Exploring the statistical properties of gamma-ray normal pulsars

To study the normal pulsars based on the observations in radio and $\gamma$ $\gamma $ -ray bands, we try to investigate their classifications by the samples with the three different emission types, i.e., radio-only, $\gamma$ $\gamma $ -only and $\gamma +$ $\gamma +$ radio emissions, and then discuss their physical causes. In the spin-down power range of $\dot{E}\sim {10}^{36}-{10}^{39}\mathrm{erg}\cdot {\mathrm{s}}^{-1}$ $\dot{E}\sim 10^{36}-10^{39}\,\mathrm{erg}\cdot \mathrm{s}^{-1}$ , three types of normal pulsars exhibit the similar distributions of the spin period– $P$ $P$ , spin-down power– $\dot{E}$ $\dot{E}$ and characteristic age– $\tau$ $\tau $ , implying that they may belong to the same category of young pulsars. Moreover, in the range of $\dot{E}\sim {10}^{33}-{10}^{36}\mathrm{erg}\cdot {\mathrm{s}}^{-1}$ $\dot{E}\sim 10^{33}-10^{36}\,\mathrm{erg}\cdot \mathrm{s}^{-1}$ , $\gamma$ $\gamma $ -only/ $\gamma +$ $\gamma +$ radio normal pulsars share the similar distributions of $P$ $P$ and $\tau$ $\tau $ values, and these two group sources exhibit the faster average spin periods ( $〈P〉\sim 0.23$ $\langle P\rangle \sim 0.23$ s/ $〈P〉\sim 0.22$ $\langle P\rangle \sim 0.22$ s), higher average spin-down powers ( $〈\dot{E}〉\sim 2.00\times {10}^{35}\mathrm{erg}\cdot {\mathrm{s}}^{-1}$ $\langle \dot{E}\rangle \sim 2.00 \times 10^{35}\,\mathrm{erg}\cdot \mathrm{s}^{-1}$ / $〈\dot{E}〉\sim 2.13\times {10}^{35}\mathrm{erg}\cdot {\mathrm{s}}^{-1}$ $\langle \dot{E}\rangle \sim 2.13 \times 10^{35}\,\mathrm{erg}\cdot \mathrm{s}^{-1}$ ) and smaller average characteristic ages ( $〈\tau 〉\sim 4.8\times {10}^5$ $\langle \tau \rangle \sim 4.8\times 10^{5}$ yr/ $〈\tau 〉\sim 4.1\times {10}^5$ $\langle \tau \rangle \sim 4.1\times 10^{5}$ yr) than radio-only normal pulsars ( $〈P〉\sim 0.42$ $\langle P\rangle \sim 0.42$ s, $〈\dot{E}〉\sim 3.2\times {10}^{34}\mathrm{erg}\cdot {\mathrm{s}}^{-1}$ $\langle \dot{E}\rangle \sim 3.2\times 10^{34}\,\mathrm{erg}\cdot \mathrm{s}^{-1}$ and $〈\tau 〉\sim 1.64\times {10}^6$ $\langle \tau \rangle \sim 1.64\times 10^{6}$ yr). We suggest that $\gamma$ $\gamma $ -only/ $\gamma +$ $\gamma +$ radio normal pulsars with $\dot{E}\sim {10}^{33}-{10}^{36}\mathrm{erg}\cdot {\mathrm{s}}^{-1}$ $\dot{E}\sim 10^{33}-10^{36}\,\mathrm{erg}\cdot \mathrm{s}^{-1}$ are the young objects emitting $\gamma$ $\gamma $ -rays due to the high voltage in the radiation region. Meanwhile, after the temporal evolution of about $\tau \sim {10}^6$ $\tau \sim 10^{6}$ yr, these two group pulsars can be hardly detected with $\gamma$ $\gamma $ -rays due to the decrease of the radiation voltage, which will finally evolve into radio-only pulsars.