Gravitational Binding Energy Research Articles

A Possible Trace Carbon Dioxide Polar Cap on Iapetus

We model ballistic transport of CO2 on the surface of Iapetus, accounting for gravitational binding energy and polar cold traps. We find that if CO2 is in the form of ice, it has a long enough residence time to be spectroscopically detected. We determine that at midlatitudes, CO2 is volatile, will rapidly ablate, and be sequestered in a polar cold trap. In addition, we find that due to the inclination of Iapetus's orbit, the poles provide only a temporary cold trap, requiring the CO2 to move to the opposite pole at the end of the winter season. During each transit, 5% of the CO2 will reach escape velocity and be lost from the system. Finally, we make a prediction of the latitudinal extent and thickness of a possible CO2 polar cap that could be detected during Cassini's 2007 September flyby of Iapetus.

Self-renormalization of the classical quasilocal energy

Pointlike objects cause many of the divergences that afflict physical theories. For instance, the gravitational binding energy of a point particle in Newtonian mechanics is infinite. In general relativity, the analog of a point particle is a black hole and the notion of binding energy must be replaced by quasilocal energy (QLE). The QLE derived by York, and elaborated by Brown and York, is finite outside the horizon but it was not considered how to evaluate it inside the horizon. We present a prescription for finding the QLE inside a horizon, and show that it is finite at the singularity for a variety of types of black holes. The energy is typically concentrated just inside the horizon, not at the central singularity.

Instabilities in rotating relativistic stars driven by viscosity

We investigate the instability driven by viscosity in rotating relativistic stars by means of an iterative approach. We focus on polytropic rotating equilibrium stars and impose an m=2 perturbation in the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study these factors on the critical value T/W for the instability. For a rigidly rotating star, the criterion T/W, where T is the rotational kinetic energy and W the gravitational binding energy, mainly depends on the compactness of the star and takes values around 0.13–0.16, which slightly differ from that of Newtonian incompressible stars (∼0.14). For differentially rotating stars, the critical value of T/W is found to span the range 0.17–0.25. The value is significantly larger than in the rigidly rotating case with the same compactness of the star. Finally we discuss the possibility of detecting gravitational waves from viscosity-driven instabilities using ground-based interferometers.

The strong equivalence principle from a gravitational gauge structure

Gravitational self-interactions are assumed to be determined by the covariant derivative acting on the Riemann–Christoffel field strength. Once imposed on a metric theory, this Yang–Mills gauge constraint extends the equality of gravitational mass and inertial mass to compact bodies with non-negligible gravitational binding energy. Applied to generalized Brans–Dicke theories, it singles out Einstein's tensor theory and Nordström scalar theory for gravity but also suggests a way to implement a minimal violation of the strong equivalence principle.

New Distant Companions to Known Nearby Stars. II. Faint Companions ofHipparcosStars and the Frequency of Wide Binary Systems

We perform a search for faint, common proper motion companions of Hipparcos stars using the recently published LSPM-north catalog of stars with proper motion mu>0.15 arcsec/yr. Our survey uncovers a total of 521 systems with angular separations 3 arcsec 15.0. Our census is statistically complete for secondaries with angular separations 20 arcsec 1,000 AU. We observe that the distribution in orbital separations is consistent with Opik's law f(s) ds ~ s^{-1} ds only up to separation s \approx 3,000 AU, beyond which it follows a more steeply decreasing power law f(s) ds ~ s^{-l} ds with l=1.6+/-0.1. We also find that the luminosity function of the secondaries is significantly different from that of the single stars field population, showing a relative deficiency in low-luminosity (8<M_V<14) objects. The observed trends suggest either a formation mechanism biased against low-mass companions, or a disruption over time of systems with low gravitational binding energy.

