General Relativistic Instability Research Articles

Linear adiabatic analysis for general-relativistic instability in primordial accreting supermassive stars

Accreting supermassive stars of $ will eventually collapse directly to a black hole via the general-relativistic (GR) instability. Such direct collapses of supermassive stars are thought to be a possible formation channel for supermassive black holes at $z > 6$. In this work, we investigate the final mass of accreting Population III stars with constant accretion rates between $0.01$ and 1000\ We determined the final mass by solving the differential equation for GR linear adiabatic radial pulsations. We find that models with accretion rates $ experience the GR instability at masses depending on the accretion rates. The critical masses are larger for higher accretion rates, ranging from $8 for $0.05\ to $ for $1000\ The $0.05\ model reaches the GR instability at the end of the core hydrogen burning. The higher-mass models with higher accretion rates reach the GR instability during the hydrogen burning stage.

Constraint on the event rate of general relativistic instability supernovae from the early JWST deep field data

ABSTRACT General relativistic instability supernovae (GRSNe) at 10 ≲ z ≲ 15 are predicted to be observed as red faint point sources, and they can be detected only in the reddest filters in James Webb Space Telescope (JWST)/NIRCam (F444W and F356W). They should be observed as persistent point sources with little flux variations for a couple of decades because of time dilation. We search for static point sources detected only in the F444W filter or only in the F444W and F356W filters in the early JWST deep field data. No real point source of such kind is identified. Therefore, the GRSN rate at 10 ≲ z ≲ 15 is constrained to be less than ∼8 × 10−7 Mpc−3 yr−1 for the first time.

Evolution and explosions of metal-enriched supermassive stars: proton rich general relativistic instability supernovae

ABSTRACT The assembly of supermassive black holes poses a challenge primarily because of observed quasars at high redshift, but additionally because of the current lack of observations of intermediate mass black holes. One plausible scenario for creating supermassive black holes is direct collapse triggered by the merger of two gas-rich galaxies. This scenario allows the creation of supermassive stars with solar metallicity. We investigate the behaviour of metal enriched supermassive stars which collapse due to the general relativistic radial instability during hydrogen burning. These stars contain both hydrogen and metals and thus may explode due to the CNO cycle (carbon–nitrogen–oxygen) and the rp process (rapid proton capture). We perform a suite of stellar evolution simulations for a range of masses and metallicities, with and without mass-loss. We evaluate the stability of these supermassive stars by solving the pulsation equation in general relativity. When the stars becomes unstable, we perform 1D general relativistic hydrodynamical simulations coupled to a 153 isotope nuclear network with cooling from neutrino reactions, in order to determine if the stars explode. If the stars do explode, we post process the nucleosynthesis using a 514 isotope network which includes additional proton rich isotopes. These explosions are characterized by enhanced nitrogen and intermediate mass elements ($16\ge \rm {A}\ge 25$), and suppressed light elements ($8\ge \rm {A}\ge 14$), and we comment on recent observations of super-solar nitrogen in GN-z11.

Modelling supermassive primordial stars with mesa

ABSTRACT Supermassive stars forming at z ∼ 15–20 are one of the leading contenders for the origin of the first quasars, over 200 of which have now been discovered at z > 6. These stars likely form in pristine, atomically cooled haloes immersed in strong Lyman–Werner ultraviolet backgrounds or in highly supersonic baryon streaming flows. Atomic cooling triggers catastrophic baryon collapse capable of building up stars at rates of up to ∼1 M⊙ yr−1. Here, we examine the evolution of supermassive stars with a much larger and finer grid of accretion rates than in previous studies with the mesa stellar evolution code. We find that their final masses range from 3.5 × 103 to 3.7 × 105 M⊙ at accretion rates of 0.001–1 M⊙ yr−1, respectively. We also find that supermassive star evolution diverges at accretion rates of 0.01–0.02 M⊙ yr−1, above which they evolve as cool red hypergiants along the Hayashi track and collapse via the general relativistic instability during central hydrogen burning, and below which they evolve as hot blue supergiants and collapse at the end of their nuclear burning lifetimes after exiting the main sequence.

