A new X-ray look into four old pulsars
Michela Rigoselli Sandro Mereghetti






INAF, Istituto di Astrofisica Spaziale e Fisica Cosmica Milano, via E. Bassini 15, I-20133 Milano, Italy
Dipartimento di Fisica G. Occhialini, Università degli Studi di Milano Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy 


m.rigoselli@campus.unimib.it



M. Rigoselli & S. Mereghetti

 

We report on the X-ray properties of four rotation-powered pulsars with characteristic ages in the range 0.3-5 Myr, derived from the analysis of archival observations.
We found convincing evidence of thermal emission only in the phase-averaged spectrum of  , that is well fitted by a blackbody with temperature kT=0.17± 0.02 keV and emitting radius R=405_-90^+110 m, consistent with the size of its polar cap.  
The other three considered pulsars, , and , have phase-averaged spectra well described by single power-laws with photon index Γ∼3. The 3σ upper limits on the bolometric luminosity of a possible thermal component with temperature in the range ∼ 0.05-2 keV are L_ bol≲ 3.2 × 10^28 and L_ bol≲ 2.4  10^29 , for and ,  respectively.  On the other hand, we found possible evidence that the pulsed emission of is thermal. 
Two absorption lines at ∼0.22 keV and ∼0.44 keV are detected in the spectrum of . They are best interpreted as proton cyclotron features, implying the presence of multipolar components with a field of a few 10^13 G at the neutron star  polar caps. 
We discuss our results in the context of high-energy emission models of old rotation-powered pulsars.



A new X-ray look into four old pulsars
    Michela Rigoselli1,2, Sandro Mereghetti1
    Received / Accepted
============================================





§ INTRODUCTION






X-rays have been detected from more than one hundred  rotation-powered pulsars.
The properties of the X-ray emission,  and in particular the relative strength of the non-thermal and thermal spectral components, depend on the  pulsar age <cit.>. 

Young pulsars have the highest surface temperatures, but their thermal flux is unobservable, being outshined by a much stronger non-thermal emission. 
The latter fades as the pulsars age and slow-down, thus unmasking the underlying thermal emission of the neutron star (NS) surface.

Indeed middle aged pulsars show a mix of non-thermal and thermal X-ray emission. The latter is often modelled with two blackbody components: the cooler have emitting areas consistent with emission from the whole NS surface and temperatures in agreement with the prediction of standard cooling theories. The hotter components have blackbody temperatures typically in the range 0.10.3 and emitting radii between a few tens and a few hundreds of meters, implying that the X-rays come from a small region of the NS (i.e. PSRB0656+14, PSRJ0633+1746, PSRB1055-52 <cit.> and PSRJ1740+1000 <cit.>).
 
X-rays have been detected also in older pulsars, that have cooled down to temperatures too low to significantly emit in the X-ray band. In these objects both non-thermal X-rays of magnetospheric origin and/or emission from hot polar caps have been observed with high confidence only in a few objects (see for example PSRB1929+10 <cit.>). In fact, most old pulsars are rather faint X-ray sources and their study can benefit of the use of maximum likelihood (ML) techniques, as demonstrated for <cit.> and   PSRB1822-09 <cit.>. 

Here, we report a reanalysis of  archival data of four  pulsars  with characteristic ages in the range 0.3-5 Myr based on  ML methods.
The main properties of our targets are summarized in Table <ref>. 





§ OBSERVATIONS AND DATA REDUCTION






We used the data obtained with the pn and the two MOS cameras, which constitute the EPIC instrument and cover the energy range 0.212 <cit.>. 
The medium optical filter was used for and for the MOS cameras data of . All the other data were obtained using the thin filter. The time resolution of the different operating modes used during  our observations are indicated in Table <ref>. Note that while the pn time resolution was adequate to reveal the  pulsations in  all our targets, this is not true for the MOS data, except in the case of .
The data reduction and analysis were done using version 15 of the Science Analysis System (SAS)[https://www.cosmos.esa.int/web/xmm-newton/sas] and XSPEC (ver. 12.8.2) for the spectral fits.

We reprocessed the pn data using the SAS task epreject to reduce the detector noise at the lowest energies. We then removed the  time intervals  of high background by rejecting all the periods with a pn count rate  in the range 1012 larger than 1.0 cts s^-1. The resulting net exposure times for each pulsar are indicated in 
Table <ref>.

We used single- and multiple-pixel events for  both  the pn and MOS.
The events detected in the two  MOS were combined into a single data set, and in their  analysis we used averaged exposure map and response files. 

