We investigated the pulsar radio luminosity (L), emission efficiency (ratio of radio luminosity to its spin-down power ), and death line in the magnetic field (B) versus spin period (P) diagram. We found that the dependence of pulsar radio luminosity on its spin-down power () is very weak, shown as , which deduces an equivalent inverse correlation between emission efficiency and spin-down power as . Furthermore, we examined the distributions of radio luminosity of millisecond and normal pulsars and found that for the similar spin-down powers, the radio luminosity of millisecond pulsars is about one order of magnitude lower than that of the normal pulsars. The analysis of pulsar radio flux suggests that these correlations are not due to a selective effect but are intrinsic to the pulsar radio emission physics. Their radio radiations may be dominated by the different radiation mechanisms. The cut-off phenomenon of currently observed radio pulsars in B – P diagram is usually referred as the “pulsar death line”, which corresponds to erg s⁻¹ and is obtained by the cut-off voltage of electron acceleration gap in the polar cap model of pulsar proposed by Ruderman and Sutherland. Observationally, this death line can be inferred by the actual observed pulsar flux S ≥ 1mJy and 1 kpc distance, together with the maximum radio emission efficiency of 1%. However, the observation data show that the 37 pulsars pass over the death line, including the recently observed two pulsars with long periods of 23.5 s and 12.1 s, which violate the prediction of the polar cap model. At present, the actual observed pulsar flux can reach 0.01mJy by FAST telescope. This will arise the observational limit of spin-down power of pulsars as low as erg s⁻¹. This means that the new death line is downward shifted two orders of magnitude, which might be favorably referred as the “observational limit–line”. Accordingly, the pulsar theoretical model for the cut-off voltage of gap should be heavily modified.

我们研究了脉冲星射电光度 ( L )、发射效率（射电光度与其自旋下降功率之比）以及磁场中的死亡线 ( B ) 与自旋周期 ( P ) 关系图。我们发现脉冲星射电光度对其自旋下降功率 ( ) 的依赖性非常弱，如 所示，由此推导出发射效率与自旋下降功率之间的等效反相关为. 此外，我们检查了毫秒脉冲星和普通脉冲星的射电光度分布，发现在相似的自旋下降功率下，毫秒脉冲星的射电光度比普通脉冲星低一个数量级。脉冲星射电通量的分析表明，这些相关性不是由于选择性效应，而是脉冲星射电发射物理学所固有的。它们的无线电辐射可能受不同的辐射机制支配。目前观测到的射电脉冲星在B - P图中的截止现象通常被称为“脉冲星死亡线”，对应于erg s ^-1由 Ruderman 和 Sutherland 提出的脉冲星极帽模型中电子加速间隙的截止电压得到。从观测上看，这条死亡线可以通过实际观测到的脉冲星通量S ≥ 1mJy 和 1 kpc 的距离以及 1% 的最大无线电发射效率来推断。但观测数据显示，这37颗脉冲星越过了死亡线，其中包括最近观测到的两颗长周期分别为23.5 s和12.1 s的脉冲星，与极冠模型的预测相违背。目前，FAST望远镜实际观测到的脉冲星通量可达0.01mJy。这将产生低至erg s ^{-1的脉冲星自旋功率的观测极限}. 这意味着新的死亡线向下移动了两个数量级，这可能被称为“观察极限线”。因此，应对间隙截止电压的脉冲星理论模型进行大量修改。