A&A 486, 485-491 (2008)
DOI: 10.1051/0004-6361:20078227
C. Y. Hui - W. Becker
Max-Planck Institut für Extraterrestrische Physik, Giessenbachstrasse 1, 85741 Garching bei München, Germany
Received 5 July 2007 / Accepted 28 April 2008
Abstract
We have studied the nearby old pulsar PSR B1929+10 and its surrounding
interstellar medium utilizing the sub-arcsecond angular resolution of the Chandra X-ray Observatory.
The Chandra data are found to be fully consistent with the results obtained
from deep XMM-Newton observations as far as the pulsar is concerned. We confirm
the non-thermal emission nature of the pulsar's X-radiation. In
addition to the X-ray trail already seen in previous observations by the ROSAT
and XMM-Newton X-ray observatories, we discovered an arc-like nebula surrounding the pulsar.
We interpret the feature as a bow-shock nebula and discuss its energetics
in the context of standard shock theory.
Key words: stars: pulsars: individual: PSR B1929+10 - stars: neutron
In 1990s, a series of powerful X-ray observatories
were launched to space. Among many great results on various aspects in
astrophysics, these observatories allowed a first detailed study of the X-ray emission
properties of rotation-powered pulsars as a class (cf., Becker & Trümper
1997; Becker & Pavlov 2001, for a review). Most old
radio pulsars, though, were still too faint for a detailed study by these
satellites (cf., Sun et al. 1993; Manning & Willmore 1994; Becker & Trümper
1997; Saito 1998). Thanks to the much improved sensitivity of the XMM-Newton and Chandra
observatories, a more detailed study of old pulsars became possible.
Observations of PSR B0950+08; B0823+26; J2043+2740 (Becker et al. 2004; Zavlin & Pavlov 2004); B0628-28 (Becker et al. 2005); B0943+10 (Zhang et al. 2005); B1133+16 (Kargaltsev et al. 2006); B1929+10 (Becker et al. 2006); and B2224+65 (Hui & Becker 2007a)
for the first time have allowed us to study the emission properties of
old pulsars as a class. Surprisingly, the X-ray emission from old pulsars
seems to be dominated by non-thermal radiation processes. Thermal components
(e.g., to account for the emission from hot polar caps) are not required to
model the X-ray spectra of these pulsars, resulting in mostly upper limits
for any thermal radiation components. Further support for an emission scenario
dominated by non-thermal radiation is found by the observed temporal emission
properties. Pulse profiles, if detected with sufficient photon statistics,
show multiple components and narrow features. This is indicative of strongly
beamed emission, which further invalidates the heated polar cap scenario as
the main source of X-ray emission in old pulsars. The pulsed fractions
in old pulsars are in the range of
.
In addition to the pulsar emission, which originates within the co-rotating magnetosphere, extended trail like X-ray emission was observed from PSR B1929+10 (Becker et al. 2006) and PSR B2224+65 (Hui & Becker 2007a) on a scale of several arc-minutes. In the case of PSR B1929+10 the X-ray emission in the trail is interpreted as synchrotron emission produced in the shock between the pulsar wind and the surrounding medium (see the discussion in Becker et al. 2006, for details). Owing to the moderate (15'' half energy width) spatial resolution of XMM-Newton, details of the nebular emission associated with PSR B1929+10 might have been remained unresolved. With a ten times improved angular resolution Chandra data can thus be essential to further constrain the properties of the nebula very near to the pulsar.
In this paper, we present a detailed analysis of multi-epoch Chandra
observations of the field around PSR B1929+10.