Pulsations of primordial supermassive stars induced by a general relativistic instability; visible to JWST at z > 12

ABSTRACT The origin of high-redshift quasars and their supermassive black hole engines is unclear. One promising solution is the collapse of a primordial supermassive star. Observational confirmation of this scenario may be challenging, but a general relativistic instability supernova provides one avenue for such. Previous studies have found that a general relativistic instability supernova has a potentially decades-long plateau phase visible to JWST at high redshift. In this work, we examine stars with mass just below the general relativistic instability supernova mass range. These stars pulsate, ejecting a portion of their envelopes. They then contract quasi-statically back to an equilibrium temperature, at which point they again become unstable and pulsate once more. Because each pulse consumes a small amount of the available nuclear fuel, there exists the possibility of multiple pulsations. We present simulations of the contracting phase, the pulsation, and the light-curve phase. We find that the lower mass pulsating models are even brighter than the higher mass supernovae because the pulsations occur in the late helium burning phase when the stars have extremely large radii. The fact that the pulsations are more luminous and occur in a wider mass range than the supernovae bodes well for observation.

Direct collapse of exceptionally heavy black holes in the merger-driven scenario

ABSTRACT We revisit the conditions present in supermassive discs (SMDs) formed by the merger of gas-rich, metal-enriched galaxies at redshift z ∼ 10. We find that SMDs naturally form hydrostatic cores which go through a rapidly accreting supermassive star phase, before directly collapsing into massive black holes via the general relativistic instability. The growth and collapse of the cores occurs within ∼5 × 105 yr from the formation of the SMD, producing bright electromagnetic, neutrino and gravitational wave transients with a typical duration of a few minutes and, respectively, a typical flux and a typical strain amplitude at Earth of ∼10−8 erg s−1 cm−2 and ∼4 × 10−21. We provide a simple fitting formula for the resulting black hole masses, which range from a few 106 to 108 M⊙ depending on the initial SMD configuration. Crucially, our analysis does not require any specific assumption on the thermal properties of the gas, nor on the angular momentum loss mechanisms within the SMD. Led by these findings, we argue that the merger-driven scenario provides a robust pathway for the rapid formation of supermassive black holes at z > 6. It provides an explanation for the origin of the brightest and oldest quasars without the need of a sustained growth phase from a much smaller seed. Its smoking gun signatures can be tested directly via multimessenger observations.

Stability analysis of supermassive primordial stars: a new mass range for general relativistic instability supernovae

ABSTRACT Observed supermassive black holes in the early Universe have several proposed formation channels in part because most of these channels are difficult to probe. One of the more promising channels, the direct collapse of a supermassive star has several possible probes including the explosion of a helium-core supermassive star triggered by a general relativistic instability. We develop a straightforward method for evaluating the general relativistic radial instability without simplifying assumptions and apply it to population III supermassive stars taken from a post Newtonian stellar evolution code. This method is more accurate than previous determinations and it finds that the instability occurs earlier in the evolutionary life of the star. Using the results of the stability analysis, we perform 1D general relativistic hydrodynamical simulations, and we find two general relativistic instability supernovae fuelled by alpha capture reactions as well as several lower mass pulsations, analogous to the puslational pair instability process. The mass range for the events ($2.6-3.0\times 10^4{\rm M}_\odot$) is lower than that had been suggested by previous works ($5.5\times 10^4{\rm M}_\odot$), because the instability occurs earlier in the star’s evolution. The explosion may be visible to among others JWST, while the discovery of the pulsations opens up additional possibilities for observation.

