On The Maximum Mass of Stellar Black Holes (0904.2784v2)

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.

• The paper derives theoretical maximum masses for stellar black holes using updated evolutionary models in StarTrack, showing how stellar metallicity and wind mass loss constrain the observed mass spectrum.
• Key findings include predicted maximum black hole masses ranging from ~15 solar masses in high-metallicity environments to 80 solar masses in low-metallicity conditions.
• These results inform gravitational wave astronomy by linking black hole mass limits to metallicity and emphasize the importance of precise wind mass loss models for stellar evolution predictions.

Analysis of Stellar Black Hole Maximum Mass

The paper, "On The Maximum Mass of Stellar Black Holes," explores the theoretical upper limits of stellar black hole masses formed from single stars, emphasizing the influence of stellar metallicity and mass loss through stellar winds. The research explores the derivation of black hole masses from evolutionary models and stellar wind prescriptions, providing a nuanced view of the mass spectrum of compact objects such as neutron stars (NSs) and black holes (BHs) in various stellar environments.

Key Findings

The authors employ a spectrum of metallicities: from solar ($Z=Z_\odot=0.02$) to very low (globular cluster-like, $Z=0.01 Z_\odot=0.0002$), and assess the impact of these environments on black hole formation. It is shown that the maximum observed black hole mass in a high metallicity environment, such as the Milky Way, is approximately 15 solar masses, and this finding is in line with the known massive black hole candidates in our galaxy. For moderate metallicity ($Z=0.3\ Z_\odot=0.006$), the paper suggests a maximum possible black hole mass of 30 solar masses. The exceptionally high black hole mass of 80 solar masses is attributed to low metallicity conditions.

Critical to these calculations is the role of wind mass loss rates, particularly those related to Wolf-Rayet (WR) stars and Luminous Blue Variables (LBVs). The authors adopt and calibrate specific wind mass loss rates using models such as those by Hurley et al. and Vink et al., demonstrating their compatibility with observed stellar mass black holes.

Methodological Approaches

The paper utilizes the single star evolutionary formulae integrated into the {\tt StarTrack} population synthesis code. Updates to the mass loss prescriptions allow for more precise modeling of massive stars' wind losses, addressing key components like O/B star winds, as well as clumping and metallicity effects on WR winds. This methodological rigor leads to improved predictions of stellar end masses and subsequent remnant black hole classifications.

Implications and Future Directions

Practically, the restrictions imposed by metallicity on black hole mass can inform gravitational wave astronomy, aiding in the identification and characterization of black hole mergers detectable by interferometers such as LIGO and VIRGO. These results underscore the nuanced interplay between stellar evolution, wind dynamics, and core-collapse scenarios.

Theoretically, this research poses new questions regarding the dependency of LBV and WR mass loss on stellar composition and metallicity. Furthermore, the paper hints at vast uncertainties in stellar evolution models, such as the potential effects of rotation on stellar mass and compact object formation.

Future studies could expand on this foundational work by incorporating more detailed rotational dynamics and binary star interactions that remain unexplored in this single-star framework. Such aspects could reveal further intricacies of stellar evolution processes and their impact on the most massive black holes.

Overall, the paper provides a robust examination of stellar evolution models, offering predictions that satisfy existing observational constraints and enhancing our understanding of mass loss dynamics across different metallicity environments.