Gravitational Bending Research Articles

Modelling the pulse profiles of accreting millisecond pulsars and X-ray bursters

The observed variability from the first discovered accreting millisecond pulsar SAX J1808.4–3658 can be explained if the X-ray emission is produced by Comptonization in a hot slab of Thomson optical depth τ es ∼1 at the neutron star surface. We construct a detailed model of the X-ray production accounting for the Doppler boosting, relativistic aberration and gravitational light bending in the Schwarzschild metric. We show that the black body radiation is strongly beamed along the normal to the slab (a “pencil”–like emission pattern), while the Comptonized luminosity has a broader angular distribution peaking at about 60° from the slab normal (a “fan”–like pattern). Our model reproduces well the pulse profiles at different energies simultaneously, corresponding phase lags, as well as the time-averaged spectrum. The observed soft phase lags result from different radiation patterns of the two main emission components. We determine the radius of the compact object to be R ∼11 km if its mass M =1.6 M ⊙ , while for M =1.4 M ⊙ the best-fitting radius is ∼8.5 km. The lower limit on the inclination of the system is 65°. We present also simple analytical formulae for computing the light curves and oscillation amplitudes expected from hot spots in X-ray bursters and millisecond pulsars.

Hollow‐Cone Accretion Columns and Light‐bending Effects

A set of new model calculations for pulse shapes from hollow cone-shaped accretion columns is carried out. The cones have a circular base on the neutron star centered on the magnetic poles and extend upward. Both straight cones and those that follow dipole field lines are considered. The difference is important only for tall cones. The emissivity dependence on the local angle normal to the emitting surface or to the magnetic field can be specified: here analytic formulae and tables to represent the Meszaros & Nagel emissivities were considered. The effects of gravitational light bending are included and have a major impact on the resulting beam patterns, as shown by comparison with patterns computed without light bending.

On the nature of the X-ray emission from the accreting millisecond pulsar SAX J1808.4-3658

We study the pulse profiles of the accreting X-ray millisecond pulsar SAX J1808.4-3658 at different energies. The two main emission components, the blackbody and the Comptonized tail, which are clearly identified in the time-averaged spectrum, show strong variability with the first component lagging the second one. The observed variability can be explained if the emission is produced by Comptonization in a hot slab (radiative shock) of Thomson optical depth ∼0.3-1 at the neutron star surface. The blackbody radiation is strongly beamed along the normal to the slab (a 'knife'-like or 'pencil'-like emission pattern), while the Comptonized emission has a broader angular distribution peaking at about 50°-60° from the slab normal (a 'fan'-like pattern). We construct a detailed model of the X-ray production accounting for the Doppler boosting, relativistic aberration and gravitational light bending in the Schwarzschild space-time. We present also accurate analytical formulae for computations of the light curves from rapidly rotating neutron stars using the formalism recently developed by Beloborodov. Our model reproduces well the pulse profiles at different energies simultaneously, corresponding phase lags, as well as the time-averaged spectrum. We constrain the compact star mass to be bounded between 1.2 and 1.6 M O .. By fitting the observed profiles, we determine the radius of the compact object to be R ∼11 km if M = 1.6 M O ., while for M = 1.2 M O . the best-fitting radius is ∼6.5 km, indicating that the compact object in SAX J1808.4-3658 can be a strange star. We obtain a lower limit on the inclination of the system of 65°.

Modeling galaxy halos using dark matter with pressure

We investigate whether dark matter with substantial amounts of pressure, comparable in magnitude to the energy density, could be a viable candidate for the constituent of dark matter halos. We find that galaxy halo models, consistent with observations of flat rotation curves, are possible for a variety of equations of state with anisotropic pressures. It turns out that the gravitational bending of light rays passing through such halos is very sensitive to the pressure. We propose that combined observations of rotation curves and gravitational lensing can be used to determine the equation of state of dark matter. Alternatively, if the equation of state is known from other observations, rotation curves and gravitational lensing can together be used to test general relativity on galaxy scales.

