Gravitationally-bound Research Articles

The stability of core-envelope models for the Crab and the Vela pulsars

The core–envelope analytic models of Negi et al. (Class. Quantum Gravity 6:1141, 1989) have been found to be consistent with both the mechanisms of glitch generation in pulsars, namely (i) the starquake model and (ii) the vortex unpinning model. In Negi (Astrophys. Space Sci. 364:149, 2019, arXiv:2105.14324), the author has been able to reproduce the observed values of the glitch healing parameter, \(G_{h}\) (\(= I_{\mathrm{core}}/I_{\mathrm{total}}\); \(G_{h}\) represents the fractional moment of inertia of the core component in the starquake mechanism of glitch generation) for the Crab as well as for the Vela pulsar. In another study, by using the models discussed in Negi et al. (Class. Quantum Gravity 6:1141, 1989), the author has obtained the minimum value of fractional moment of inertia of the crust about 7.4% and larger for all the values of masses in the range \(1M_{\odot }\)–\(1.96M_{\odot }\) considered for the Vela pulsar (Negi in J. Eng. Sci. 11:86, 2020a, arXiv:2106.02439). The latter study of the author is found to be consistent with the recent requirement (on the basis of vortex unpinning model of the glitch generation) which reveals that the minimum fractional crustal moment of inertia of the Vela pulsar should be about 7% for a mass higher than about 1\(M_{\odot }\). However, a thorough study which requires investigation of pulsational stability and gravitational binding of the models of Negi et al. (Class. Quantum Gravity 6:1141, 1989) has not been carried out so far. The present paper deals with such a study of the models (Negi et al. in Class. Quantum Gravity 6:1141, 1989) for all permissible values of the compactness parameter \(u\) (\(\equiv M/a\), the total mass to size ratio in geometrized units) and compressibility factor \(Q\) (defined in Tolman’s VII solution as \(x = r^{2}/K^{2} = r^{2}/a^{2}Q\)). It is seen that the configurations remain pulsationally stable and gravitationally bound for all permissible values of \(u\) \((\leq 0.25)\) and \(Q\) (\(0 < Q \leq 1.2\)).

Dark matter density distributions and dark energy constraints on structure formation including MOND

In recent papers, it was shown explicitly that the sizes of gravitationally bound large-scale cosmic structures can be constrained from the requirement that their gravitational binding self-energy density should at least be equal to the background repulsive dark energy density (for them to be bound). Here, we extend this model to incorporate various dark matter density distributions in the galaxy which are consistent with observation. We also show that the constraints set using modified Newtonian dynamics (MOND) is again consistent with observations and the same as that in the Newtonian case, hence making it impossible to distinguish between the two as also pointed out recently. We also point out that the recent observations of baryon-dominated disk galaxies formed about ten billion years ago indicate the consistency of MOND with observations.

Exploring the Formation of Gravitationally Bound Objects Across the Universe

Exploring the Formation of Gravitationally Bound Objects Across the Universe

The James Clerk Maxwell telescope Legacy Survey of the Gould Belt: a molecular line study of the Ophiuchus molecular cloud

CO, $^{13}$CO and C$^{18}$O ${\it J}$ = 3--2 observations are presented of the Ophiuchus molecular cloud. The $^{13}$CO and C$^{18}$O emission is dominated by the Oph A clump, and the Oph B1, B2, C, E, F and J regions. The optically thin(ner) C$^{18}$O line is used as a column density tracer, from which the gravitational binding energy is estimated to be $4.5 \times 10^{39}$ J (2282 $M_\odot$ km$^2$ s$^{-2}$). The turbulent kinetic energy is $6.3 \times 10^{38}$ J (320 $M_\odot$ km$^2$ s$^{-2}$), or 7 times less than this, and therefore the Oph cloud as a whole is gravitationally bound. Thirty protostars were searched for high velocity gas, with eight showing outflows, and twenty more having evidence of high velocity gas along their lines-of-sight. The total outflow kinetic energy is $1.3 \times 10^{38}$ J (67 $M_\odot$ km$^2$ s$^{-2}$), corresponding to 21$\%$ of the cloud's turbulent kinetic energy. Although turbulent injection by outflows is significant, but does ${\it not}$ appear to be the dominant source of turbulence in the cloud. 105 dense molecular clumplets were identified, which had radii $\sim$ 0.01--0.05 pc, virial masses $\sim$ 0.1--12 $M_\odot$, luminosities $\sim$ 0.001--0.1 K~km s$^{-1}$ pc$^{-2}$, and excitation temperatures $\sim$ 10--50K. These are consistent with the standard GMC based size-line width relationships, showing that the scaling laws extend down to size scales of hundredths of a parsec, and to sub solar-mass condensations. There is however no compelling evidence that the majority of clumplets are undergoing free-fall collapse, nor that they are pressure confined.

