Tidal disruption of a neutron star near naked singularity

TL;DR

The paper investigates tidal disruption of a neutron star (NS) by black holes (BH) and naked singularities (NaS), focusing on the tidal disruption radius in Schwarzschild and Joshi-Malafarina-Narayan (JMN1) spacetimes. It derives Roche-limit expressions for Schwarzschild ($R_t^r = R_n (2M/m)^{1/3}$) and JMN1 ($R_T = R_n \sqrt{\frac{(1 - \frac{3GM}{c^2 R_b}) M R_n}{(1 - \frac{2GM}{c^2 R_b}) m R_b}}$), showing NS disruption in BHs is typically unobservable due to horizons, while NaS can produce observable disruption and kilonova-like transients with possible enhanced r-process yields. The study analyzes relativistic debris timescales, differentiating bound and unbound debris in Schwarzschild and JMN1 backgrounds, and demonstrates that NaS light curves depend on the compactness parameter $M_0$, with $M_0\in(0,2/3)$ yielding $dE/d\tau$ trends consistent with observed TDE power-laws ($t^{-5/3}$) and broader implications for multi-messenger observations. Overall, NS disruptions near NaS offer a novel probe of strong gravity and a potential channel for heavy-element production, with distinctive observational signatures that could differentiate horizonless objects from BHs.

Abstract

We investigate the tidal disruption of a neutron star (NS) near a black hole (BH), and for the first time, to the best of our knowledge, near a naked singularity (NaS). For a BH with a mass greater than about $10 M_{\odot}$, the tidal disruption of NS should occur within the event horizon, and hence neither can the stellar material escape nor a distant observer observe the disruption. Since NaS does not have an event horizon, a significant portion of the NS's material can escape, and the tidal disruption can be observed by a distant observer. One could identify such an event from the observed emission from the disrupted NS's material and the decay of the light curve of the disruption event. The escape of a significant fraction of the NS's material may also have implications for the heavy elements in the universe. Moreover, observing such an event can be useful for confirming a NaS, probing its spacetime, and studying the motion of matter in such a geometry. This may help constrain the NS parameters and equation of state models. As a first step in this direction, we calculate here the tidal disruption radius and other parameters for a specific type (Joshi-Malafarina-Narayan type 1) of NaS and compare our results with observations.

Figures (3)

• Figure 1: In figures, the tidal disruption radius versus the solar mass of the central compact object is shown. Fig. (\ref{['sch']}) illustrates how the tidal disruption radius changes with changing the mass of the central Schwarzschild BH. Black, red, and blue lines show the event horizon, innermost stable circular orbit (ISCO), and tidal disruption radius, respectively. Fig. (\ref{['jmn']}) demonstrates tidal disruption radius in JMN1 NaS for $M_{0}<2/3$. In the JMN1 case, the tidal disruption radius is directly dependent on the compactness ratio $M_{0}$. We take the NS mass $1.4M\odot$, and the diameter of the NS is $15 \text{km}$. For the JMN1 case, for $R_{b1}$, $R_{b2}$, and $R_{b3}$ are $1.0 \times 10^{-6} Pc$ (black line), $2.0 \times 10^{-6} Pc$ (blue line), $3.0 \times 10^{-6} Pc$ (red line), respectively.
• Figure 2: The figure shows a light curve in the BH and JMN1 NaS. The red and blue curves show the light curve in the BH and JMN1 NaS, respectively. We considered both have $10M_\odot$ and in JMN1 boundary radius $R_{b} = 10GM/c^2$.
• Figure 3: This figure shows the radial and angular tidal force components ($\eta^{\hat{r}"} / \eta^{\hat{r}}$) and ($\eta^{\hat{\theta}"} / \eta^{\hat{\theta}}$) versus coordinate radius $(r)$, respectively. Figures (a) and (b)show the radial tidal force for $M_{0}<2/3$ and $M_{0}>2/3$, respectively. Similarly, figures (c) and (d)show the angular tidal force for $M_{0}<2/3$ and $M_{0}>2/3$, respectively. For (a) red, blue, and magenta lines show $R_{b} = 6M$, $R_{b} = 3.2M$ and, $R_{b} = 3.01M$, respectively. For (b) red, blue, and magenta lines show $R_{b} = 2.1M$, $R_{b} = 2.5M$, and $R_{b} = 2.95M$, respectively. (c) for red $R_{b} = 6M$ and $r_{0} = 5.5M$, for blue $R_{b} = 3.2M$ and $r_{0} = 3.0M$, for magenta line $R_{b} = 3.01M$ and $r_{0} = 3.0M$. (d) for red $R_{b} = 2.1M$ and $r_{0} = 2.0M$, for blue $R_{b} = 2.5M$ and $r_{0} = 2.4M$, for magenta line $R_{b} = 2.95M$ and $r_{0} = 2.9M$. In the above figures, the radial ($\eta^{\hat{r}}$) and angular ($\eta^{\hat{\theta}}$) components of the Jacobi field versus coordinate radius for JMN1 spacetime are shown. Fig. (\ref{['jacobiradial']}) illustrates how the radial components of the Jacobi field change with coordinate radius $r$. Fig. (\ref{['jacobiangular']}) demonstrates how the angular components of the Jacobi field change with coordinate radius $r$. The initial conditions chosen are $\eta^{\hat{r}} = 1$, $\eta^{\hat{\theta}} = 1$, $\dot{\eta}^{\hat{r}} = 0$, and $\dot{\eta}^{\hat{\theta}} = 0$, where the overdot represents the derivative with respect to proper time $\tau$. Red and blue lines show for $R_{b} = r_{0} = 7.5M$ and $R_{b} = r_{0} = 2.6M$, respectively. Here we take $M = 1$.