The iron line in MCG--6-30-15 from XMM--Newton: evidence for gravitational light bending?

The lack of variability of the broad iron line seen in the Seyfert 1 galaxy MCG—6-30-15 is studied using the EPIC pn data obtained from a 2001 observation of 325 ks, during which the count rate from the source varied by a factor of 5.The spectrum of 80 ks of data from when the source was bright, using the lowest 10 ks as background, is well fitted over the 3–10 keV band with a simple power law of photon index Γ= 2.11.The source spectrum can therefore be decomposed into an approximately constant component, containing a strong iron emission line, and a variable power law component.Assuming that the power-law continuum extends down to 0.5 keV enables us to deduce the absorption acting on the nucleus.A simple model involving Galactic absorption and two photoelectric edges (at 0.72 and 0.86 keV) is adequate for the EPIC spectrum above 1 keV.It still gives a fair representation of the spectrum at lower energies where absorption lines, Unresolved Transition Arrays (UTAs), etc.are expected.Applying the absorption model to the low flux spectrum enables us to characterize it as reflection-dominated with iron about three times Solar.Fitting this model, with an additional power-law continuum, to 32 × 10 ks spectra of the whole observation reveals that Γ lies mostly between 2 and 2.3 and the normalization of the reflection-dominated component varies by up to 25 per cent.The breadth of the iron line suggests that most of the illumination originates from about 2 gravitational radii.Gravitational light bending will be very strong there, causing the observed continuum to be a strong function of the source height and much of the continuum radiation to return to the disc.Together these effects can explain the otherwise puzzling disconnectedness of the continuum and reflection components of MCG—6-30-15.

Gravitational light bending and the lightcurves of HMXBs

We calculate the magnitude of gravitational light bending for a set of neutron stars described by various equations of state. We analyze the size of the parameter space for the visibility of one or two magnetic polar caps, corresponding to single and double peaked lightcurves. We show that the expected fraction of single peaked lightcurves should be less than 20%, while the observations seem to show a larger fraction. We also discuss the volume of the parameter space for accretion flow eclipses (or dips) such as these seen in e.g. A0535+262, GX1+4, and LS992. We conclude that the data favors a model where the magnetic axis tends to alignment with the rotation axis.

Multiple X-ray reflection from ionized slabs

Multiple reflection of X-rays may be important when an accretion disc and its hot corona have a complicated geometry, or if returning radiation due to gravitational light bending is important, or in emission from a funnel such as proposed in some gamma-ray burst models. We simulate the effects of multiple reflection by modifying the boundary condition for an X-ray illuminated slab. Multiple reflection makes the soft X-ray spectrum steeper (softer) and strengthens broad emission and absorption features, especially the K-shell features of iron. This may be important in explaining the spectra of sources such as the Narrow-Line Seyfert 1 galaxy 1H0707-495.

Microlensing by compact objects associated with gas clouds

We investigate gravitational microlensing of point-like lenses surrounded by diffuse gas clouds. Besides gravitational bending, one must also consider refraction and absorption phenomena. According to the cloud density, the light curves may suffer small to large deviations from Paczyński curves, up to complete eclipses. Moreover, the presence of the cloud endows this type of microlensing event with a high chromaticity and absorption lines recognizable by spectral analysis. It is possible that these objects populate the halo of our galaxy, giving a conspicuous contribution to the fraction of the baryonic dark matter. The required features for the extension and the mass of the cloud to provide appreciable signatures are also met by several astrophysical objects.