Ultraluminous X‐Ray Sources Powered by Radiatively Efficient Two‐Phase Super‐Eddington Accretion onto Stellar‐Mass Black Holes

A hard power-law component dominates the radiation spectra of many of the brightest ultraluminous X-ray sources (ULXs). Therefore, a hot, optically thin corona likely powers the emission by Comptonizing seed photons emitted by a cooler, optically thick accretion disk. Before its dissipation and conversion into coronal radiation, the randomized gravitational binding energy responsible for powering ULXs must separate from the mass of its origin by a means quicker than electron-scattering-mediated radiative diffusion. Therefore, the accretion power released in ULXs is not necessarily subject to photon trapping, as long as it occurs in a corona. Motivated by these considerations, we present a model of ULXs powered by geometrically thin accretion onto stellar-mass black holes. In the innermost region of the disk, where the majority of the binding energy is released, an adjacent corona covering the entire disk surface Comptonizes the cool thermal radiation. The intense photoionizing flux and subsequent high ionization level produces an albedo near unity for X-ray photons. Therefore, the amount of reprocessed emission in this region is small relative to the non-thermal output. If dissipation takes place within an optically thin corona, Compton drag and the wind's low optical depth hamper the driving of a wind. If the magnetic field geometry of the corona is primarily closed, then fields of modest strength can, in principle, prevent the launching of a wind. In the outer region, the albedo is lower, and the surface area is larger. Therefore, the disk emits lower temperature thermal radiation resulting from both viscous dissipation within the body of the disk and reprocessed coronal power. Thus, this model qualitatively reproduces the main features of most highly luminous ULX spectra.

Viscosity driven instability in rotating relativistic stars

We investigate the viscosity driven instability in rotating relativistic stars by means of an iterative approach. We focus on polytropic rotating equilibrium stars and impose an m=2 perturbationin the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study those effects on the value of the threshold. For a uniformly rotating star, the criterion T/W, where T is the rotational kinetic energy and W is the gravitational binding energy, mainly depends on the compactness of the star and takes values around 0.13 ~ 0.16, which differ slightly from that of Newtonian incompressible stars (~ 0.14). For differentially rotating stars, the critical value of T/W is found to span the range 0.17 - 0.25. This is significantly larger than the uniformly rotating case with the same compactness of the star. Finally we discuss a possibility of detecting gravitational waves from viscosity driven instability with ground-based interferometers.

Technical Report: The Fastest Relativistic Jets from Quasars and Active Galactic Nuclei

Among the major advances in astronomy over the past several decades has been the realization that supermassive black holes (up to of order 109 solar masses) are a ubiquitous feature at the centers of bright galaxies [1], including the center of our own Milky Way. Material from the host galaxy that is drawn close to the central supermassive black hole can form a rotating accretion disk around the central object. This infalling matter can liberate large amounts of gravitational binding energy as radiation, causing the hot accretion disk and surrounding gas to far outshine the host galaxy, and forming an object known as a quasar, or, at lower luminosity, an active galactic nucleus (AGN). Quasars are predominantly seen at large cosmological distances, and therefore at remote times in the past, presumably before they have exhausted the reserves of fuel surrounding the central black hole and become quiescent. Since quasars were first detected in 1963 [2], they have fascinated astronomers with their enormous energy outputs, far in excess of any other known type of object. These energy outputs allow them to be seen out to vast distances (out to redshifts greater than 6, corresponding to light travel times exceeding 12 billion years [3]).

Dynamical bar instability in a relativistic rotational core collapse

We investigate the rotational core collapse of a rapidly rotating relativistic star by means of a 3+1 hydrodynamical simulations in conformally flat spacetime of general relativity. We concentrate our investigation to the bounce of the rotational core collapse, since potentially most of the gravitational waves from it are radiated around the core bounce. The dynamics of the star is started from a differentially rotating equilibrium star of T/W ~ 0.16 (T is the rotational kinetic energy and W is the gravitational binding energy of the equilibrium star), depleting the pressure to initiate the collapse and to exceed the threshold of dynamical bar instability. Our finding is that the collapsing star potentially forms a bar when the star has a toroidal structure due to the redistribution of the angular momentum at the core bounce. On the other hand, the collapsing star weakly forms a bar when the star has a spheroidal structure. We also find that the bar structure of the star is destroyed when the torus is destroyed in the rotational core collapse. Since the collapse of a toroidal star potentially forms a bar, it can be a promising source of gravitational waves which will be detected in advanced LIGO.

