Non-thermal Component Research Articles

TOWARD A BETTER UNDERSTANDING OF THE GRB PHENOMENON: A NEW MODEL FOR GRB PROMPT EMISSION AND ITS EFFECTS ON THE NEW LiNT–Epeak,irest,NTRELATION

We reanalyze the prompt emission of two of the brightest Fermi GRBs (080916C and 090926A) with a new model composed of 3 components: (i) a thermal-like component--approximated with a black body (BB)--interpreted as the jet photosphere emission of a magnetized relativistic outflow, (ii) a non-thermal component--approximated with a Band function--interpreted as synchrotron radiation in an optically thin region above the photosphere either from internal shocks or magnetic field dissipation, and (iii) an extra power law (PL) extending from low to high energies likely of inverse Compton origin, even though it remains challenging. Through fine-time spectroscopy down to the 100 ms time scale, we follow the smooth evolution of the various components. From this analysis the Band function is globally the most intense component, although the additional PL can overpower the others in sharp time structures. The Band function and the BB component are the most intense at early times and globally fade across the burst duration. The additional PL is the most intense component at late time and may be correlated with the extended high-energy emission observed thousands of seconds after the burst with the Fermi/Large Area Telescope (LAT). Unexpectedly, this analysis also shows that the additional PL may be present from the very beginning of the burst. We investigate the effect of the three components on the new time-resolved luminosity-hardness relation in both the observer and rest frames and show that a strong correlation exists between the flux of the non-thermal component and its E$_{peak}$ only when the three components are fitted simultaneously to the data (i.e., F$_i^{NT}$-E$_{peak,i}^{NT}$ relation). In addition, this result points toward a universal relation between those two quantities for all GRBs when transposed to the central engine rest frame (i.e., L$_i^{NT}$-E$_{peak,i}^{rest,NT}$ relation).

THE INFLUENCE OF MERGERS ON SCATTER AND EVOLUTION IN SUNYAEV–ZEL’DOVICH EFFECT SCALING RELATIONS

The Sunyaev-Zel'dovich effect (SZE) observable-mass (Y-M) scaling relation is a promising technique for obtaining mass estimates for large samples of galaxy clusters and holds a key to studying the nature of dark matter and dark energy. However, cosmological inference based on SZE cluster surveys is limited by our incomplete knowledge of bias, scatter, and evolution in the Y-M relation. In this work, we investigate the effects of galaxy cluster mergers on the scaling relation using the Omega500 high-resolution cosmological hydrodynamic simulation. We show that the non-thermal pressure associated with merger-induced gas motions contributes significantly to the bias, scatter, and evolution of the scaling relation. After the merger, the kinetic energy of merging systems is slowly converted into thermal energy through dissipation of turbulent gas motions, which causes the thermal SZE signal to increase steadily with time. This post-merger evolution is one of the primary source of bias and scatter in the Y-M relation. However, we show that when the missing non-thermal energy is accounted for, the resulting relation exhibits little to no redshift evolution and the scatter around the scaling relation is ~20-30 % smaller than that of the thermal SZE signal alone. Our work opens up a possibility to further improve the current robust mass proxy, Y, by accounting for the missing non-thermal pressure component. We discuss future prospect of measuring internal gas motions in galaxy clusters and its implication for cluster-based cosmological tests.

X-ray softening during the 2008 outburst of XTE J1810-189

XTE J1810-189 underwent an outburst in 2008, and was observed over $\sim 100$ d by RXTE. Performing a time-resolved spectral analysis on the photospheric radius expansion burst detected on 2008 May 4, we obtain the source distance in the range of 3.5--8.7 kpc for the first time. During its outburst, XTE J1810-189 did not enter into the high/soft state, and both the soft and hard colours decreased with decreasing flux. The fractional rms remained at high values ($\sim 30$ per cent). The RXTE/PCA spectra for 3-25 keV can be described by an absorbed power-law component with an additional Gaussian component, and the derived photon index $\Gamma$ increased from $1.84\pm0.01$ to $2.25\pm0.04$ when the unabsorbed X-ray luminosity in 3-25 keV dropped from $4\times10^{36}$ ergs s$^{-1}$ to $6\times10^{35}$ ergs s$^{-1}$. The relatively high flux, dense observations and broadband spectra allow us to provide strong evidence that the softening behaviour detected in the outburst of XTE J1810-189 originates from the evolution of non-thermal component rather than the thermal component (i.e. neutron star surface emission).

