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Register a new userOn the Maximum Mass of Accreting Primordial Supermassive Stars
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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.
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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 less concentrated structure than 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 $gtrsim 10^5~M_odot$ 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 $dot M lesssim 0.1~M_odot~{rm yr}^{-1}$. With $dot{M} simeq 0.3 - 1~M_odot~{rm yr}^{-1}$, the star becomes GR-unstable during the helium-burning stage at $M simeq 2 - 3.5~times 10^5~M_odot$. In an extreme case with $10~M_odot~{rm yr}^{-1}$, the star does not collapse until the mass reaches $simeq 8.0times 10^5~M_odot$, 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.
The collapse of supermassive primordial stars in hot, atomically-cooled halos may have given birth to the first quasars at $z sim$ 15 - 20. Recent numerical simulations of these rapidly accreting stars reveal that they are cool, red hypergiants shrouded by dense envelopes of pristine atomically-cooled gas at 6,000 - 8,000 K, with luminosities $L$ $gtrsim$ 10$^{10}$ L$_{odot}$. Could such luminous but cool objects be detected as the first stage of quasar formation in future near infrared (NIR) surveys? We have now calculated the spectra of supermassive primordial stars in their birth envelopes with the Cloudy code. We find that some of these stars will be visible to JWST at $z lesssim$ 20 and that with modest gravitational lensing Euclid and WFIRST could detect them out to $z sim$ 10 - 12. Rather than obscuring the star, its accretion envelope enhances its visibility in the NIR today by reprocessing its short-wavelength flux into photons that are just redward of the Lyman limit in the rest frame of the star.
Primordial supermassive stars (SMSs) formed in atomic-cooling halos at z ~ 15 - 20 are leading candidates for the seeds of the first quasars. Past numerical studies of the evolution of SMSs have typically assumed constant accretion rates rather than the highly variable flows in which they form. We model the evolution of SMSs in the cosmological flows that create them using the Kepler stellar evolution and implicit hydrodynamics code. We find that they reach masses of 1 - 2 x $10^5 M_{odot}$ before undergoing direct-collapse to black holes (DCBHs) during or at the end of their main-sequence hydrogen burning, at 1 - 1.5 Myr, regardless of halo mass, spin, or merger history. We also find that realistic, highly-variable accretion histories allow for a much greater diversity of supermassive stellar structures, including in some cases largely thermally relaxed objects, which may provide a significant source of radiative feedback. Our models indicate that the accretion histories predicted for purely atomic-cooling halos may impose a narrow spectrum of masses on the seeds of the first massive quasars, however further studies incorporating realistic feedback will be essential in order to confirm whether or not this holds true in all cases. Our results also indicate that multiple SMSs at disparate stages of evolution can form in these halos, raising the possibility of SMS binaries and supermassive X-ray binaries (SMXBs), as well as DCBH mergers which could be detected by LISA.
The fate of massive stars up to 300 Msun is highly uncertain. Do these objects produce pair-instability explosions, or normal Type Ic supernovae? In order to address these questions, we need to know their mass-loss rates during their lives. Here we present mass-loss predictions for very massive stars (VMS) in the range of 60-300 Msun. We use a novel method that simultaneously predicts the wind terminal velocities (vinf) and mass-loss rate (dM/dt) as a function of the stellar parameters: (i) luminosity/mass Gamma, (ii) metallicity Z, and (iii) effective temperature Teff. Using our results, we evaluate the likely outcomes for the most massive stars.
Utrecht has a long tradition in both spectroscopy and mass-loss studies. Here we present a novel methodology to calibrate mass-loss rates on purely spectroscopic grounds. We utilize this to predict the final fates of massive stars, involving pair-instability and long gamma-ray bursts (GRBs) at low metallicity Z.
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