Investigation of the effective space-time of the vacuum nonlinear electrodynamics in a magnetic dipole field

The metric tensor of the effective pseudo-Riemannian space–time for an electromagnetic wave propagating in the magnetic dipole field and the gravitational field of a neutron star is obtained within a parameterized post-Maxwellian vacuum electrodynamics. The angles of the nonlinear electrodynamic and gravitational ray bending for electromagnetic waves propagating in the magnetic equatorial plane of the star are calculated based on an analysis of isotropic geodesics of this space. We show that for all nonlinear theories whose post-Maxwellian parameters do not coincide, the velocity of the electromagnetic signal propagation in external fields and the rays along which these signals propagate depend on the polarization of the electromagnetic waves. The difference of the source-to-detector propagation time of these signals for two principal polarization states is calculated.

Schwarzschild black hole in the background of the Einstein universe: some physical effects

A prototype of an asymptotically non-flat black hole spacetime is that of a Schwarzschild black hole in the background of the Einstein universe, which is a special case of the representation of a black hole in a cosmological background given by Vaidya. Recently, this spacetime has been studied in detail by Nayak et al. They constructed a composite spacetime called the Vaidya–Einstein–Schwarzschild (VES) spacetime. We investigate some of the physical effects inherent to this spacetime. We carry out a background–black hole decomposition of the spacetime in order to separate out the effects due to the background spacetime and the black hole. The physical effects we study include the classical tests—the gravitational redshift, perihelion precession and light bending—and circular geodesics. A detailed classification of geodesics, in general, is also given.

Hollow Accretion Columns on Neutron Stars and the Effects of Gravitational Light Bending

This study investigates the beam patterns for radiation originating in a hollow column on a slowly rotating neutron star where the Schwarzschild metric is appropriate for calculating photon paths. The beam pattern of a hollow column is the sum of contributions from the two emitting surfaces on the inside and the outside of the column, which combine into a two-component beam pattern. The shapes of the inside beam pattern, the outside beam pattern, and the combined beam pattern are studied for radial cones of different height and width, for isotropic and beamed emission, and for different values of mass and radius of the neutron star. It is argued that the hollow cone model provides an interpretation of the pulse profiles of the X-ray pulsar Centaurus X-3.

A Slope Movement by Gravitational Bending of Hard Shale Beds

In early September 1997, hillside cut for road construction caused small-scale landslide in the northeastern mountains of Matsumae peninsula, Hokkaido. The slope movement is characterized that bedded hard shale bent valleyward and back-facing steps occurred on the cut-slope. Morphology and geology of the slope indicate that gravitational bending fold had already formed in the Miocene hard shale formation before breaking out of the movement. Therefore, it seems that the landslide was gravitational fold rapidly proceeded by unloading of the lower slope. One of the geological causes of the movement is existence of fine acid tuff, includes smectite clay and been easily changed to slip surface by bending, interbedded in the hard shale. Thick and hard shale intimately developing small joints is relatively flexible to deformation.

A Three‐dimensional Outer Magnetospheric Gap Model for Gamma‐Ray Pulsars: Geometry, Pair Production, Emission Morphologies, and Phase‐resolved Spectra

A three-dimensional pulsar magnetosphere model is used to study the geometry of outer magnetospheric gap accelerators, following seminal work of Romani and coworkers. The size of the outer gap is self-consistently limited by pair production from collisions of thermal photons from polar cap heating of backflow outer gap current with curvature photons emitted by gap-accelerated charged particles. In principle, there could be two topologically disconnected outer gaps. Conditions for local pair production such as local field line curvature, soft X-ray density, electric field, etc., support pair production inside an outer gap only between rin() (the radius of the null surface at azimuthal angle ) and rlim() ≈ 6rin( = 0) RL (the light cylinder radius). Secondary pairs, on the other hand, are produced almost everywhere outside the outer gap by collisions between curvature photons and synchrotron X-rays emitted by these secondary pairs. These processes produce a wide X-ray fan beam in the outgoing direction and a very narrow beam in the incoming direction for each outer gap. For pulsars with a large magnetic dipole inclination angle, part of the incoming γ-ray beam will be absorbed by the stellar magnetic field. If the surface magnetic field is dominated by a far off-center dipole moment (e.g., as in a proposed plate tectonic model), gravitational bending of photons from polar cap accelerators and their ultimate conversion into outflowing e± pairs can result in the quenching of one of these two outer gaps. Various emission morphologies for the pulsar (depending on magnetic inclination angle and viewing angle) are presented. Double-peak light curves with strong bridges are most common. From the three-dimensional structure of the outer gap and its local properties, we calculate phase-resolved spectra of gamma-ray pulsars and apply them to observed spectra of the Crab pulsar.