Maximum accretion rate of supermassive stars

Context. 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. Aims. 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. Methods. We use the continuity equation and the assumption of spherical symmetry and free fall to derive the 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. Results. We find that, as long as the density of the accreted gas is smaller than or equal to the average density of the accretor, the maximum allowed rate, Ṁmax, is given uniquely by the compactness of the accretor. We argue that a density inversion between accreting matter and the accretor is inconsistent with gravitational collapse. For the compactness of rapidly accreting supermassive stars, Ṁmax is related to the stellar mass, M, by a power law, Ṁmax ∝ M3/4. The rates of atomically cooled halos (0.1−10 M⊙ yr−1) are allowed as soon as M ≳ 1 M⊙. The largest rates expected in galaxy mergers (104 − 105 M⊙ yr−1) become accessible once the accretor is supermassive (M ≳ 104 M⊙). Conclusions. These results suggest that supermassive stars can accrete up to masses > 106 M⊙ 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.

General-relativistic instability in rapidly accreting supermassive stars: The impact of rotation

Context. Supermassive stars (SMSs) collapsing via the general-relativistic (GR) instability are invoked as the possible progenitors of supermassive black holes. Their mass and angular momentum at the onset of the instability are key in many respects, in particular regarding the possibility for observational signatures of direct collapse. Accretion dominates the evolution of SMSs and, similar to rotation, it has been shown to impact their final properties significantly. However, the combined effect of accretion and rotation on the stability of these objects is not known. Aims. Here, we study the stability of rotating, rapidly accreting SMSs against GR perturbations and derive the properties of these stars at death. Methods. On the basis of hylotropic structures, which are relevant for rapidly accreting SMSs, we define rotation profiles under the assumption of local angular momentum conservation in radiative regions, which allows for differential rotation. We account for rotation in the stability of the structure by adding a Newtonian rotation term in the relativistic equation of stellar pulsation, which is justified by the slow rotations imposed by the ΩΓ-limit. Results. We find that rotation favours the stability of rapidly accreting SMSs as soon as the accreted angular momentum represents a fraction of f ≳ 0.1% of the Keplerian angular momentum. For f ∼ 0.3−0.5%, the maximum masses consistent with GR stability are increased by an order of magnitude compared to the non-rotating case. For f ∼ 1%, the GR instability cannot be reached if the stellar mass does not exceed 107 − 108 M⊙. Conclusions. These results imply that, as in the non-rotating case, the final masses of the progenitors of direct collapse black holes range in distinct intervals depending on the scenario considered: 105 M⊙ ≲ M ≲ 106 M⊙ for primordial atomically cooled haloes and 106 M⊙ ≲ M ≲ 109 M⊙ for metal-rich galaxy mergers. The models suggest that the centrifugal barrier is inefficient to prevent the direct formation of a supermassive black hole at the collapse of a SMS. Moreover, the conditions of galaxy mergers appear to be more favourable than those of atomically cooled haloes for detectable gravitational wave emission and ultra-long gamma-ray bursts at black hole formation.

Seeding Supermassive Black Holes with Self-interacting Dark Matter: A Unified Scenario with Baryons

Abstract Observations show that supermassive black holes (SMBHs) with a mass of ∼109 M ⊙ exist when the universe is just 6% of its current age. We propose a scenario where a self-interacting dark matter halo experiences gravothermal instability and its central region collapses into a seed black hole. The presence of baryons in protogalaxies could significantly accelerate the gravothermal evolution of the halo and shorten collapse timescales. The central halo could dissipate its angular momentum remnant via viscosity induced by the self-interactions. The host halo must be on high tails of density fluctuations, implying that high-z SMBHs are expected to be rare in this scenario. We further derive conditions for triggering general relativistic instability of the collapsed region. Our results indicate that self-interacting dark matter can provide a unified explanation for diverse dark matter distributions in galaxies today and the origin of SMBHs at redshifts z ∼ 6–7.