We applied a maximum likelihood (ML) analysis to extract the net (i.e. background-subtracted) source counts used for the spectral and timing analysis. The resulting counts spectra were put in a format compatible with analysis in XSPEC. By exploiting the knowledge of the instrumental point spread function (PSF), this method  provides spectra and light curves with a  number of source counts larger than what is typically  obtained with the traditional method based on “source” and “background” extraction regions.  Another advantage is that the background is directly measured at the position of the source, contrary to what is done with the traditional analysis in which it is estimated from  “source free” regions of the image.

The ML method measures the source counts taking into account all the events of the region of interest. 
Specifically,  it finds the source flux and background level which maximise  the probability  of obtaining the number of total counts, N_ij,  measured in each spatial pixel. 
The values of  N_ij follow a  Poissionian probability distribution, with  expectation value μ_ij = β + σ×PSF_ij, where β is the background level, that we assumed to be uniform, σ is the number of source counts,  and PSF_ij gives the relative contribution of the source flux in the  pixel (i,j) taking into account the instrumental PSF, which depends on the position in the field of view and on the energy of the event. 
We used  spatial pixels of 1×1 arcsec^2 and we analysed separately the data of the pn and of the sum of the two MOS, adopting the respective PSFs, derived from in-flight calibrations[http://www.cosmos.esa.int/web/xmm-newton/calibration/documentation], with parameters appropriate for the average energy value in the considered bin. 


Following <cit.>, we generalized the above method to take into account also the pulse phase information of the events.
In this “3D-ML” approach, the events are binned in spatial and phase coordinates and the expectation value of bin (i,j,k) is μ_ijk = β + σ_u ×PSF_ij + σ_p ×PSF_ij×Φ_k.

Now σ_u and σ_p represent the source counts for the unpulsed and pulsed components, while Φ_k is the normalized pulse profile at phase bin k. With this approach, and assuming a sinusoidal pulse  (consistent with the data of our targets),  we could simultaneously derive the fluxes (and spectra) for  the unpulsed and the pulsed components. 
We define the pulsed fraction as the ratio between the pulsed and the total counts, σ_p/(σ_p+σ_u).




§ RESULTS



	


 




 §.§ (J0630–2834)


We applied the ML analysis to a circular region of radius 60” centred at 06305101-2835068. In the energy range 0.310, this yielded     1021±40 source counts in the pn and 527±28 in the MOS, corresponding to  a total count rate of (4.0 ± 0.1) × 10^-2 cts s^-1.  

The spectral analysis was carried out in 20 energy bins for the pn and in 13 for the MOS. The two spectra were fitted simultaneously. Among single-component  models, an absorbed power-law gave the best  fit   with Γ=2.85_-0.15^+0.16 and  =(8.5_-2.1^+2.3) × 10^20 cm^-2 (χ_ν^2=0.67 for 30 degrees of freedom (d.o.f.)). 
The error regions of the parameters  are shown in  Fig. <ref> (a).  A fit with a single blackbody was not acceptable (χ_ν^2 = 3.9 for 30 d.o.f.).
The best fit power-law spectrum, together with its  residuals and those of the blackbody fit are shown in Fig. <ref>.

The best fit is within 1σ of the value of 10^21 cm^-2, derived from the pulsar dispersion measure with the usual assumption of a 10% ionization of the interstellar medium <cit.>. Fixing to this value, we get tighter constraints on the photon index, Γ=2.95 ± 0.06. The corresponding unabsorbed flux  in the 0.210 energy range is f_0.2-10 = (1.08 ± 0.05)  10^-13 . 




All the above results are in agreement with those of standard spectral analysis of the same data.  In fact, <cit.>  found a power-law with photon index Γ=2.63_-0.15^+0.22, while <cit.>, simultaneously fitting the and spectra, obtained Γ=3.20_-0.23^+0.26 (1σ errors in both cases). These authors considered also a power-law plus blackbody model, obtaining acceptable fits with slightly harder power-laws and blackbody temperatures kT ∼ 0.3 keV.

