Could the stochastic gravitational wave background from newborn magnetars be detected by the advanced LIGO and Einstein Telescope?

TL;DR

The paper investigates whether the stochastic gravitational wave background (SGWB) from newborn magnetars could be detected by advanced LIGO ($a$LIGO) and the Einstein Telescope (ET). It builds a physically motivated model of magnetar evolution, including spin-down via magnetic-dipole radiation and gravitational-wave emission, tilt-angle evolution, and thermal cooling, then computes the SGWB via $\Omega_{\rm GW}(\nu_{\rm obs})$ by integrating over redshift with a magnetar formation rate $R_s(z)$ and a dipole-field distribution $P_{B_{\rm d}}(B_{\rm d};\mu,\sigma)$ for three formation channels: $\alpha-\Omega$ dynamo, convective dynamo, and magnetic flux conservation. The results show SNRs for ET of about 0.37 ( model A ), $3\times10^{-4}$ ( model B ), and 0.21 ( flux-conservation with $\bar{B_t}=10B_d$), with a more conservative $1.9\times10^{-2}$ for $\bar{B_t}=5B_d$; all are far below the ET detection threshold, implying the SGWB from newborn magnetars is unlikely to be detected under these realistic scenarios. The study highlights the critical role of correlations between initial spin and magnetic field—and the chosen magnetic-field distributions—in shaping the SGWB, and points to future work that combines multiple field-amplification channels and more comprehensive population synthesis and MHD modeling to refine the prospects of detection.

Abstract

Newborn magnetars are important gravitational wave sources due to their ultra-strong magnetic fields and fast spins, and the entire population in the Universe may significantly contribute to the stochastic gravitational wave background (SGWB). In this work, we investigate the SGWB from newborn magnetars and assess its detectability by the advanced LIGO (aLIGO) and Einstein Telescope (ET) based on three typical formation mechanisms of magnetars, i.e., the $α-Ω$ dynamo, convective dynamo, and magnetic flux conservation. For the two dynamo scenarios, when calculating the SGWB, we creatively incorporate the anti-correlations between the magnetic fields and initial spin periods $P_{\rm i}$ with the initial dipole-field distribution of newborn magnetars. For the flux-conservation scenario, a bimodal lognormal form is adopted to describe the distribution of initial dipole fields, and all magnetars are assumed to have the same $P_{\rm i}$. Our results show that the SGWB from newborn magnetars may be undetectable by the aLIGO and ET if the magnetars are formed due to these mechanisms since the signal-to-noise ratio of the SGWB with respect to the ET for an observation time of one year is only 0.37 for the $α-Ω$ dynamo, $3\times10^{-4}$ for the convective dynamo, and at most 0.21 for the flux conservation.

Figures (2)

• Figure 1: The dimensionless GW energy density $\Omega_{\rm GW}$ versus the observed frequency $\nu_{\rm obs}$ from newborn magnetars formed due to the two dynamo models. See the text for details.
• Figure 2: $\Omega_{\rm GW}$ versus $\nu_{\rm obs}$ from newborn magnetars formed due to magnetic flux conservation. The colored curves show the SGWB spectra obtained by assuming $\bar{B_{\rm t}}=10B_{\rm d}$ and $\bar{B_{\rm t}}=5B_{\rm d}$ for the newborn magnetars (see the legends).