♔ Line Expansion Opacity in Relativistically Expanding Media: Spectral lines of heavy atomic elements in the ejecta of supernovae and neutron star mergers can have important contribution to the opacity of the ejecta matter even when the abundance of the elements is very small. Under favorable conditions, the line expansion opacity arising from spectral lines and the expansion of the medium can be orders of magnitude larger than the opacity of electron scattering. In this paper, we derive the formulae for evaluating the line expansion opacity and its Rosseland mean in an expanding medium in the framework of special relativity, which can be considered as a generalization of previous work in the Newtonian approximation. Then we compare the derived relativistic formulae to the Newtonian ones to explore the relativistic effect on the opacity and test the new formulae with the spectral lines of some heavy atomic elements. We also derive some approximation formulae for the Rosseland mean of the line expansion opacity that are easy to use in numerical works while still maintaining a high-enough accuracy relative to exact solutions. The formulae derived in this paper are expected to have important applications in radiative problems related to relativistic astrophysical phenomena such as neutron star mergers, supernovae, and gamma-ray bursts where relativistic or subrelativistic expansions are involved. [Astrophys. J. 887, 60 (2019)]
☠ Radioactive Gamma-Ray Emissions from Neutron Star Mergers: Gravitational waves and electromagnetic radiations from a neutron star merger were discovered on 2017 August 17. Multiband observations of the optical transient have identified brightness and spectrum features broadly consistent with theoretical predictions. According to the theoretical model, the optical radiation from a neutron star merger originates from the radioactive decay of unstable nuclides freshly synthesized in the merger ejecta. In about a day the ejecta transits from an optically thick state to an optically thin state owing to its subrelativistic expansion. Hence, we expect that about a day after the merger the gamma-ray photons produced by radioactive decays start to escape from the ejecta and make it bright in the MeV band. In this paper, we study the features of the radioactive gamma-ray emission from a neutron star merger, including the brightness and the spectrum, and discuss the observability of the gamma-ray emission. We find that more than 95% of the radiated gamma-ray energy is carried by photons of 0.2-4 MeV, with a spectrum shaped by the nucleosynthesis process and the subrelativistic expansion of the ejecta. Under favorable conditions, a prominent pair annihilation line can be present in the gamma-ray spectrum with the energy flux about 3%-5% of the total. For a merger event similar to GW170817, the gamma-ray emission attains a peak luminosity of ≈ 2 × 1041 erg s-1 at ≈ 1.2 days after the merger and fades by a factor of two in about 2 days. Such a source will be detectable by satellite-ETCC if it occurs at a distance ≲ 12 Mpc. [Astrophys. J. 872, 19 (2019)]
♫ Electromagnetic Force on a Brane: A fundamental assumption in the theory of brane world is that all matter and radiation are confined on the four-dimensional brane and only gravitons can propagate in the five-dimensional bulk spacetime. The brane world theory did not provide an explanation for the existence of electromagnetic fields and the origin of the electromagnetic field equation. In this paper, we propose a model for explaining the existence of electromagnetic fields on a brane and deriving the electromagnetic field equation. Similar to the case in Kaluza-Klein theory, we find that electromagnetic fields and the electromagnetic field equation can be derived from the five-dimensional Einstein field equation. However, the derived electromagnetic field equation differs from the Maxwell equation by containing a term with the electromagnetic potential vector coupled to the spacetime curvature tensor. So it can be considered as generalization of the Maxwell equation in a curved spacetime. The gravitational field equation on the brane is also derived with the stress-energy tensor for electromagnetic fields explicitly included and the Weyl tensor term explicitly expressed with matter fields and their derivatives in the direction of the extra-dimension. The model proposed in the paper can be regarded as unification of electromagnetic and gravitational interactions in the framework of brane world theory. [Class. Quant. Grav. 33, 225008 (2016)]
☼ A New Unified Theory of Electromagnetic and Gravitational Interactions: In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the fivedimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is obtained: ∇aFab - ξRbaAa = -4π Jb with ξ = -2, where Fab is the antisymmetric electromagnetic field tensor defined by the potential vector Aa, Rab is the Ricci curvature tensor of the hypersurface, and Ja is the electric current density vector. The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term ξRbaAa, whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge, as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. 48, 28 (2016)]. Hence, the new unified theory is physically different from Kaluza-Klein theory and its variants in which the Einstein-Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under certain conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe. [Front. Phys. 11, 110402 (2016)]