Observational properties of a general relativistic instability supernova from a primordial supermassive star

ABSTRACT We present the expected observational properties of a general relativistic instability supernova (GRSN) from the 55 500 M⊙ primordial (Population III) star. Supermassive stars exceeding $10^4\, \mathrm{M}_\odot$ may exist in the early Universe. They are generally considered to collapse through the general relativistic instability to be seed black holes to form supermassive ($\sim 10^9\, \mathrm{M}_\odot$) black holes observed as high-redshift quasars. Some of them, however, may explode as GRSNe if the explosive helium burning unbinds the supermassive stars following the collapse triggered by the general relativistic instability. We perform the radiation hydrodynamics simulation of the GRSN starting shortly before the shock breakout. We find that the GRSN is characterized by a long-lasting (550 d) luminous ($1.5\times 10^{44}\, \mathrm{erg\, s^{-1}}$) plateau phase with the photospheric temperature of around 5000 K in the rest frame. The plateau phase lasts for decades when it appears at high redshifts and it will likely be observed as a persistent source in the future deep near-infrared imaging surveys. Especially, the near-infrared images reaching 29 AB magnitude that can be obtained by Galaxy and Reionization EXplorer (G-REX) and James Webb Space Telescope (JWST) allow us to identify GRSNe up to z ≃ 15. Deeper images enable us to discover GRSNe at even higher redshifts. Having extremely red colour, they can be distinguished from other persistent sources such as high-redshift galaxies by using colour information. We conclude that the deep near-infrared images are able to constrain the existence of GRSNe from the primordial supermassive stars in the Universe even without the time domain information.

Establishing a reliable determination of the final mass for rapidly accreting supermassive stars

Context. The formation of supermassive black holes possibly takes place via direct collapse, with a supermassive star (SMS) as its progenitor. In this scenario, the SMS accretes at > 0.1 M⊙ yr−1 until it collapses into a massive black hole seed as a result of the general-relativistic (GR) instability. However, the exact mass at which the collapse occurs is not known, as existing numerical simulations give us a divergent range of results. Aims. Here, we address this problem analytically, which allows for reliable ab initio determination of the onset point of the GR instability, for given hydrostatic structures. Methods. We applied the relativistic equation of radial pulsations in its general form to the hydrostatic GENEC models already published in the literature. Results. We show that the mass of spherical SMSs forming in atomically cooled halos cannot exceed 500 000 M⊙, which stands in contrast to previous claims. On the other hand, masses in excess of this limit, possibly up to ∼106 M⊙, could be reached in alternative versions of direct collapse. Conclusions. Our method can be used to test the consistency of GR hydrodynamical stellar evolution codes.

General-relativistic instability in hylotropic supermassive stars

Context. The formation of supermassive black holes by direct collapse would imply the existence of supermassive stars (SMSs) and their collapse through the general-relativistic (GR) instability into massive black hole seeds. However, the final mass of SMSs is weakly constrained by existing models, in spite of the importance of this value for the consistency of the direct collapse scenario. Aims. We estimate the final masses of spherical SMSs within the whole parameter space that is relevant to these objects. Methods. We built analytical stellar structures (hylotropes) that mimic existing numerical SMS models, accounting for full stellar evolution with rapid accretion. From these hydrostatic structures, we determine ab initio the conditions for GR instability and compare the results with the predictions for full stellar evolution. Results. We show that hylotropic models predict the onset of GR instability with a high level of precision. The mass of the convective core appears as a decisive quantity. The lower it is, the larger the total mass required for GR instability. The typical conditions for GR instability feature a total mass of ≳105 M⊙ with a core mass of ≳104 M⊙. If the core mass remains below 104 M⊙, total masses in excess of 106 − 107 M⊙ can be reached. Conclusions. Our results confirm that spherical SMSs forming in primordial, atomically cooled haloes collapse at masses below 500 000 M⊙. On the other hand, accretion rates in excess of 1000 M⊙ yr−1, leading to final stellar masses of ≳106 M⊙, are required for massive black hole formation in metal-rich gas. Thus, the different channels of direct collapse imply distinct final masses for the progenitor of the black hole seed.

The final fate of supermassive M ∼ 5 × 104 M⊙ Pop III stars: explosion or collapse?

