Ultracompact Stars Research Articles

Ultra compact stars: reconstructing the perturbation potential

In this work we demonstrate how different semi-classical methods can be combined in a novel way to reconstruct the perturbation potential of ultra compact stars. Besides rather general assumptions, the only specific information entering this approach is the spectrum of the trapped axial quasi-normal modes. In general it is not possible to find a unique solution for the potential in the inverse problem, but instead a family of potentials producing the same spectrum. Nevertheless, this already determines important properties of the involved potential and can be used to rule out many candidate models. A unique solution was found based on the additional natural assumption that the exterior part () is described by the Regge–Wheeler potential. This is true in general relativity for any non-rotating spherically symmetric object. This technique can be potentially applied for the study of deviations from general relativity. The methods we demonstrate are easy to implement and rather general, therefore we expect them also to be interesting for other fields where inverse spectrum problems are studied, e.g. quantum physics and molecular spectroscopy.

A semi-analytic study of axial perturbations of ultra compact stars

Compact object perturbations, at linear order, often lead in solving one or more coupled wave equations. The study of these equations was typically done by numerical or semi-analytical methods. The WKB method and the associated Bohr–Sommerfeld rule have proved extremely useful tools in the study of black-hole perturbations and the estimation of the related quasi-normal modes. Here we present an extension of the aforementioned semi-analytic methods in the study of perturbations of ultra-compact stars and gravastars.

Gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale

Gravitational waves from binary coalescences provide one of the cleanest signatures of the nature of compact objects. It has been recently argued that the post-merger ringdown waveform of exotic ultracompact objects is initially identical to that of a black-hole, and that putative corrections at the horizon scale will appear as secondary pulses after the main burst of radiation. Here we extend this analysis in three important directions: (i) we show that this result applies to a large class of exotic compact objects with a photon sphere for generic orbits in the test-particle limit; (ii) we investigate the late-time ringdown in more detail, showing that it is universally characterized by a modulated and distorted train of "echoes" of the modes of vibration associated with the photon sphere; (iii) we study for the first time equal-mass, head-on collisions of two ultracompact boson stars and compare their gravitational-wave signal to that produced by a pair of black-holes. If the initial objects are compact enough as to mimic a binary black-hole collision up to the merger, the final object exceeds the maximum mass for boson stars and collapses to a black-hole. This suggests that - in some configurations - the coalescence of compact boson stars might be almost indistinguishable from that of black-holes. On the other hand, generic configurations display peculiar signatures that can be searched for in gravitational-wave data as smoking guns of exotic compact objects.

Slowly decaying waves on spherically symmetric spacetimes and ultracompact neutron stars

We prove that, in a class of spherically symmetric spacetimes exhibiting stable trapping of null geodesics, linear waves cannot (uniformly) decay faster than logarithmically. When these linear waves are treated as a model for nonlinear perturbations, this slow decay is highly suggestive of nonlinear instability. We also prove that, in a large class of asymptotically flat, spherically symmetric spacetimes, logarithmic decay actually holds as a uniform upper bound. In the presence of stable trapping, this result is therefore the best one can obtain. In addition, we provide an application of these results to ultracompact neutron stars, suggesting that all stars with might be unstable.

The OmegaWhite survey for short-period variable stars – I. Overview and first results

We present the goals, strategy and first results of the OmegaWhite survey: a wide-field high-cadence $g$-band synoptic survey which aims to unveil the Galactic population of short-period variable stars (with periods $<$ 80 min), including ultracompact binary star systems and stellar pulsators. The ultimate goal of OmegaWhite is to cover 400 square degrees along the Galactic Plane reaching a depth of $g = $ 21.5 mag (10$\sigma$), using OmegaCam on the VLT Survey Telescope (VST). The fields are selected to overlap with surveys such as the Galactic Bulge Survey (GBS) and the VST Photometric H$\alpha$ Survey of the Southern Galactic Plane (VPHAS+) for multi-band colour information. Each field is observed using 38 exposures of 39 s each, with a median cadence of $\sim$2.7 min for a total duration of two hours. Within an initial 26 square degrees, we have extracted the light curves of 1.6 million stars, and have identified 613 variable candidates which satisfy our selection criteria. Furthermore, we present the light curves and statistical properties of 20 sources which have the highest-likelihood of being variable stars. One of these candidates exhibits the colours and light curve properties typically associated with ultracompact AM CVn binaries, although its spectrum exhibits weak Balmer absorption lines and is thus not likely to be such a binary system. We also present follow-up spectroscopy of five other variable candidates, which identifies them as likely low-amplitude $\delta$ Sct pulsating stars.

