Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Magnetically arrested transmutation of a compact star

H. A. Adarsha, Chandrachur Chakraborty, Sudip Bhattacharyya

Abstract

We introduce a novel mechanism -- Magnetically Arrested Transmutation (MAT) -- which could be a viable model to account for the observed over-representation of magnetic white dwarfs (WDs) near the Galactic centre (GC), and the presence of a magnetar as opposed to the absence of ordinary pulsars in the same region. In this scenario, compact stars accumulate asymmetric or non-self-annihilating dark matter particles, eventually forming an endoparasitic black hole (EBH) of initial mass $M_0$ at their core. Although such EBHs generally grow by accreting host matter, we show that sufficiently strong core magnetic fields can establish pressure equilibrium, thereby stalling further accretion and halting the star's transmutation into a black hole. We derive the conditions for this MAT to occur, identifying a critical parameter $β$, that encapsulates the interplay between the magnetic field strength, host matter density, and EBH mass. For $0 < β\leq 4/27$, the growth of the EBH is arrested, limiting its final mass ($M_{\rm f}$) to $M_0 <M_{\rm f} \leq 3/2M_0$, whereas for $β> 4/27$, full transmutation may ensue. We argue that highly magnetized WDs may survive near the GC due to the MAT mechanism, as do high-spin ordinary WDs, despite hosting a central EBH. We also speculate a possibility that the magnetar PSR J1745-2900 survives near the GC due to the MAT mechanism. Overall, the MAT framework may explain an elevated population of magnetic WDs in dense dark matter environments, and hence could be tested and should have implications for understanding dark matter and compact objects.

Magnetically arrested transmutation of a compact star

Abstract

We introduce a novel mechanism -- Magnetically Arrested Transmutation (MAT) -- which could be a viable model to account for the observed over-representation of magnetic white dwarfs (WDs) near the Galactic centre (GC), and the presence of a magnetar as opposed to the absence of ordinary pulsars in the same region. In this scenario, compact stars accumulate asymmetric or non-self-annihilating dark matter particles, eventually forming an endoparasitic black hole (EBH) of initial mass at their core. Although such EBHs generally grow by accreting host matter, we show that sufficiently strong core magnetic fields can establish pressure equilibrium, thereby stalling further accretion and halting the star's transmutation into a black hole. We derive the conditions for this MAT to occur, identifying a critical parameter , that encapsulates the interplay between the magnetic field strength, host matter density, and EBH mass. For , the growth of the EBH is arrested, limiting its final mass () to , whereas for , full transmutation may ensue. We argue that highly magnetized WDs may survive near the GC due to the MAT mechanism, as do high-spin ordinary WDs, despite hosting a central EBH. We also speculate a possibility that the magnetar PSR J1745-2900 survives near the GC due to the MAT mechanism. Overall, the MAT framework may explain an elevated population of magnetic WDs in dense dark matter environments, and hence could be tested and should have implications for understanding dark matter and compact objects.

Paper Structure

This paper contains 5 sections, 16 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Magnetically arrested transmutation: Formalism
  3. Application to compact stars
  4. Conclusion and discussion
  5. Mathematical Formulation for Determining the Final Mass ($M_{\rm f}$) of an EBH

Figures (2)

  • Figure 1: Plot of the dimensionless MAT parameter $\beta :=\left(2048\,G^{3}\pi^4\rho^4\right)M_0^2/\left(3\,(B^2-8\pi P_{\rm h})^{3}\right)$ as a function of the core magnetic field $B$, for the EBH mass range : $10^{15}$g $\leq M_0 \leq 10^{30}$ g formed at the cores of magnetized compact stars. Panel (a): Light red (light blue) shaded region shows the range of $B$ for which $\beta \leq 4/27$ (dashed line), ensuring suppression of EBH growth via the MAT mechanism inside a WD (NS) of mass $1M_\odot$ ($2M_\odot$). The boundaries of each shaded region correspond to $M_0=10^{15}$ g (lower) and $10^{30}$ g (upper). Below the lower curves (i.e., the green shaded regions), Hawking Evaporation (H.E.) of the EBH ensues, and the host does not undergo transmutation, as the EBH eventually disappears, aided by the MAT mechanism. Panel (b): Same as (a), but for a range of WD (NS) masses and densities. Left of the shaded region, $B$ is insufficient to stall the growth of EBH and to the right, $B$ is unphysical since the magnetic energy density exceeds the energy density and pressure of the matter. This figure shows that the WDs (NSs) with a core magnetic field in the lower range than the shaded region transmute into BHs, while those with fields within the horizontal extent of the shaded region avoid transmutation due to the MAT mechanism or Hawking evaporation. Note that, although H.E. region for lowest mass mWD is shown exactly in Panel (b), for mWD of higher masses, the H.E. region slightly overlaps with the red-shaded region, since the lower curve (corresponding to $M_0=10^{15}$ g) for those mWD masses is at a slightly greater value of $\beta$ than those with lower masses.
  • Figure 2: Plot for the nested infinite series $S(\beta)$ as a function of $\beta$. The solid orange curve shows that $S(\beta)$ has finite values for $\beta \leq 4/27$, but it diverges sharply for $\beta > 4/27$.