Polar Mounds on Strangeon Stars: the Neutrino Emission from Ultraluminous X-ray Pulsars

TL;DR

This paper addresses whether the equation of state of supranuclear matter can be distinguished by studying ULXPs within the strangeon-star framework. It develops a one-dimensional steady-state model of the polar accretion column, incorporating Coulomb and strangeness barriers to estimate the thermal mound height and resulting neutrino emission from electron-positron annihilation. The results show a mound height of about 0.7–0.95 km with base temperatures exceeding $10^9$ K, where neutrino cooling can dominate at high accretion rates and the total luminosity can reach ~10^{41} erg s^{-1}. Despite the potentially enhanced neutrino output, the predicted flux at Earth is generally far below the MeV background for extragalactic ULXPs, making detection unlikely with current instruments, though such neutrino observations could in principle probe strangeon-star physics and supranuclear matter.

Abstract

Ultraluminous X-ray pulsars (ULXPs) serve as unique astrophysical laboratories, offering critical insights into accretion physics under extreme conditions, such as strong magnetic fields and super-Eddington accretion rates. Additionally, the nature of pulsars, i.e., the equation of state of supranuclear matter, is still a matter of intense debate, basing on either conventional neutron stars or strange stars. In this work, in order to differentiate the conjectured states of matter, we investigate accretion columns of ULXPs based on the strangeon-star (SS) model, focusing on the thermal mound at the column base. Accounting for Coulomb and strangeness barriers of SSs, we find that the mound can reach $0.7-0.95\,\rm km$ in height with temperatures above $10^9\, \rm K$, enabling substantial neutrino emission via electron-positron annihilation. At low accretion rates ($< 10^{20}\, \rm g\,s^{-1}$), photons dominate the luminosity, while at higher rates ($> 10^{21}\, \rm g\, s^{-1}$), photon trapping makes neutrino emission the main cooling channel, with total luminosity exceeding photon emission, which saturates near $10^{41}\, \rm erg\,s^{-1}$. Even though the predicted neutrino flux from the nearest system, Swift J0243.6$+$6124, lies well below the diffuse MeV background--implying that detectable emission would require substantially closer or more luminous sources--these results demonstrate the key role of the thermal mound and SS properties in accretion, providing a foundation for future ULXP studies and suggesting that neutrino observations could, in principle, offer a novel probe of SSs and extreme supranuclear matter.

Figures (5)

• Figure 1: Schematic depiction of the magnetic polar regions with radius $R_{\rm s} \simeq10^{5}\, \rm cm$ and height $H_{\rm mound}$ of polar mound in an X-ray pulsar. $\Theta$ is the opening angle of the magnetic funnel. This diagram is adapted from 2020PASJ...72...12I.
• Figure 2: Profiles of physical quantities within the magnetic polar regions as functions of height, with different colors indicating different mass accretion rates. We adopt a stellar model with $M = 1.4 \, M_{\odot}$ and $R = 10^{6}\, \rm cm$. The first column presents the radiation energy density, mass density, and pressure, while the second column shows the corresponding velocity, optical depth, and temperature profiles. Normalization parameters are defined as $\varepsilon_{0} = GM/R$, $\rho_{0}=3 B^2 R/ (8 \pi G M) \sim 10^{2}\, \rm g\,cm^{-3}$, and $P_0 =B^2/ (8\pi)$, assuming a surface magnetic field strength of $B = 10^{12}\, \rm G$. The characteristic temperature, $T_{\rm C}$, is calculated via $T_{\rm C} = (\rho \varepsilon/a)^{1/4}$, where $a$ is the radiation constant. The height of the polar mound $H_{\rm mound} \approx 0.8 \, \rm km$.
• Figure 3: Mass density of the thermal mound as a function of thermal mound height for different weak interaction timescales with a fixed mass accretion rate $\dot{M}= \dot{M}_{\rm Edd}$ ( upper panel), and for different mass accretion rates with a fixed weak interaction timescale $t^{*}_{\rm weak} = 10^{-10}\, \rm s$ ( lower panel). We set magnetic field strength $B = 10^{12}\, \rm G$.
• Figure 4: The neutrino luminosity of our work (solid line), neutrino luminosity of Asthana:2023vvk (dashed line), and the photon luminosity as functions of the mass accretion rate. The dash-dotted line is total luminosity is the dash-dotted line. The horizontal dash lines are show the observed luminosity for some ULXPs. We calculate the neutrino luminosity with $t = t^{*}_{\rm weak}$ and the magnetic field strength $B = 10^{12}\, \rm G$ in our work.
• Figure 5: The energy spectrum of neutrino background at Earth in the energy range from $10^4 \, \rm eV$ to $10^{12}\, \rm eV$. The background component of the neutrino flux includes contributions from atmospheric neutrinos, nuclear reactors, old supernovae, and geoneutrinos. These data were taken from Vitagliano:2019yzm. The open solid rectangles show the neutrino fluxes predicted by the SS model in the MeV energy band. For PULXs, Case A corresponds to Swift J0243.6$+$6124 and RX J0209.6$-$7427, while Case B includes NGC 5907 ULX-1 and M51 ULX-8. The open dashed rectangles represent the neutrino fluxes of Be X-ray pulsars and ULX pulsars, respectively, with values taken from Asthana:2023vvk.