☽ Electrodynamics on Cosmological Scales: Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero net charge, Maxwell's equations always fail regardless of the spacetime symmetry and the charge distribution. The two paradoxes indicate that Maxwell's equations need be modified to be applicable to the universe as a whole. We consider two types of modified Maxwell equations, both can address the paradoxes. One is the Proca-type equation which contains a photon mass term. This type of electromagnetic field equations can naturally arise from spontaneous symmetry breaking and the Higgs mechanism in quantum field theory, where photons acquire a mass by eating massless Goldstone bosons. However, photons loose their mass again when the symmetry is restored, and the paradoxes reappear. The other type of modified Maxwell equations, which are more attractive in our opinions, contain a term with the electromagnetic field potential vector coupled to the spacetime curvature tensor. This type of electromagnetic field equations do not introduce a new dimensional parameter and return to Maxwell's equations in a flat or Ricci-flat spacetime. We show that the curvature-coupled term can naturally arise from the ambiguity in extending Maxwell's equations from a flat spacetime to a curved spacetime through the "minimal substitution rule". Some consequences of the modified Maxwell equations are investigated. The results show that for reasonable parameters the modification does not affect existing experiments and observations. However, we argue that, the field equations with a curvature-coupled term can be testable in astrophysical environments where the mass density is high or the gravity of electromagnetic radiations plays a dominant role in dynamics, e.g., the interior of neutron stars and the early universe. [Gen. Relativ. Gravit. 48, 28 (2016)]
♁ Photon Diffusion in a Relativistically Expanding Sphere: A relativistically expanding sphere exists in many explosive astrophysical systems, including gammaray bursts, neutron star mergers, and some supernovae. In this paper we investigate the photon diffusion process in a relativistically expanding sphere, which is important for understanding the energetic and radiative characters of the above mentioned explosive systems. The following contents are discussed in the frame work of special relativity: random walks of photons by scattering with electrons, photospheres, photon diffusion, and the energy flux density emerging from the surface of the expanding sphere. Some of the results are also applicable to the Universe since the Universe is also a spherical expanding system. [Front. Phys. 8, 555 (2013)]
♆ Accretion, Growth of Supermassive Black Holes, and Feedback in Galaxy Mergers: Super-Eddington accretion is very efficient in growing the mass of a black hole: in a fraction of the Eddington time its mass can grow to an arbitrary large value if the feedback effect is not taken into account. However, since super-Eddington accretion has a very low radiation efficiency, people have argued against it as a major process for the growth of the black holes in quasars since observations have constrained the average accretion efficiency of the black holes in quasars to be ≳ 0.1. In this paper, we show that the observational constraint does not need to be violated if the black holes in quasars have undergone a two-phase growing process: with a short super-Eddington accretion process they get their masses inflated by a very large factor until the feedback process becomes important, then with a prolonged sub-Eddington accretion process they have their masses increased by a factor of ≳ 2. The overall average efficiency of this two-phase process is then ≳ 0.1, and the existence of black holes of masses ∼ 109 M⊙ by redshift 6 is easily explained. An observational test of the existence of the super-Eddington accretion phase is briefly discussed. [Mon. Not. Roy. Astron. Soc. 424, 1461 (2012)]
☞ Inferring the Inclination of a Black Hole Accretion Disk from Observations of its Polarized Continuum Radiation: Spin parameters of stellar-mass black holes in X-ray binaries are currently being estimated by fitting the X-ray continuum spectra of their accretion disk emission. For this method, it is necessary to know the inclination of the X-ray-producing inner region of the disk. Since the inner disk is expected to be oriented perpendicular to the spin axis of the hole, the usual practice is to assume that the black hole spin is aligned with the orbital angular momentum vector of the binary, and to estimate the inclination of the latter from ellipsoidal modulations in the light curve of the secondary star. We show that the inclination of the disk can be inferred directly if we have both spectral and polarization information on the disk radiation. The predicted degree of polarization varies from 0% to 5% as the disk inclination changes from face-on to edge-on. With current X-ray polarimetric techniques the polarization degree of a typical bright X-ray binary could be measured to an accuracy of 0.1% by observing the source for about 10 days. Such a measurement would constrain the disk inclination to within a degree or two and would significantly improve the reliability of black hole spin estimates. In addition, it would provide new information on the tilt between the black hole spin axis and the orbital rotation axis of the binary, which would constrain any velocity kicks experienced by stellar-mass black holes during their formation. [Astrophys. J. 691, 847 (2009)]