Using a power-law plus blackbody model we found that several combinations of blackbody temperature and normalization, which give only a limited flux contribution, are consistent with the data. The best fit parameters were Γ=2.92±0.07 and kT∼0.02 keV, while the emitting radius is poorly constrained. However, the addition of a blackbody is not statistically required. Therefore, we  derived an upper limit on its intensity as follows. We fitted the spectrum with a blackbody plus power-law model (fixed to 10^21 cm^-2) and computed the 3σ  confidence ranges of the blackbody normalization and temperature, leaving the power-law parameters free to vary. The results are shown in Fig. <ref>, where the upper panel refers to  the  emitting radius and the lower panel to the  bolometric luminosity. The latter has been computed as 
L_ bol= π R^2 σ T^4, because we are considering emission from a  hot spot on the stellar surface.

	



To investigate the spectral properties of the pulsed and unpulsed emission, 
we performed a 3D-ML analysis on the pn data in 7 energy bins in the range 0.310. 
The phases of the detected counts were computed using the period at the epoch of the observation, P=1.2444225976(2) s,  obtained from the ephemeris reported in the   online[http://www.atnf.csiro.au/people/pulsar/psrcat/] ATNF Pulsar  Catalogue <cit.>.
The pulsed fraction is higher in the  0.400.65 range, with an average value of 0.46±0.05 and decreases at lower and higher energies (Fig. <ref> left). 
The energy-dependence of the pulsed fraction is reflected also in the different shape of the pulsed and unpulsed spectra (Fig. <ref> right). 
The unpulsed spectrum is well fitted by a power-law with the same slope of that of the  total spectrum, while that
of the pulsed emission requires a significantly steeper power-law or a blackbody (Table <ref>).









 §.§ (J0922+0638)
 





The faint X-ray counterpart of was first reported by <cit.>. Based on a spectrum  with 171±18  counts, they rejected the blackbody model and found a good power-law fit with Γ=2.3_-0.4^+0.8. 
Our ML analysis of  the same data  was carried out in circular region  with  radius of 45” 
centred at 09221420+0638337. In the energy range 0.210 we obtained 223±25 (pn) and 91±15 (MOS) source  counts, corresponding to a total count rate of (1.3 ± 0.1) × 10^-2 cts s^-1. 

We simultaneously fitted the pn (8 energy bins) and the MOS (7 energy bins) spectra. The single-component model that best fits the data is an absorbed power-law (see Fig. <ref> (b) and Table <ref>). The single blackbody model is statistically unacceptable (χ_ν^2=1.92 for 12 d.o.f.).
We show the comparison between the power-law and the blackbody best fits in Fig. <ref>.
Fixing the absorption to the DM-based value 8  10^20 cm^-2,  we obtain Γ=3.1±0.2 and an unabsorbed flux f_0.2-10 = (3.0 ± 0.4)  10^-14 . 

Although a good fit is also obtained with a  power-law  plus blackbody (Table <ref>), the addition of a blackbody is not statistically required. 
Therefore, as we did for , we derived the upper limits on its intensity as a function of T shown in  Fig. <ref>. 










 §.§ (J0117+5914)


This faint pulsar,  observed with  only  for less than 6 ks, is the one with the smallest number of counts in our sample. 
<cit.> obtained a poorly constrained  spectrum, which could be fitted equally well by a power-law with Γ=3.3±0.5 or by a blackbody with temperature kT = 0.18 ± 0.03 keV and emitting radius R=322±161 m (for d=1.77 kpc).

We applied the ML analysis in a circular region centred at 01173824+5915078 with a radius of 60”, from which we excluded a circle centred in 01173487+5915154 with a radius of 20” to avoid a nearby source.
This resulted in  85 ± 13 pn counts and 44 ± 9 MOS counts in the range 0.210,  corresponding to a total count rate of (2.2 ± 0.3) × 10^-2 cts s^-1.

Simultaneously fitting the pn and the MOS spectra it was impossible to discriminate between a power-law  (χ_ν^2=0.58 for 7 d.o.f.) and a blackbody (χ_ν^2=0.62 for 7 d.o.f.). However, restricting the analysis only to the pn spectrum, which is of better statistical quality, and fixing the absorption to the DM-based value of 1.5  10^21 cm^-2, we found that the blackbody is preferred (χ_ν^2=0.32 for 4 d.o.f., compared to χ_ν^2=1.80 for the power-law).  The best fit  temperature is kT = 0.17 ± 0.02 keV, the   radius of the emitting area  is R=405_-90^+110 m, and the 0.210 unabsorbed flux is f_0.2-10 = (4.7 ± 0.7)  10^-14 (see Table <ref> and Fig. <ref> (c)).
Letting the absorption free to vary, also the power-law is acceptable, but with an unphysical photon index Γ = 6.5_-2.0^+3.0. 








