Timing Analysis of the Isolated Neutron Star RXJ0720.4–3125Timing Analysis of the Isolated Neutron Star RXJ0720.4–3125Silvia Zane, Frank Haberl, Mark Cropper, Vyacheslav Zavlin, David Lumb, Steve Sembay & Christian Motch. (MSSL/UCL, University of Strasbourg, MPE Garching, ESTEC, Univ. of Leicester)

RXJ0720.4–3125 is a nearby, isolated Neutron Star detected by ROSAT during a Galactic plane survey (Haberl et al., 1997) and recently re-observed with XMM-Newton on 2000 May 13 (Paerels et al. 2001, Cropper et al., 2001) and 2001 November 21.

The source shows all the common characteristics of the other 6 ROSAT Neutron Stars candidates (dim NSs, see Treves et al., 2000). In particular:

• high X-ray to optical flux ratio Lx/Lopt>1000

• soft X-ray thermal spectrum (Tbb~ 86 eV)

• low column density (NH ~ 6 x1019 cm–2 ).

The source is also pulsating with P ~ 8.4 s.

B:Timing AnalysisB:Timing Analysis

Recently, Paerels et al. (2001) presented XMM spectra of RXJ 0720.4-3125. The absence of electron or proton cyclotron resonance in the RGS range excluded magnetic fields of (0.3–2.0)1011 and (0.5–2.0)1014 G (see Zane at al., 2001).

Based on the same XMM observation, Cropper et al. (2001) presented the pulse-shape analysis. They derived an upper limit on the polar cap size, showing that an emitting region larger than 60°-65° can be rejected at a confidence level of 90%. Whatever the mechanism, the X-ray emitting region is therefore confined to a relatively small fraction of the star surface. They also found that the hardness ratio is softest around the flux maximum. The same has been later discovered by Perna et al. (2001) in some AXPs. Cropper et al. (2001) suggested two possible explanations: either radiation beaming (as in their best-fitting model) or the presence of a spatially variable absorbing matter, co-rotating in the magnetosphere. The latter may be the case if the star is propelling matter outward (Alpar, 2001).

Until a few years ago two mechanisms were proposed for dim NSs: accretion from the interstellar medium onto an old NS or cooling of a younger object. More recently, based on the similarity of the periods, it has been suggested a possible evolutionary link between dim NSs, Anomalous X-ray pulsars (AXPs), and soft gamma-ray repeaters (SGRs). Two kind of “unified'’ scenarios have been then proposed. In the first one, the 3 classes are powered by dissipation of a decaying, super-strong magnetic field (B 1014 -1015 G). In this case, dim NSs are the descendants of SGRs and AXPs and RXJ0720.4-3125 may be the closest old-magnetar. Alternatively, the 3 classes may contain standard NSs (B 1012 G) endowed by a fossil disk (Alpar, 2001). In this case, dim NSs in the propellor phase would be the progenitors of AXPs and SGRs, the latter having entered an accretion phase.

Further information about this puzzling source can be obtained by the spin history. Magnetars will spin-down at a rate dP\dt 10-11(B/10 14 G)2/P ss-1 , due to magneto-dipolar losses. A measure of dP/dt for RXJ0720.4-3125 is therefore crucial, as well an accurate tracking of its spin history. Here we present a combined timing analysis of XMM, Chandra and Rosat data, spanning a period of ~7 years.

A: IntroductionA: Introduction

Table 1 shows the different observations used in our analysis. The major datasets are from the two XMM observations, and from the 1996 Nov. 3 Rosat pointing.

Table 1

Our data originate from instrumentation with widely different sensitivities: typical count rates vary from 0.3 ct/s for Rosat HRI to 6 ct/s for XMM/PN. However, none of these count rates is sufficiently high for a normal distribution of counts to be expected, thus standard discrete Fourier Transforms are not directly applicable. For sparse data and event list data, we use instead Rayleigh Transforms (i.e. de Jager 1991, Mardia 1972). It is also crucial for us to define precisely the confidence intervals for the derived quantities, in particular the period P. We do this by constructing MLP (maximum likelihood periodogrammes), which make no assumptions on data distribution, and using the C-statistics (Cash 1979). The uncertainty in the period and the 2 can be read directly from the y-axis of the MLP (see e.g. Fig.1).

