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A&A 425, 1041-1060 (2004)
DOI: 10.1051/0004-6361:20040499
N. I. Serafimovich1,2 - Yu. A. Shibanov1 - P. Lundqvist2 - J. Sollerman2
1 - Ioffe Physical Technical Institute, Politekhnicheskaya 26,
St. Petersburg, 194021, Russia
2 - Stockholm Observatory, AlbaNova Science Center, Department
of Astronomy, SE-106 91 Stockholm, Sweden
Received 22 March 2004 / Accepted 22 June 2004
Abstract
The young PSR B0540-69.3 in the LMC is the only pulsar (except the Crab
pulsar) for which a near-UV spectrum has been obtained.
However, the absolute flux and spectral index of the HST/FOS spectrum are
significantly higher than suggested by previous broad-band time-resolved
groundbased UBVRI photometry. To investigate this difference,
observations with ESO/VLT/FORS1 and analysis of HST/WFPC2 archival data
were done. We show that the HST and VLT spectral data for the pulsar
have 
50% nebular contamination and that this is the reason for
the above-mentioned difference. The broadband HST spectrum
for the range 3300-8000 Å is clearly nonthermal and has a negative
spectral index,
with
.
This is different from the almost flat spectrum of the Crab pulsar, and
also steeper than for the previously published broadband photometry of PSR B0540-69.3.
We have also studied the spatial
variations of the brightness and spectral index of the Pulsar Wind Nebula
(PWN) around the pulsar, and find no significant spectral index variation
over the PWN. The HST data show a clear asymmetry of the surface brightness
distribution along the major axis of the torus-like structure of the PWN with
respect to the pulsar position, also seen in Chandra/HRC X-ray images.
This is different from the Crab PWN and likely
linked to the asymmetry of the surrounding SN ejecta.
The HST/WFPC2 archival data have an epoch separation of 4 years, and this
allows us to estimate the proper motion of the pulsar. We find a motion
of 
mas yr-1 (corresponding to a transverse velocity
of
)
along the southern jet of the PWN.
If this is confirmed at a higher significance level
by future observations, this makes PSR B0540-69.3
the third pulsar with
a proper motion aligned with the jet axis of its PWN, which poses
constraints on pulsar kick models. To establish the multiwavelength
spectrum of the pulsar and its PWN, we have included recent Chandra
X-ray data, and discuss the soft pulsar X-ray spectrum based on spectral fits
including absorption by interstellar gas in the Milky Way, LMC as well as the
supernova ejecta. We have compared the multiwavelength spectra of PSR B0540-69.3 and
the Crab pulsar, and find that both PSR B0540-69.3 and the Crab pulsar have a weaker
flux in the optical than suggested by a low-energy power-law extension of
the X-ray spectrum. This optical depression is more severe for PSR B0540-69.3 than for
the Crab pulsar. The same trend is seen for the PWNe of the two pulsars,
and continues for low energies also out in the radio band. We discuss
possible interpretations of this behavior.
Key words: stars: pulsars: general - stars: pulsars: individual: PSR B0540-69.3 - ISM: supernova remnants - stars: supernovae: general - astrometry
PSR B0540-69.3 in the Large Magellanic Cloud (LMC) was discovered as a pulsed
(P = 50.2 ms) X-ray source by Seward et al. (1984). Pulsations
have since also been detected in the optical and at radio
wavelengths (Middleditch & Pennypacker 1985; Manchester et al. 1993a).
The pulse profile in the optical (Boyd et al. 1995) is broad and double-peaked,
with a separation of 
0.2
in phase between the two maxima, consistent with what is also seen in
X-rays (Seward et al. 1984; de Plaa et al. 2003).
The profile is also broad in the radio (the duty cycle is 80%),
and there is a hint of a double structure (Manchester et al. 1993a).