ABSTRACT We investigate the possibility of a supernova in supermassive (5 × 104 M⊙) population III stars induced by a general relativistic instability occurring in the helium burning phase. This explosion could occur via rapid helium burning during an early contraction of the isentropic core. Such an explosion would be visible to future telescopes and could disrupt the proposed direct collapse formation channel for early Universe supermassive black holes. We simulate first the stellar evolution from hydrogen burning using a 1D stellar evolution code with a post-Newtonian approximation; at the point of dynamical collapse, we switch to a 1D (general relativistic) hydrodynamic code with the Misner-Sharpe metric. In opposition to a previous study, we do not find an explosion in the non-rotating case, although our model is close to exploding for a similar mass to the explosion in the previous study. When we include slow rotation, we find one exploding model, and we conclude that there likely exist additional exploding models, though they may be rare.

On monolithic supermassive stars

ABSTRACT Supermassive stars have been proposed as the progenitors of the massive ($\sim \!10^{9}\, \mathrm{M}_{\odot }$) quasars observed at z ∼ 7. Prospects for directly detecting supermassive stars with next-generation facilities depend critically on their intrinsic lifetimes, as well as their formation rates. We use the one-dimensional stellar evolution code kepler to explore the theoretical limiting case of zero-metallicity non-rotating stars, formed monolithically with initial masses between $10$ and $190\, \mathrm{kM}_{\odot }$. We find that stars born with masses between $\sim\! 60$ and $\sim\! 150\, \mathrm{kM}_{\odot }$ collapse at the end of the main sequence, burning stably for $\sim\! 1.5\, \mathrm{Myr}$. More massive stars collapse directly through the general relativistic instability after only a thermal time-scale of $\sim\! 3$–$4\, \mathrm{kyr}$. The expected difficulty in producing such massive thermally relaxed objects, together with recent results for currently preferred rapidly accreting formation models, suggests that such ‘truly direct’ or ‘dark’ collapses may not be typical for supermassive objects in the early Universe. We close by discussing the evolution of supermassive stars in the broader context of massive primordial stellar evolution and the possibility of supermassive stellar explosions.

The evolution of supermassive Population III stars

Supermassive primordial stars forming in atomically-cooled halos at $z \sim15-20$ are currently thought to be the progenitors of the earliest quasars in the Universe. In this picture, the star evolves under accretion rates of $0.1 - 1$ $M_\odot$ yr$^{-1}$ until the general relativistic instability triggers its collapse to a black hole at masses of $\sim10^5$ $M_\odot$. However, the ability of the accretion flow to sustain such high rates depends crucially on the photospheric properties of the accreting star, because its ionising radiation could reduce or even halt accretion. Here we present new models of supermassive Population III protostars accreting at rates $0.001 - 10$ $M_\odot$ yr$^{-1}$, computed with the GENEVA stellar evolution code including general relativistic corrections to the internal structure. We use the polytropic stability criterion to estimate the mass at which the collapse occurs, which has been shown to give a lower limit of the actual mass at collapse in recent hydrodynamic simulations. We find that at accretion rates higher than $0.001$ $M_\odot$ yr$^{-1}$ the stars evolve as red, cool supergiants with surface temperatures below $10^4$ K towards masses $>10^5$ $M_\odot$, and become blue and hot, with surface temperatures above $10^5$ K, only for rates $\lesssim0.001$ $M_\odot$ yr$^{-1}$. Compared to previous studies, our results extend the range of masses and accretion rates at which the ionising feedback remains weak, reinforcing the case for direct collapse as the origin of the first quasars.