Based on its X-ray emission properties, this source is considered
prototypical of an old pulsar (Becker et al. 2006). With a pulse period
of P=226.5 ms and a period derivative of
10-15,
its characteristic age is determined to be
3
106 years. These
spin parameters imply a spin-down luminosity of
and a magnetic field at the neutron star magnetic poles of
1011 G. With a radio dispersion measure of
,
the NE2001 Galactic free electron density model of Cordes & Lazio (2002) predicts a distance of 170 pc. However, the recent astrometric measurements by Chatterjee et al. (2004) yielded a precise proper
motion and parallax determination that translates into an accurate distance
measurement of
d=361+10-8 pc and a proper motion of
km s-1. The ephemerides of PSR B1929+10, which we made
use of in this paper, are listed in Table 1.
Table 1: Ephemerides of PSR B1929+10a.
The paper is organized as follows: in Sect. 2 we describe the observations and data analysis; and in Sect. 3 we summarize the results and provide a discussion in the context of a standard shock model for the nebular emission.
Data analysis is restricted to the energy range 0.5-8.0 keV. All energy fluxes, however, are computed for the 0.5-10 keV band for better comparison with the results based on XMM-Newton data (Becker et al. 2006).
The object PSR B1929+10 was observed with Chandra in 2005 December 04 (Obs ID: 6657)
and 2006 May 28 (Obs ID: 7230) with the Advanced CCD Imaging Spectrometer
(ACIS). In both observations, PSR B1929+10 was located on the back-illuminated (BI)
ACIS-S3 chip with an off-axis angle of 0.1 arcmin. We used standard processed
level-2 data. The effective exposures are
21 ks and
25 ks
for the observations in 2005 December and 2006 May, respectively.
With the objective obtaining better statistics for the analysis, we combined both datasets to produce better images. We carefully checked and corrected the aspect offsets for each observation prior to the merging.
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Figure 1:
a) 4 ![]() ![]() ![]() ![]() |
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The combined X-ray images of the 4
4 arcmin field centered on PSR B1929+10 as well
as a close-up of the central 1
1 arcmin regions are shown in Fig. 1.
A compact nebula, which has an arc-like morphology somewhat resembling a bow-shock,
is clearly detected around PSR B1929+10. X-ray contours were calculated at the levels of
(6-26)
10-6 counts arcsec-2 s-1 and overlaid on the image in
Fig. 1b. Assuming this arc-like compact feature is a bow-shock pulsar wind
nebula, it is interesting to estimate the stand-off angle
which is
a crucial parameter in discussing the shock physics (see also Sect. 3). By fitting
a 2D Gaussian model to the raw image of the field around PSR B1929+10, we obtained
a full width at half maximum (FWHM) of 1.13
0.02 arcsec (
error). We take this as an estimate for the lower bound of
.
To further examine the extent of the compact nebula, we computed the brightness
profile in the energy band 0.5-8 keV from the raw image of bin size of 0.5 arcsec. We estimated the counts in sixteen consecutive boxes of dimensions 1
15 arcsec, oriented along the nebula. The vignetting corrected brightness profile
and the orientation of the 16 spatial bins are shown in Fig. 2.
The arc-like nebula extends up to
10 arcsec from the pulsar before
fading into the background. Because of the wings of the ACIS-S point spread function, the pulsar is expected to contribute to its surrounding
nebula. To estimate this, we compared the observed data with the
ACIS-S instrumental point spread function. To do so, we simulated a point source observation
using MARX (ver. 4.2.1). The adopted inputs were the pulsar spectrum and the same
exposure, roll, and off-axis angle as in the actual data.
We then computed the brightness profile of the simulated data in the same way as
aforementioned. The estimated point source profile is shown in Fig. 2
as a dotted line. The brightness profile of the arc-like nebula computed from the
actual observation is significantly different from the expected distribution
of a point source. On the other hand, there is no significant extended emission
detected ahead of PSR B1929+10.
In addition to the arc-like nebula near the pulsar, we observed a clumpy structure (which is
labeled as C in Fig. 1b). There are only 24 net counts from
this clump, which does not allow for a more detailed analysis. The signal-to-noise
ratio of this clump is estimated to be
2, and thus is consistent with
background fluctuations.