Evidence for event horizons: Long-lived modes in ultracompact objects

Gravitational compact astrophysical objects are excellent laboratories to test the strong field regime of theories of gravity. Among these compact objects, lies the ultracompact class: stellar structures that possess a light ring (circular null geodesic). Such ultracompact stars were presented in literature in the earlier solutions of general relativity, and some are claimed to be good candidates to the supermassive objects present at the center of galaxies. In this paper, we present evidences for the claim that compact objects with a light ring should be black holes, based on the existence of long-lived modes obtained through a first-order perturbation theory. These first-order long-lived modes can source nonlinear terms which could turn the star unstable. We show, in particular, a comparison between modes computed through an exact direct integration and through the WKB approximation. Moreover, we present the time evolution of wavepackets for different field configurations. We conjecture some possible outcomes of the nonlinear instability. The discussion presented in this work complements our previous paper [Phys. Rev. D90 (2014) 044069].

Light rings as observational evidence for event horizons: Long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects

Ultracompact objects are self-gravitating systems with a light ring. It was recently suggested that fluctuations in the background of these objects are extremely long-lived and might turn unstable at the nonlinear level, if the object is not endowed with a horizon. If correct, this result has important consequences: objects with a light ring are black holes. In other words, the nonlinear instability of ultracompact stars would provide a strong argument in favor of the "black hole hypothesis," once electromagnetic or gravitational-wave observations confirm the existence of light rings. Here we explore in some depth the mode structure of ultracompact stars, in particular constant-density stars and gravastars. We show that the existence of very long-lived modes -- localized near a second, stable null geodesic -- is a generic feature of gravitational perturbations of such configurations. Already at the linear level, such modes become unstable if the object rotates sufficiently fast to develop an ergoregion. Finally, we conjecture that the long-lived modes become unstable under fragmentation via a Dyson-Chandrasekhar-Fermi mechanism at the nonlinear level. Depending on the structure of the star, it is also possible that nonlinearities lead to the formation of small black holes close to the stable light ring. Our results suggest that the mere observation of a light ring is a strong evidence for the existence of black holes.

Some electrically charged relativistic stellar models in general relativity

Some new families of electrically charged stellar models of ultra-compact star have been studied. With the help of particular form of one of the metric potentials the Einstein–Maxwell field equations in general relativity have been transformed to a system of ordinary differential equations. The interior matter pressure, energy–density, and the adiabatic sound speed are expressed in terms of simple algebraic functions. The constant parameters involved in the solution have been set so that certain physical criteria satisfied. Based on the analytic model developed in the present work, the values of the relevant physical quantities have been calculated by assuming the estimated masses and radii of some well known potential strange star candidates like X-ray pulsar Her X-1, millisecond X-ray pulsar SAX J 1808.4-3658, and 4U 1820-30. The analytical equations of state of the charged matter distribution may play a significant role in the study of the internal structure of highly compact charged stellar objects in general relativity.

General relativity passes a new test

Observers search near ultracompact stars for departures from the standard theory of gravity.