The spinal curve in standing and sitting postures in children with idiopathic scoliosis.

A sample of convenience of children with moderate idiopathic scoliosis without bracing or surgery was studied. The sample consisted of 19 children, aged 9 to 16 years, with mean Cobb angle of 24 degrees. The spinal configurations and paraspinal muscle activity in several commonly assumed postures were examined. To determine how the apex angles, verticality of spine, and muscle activity vary with the assumed posture and whether the location and the number of spinal curves affect these variables. It has been suggested that the configuration of the spine in commonly assumed postures can affect the spinal curve in scoliosis because of gravitational bending moments. There is, however, a paucity of data obtained in subjects in sitting postures that school-age children assume daily for prolonged periods. Absence of bilateral symmetry in pressure during sitting has been described, but its effect on the spinal apex angle has not been investigated. Infrared-emitting markers, whose three-dimensional positions could be tracked by a pair of cameras, were affixed to the spine. The natural postures studied were relaxed standing, relaxed sitting, erect sitting, and writing while seated. Electromyographic activity in muscles close to the spinal apexes was recorded bilaterally for each test posture. Subjects leaned laterally and, in general, anteriorly, in all test postures, rather than placing the C7 vertebra vertically above S1. The direction of lean and the change in the spinal apex angle from standing to sitting varied depending on whether the spinal curve was single or double, thoracic or lumbar. Subjects with single curves, whether thoracic or lumbar, tended to lean laterally toward the convexity of their curve apex--that is, the lean was in a direction that reduced the apex angle. Subjects with double curves (thoracic and lumbar), in all postures except relaxed sitting, tended to lean toward the convexity of the lumbar curve, thereby reducing the lumbar apex angle and exacerbating the thoracic angle. Most subjects' apex angles were smaller in relaxed or erect sitting than in relaxed standing. Electromyographic activity was in general greater on the convex side of the curve, with greatest activity in erect sitting. The findings indicate that in self-selected postures the gravitational effect of leaning and the muscle activity in paraspinal muscles may serve to reduce the apex angle. Thus, a fully upright, centered posture may not be best for correction of every patient's spinal curve.

The influence of gravity and wind on land plant evolution

Aspects of the engineering theory treating the elastic stability of vertical stems and cantilevered leaves supporting their own weight and additional wind-induced forces (drag) are reviewed in light of biomechanical studies of living and fossil terrestrial plant species. The maximum height to which arborescent species can grow before their stems elastically buckle under their own weight is estimated by means of the Euler–Greenhill formula which states that the critical buckling height scales as the 1/3 power of plant tissue-stiffness normalized with respect to tissue bulk density and as the 2/3 power of stem diameter. Data drawn from living plants indicate that progressively taller plant species employ stiffer and lighter-weight plant tissues as the principal stiffening agent in their vertical stems. The elastic stability of plants subjected to high lateral wind-loadings is governed by the drag torque (the product of the drag force and the height above ground at which this force is applied), which cannot exceed the gravitational bending moment (the product of the weight of aerial organs and the lever arm measured at the base of the plant). Data from living plants indicate that the largest arborescent plant species rely on massive trunks and broad, horizontally expansive root crowns to resist drag torques. The drag on the canopies of these plants is also reduced by highly flexible stems and leaves composed of tissues that twist and bend more easily than tissues used to stiffen older, more proximal stems. A brief review of the fossil record suggests that modifications in stem, leaf, and root morphology and anatomy capable of simultaneously coping with self-weight and wind-induced drag forces evolved by Devonian times, suggesting that natural selection acting on the elastic stability of sporophytes occurred early in the history of terrestrial plants.