Analysis of optical scattering losses in vertical-external-cavity surface-emitting lasers

We report on an analysis of optical surface-scattering losses in vertical-external-cavity surface-emitting lasers. In this study, a laser chip with enhanced surface roughness compared with a high-quality chip is employed in order to allow for investigation of a scattering loss component described in theoretical considerations. A simple model for the extraction of the laser chip’s thermal resistance from experimental input–output characteristics based on thermal roll-over is expanded with respect to a non-thermal component of losses. Thereby, we demonstrate good agreement of experimental data with theoretical modeling when taking into account a power loss component proportional to an optical surface-scattering-loss coefficient in relation to photon out-coupling rates.

Anisotropy of the extragalactic radio background from dark matter annihilation

Observations of the extragalactic radio background have uncovered a significant isotropic emission across multiple frequencies spanning from 22 MHz to 10 GHz. The intensity of this non-thermal emission component significantly exceeds the expected contribution from known astrophysical sources. Interestingly, models have indicated that the annihilation of dark matter particles may reproduce both the flux and spectrum of the excess. However, the lack of a measurable anisotropy in the residual emission remains challenging for both dark matter and standard astrophysical interpretations of the ARCADE-2 data. We calculate the expected synchrotron anisotropy from dark matter annihilation and show that these models can produce very small anisotropies, though this requires galaxy clusters to have large substructure contributions and strong magnetic fields. We show that this constraint can be significantly relaxed, however, in scenarios where electrons produced via dark matter annihilation can be efficiently reaccelerated by Alfv\'en waves in the intra-Cluster medium. Our analysis indicates that any source capable of explaining the intensity and isotropy of the extragalactic radio excess must have a spatial extension far larger than typical for baryons in galaxies, suggesting a novel physics interpretation.

Investigating variability of quiescent neutron stars in the globular clusters NGC 6440 and Terzan 5

The quiescent spectrum of neutron star low-mass X-ray binaries typically consists of two components - a thermal component associated with emission from the neutron star surface, and a non-thermal power-law component whose origin is not well understood. Spectral fitting of neutron star atmosphere models to the thermal component is one of the leading methods for measuring the neutron star radius. However, it has been known for years that the X-ray spectra of quiescent neutron stars vary between observations. While most quiescent variability is explained through a variable power-law component, the brightest and best-studied object, Cen X-4, requires a change in the thermal component and such thermal variability could be a problem for measuring neutron star radii. In this paper, we significantly increase the number of sources whose quiescent spectra have been studied for variability. We examine 9 potential quiescent neutron stars with luminosities <1E34 erg/s over the course of multiple Chandra observations of the globular clusters NGC 6440 and Terzan 5 and find no strong evidence for variability in the effective temperature in 7 of the 9 sources. Two sources show a potential change in temperature, though this depends on the exact model fitted. CX1 in NGC 6440 is equally well fit by a variable thermal component or a variable power law. Therefore, the results are inconclusive and we cannot exclude or require thermal variability in that source. CX5 in NGC 6440 shows a potential change in temperature, though this depends on whether a power-law is included in the spectral fit or not. This suggests that thermal variability may not be widespread among quiescent neutron stars with luminosities < 1E34 erg/s, and hence thermal radiation remains a promising means to constraining neutron star radii.

A radio and X-ray study of the merging cluster A2319

A2319 is a massive, merging galaxy cluster with a previously detected radio halo that roughly follows the X-ray emitting gas. We present the results from recent observations of A2319 at ∼20 cm with the Karl G. Jansky Very Large Array and a re-analysis of the X-ray observations from XMM–Newton, to investigate the interactions between the thermal and non-thermal components of the intracluster medium. We confirm previous reports of an X-ray cold front, and identify a distinct core to the radio halo, ∼800 kpc in extent, that is strikingly similar in morphology to the X-ray emission, and drops sharply in brightness at the cold front. We also detect radio emission trailing off from the core that blends smoothly into the ∼2 Mpc halo detected with the Green Bank Telescope (GBT). We speculate on the possible mechanisms for such a two-component radio halo, with sloshing playing a dominant role in the core. By directly comparing the X-ray and radio emission, we find that a hadronic origin for the cosmic ray electrons responsible for the radio halo would require a magnetic field and/or cosmic ray proton distribution that increases with radial distance from the cluster centre, and is therefore disfavoured.