 §.§ (J1136+1551)




has both optical <cit.> and X-ray <cit.> counterparts. According to these works, its  X-ray spectrum   can be described by either a   power-law or a   blackbody (or a combination of them), but the statistics is  too poor to distinguish between these models.  

was observed with five separate pointings spanning about one month. With a simultaneous fit of the separate spectra,  <cit.> found a power-law   with Γ≈ 2.5 and reported that the addition of a blackbody  with T=0.25_-0.03^+0.05 keV and a radius of 14_-5^+7 m (for d = 350 pc) is also consistent with the data.


We verified that the analysis of the single observations gave fully consistent results. Therefore, we report only those  obtained by combining  the five pointings  to extract  a single pn and a single MOS spectrum. 
We applied the ML analysis in a circular region of radius 35” and centred at 11360252715505990. We detected the source with a count rate of (1.06 ± 0.05) × 10^-2 cts s^-1 in the energy range 0.210. For the spectral analysis the 887 ± 46 pn and 363 ± 29 MOS counts  were divided into 19 and 11 energy bins, respectively.

The pn and the MOS spectra were fitted simultaneously. 
We could not obtain acceptable fits with a single power-law or  blackbody, or any combination of them (including a power-law plus two blackbodies), because, in all cases, significant residuals were  present below 0.5 keV.
It is very unlikely  that this is due to an instrumental or calibration problem  because the spectra of two nearby  soft and very bright sources do not show similar features.


Excluding the energy channels below 0.5 keV, we could obtain a good fit with an absorbed power-law with photon index Γ = 3.2± 0.4 and = (8_-6^+7)  10^20 cm^-2  (Fig. <ref>, panel (d)). With fixed to the DM-based value of 1.5  10^20 cm^-2 we obtained a photon index of 2.8 ± 0.1 (χ_ν^2=0.82, for 18 d.o.f.). A blackbody fit was rejected (χ_ν^2 ≈ 2 both for free and fixed ).

A power-law fit of the  pn spectrum over the whole energy range suggests the presence of two absorption lines  at ∼0.2 keV and ∼0.44 keV. We therefore fitted it with a  model consisting of a  power-law with fixed to 1.5 × 10^20 cm^-2  and two gaussian absorption lines. We constrained the lines to be centred at E_2=2× E_1 and to have the same width  σ_1=σ_2.
This model gave  a good fit with E_1=0.222±0.006 keV and  σ_1=0.015_-0.004^+0.012 keV (χ_ν^2 = 0.78 for 13 d.o.f.). The best fit photon index is 2.9 ± 0.2,   in good agreement with that found in the hardest part of the spectrum.
The strength of the lines are poorly constrained, but they are 3 σ above the 0 level (see Fig. <ref>).
The best fit spectrum, together with its  residuals and those of the single power-law fit are shown in Fig. <ref>.


A good fit could also be obtained with a power-law plus blackbody with an absorption line at ∼0.45 keV (χ_ν^2= 0.83 for 11 d.o.f.). However, the =(22_-10^+12)  10^20 cm^-2 is much higher than expected, the power-law is quite steep (Γ=3.5_-0.5^+0.7), and the blackbody has kT=0.045±0.010 keV and a poorly constrained radius (1<R<70 km). This is compatible with emission from the cooling of the whole surface, but for an old pulsar such as we would expect a lower temperature, unless some reheating mechanism is operating.

To assess  the statistical significance of the lines we estimated the probability of obtaining by chance a fit improvement as the observed one  through Monte Carlo simulations.
We simulated  pn spectra of with the same  exposure time as in our observations  using a model without lines, i.e.  the best fit power-law model with Γ=2.36 (Table <ref>). 
We fitted each simulated spectrum with a single power-law and with a power-law plus two harmonically spaced lines and computed the ratio of  the corresponding χ^2 values F = χ_ PL^2 / χ_ PL+lines^2.
We found a probability of 8 × 10^-4 to have a  fit improvement better than that observed in the real data (i.e. F>2.47), corresponding to a ∼3.1σ significance of the lines.