Parameters of PSR B0540-69.3 are compiled in Table 1. The pulsar spins rapidly, is young (spin down age 1660 yr), and sits in a compact synchrotron nebula (see Fig. 1), which we will henceforth refer to as its pulsar wind nebula (PWN). The similarities with the Crab pulsar and its nebula are such that PSR B0540-69.3 with its supernova remnant, SNR 0540-69.3, are sometimes referred to as the "Crab twin''. Even the structures of the PWNe appear to be similar. Both have a torus and jets (Gotthelf & Wang 2000), although the proper motion for PSR B0540-69.3, suggested by Manchester et al. (1993b) based on a displacement between the pulsar optical position and the center of the PWN as seen in radio, seems not to be along the spin axis as it is in the Crab case.
Table 1: Parameters of PSR B0540-69.3 (Manchester et al. 1993a, unless specified otherwise).
There are, however, differences on a larger scale. While the PWN of PSR B0540-69.3 is
surrounded by an X-ray and radio emitting outer shell of
radius 30
,
or 7.3 pc
(Manchester et al. 1993b; Gotthelf & Wang 2000), an
outer shell around the Crab is still not confirmed (although high-velocity
gas has been revealed in the UV, Sollerman et al. 2000).
Another difference is that SNR 0540-69.3 is oxygen-rich (e.g., Kirshner et al. 1989;
Serafimovich et al. 2004), whereas the Crab Nebula has nearly
normal solar abundances of metals (Blair et al. 1992, and references therein).
It is therefore believed that the progenitor
to PSR B0540-69.3 was a much more massive star than the Crab progenitor (Kirshner et al. 1989).
PSR B0540-69.3 is one of few pulsars for which a near-UV or optical spectrum has been reported. Hill et al. (1997) obtained a time-integrated near-UV spectrum with HST/FOS and Middleditch & Pennypacker (1985) used time-resolved photometry to establish a broadband ground-based UBVRI spectrum in the optical. These two spectra show, however, a significant difference in absolute flux in the spectral range where they overlap. To investigate this mismatch we have added two recent sets of data, one is the ESO/VLT/FORS spectroscopy of SNR 0540-69.3 analyzed by Serafimovich et al. (2004), and the other is HST/WFPC2 imaging (Caraveo et al. 2000; Morse 2003) retrieved from the HST archive. A bonus of our study is that we also obtain the optical spectrum of the PWN around PSR B0540-69.3. This was first studied quantitatively by Chanan et al. (1984), albeit at a low spatial resolution which did not allow them to resolve the pulsar from the PWN.
To connect the optical pulsar emission to the emission at other wavelengths,
we have also included recent results from radio and X-rays. Previous attempts
to establish the multiwavelength spectrum of PSR B0540-69.3 have assumed a rather
high hydrogen column density for the X-ray
absorption,
cm-2 (Kaaret et al. 2001).
With this value for 
it is possible to fit the
soft X-ray spectrum with a single power-law.
This suggests a non-thermal nature of
the emission, likely to be formed in the magnetosphere
of the rotating neutron star (NS).
There are, however, reasons to reinvestigate this since the spectral
fits have not considered the fact that a large fraction of the absorbing gas
has LMC abundances rather than Milky Way abundances.
It could even be that the supernova ejecta can contribute to the
absorption of the X-ray emission. Taking these
considerations into account, we show that the situation is more
complicated than assuming a single power-law for the optical/X-ray spectrum.
We have also done the same exercise for the PWN.
The outline of the paper is as follows: in Sect. 2 we describe the optical spectroscopic and photometric observations of PSR B0540-69.3 and its PWN, as well as a reinvestigation of the X-ray data of Kaaret et al. (2001). In Sect. 3 we discuss these results and put them in a multiwavelength context. We also discuss results we find for the proper motion of the pulsar, and their possible interpretation.
Table 2: Log of VLT observations of PSR B0540-69.3 on 2002 January 9.
Spectroscopic observations of PSR B0540-69.3 were performed on 2002 January 9 with
the FOcal Reducer/low dispersion Spectrograph (FORS1) on the
8.2 m UT3 (MELIPAL) of the ESO/VLT, using a slit width of 1
and the grism
GRIS_600B.