SUPERMODEL ANALYSIS OF A1246 AND J255: ON THE EVOLUTION OF GALAXY CLUSTERS FROM HIGH TO LOW ENTROPY STATES

We present an analysis of high-quality X-ray data out to the virial radius for the two galaxy clusters Abell 1246 and GMBCG J255.34805+64.23661 (J255) by means of our entropy-based SuperModel. For Abell 1246 we find that the spherically-averaged entropy profile of the intracluster medium (ICM) progressively flattens outwards, and that a nonthermal pressure component amounting to ~20% of the total is required to support hydrostatic equilibrium in the outskirts; there we also estimate a modest value C~1.6 of the ICM clumping factor. These findings agree with previous analyses on other cool-core, relaxed clusters, and lend further support to the picture by Lapi et al. (2010) that relates the entropy flattening, the development of nonthermal pressure component, and the azimuthal variation of ICM properties to weakening boundary shocks. In this scenario clusters are born in a high-entropy state throughout, and are expected to develop on similar timescales a low entropy state both at the center due to cooling, and in the outskirts due to weakening shocks. However, the analysis of J255 testifies how such a typical evolutionary course can be interrupted or even reversed by merging especially at intermediate redshift, as predicted by Cavaliere et al. (2011b). In fact, a merger has rejuvenated the ICM of this cluster at z~0.45 by reestablishing a high entropy state in the outskirts, while leaving intact or erasing only partially the low-entropy, cool core at the center.

Structures and Components in Galaxy Clusters: Observations and Models

Clusters of galaxies are the largest gravitationally bounded structures in the Universe dominated by dark matter. We review the observational appearance and physical models of plasma structures in clusters of galaxies. Bubbles of relativistic plasma which are inflated by supermassive black holes of AGNs, cooling and heating of the gas, large scale plasma shocks, cold fronts, non-thermal halos and relics are observed in clusters. These constituents are reflecting both the formation history and the dynamical properties of clusters of galaxies. We discuss X-ray spectroscopy as a tool to study the metal enrichment in clusters and fine spectroscopy of Fe X-ray lines as a powerful diagnostics of both the turbulent plasma motions and the energetics of the non-thermal electron populations. The knowledge of the complex dynamical and feedback processes is necessary to understand the energy and matter balance as well as to constrain the role of the non-thermal components of clusters.

Electron acoustic solitons in magneto-rotating electron-positron-ion plasma with nonthermal electrons and positrons

The propagation of electron acoustic solitary waves (EASWs) in a magneto-rotating electron-positron-ion (epi) plasma containing cold dynamical electrons, nonthermal electrons and positrons obeying Cairns’ distribution have been explored in the stationary background of massive positive ions. Through the linear dispersion relation (LDR) the effects of nonthermal components, magnetic field and rotation have been analyzed, wherein, various limiting cases have been deduced from the LDR. For nonlinear analysis, Korteweg-de Vries (KdV) equation is obtained using the reductive perturbation technique. It is found that in the presence of nonthermal positrons both hump and dip type solitons appear to excite, the structural properties of these solitary waves change drastically with magneto-rotating effects. The present work may be employed to explore and to understand the formation of electron acoustic solitary structures in the space and laboratory plasmas with nonthermal electrons and positrons under magneto-rotating effects.

Galaxy evolution: modelling the role of non-thermal pressure in the interstellar medium

Galaxy evolution depends strongly on the physics of the interstellar medium (ISM). Motivated by the need to incorporate the properties of the ISM in cosmological simulations we construct a simple method to include the contribution of non-thermal components in the calculation of pressure of interstellar gas. In our method we treat three non-thermal components - turbulence, magnetic fields and cosmic rays - and effectively parametrize their amplitude. We assume that the three components settle into a quasi-steady-state that is governed by the star formation rate, and calibrate their magnitude and density dependence by the observed Radio-FIR correlation, relating synchrotron radiation to star formation rates of galaxies. We implement our model in single cell numerical simulation of a parcel of gas with constant pressure boundary conditions and demonstrate its effect and potential. Then, the non-thermal pressure model is incorporated into RAMSES and hydrodynamic simulations of isolated galaxies with and without the non-thermal pressure model are presented and studied. Specifically, we demonstrate that the inclusion of realistic non-thermal pressure reduces the star formation rate by an order of magnitude and increases the gas depletion time by as much. We conclude that the non-thermal pressure can prolong the star formation epoch and achieve consistency with observations without invoking artificially strong stellar feedback.