The Neutrino Bubble Instability: A Mechanism for Generating Pulsar Kicks

An explanation for the large random velocities of pulsars is presented. Like many other models, we propose that the momentum imparted to the star is given at birth. The ultimate source of energy is provided by the intense optically thick neutrino flux that is responsible for radiating the proto-neutron star's gravitational binding energy during the Kelvin-Helmholtz phase. The central feature of the kick mechanism is a radiative-driven magnetoacoustic instability, which we refer to as ``neutrino bubbles.'' Identical in nature to the photon bubble instability, the neutrino bubble instability requires the presence of an equilibrium radiative flux as well as a coherent steady background magnetic field. Over regions of large magnetic flux densities, the neutrino bubble instability is allowed to grow on dynamical timescales ~ 1ms, potentially leading to large luminosity enhancements and density fluctuations. Local luminosity enhancements, which preferentially occur over regions of strong magnetic field, lead to a net global asymmetry in the neutrino emission and the young neutron star is propelled in the direction opposite to these regions. For favorable values of magnetic field structure, size, and strength as well as neutrino bubble saturation amplitude, momentum kicks in excess of 1000 km/s can be achieved. Since the neutrino-powered kick is delivered over the duration of the Kelvin-Helmholtz time ~ a few seconds, one expects spin-kick alignment from this neutrino bubble powered model.

The Effect of Neutron Star Gravitational Binding Energy on Gravitational Radiation–driven Mass‐Transfer Binaries

In a relativistic model of a neutron star, the star's mass is less than the mass of the individual component baryons, because the star's negative binding energy makes a contribution to the star's total energy and its mass. A consequence of this relativistic mass deficit is that a neutron star that is accreting matter increases its mass at a rate that is slower than the mass of a baryon times the rate that baryons are accreted. This difference in the rate of change of the masses has a simple relation with the star's gravitational redshift. We show that this effect has the potential to be observed in binaries where the mass transfer is driven by angular momentum losses from the gravitational radiation emitted by the binary motion, if the physics of the donor star is understood well enough.

Evolution of dwarf-elliptical galaxies

Here we present as an extension to already published models of massive spherical galaxies one-dimensional chemo-dynamical models of dwarf elliptical galaxies in the mass range between 109 and 1010 and initial density fluctuation of 1σ and 3σ. Because of their vanishing angular momentum the models are restricted to spherical symmetry. Due to this limitation the dynamics of the different components consider only radial motions and also their interaction processes have only one degree of freedom. Therefore, the galaxy evolution is preferably determined by radial oscillatory phenomena caused by heating and cooling of the interstellar gas, which reenforce effects like starbursts. Nevertheless, the low gravitational binding energy of dwarf ellipticals can easily be exceeded by thermal and turbulent energy production in the interstellar medium, leading to gas expansion and even to galactic winds. Furthermore, gas phases as well as gas and stars can decouple dynamically during the galactic evolution. For comparison with observational signatures like stellar kinematics, radial densities and metallicity distributions of the different components, the chemo-dynamical treatment of galaxy evolution must take the multi-phase character of the interstellar medium and self-regulation of star formation at low gravitation into account. Since non-rotating low-mass galaxies with stochastic star-formation episodes are seen as dwarf ellipticals, the aim of this paper is to compare the 1d chemo-dynamical models with observed characteristics of this type of dwarf galaxies. Several features like stellar populations from separate formation episodes, low metallicities, significant mass loss, etc. can be reproduced by the models in a global manner. Quantitative disagreements between model predictions and observations provide insight into necessary improvements of subsequent chemo-dynamical models implying rotation, dark matter halos, and external effects by an intergalactic gas, like its pressure, gas infall and stripping of galactic gas. The results can be summarized as follows: 109 models are characterised by a single star-formation event during the initial collapse with an active self-regulation leading to reexpansion and massive gas loss as well as remaining at very low metallicities; 1010 dwarf elliptical models become almost gas-free due to large initial star formation and a strong galactic wind. These as well as a and 3σ model experience oscillatory but non-negligible later star-formation histories that can account for the observed intermediate-age stellar populations.