♘ Star Formation History up to z = 7.4: Implications for Gamma-Ray Bursts and the Cosmic Metallicity Evolution: The current Swift sample of gamma-ray bursts (GRBs) with measured redshifts allows to test the assumption that GRBs trace the star formation in the Universe. Some authors have claimed that the rate of GRBs increases with cosmic redshift faster than the star formation rate, whose cause is not known yet. In this paper, I investigate the possibility for interpreting the observed discrepancy between the GRB rate history and the star formation rate history by the cosmic metallicity evolution, motivated by the observation that the cosmic metallicity evolves with redshift and GRBs prefer to occur in low metallicity galaxies. First, I derive a star formation history up to redshift z = 7.4 from an updated sample of star formation rate densities obtained by adding the new UV measurements of Bouwens et al. and the new UV and infrared measurements of Reddy et al. to the existing sample compiled by Hopkins & Beacom. Then, adopting a simple model for the relation between the GRB production and the cosmic metallicity history as proposed by Langer & Norman, I show that the observed redshift distribution of the Swift GRBs can be reproduced with a fairly good accuracy. Although the results are limited by the small size of the GRB sample and the poorly understood selection biases in detection and localization of GRBs and in redshift determination, they suggest that GRBs trace both the star formation and the metallicity evolution. If the star formation history can be accurately measured with other approaches, which is presumably achievable in the near future, it will be possible to determine the cosmic metallicity evolution with the study on th redshift distribution of GRBs. [Mon. Not. Roy. Astron. Soc. 388, 1487 (2008)]
♧ The X-Ray Transient 080109 in NGC 2770: an X-Ray Flash Associated with a Normal Core-Collapse Supernova: Although it is generally thought that long-duration gamma-ray bursts (LGRBs) are associated with core-collapse supernovae (SNe), so far only four pairs of GRBs and SNe with firmly established connection have been found. All the four GRB-SNe belong to special class of Type Ic - called the broad-lined SNe indicative of a large explosion energy, suggesting that only a small fraction of SNe Ibc have GRBs associated with them. This scheme has been refreshed by the discovery of a bright X-ray transient in NGC 2770 on 2008 January 9, which was followed by a rather normal Type Ib SN 2008D. In this paper, I argue that the transient 080109 is an X-ray flash (XRF, the soft version of a GRB) because of the following evidence. (1) The transient cannot be interpreted as a SN shock breakout event. (2) The GRB X-ray flare interpretation is not supported by the high-energy observation. I then show that XRF 080109 satisfies the well-known relation between the isotropic-equivalent energy and the peak spectral energy for LGRBs, which highly strengthens the XRF interpretation. Finally, I point out that the peak spectral energy of XRF 080109 and the maximum bolometric luminosity of SN 2008D agree with the Eγ,peak - LSN,max relationship of Li, strengthening the validity of the relationship. I speculate that events like XRF 080109 may occur at a rate comparable to SNe Ibc, and a soft X-ray telescope devoted to surveying for nearby X-ray flares will be very fruitful in discovering them. [Mon. Not. Roy. Astron. Soc. 388, 603 (2008)] Supernova Outbreak: X rays signal earliest alert
♱ Variation of the Amati Relation with the Cosmological Redshift: a Selection Effect or an Evolution Effect?: Because of the limit in the number of gamma-ray bursts (GRBs) with available redshifts and spectra, all current investigations on the correlation among GRB variables use burst samples with redshifts that span a very large range. Evolution and selection effects have thus been ignored, which might have an important influence on the results. In this Letter, we divide the 48 long-duration GRBs studied by Amati into four groups with redshift from low to high, each group containing 12 GRBs. Then we fit each group with the Amati relation log Eiso = a + b log Epeak, and check whether the parameters a and b evolve with the GRB redshift. We find that a and b vary with the mean redshift of the GRBs in each group systematically and significantly. Monte Carlo simulations show that there is only a ∼ 4 per cent chance that the variation is caused by the selection effect arising from the fluence limit. Hence our results may indicate that GRBs evolve strongly with cosmological redshift. [Mon. Not. R. Astron. Soc. 379, L55 (2007)]
♢ Shock Breakout in Type Ibc Supernovae and Application to GRB 060218/SN 2006aj: Recently, a soft blackbody component was observed in the early X-ray afterglow of GRB 060218, which was interpreted as shock breakout from the thick wind of the progenitor Wolf-Rayet (WR) star of the underlying Type Ic supernova 2006aj. In this paper, we present a simple model for computing the characteristic quantities (including energy, temperature and time duration) for the transient event from the shock breakout in Type Ibc supernovae produced by the core-collapse of WR stars surrounded by dense winds. In contrast to the case of a star without a strong wind, the shock breakout occurs in the wind region rather than inside the star, caused by the large optical depth in the wind. We find that, for the case of a WR star with a dense wind, the total energy of the radiation generated by the supernova shock breakout is larger than that in the case of the same star without a wind by a factor of >10. The temperature can be either hotter or colder, depending on the wind parameters. The time duration is larger caused by the increase in the effective radius of the star due to the presence of a thick wind. Then, we apply the model to GRB 060218/SN 2006aj. We show that, to explain both the temperature and the total energy of the blackbody component observed in GRB 060218 by the shock breakout, the progenitor WR star has to have an unrealistically large core radius (the radius at optical depth of 20), larger than 100 R⊙. In spite of this disappointing result, our model is expected to have important applications to the observations on Type Ibc supernovae in which the detection of shock breakout will provide important clues to the progenitors of Type Ibc supernovae. [Mon. Not. R. Astron. Soc. 375, 240 (2007)]