This grism has a dispersion of 50 Å/mm, or 1.18 Å/pixel,
and a wavelength range of 3605-6060 Å.
The optical path also includes a Linear Atmospheric Dispersion Corrector that
compensates for the effects of atmospheric dispersion (Avila et al. 1997).
The pixel scale of the detector is 0
2 per pixel.
We obtained 7 exposures of 1320 s
each (see Table 2), in total 154 min of exposure time.
The position angle, PA = 88
,
was the same in all these exposures.
The slit crosses the pulsar and its PWN as shown in Fig. 1.
The mean seeing was 1
15.
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Figure 1:
A 15
 15
image of the field
around PSR B0540-69.3 obtained in the F547M band with the HST/WFPC2 (Morse 2003).
The pulsar was exposed on the PC chip and its position is marked by an
arrow. The slit position of the VLT observations is marked by thin
parallel lines. The slit width is 1
.
The diffuse emission surrounding
the pulsar is the pulsar wind nebula (PWN). Note its elongation
in the NE-SW direction.
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The spectroscopic images were bias-subtracted and flat-fielded using standard
procedures within the NOAO IRAF Longslit package.
We used the averaged sigma clipping algorithm avsigclip with the
scale parameter set equal to none to combine the images.
Wavelength calibration of the combined images was done using arc frames
obtained with a helium-argon lamp.
The spectra of the objects were then extracted from the 2D image
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Figure 2:
Spatial profiles of PSR B0540-69.3 and its PWN along the slit
in Fig. 1 (in counts, VLT data)
at the continuum wavelengths
4600.0 Å, 5248.7 Å and 5450.0 Å,
from top to bottom, respectively. In each panel the pulsar is assumed to sit
at the main peak of the profile. Thin lines mark the six-pixel wide
extraction window chosen for the spectral analysis of the pulsar (where
1 pixel corresponds to 0
2).
The regions outside the thin lines, but within the solid lines have also
a width of six pixels, and mark the regions used for the nebular subtraction
in the spectral analysis. The spatial profile of a background star is shown in
the inset in the bottom panel for comparison.
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Figure 3:
Spatial profiles as in Fig. 2, but using
the HST/WFPC2/F547M image shown in Fig. 1.
The pivot wavelength is 5483 Å.
We show profiles obtained along the VLT slit
with the spatial resolution of 0
046 provided by the PC chip
pixel-size (top), rebinned to the VLT CCD-pixel
scale of 0
2 (middle),
and smoothed using a Gaussian with the FWHM of 1
2,
comparable to the seeing value of the VLT observations,
and then rebinned to the VLT CCD-pixel scale
(bottom). The VLT six pixel extraction window is marked by vertical
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. A significant flux (response) degradation
was found at wavelengths below 3860 Å where the standard star
spectrum displays many deep spectral features,
as well as in the very red end at
6030 Å.
We therefore excluded these wavelength regions from our analysis.
In Fig. 2
we have plotted spatial profiles for the emission from
the pulsar+nebula along the slit at several
wavelengths where the contribution of nebular lines is negligible.
Despite some minor variation of the shape of the profile
with wavelength, the profile has a strong peak around the pulsar position.
However, with a seeing of 1
the
pulsar and nebular emissions are strongly blended.
This is partially confirmed by a comparison of the profile
with the PSF of a background star shown in the inset of
the bottom panel of Fig. 2.
To illustrate this further we have compared the VLT profiles with the profiles obtained
from the HST/WFPC2/F547M image, shown in Fig. 1.
From the F547M image we first extracted the data covered by the
VLT slit, and then we averaged the emission across the slit for each position
along the slit.
The peak position of the flux along the slit varies with the wavelength of
the spectroscopic image by 
1 VLT pixel.
To take this into account in our test we extended the slit width by one pixel.
