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Abstract The cosmic-ray flux of positrons is measured with high precision by the space-borne particle spectrometer AMS-02. The hypothesis that pulsars and their nebulae can significantly contribute to the excess of the AMS-02 positron flux has been consolidated after the observation of aγ-ray emission at GeV and TeV energies of a few degree size around a few sources, that provide indirect evidence that electron and positron pairs are accelerated to very high energies from these sources.By modeling the emission from pulsars in the ATNF catalog, we find that combinations of positron emission from cataloged pulsars and secondary production can fit the observed AMS-02 data. Our results show that a small number of nearby, middle-aged pulsars, particularly B1055-52, Geminga (J0633+1746), and Monogem (B0656+14), dominate the positron emission, contributing up to 80% of the flux at energies above 100 GeV. From the fit to the data, we obtain a list of the most important sources for which we recommend multi-wavelength follow-up observations, particularly in theγ-ray and X-ray bands, to further constrain the injection and diffusion properties of positrons. 

Geminga is the first pulsar around which a remarkable gamma-ray halo extending over a few degrees was discovered at TeV energies by MILAGRO and HAWC and later by H.E.S.S., and byFermi-LAT in the GeV band. More middle-aged pulsars have exhibited gamma-ray halos, and they are now recognised as an emerging class of Galactic gamma-ray sources. The emission appears in the late evolution stage of pulsars, and is most plausibly explained by inverse Compton scattering of CMB and interstellar photons by relativistic electrons and positrons escaping from the pulsar wind nebulae. These observations pose a number of theoretical challenges, particularly the origin of the inferred, significantly lower effective diffusion coefficients around the pulsar when compared to typical Galactic values. Tackling these questions requires constraining the ambient magnetic field properties, which can be achieved through X-ray observations. If the gamma-ray halos originate from a distribution of highly energetic electrons, synchrotron losses in the ambient magnetic fields of the same particles are expected to produce a diffuse X-ray emission with a similar spatial extension. We present the most comprehensive X-ray study of the Geminga pulsar halo to date, utilising archival data fromXMM-NewtonandNuSTAR. Our X-ray analysis covers a broad bandwidth (0.5 − 79 keV) and large field of view (θ ∼ 4°) for the first time. This was achieved by accurately measuring the background over the entire field of view, and taking into account both focused and stray-light X-ray photons from the pulsar halo withNuSTAR. We find no significant emission and set robust constraints on the X-ray halo flux. These are translated to stringent constraints on the ambient magnetic field strength and the diffusion coefficient by using a physical model considering particle injection, diffusion, and cooling over the pulsar’s lifetime, which is tuned by fitting multi-wavelength data. Our novel methodology for modelling and searching for synchrotron X-ray halos can be applied to other pulsar halo candidates. 

Abstract Pulsar halos are regions around middle-aged pulsars extending out to tens of parsecs. The large extent of the halos and well-defined central cosmic-ray accelerators make this new class of Galactic sources an ideal laboratory for studying cosmic-ray transport. LHAASO J0621+3755 is a candidate pulsar halo associated with the middle-aged gamma-ray pulsar PSR J0622+3749. We observed LHAASO J0621+3755 with VERITAS and XMM-Newton in the TeV and X-ray bands, respectively. For this work, we developed a novel background estimation technique for imaging atmospheric Cherenkov telescope observations of such extended sources. No halo emission was detected with VERITAS (0.3–10 TeV) or XMM-Newton (2–7 keV) within 1^∘and $10^{\prime }$around PSR J0622+3749, respectively. Combined with the LHAASO Kilometer Square Array (KM2A) and Fermi-LAT data, VERITAS flux upper limits establish a spectral break at  ∼1–10 TeV, a unique feature compared with Geminga, the most studied pulsar halo. We model the gamma-ray spectrum and LHAASO-KM2A surface brightness as inverse Compton emission and find suppressed diffusion around the pulsar, similar to Geminga. A smaller diffusion suppression zone and harder electron injection spectrum than Geminga are necessary to reproduce the spectral cutoff. A magnetic field ≤1μG is required by our XMM-Newton observation and synchrotron spectral modeling, consistent with Geminga. Our findings support slower diffusion and lower magnetic field around pulsar halos than the Galactic averages, hinting at magnetohydrodynamic turbulence around pulsars. Additionally, we report the detection of an X-ray point source spatially coincident with PSR J0622+3749, whose periodicity is consistent with the gamma-ray spin period of 333.2 ms. The soft spectrum of this source suggests a thermal origin.