HIGH-ENERGY PROPERTIES OF THE ENIGMATIC Be STAR γ CASSIOPEIAE

We present the results of a broad-band X-ray study of the enigmatic Be star Gamma Cassiopeiae (herein gamma Cas) based on observations made with both the Suzaku and INTEGRAL observatories. gamma Cas has long been recognized as the prototypical example of a small subclass of Be stars with moderately strong X-ray emission dominated by a hot thermal component in the 0.5-12 keV energy range Lx ~ 10^32 - 10^33 erg s^-1. This places them at the high end of the known luminosity distribution for stellar emission, but several orders of magnitude below typical accretion powered Be X-ray binaries. The INTEGRAL observations spanned an 8 year baseline and represent the deepest measurement to date at energies above ~50 keV. We find that the INTEGRAL data are consistent within statistics to a constant intensity source above 20 keV, with emission extending up to ~100 keV and that searches for all of the previously reported periodicities of the system at lower energies led to null results. We further find that our combined Suzaku and INTEGRAL spectrum, which we suggest is the most accurate broad-band X-ray measurement of gamma Cas to date, is fitted extremely well with a thermal plasma emission model with a single absorption component. We found no compelling need for an additional non-thermal high-energy component. We discuss these results in the context of a currently favored models for gamma Cas and its analogs.

INTEGRATED RADIO CONTINUUM SPECTRA OF GALAXIES

We investigate the spectral shape of the total continuum radiation, between 74 MHz and 5 GHz (400 to 6 cm in wavelength), for a large sample of bright galaxies. We take advantage of the overlapping survey coverage of the VLA Low-Frequency Sky Survey, the Westerbork Northern Sky Survey, the NRAO VLA Sky Survey, and the Green Bank 6 cm survey to achieve significantly better resolution, sensitivity, and sample size compared to prior efforts of this nature. For our sample of 250 bright galaxies we measure a mean spectral index, ${\alpha}$, of -0.69 between 1.4 and 4.85 GHz, -0.55 between 325 MHz and 1.4 GHz, and -0.45 between 74 and 325 MHz, which amounts to a detection of curvature in the mean spectrum. The magnitude of this curvature is approximately ${\Delta \alpha}$ = -0.2 per logarithmic frequency decade when fit with a generalized function having constant curvature. No trend in low frequency spectral flattening versus galaxy inclination is evident in our data, suggesting that free-free absorption is not a satisfying explanation for the observed curvature. The ratio of thermal to non-thermal emission is estimated by two independent methods, (1) using the IRAS far-IR fluxes, and (2) with the value of the total spectral index. Method (1) results in a distribution of 1.4 GHz thermal fractions of 9% ${\pm}$ 3%, which is consistent with previous studies, while method (2) produces a mean 1.4 GHz thermal fraction of 51% with dispersion 26%. The highly implausible values produced by method (2) indicate that the sum of typical power-law thermal and non-thermal components is not a viable model for the total spectral index between 325 and 1.4 GHz.

The γ-ray Pulsar J0633+0632 in X-rays

AbstractWe analysedChandraobservations of the brightFermipulsar J0633+0632 and found evidence of an absorption feature in its spectrum at 804+42−26eV (the errors are at 90% confidence) with equivalent width of 63+47−36eV. In addition, we analysed in detail the X-ray spectral continuum taking into account correlations between the interstellar absorption and the distance to the source. We confirm early findings that the spectrum contains non-thermal and thermal components. The latter is equally well described by the blackbody and magnetised atmosphere models and can be attributed to the emission from the bulk of the stellar surface in both cases. The distance to the pulsar is constrained in a range of 1–4 kpc from the spectral fits. We infer the blackbody surface temperature of 108+22−14eV, while for the atmosphere model, the temperature, as seen by a distant observer, is 53+12−7eV. In the latter case, J0633+0632 is one of the coldest middle-aged isolated neutron stars. Finally, it powers an extended pulsar wind nebula whose shape suggests a high pulsar proper motion. Looking backwards the direction of the presumed proper motion, we found a likely birthplace of the pulsar—the Rosette nebula, a 50-Myr-old active star-forming region located at about 1.5° from the pulsar. If true, this constrains the distance to the pulsar in the range of 1.2–1.8 kpc.

