Observational Relationship between Spectral Properties of Gamma-ray and X-ray Emissions from Pulsars

TL;DR

This study probes cross-band correlations between GeV gamma-ray and keV X-ray emission in pulsars. Using a sample of 44 pulsars with gamma-ray data from the Fermi 3PC and X-ray data from HK2023, it applies Spearman ranking and orthogonal distance regression to quantify relationships among spectral properties, timing parameters, and thermal components. The standout result is a strong L_γ–L_p relation with $L_\gamma \propto L_{\rm p}^{0.49 \pm 0.05}$, along with a pronounced dependence of L_γ on surface temperature $kT$ and a fundamental-plane description $L_\gamma \propto kT^{4.79 \pm 0.90} R^{2.55 \pm 0.58}$ that couples thermal and non-thermal emissions. The data also reveal a dichotomy between Group 1 and Group 2 pulsars (based on detected thermal X-ray emission), suggesting two populations with differing emission or cooling physics, and indicate that gamma-ray and X-ray processes are connected but not simply the same spectral component. These results provide observational constraints for high-energy emission models, informing theories on particle acceleration, pair production, and the role of thermal photons in pulsar magnetospheres.

Abstract

Correlations between gamma-ray and X-ray spectral properties of pulsars are investigated in order to provide observational hints on physics involved in pulsars' high-energy emissions. Using a sample of 43 pulsars detected in both X-ray and gamma-ray bands, we find that pulsars' gamma-ray luminosity, $L_γ$, clearly correlates with the luminosity of non-thermal X-ray emission, $L_{\rm p}$, and anti-correlates with non-thermal X-ray photon index. Other gamma-ray spectral parameters show weaker or negligible correlations. The found relation that $L_γ\propto L_{\rm p}^{0.49\pm 0.05}$ implies a certain connection between radiation mechanisms and energy distributions of radiating particles for these high-energy emissions. Pulsars with and without detected thermal emissions seem to show different dependencies in those correlations, suggesting the possible existence of two different kinds of pulsars. The ones without detected thermal emissions may represent a population of pulsars with low surface temperature. The origin and energetics of high-energy emitting electron-positron pairs for this group of pulsars probably do not depend on their surface thermal emissions, while that of the other group do. The low surface temperatures might be evidence for the working of some exotic processes of neutron-star cooling. Similar to $L_{\rm p}$, some tempting relationships are found among each gamma-ray spectral parameter, surface temperature and thermally radiating area radius. It again strengthens the connection between gamma-ray and X-ray emissions from pulsars.

Figures (12)

• Figure 1: Gamma-ray luminosity ($L_{\gamma}$) versus timing parameters ($P$, $\dot{P}$, $\tau$, $\dot{E}$, $B_{\rm lc}$, $B_{\rm s}$). $r_{\rm s}$ in the legend is the Spearman rank-order correlation coefficient, followed by its corresponding p-value. Green solid data points are for Group-1 pulsars (without detected thermal X-rays) and blue solid ones are for Group 2 (with detected thermal X-rays). These two groups do not distinguish themselves in these distributions. The straight line is the best linear fit.
• Figure 2: Gamma-ray spectral parameters versus non-thermal X-ray luminosity ($L_{\rm p}$). $r_{\rm s}$ in the legend is the Spearman rank-order correlation coefficient,followed by its corresponding p-value. Green solid data points are for Group-1 pulsars (without detected thermal X-rays) and blue solid ones are for Group 2 (with detected thermal X-rays). The black line indicates the best-fit for all data points, green line indicates the best-fit for Group 1 data and blue line indicates the best-fit for Group 2 data.
• Figure 3: Gamma-ray spectral parameters vs non-thermal X-ray photon index ($\Gamma_{\rm p}$). Legends are the same as previous figures.
• Figure 4: Gamma-ray spectral parameters versus blackbody temperature ($kT$)
• Figure 5: Gamma-ray spectral parameters versus blackbody radius ($R$)