♕ Correlation between the Peak Spectral Energy of Gamma-Ray Bursts and the Peak Luminosity of the Underlying Supernovae: Implication for the Nature of GRB-SN Connection: In this paper, we present a correlation between the peak spectral energy of gamma-ray bursts (GRBs) and the peak bolometric luminosity of the underlying supernovae (SNe), based on a sample of four pairs of GRBs-SNe with a spectroscopically confirmed connection. Combining it with the well-known relation between the peak spectral energy and the isotropic equivalent energy of GRBs, we obtain an upper limit on the isotropic energy of GRBs, which is ~ 1052erg (LSN,peak/1043 erg s-1)10, where LSN,peak is the peak bolometric luminosity of the SNe. Our results suggest that the critical parameter determining the GRB-SN connection is the peak luminosity of SNe, rather than the feature of the SN spectra and/or the SN explosion energy as commonly hypothesized. Because it is generally believed that the peak luminosity of SNe powered by radioactive decays is related to the amount of 56Ni produced in the SN explosion, the mass of 56Ni may be a key physical factor for understanding the nature of GRBs and their connection with SNe. Application of our relation to Type Ibc SNe with normal peak luminosities indicates that, if those normal SNe have GRBs accompanying them, the GRBs would be extremely soft and subenergetic in gamma-rays and, hence, easier to detect with X-ray or UV detectors than with gamma-ray detectors. [Mon. Not. R. Astron. Soc. 372, 1357 (2006)]
☪ Improved Correlation between the Variability and Peak Luminosity of Gamma-ray Bursts: A new procedure for smoothing a gamma-ray burst (GRB) light curve and calculating its variability is presented. Applying the procedure to a sample of 25 long GRBs, we have obtained a very tight correlation between the variability and the peak luminosity. The only significant outlier in the sample is GRB 030329. With this outlier excluded, the data scatter is reduced by a factor of ~3 compared to that of Guidorzi et al., measured by the deviation of fit. Possible causes for the outlier are discussed. [Mon. Not. R. Astron. Soc. 366, 219 (2006)]
☮ Multi-Temperature Blackbody Spectrum of a Thin Accretion Disk around a Kerr Black Hole: Model Computations and Comparison with Observations: We use a ray-tracing technique to compute the observed spectrum of a thin accretion disk around a Kerr black hole. We include all relativistic effects such as frame-dragging, Doppler boost, gravitational redshift, and bending of light by the gravity of the black hole. We also include self-irradiation of the disk as a result of light deflection. Assuming that the disk emission is locally blackbody, we show how the observed spectrum depends on the spin of the black hole, the inclination of the disk, and the torque at the inner edge of the disk. We find that the effect of a nonzero torque on the spectrum can, to a good approximation, be absorbed into a zero-torque model by adjusting the mass accretion rate and the normalization. We describe a computer model, called KERRBB, which we have developed for fitting the spectra of black hole X-ray binaries. Using KERRBB within the X-ray data reduction package XSPEC, and assuming a spectral hardening factor fcol = 1.7, we analyze the spectra of three black hole X-ray binaries: 4U 1543-47, XTE J1550-564, and GRO J1655-40. We estimate the spin parameters of the black holes in 4U 1543-47 and GRO J1655-40 to be a/M ~ 0.6 and ~ 0.6-0.7, respectively. If fcol ~ 1.5-1.6, as in a recent study, then we find a/M ~ 0.7-0.8 and ~ 0.8-0.9, respectively. These estimates are subject to additional uncertainties in the assumed black hole masses, distances, and disk inclinations. [Astrophys. J. Suppl. 157, 335 (2005)]
☫ Quasi-periodic Oscillations from Rayleigh-Taylor and Kelvin-Helmholtz Instability at a Disk-Magnetosphere Interface: We consider the interface between an accretion disk and a magnetosphere surrounding the accreting mass. We argue that such an interface can occur not only with a magnetized neutron star but also sometimes with an unmagnetized neutron star or a black hole. The gas at the magnetospheric interface is generally Rayleigh-Taylor unstable and may also be Kelvin-Helmholtz unstable. Because of these instabilities, modes with low azimuthal wavenumbers m are expected to grow to large amplitude. It is proposed that the resulting nonaxisymmetric structures contribute to the high-frequency quasi-periodic oscillations that have been seen in neutron star and black hole X-ray binaries. The mode oscillation frequencies are calculated to be approximately equal to mΩm, where Ωm is the angular velocity of the accreting gas at the magnetospheric radius. Thus, mode frequencies should often be in the approximate ratio 1:2:3, etc. If the pressure of the gas in the disk is not large, then the m=1 mode will be stable. In this case, the mode frequencies should be in the approximate ratio 2:3, etc. There is some observational evidence for such simple frequency ratios. [Astrophys.J. 601, 414 (2004)]