TWO POPULATIONS OF MOLECULAR CLOUDS IN THE ANTENNAE GALAXIES

Super star clusters --- extremely massive clusters found predominately in starburst environments --- are essential building blocks in the formation of galaxies and thought to dominate star formation in the high-redshift universe. However, the transformation from molecular gas into these ultra-compact star clusters is not well understood. To study this process, we used the Submillimeter Array and the Plateau de Bure Interferometer to obtain high angular resolution (~1.5" or 160 pc) images of the Antennae overlap region in CO(2--1) to search for the molecular progenitors of the super star clusters. We resolve the molecular gas distribution into a large number of clouds, extending the differential cloud mass function down to a 5\sigma completeness limit of 3.8x10^5 M_sun. We identify a distinct break in the mass function around log M_mol/M_sun ~ 6.5, which separates the molecular clouds into two distinct populations. The smaller, less massive clouds reside in more quiescent areas in the region, while the larger, more massive clouds cluster around regions of intense star formation. A broken power-law fit to the mass function yields slopes of \alpha = -1.39+/-0.10 and \alpha = -1.44+/-0.14 for the low- and high-mass cloud population, well-matched to the mass function found for super star clusters in the Antennae galaxies. We find large velocity gradients and velocity dispersions at the locations of intense star formation, suggestive of compressive shocks. It is likely that these environmental factors contribute to the formation of the observed massive molecular clouds and super star clusters in the Antennae galaxies.

CLOSE BINARY PROGENITORS OF HYPERNOVAE

In this paper we propose a new plausible mechanism of supernova explosions specific to close binary systems. The starting point is the common envelope phase in the evolution of a binary consisting of a red super giant and a neutron star. As the neutron star spirals towards the center of its companion it spins up via disk accretion. Depending on the specific angular momentum of gas captured by the neutron star via the Bondi-Hoyle mechanism, it may reach millisecond periods either when it is still inside the common envelope or after it has merged with the companion core. The high accretion rate may result in strong differential rotation of the neutron star and generation of a magnetar-strength magnetic field. The magnetar wind can blow away the common envelope if its magnetic field is as strong as 1015 G, and can destroy the entire companion if it is as strong as 1016 G. The total explosion energy can be comparable to the rotational energy of a millisecond pulsar and reach 1052 erg. The result is an unusual type-II supernova with very high luminosity during the plateau phase, followed by a sharp drop in brightness and a steep light-curve tail. The remnant is either a solitary magnetar or a close binary involving a Wolf-Rayet star and a magnetar. When this Wolf-Rayet star explodes this will be a third supernovae explosion in the same binary. A particularly interesting version of the binary progenitor involves merger of a red super giant star with an ultra-compact companion, neutron star or black hole. In the case if a strong magnetic field is not generated on the surface of a neutron star then it will collapse to a black hole. After that we expect the formation of a very long-lived accretion disk around the black hole. The Blandford-Znajek driven jet from this black hole may drive not only hypernovae explosion but produce a bright X-ray transient event on a time scale of 104 s.

Close binary progenitors of gamma-ray bursts

The strong dependence of the neutrino annihilation mechanism on the mass accretion rate makes it difficult to explain the LGRBs with duration in excess of 100 seconds as well as the precursors separated from the main gamma-ray pulse by few hundreds of seconds. Even more difficult is to explain the Swift observations of the shallow decay phase and X-ray flares, if they indeed indicate activity of the central engine for as long as 10,000 seconds. These data suggest that some other, most likely magnetic mechanisms have to be considered. The magnetic models do not require the development of accretion disk within the first few seconds of the stellar collapse and hence do not require very rapidly rotating stellar cores at the pre-supernova state. This widens the range of potential LGRB progenitors. In this paper, we re-examine the close binary scenario allowing for the possibility of late development of accretion disks in the collapsar model and investigate the available range of mass accretion rates, black hole masses, and spins. A particularly interesting version of the binary progenitor involves merger of a WR star with an ultra-compact companion, neutron star or black hole. In this case we expect the formation of very long-lived accretion disks, that may explain the phase of shallow decay and X-ray flares observed by Swift. Similarly long-lived magnetic central engines are expected in the current single star models of LGRB progenitors due to their assumed exceptionally fast rotation.

