Subsolar mass black holes from stellar collapse induced by primordial black holes

The paper proposes that subsolar mass black holes could originate from an "indirect PBH scenario," where a small primordial black hole is captured by a dwarf star and subsequently consumes it, rather than the black hole being a primordial object itself.

The Gist

The Cosmic "Trojan Horse": How Tiny Black Holes Could Eat Stars to Become Giants

Imagine you are looking at a crime scene. You find a massive, heavy safe that has been completely crushed. Most detectives would assume the "culprit" was a giant, heavy sledgehammer. In space, if astronomers find a black hole that is smaller than our Sun (a "subsolar mass" black hole), they usually assume it was born that way—like a tiny, heavy marble created at the very beginning of the universe. This is what scientists call the "Direct Scenario."

But this paper suggests a much more sneaky, "heist-style" alternative: The Indirect Scenario.

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The Concept: The Cosmic Trojan Horse

Instead of a giant sledgehammer, imagine a tiny, microscopic needle. On its own, the needle is nothing. But what if that needle was actually a tiny, invisible "seed" (a very small Primordial Black Hole) that snuck inside a large, soft object (a dwarf star)?

Once inside, the tiny black hole doesn't just sit there. It starts eating. It acts like a cosmic parasite. It begins to consume the star from the inside out, growing larger and larger as it gobbles up the stellar material. Eventually, the star is completely gone, leaving behind a black hole that is much larger than the "seed" that started it.

The result? You end up with a medium-sized black hole that looks like it was "born" that way, but it was actually "built" by eating a star.

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The Setting: The Quiet Neighborhoods of Space

The authors explain that this "eating" process is most likely to happen in Dwarf Galaxies.

Think of the Milky Way as a bustling, high-speed metropolis. Cars (stars and dark matter) are zooming around at hundreds of miles per hour. In such a fast-paced environment, it’s hard for a tiny black hole to "catch" a star; they usually just zip past each other like two ships in the night.

Dwarf galaxies, however, are like quiet, sleepy suburbs. Everything moves much more slowly there. Because the "traffic" is so slow, a tiny primordial black hole has a much better chance of bumping into a star, getting stuck, and starting its feast.

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The Math: Why This Matters

The researchers did some "back-of-the-envelope" math to see if this could actually happen often enough to be noticed. Here is what they found:

1. The Seeds are Everywhere: Even if these tiny black holes make up only a small fraction of "Dark Matter," there would still be billions of them floating around.
2. The Feast is Fast: Once the tiny black hole is inside the star, it eats through the star's mass relatively quickly (in cosmic terms).
3. The Population is Significant: They estimate that in a galaxy like our own, this "indirect" method could create about 100,000 subsolar black holes.

While 100,000 is a small number compared to the billions of stars in the galaxy, it is plenty large enough to explain the "mystery signals" that gravitational-wave detectors (like LIGO) have been picking up lately.

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The Big Picture

If we eventually confirm that these small black holes exist, we won't know for sure if they were "born small" (the Direct Scenario) or "grown through eating" (the Indirect Scenario).

However, this paper gives astronomers a new clue: if we see these black holes mostly in quiet, dwarf galaxies, it’s a smoking gun that they might be "cosmic parasites" that grew by consuming their hosts!

Technical Summary

Technical Summary: Subsolar Mass Black Holes from Stellar Collapse Induced by Primordial Black Holes

Authors: Thomas W. Baumgarte and Stuart L. Shapiro
Subject Area: Astrophysics / Gravitational Wave Astronomy / Dark Matter

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1. The Problem: The Origin of Subsolar Mass Black Holes

Current gravitational-wave (GW) observations by the LIGO-Virgo-Kagra (LVK) collaboration have primarily identified stellar-mass black holes ($> 5 M_\odot$). However, several candidate signals (e.g., SSM170401, SSM200308, and S251112cm) suggest the potential existence of subsolar mass black holes ($M < 1 M_\odot$).