☥ Gravitational Lensing by a Compound Population of Halos: Standard Models: Based on observed rotation curves of galaxies and theoretical simulations of dark matter halos, there are reasons for believing that at least three different types of dark matter halos exist in the universe classified by their masses M and the inner slope of mass density -α: population A (galaxies): 1010h-1M⊙≲M≲2×1013h-1M⊙, α~2 population B (cluster halos): M≳2×1013h-1M⊙, α~1.3 and population C (dwarf halos): M≲1010h-1M⊙, α~1.3. In this paper we calculate the lensing probability produced by such a compound population of dark halos for both image separation and time delay, assuming that the mass function of halos is given by the Press-Schechter function and the universe is described by a cold dark matter (CDM) LCDM, OCDM, or SCDM model. The LCDM model is normalized to the Wilkinson Microwave Anisotropy Probe observations; OCDM and SCDM models are normalized to the abundance of rich clusters. We compare the predictions of the different cosmological models with observational data and show that both LCDM and OCDM models are marginally consistent with the current available data, but the SCDM model is ruled out. The fit of the compound model to the observed correlation between splitting angle and time delay is excellent, but the fit to the number versus splitting angle relation is only adequate using the small number of sources in the objective Jodrell-VLA Astrometric Survey/Cosmic Lens All-Sky Survey. A larger survey of the same type would have great power in discriminating among cosmological models. Furthermore, population C in a LCDM model has a unique signature in the time domain, an additional peak at ~3 s potentially observable in GRBs, which makes it distinguishable from variants of CDM scenarios, such as warm dark matter, repulsive dark matter, or collisional dark matter. For image separations greater than 10 arcsec the differently normalized LCDM models predict significantly different lensing probabilities, affording an additional lever to break the degeneracies in the CMB determination of cosmological parameters. [Astrophys. J. 595, 603 (2003)]
☤ Nonaxisymmetric g-Mode and p-Mode Instability in a Hydrodynamic Thin Accretion Disk: It has been suggested that quasi-periodic oscillations of accreting X-ray sources may relate to the modes named in the title. We consider nonaxisymmetric linear perturbations to an isentropic, isothermal, unmagnetized thin accretion disk. The radial wave equation, in which the number of vertical nodes (n) appears as a separation constant, admits a wave action current that is conserved except, in some cases, at corotation. Waves without vertical nodes amplify when reflected by a barrier near corotation. Their action is conserved. As was previously known, this amplification allows the n=0 modes to be unstable under appropriate boundary conditions. In contrast, we find that waves with n>0 are strongly absorbed at corotation rather than amplified; their action is not conserved. Therefore, nonaxisymmetric p-modes and g-modes with n>0 are damped and stable even in an inviscid disk. This eliminates a promising explanation for quasi-periodic oscillations in neutron star and black hole X-ray binaries. [Astrophys.J. 593, 980 (2003)]
☡ The Giant X-Ray Flare of NGC 5905: Tidal Disruption of a Star, a Brown Dwarf, or a Planet?: We model the 1990 giant X-ray flare of the quiescent galaxy NGC 5905 as the tidal disruption of a star by a supermassive black hole. From the observed rapid decline of the luminosity, over a timescale of a few years, we argue that the flare was powered by the fallback of debris rather than subsequent accretion via a thin disk. The fallback model allows constraints to be set on the black hole mass and the mass of debris. The latter must be very much less than a solar mass to explain the very low luminosity of the flare. The observations can be explained either as the partial stripping of the outer layers of a low-mass main-sequence star or as the disruption of a brown dwarf or a giant planet. We find that the X-ray emission in the flare must have originated within a small patch rather than over the entire torus of circularized material surrounding the black hole. We suggest that the patch corresponds to the ``bright spot'' where the stream of returning debris impacts the torus. Interestingly, although the peak luminosity of the flare was highly sub-Eddington, the peak flux from the bright spot was close to the Eddington limit. We speculate on the implications of this result for observations of other flare events. [Astrophys. J. 576, 753 (2002)]