In Fig. 1a, no prominent structure resembling the X-ray trail
seen by ROSAT and XMM-Newton opposite to the pulsar's proper motion
direction can be identified (cf. Fig. 2 in Becker et al. 2006).
We have examined the Chandra image further by smoothing the
raw data with a kernel of arcsec, which is comparable with the FWHM
of XMM-Newton's PSF. The smoothed image is displayed in Fig. 3. Comparing
the image with the contours calculated from XMM-Newton MOS1/2 data, a faint
trail like feature is noticed. However, the background contribution of this
feature is estimated to be
.
The unabsorbed X-ray flux of a 1 arcmin circular trail region near the pulsar, as detected by XMM-Newton, is
within the 0.5-10 keV band
(Becker et al. 2006). The low significance of the trail in the two Chandra
observations, thus, is in agreement with Chandra's lower sensitivity. We,
therefore, will not further consider the X-ray trail emission in this paper, and
alert the interested reader to the XMM-Newton results reported by
Becker et al. (2006), for a detailed discussion of its emission properties.
Although the spectrum from PSR B1929+10 has already been tightly constrained by the XMM-Newton data (Becker et al. 2006) it is important for us to re-examine its spectral properties with Chandra since it resolves the pulsar emission from the compact surrounding nebular component better.
We extracted the pulsar spectrum in both data sets from a circle of 2 arcsec
radius (encircled energy 95%), centered on the pulsar, and fitted them
simultaneously. The background spectrum was extracted from a source-free region
within a 10 arcsec radius centered at RA =
,
Dec =
(J2000). After background subtraction, 593
24 and
682
26 net counts were available for the spectral analysis. These values
imply the net counting rates of
10-2 cts/s and
10-2 cts/s for the observations in 2005 December and 2006 May, respectively.
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Figure 2:
Vignetting corrected brightness profile of the field around PSR B1929+10.
The energy range is 0.5-8 keV. The profile expected for a point source is
indicated by a dotted line. The average background level and its ![]() ![]() ![]() |
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Figure 3:
The 5 ![]() ![]() |
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We computed the response files with the tools MKRMF and MKARF in CIAO 3.4.
Utilizing the most updated calibration data, CALDB 3.4.1, the generated response
files corrected the degradation of the quantum efficiency in the ACIS CCD, accordingly.
Each spectrum was dynamically binned so as to have at least 30 counts per bin.
To better constrain the spectral properties, we fitted simultaneously the spectra obtained from both observations. We performed all the spectral fittings in 0.5-8 keV with
XSPEC 11.3.2. The parameters of all fitted model spectra are summarized in Table 2.
All the quoted errors are 1-,
and were computed for 1 parameter of interest.
Among the single component models tested, we found that a power-law model fits
the data best (
for 36 d.o.f.). This model yields a column
density of
1021 cm-2, a photon index of
,
and a normalization at 1 keV of
8.12+1.04-0.90
10-5 photons keV-1 cm-2 s-1. These best-fit values are
fully consistent with those obtained by XMM-Newton for power-law fits (see Table 3
in Becker et al. 2006). The best-fit power-law spectrum and residuals are shown in
Fig. 4. The column density inferred from both Chandra and XMM-Newton spectra is
relatively high in comparison with the mean value obtained from the Extreme UltraViolet
Explorer (EUVE) measurements of the stars in the neighborhood of the pulsar
(Slowikowska et al. 2005). However, as discussed by Slowikowska et al. (2005),
the interstellar medium is very patchy in the region around PSR B1929+10 (cf., Table 3 in
Slowikowska et al. 2005, for more details). Merely on the basis of the comparison
with the mean value, the
we report and in Becker et al. (2006)
cannot be invalidated. A more detailed mapping is thus needed to better constrain
the
toward the pulsar.
Table 2: Spectral parameters inferred from fitting the Chandra ACIS-S data obtained from PSR B1929+10 and its associated extended feature.