Because standard stellar evolution (supernova explosions) cannot produce black holes below the Chandrasekhar limit, a confirmed detection of such objects would be a "smoking gun" for Primordial Black Holes (PBHs)—black holes formed in the early universe. The prevailing scientific assumption is the "Direct PBH Scenario," where the observed mass ($M_{obs}$) is equal to the primordial mass ($M_{PBH}$). However, this scenario faces theoretical constraints and potential conflicts with pulsar-timing array observations.

2. Methodology: The "Indirect PBH Scenario"

The authors propose an alternative mechanism: the "Indirect PBH Scenario." Instead of the observed black hole being a primordial object itself, it is the result of a much smaller PBH consuming a star.

The authors model the following process:

1. Capture: A very small PBH ($M_{PBH} \ll M_{obs}$) undergoes a collision with a dwarf star ($M_* \simeq M_{obs}$).
2. Dissipation: For capture to occur, the PBH must dissipate enough kinetic energy through hydrodynamic friction during its first transit through the star to become gravitationally bound.
3. Accretion/Consumption: Once bound, the PBH settles at the stellar center and accretes the stellar material via Bondi accretion.
4. Final State: The PBH consumes the entire star, resulting in a new black hole with a mass approximately equal to the original stellar mass ($M_{BH} \simeq M_*$).

To test the feasibility of this, the authors perform astrophysical estimates focusing on dwarf galaxies, which are ideal environments due to their high dark-matter density and low stellar dispersion velocities ($\sigma \simeq 10 \text{ km/s}$), both of which maximize capture rates.

3. Key Contributions and Mathematical Framework

• Minimum Mass for Capture: The authors derive a minimum mass requirement for a PBH to be captured by a star, showing that PBHs in "Window B" ($\sim 10^{-6} M_\odot$) are capable of being captured by dwarf stars.
• Accretion Timescale: Using the Bondi accretion rate and assuming a $\Gamma = 5/3$ polytrope (typical for convective dwarf stars), they calculate the timescale for total stellar consumption ($\tau_{acc}$). They demonstrate that for $M_{PBH} \gtrsim 2 \times 10^{-15} M_\odot$, the consumption time is significantly shorter than the age of the universe.
• Collision Rate Modeling: They provide a formula for the total number of collisions ($N_{tot}$) an individual star experiences over its lifetime, accounting for dark matter density ($\rho_{DM}$), stellar radius ($R_*$), and relative velocity ($v_\infty$).

4. Results

• Population Estimates: In a typical dwarf galaxy, the authors estimate that the indirect scenario could produce approximately $3 \times 10^3$ to $3 \times 10^4$ subsolar mass black holes (assuming $f_{PBH} = 0.1$).
• Galactic Scale: Scaling this to a Milky Way-type galaxy (assuming $\sim 50$ dwarf galaxies), the total population of induced subsolar mass black holes could reach $\sim 10^5$.
• Comparison to Direct Scenario: While the indirect population is significantly smaller than the "Direct Scenario" (which could yield $10^9$ black holes) and much smaller than the standard stellar-mass black hole population ($\sim 10^8$), it is still large enough to account for the rare, low-mass GW events currently being searched for.

5. Significance and Implications

• Reinterpreting GW Detections: The paper suggests that if subsolar mass black holes are detected, we cannot immediately assume $M_{obs} = M_{PBH}$. The observed mass might actually reflect the mass of a captured dwarf star rather than the primordial mass of the black hole.
• Observational Distinctions: While GW signals alone may not distinguish between the direct and indirect scenarios, the authors suggest that the mass distribution of these black holes could serve as a discriminator. The indirect scenario would leave a specific imprint on the mass function, particularly in ultra-faint dwarf galaxies.
• Dark Matter Constraints: This mechanism provides a way for PBHs in "Window B" (Earth-mass range) to manifest as observable subsolar mass black holes in "Window C" (0.1 $M_\odot$ range), potentially bypassing certain observational constraints.