Revealing the X-ray emission processes of old rotation-powered pulsars:: XMM-Newton observations of PSR B0950+08, PSR B0823+26, and PSR J2043+2740

We have completed part of a program to study the X-ray emission properties of old rotation-powered pulsars with XMM-Newton in order to probe and identify the origin of their X-radiation. The X-ray emission from these old pulsars is largely dominated by nonthermal processes. None of the observed spectra required adding a thermal component consisting of either a hot polar cap or surface cooling emission to model the data. The X-ray spectrum of PSR B0950+08 is best described by a single power law of photon index alpha = 1.93(-0.12)(+0.14) Taking optical data from the VLT FORS1 into account, a broken power-law model with the break point E-break = 0.67(-0.41)(+0.18) keV and the photon indices alpha(1) = 1.27-0.01+0.02 and alpha(2) = 1.88-0.11+0.14 for E < E-break and E > E-break, respectively, is found to describe the pulsar's broadband spectrum from the optical to the X-ray band. Three sigma temperature upper limits for possible contributions from a heated polar cap or the whole neutron star surface are T-pc(infinity) < 0.87 x 10(6) and T-s(infinity) < 0.48 x 10(6) K, respectively. We also find that the X-ray emission from PSR B0950+08 is pulsed with two peaks per rotation period. The phase separation between the two X-ray peaks is similar to 144 degrees (maximum to maximum), which is similar to the pulse peak separation observed in the radio band at 1.4 GHz. The main radio peak and the trailing X-ray peak are almost phase-aligned. The fraction of X-ray pulsed photons is similar to 30%. A phase-resolved spectral analysis confirms the nonthermal nature of the pulsed emission and finds no spectral variations as a function of pulse phase. Detailed pulse profile simulations using the polar gap, the outer gap, and the two-pole caustic model constrain the pulsar's emission geometry to be that of an almost orthogonal rotator, for which the two-pole caustic model can reproduce the observed doubly peaked X-ray pulse profile. The spectral emission properties observed for PSR B0823+26 are similar to those of PSR B0950+08. Its energy spectrum is very well described by a single power law with photon index alpha = 2.5(-0.45)(+0.9). Three sigma temperature upper limits for thermal contributions from a hot polar cap or from the entire neutron star surface are T-pc(infinity) < 1.17 x 10(6) and T-s(infinity) < 0.5 x 10(6) K, respectively. There is evidence for pulsed X-ray emission at the similar to 97% confidence level with a pulsed fraction of 49%+/- 22%. For PSR J2043+2740, which is located similar to 1 degrees outside the boundary of the Cygnus Loop, we report the first detection of X-ray emission. A power-law spectrum or a combination of a thermal and a power-law spectrum both yield acceptable descriptions of its X-ray spectrum. No X-ray pulses are detected from PSR J2043+2740 and the sensitivity is low-the 2 sigma pulsed fraction upper limit is 57% assuming a sinusoidal pulse profile.