High energy neutrinos from pulsar-powered optical transients: LFBOTs as potential origin of the KM3NeT event KM3-230213A

Technical Summary: High Energy Neutrinos from Pulsar-Powered Optical Transients

Problem Statement
The recent detection of an ultra-high energy (UHE) neutrino event, KM3-230213A, by the KM3NeT collaboration (reconstructed parent neutrino energy $\sim 220$ PeV) necessitates an explanation for its origin. While various astrophysical and cosmogenic models have been proposed, this work investigates the hypothesis that the event arises from a diffuse flux of high-energy neutrinos produced by a population of pulsar-powered optical transients. Specifically, the authors examine whether core-collapse events resulting in newly formed millisecond pulsars (magnetars) can generate the required neutrino energy and fluence to match the "joint flux" normalization derived from KM3NeT, IceCube, and Pierre Auger data.

Methodology
The authors employ a comprehensive physical model of a central engine consisting of a newly born millisecond pulsar embedded within supernova ejecta. The model tracks the deposition of pulsar spindown energy into a surrounding nebula and the subsequent interaction with the ejecta. Key components of the methodology include:

1. Central Engine Physics: The spindown luminosity ($L_{sd}$) is governed by the initial spin period ($P_i$) and dipolar magnetic field strength ($B_d$). The model assumes $P_i \in [1, 10]$ ms and $B_d \in [10^{12}, 10^{15}]$ G. The spindown energy is partitioned into thermal, non-thermal, magnetic, and kinetic components.
2. Particle Acceleration: Protons are accelerated via two mechanisms: the polar cap region (reaching $\sim 10^9$ GeV) and the termination shock (TS) region. These accelerated protons interact with thermal and non-thermal photons in the nebula via photomeson ($p\gamma$) processes to produce high-energy neutrinos.
3. Transient Classes: The study surveys three distinct classes of optical transients powered by such pulsars, differentiated primarily by ejecta mass ($M_{ej}$) and composition:
   • Ordinary Core-Collapse Supernovae (CCSNe): $M_{ej} \approx 2.23 M_\odot$, slower ejecta velocity ($\sim 0.05c$).
   • Super-Luminous Supernovae (SLSNe): Similar ejecta mass to CCSNe but powered by more energetic central engines.
   • Luminous Fast Blue Optical Transients (LFBOTs): Low ejecta mass ($M_{ej} \approx 0.1 M_\odot$), high ejecta velocity ($\sim 0.24c$), and hydrogen/helium-dominated composition.
4. Parameter Space Scan: The authors systematically scan the $B_d - P_i$ parameter space to determine the resulting optical lightcurve properties (peak magnitude $M_{AB}$, fall time $t_-$) and neutrino emission characteristics (total energy fluence $E_{\nu, tot}$, peak neutrino energy $\epsilon_{\nu}^{peak}$).
5. Diffuse Flux Calculation: The single-source neutrino fluence required to match the observed joint diffuse flux is calculated using local transient rate densities ($\dot{\rho}_0$) and the Hubble constant.

Key Results
The survey of the parameter space yields the following critical findings:

• Optical Constraints:
  • Ordinary SNe: Typically exhibit $M_{AB} \sim -17$ and fall times $t_- \sim 25$ days. They require lower $B_d$ and higher $P_i$.
  • SLSNe: Exhibit $M_{AB} \sim -21$ and $t_- \sim 40$ days, favoring lower $P_i$ and higher $B_d$.
  • LFBOTs: Exhibit $M_{AB} \sim -22$ and rapid fall times $t_- \sim 6$ days. This class requires very fast spinning pulsars ($P_i < 5$ ms) and strong magnetic fields ($B_d > 10^{13}$ G) to achieve the necessary peak luminosity given their low ejecta mass.
• Neutrino Emission Capabilities:
  • Ordinary SNe: The total neutrino energy is limited to $\sim 10^{46} - 10^{47}$ erg, with peak neutrino energies $\epsilon_{\nu}^{peak} < 10^7$ GeV. This falls short of the energy requirements for the KM3NeT event.
  • SLSNe and LFBOTs: Both classes can produce total neutrino energies $\gtrsim 10^{48}$ erg with peak energies in the range of $10^7 - 10^8$ GeV, matching the UHE regime.
• Viability for KM3-230213A:
  • While both SLSNe and LFBOTs possess the necessary central engine power to produce UHE neutrinos, LFBOTs are identified as the most plausible source.
  • A specific LFBOT parameter set ($P_i = 1.6$ ms, $B_d = 6 \times 10^{13}$ G) is highlighted as the dominant contributor to the diffuse flux. This configuration produces a peak neutrino energy and fluence consistent with the joint flux normalization.
  • Although individual SLSNe can produce comparable neutrino energies, the LFBOT population is favored because their lower ejecta masses allow for a broader range of parameters to satisfy the peak energy constraints ($\epsilon_{\nu}^{peak}$), and their systematically higher population-averaged peak energies better align with the diffuse spectrum required to explain the event.

Significance and Claims
The paper concludes that a diffuse neutrino flux originating from a population of LFBOTs, powered by newly formed millisecond pulsars, provides a plausible astrophysical explanation for the KM3NeT event KM3-230213A. The authors assert that LFBOTs are ideally suited to reproduce the required neutrino energy and fluence levels without violating constraints from optical observations. Consequently, the work suggests that pulsar-powered optical transients, particularly LFBOTs, represent promising sources for current and upcoming high-energy and ultra-high-energy neutrino telescopes. The study does not claim to definitively prove this origin but demonstrates its theoretical viability within the explored parameter space.