Title: Finding Candidate TeV Halos among Very-High Energy Sources

Abstract: We search for possible pulsar TeV halos among the very-high-energy (VHE) sources reported in different VHE surveys, among which in particular we use the results from the first Large High Altitude Air Shower Observatory (LHAASO) catalog of $\gamma$-ray sources. Six candidates are found. They share similar properties of containing a middle-aged, gamma-ray--bright pulsar in their positional error circles (the respective pulsars are J0248+6021, J0359+5414, J0622+3749, J0633+0632, J2006+3102, and J2238+5903), being in a rather clean field without any common Galactic VHE-emitting supernova remnants or (bright) pulsar wind nebulae (PWNe), and showing an absence of any gamma-ray emissions in 0.1--500\,GeV after removing the pulsars' emissions. Combining these candidates with several reported (candidate) TeV halos, we obtain the relationships between their luminosity at 50\,TeV ($L_{\rm 50TeV}$) and the corresponding pulsars' spin-down energy ($\dot{E}$), which are $L_{\rm 50TeV}\sim \dot{E}^{0.9}$ and $L_{\rm 50TeV}/\dot{E}\sim 6.4\times 10^{-4}$. The relationships are nearly identical to previously reported ones. We probe possible connections between the extension sizes of the VHE sources and the pulsars' ages, and find a weak older-and-smaller trend. By comparing to the VHE detection results for PWNe, it is clear that the (candidate) TeV halos have hard emissions by either having their power-law indices be smaller than 2 in 1--25\,TeV or by only being detected in 25--100\,TeV. In addition, we also consider seven other VHE sources as possible TeV halos based on the results from different studies of them, but they do not fit cleanly with the properties listed above, indicating their potentially complex nature.