Monitoring PSR B1509–58 with RXTE: Spectral analysis 1996–2010

We present an analysis of the X-ray spectra of the young, Crab-like pulsar PSR B1509–58 (pulse period P ∼ 151ms) observed by RXTE over 14 years since the beginning of the mission in 1996. The uniform dataset is especially well suited for studying the stability of the spectral parameters over time as well as for determining pulse phase resolved spectral parameters with high significance. The phase averaged spectra as well as the resolved spectra can be well described by an absorbed power law.

PSR B1509-58 has been established as one of only a few known Crab-like sources, i.e., a young pulsar powering a synchrotron nebula [6].PSR B1509-58's nebula is considerably larger, its surface brightness is lower and the pulse period of P ∼ 151 ms is slower than that of the Crab.Due to a very high spin-down rate of Ṗ ∼ 1.5 × 10 −12 s s −1 , however, the characteristic age P/2 Ṗ of PSR B1509-58 is ∼ 1.6 × 10 3 yr (e.g., [7]), i.e., comparable to that of the Crab (∼ 1.3 × 10 3 yr).
In the following we analyse the phase averaged spectra (Sec.2) and the phase resolved spectra (Sec.5) from calculated ephemerides (Sec.3) for the three major calibration epochs 3-5 for the RXTE.Pulse profiles for the epochs are presented in Sec. 4. A short summary of the results and the implications for further spectral analysis with RXTE are given in Sec.6

Phase averaged spectra
From approximately monthly monitoring observations of PSR B1509-58 time averaged PCA (PCU2 top layer, [1,2]) and HEXTE (cluster A and B, [4]) spectra were created by averaging individual monitoring spectra over major instrument calibration epochs, i.e. between MJD 50188 and 51259 (epoch 3), MJD 51259 and 51677 (epoch 4), and from MJD 51677 onward (epoch 5). Figure 1 shows the epoch averaged counts spectra for epoch 5. Some spectral parameters and their uncertainties for the three fits are given in Table 1.No systematic uncertainties have been added to the spectra.The spectra are modeled by an absorbed power law.In addition we found clear indications of a narrow iron Kα line which is included by a Gaussian component added to the power law.
Because of the long monitoring time of epoch 5 (ten years) systematic features are visible in the spectra.For the PCA there are strong residuals around 5 keV depending on the three xenon L edges.Around 9.3 keV a broad negative residual is visible.We model it with an additional negative Gaussian line at this energy with a flux of −3 × 10 −5 cm −2 s −1 .We speculate that this residual might be related to imperfect modeling of the copper Kα emission line at 8.04 keV.Also events from the americium calibration source of the PCA at 33 keV are visible.They were also modeled with a negative Gaussian line with a flux of −1.4 × 10 −4 cm −2 s −1 .

Pulse period ephemeris
The pulse phase resolved analysis for the PCA is based on high time-resolution GoodXenon event mode data, filtered for PCU2 top layer events.Ephemerides for PSR B1509-58 were calculated from the pulse frequencies of each observation.The reference epoch was set to t 0 (MJD) = 52 921.0, the averaged time of the monitoring (see Figure 2, Table 2).With this result barycentered pulse phaseand energy resolved source count rates (pha2 files) were created using a modified version of the FTOOL fasebin [3].All pulsed (i.e., peak minus off-peak) and unpulsed (regular background) spectra were summed to obtain averaged spectra for epochs 3-5, respectively.For the averaged phase resolved spectra, as for the phase averaged spectra before, an absorbed power law was fitted (energy range 3-20 keV).For epoch 5 it showed that the residuals for the pulsed emission improved by including a cutoff (see Figures 4 and 5).The pulsed spectra showed no indication for an iron line at 6.4 keV.The line is part of the unpulsed spectra and hence of the PWN of PSR B1509-58.This is also the explanation for the different values of the N H .In the pulsed emission we see the beam of the pulsar and the galactic extinction.In the unpulsed emission we see the surrounding PWN without the pulsar and the galactic extinction.Therefore the value for the latter is smaller than for the pulsed emission.The best fit parameters for epoch 5 are shown in Table 3.

Fig. 1 :
Fig. 1: (a) PCU2 top layer and HEXTE counts spectra obtained by accumulating all suitable monitoring spectra of epoch 5 and best simultaneous fit model (absorbed power law with an iron line), (b) Best fit residuals

Fig. 2 :
Fig. 2: Frequencies of each observation, calculated by epoch folding the barycentered GoodXenon lightcurve, vs. time with the best fit of a polynomial of quartic grade.A linear decline is visible Table 2: Values for the pulse frequency and its first three derivatives ν s −1 ν 10 −11 s −2 ν 10 −21 s −3

Fig. 4 :Fig. 5 :
Fig. 4: PCU2 top layer counts spectra of the pulsed emission of epoch 5. Residuals are shown for an absorbed power law and after including a cutoff