For the 3D-ML spectral-timing analysis, the phases were computed using the period at the epoch of the observation, P=1.187916418694(5) s given by <cit.>. 
We found an average pulsed fraction of 0.29±0.05, and no significant energy  variation  over the  range 0.23 in the pn (see Fig. <ref>, left). A hint of pulsation was also found in the MOS, with a pulsed fraction of 0.25±0.07 in the range 0.23, but it was no possible to extract the 3D spectra.
The pn spectra of the total, pulsed and unpulsed flux are plotted in Fig. <ref> (right).
The unpulsed spectrum cannot be fitted by a single power-law (χ_ν^2 = 2.12 for 5 d.o.f.), while  it is well fitted by the same absorption features of the total model. On the contrary, the spectrum of the pulsed emission does not require the addition of the absorption lines, and a power-law with Γ = 2.4_-0.4^+0.5  satisfactorily fits the spectrum.
All the results of the spectral fits are summarized in Table <ref>.

















§ DISCUSSION


Our ML analysis of the X-ray emission of four old rotation-powered pulsars has,  in general, confirmed previous results, providing in some cases smaller  uncertainties on the parameters and additional information on the spectral properties of these objects. Here, we first discuss the main results for the individual pulsars  and then we put them in the broader context of the class of old rotation-powered pulsars.


In the case of , previous analysis could not distinguish between a thermal and a non-thermal spectrum <cit.>, while we found that its emission is primarily thermal, being  well fitted by a blackbody with kT=0.17 ± 0.02 keV, emitting radius R=405_-90^+110 m, and bolometric luminosity  L_ bol = (4.4 ± 3.0)  10^30 . 
The small emitting area indicates that the thermal radiation comes from a hot spot of the stellar surface, most likely from the polar cap: in fact, the expected polar cap radius for is R_ PC=((2 π R_*^3)/(P c))^1/2≈ 455 m (for a NS radius of R_* = 10 km). 

We found no evidence for thermal components in the phase-averaged spectra of the other  targets and derived 3σ upper limits on their bolometric luminosity of L_ bol≲ 3.2 × 10^28 in and L_ bol≲ 2.4  10^29 in . These limits apply for temperatures in the range ∼0.052 (see Fig. <ref> and <ref>).  However, the  possible presence of a thermal component in  is suggested by the fact that its pulsed emission is softer than the unpulsed one and it can be fitted by a blackbody  with parameters consistent, within the errors, with the above luminosity limit (kT=0.10_-0.01^+0.02 keV, R=150_-50^+80 m).

Finally, we found  features below 0.5 keV with a statistical significance of ≳3σ in the  spectrum of . This could be fitted  either with a power-law plus blackbody model and an absorption line at ∼0.45 keV,  or  with a power-law and  two absorption lines at harmonically spaced energies  E_1=0.222 keV and E_2 = 0.444 keV. The more realistic best fit parameters of the continuum component lead us to prefer the second interpretation.  If the lowest energy line is an electron cyclotron feature, the implied magnetic field  (B_e=1.9 × 10^10 (1+z) G, where z is the gravitational redshift), is two orders of magnitude smaller than the surface field derived from the timing parameters of the pulsar (B_d=2.1 × 10^12 G, under the usual dipole approximation). The electrons responsible for the feature should be high in the magnetosphere, and it is unclear how they could be confined in a small region with the appropriate magnetic field value.
Alternatively, if the line is attributed to protons that could be in the atmosphere close to the NS surface, the required magnetic field is B_p = 3.5 × 10^13 (1+z) G, implying the presence of multipolar field components, as required, for example, in the Partially Screened Gap model <cit.>. 



 §.§ Thermal X-rays from hot polar caps
 






In Table <ref>, we collected the information on the (non-recycled) rotation-powered pulsars with evidence of thermal emission from a small region of their surface. Besides the objects in which the presence of such emission is well established (first part of the table),  we have included pulsars, like , for which there is only some evidence  for it (second part of the table).

The values of temperature and radius of each blackbody, with the corresponding errors, are taken from the most recent works present in literature (references in the last column of Table <ref>), and, when needed, we rescaled the radii using updated distance values.
The bolometric luminosities of these thermal components are evaluated as L_ bol=π R^2 σ T^4 and we included the distance uncertainties in their errors.