Modeling Spatial and Temporal pCO2 Variability at 49°N/16.5°W and 56.5°N/52.6°W in the North Atlantic Ocean

Numerical models have been employed in understanding and capturing spatiotemporal CO2 trends, inter seasonal to decadal variability, and the characterization of thermal (pCO2-T) and non-thermal (pCO2-nonT) components of surface ocean pCO2 and air-sea CO2 flux variability. We employed the MIT Ocean General Circulation Model and available data from two sub polar North Atlantic observatories at 49°N, 16.5°W and 56.5°N, 52.6°W to capture in situ pCO2 observations and deconvolute bio-physical controlling processes. The model suggests that the pCCO2 cycle is marked by a summertime minimum and wintertime maximum. The physical-chemical and biological response pattern of the model is in good accordance with the observed pCO2, pCO2-T and pCO2-nonT trends. Model outputs suggest that the CO2 cycle is governed by contrasting effects of seasonal cooling and warming on one side and spring and summer net biology activities on the other side. It also predicts year-round under saturation, indicating that the region is a weak to moderate sink for CO2.

G192.8-1.1: A CANDIDATE OF AN EVOLVED THERMAL COMPOSITE SUPERNOVA REMNANT REIGNITED BY NEARBY MASSIVE STARS

G192.8-1.1 has been known as one of the faintest supernova remnants (SNRs) in the Galax until the radio continuum of G192.8-1.1 is proved to be thermal by Gao et al. (2011). Yet, the nature of G192.8-1.1 has not been fully investigated. Here, we report the possible discovery of faint non-thermal radio continuum components with a spectral index <TEX>${\alpha}{\sim}0.56(S_{\nu}{\propto}{\nu}^{-{\alpha}})$</TEX> around G192.8-1.1, while of the radio continuum emission is thermal. Also, our Arecibo <TEX>$H_I$</TEX> data reveal an <TEX>$H_I$</TEX> shell, expanding with an expansion velocity of <TEX>$20-60km\;s^{-1}$</TEX>, that has an excellent morphological correlation with the radio continuum emission. The estimated physical parameters of the <TEX>$H_I$</TEX> shell and the possible association of non-thermal radio continuum emission with it suggest G192.8-1.1 to be an~0.3 Myr-old SNR. However, the presence of thermal radio continuum implies the presence of early-type stars in the same region. One possibility is that a massive star is ionizing the interior of an old SNR. If it is the case, the electron distribution assumed by the centrally-peaked surface brightness of thermal emission implies that G192.8-1.1 is a "thermal-composite" SNR, rather than a typical shell-type SNR, where the central hot gas that used to be bright in X-rays has cooled down. Therefore, we propose that G192.8-1.1 is an old evolved thermal-composite SNR showing recurring emission in the radio continuum due to a nearby massive star. The infrared image supports that the <TEX>$H_I$</TEX> shell of G192.8-1.1 is currently encountering a nearby star forming region that possibly contains an early type star(s).

KINEMATICS IN PARTIALLY IONIZED MOLECULAR CLOUDS: IMPLICATIONS FOR THE TRANSITION TO COHERENCE

Bailey & Basu (2014) show analysis of density and mass-to-flux ratio maps for simulations with either an ionisation profile which takes into account photoionisation (step-like profile) or a cosmic ray only ionisation profile. We extend this study to analyse the effect of these ionisation profiles on velocity structures, kinematics, and synthetic spectra. Clump regions are found to occur at the convergence of two flows with a low velocity region and velocity direction transition occurring at the junction. Models with evident substructure show that core formation occurs on the periphery of these velocity valleys. Analysis of synthetic spectra reveals the presence of large non-thermal components within low-density gas, especially for models with the step-like ionisation profile. All cores show small, sub-thermal relative motions compared to background gas. Large deviations within this analysis are due to the line of sight intersecting low- and high-density regions across the velocity switch transition. Positive deviations correspond to a foreground core moving away from the observer while negative deviations correspond to a background core moving toward the observer. Comparison of velocities resulting from different ionisation profiles suggest that high ionisation fractions yield supersonic velocities, up to two times the sound speed, while regions with low ionisation fractions tend to be subsonic or mildly supersonic. This suggests that the transition to coherence within cores could be a transition between high and low ionisation fractions within the gas.