In the first test case we kept the high spatial resolution in the HST image
(0
046, Fig. 3 top),
while in the second case we averaged over a coarser pixel scale (0
2) to
simulate the VLT pixel size (Fig. 3 middle).
In a third experiment we
smoothed the initial image using a Gaussian with a FWHM of 1
2 to model
the VLT seeing conditions and we then rebinned it to the VLT CCD-pixel scale
(Fig. 3 bottom).
The pivot wavelength of the F547M filter is 5483 Å,
which is close to 5450 Å, chosen for the profile
shown at the bottom of Fig. 2.
As seen from Fig. 3,
the pulsar is clearly resolved
from the extended PWN at the PC chip spatial
resolution as a narrow central peak
on a broad (7
in size)
asymmetric pedestal formed by the PWN.
It is still resolved at the VLT CCD-pixel scale of 0
2, while it is not
resolved after the 1
2 smoothing, i.e., close to the seeing conditions
of the VLT observations.
Although the pulsar should contribute significantly to the flux within
the spatial strip of six VLT pixels
centered on the main peak of the whole profile, it is obvious
that the nebula will contaminate severely the spectral VLT observations.
With this in mind,
we extracted a 1D spectrum averaged over 6 pixels, equal to
,
along the slit centered at the pulsar position, as shown
by thin vertical lines in Figs. 2 and 3.
To subtract the nebular contribution we extracted 1D spectra averaged over
six adjacent pixels to the east and an equal number to the west of
the central strip, as indicated by thick lines in Fig. 2.
An averaged spectrum was constructed from the two adjacent spectra and
subtracted from the spectrum for the central region.
The resulting spectrum contains no significant emission from nebular lines,
except for [O III]
4959, 5007,
which has a high spatial variability within the nebula.
The resulting spectrum, with the [O III]-feature removed,
is presented in Fig. 4. As can be seen from this
figure, our spectroscopic data agree well with the result
by Hill et al. (1997) at the lower boundary of their 1
uncertainty range, but give about 2-4 times
higher flux than the photometric data of Middleditch et al. (1987).
This can partly be understood from our method of correcting for the
PWN emission. We averaged this by using the emission
away
from the center of the spatial profile. One problem is
that Fig. 2
shows that the center of the profile in the VLT data may not coincide exactly
with the pulsar position. A second, and more serious problem, is that
the seeing spreads out much of the weak pulsar emission from the central region
whereas seeing makes the PWN emission peak toward the center regardless of
whether there is a pulsar or not. This will most likely lead to erroneous
background subtraction so that the VLT spectrum shown in Fig. 4 is
contaminated with significant PWN emission.
The agreement with Hill et al. (1997)
indicates that also their analysis overestimated the pulsar emission.
The data using the wide and medium band filters
F336W,
F547M, and F791W, obtained on 1999 October 17 with 600 s, 800 s, and 400 s
total exposure times, respectively (Morse 2003), are
particularly useful for the continuum emission analysis
since these filters do not cover any bright emission lines from the LMC
or the supernova remnant.
We also retrieved data sets for the narrow band F658N and wide band F555W
filters, both of which were obtained on 1995 October 19 with 4000 s,
and 600 s exposures, respectively (Caraveo et al. 2000).
The pulsar and its PWN are clearly detected on the PC chip in all these
images. This is illustrated in Figs. 1 and 3
which present the data for the F547M band.
The F658N filter includes the 6576-6604 Å range,
which means that contamination from high-velocity H
emission
from the supernova remnant at central wavelength 6578 Å
(Serafimovich et al. 2004) can enter into the filter passband, as well as
[N II] emission from the LMC. This can also be seen in Fig. 3b of
Caraveo et al. (2000) where it is shown that a filament passes across the
pulsar along the NW direction. Although the pulsar stands out rather
clearly on the image, the uneven background introduces some uncertainty
to the estimated pulsar flux. The background contamination is more severe in
the F555W band as it captures the bright [O III]
4959, 5007 Å lines
which are much more difficult to spatially disentangle from the pulsar.