A new white dwarf constraint on the rate of change of the gravitational constant

In this paper we derive a bound on the rate of change of the gravitational constant G based on observations of the pulsating white dwarf G117-B15A. This star is a ZZ Ceti pulsator which has been extensively studied with astroseismological techniques for the last three decades. The most recent determination of for the 215.2-s fundamental mode agrees very well with predictions of the best-fitting theoretical model. The rate of change of the oscillation period can be explained by two effects: the cooling (dominant factor) and change of gravitational binding energy (residual gravitational contraction). Since the white dwarfs are pulsating in g-modes, the frequencies of which are related to the Brunt–Väisälä frequency (explicitly dependent on G), observational determination of the change of the period (more precisely the difference between the observed and calculated ) can be used to set an upper bound on the rate of change of G. In light of the current data concerning G117-B15A we derive the following bound: . We also demonstrate that a varying gravitational constant G does not modify the cooling of white dwarfs in a significant way, at least at the luminosities where white dwarfs are pulsationally unstable.

The physics of type Ia supernovae

The basic recipe for SN Ia explosions is simple. A white dwarf in a binary system, growing towards the limiting Chandrasekhar mass, contracts and ignites under degenerate (electron gas) conditions, causing a thermonuclear runaway. Burning 1.4 M ⊙ of 12C and 16O in equal proportions to 1.398776 M ⊙ of 56Ni releases the mass difference in nuclear binding energy, i.e., a thermonuclear explosion of about about 2.19×10 51 erg, which disrupts the original white dwarf completely. The subtraction of the gravitational binding energy of the white dwarf of (≈(5–6)×10 50 erg), plus the observed fact that not all material is burned to Fe/Ni (rather to intermediate elements like Mg, Si, S, Ca), leads to the observed explosion energies (≈1.3×10 51 erg). The decay chain 56Ni → 56Co → 56Fe can explain the lightcurve. The remaining questions are: how can cool and stable white dwarfs be turned into exploding objects via binary mass exchange; what variety of original white dwarf sizes, metallicities and accretion scenarios is expected; how does the ignition occur and does the burning front propagate; how does this relate to burning conditions, energy generation, nucleosynthesis results, 56Ni masses and the small observed variety in explosive events; how can observed spectra (and their Doppler broadening) act as diagnostics for explosion models and nucleosynthesis predictions? We will address these issues within existing 1D spherically symmetric models with parameterized burning front prescriptions and attempt to discuss the relation to multi-D models.

Viscosity and Rotation in Core‐Collapse Supernovae

We construct models of core-collapse supernovae in one spatial dimension, including rotation, angular momentum transport, and viscous dissipation employing an alpha-prescription. We compare the evolution of a fiducial 11 M_sun non-rotating progenitor with its evolution including a wide range of imposed initial rotation profiles (1.25<P_0<8 s, where P_0 is the initial, approximately solid-body, rotation period of the iron core). This range of P_0 covers the region of parameter space from where rotation begins to modify the dynamics (P_0~8 s) to where angular velocities at collapse approach Keplerian (P_0~1 s). Assuming strict angular momentum conservation, all models in this range leave behind neutron stars with spin periods <10 ms, shorter than those of most radio pulsars, but similar to those expected theoretically for magnetars at birth. A fraction of the gravitational binding energy of collapse is stored in the free energy of differential rotation. This energy source may be tapped by viscous processes, providing a mechanism for energy deposition that is not strongly coupled to the mass accretion rate through the stalled supernova shock. This effect yields qualitatively new dynamics in models of supernovae. We explore several potential mechanisms for viscosity in the core-collapse environment: neutrino viscosity, turbulent viscosity caused by the magnetorotational instability (MRI), and turbulent viscosity by entropy- and composition-gradient-driven convection. We argue that the MRI is the most effective. We find that for rotation periods in the range P_0<~5 s, and a range of viscous stresses, that the post-bounce dynamics is significantly effected by the inclusion of this extra energy deposition mechanism; in several cases we obtain strong supernova explosions.