Dynamics of the coronas of open star clusters

A method for distinguishing coronas in models of open star clusters is proposed. The method uses trajectories of stars that do not leave the coronas over time intervals t comparable to the mean lifetime τ of the clusters. Corona models are constructed for six numerical cluster models, and the direction and character of the dynamical evolution of the coronas are determined. Retrograde stellar motions are dominant in the coronas. In spite of some signs of dynamical instability of the coronas (small densities compared to the critical density and accelerated expansion of the coronas), the formation of close-toequilibrium density and phase-density distributions at distances from one to three cluster tidal radii from the cluster center can be seen. Approximations are constructed for the corona and cluster phase density using distributions that depend on three parameters (the parameters of the stellar motion in the Lindblad rotating coordinate system). This temporary equilibrium of the corona is due to balance in the number of starsmoving from the central areas of the cluster to the corona, and from the corona to the corona periphery or beyond. Evidence that corona stars can be gravitationally bound at distances out to four tidal radii from the cluster center is found: the presence of nearly periodic retrograde mean motions of a large number of corona stars in the Galactic plane; 91–99% of corona stars satisfy the gravitational binding criterion of Ross, Mennim and Heggie over time intervals that are close to the mean cluster lifetime. The escape rate from the corona is estimated for t ≥ τ, and found to be from 0.03 to 0.23 of the number of corona stars per violent relaxation time.

Dissecting the spin distribution of dark matter haloes

(Abridged) We apply a very general statistical theorem introduced by Cramer (1936) to study the origin of the deviations of the halo spin PDF from the reference lognormal shape. We find that these deviations originate from correlations between two quantities entering the definition of spin, namely the ratio $J/M^{5/2}$ (which depends only on mass) and the total gravitational binding energy $E$. To reach this conclusion, we have made usage of the results deduced from two high spatial- and mass resolution simulations. Our simulations cover a relatively small volume and produce a sample of more than 16.000 gravitationally bound halos, each traced by at least 300 particles. We verify that our results are stable to different systematics, by comparing our results with those derived by the GIF2 and by a more recent simulation performed by Maccio' et al. We find that the spin probability distribution function shows systematic deviations from a lognormal, at all redshifts z <= 1. These deviations depend on mass and redshift: at small masses they change little with redshift, and also the best lognormal fits are more stable. The J-M relationship is well described by a power law of exponent $\alpha$ very near to the linear theory prediction (alpha=5/3), but systematically lower than this at z<= 0.3. We argue that the fact that deviations from a lognormal PDF are present only for high-spin halos could point to a role of large-scale tidal fields in the evolution of the spin PDF.

Reaching the boundary between stellar kinematic groups and very wide binaries

<i>Aims. <i/>I investigate the gravitational binding of a nearby common proper motion system in the young Castor moving group (<i>τ<i/> ~ 200 Ma), which is formed by the bright quadruple star <i>α<i/> Lib (Zubenelgenubi) and the young solar analogue KU Lib. The system has an exceptionally wide angular separation of about 2.6 deg, which corresponds to a projected physical separation of about 1.0 pc.<i>Methods. <i/>I compiled basic information on the system, compared its binding energy with those of other weakly bound systems in the field, and studied the physical separations of resolved multiple systems in Castor.<i>Results. <i/>KU Lib has roughly the same proper motion, parallactic distance, radial velocity, and metallicity as the young hierarchical quadruple system <i>α<i/> Lib. It also displays youth features. The resemblance between these basic parameters and the relatively high estimated binding energy indicate that the five stars are gravitationally bound. KU Lib and <i>α<i/> Lib constitute the widest known multiple system in all mass domains, and probably represent the most extreme example of young wide binaries on the point of being disrupted. Besides this, I make a comprehensive compilation of star candidates in Castor, including new ones.

Kinetic and Structural Evolution of Self‐gravitating, Magnetized Clouds: 2.5‐dimensional Simulations of Decaying Turbulence