Shock finding on a moving mesh – I. Shock statistics in non-radiative cosmological simulations

Cosmological shock waves play an important role in hierarchical structure formation by dissipating and thermalizing kinetic energy of gas flows, thereby heating the universe. Furthermore, identifying shocks in hydrodynamical simulations and measuring their Mach number accurately is critical for calculating the production of non-thermal particle components through diffusive shock acceleration. However, shocks are often significantly broadened in numerical simulations, making it challenging to implement an accurate shock finder. We here introduce a refined methodology for detecting shocks in the moving-mesh code AREPO, and show that results for shock statistics can be sensitive to implementation details. We put special emphasis on filtering against spurious shock detections due to tangential discontinuities and contacts. Both of them are omnipresent in cosmological simulations, for example in the form of shear-induced Kelvin-Helmholtz instabilities and cold fronts. As an initial application of our new implementation, we analyse shock statistics in non-radiative cosmological simulations of dark matter and baryons. We find that the bulk of energy dissipation at redshift zero occurs in shocks with Mach numbers around ${\cal M}\approx2.7$. Furthermore, almost $40\%$ of the thermalization is contributed by shocks in the warm hot intergalactic medium (WHIM), whereas $\approx60\%$ occurs in clusters, groups and smaller halos. Compared to previous studies, these findings revise the characterization of the most important shocks towards higher Mach numbers and lower density structures. Our results also suggest that regions with densities above and below $\delta_b=100$ should be roughly equally important for the energetics of cosmic ray acceleration through large-scale structure shocks.

VERY LARGE ARRAY AND JANSKY VERY LARGE ARRAY OBSERVATIONS OF THE COMPACT RADIO SOURCES IN M8

We analyze high-resolution Very Large Array and Jansky Very Large Array continuum observations of the M8 region carried out at several epochs that span a period of 30 yr. Our maps reveal two compact sources. One is associated with Her 36 SE, a possible companion of the O7 luminous massive star Her 36, and the other is associated to G5.97-1.17, whose proplyd nature was previously established. With the analyzed data, we do not find significant time variability in any of these sources. The derived spectral index of $\ge 0.1$ for Her~36 SE, the marginal offset of the radio emission with the previous IR detection and the associated X-ray emission previously reported suggest the presence of an unresolved interaction region between the strong winds of Her~36 and Her~36 SE. This region would produce non-thermal contamination to the global wind emission of Her~36 flattening its spectral index. On the other hand, the emission of G5.97-1.17 can be also explained by a mixture of thermal and non-thermal emission components, with different relative contribution of both emission mechanisms along the proplyd. We argue that the shock created by the photo-evaporation flow of the proplyd with the collimated stellar wind of Her~36 accelerates charged particles in G5.97-1.17 producing considerable synchrotron emission. On the contrary, an electron density enhancement at the southwest of G5.97-1.17 makes the thermal emission dominant over this region.

Polytropic models of filamentary interstellar clouds – I. Structure and stability

The properties of filamentary interstellar clouds observed at sub-millimetre wavelengths, especially by the Herschel Space Observatory, are analysed with polytropic models in cylindrical symmetry. The observed radial density profiles are well reproduced by negative-index cylindrical polytropes with polytropic exponent $1/3\lesssim \gamma_{\rm p} \lesssim 2/3$ (polytropic index $-3\lesssim n \lesssim -3/2$), indicating either external heating or non-thermal pressure components. However, the former possibility requires unrealistically high gas temperatures at the filament's surface and is therefore very unlikely. Non-thermal support, perhaps resulting from a superposition of small-amplitude Alfv\'en waves (corresponding to $\gamma_{\rm p}=1/2$), is a more realistic possibility, at least for the most massive filaments. If the velocity dispersion scales as the square root of the density (or column density) on the filament's axis, as suggested by observations, then polytropic models are characterised by a uniform width. The mass per unit length of pressure-bounded cylindrical polytropes depends on the conditions at the boundary and is not limited as in the isothermal case. However, polytropic filaments can remain stable to radial collapse for values of the axis-to-surface density contrast as large as the values observed only if they are supported by a non-isentropic pressure component.