The uneven background is most clearly seen in the image obtained with the
F502N narrow band filter centered at these lines and overlapping with the
F555W band. Therefore, the pulsar and PWN continuum flux measurements
in the F555W band can only be considered as upper limits.
![\begin{figure}
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Figure 4:
Optical spectrum of PSR B0540-69.3 obtained with different telescopes and
instruments. The uppermost spectrum is the VLT spectrum
for the 6-pixel area discussed in Figs. 2
and 3.
The bright [O III] nebular lines have been removed.
The dashed line and associated hexagonal region
show the power law fit and  -uncertainties
of the UV spectrum obtained by Hill et al. (1997).
Filled triangles show the HST photometry with a 10-pixel circular
aperture to compare with the above spectra.
Filled ellipses show our HST photometry results presented in
Table 3.
Open rectangles are the photometric UBVRI data by Middleditch et al. (1987).
All data are dereddened using
E(B-V)=0.20.
Solid lines show power law fits to the photometric data sets.
Parameters of the fits are presented in Table 5.
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in each filter. For a point-like source,
and S/N
are defined in the standard way as
is the flux in counts for a given aperture,
is the standard deviation in counts per pixel,
A is the number of pixels in the aperture,
G is the gain, and
is the number of pixels
in the annulus used for background measurements.
The optimal aperture radii were found to be
2.5, 3.0, 4.0, 2.5, and 3.5 pixels, providing S/N of 8, 10, 25,
7.5, and 8 in the F336W, F547M, F555W, F658N,
and F791W bands, respectively.
Aperture corrections for the magnitudes
were derived with the mkapfile package
using several relatively bright nearby
field stars in the PC images.
Pipeline-provided zeropoints
PHOTFLAM (flux densities in wavelength units) and
pivot wavelengths PHOTPLAM (in Å) taken from
the fits header of each image were used for the flux calibration
(see handbook for WFPC2).
Fluxes in units of 
Jy
at the pivot frequencies
c/PHOTPLAM (in Hz)
were derived from the aperture corrected source counts using the expression
is the exposure time in seconds.
We also calculated dereddened fluxes by multiplying
with
the extinction correction factors
,
where ki is the interstellar extinction
magnitude for the "ith'' passband
determined using the extinction color excess
toward SNR 0540-69.3. In order to compare with Middleditch et al. (1987)
we have used the same values for E(B-V) and R, i.e., 0.20 and 3.1,
respectively, for both data sets, but
a more recent extinction curve (Cardelli et al. 1989).
We will discuss the extinction in greater detail in Sect. 2.8.
The results of the pulsar photometry are presented in Table 3 and shown in Fig. 4. The measured fluxes are about a factor of 2-4 lower than the spectroscopic results in Sect. 2.2, except for the F555W filter which includes contamination from [O III]. The fluxes in this filter are presented as upper limits (see above). On the other hand, the HST photometry is compatible with the results obtained by Middleditch et al. (1987), but the uncertainties are several times smaller.
Table 3: Broad-band fluxesa from PSR B0540-69.3.
Table 4: Broad-band fluxes from a 10 pixel aperture around PSR B0540-69.3.
Table 5:
Parameters of the power law spectral fits (
)
of the pulsar data shown in Fig. 4.
92) centered on the pulsar, without subtraction of the background.
These conditions should approximately reproduce the parameters of the spectral
measurements within a circular aperture of almost the same diameter (0
86)
made with the HST/FOS by Hill et al. (1997). The measured fluxes
are presented in Table 4 and
shown by triangles in Fig. 4. They are much
closer to the HST and VLT spectral fluxes.
The 20-70% discrepancy between these HST/WFPC2
and FOS fluxes must be considered as small compared with the large
uncertainties of the FOS flux.