Magnetic braking in differentially rotating, relativistic stars

We study the magnetic braking and viscous damping of differential rotation in incompressible, uniform density stars in general relativity. Differentially rotating stars can support significantly more mass in equilibrium than nonrotating or uniformly rotating stars. The remnant of a binary neutron star merger or supernova core collapse may produce such a "hypermassive" neutron star. Although a hypermassive neutron star may be stable on a dynamical timescale, magnetic braking and viscous damping of differential rotation will ultimately alter the equilibrium structure, possibly leading to delayed catastrophic collapse. Here we consider the slow-rotation, weak-magnetic field limit in which E_rot << E_mag << W, where E_rot is the rotational kinetic energy, E_mag is the magnetic energy, and W is the gravitational binding energy of the star. We assume the system to be axisymmetric and solve the MHD equations in both Newtonian gravitation and general relativity. Toroidal magnetic fields are generated whenever the angular velocity varies along the initial poloidal field lines. We find that the toroidal fields and angular velocities oscillate independently along each poloidal field line, which enables us to transform the original 2+1 equations into 1+1 form and solve them along each field line independently. The incoherent oscillations on different field lines stir up turbulent-like motion in tens of Alfven timescales ("phase mixing"). In the presence of viscosity, the stars eventually are driven to uniform rotation, with the energy contained in the initial differential rotation going into heat. Our evolution calculations serve as qualitative guides and benchmarks for future, more realistic MHD simulations in full 3+1 general relativity.

Carbon‐Oxygen White Dwarf Accreting CO‐Rich Matter. II. Self‐Regulating Accretion Process up to the Explosive Stage

We investigate the effect of rotation on the evolution of double-degenerate white dwarf systems, which are possible progenitors of Type Ia supernovae. We assume that prior to merging, the two white dwarfs rotate synchronously at the orbital frequency and that in the merger process, the lighter white dwarf is transformed into a thick disk from which the more massive white dwarf initially accretes at a very high rate (~10-5 M☉ yr-1). Because of the lifting effect of rotation, the accreting white dwarf expands until the gravitational acceleration and centripetal acceleration required for binding at the surface become equal, initiating a Roche instability. The white dwarf continues to accrete matter from the disk, but at a rate that is determined by the balance between two competing processes operating in outer layers: (1) heating, expansion, and spin-up due to accretion and (2) cooling and contraction due to thermal diffusion. The balance produces an accretion rate such that the angular velocity of the white dwarf ωWD and the break-up angular velocity ωcr remain equal. Because of the deposition of angular momentum by accreted matter and the contraction of the accreting star, ωWD increases continuously until the rotational energy reaches about 14% of the gravitational binding energy; then, another instability sets in: the structure is forced to adopt an elliptical shape and emit gravitational waves. Thereafter, a balance between the rate of deposition of angular momentum by accreted matter and the rate of loss of angular momentum by gravitational waves produces a nearly constant or plateau accretion rate of ~4 × 10-7 M☉ yr-1. The mass of the accreting white dwarf can increase up to and beyond the Chandresekhar mass limit for nonrotating white dwarfs before carbon ignition occurs. Independent of the initial value of the accretion rate, the physical conditions suitable for carbon ignition are achieved at the center of the accreting white dwarf and, because of the high electron degeneracy, the final outcome is an event of SN Ia proportions. Our results apply to merged binary white dwarf systems which, at the onset of explosive carbon ignition, have a total mass in the range 1.4-1.5 M☉.

