# The LHAASO PeVatron Bright Sky: What We Learned
## 2 PeVatron Candidate Source Typologies
### Pulsar Wind Nebulae: The Crab and the Others  
PWNe should be the most numerous of the different kinds of galactic source [48] and their \(\gamma\)-ray emission is estimated to last a very long time (\(\sim\)100 kyrs) [70]. This is likely one of the reasons why more than 30% of the candidate PeVatrons detected by LHAASO seem to be associated with PWNe [26]. They are the most efficient accelerators in the galaxy (up to 30% acceleration efficiency), with no signs of thermal particles, and are the only sources in which we have direct proof of PeV electron acceleration, thanks to their synchrotron spectrum. The location of particle acceleration is likely the termination shock of the young PWN, generated by the friction between the pulsar wind and the parent SNR.  
With their UHE detection by LHAASO and other EAS experiments, PWNe respect all the observational requirements to be PeVatrons (and possibly hadronic PeVatrons): extended HE \(\gamma\)-ray emission; multiwavelength counterparts, from radio to X-rays; and a nonthermal spectrum, with spectral curvature [26; 70]. The main mechanism producing this UHE emission is the IC scattering of UHE accelerated electrons with cosmic microwave background radiation (CMBR). From a theoretical point of view, however, the context is more complex. The first issue is the energetics. At the LHAASO detected energies, the Klein-Nishina regime is the dominant one and, in order to explain leptonic UHE \(\gamma\)-ray, a very high acceleration rate is required [69]. Indeed, in spite of the acceleration mechanism of PWNe still being unknown, we know that there are two constraints on the maximum reachable particle energy. The first strong limit is due to the polar cap potential drop: \(E_{max}=q(\dot{E}/c)^{1/2}\), where q is the particle charge (see [26; 115], for a quick review). In order to make a direct link between theory and observation [26], we can write this relation as: \(E_{\gamma,max}\approx 0.9\eta_{e}^{1/3}\eta_{B}^{0.65}\dot{E}_{36}^{0.65}\) PeV, where \(\eta_{B}\) is the fraction of the PWN energy flux transformed in magnetic energy density and \(\eta_{e}\) is the ratio between the electric and magnetic fields. This expression tells us that only a very energetic pulsars (\(\dot{E}\gtrsim 10^{36}\) erg/s) can reach PeV energies. The second constraint is due to the condition that the acceleration rate must be higher than the electron radiative losses: \(E_{\gamma,max}\approx 2.7\eta_{e}^{0.65}\eta_{B}^{-0.33}R_{0.1}^{0.65}\dot{E}_{36} ^{-0.33}\) PeV, where \(R_{0.1}\) is the termination shock radius in units of 0.1 pc [26]. This condition is more stringent for young energetic pulsars (\(\dot{E}\gtrsim 10^{37}\) erg/s), such as the Crab Nebula.  
In this scenario, the presence of accelerated hadrons cannot be excluded, but some basic calculations show that PWN cannot be the main CR contributors. In order to produce an amount of energy comparable with the energy expected from SNRs, they would have to have too small an initial spin period with respect to that provided by theoretical models [46]. This implies that, even if PWN contribute to galactic CRs, they have no chance of explaining CR composition or anisotropy.  
A very good summary of LHAASO PWNe candidate PeVatrons and their characteristics can be found in [26], where all the LHAASO sources with a PWN as potential TeV counterpart are analyzed in the PWN parameter space based on energetic constraints. According to this work, all of these LHAASO \(\gamma\)-ray emissions near a PSR could have been produced by a PWN, except LHAASO J2032+4127 (see Figure 5 and the paragraph dedicated to this in Section 3.10).