Off-equatorial orbits in strong gravitational fields near compact objects

Near a black hole or an ultracompact star, the motion of particles is governed by a strong gravitational field. Electrically charged particles also feel the electromagnetic force arising due to currents inside the star or plasma circling around. We study the possibility that the interplay between gravitational and electromagnetic actions may allow for the stable, energetically bound off-equatorial motion of charged particles. This would represent the well-known generalized Störmer's ‘halo orbits’, which have been discussed in connection with the motion of dust grains in planetary magnetospheres. We demonstrate that such orbits exist and can be astrophysically relevant when a compact star or a black hole is endowed with a dipole-type magnetic field. In the case of the Kerr–Newman solution, numerical analysis shows that the mutually connected gravitational and electromagnetic fields do not allow the existence of stable halo orbits above the outer horizon of black holes. Such orbits are either hidden under the inner black-hole horizon, or they require the presence of a naked singularity.

Constraints on Neutron Star Properties from X‐Ray Observations of Millisecond Pulsars

We present a model of thermal X-ray emission from hot spots on the surface of a rotating compact star with an unmagnetized light-element atmosphere. An application to ROSAT, Chandra, and XMMNewton X-ray observations of the nearest known rotation-powered millisecond pulsar (MSP) PSR J0437–4715 reveals that the thermal emission from this pulsar is fully consistent with such a model, enabling constraints on important properties of the underlying neutron star. We confirm that the observed thermal X-ray pulsations from J0437–4715 are incompatible with blackbody emission and require the presence of an optically thick, light element (most likely hydrogen) atmosphere on the neutron star surface. The morphology of the X-ray pulse profile is consistent with a global dipole configuration of the pulsar magnetic field but suggests an off-center magnetic axis, with a displacement of 0.8 −3 km from the stellar center. For an assumed mass of 1.4 M⊙, the model restricts the allowed stellar radii to R = 6.8 − 13.8 km (90% confidence) and R > 6.7 km (99.9% confidence), which is consistent with standard NS equations of state and rules out an ultracompact star smaller than its photon sphere. Deeper spectroscopic and timing observations of this and other nearby radio MSPs with current and future X-ray facilities (Constellation-X and XEUS) can provide further insight into the fundamental properties of neutron stars. Subject headings: pulsars: general — pulsars: individual (PSR J0437–4715) — stars: neutron — X-rays: stars — gravitation — relativity

On the role of strong gravity in polarization from scattering of light in relativistic flows

We study linear polarization due to scattering of light on a cloudlet of particles, taking into account the radiation drag and the gravitational pull exerted on them by a central body. Effects of special and general relativity are included by connecting a model of Beloborodov (1998) for the local polarization of scattered light with Abramowicz, Ellis & Lanza (1990) formalism for the particle motion near an ultra-compact star. Compactness of the central body and its luminosity are two critical parameters of the model. We discuss the polarization magnitude of photons, which are Thomson-scattered into direct and higher-order images. Importance of the latter is only moderate under typical conditions, but they may give rise to distinct features, which we explore in terms of a toy model. The scattered signal exhibits variations of intensity and of polarization with mutual time-lags depending on the beaming/focusing effects and the light travel time.

Gravitational waves from a spinning particle scattered by a relativistic star: Axial mode case

We study gravitational waves from a spinning test particle scattered by a relativistic star using a perturbation method. The present analysis is restricted to axial modes. By calculating the energy spectrum, the waveforms and the total energy and angular momentum of gravitational waves, we analyze the dependence of the emitted gravitational waves on a particle spin. For a normal neutron star, the energy spectrum has one broad peak whose characteristic frequency corresponds to the angular velocity at the turning point (a periastron). Since the turning point is determined by the orbital parameter, there exists the dependence of the gravitational wave on a particle spin. We find that the total energy of $l = 2$ gravitational waves gets larger as the spin increases in the anti-parallel direction to the orbital angular momentum. For an ultracompact star, in addition to such an orbital contribution, we find the quasi-normal modes exited by a scattered particle, whose excitation rate to gravitational waves depends on the particle spin. We also discuss the ratio of the total angular momentum to the total energy of gravitational waves and explain its spin dependence.

