[Paper Review] Primordial black holes are again on the limelight

M. Roncadelli, A. Treves+1 more|ArXiv.org|Jan 8, 2009

Stellar, planetary, and galactic studies1 references3 citations

TL;DR

This paper derives a strong upper bound on the present-day abundance of primordial black holes (PBHs) with masses >10^15 g by modeling gravitational capture of PBHs by stars during Milky Way star formation and subsequent accretion. It shows that even a small fraction of captured PBHs would lead to catastrophic depletion of disk stars and white dwarfs unless PBHs are extremely rare, thereby constraining their cosmic density and suggesting that low-mass stellar black holes (M < 1 M☉) could originate from PBHs swallowing white dwarfs.

ABSTRACT

We derive a strong upper bound on the amount of Primordial Black Holes (PBHs) that can still be present in the Universe. Gravitational capture of PBHs by the Milky Way stars during their formation and subsequent accretion would produce a dramatic depletion of disk stars and especially of white dwarfs, unless the average cosmic density and mass of PBHs are severely constrained. Our finding also helps to discriminate among the various production mechanisms of PBHs. Moreover, we show that a star becomes overluminous before its disappearance into a PBH for a time span independent of its mass, thereby providing a characteristic observational signature of the considered scenario. We stress that our result allows for the existence of stellar-mass black holes in a mass range that is forbidden by standard stellar evolution.

Motivation & Objective

• To assess the astrophysical consequences of primordial black holes (PBHs) with masses >10^15 g capturing stars during Milky Way star formation.
• To constrain the present-day cosmic density of PBHs by analyzing the accretion-induced depletion of disk stars and white dwarfs.
• To evaluate whether PBHs could explain low-mass stellar black holes (M < 1 M☉), which are forbidden by standard stellar evolution.
• To identify a characteristic observational signature—overluminous phase before collapse—whose duration is independent of stellar mass.
• To discriminate among various PBH production mechanisms via the derived density constraints.

Proposed method

• Assumes PBHs follow a Cored Spherical Isothermal (CSI) distribution in the Milky Way halo, matching the dark matter density profile and velocity dispersion.
• Uses the Bondi accretion model to compute the accretion rate of PBHs onto stars, transitioning to Eddington-limited accretion when the PBH mass exceeds ~7.6×10^14 g/ε.
• Applies the condition that the star’s luminosity exceeds 0.1 L* during the final phase before collapse to estimate the time to over-luminosity (t_lum).
• Derives the time to swallow (t_sw) by requiring the PBH mass to grow to the star’s mass via accretion, assuming Eddington-limited growth.
• Imposes a constraint that only a small fraction of stars can capture PBHs to avoid catastrophic depletion, leading to a bound on the PBH density parameter Ω_PBH < 10^{-8}.
• Evaluates the turnover time (t_to) when accretion shifts from Bondi to Eddington-limited regime, using the PBH mass threshold of ~7.6×10^14 g/ε.

Experimental results

Research questions

• RQ1 What is the maximum allowed cosmic density of primordial black holes (PBHs) with masses >10^15 g, given their gravitational capture by forming stars?
• RQ2 Can PBHs with masses >10^15 g survive in the Milky Way disk without causing observable depletion of stars and white dwarfs?
• RQ3 Does the time span of the pre-collapse overluminous phase depend on the initial stellar mass?
• RQ4 Can PBHs explain the existence of low-mass stellar black holes (M < 1 M☉), which are not predicted by standard stellar evolution?
• RQ5 What constraints do these astrophysical effects place on the initial mass function and production mechanisms of PBHs?

Key findings

• The present-day cosmic density parameter of PBHs with masses >10^15 g is constrained to Ω_PBH < 10^{-8}, based on the requirement that PBH capture does not lead to catastrophic depletion of stars.
• A star becomes overluminous for approximately 8.3×10^4 years before being swallowed by a PBH, and this duration is independent of the stellar mass.
• The time to swallow a star via accretion is less than 1.4×10^5 years for PBHs with masses >7.6×10^19 g, assuming Eddington-limited accretion.
• Accretion transitions from Bondi to Eddington-limited regime at a PBH mass of ~7.6×10^14 g/ε, with the turnover time t_to < 3.3×10^8 years.
• PBHs with masses >10^25 g are required to make a substantial contribution to dark matter, implying that only the most massive PBHs can be significant dark matter candidates.
• Observational evidence for black holes with masses M < 1 M☉ would strongly suggest a PBH origin, as such masses cannot form via standard stellar evolution.