulse. For a small angle between the pulsar magnetic and spin axes, as has been inferred for PSR J0737-3039A from polarimetric observations, the pulse distortion is significant (~1%) and the associated aberration delay is much larger than the longitudinal one. We show that by monitoring the arrival time of separate pulse components as a function of pulsar orbital phase, the latitudinal aberration delay may be easily measured with the current timing precision. Such a measurement would constrain the spin geometry of the system. The latitudinal delay can also be detected by monitoring the system's orbital parameters on the geodetic precession timescale. Because of the near-edge-on orbital orientation of the PSR J0737-3039 system, general relativistic bending of pulsar A's radio beam near its superior conjunction also introduces spin-dependent time delays of similar orders of magnitude as the aberration delays. In addition, light bending splits the pulse profile into two variable components, corresponding to two gravitationally lensed images of the source. Detection of lensing effects is challenging, but it may be possible with existing technology.

The Theory of Spectral Evolution of the Gamma‐Ray Burst Prompt Emission

We develop the theory of jitter radiation from GRB shocks containing small-scale magnetic fields and propagating at an angle with respect to the line of sight. We demonstrate that the spectra vary considerably: the low-energy photon index α ranges from 0 to -1 as the apparent viewing angle goes from 0 to π/2. Thus, we interpret the hard-to-soft evolution and the correlation of α with the photon flux observed in GRBs as a combined effect of temporal variation of the viewing angle and relativistic aberration of an individual thin, instantaneously illuminated shell. The model predicts that about a quarter of time-resolved spectra should have hard spectra, violating the synchrotron α = -2/3 line of death. The model also naturally explains why the peak of the distribution of α is at α ≈ -1. The presence of a low-energy break in the jitter spectrum at oblique angles also explains the appearance of a soft X-ray component in some GRBs and a relatively small number of them. We emphasize that our theory is based solely on the first principles and contains no ad hoc (phenomenological) assumptions.

Adsorption of bi-isonicotinic acid on anatase TiO 2(1 0 1) and (0 0 1) studied by photoemission and NEXAFS spectroscopy

The adsorption of bi-isonicotinic acid (2,2′-bipyridyl-4,4′-dicarboxylic acid) on the surface of anatase TiO 2(1 0 1) and (0 0 1) single crystals has been investigated using XPS and NEXAFS. The searchlight effect of NEXAFS has been used to determine the adsorption geometry of BINA on these surfaces. The pyridyl rings in BINA are found to be oriented at 20° ± 3° from the surface normal on the (1 0 1) surface and at 53° ± 5° from the surface normal on the reconstructed (0 0 1) surface.

Spatial Variation of the X‐Ray Spectrum of the Crab Nebula

We present a spectral analysis of the Crab Nebula obtained with the Chandra X-ray observatory. The X-ray spectrum is characterized by a power law whose index varies across the nebula. The variation can be discussed in terms of the particle injection from the pulsar in two different directions: the equatorial plane containing the torus and the symmetry axis along the jet. In the equatorial plane, spectra within the torus are the hardest, with a photon index α ≈ 1.9, and are almost independent of the surface brightness. At the periphery of the torus, the spectrum gradually softens in the outer, lower surface brightness regions, up to α ≈ 3.0. This indicates that synchrotron losses become significant to X-ray-emitting particles at the outer boundary of the torus. We discuss the nature of the torus, incorporating information from observations at other wavelengths. Spectral variations are also seen within the southern jet. The core of the jet is the hardest, with α ≈ 2.0, and the outer sheath surrounding the core becomes softer with α up to 2.5 at the outermost part. Based on the similarity between the spectra of the jet core and the torus, we suggest that the electron spectra of the particles injected from the pulsar are also similar in these two different directions. The brightness ratio between the near and far sides of the torus can be explained by Doppler boosting and relativistic aberration; however, the observed ratio cannot be derived from the standard weakly magnetized pulsar wind model. We also found a site where an optical filament comprising supernova ejecta is absorbing the soft X-ray emission (<2 keV).