Dynamic collapses of relativistic degenerate stellar cores and radiation pressure dominated stellar interiors

We investigate and explore self-similar dynamic radial collapses of relativistic degenerate stellar cores (RDSCs) and radiation pressure dominated stellar interiors (RPDSIs) of spherical symmetry by invoking a conventional polytropic (CP) equation of state (EoS) with a constant polytropic index γ=4/3 and by allowing free-fall non-zero RDSC or RPDSI surface mass density and pressure due to their sustained physical contact with the outer surrounding stellar envelopes also in contraction. Irrespective of the physical triggering mechanisms (including, e.g., photodissociation, electron-positron pair instability, general relativistic instability etc.) for initiating such a self-similar dynamically collapsing RDSC or RPDSI embedded within a massive star, a very massive star (VMS) or a supermassive star (SMS) in contraction and by comparing with the Schwarzschild radii associated with their corresponding RDSC/RPDSI masses, the emergence of central black holes in a wide mass range appears inevitable during such RDSC/RPDSI dynamic collapses inside massive stars, VMSs, and SMSs, respectively. Radial pulsations of progenitor cores or during a stellar core collapse may well leave imprints onto collapsing RDSCs/RPDSIs towards their self-similar dynamic evolution. Massive neutron stars may form during dynamic collapses of RDSC inside massive stars in contraction under proper conditions.

On the Maximum Mass of Accreting Primordial Supermassive Stars

Abstract 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 M ⊙ yr−1 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 M ⊙ for accretion rates of 0.1–10 M ⊙ yr−1, 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.

THE FINAL FATES OF ACCRETING SUPERMASSIVE STARS

ABSTRACT The formation of supermassive stars (SMSs) via rapid mass accretion and their direct collapse into black holes (BHs) is a promising pathway for sowing seeds of supermassive BHs in the early universe. We calculate the evolution of rapidly accreting SMSs by solving the stellar structure equations including nuclear burning as well as general relativistic (GR) effects up to the onset of the collapse. We find that such SMSs have a less concentrated structure than a fully convective counterpart, which is often postulated for non-accreting ones. This effect stabilizes the stars against GR instability even above the classical upper mass limit ≳105 M ⊙ derived for the fully convective stars. The accreting SMS begins to collapse at the higher mass with the higher accretion rate. The collapse occurs when the nuclear fuel is exhausted only for cases with . With , the star becomes GR unstable during the helium-burning stage at M ≃ 2–3.5 × 105 M ⊙. In an extreme case with 10 , the star does not collapse until the mass reaches ≃8.0 × 105 M ⊙, where it is still in the hydrogen-burning stage. We expect that BHs with roughly the same mass will be left behind after the collapse in all the cases.

Supermassive star formation via episodic accretion: protostellar disc instability and radiative feedback efficiency

The formation of SMSs is a potential pathway to seed SMBHs in the early universe. A critical issue for forming SMSs is stellar UV feedback, which may limit the stellar mass growth via accretion. In this paper we study the evolution of an accreting SMS and its UV emissivity under conditions of realistic variable accretion from a self-gravitating circumstellar disc. First we conduct a 2D hydrodynamical simulation to follow the long-term protostellar accretion until the stellar mass exceeds $10^4~M_\odot$. The disc fragments due to gravitational instability, creating a number of small clumps that rapidly migrate inward to fall onto the star. The resulting accretion history is thus highly time-dependent: short episodic accretion bursts are followed by longer, relative quiescent phases. We show that the circumstellar disc for the so-called direct collapse model is more unstable and generates greater variability over shorter timescales than normal Pop III cases. We conduct a post-process stellar evolution calculation using the obtained accretion history. Our results show that, regardless of the strong variability of the accretion rates, the stellar radius monotonically increases with almost constant effective temperature at $T_{\rm eff} \simeq 5000$ K as the stellar mass increases. The resulting UV feedback is too weak to hinder mass accretion due to the low flux of stellar UV photons, thus verifying our implicit assumption of no stellar feedback during the hydrodynamic simulations. The insensitivity of stellar evolution to variable accretion is attributed to the fact that typical timescales of variability, $\lesssim 10^3$ years, are too short to affect the stellar structure. We argue that this evolution will continue until the SMS eventually collapses to produce a massive black hole by the general relativistic instability after the stellar mass reaches $\gtrsim 10^5~M_\odot$.