☧ Accretion Disk Torqued by a Black Hole: If a Kerr black hole is connected to a disk rotating around it by a magnetic field, the rotational energy of the Kerr black hole provides an energy source for the radiation of the disk in addition to disk accretion. The black hole exerts a torque on the disk, which transfers energy and angular momentum between the black hole and the disk. If the black hole rotates faster than the disk, energy and angular momentum are extracted from the black hole and transferred to the disk. The energy deposited into the disk is eventually radiated away by the disk, which will increase the efficiency of the disk. If the black hole rotates slower than the disk, energy and angular momentum are transferred from the disk to the black hole, which will lower the efficiency of the disk. With suitable boundary conditions, quasi-steady state solutions are obtained for a thin Keplerian disk magnetically coupled to a Kerr black hole. By "quasi-steady state" we mean that any macroscopic quantity at a given radius in the disk slowly changes with time: the integrated change within one rotation period of the disk is much smaller than the quantity itself. We find that the torque produced by magnetic coupling propagates outward only in the disk, and the total radiation flux of the disk is a superposition of the radiation flux produced by magnetic coupling and that produced by accretion. Interestingly, a disk magnetically coupled to a rapidly rotating black hole can radiate without accretion: the total power of the disk comes from the rotational energy of the black hole. With a simple example that the magnetic field touches the disk at a single radius, we show that the radial radiation profile produced by magnetic coupling can be very different from that of a standard accretion disk: the emissivity index is significantly larger, and most radiation can come from a region that is closer to the center of the disk. While the shape of the radiation flux curve sensitively depends on the extension of the magnetic field in the disk, the spectral signature of magnetic coupling can be robust. The limitations of our model are briefly discussed, which include the assumption of a weak magnetic field, the ignorance of the instabilities of the disk and the magnetic field, and the ignorance of the radiation captured by the black hole and the radiation returning to the disk. [Astrophys. J. 567, 463 (2002)]
☣ Semi-Analytical Models for Lensing by Dark Halos: I. Splitting Angles: We use the semianalytical approach to analyze gravitational lensing of remote quasars by foreground dark halos in various cold dark matter (CDM) cosmologies in order to determine the sensitivity of the predictions for probabilities of image separations to the input assumptions regarding the properties of halos and cosmological models. The power spectrum of primordial fluctuations is normalized by the cluster abundance constraints. The mass function of dark halos is assumed to be given by the Press-Schechter function. The mass density profile of dark halos is alternatively taken to be the singular isothermal sphere (SIS), the Navarro-Frenk-White (NFW) profile, or the generalized NFW profile. The cosmologies being considered include the Einstein-de Sitter model (SCDM), the open model (OCDM), and the flat Λ-model (LCDM). As expected, we find that the lensing probability is extremely sensitive to the mass density profile of lenses (dark halos) and somewhat less so to the mean mass density in the universe and the amplitude of primordial fluctuations. NFW halos are very much less effective in producing multiple images than SIS halos. For NFW lenses, the SCDM model produces fewer lensing events than the OCDM/LCDM models by 2 orders of magnitude. For SIS lenses, the SCDM model produces more lensing events with small splitting angles and fewer lensing events with large splitting angles than the OCDM/LCDM models, which is due to the fact that for large-mass halos, the Press-Schechter function is very sensitive to the amplitude of primordial fluctuations. In all cases the difference between the OCDM model and the LCDM model is not dramatic. None of these models are consistent with current observations: the SIS models predict too many large splitting lenses, while the NFW models predict too few small splitting lenses. Essentially, the observed high ratio of small splitting to large splitting lenses is not predicted correctly. This indicates that there must be at least two populations of halos in the universe: small-mass halos with a steep inner density slope and large-mass halos with a shallow inner density slope. A combination of SIS and NFW halos can reasonably reproduce the current observations if we choose the mass for the transition from SIS to NFW to be ~1013 M⊙, as might plausibly occur because of baryonic cooling and contraction in lower mass systems. Additionally, there is a tendency for CDM models to have too much power on small scales, i.e., too much mass concentration. From our sensitivity studies it appears that the cures proposed for other apparent difficulties of CDM would help here as well, an example being the warm dark matter variant, which is shown to produce fewer large splitting lenses than the corresponding CDM model by 1 order of magnitude. [Astrophys. J. 566, 652 (2002)]
☍ Two Open Universes Connected by a Wormhole: Exact Solutions: In this paper, I present a space-time of two open universes connected by a Lorentzian wormhole. The space-time has the following features: (1) it can exactly solve the Einstein equations; (2) the weak energy condition is satisfied everywhere; (3) it has a topology of R2×Tg (g≥2) (4) it has no event horizons. [J. Geom. Phys. 40, 154 (2001)] Heavenly twins
