Transmutation Timescales for Dark Matter Induced Collapse of Compact Stars into Black Holes

Ultra-heavy asymmetric dark matter (DM) particles captured by compact stars can thermalize, self-gravitate, and collapse to form an endoparasitic black hole (EBH), whose subsequent growth may transmute the host star into a black hole. The continued existence of old millisecond pulsars (MSPs) and white dwarfs (WDs) thus places powerful constraints on the DM particle mass mχ and the DM-nucleon scattering cross-section σnχ. In this work, we derive an analytical expression for the transmutation timescale by solving the EBH growth equation while consistently accounting for the Bondi accretion of stellar matter, Hawking evaporation, and allowing for the possibility of sustained DM feeding of the EBH in a steady-state capture regime. We also incorporate quantum mechanical effects in the baryonic accretion process by modeling particle absorption in regimes where the hydrodynamic description breaks down, thereby providing a unified treatment of EBH growth across both particle and fluid regimes. Adopting a physically transparent collapse criterion for both fermionic and bosonic asymmetric DM, we compute the EBH transmutation timescales for representative MSPs and WDs residing in environments with different DM densities. Although the underlying physical ingredients are broadly the same as those considered in previous studies, the present work derives updated constraints through a closed-form analytical treatment of EBH growth, together with the adopted prescription for the EBH formation timescale. Consequently, we obtain a lower critical EBH mass for sustained growth and revised transmutation timescales. Requiring the transmutation time to exceed ∼ 1 Gyr for MSPs and ∼ 10 Gyr for WDs, we derive revised constraints on σnχ over the DM mass range 10 6 −10 14 GeV. Notably, we show that EBHs with initial masses as small as ∼ 4 × 10 4 kg can undergo sustained growth, thereby extending the region of the DM parameter space that can be probed using compact stars.

Improvements to AI Systems:

1. Unified Multi-Regime Accretion Modeling

• Improvement: Implement a hybrid physics engine that automatically switches between hydrodynamic (Bondi) and quantum-mechanical particle-absorption regimes based on local conditions (e.g., mean free path vs. EBH size).

• Capability: AI can accurately simulate black hole growth in dense stellar interiors across 12+ orders of magnitude in mass and density, avoiding numerical discontinuities.

2. Closed-Form Analytical Solver for Coupled Differential Equations

• Improvement: Train a neural solver to derive and invert closed-form expressions for transmutation timescales, incorporating Bondi accretion, Hawking radiation, and steady-state DM feeding simultaneously.

• Capability: AI can instantly compute transmutation times for arbitrary compact-star parameters (mass, radius, DM density) without iterative numerical integration, enabling real-time parameter sweeps.

3. Quantum-Corrected Accretion Rate Predictor

• Improvement: Add a sub-model that predicts when the hydrodynamic approximation fails and applies quantum scattering cross-sections for baryon absorption (e.g., using geometric vs. de Broglie wavelength limits).

• Capability: AI can correctly estimate EBH growth in low-density regimes where classical Bondi overestimates accretion, improving accuracy for white dwarfs and low-mass stars.

4. Self-Gravitating Collapse Criterion Classifier

• Improvement: Integrate a decision module that distinguishes fermionic (Pauli-blocking) vs. bosonic (Bose-Einstein condensation) DM collapse thresholds, using the paper’s physically transparent criterion.

• Capability: AI can automatically select the correct collapse condition for a given DM particle type, avoiding erroneous constraints for unknown DM candidates.

5. Revised Constraint Extrapolator

• Improvement: Use the derived lower critical EBH mass (4×104 kg) to retrain a Bayesian inference model that maps observed MSP/WD survival times to exclusion regions in (mχ, σnχ) space.

• Capability: AI can produce updated, analytical DM parameter constraints for masses 106–1014 GeV, extending sensitivity to previously untested parameter space (e.g., lighter DM or weaker interactions).

6. Steady-State Capture Feedback Loop

• Improvement: Add a feedback mechanism that recalculates DM capture rate as the EBH grows, accounting for reduced stellar density and modified gravitational potential.

• Capability: AI can simulate long-term (Gyr) evolution of EBH-host systems, predicting whether DM feeding sustains growth or stalls—critical for distinguishing viable DM models.

7. Timescale-to-Survival Probability Mapper

• Improvement: Train a classifier that converts computed transmutation timescales into survival probabilities for MSPs (>1 Gyr) and WDs (>10 Gyr), with uncertainty propagation from input parameters.

• Capability: AI can output probabilistic exclusion contours, replacing binary “allowed/forbidden” constraints with statistically robust limits for future dark matter searches.

What the Improved AI System Can Do:

• Instantly generate full DM parameter-space exclusion plots for any compact-star population, using only stellar mass, radius, and local DM density as inputs.

• Run real-time simulations of EBH growth from formation to host-star destruction, including quantum-to-fluid transitions and Hawking radiation feedback.

• Provide a unified framework for testing arbitrary DM particle types (fermionic/bosonic, asymmetric) against astrophysical observations, with analytical transparency and computational efficiency.

• Enable rapid re-analysis of existing pulsar and white dwarf data to set the most stringent current bounds on ultra-heavy DM, directly informing experimental searches (e.g., LIGO, LZ, XENONnT).