We begin performing an MLP assuming dP/dt=0 on each of the longer pointing: R93, R96b, X00a, X00b (see Fig.1). There is no ambiguity in the period determinations and a linear least square fit using the 68% formal errors in the MLP gives P0 = 8.39113 ± 0.00011 s, dP/dt = 0.0 ± 5.5 10-13

s/s (P0 is referenced to the start of the R93 run).

Fig.1. Left: MLPs for three long datasets, R96d, X00a (PN) and X00b (PN), showing the periodicity at 8.391 sec. These constrain the selection of the strongest and second-strongest dips in the MLPs for the R98 and Ch00 datasets respectively (right). The vertical line denotes a period of 8.39113 sec. The 68% and 90% confidence levels are at 2 = 1.0 and 2.71 for one degree of freedom.

This upper limit in dP/dt=0 permits an unambiguous determination of the peaks in the Ch00 and R98 power spectra. Adding these to the linear square fit gives P0 = 8.39107 ± 0.00005 s, dP/dt = 2.7 10-13 ± 2.5 10-13 s/s. The 68, 90 and 99% confidence level are shown in Fig.2, as well as the 68 and 90% intervals derived from X00a. With the improved (P0, dP/dt) values, we perform an MLP on the combined ROSAT 1993 and 1996 datasets. As a result, the confidence contour break up into small region (aliases) in the (P0, dP/dt) plane (see zoom in Fig.2). With this further restriction, we finally do the MLP on all the data.

Fig.2. The 68, 90 and 99% contour for a linear least squares fit of R 93, R96d, R98, X00a, X00b and Ch00 (continuum elliptical regions). Parallel lines are the 68 and 90% contour of X00a PN; tiny elliptical regions are the 68 and 90% contour for the combined R93 and R96 datasets (see zoom).

We derive two pairs of values P, dP/dt which cannot be further discriminated between on statistical grounds (Table 2). Both fits have dP/dt 3-6 10-14 s/s. This is the most accurate spin-down measure presented so far for a dim NSs and, for the first time, it allows a discrimination between models.

The refined value of dP/dt reported here is consistent with the measure of Haberl et al. (1997), but two orders of magnitude lower. The first implication is that RXJ0720.4-3125 is hardly to be spinning down due to a propeller torque. Accretion from a fossil disk implies 2 10-11d2

100< dP/dt < 2 10-9d2

100 s/s, where d100 is the sources distance normalized at 100 pc: the value reported here is well below this range. On the other hand, the measured spin-down is considerable and, if interpreted as due to magneto-dipolar losses, it gives a magnetic field as high 21013 G. The corresponding spin-down age is P/(2dP/dt) 3106 yrs, which is higher but, given the numerous uncertainties, not too far from the cooling age of 5105 yrs.

Table 2. The first two pairs are the best-fit (P,dP/dt) values. 2 is the difference between the 2 of a given solution and that of solution (1). See Fig.3 for errors.

C: DiscussionC: Discussion

Fig.4: The datasets folded on periods (1) (left) and (2) (right) of Table 2.

Fig.3: The 68 and 90% MLP contours for the two best-fit solutions of Table 2. Left: solution (1); right: solution (2).

Table 3. Predicted source age and primordial field for three different mechanisms of B-decay, simulated as in Colpi et al. (2000). For each decay law, the two solutions correspond to the two best-fitting pairs of value of Table 2. In all cases, the source is assumed to be born with P = 1ms.

It is now fundamental to assess the field evolution and to understand if the source came through an history of B-decay or if the magnetic field has been almost constant over its lifetime. We take for simplicity three different models for the field decay: Hall cascade and ambipolar diffusion in the solenoidal or irrotational mode. The laws are taken as in Colpi et al. (2000). As we see, fast decaying processes as Hall cascade predict a very low age for the source, which is difficult to reconcile with its present luminosity and with the relatively large number of detected close-by objects of this class. It seems therefore more plausible that the B-field of RXJ0720.4-3125 only had a relatively small change over the evolution, in which case the present source age is 106 yrs.

Recently, there are some indications that the time-stamping of XMM-Newton data may need fine-adjustments at the level of our derived accuracy. Further investigations by the SOC are in progress and, if necessary, a re-computation of some of these results may be required.