♃ Making Clean Energy with a Kerr Black Hole: a Tokamak Model for Gamma-Ray Bursts: In this paper we present a model for making clean energy with a Kerr black hole. Consider a Kerr black hole with a dense plasma torus spinning around it. A toroidal electric current flows on the surface of the torus, which generates a poloidal magnetic field outside the torus. On the surface of the torus the magnetic field is parallel to the surface. The closed magnetic field lines winding around the torus compress and confine the plasma in the torus, as in the case of tokamaks. Although it is unclear whether such a model is stable, we look into the consequences if the model is stable. If the magnetic field is strong enough, the baryonic contamination from the plasma in the torus is greatly suppressed by the magnetic confinement, and a clean magnetosphere of electron-positron pairs is built up around the black hole. Since there are no open magnetic field lines threading the torus and no accretion, the power of the torus is zero. If some magnetic field lines threading the black hole are open and connect with loads, clean energy can be extracted from the Kerr black hole by the Blandford-Znajek mechanism. The model may be relevant to gamma-ray bursts. The energy in the Poynting flux produced by the Blandford-Znajek mechanism is converted into the kinetic energy of the electron-positron pairs in the magnetosphere around the black hole, which generates two oppositely directed jets of electron-positron pairs with superhigh bulk Lorentz factors. The jets collide and interact with the interstellar medium, which may produce gamma-ray bursts and the afterglows. [Astrophys. J. 544, 375 (2000)]
☿ Extracting Energy from Accretion into a Kerr Black Hole: The highest efficiency of converting rest mass into energy by accreting matter into a Kerr black hole is ~31% (Thorne 1974). We propose a new process in which periods of accretion from a thin disk, and the associated spin-up of the black hole, alternate with the periods of no accretion and magnetic transfer of energy from the black hole to the disk. These cycles can repeat indefinitely, at least in principle, with the black hole mass increasing by ~66% per cycle and up to ~43% of accreted rest mass radiated away by the disk. [Astrophys. J. 534, L197 (2000)] Cosmic Powerhouses
♅ Extracting Energy from a Black Hole through Its Disk: When some magnetic field lines connect a Kerr black hole with a disk rotating around it, energy and angular momentum are transferred between them. If the black hole rotates faster than the disk, ca/GMH>0.36 for a thin Keplerian disk, then energy and angular momentum are extracted from the black hole and transferred to the disk (MH is the mass and aMH is the angular momentum of the black hole). This way, the energy originating in the black hole may be radiated away by the disk. The total amount of energy that can be extracted from the black hole spun down from ca/GMH=0.998 to ca/GMH=0.36 by a thin Keplerian disk is ~0.15MHc2. This is larger than ~0.09MHc2, which can be extracted by the Blandford-Znajek mechanism. [Astrophys. J. 533, L115 (2000)]
♇ Time Machines Constructed from Anti-de Sitter Space: In this paper time machines are constructed from anti-de Sitter space. One is constructed by identifying points related via boost transformations in the covering space of anti-de Sitter space and it is shown that this Misner-like anti-de Sitter space is just the Lorentzian section of the complex space constructed by Li, Xu, and Liu [Phys. Rev. D 48, 4735 (1993)]. The others are constructed by gluing an anti-de Sitter space to a de Sitter space, which could describe an anti-de Sitter phase bubble living in a de Sitter phase universe. Self-consistent vacua for a massless conformally coupled scalar field are found for these time machines, whose renormalized stress-energy tensors are finite and solve the semiclassical Einstein equations. The extensions to electromagnetic fields and massless neutrinos are discussed. It is argued that, in order to make the results consistent with Euclidean quantization, a new renormalization procedure for quantum fields in Misner-type spaces (Misner space, Misner-like de Sitter space, and Misner-like anti-de Sitter space) is required. Such a ``self-consistent'' renormalization procedure is proposed. With this renormalization procedure, self-consistent vacua exist for massless conformally coupled scalar fields, electromagnetic fields, and massless neutrinos in these Misner-type spaces. [Phys. Rev. D 59, 084016 (1999)]
☀ Transient Events from Neutron Star Mergers: Mergers of neutron stars (NS + NS) or neutron stars and stellar-mass black holes (NS + BH) eject a small fraction of matter with a subrelativistic velocity. Upon rapid decompression, nuclear-density medium condenses into neutron-rich nuclei, most of them radioactive. Radioactivity provides a long-term heat source for the expanding envelope. A brief transient has a peak luminosity in the supernova range, and the bulk of radiation in the UV-optical domain. We present a very crude model of the phenomenon, and simple analytical formulae that can be used to estimate the parameters of a transient as a function of poorly known input parameters. The mergers may be detected with high-redshift supernova searches as rapid transients, many of them far away from the parent galaxies. It is possible that the mysterious optical transients detected by Schmidt et al. are related to neutron star mergers, since they typically have no visible host galaxy. [Astrophys. J. 507, L59 (1998)] Spotlight: From theory prediction to bold observatory, Chinese researchers help usher in new era in astrophysics