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Figure 4:
Energy spectra of PSR B1929+10 as observed with the Chandra
ACIS-S3 detector on 04 Dec. 2005 and 28 May 2006 and simultaneously
fitted to an absorbed power-law model
( upper panel) and contribution to the ![]() |
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We have also computed the error contours to demonstrate the relative parameter
dependences of the photon index vs. the hydrogen column density and plotted this
in Fig. 5. The unabsorbed flux deduced for the best fit power-law model
parameters is
10-13 erg s-1 cm-2 within 0.5-10 keV.
At a distance of 361 pc it implies a luminosity of
1030 erg s-1.
As for the XMM-Newton data it is obvious that the single power-law model already
describes the observed pulsar spectrum very well. Hence, the justification of
including an additional thermal component is absent. In the Chandra data, we
found that fitting with a power-law plus blackbody model does not yield a reasonable
solution if we allow the blackbody radius and the temperature to be free parameters.
It resulted in a blackbody radius of
m.
This is much smaller than the canonical size of a polar cap,
m, which suggests the contribution from
the additional blackbody component is insignificant. We quantified the statistical
significance for adding this extra component to the power-law model with the
F-test which suggests that inclusion of this thermal components is only required
at a confidence level of
.
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Figure 5:
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Figure 6:
1 ![]() |
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We have also examined the possible contributions from a polar cap and the neutron
star surface by fixing the blackbody radii at R=300 m and R=10 km, respectively.
These fits yield temperatures of
105 K and
105 K. The F-test suggests that adding these thermal components to the power-law model
is only significant at a confidence level
.
Due to the better photon-statistics this number was even
smaller in the XMM-Newton data (Becker et al. 2006). This low significance
is also reflected by the relative contribution of the thermal component in
the total energy flux observed by Chandra. We estimated the
upper limits for the polar cap temperature and its flux contribution
by adding a blackbody component to the power-law model.
Fixing the blackbody radius at a polar cap size of R=300 m, a
upper limit of T<1.2
106 K was computed by assuming contribution from one polar cap only. This implies that the 1
limit contribution from the polar cap in the total energy flux is
.
For the spectral model consisting of two blackbody components, we found that the
best-fit model parameters also agree well with those inferred from the XMM-Newton
spectra (Becker et al. 2006). Despite the acceptable value of the goodness-of-fit,
the inferred blackbody radii are too small to be considered as a reasonable description.
Moreover, the pulsar spectrum obtained by XMM-Newton and fitted together with the
spectrum obtained by the ROSAT PSPC have already shown that this model cannot
describe the data beyond 5 keV (see Becker et al. 2006).
Since the arc-like nebula is resolved by Chandra for the first time,
it is instructive to examine its energy spectrum, despite the poor photon
statistics. We extracted the nebular spectra from the regions
in accordance with its observed morphology. For the sake of consistency,
we adopted the same extraction regions in both datasets, which are
illustrated in Fig. 6. It consists of an annular region centered on
the pulsar position with inner and outer radii of 2 arcsec and 5 arcsec,
a circular region with a radius of 2.2 arcsec, as well as a ellipse
of 4 arcsec 8 arcsec.
The background spectra were extracted from each dataset within a nearby
source-free region of a 10 arcsec radius, centered at RA =
and Dec =
(J2000). After background subtraction, there
were 29
5 and 41
7 net counts extracted from the arc-like feature, implying
the net counting rates of
10-3 cts/s and
10-3 cts/s for the observations in 2005 December and
2006 May, respectively. Within the
errors of these count rates, no
variability is apparent on the basis of these two observations.
The response files were computed in the same manner as those for the pulsar spectra.
Each spectrum was dynamically binned so as to have at least 10 counts per bin. In order to
obtain a better statistic, we analyzed both spectra simultaneously.
We hypothesized that the nebular emission originates from the interaction of the
pulsar wind and the ISM. Synchrotron radiation from the ultra-relativistic
electrons is generally believed to be the emission mechanism of the pulsar
wind nebula, which is characterized by a power-law spectrum. We tested this
hypothesis by fitting an absorbed power-law model to the nebular spectra.