All the temperatures are in the narrow range 0.10.3 and do not depend significantly on the  characteristic age. On the contrary, the emission radii span nearly two orders of magnitudes. We expect that the emitting region be related to the polar cap size, so we compare R_ BB with the radius of the polar cap defined by the last closed lines in a dipolar field geometry, R_ PC=((2 π R_*^3)/(P c))^1/2.
As shown in Fig. <ref>, in most pulsars with 0.1<τ< 10 Myr the two radii are consistent, considering the errors, and  there is no clear correlation between  R_ BB/R_ PC  and   characteristic age.
Some pulsars have R_ BB significantly smaller than R_ PC, but this can be explained by geometrical effects.
In fact, the radii inferred from the spectral fits correspond to the projected area of the emitting region averaged over the star rotational phase.
Only for nearly aligned rotators (small angles between rotation and magnetic axis) seen pole-on  π R_ BB^2 corresponds to the real emitting area. This should occur, e.g., for PSR B0943+10 <cit.>, which, however, has R_ BB < R_ PC, possibly indicating that the magnetic field is not purely dipolar. 
In fact, the presence of multipolar components of the field can cause a reduction of the polar cap area by a factor B_s / B_d, where B_s and B_d are the actual magnetic field at the star surface and that of the dipole, respectively <cit.>.
PSRB0656+14, on the other hand, has a blackbody radius that is nearly 10 times larger than R_ PC, as already noticed by <cit.>, suggesting the need for  a different explanation of the hot thermal component in this pulsar. One possibility is that anisotropic thermal conduction in the crust is playing a role in causing temperature gradients on the surface and the oversimplified modelling   with just two blackbodies at different temperatures give unrealistic parameters. 



It is also interesting to compare the thermal polar cap emission of  old (non-recycled) pulsars with that observed in millisecond pulsars.
Thermal X-rays have been  detected in several millisecond pulsars <cit.>. For two of them (PSRJ0030+0451 <cit.> and PSRJ0437-4715 <cit.>) at least two thermal components are needed, that are interpreted as emission from the polar cap having a non-uniform temperature distribution with a hot core and a cooler rim. 
We have included millisecond pulsars  in Fig. <ref>, where, in order to make a consistent comparison with the values of non-recycled pulsars, we used the emission radii derived from blackbody fits. Note that fits with non-magnetized hydrogen atmosphere model, which are appropriate for millisecond pulsars, would result in emitting radii larger by a factor ∼4, thus making  most of them consistent with the polar caps radii in the centred dipole approximation. 

Thermal emission from small hot spots has been explored in detail by <cit.> in the context of polar cap models.
In their “Space Charge Limited Flow” model, primary particles accelerated above the polar cap produce a photons-pairs cascade in an avalanche process.
Backward particles  screen the acceleration voltage drop and  heat the  polar cap.  
The pair cascade can be initiated either by curvature radiation (CR) or by inverse-Compton scattering (ICS) of thermal X-rays by primary electrons. The production  of CR photons requires a  much  higher energy of the primary particles, and therefore the pair production occurs at higher altitude and the pair heating luminosity is expected to be much higher in the CR rather than in the ICS scenario.
These processes can occur only above the corresponding “death lines” in the  -P diagram. 
Pulsars in the region below the CR pairs death line, but above the ICS one, can produce pairs only from ICS photons. 


<cit.> give analytic expressions for the expected surface X-ray luminosity, depending on the pair fronts creation mechanism. In case of non-recycled pulsars, L_ bol≈ 10^31 erg s^-1 P^-1/2 for CR and L_ bol≈ 2.0  10^27 erg s^-1 P^-3/2 for ICS. These relations, which should be considered as upper limits in case of incomplete screening,  are compared with the observed thermal  luminosities of the pulsars in Fig. <ref>. Although there is a general agreement between the data and the model predictions, we note that among the three pulsars for which only the ICS mechanism should operate (indicated in Fig. <ref> by a square), two have luminosities above the maximum predicted in this scenario.  One of them is , for which the possible thermal origin of the pulsed flux is admittedly not very compelling. On the other hand, the presence of a thermal component in is well established <cit.> and possibly requires a different explanation. 






§ CONCLUSIONS

 
We applied the powerful ML technique to the spectral X-ray analysis of four dim rotation-powered old pulsars and found evidence for absorption lines at 0.22 keV and 0.44 keV in the spectrum of . If these lines are interpreted as cyclotron features due to protons they imply a magnetic field of a few 10^13 G, higher than the dipole field inferred from the timing parameters of the pulsar (B_d = 2 × 10^12 G). 
 
The presence of thermal emission from a hot polar cap could be established only for .  Data of better statistical quality are required to ascertain if thermal components are really needed also in the other three pulsars considered here: , and . Several old pulsars show the presence of thermal components in their X-ray spectra. By using the most updated spectral results and distance estimates, we found that the size of the emitting hot spots in these pulsars are generally consistent with the expected dimensions of the polar caps, once projection effects are taken into account.

aa

   