Investigating Pulse Morphology in GX 1+4

AbstractObservational and theoretical evidence points to the existence of an unusually high magnetic field on GX 1+4. The pulsar is thus an ideal laboratory for studying two-photon cyclotron emission, an important source of photons of frequency significantly less than the cyclotron frequency in X-ray pulsars. Low-frequency approximations to the two-photon cyclotron emission transition probabilities are derived. These are used to calculate the theoretical opening angle of the double-humped pulse shape predicted by the two-photon cyclotron emission model. The theoretical pulse shape, incorporating the effects of gravitational light bending, is compared with observations of GX 1+4. Observed light curves have opening angles consistent with the theoretically predicted maximum value.

Cross‐correlating Cosmic Microwave Background Radiation Fluctuations with Redshift Surveys: Detecting the Signature of Gravitational Lensing

Density inhomogeneities along the line of sight distort fluctuations in the cosmic microwave background. Usually, this effect is thought of as a small second-order effect that mildly alters the statistics of the microwave background fluctuations. We show that there is a first-order effect that is potentially observable if we combine microwave background maps with large redshift surveys. We introduce a new quantity that measures this lensing effect, T(δθ ∇ T), where T is the microwave background temperature and δθ is the lensing due to matter in the region probed by the redshift survey. We show that the expected signal is first order in the gravitational lensing bending angle, (δθ)21/2, and find that it should be easily detectable, signal-to-noise ratio ~ 15-35, if we combine the Microwave Anisotropy Probe satellite and Sloan Digital Sky Survey data. Measurements of this cross-correlation will directly probe the bias factor, i.e., the relationship between fluctuations in mass and fluctuations in galaxy counts.

Monte Carlo simulation of the nonstationary transport of very cold and ultracold neutrons in vertical neutron guides and the storage of ultracold neutrons

Abstract The results are presented of Monte Carlo simulation of the transport of very cold (VCN) and ultracold neutrons (UCN) in straight and curved vertical neutron guides with a rectangular cross section in the presence of neutron losses due to neutron capture and diffuse scattering on imperfectly smooth reflecting surface of the guides wall. The gravitational neutron deceleration and bending of neutron trajectories are rigorously taken into account. The nonstationary storage of UCN in experimental chambers is modelled for a low periodic or a periodic pulse neutron source.

Optical and 21 CM Observations of the Warped, Edge-On Galaxy UGC 7170

Aperture synthesis observations in the 21 cm line of H I are presented for UGC 7170, an edge-on disk galaxy with an optical warp. For a derived distance of 31.8 Mpc, we find an HI mass of 4.5 x 10^9^ M_sun_. The HI gas does not extend much beyond the stellar light, reaching only to about three exponential scale lengths of the stellar disk. The ratio of the H I mass to the dynamical mass is normal for a late-type spiral, but the mass-to-light ratio is high, M_dyn_/L_B_ = 43 in solar units, indicating that most of the mass is in a dark halo. Since we observe the rotation curve to flatten at about 1.3 scale lengths of the optical disk, the core radius of the dark halo must be comparable to the disk scale length. UGC 7170 has an asymmetric warp that bends more strongly on the southern side than on the northern side of the galaxy. This warp is evident at both optical and 21 cm wavelengths, and the similarities of the stellar and gaseous warps are consistent with a gravitational origin for the warp. The relatively small size of the halo core makes it possible to explain the warp as a gravitational bending mode of the galactic disk, if the dark halo is assumed to be slightly flattened.

Including the effect of gravitational light bending in X-ray profile modelling

Including the effect of gravitational light bending in X-ray profile modelling