Abstract

We present the spectrum of compact object masses: neutron stars and black holes that originate from single stars in different environments. In particular, we calculate the dependence of maximum black hole mass on metallicity and on some specific wind mass loss rates (e.g., Hurley et al. and Vink et al.). Our calculations show that the highest mass black holes observed in the Galaxy M_bh = 15 Msun in the high metallicity environment (Z=Zsun=0.02) can be explained with stellar models and the wind mass loss rates adopted here. To reach this result we had to set Luminous Blue Variable mass loss rates at the level of about 0.0001 Msun/yr and to employ metallicity dependent Wolf-Rayet winds. With such winds, calibrated on Galactic black hole mass measurements, the maximum black hole mass obtained for moderate metallicity (Z=0.3 Zsun=0.006) is M_bh,max = 30 Msun. This is a rather striking finding as the mass of the most massive known stellar black hole is M_bh = 23-34 Msun and, in fact, it is located in a small star forming galaxy with moderate metallicity. We find that in the very low (globular cluster-like) metallicity environment the maximum black hole mass can be as high as M_bh,max = 80 Msun (Z=0.01 Zsun=0.0002). It is interesting to note that X-ray luminosity from Eddington limited accretion onto an 80 Msun black hole is of the order of about 10^40 erg/s and is comparable to luminosities of some known ULXs. We emphasize that our results were obtained for single stars only and that binary interactions may alter these maximum black hole masses (e.g., accretion from a close companion). This is strictly a proof-of-principle study which demonstrates that stellar models can naturally explain even the most massive known stellar black holes.

Highlights

  • Measuring the masses of celestial objects is one of the principal challenges in astrophysics

  • For high (Galaxy-like; Z = Z⊙ = 0.02) metallicity, neutron star formation begins at Mzams = 7.7 M⊙ with low mass NSs (Mns = 1.26 M⊙) formed through electron capture supernovae (e.g., Podsiadlowski et al 2004), while for higher initial masses NSs form through regular core collapse

  • The detailed study of an alternative neutron star formation mass is underway (Fryer & Belczynski, in preparation), we just note that the details of neutron star formation do not play crucial role in conclusions derived in this study

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Summary

INTRODUCTION

Measuring the masses of celestial objects is one of the principal challenges in astrophysics. The measurement of X-ray luminosity leads to a lower limit on the mass of the accreting body arising from the Eddington limit This method, which was applied in the case of ultra luminous X-ray sources (ULX) has hinted that these systems are BHs with masses in excess of 100 M⊙ (Miller et al 2004). We combine the wind mass loss rates with the stellar evolution models and investigate the initial-remnant mass relation of stars for different metallicities. It is noted that both stellar models (e.g., mixing or reaction rates; Cassisi 2009) and wind mass loss rates (e.g., clumping or LBV phase; Vink 2008) are burdened with a number of uncertainties, rendering any estimate of a black hole mass a subject to large systematic errors. The wind mass loss rates are denoted as dM/dt ([ M⊙ yr−1])

Hurley et al winds: previous reference model
Vink et al winds: new reference model
Compact object masses: maximum BH mass
Standard Prediction
Examples of Mass Loss
Effect of LBV Mass Loss
Wolf-Rayet winds
Comments on Black Hole Masses
General Remarks

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