The Galactic Population of Pulsar Wind Nebulae and the Contribution of Its Unresolved Component to the Diffuse High-Energy Gamma-ray Emission

Abstract

In this work, we provide a phenomenological description of the population of galactic TeV pulsar wind nebulae (PWNe) based on suitable assumptions for their space and luminosity distribution. We constrain the general features of this population by assuming that it accounts for the majority of bright sources observed by H.E.S.S. Namely, we determine the maximal luminosity and fading time of PWNe (or, equivalently, the initial period and magnetic field of the pulsar powering the observed emission) by performing a statistical analysis of bright sources in the H.E.S.S. galactic plane survey. This allows us to estimate the total luminosity and flux produced by galactic TeV PWNe. We also evaluate the cumulative emission from PWNe that cannot be resolved by H.E.S.S., showing that this contribution can be as large as ∼40% of the total flux from resolved sources. We argue that also in the GeV domain, a relevant fraction of this population cannot be resolved by Fermi-LAT, providing a non-negligible contribution to the large-scale diffuse emission in the inner galaxy. This additional component could naturally account for a large part of the spectral index variation observed by Fermi-LAT, weakening the evidence of cosmic ray spectral hardening in the inner galaxy. Finally, the same result is obtained for PeV energy, for which the sum of the diffuse component, due to unresolved PWNe, and the truly diffuse emission well saturates the recent Tibet AS-γ data, without the need to introduce a progressive hardening of the cosmic-ray spectrum toward the galactic centre.

The Galactic population of Pulsar Wind Nebulae and the contribution of its unresolved component to the diffuse high energy gamma-ray emission

“…As it was shown in [8,11], it is possible to constrain the source population by fitting the flux, latitude, and longitude distributions of bright sources in HGPS catalog. In order to avoid selection effects, we include in the fit only sources above the H.E.S.S.…”

“…where ⟨𝐸⟩ = 3.25 TeV is the average energy of photons (see [8,11] for details), 𝜉 ≡ ∫ OW 𝑑 3 𝑟 𝜌(r) = 0.812 represents the fraction of sources of the considered population which are included in the H.E.S.S. OW, while ⟨𝑟 −2 ⟩ ≡ 1 𝜉 ∫ OW 𝑑 3 𝑟 𝜌(r) 𝑟 −2 = 0.0176 kpc −2 is the average value of their inverse square distance.…”

“…These quantities are relatively well determined by observational data, due to the fact that they depend on the product 𝐿 max 𝜏 sd , see eqs. (11,12).…”

“…is limited, while sources are expected to be distributed everywhere in the Galaxy2. As it is discussed in [11], a lower (upper) bound for the unresolved flux is provided by the cumulative emission of faint sources with flux below H.E.S.S. sensitivity limit 0.01 𝜙 CRAB (completeness threshold 0.1 𝜙 CRAB ).…”

“…In this review, following the lines of our previous works on this subject [8][9][10][11], we discuss the general properties of this source class. By assuming that TeV emission is proportional to the pulsar spin-down power, we model the luminosity function of galactic PWNe in terms of few parameters, namely the PWNe maximal luminosity 𝐿 max and fading (or spin-down) time scale 𝜏 sd (or, equivalently, the initial pulsar period 𝑃 0 and magnetic field 𝐵 0 ).…”