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Register a new userOn the maximum accretion rate of supermassive stars
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The formation of the most massive quasars observed at high redshifts requires extreme inflows of gas down to the length scales of the central compact object. Here, we estimate the maximum inflow rate allowed by gravity down to the surface of supermassive stars, the possible progenitors of these supermassive black holes. We use the continuity equation and the assumption of free-fall to derive maximum allowed inflow rates for various density profiles. We apply our approach to the mass-radius relation of rapidly accreting supermassive stars to estimate an upper limit to the accretion rates allowed during the formation of these objects. We find that the maximum allowed rate $dot M_{rm max}$ is given uniquely by the compactness of the accretor. For the compactness of rapidly accreting supermassive stars, $dot M_{rm max}$ is related to the stellar mass $M$ by a power-law $dot M_{rm max}propto M^{3/4}$. The rates of atomically cooled halos (0.1 -- 10 M$_odot$ yr$^{-1}$) are allowed as soon as $Mgtrsim1$ M$_odot$. The largest rates expected in galaxy mergers ($10^4-10^5$ M$_odot$ yr$^{-1}$) become accessible once the accretor is supermassive ($Mgtrsim10^4$ M$_odot$). These results suggest that supermassive stars can accrete up to masses $>10^6$ M$_odot$ before they collapse via the general-relativistic instability. At such masses, the collapse is expected to lead to the direct formation of a supermassive black hole even within metal-rich gas, resulting in a black hole seed that is significantly heavier than in conventional direct collapse models for atomic cooling halos.
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Supermassive primordial stars are suspected to be the progenitors of the most massive quasars at z~6. Previous studies of such stars were either unable to resolve hydrodynamical timescales or considered stars in isolation, not in the extreme accretion flows in which they actually form. Therefore, they could not self-consistently predict their final masses at collapse, or those of the resulting supermassive black hole seeds, but rather invoked comparison to simple polytropic models. Here, we systematically examine the birth, evolution and collapse of accreting non-rotating supermassive stars under accretion rates of 0.01-10 solar masses per year, using the stellar evolution code KEPLER. Our approach includes post-Newtonian corrections to the stellar structure and an adaptive nuclear network, and can transition to following the hydrodynamic evolution of supermassive stars after they encounter the general relativistic instability. We find that this instability triggers the collapse of the star at masses of 150,000-330,000 solar masses for accretion rates of 0.1-10 solar masses per year, and that the final mass of the star scales roughly logarithmically with the rate. The structure of the star, and thus its stability against collapse, is sensitive to the treatment of convection, and the heat content of the outer accreted envelope. Comparison with other codes suggests differences here may lead to small deviations in the evolutionary state of the star as a function of time, that worsen with accretion rate. Since the general relativistic instability leads to the immediate death of these stars, our models place an upper limit on the masses of the first quasars at birth.
Nuclear burning and its dependence on the mass accretion rate are fundamental ingredients for describing the complicated observational phenomenology of neutron stars in binary systems. Motivated by high quality burst rate data emerging from large statistical studies, we report general calculations relating bursting rate to mass accretion rate and neutron star rotation frequency. In this first work we neglect general relativistic effects and accretion topology, though we discuss where their inclusion should play a role. The relations we derive are suitable for different burning regimes and provide a direct link between parameters predicted by theory and what is to be expected in observations. We illustrate this for analytical relations of different unstable burning regimes that operate on the surface of an accreting neutron star. We also use the observed behaviour of burst rate to suggest new constraints on burning parameters. We are able to provide an explanation for the long standing problem of the observed decrease of burst rate with increasing mass accretion that follows naturally from these calculations: when accretion rate crosses a certain threshold, ignition moves away from its initially preferential site and this can cause a net reduction of the burst rate due to the effects of local conditions that set local differences in both burst rate and stabilization criteria. We show under which conditions this can happen even if locally the burst rate keeps increasing with accretion.
We study properties of luminous X-ray pulsars using a simplified model of the accretion column. The maximal possible luminosity is calculated as a function of the neutron star (NS) magnetic field and spin period. It is shown that the luminosity can reach values of the order of $10^{40},{rm erg/s}$ for the magnetar-like magnetic field ($Bgtrsim 10^{14},{rm G}$) and long spin periods ($Pgtrsim 1.5,{rm s}$). The relative narrowness of an area of feasible NS parameters which are able to provide higher luminosities leads to the conclusion that $Lsimeq 10^{40},,{rm erg/s}$ is a good estimate for the limiting accretion luminosity of a NS. Because this luminosity coincides with the cut-off observed in the high mass X-ray binaries luminosity function which otherwise does not show any features at lower luminosities, we can conclude that a substantial part of ultra-luminous X-ray sources are accreting neutron stars in binary systems.
The disruption of a star by a supermassive black hole generates a sudden bright flare. Previous studies have focused on the disruption by single black holes, for which the fallback rate decays as~$propto t^{-5/3}$. In this paper, we generalise the study to the case of a supermassive black hole binary (SMBHB), using both analytical estimates and hydrodynamical simulations, looking for specific observable signatures. The range of binary separation for which it is possible to distinguish between the disruption created by a single or a binary black hole concerns typically separations of order a few milliparsecs for a primary of mass $sim 10^6M_{odot}$. When the fallback rate is affected by the secondary, it undergoes two types interruptions, depending on the initial inclination $theta$ of the orbit of the star relative to the plane of the SMBHB. For $theta lesssim 70^circ$, periodic sharp interruptions occur and the time of first interruption depends on the distance of the secondary black hole with the debris. If $theta gtrsim 70^circ$, a first smooth interruption occurs, but not always followed by a further recovery of the fallback rate. This implies that most of the TDEs around a SMBHB will undergo periodic sharp interruptions of their lightcurve.
Supermassive stars born from pristine gas in atomically-cooled haloes are thought to be the progenitors of supermassive black holes at high redshifts. However, the way they accrete their mass is still an unsolved problem. In particular, for accretion to proceed, a large amount of angular momentum has to be extracted from the collapsing gas. Here, we investigate the constraints stellar evolution imposes on this angular momentum problem. We present an evolution model of a supermassive Population III star including simultaneously accretion and rotation. We find that, for supermassive stars to form by accretion, the accreted angular momentum has to be about 1% of the Keplerian angular momentum. This tight constraint comes from the $OmegaGamma$-limit, at which the combination of radiation pressure and centrifugal force cancels gravity. It implies that supermassive stars are slow rotators, with a surface velocity less than 10-20% of their first critical velocity, at which the centrifugal force alone cancels gravity. At such low velocities, the deformation of the star due to rotation is negligible.
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