☎ Can the Universe Create Itself?: The question of first-cause has troubled philosophers and cosmologists alike. Now that it is apparent that our universe began in a big bang explosion, the question of what happened before the big bang arises. Inflation seems like a very promising answer, but as Borde and Vilenkin have shown, the inflationary state preceding the big bang could not have been infinite in duration-it must have had a beginning also. Where did it come from? Ultimately, the difficult question seems to be how to make something out of nothing. This paper explores the idea that this is the wrong question-that that is not how the Universe got here. Instead, we explore the idea of whether there is anything in the laws of physics that would prevent the Universe from creating itself. Because spacetimes can be curved and multiply connected, general relativity allows for the possibility of closed timelike curves (CTCs). Thus, tracing backwards in time through the original inflationary state we may eventually encounter a region of CTCs-giving no first-cause. This region of CTCs may well be over by now (being bounded toward the future by a Cauchy horizon). We illustrate that such models-with CTCs-are not necessarily inconsistent by demonstrating self-consistent vacuums for Misner space and a multiply connected de Sitter space in which the renormalized energy-momentum tensor does not diverge as one approaches the Cauchy horizon and solves Einstein's equations. Some specific scenarios (out of many possible ones) for this type of model are described. For example, a metastable vacuum inflates producing an infinite number of (big-bang-type) bubble universes. In many of these, either by natural causes or by action of advanced civilizations, a number of bubbles of metastable vacuum are created at late times by high energy events. These bubbles will usually collapse and form black holes, but occasionally one will tunnel to create an expanding metastable vacuum (a baby universe) on the other side of the black hole's Einstein-Rosen bridge as proposed by Farhi, Guth, and Guven. One of the expanding metastable-vacuum baby universes produced in this way simply turns out to be the original inflating metastable vacuum we began with. We show that a Universe with CTCs can be stable against vacuum polarization. And it can be classically stable and self-consistent if and only if the potentials in this Universe are retarded-which gives a natural explanation of the arrow of time in our universe. Interestingly, the laws of physics may allow the Universe to be its own mother. [Phys. Rev. D 58, 023501 (1998)] In the beginning - It's hard to grasp, but the Universe may have made itself Where Does the Time Go? Forward, Physics Shows All Spaced Out by Henry M. Morris A self-creating universe? - McCabism Before the Big Bang 6: Can the Universe Create Itself?
☊ Self-Consistent Vacuum for Misner Space and the Chronology Protection Conjecture: In this paper we find a self-consistent vacuum for Misner space. For this ``adapted'' Rindler vacuum the renormalized stress-energy tensor is zero throughout the Misner space (except on the Cauchy horizon itself, a set of measure zero on which it remains formally ill-defined). A pointlike particle detector traveling on a timelike geodesic in a Misner space with this vacuum detects nothing, but a time traveler may pose a danger to himself and to the space-time. [Phys. Rev. Lett. 80, 2980 (1998)] All Spaced Out by Henry M. Morris
☂ Effect of the Global Rotation of the Universe on the Formation of Galaxies: The effect of the global rotation of the universe on the formation of galaxies is investigated. It is found that the global rotation provides a natural origin for the rotation of galaxies, and the morphology of the objects formed from gravitational instability in a rotating and expanding universe depends on the amplitude of the density fluctuation, different values of the amplitude of the fluctuation lead to the formation of elliptical galaxies, spiral galaxies, and walls. The global rotation gives a natural explanation of the empirical relation between the angular momentum and mass of galaxies: J ∝ M5/3. The present angular velocity of the universe is estimated at ~10-13rad yr-1. [Gen. Relativ. Gravit. 30, 497 (1998)]
☃ Must Time Machines Be Unstable against Vacuum Fluctuations?: In the appearance of an absorption material, the quantum vacuum fluctuations of all kinds of fields may be smoothed out and the spacetime with time machines may be stable against vacuum fluctuations. The chronology protection conjecture may break down and the anti-chronology protection conjecture may hold: there is no law of physics preventing the appearance of closed timelike curves. [Class. Quant. Grav. 13, 2563 (1996)]
⅋ New Light on Time Machines: Against the Chronology Protection Conjecture: I construct a spacetime with closed timelike curves and without closed causal geodesics. There is a noncompactly generated Cauchy horizon separating the region with closed timelike curves from that without closed causal curves. This spacetime might be stable against the vacuum fluctuation of matter fields. Whether such a spacetime is stable against the vacuum fluctuation of a gravitational field is an open question. [Phys. Rev. D. 50, R6037 (1994)] Time travel: it's all done with smoke and mirrors
☯ Complex Geometry, Quantum Tunneling, and Time Machines: A space with a complex metric permitted by quantum cosmology is given; two regions, one containing no closed causal curve and one containing closed timelike curves, are separated by a complex region. Through quantum tunneling one can travel from one region to the other. The vacuum polarization stress-energy tensor converges everywhere so the space is stable. This challenges Hawking's chronology protection conjecture and highlights on building a time machine. [Phys. Rev. D. 48, 4735 (1993)]
Back to Li-Xin Li's Web Page