We fixed the column density at the value
1021 cm-2 inferred from fitting the pulsar spectrum. The power-law model describes the
observed spectrum reasonably well (
for 6 d.o.f.).
The best-fit power-law spectrum and residuals are shown in Fig. 7.
This model yields a photon index of
and a normalization at 1 keV of
3.63+0.78-0.74
10-6 photons keV-1 cm-2 s-1. The unabsorbed flux
deduced for the best-fitted model parameters are
10-14 erg s-1 cm-2 in the energy range of 0.5-10 keV. The pulsar distance
of 361 pc implies a luminosity of
1029 erg s-1.
We have checked the robustness of all the spectral parameters quoted here
by incorporating background spectra extracted from different source-free regions. We
found that within the errors the spectral parameters inferred
from independent fittings are all consistent with each other.
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Figure 7:
Energy spectra of the arc-like structure associated with
PSR B1929+10 as observed by the Chandra ACIS-S3 detector on 04 Dec. 2005 and 28 May 2006, and simultaneously fitted to an absorbed power-law model
( upper panel) and contribution to the ![]() |
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Complementing the XMM-Newton observation, we have studied PSR B1929+10 and its surrounding medium with Chandra, which provides data with sub-arcsecond resolution. So far, three distinct components have been resolved, namely the pulsar itself, the X-ray trail opposite to the pulsar's proper motion direction as well as the arc-like nebula surrounding the pulsar. The flux contributions from these components and the corresponding X-ray conversion efficiencies are summarized in Table 3.
Table 3: Unabsorbed fluxes, luminosities, and the conversion efficiencies of PSR B1929+10 and the nebular components in 0.5-10 keV.
The morphology of the arc-like nebula and the orientation with respect to the pulsar's proper motion direction suggest a bow-shock nature. This is the first well-defined bow-shock morphology observed from an old pulsar.
A bow-shock nebula as observed in PSR B1929+10 can be produced by a pulsar in supersonic motion.
In this case, the termination shock radius
is determined by the balance of the
ram pressure between the relativistic pulsar wind particles and the ISM at the head of the shock
(cf. Hui & Becker 2007b):
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(1) |
At a distance of 361 pc, the proper motion velocity and the size of the arc-like nebula imply
the pulsar took 150 years to pass through the sky region of the nebula.
We estimated the magnetic field in this shocked region by equating the passage time to the
synchrotron cooling timescale
yr,
where
is the Lorentz factor of the wind, taken to be
106 (cf., Cheng et al. 2004),
is the Thompson cross
section, and
is the magnetic field in the shocked region in units of micro gauss.
This implies a magnetic field of
75
for the region near to the pulsar.
For comparison, the typical field
strength in the ISM is
2-6
(cf., Beck et al. 2003, and references therein). If the magnetic field in the neighborhood of PSR B1929+10 is comparable
with this estimate, the inferred compression factor is
13-38 in the
bow-shock region, which is rather high in comparison with other pulsar wind
nebulae (e.g., Hui & Becker 2006, 2007b). Polarization measurements of the
sky region around PSR B1929+10 in the radio band can help to better constrain the
magnetic field of this system and hence the compression factor.
In the context of the standard shock theory (Chevalier 2000), the X-ray
luminosity and spectral index depend on the inequality between the characteristic
observed frequency
and the electron synchrotron cooling
frequency:
(cf., Chevalier 2000, and references therein), which is estimated to be
1017 Hz. Since, in general
,
this suggests the X-ray emission is in a fast cooling regime.
We further probed the energy distribution of the synchrotron radiating
electrons in the shock. The emitting electrons are distributed as
.