Using a WFPC2 image Hill et al. (1997) estimated the PWN
contribution to be 30% in their FOS aperture. Note that this has not been
accounted for in the spectrum in Fig. 4. However, their estimate assumed a
uniform nebular background and was performed on an image with a PSF
affected by spherical abberation.
We have redone the exercise with the
F574M image from 1999, and estimate that within a 10 pixel radius, the PWN
contributes at least 50%.
This can also be seen by comparing our accurate pulsar photometry
with our 10 pixel test. The contamination of the HST/FOS spectrum would
be even larger if the centering was not perfect.
Although formal uncertainties of the VLT spectral flux appear to be smaller,
the contamination from the nebula in the optical range
is even stronger than in the UV, exceeding 250% at the redmost wavelengths
of the VLT spectral range. This is natural,
since the brightness of the PWN increases more steeply with the
wavelength than does the pulsar brightness (see below).
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Figure 5:
10
10
region of the field around PSR B0540-69.3 as
observed in the F547M band with the HST/WFPC2 (Morse 2003).
Background stars and the pulsar projected on the PWN have been subtracted
off (cf. Fig. 1).
We have marked six selected areas in the plane of the assumed torus as well
as two areas in the jets. The ellipse shows the aperture used to measure the
flux from the whole PWN. The pulsar position is marked by a white cross.
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,
then our power-law index
is
while that of Middleditch et al.
is
(see Table 5) using updated
dereddening corrections. (The method how to calculate these power-law
indices is described in Sect. 2.5.)
The flatter spectrum of Middleditch et al. is partially due to a spectral
jump upwards for the U band, whereas our flux toward the overlapping F336W
band goes down smoothly, as would be expected
from the extrapolation of the longer wavelength data. This upturn in
Middleditch et al. (1987) could be due to a systematic error in their U band
flux. We note that also the Crab-pulsar broadband spectrum by Middleditch et
al. (1987) has a significant excess in the U band, which has not been
confirmed by more recent spectral observations extending even further into
the UV (Sollerman et al. 2000).
However, possible variability of the pulsar
emission in the UV range cannot be excluded as another cause of the
difference between our results for PSR B0540-69.3 and the result by Middleditch
et al. (1987). We also note that while we are studying the time-integrated
flux, Middleditch et al. studied the time-resolved flux,
albeit with a poor signal-to-noise and spatial resolution.
emission
from the SNR. To make an accurate analysis we first subtracted off
all stars in the
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Figure 6:
Broad-band fluxes from the full PWN obtained with the HST
(thick errorbars) using the elliptical aperture shown in Fig. 5.
The thick line and filled area provide the best power-law fit to the
data and its 1
uncertainties, respectively (see Table 6).
Previous data by Chanan et al. (1984) in the I and B bands
(thin errorbars and dashed line), as well as the slope of the pulsar spectrum
(cf. Fig. 4), normalized arbitrary (dot-dashed line),
are shown for comparison. Numbers near the lines denote spectral indices.
Note that Chanan et al. (1984) did not correct for contaminating flux from
background stars and nebular line emission.
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The PWN of PSR B0540-69.3 has a remarkable structure that can be seen clearly in
Figs. 1 and 5. To sample different regions,
we have put circle apertures at eight
different positions, one in each jet (with an aperture radius of 12 pixels,
i.e. 0
55), and three (with an aperture radius of 7 pixels, i.e. 0
32) on each
side of the pulsar in the plane of the presumed torus. We also constructed
an elliptical aperture with
a 74 pixel (i.e. 3
4) semi-major axis, ellipticity 0.3, and positional
angle 45 degrees,
that encapsulates the entire PWN (cf. Fig. 5), except for the weak northern jet.
The apertures are marked and identified in Fig. 5.
All regions show emission
in all filters, except for the northern jet ("North Jet'') and "Area 6''
which are not detected in the F336W band. For these two regions we
provide 3
upper limits, based on the standard
sky deviations per pixel within the respective areas.
The results are presented in Table 6.