Ultracompact X-Ray Binaries in Globular Clusters: Variability of the Optical Counterpart of X1832-330 in NGC 6652.

Evidence is emerging that the luminous X-ray sources in the cores of globular clusters may often consist of, or perhaps even as a class be dominated by, ultracompact (P less, similar1 hr) binary stars. To the two such systems already known, in NGC 6624 and NGC 6712, we now add evidence for two more. We detect large-amplitude variability in the candidate optical counterpart for the X-ray source in the core of NGC 6652. Although the available observations are relatively brief, the existing Hubble Space Telescope data indicate a strong 43.6 minute periodic modulation of the visible flux of semiamplitude 30%. Further, although the orbital period of the source in NGC 1851 is not yet explicitly measured, we demonstrate that previous correlations of optical luminosity with X-ray luminosity and accretion disk size, strengthened by recent data, strongly imply that the period of that system is also less than 1 hr. Thus, currently there is evidence that four of the seven globular cluster X-ray sources with constrained periods are ultracompact, a fraction far greater than that found in X-ray binaries the field.

Gravitational waves from a test particle scattered by a neutron star: Axial mode case

Using a metric perturbation method, we study gravitational waves from a test particle scattered by a spherically symmetric relativistic star. We calculate the energy spectrum and the waveform of gravitational waves for axial modes. Since metric perturbations in axial modes do not couple to the matter fluid of the star, emitted waves for a normal neutron star show only one peak in the spectrum, which corresponds to the orbital frequency at the turning point, where the gravitational field is strongest. However, for an ultracompact star (the radius $R\ensuremath{\lesssim}3M),$ another type of resonant periodic peak appears in the spectrum. This is just because of an excitation by a scattered particle of axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This excitation comes from the existence of the potential minimum inside of a star. We also find for an ultracompact star many small periodic peaks at the frequency region beyond the maximum of the potential, which would be due to a resonance of two waves reflected by two potential barriers (Regge-Wheeler type and one at the center of the star). Such resonant peaks appear neither for a normal neutron star nor for a Schwarzschild black hole. Consequently, even if we analyze the energy spectrum of gravitational waves only for axial modes, it would be possible to distinguish between an ultracompact star and a normal neutron star (or a Schwarzschild black hole).

General solution for a relativistic star

In a spherically symmetric spacetime we find the general solution for a relativistic star in hydrostatic equilibrium having the spheroidal geometry for the 3-space embedded in 4-Euclidean space. The parameter is the measure of spheroidal character and determines the physical properties of the star. It has a lower bound ; stars with smaller mass to radius ratio can occur for all allowed while ultracompact stars, having ratios between 1/3 and 1/2, will have . It turns out that a wide range of values of can represent objects with the fluid density of a neutron star. The model is shown to possess all the desirable physical features.

Ergoregion instability revisited -- a new and general method for numerical analysis of stability

Ergoregion instability of rapidly rotating relativistic stars found by Friedman is investigated numerically by developing a totally different formulation from the one presented by Comins & Schutz. Our new scheme can provide solutions even for modes of small azimuthal number m, which Comins & Schutz could not precisely investigate because of their use of the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation. For several models with stronger gravity and more rapid rotation than those investigated by Comins & Schutz, we have shown that e-folding times for lower modes are sufficiently short compared with the age of the universe. Although the new method is applied here to a one-dimensional problem which is devised to mimic the ergoregion instability in two-dimensional space by Comins & Schutz, there is no obstacle to extending the analysis to the original problems in two dimensions. Moreover our scheme seems suitable for the mode analysis of rapidly rotating and highly deformed systems. Since we have made our formulation as general as possible, we have applied our new method to the analysis of axial modes of the non-rotating ultracompact stars investigated by Chandrasekhar & Ferrari and Kokkotas. Our results agree well with those of both groups.