Testing the Equivalence Principle with laser ranging to the Moon

Equality of the rate of acceleration of Earth and Moon by the Sun is confirmed to 5×10 −13 using laser ranging data. This experiment not only matched those in the laboratory in showing composition-independence of gravity's acceleration, but it also has become the tightest constraint on general relativity's 1/c 2 order, non-linear structure which couples the Sun's accelerating gravity to the Earth's internal gravitational binding energy. But the ability of LLR data to test theory at even higher levels of precision is restrained by presence of systematic range residual signals from unmodeled physics. This suggests the need for a new priority and approach — redesigning the data-fitting hypotheses for mapping out the unmolded signal, whatever its source, rather than simply trying to fit for a pre-defined relativity signal. Initial work in this direction is described. The goal is model improvement and the ability to measure gravity theory signals closer to the inherent noise limits of the data, being in this case a factor 4 or 5 smaller than the present ‘realistic uncertainties’ allowed for incomplete modeling.

Galaxies and the magnetization of intergalactic space

There is increasing evidence that widespread magnetic fields in the intergalactic medium (IGM) originate in galaxies. Up to now the field strengths have been easiest to estimate where the ambient intergalactic (i.g.) nonrelativistic gas density is highest, i.e., in galaxy clusters, the gravitational “sinks” of large scale matter flows. Intracluster gas densities reach 10−3–10−2 cm−3, and magnetic field strength estimates range from 1 to 40 μG. For much of the intracluster volume the plasma β∼1, a consequence of the intracluster magnetic field measurements, and x-ray-determined densities and temperatures of the thermal intracluster (ic) gas. While these ic gas densities represent an impressively good vacuum by terrestrial standards, they are still about 1000× more than in the general IGM. The logical next question is: Are there significant magnetic fields in the wider IGM beyond clusters? Recent, preliminary estimates in i.g. zones beyond, but not far from clusters are 10−6–10−7 G. Integrating this field strength over a typical intergalaxy separation volume gives an average magnetic energy density within the “walls and filaments” of intergalactic space of ∼10−15 B−6.5 ergs cm−3. Interestingly, for Big∼3×10−7 G, and plausible values of nig∼5×10−6 cm−3, and Tig∼108 K—the intergalactic plasma β may be within a factor 10 of unity, roughly comparable to β within the ∼103 times denser medium in galaxy clusters. It is now widely accepted that the only plausible energy source for these intergalactic fields is gravitational, e.g., not the aggregate thermonuclear energy from stars. Two sufficiently large gravitational energy reservoirs are (1) the kinetic energy from large scale intergalactic matter flows, and (2) the gravitational binding energy of supermassive black holes that have been found to be nearly ubiquitous in the nuclei of medium-to-large galaxies. This paper focuses mostly on (2), and also discusses why the largest radio sources are the best independent calibrators, and calorimeters of magnetic energy release into i.g. space from individual galaxy systems.

Clustered Star Formation in W75 N

We present 2 to 7 resolution 3 mm continuum and CO(J=1-0) line emission and near infrared Ks, H2, and [FeII] images toward the massive star forming region W75 N. The CO emission uncovers a complex morphology of multiple, overlapping outflows. A total flow mass of greater than 255 Msun extends 3 pc from end-to-end and is being driven by at least four late to early-B protostars. More than 10% of the molecular cloud has been accelerated to high velocities by the molecular flows (> 5.2 km/s relative to v{LSR}) and the mechanical energy in the outflowing gas is roughly half the gravitational binding energy of the cloud. The W75 N cluster members represent a range of evolutionary stages, from stars with no apparent circumstellar material to deeply embedded protostars that are actively powering massive outflows. Nine cores of millimeter-wavelength emission highlight the locations of embedded protostars in W75 N. The total mass of gas & dust associated with the millimeter cores ranges from 340 Msun to 11 Msun. The infrared reflection nebula and shocked H2 emission have multiple peaks and extensions which, again, suggests the presence of several outflows. Diffuse H2 emission extends about 0.6 parsecs beyond the outer boundaries of the CO emission while the [FeII] emission is only detected close to the protostars. The infrared line emission morphology suggests that only slow, non-dissociative J-type shocks exist throughout the pc-scale outflows. Fast, dissociative shocks, common in jet-driven low-mass outflows, are absent in W75 N. Thus, the energetics of the outflows from the late to early B protostars in W75 N differ from their low-mass counterparts -- they do not appear to be simply scaled-up versions of low-mass outflows.