Table 6:
Broad-band fluxes
and power-law fit (
)
parameters of the emission from different regions of the PWN marked in Fig. 5.
Their offsets from the pulsar and areas are given in the 2nd and 3rd columns.
Upper and lower
values for each entry of the fluxes are the measured and dereddened fluxes
with
E(B-V)=0.20 (AV=0.62), respectively.
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Figure 7:
Broad-band optical spectra for all the selected areas of the PWN
shown in Fig. 5. The filled hexagons show 1
uncertainty
regions around the best-fit power laws indicated by thick lines.
The fluxes of the "jets'' are normalized to a 7-pixel aperture
area for convenience in order to compare their brightnesses
with the brightness of other parts of the PWN.
The spectral slopes of the whole PWN (thin lines) and the pulsar
(dot-dashed lines) are shown for comparison. The dot-dashed and thin lines
have been shifted arbitrarily in the vertical direction.
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As expected, the measured broadband spectra from the whole PWN and its
different parts are well described by power-laws with negative spectral index,
which confirm the nonthermal origin of the continuum nebular emission.
To derive the spectral indices we used the following method.
For each data point we made Gaussian fits in log space to the flux and
the filter function. We then simulated 10 000 sets of data using a
Monte Carlo code which uses a fast portable random
generator,
and for each data set we made a linear fit to obtain a power-law.
The power laws were then ordered in increasing value of the power law index,
and the median value was chosen to represent the best fit power law. In
order not to be dependent on the seed value for the random number series,
we ran the code 500 times with different seed values, and then took the
average value for the power-law index to be the final estimate of the
index. The filled hexagons in Figs. 6 and 7
show 1
errors estimated from the constraint that 68% of the
constructed power laws must lie within a 1
area.
The advantage of using a Monte Carlo code rather than simple weighted means to
estimate power law indices is that we can allow and test for non-Gaussian
distributions in log space. This is obviously not the case with a steep
spectrum, non-Gaussian filter functions, as well as upper limits.
Our tests, however, show that
the filters are narrow enough to get good fits from Gaussian fits to
the points with estimated fluxes. From our Monte Carlo code approach it is also
easy to estimate the error of the derived power-law index. The same approach
was also used to fit the pulsar spectrum in Sect. 2.4.
The results are presented in
Tables 5, 6 and shown
for the emission from the whole PWN in Fig. 6
and from its different regions in Fig. 7.
According to Chanan et al. (1984) the fluxes (in Jy)
from the whole PWN are
and
.
Our values are
much lower (60% and 40%, respectively, see Fig. 6).
The main reason is that we have subtracted off the pulsar
and stars overlapping with the PWN, whereas these objects are not resolved
from the PWN in the B and I images of Chanan et al. (1984) which were obtained
at 1
2-1
4 seeing. Hence, their B and I fluxes are contaminated
by non-PWN emission and this changes significantly the derived spectral slope
of the PWN: Chanan et al. (1984) obtain
(after dereddening
with
E(B-V)=0.20) whereas we get
from
the HST data.
Compared with the pulsar the whole PWN is more than an order of magnitude brighter, and its spectrum is significantly softer (cf. Tables 3 and 6 and thick solid and thin dot-dashed lines in Fig. 6). This shows that the NS spindown power is transformed to optical emission more efficiently in the PWN than in the pulsar magnetosphere (see below).
A more detailed study shows that the spectrum may vary
over the PWN. This is seen from
Fig. 7 where we have plotted the results of the HST photometry
of different parts of the PWN and the respective power-law spectral fits
(thick lines) with their
uncertainties (uniformly filled regions).
Stripe-filled regions show extensions of the fits in cases when
only upper limits in one of the three bands were obtained.
The spectral hardness of some parts of the nebula is comparable or even higher
to that of the pulsar, as it is for "Areas 1, 5, 6'', and both "jets''.
The spectra of the N-E part of the torus-like structure appear to become
harder toward the outer boundary of the nebula.
