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Derivation of the injection spectrum of positrons and electrons from Geminga and Monogem

Qian Zhong

Abstract

Extended $γ$-ray emission has been observed around several nearby pulsars and is commonly interpreted as inverse-Compton radiation produced by relativistic electrons and positrons diffusing in the surrounding interstellar medium. In this work, a unified analysis of the halos associated with the Geminga and Monogem pulsars is presented, combining GeV--TeV $γ$-ray observations within a common physical framework. Assuming continuous injection of $e^\pm$ pairs from the pulsar wind nebulae, the resulting $γ$-ray emission is modeled by accounting for particle diffusion and radiative energy losses. I find that the observed spectra of both Geminga and Monogem can be reproduced within this framework, provided that particle transport in the vicinity of the sources is significantly suppressed with respect to the average Galactic diffusion. The fits favor hard injection spectra and cutoff energies of order $10^5$--$10^6$~GeV, consistent with efficient lepton acceleration in pulsar environments. Using the best-fit injection models inferred from the $γ$-ray data, then I estimate the contribution of Geminga and Monogem to the local cosmic-ray positron flux measured by AMS-02. I find that the slow-diffusion region surrounding the sources strongly suppresses the positron flux reaching the Earth, leading to a subdominant contribution over most of the AMS-02 energy range, with a possible effect only near the upper end of the measured spectrum. The results support an interpretation in which TeV halos trace regions of inhibited particle diffusion around pulsars, while at the same time implying only a limited impact on the local positron flux. This combined analysis highlights the importance of extended $γ$-ray observations for constraining particle transport in the vicinity of Galactic cosmic-ray sources.

Derivation of the injection spectrum of positrons and electrons from Geminga and Monogem

Abstract

Extended -ray emission has been observed around several nearby pulsars and is commonly interpreted as inverse-Compton radiation produced by relativistic electrons and positrons diffusing in the surrounding interstellar medium. In this work, a unified analysis of the halos associated with the Geminga and Monogem pulsars is presented, combining GeV--TeV -ray observations within a common physical framework. Assuming continuous injection of pairs from the pulsar wind nebulae, the resulting -ray emission is modeled by accounting for particle diffusion and radiative energy losses. I find that the observed spectra of both Geminga and Monogem can be reproduced within this framework, provided that particle transport in the vicinity of the sources is significantly suppressed with respect to the average Galactic diffusion. The fits favor hard injection spectra and cutoff energies of order --~GeV, consistent with efficient lepton acceleration in pulsar environments. Using the best-fit injection models inferred from the -ray data, then I estimate the contribution of Geminga and Monogem to the local cosmic-ray positron flux measured by AMS-02. I find that the slow-diffusion region surrounding the sources strongly suppresses the positron flux reaching the Earth, leading to a subdominant contribution over most of the AMS-02 energy range, with a possible effect only near the upper end of the measured spectrum. The results support an interpretation in which TeV halos trace regions of inhibited particle diffusion around pulsars, while at the same time implying only a limited impact on the local positron flux. This combined analysis highlights the importance of extended -ray observations for constraining particle transport in the vicinity of Galactic cosmic-ray sources.

Paper Structure

This paper contains 12 sections, 23 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Physical model
  3. Source properties: Geminga and Monogem
  4. Injection of electrons and positrons
  5. Transport: diffusion--loss equation and diffusion models
  6. Solution for the $e^\pm$ density
  7. Inverse-Compton $\gamma$-ray emission
  8. Positron flux at Earth
  9. Results
  10. Fit to the GeV--TeV halo spectra
  11. Predicted positron flux at Earth
  12. Conclusions and discussion

Figures (3)

  • Figure 1: Comparison fit for Geminga obtained using the older HAWC data set. The left panel shows the best-fit $\gamma$-ray spectral energy distribution, $E^2 \Phi_\gamma$, obtained by fitting the Fermi-LAT data DiMauro:2019yvh together with the earlier HAWC measurement Abeysekara:2017science, for $E_c = 10^6$ GeV and $\gamma_e = 1.8$. The right panel shows the corresponding positron energy flux at Earth, $E^3 \Phi_{e^+}$, for the same injection model.
  • Figure 2: Best-fit $\gamma$-ray spectral energy distributions of the Geminga (left) and Monogem (right) halos in the continuous-injection scenario. The black dashed lines show the model predictions, while the blue and red points correspond to the Fermi-LAT dimauroDetectionGrayHalo2019 and HAWC HAWC:2024GemingaMonogem data, respectively. For the $\gamma$-ray calculation, a one-zone transport model is adopted with a diffusion coefficient $D = 10^{26}\,\mathrm{cm^2\,s^{-1}}$ at 1 GeV and $\delta = 1/3$.
  • Figure 3: Predicted positron energy flux at Earth, $E^3 \Phi_{e^+}$, from Geminga (left) and Monogem (right) for the best-fit injection parameters shown in Figure \ref{['fig:gemmon_gamma']}, compared with AMS-02 measurements. For the positron-flux calculation a two-zone model is adopted with $r_b = 100$ pc, $D_{\rm in} = 10^{26}\,\mathrm{cm^2\,s^{-1}}$, and $D_{\rm out} = 10^{28}\,\mathrm{cm^2\,s^{-1}}$ at 1 GeV, with the same energy dependence in both regions.