The molecular component of the Galaxy is comprised of turbulent, magnetized clouds, many of which are self-gravitating and form stars. To develop an understanding of how these clouds' kinetic and structural evolution may depend on their level of turbulence, mean magnetization, and degree of self-gravity, we perform a survey of direct numerical MHD simulations in which three parameters are independently varied. Our simulations consist of solutions to the time-dependent MHD equations on a two-dimensional grid with periodic boundary conditions; an additional half dimension is also incorporated as dependent variables in the third Cartesian direction. Two of our survey parameters, the mean magnetization parameter β≡c2sound/v2Alfven and the Jeans number nJ≡Lcloud/LJeans, allow us to model clouds that either meet or fail conditions for magneto-Jeans stability and magnetic criticality. Our third survey parameter, the sonic Mach number ≡σvelocity/csound, allows us to initiate turbulence of either sub- or super-Alfvenic amplitude; we employ an isothermal equation of state throughout. We evaluate the times for each cloud model to become gravitationally bound and measure each model's kinetic energy loss over the fluid-flow crossing time. We compare the evolution of density and magnetic field structural morphology and quantify the differences in the density contrast generated by internal stresses for models of differing mean magnetization. We find that the values of β and nJ, but not the initial Mach number , determine the time for cloud gravitational binding and collapse: for mean cloud density nH2=100 cm-3, unmagnetized models collapse after ~5 Myr, and magnetically supercritical models generally collapse after 5-10 Myr (although the smallest magneto-Jeans stable clouds survive gravitational collapse until t~15 Myr), while magnetically subcritical clouds remain uncollapsed over the entire simulations; these cloud collapse times scale with the mean density as tg∝n−½H2. We find, contrary to some previous expectations, less than a factor of 2 difference between turbulent decay times for models with varying magnetic field strength; the maximum decay time, for B~14 μG and nH2=100 cm-3, is 1.4 flow crossing times tcross=L/σvelocity (or 8 Myr for typical giant molecular cloud parameters). In all models we find turbulent amplification in the magnetic field strength up to at least the level βpert≡c2sound/δv2Alfven=0.1, with the turbulent magnetic energy between 25% and 60% of the turbulent kinetic energy after one flow crossing time. We find that for non-self-gravitating stages of evolution, when clouds have =5-10, the mass-averaged density contrast magnitudes log(ρ/) are in the range 0.2-0.5, with the contrast increasing both toward low and high β. Although our conclusions about density statistics may be affected by our isothermal assumption, we note that only the more strongly magnetized models appear to be consistent with estimates of clump/interclump density contrasts inferred in Galactic giant molecular clouds.

Dynamical model ofSU 3 for baryons based on a gravitationally bound linear rotator

A model of baryons is presented according to which each baryon consists of 3 real massive constituent particles (quarks or unitons) bound together by superstrong gravitational forces. Such strong gravitational forces arise because the free mass of each constituent particle is of the order of 1/2(ħc/G)1/2, whereG is the universal gravitational constant. Applying Lagrange’s analysis of the gravitational 3-body problem to this model, we obtain the straight-line configuration (linear rotator or gravitational string) as the only stable solution (the other solution is the equilateral triangle) that is consistent with the Pauli principle and with the observed data for the proton and neutron. This gravitational model accounts for the 3-quark saturation of baryons, since no stable gravitational configuration consisting of more than 3 particles exists. The very strong gravitational binding of the three quarks-of the order of 1019 GeV-accounts for the fact that no free quarks have been knocked out of baryons in even the most energetic scattering experiments performed thus far. With two of the bound quarks in our model in one rotational state (at the end points) and the third at the center of our linear configuration it is unnecessary to introduce para-Fermi statistics to satisfy the exclusion principle so that colored quarks are not required. If we introduce three distinct quarks p, n, λ, where n and λ have the same charge, but differ in strangeness, we obtain a total of 27 linear configurations by considering all possible triplet combinations. Only 18 of these survive as distinct however, since the interchange of the two end quarks in any one of the linear configurations gives no new configuration. We show that this group of 18 distinct configurations breaks up quite naturally into an octet and a decimet, so that a correct count of baryon states, with their correct quantum numbers, is a natural consequence of our model. Applying a straightforward first-order Bohr-type calculation to our rigid-rotator model for a nucleon, we obtain 1.02 · 10−13 cm for the nucleon radius and + 0.8 MeV for the neutron-proton mass difference, which is about e of the correct value. In the same way, assuming that both the p and n quarks haveg-factors of 1, we obtain +2.5 and −2.0 nuclear magnetons for the magnetic moments of the proton and neutron, respectively. If, however, theg-factor of the n-quark is 2 and that of the p-quark is 1, for which we present strong theoretical evidence, the two magnetic moments are +3.0 and −2.0 nuclear magnetons. We show that the matrix representation of theSU3-group for baryons can be factorized into a product of threeSU2 rotations. This leads to a natural dynamical interpretation of the baryon quantum numbers, if we assume that each of the three matrix factors represents the rotational degrees of freedom of one of the quarks in our dynamical model. In particular, we find that «strangeness» is related to the relativistic precession of the end quark in the strong gravitational field of the center quark. This conclusion is strengthened by two facts: 1) the strangeness quantum number enters into the Gell-Mann-Okubo mass formula in exactly the same way as the precession of an atom in a diatomic molecule enters into the energy level formula for the diatomic molecule, 2) the relativistic precession of the quark in our model leads us again to the quantization conditionGm2 ≈ħc.

Physical Sciences: X-rays from the Coma Cluster of Galaxies

THE Coma cluster of galaxies is usually considered to contain insufficient matter in the form of galaxies to be gravitationally bound, but the high degree of symmetry of the cluster, and the presumed age of its galaxies, suggest that the cluster is, in fact, gravitationally bound. It is possible that the missing mass takes the form of ionized intracluster gas, and Woolf1 has used radio, visible light and X-ray observations to set upper limits for the amount of such matter and, more recently, Turnrose and Rood2 have discussed the problems of heating and supporting such a gas against gravitational collapse. We present here new observational evidence of X-ray emission which limits the amount of hot intracluster gas to less than 2 % of that required for gravitational binding.