Chandra and XMM-Newton resolved extremely long tails behind two middle-aged pulsars , J1509–5850 and J1740+1000 .
The tail of PSR J1509–5850 is discernible up to 5.6 ^ { \prime } from the pulsar , which corresponds to the projected length l _ { \perp } = 6.5 d _ { 4 } pc , where d = 4 d _ { 4 } kpc is the distance to the pulsar .
The observed tail flux is 2 \times 10 ^ { -13 } erg s ^ { -1 } cm ^ { -2 } in the 0.5–8 keV band .
The tail spectrum fits an absorbed power-law ( PL ) model with the photon index \Gamma = 2.3 \pm 0.2 , corresponding to the 0.5–8 keV luminosity of 1 \times 10 ^ { 33 } d _ { 4 } ^ { 2 } ergs s ^ { -1 } , for n _ { H } = 2.1 \times 10 ^ { 22 } cm ^ { -2 } .
The tail of PSR J1740+1000 is firmly detected up to 5 ^ { \prime } ( l _ { \perp } \sim 2 d _ { 1.4 } pc ) , with a flux of 6 \times 10 ^ { -14 } ergs cm ^ { -2 } s ^ { -1 } in the 0.4–10 keV band .
The PL fit to the spectrum measured from a brighter , 3 ^ { \prime } -long , portion of the tail yields \Gamma = 1.4 –1.5 and n _ { H } \approx 1 \times 10 ^ { 21 } cm ^ { -2 } ; its 0.4–10 keV luminosity is \sim 2 \times 10 ^ { 31 } d _ { 1.4 } ^ { 2 } ergs s ^ { -1 } .
The luminosity of the entire tail is likely a factor of 3–4 higher .
The large extent of the tails suggests that the bulk flow in the tails starts as mildly relativistic downstream of the termination shock , and then gradually decelerates .
Within the observed extent of the J1509–5850 tail , the average flow speed exceeds 5,000 km s ^ { -1 } , and the equipartition magnetic field is a few \times 10 ^ { -5 } G. For the J1740+1000 tail , the equipartition field is a factor of a few lower .
The harder spectrum of the J1740+1000 tail implies either less efficient cooling or a harder spectrum of injected electrons .
For the high-latitude PSR J1740+1000 , the orientation of the tail on the sky shows that the pulsar is moving toward the Galactic plane , which means that it was born from a halo-star progenitor .
The comparison between the J1509 and J1740 tails and the X-ray tails of other pulsars shows that the X-ray radiation efficiency correlates poorly with the pulsar spin-down luminosity or age .
The X-ray efficiencies of the ram-pressure confined pulsar wind nebulae ( PWNe ) are systematically higher than those of PWNe around slowly moving pulsars with similar spin-down parameters .