In a fast cooling regime, the
theoretical luminosity per unit frequency is given by (cf., Cheng et al. 2004):
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(2) |
The arc-shaped morphology of the nebula observed in PSR B1929+10 is similar to that of Geminga (Caraveo et al. 2003). However, there is a main difference between these two cases. While the arc-like nebula of Geminga is rather symmetric with respect to the direction of proper motion, asymmetry is indicated in the case of PSR B1929+10 (see Fig. 1b). Its asymmetric shape might be a result of the anisotropic pulsar wind and/or inhomogeneities in the surrounding ISM (see Hui & Becker 2006).
For the pulsar PSR B1929+10, we found that the spectral properties inferred from our analysis are in good
agreement with the results obtained by XMM-Newton, which did not allow the
pulsar emission to be separated from the compact nebular component. The consistency is
expected even in the presence of the diffuse compact nebulae as it contributes only
to the observed energy flux (see Table 3). Thus, the non-thermal
emission scenario of PSR B1929+10 is confirmed. Hui & Becker (2007a) had argued that
it is possible to sustain particle acceleration regions in PSR B1929+10's outer-magnetosphere
(so-called outer-gap) if the inclination of the magnetic axis with respect to the rotational
axis is taken into account. This inference is supported by the ability of
the outer-gap model in reproducing the observed X-ray
pulse profile and its phase shift relative to the radio pulse (see Fig. 16 Becker et al. 2006). However, this model has difficulty in explaining the observed spectral
properties of PSR B1929+10.
In the outer-gap model, the non-thermal X-rays result from the back-flowing charge particles
from the outer gap (Cheng & Zhang 1999). When the primary electrons/positrons leave the outer-gap, they will emit curvature photons that are subsequently converted into secondary pairs in the presence of the strong magnetic field.
Synchrotron photons will then be emitted by these secondary electrons/positrons. If these photons are energetic enough, they will further be converted into pairs that again lose their energy via
synchrotron radiation. Therefore, an electromagnetic cascade is developed. Based on this model,
Cheng & Zhang (1999) argued that the X-ray photon index resulting from such cascades
should be 2. This is obviously not
in agreement with the observed photon index for PSR B1929+10, which is as steep as
2.91+0.16-0.13.
Observations of five other old pulsars: B1133+16 (Kargaltsev et al. 2006);
B0943+10 (Zhang et al. 2005); B0628-28 (Becker et al. 2005);
B0823+26 (Becker et al. 2004); and J2043+2740 (Becker et al. 2004),
also found the photon indices steeper than 2.
This gives the outer-gap emission model a challenge. Re-examination of the model is thus required.
After this work was submitted to A&A for publication, we became aware that a paper on the similar subject as presented here was submitted to ApJ by Misanovic et al. (2007). The results reported by these authors agree well with the results presented here. Misanovic et al., though, report to have detected a thermal component in the spectrum of PSR B1929+10. While their parameters inferred from the single power-law fittings are consistent with ours, they suggested that a model of power-law plus blackbody model provides a statistically better description. This obviously contradicts with the conclusion presented here and in Becker et al. (2006). From a closer inspection of their spectral fits we conclude that their apparent detection is probably biased by a too small signal-to-noise ratio per spectral bin. While we binned the Chandra spectrum so as to have at least 30 counts per bin Misanovic et al. (2007) grouped the data so as to have only about 15 counts per spectral bin. For the spectral fitting of XMM-Newton data, the parameters obtained by Misanovic et al. (2007) are for 190 degree of freedom whereas Becker et al. (2006) had only 121 degrees of freedom for their analysis. Becker et al. (2006) thus used a much higher photon statistics per spectral bin. The higher signal-to-noise ratio per spectral bin yielded a more stringent discrimination among competing spectral models. For this reason, the spectral results presented here as well as in Becker et al. (2006) provide more stringent constraints on the pulsar's X-ray emission properties than those in Misanovic et al. (2007).
Acknowledgements
We thank the referee Patrizia Caraveo for providing many useful suggestions to improve the quality of the manuscript considerably. We would also thank Bernd Aschenbach for thoroughly reading the manuscript and K. S. Cheng for discussing the shock physics with us.