On the other hand, "Area 2'', which is the brightest
among the three selected areas S-W of the pulsar, has a steeper spectrum
than its closest neighbors.
Another feature of the spatial flux and spectral variations
of the PWN is demonstrated by Figs. 8 and 9 where we have
plotted the distributions of the frequency-integrated optical fluxes F,
derived from the above spectral fits, and the spectral
indices
versus the angular distance from the pulsar
along the major axis of the torus-like structure of the PWN.
There is a significant decrease of the surface brightness going from
the brightest area, area 2, toward the N-E edge of the torus (Fig. 8).
The brightness difference exceeds the 6-sigma level of the uncertainty level
of the dimmest area, area 6, and shows an asymmetry of the flux distribution
with respect to the pulsar position which is similar to what is also seen in
X-rays with Chandra/HRC.
In the Crab PWN, the brightness difference between the near and far sides of
the torus, for a given viewing angle, is usually explained by Doppler
boosting and relativistic aberration of the synchrotron radiation from
relativistic particles flowing at subrelativistic velocities from the pulsar
in the torus plane, assuming an axisymmetric distribution of the pulsar wind
around the pulsar rotation axis (e.g., Komissarov & Lubarsky 2004).
However, the considerable asymmetry of the brightness distribution
between the two sides (N-E versus S-W) of the torus of PSR B0540-69.3, as seen in
projection, makes axial symmetry less obvious in a general picture.
This is further strengthened by a similar asymmetry in the torus-plane,
albeit less pronounced, seen in recent X-ray images of the Crab PWN
(e.g., Mori et al 2004). The asymmetry can be produced either
by breakdown of axial symmetry in the pulsar wind (e.g., due to plasma
instabilities) or by inhomogeneity of the PWN environment, i.e.,
an asymmetry of the SN ejecta. The latter is indeed indicated by the
asymmetric distribution of optical filaments projected on the PWN of PSR B0540-69.3
(Morse 2003), as well as the general redshift of the gas emitting optical
lines (Kirshner et al. 1989; Serafimovich et al. 2004).
![\begin{figure}
\par\includegraphics[width=60mm, clip, angle=270]{0499fig8.eps}\par\end{figure}](/articles/aa/full/2004/39/aa0499-04/img95.gif) |
Figure 8:
Optical fluxes F in the
Hz frequency
range from different parts of the PWN marked according to notations in
Fig. 5
versus the distance from the pulsar along the major axis of the
torus-like structure of the PWN.
Negative and positive labels on the horizontal axis correspond to the N-E
and S-W directions from the pulsar, respectively. The bold errorbar at the
center shows the flux from the whole PWN rescaled to the 7 pixel aperture
area used for measurements in "Areas 1-6''.
|
| Open with DEXTER | |
![\begin{figure}
\par\includegraphics[width=60mm, clip, angle=270]{0499fig9.eps}\par\end{figure}](/articles/aa/full/2004/39/aa0499-04/img96.gif) |
Figure 9: Same as in Fig. 8 but for spectral indices. Symbols denote the same area numbers as in Fig. 8. |
| Open with DEXTER | |
The spatial distributions of F and
in Figs. 8 and 9
appear to have similar shapes and may suggest a harder spectrum from
the dimmer outer areas of the PWN. The data are, however, rather uncertain
and a constant spectral index of 1 seems to be compatible with
all errorbars in Fig. 9.
To check that more thoroughly we analyzed the
-F
distribution presented in Fig. 10 which also includes both jet areas.
A linear regression fit to
versus log (F) using
the method described in this Sect. above yields
 |
(4) |
uncertainty of the fit.
The range of the line slopes within this area
is
1.35+1.02-0.98. A zero slope, and thus no correlation, is allowed
only if we increase the uncertainty area to 1.4.
This value
can be considered as an overall significance of a possible
-log (F) correlation.
We also checked the spectral index-flux correlation using the spectral
fit parameter 
as well as the measured flux
value
in the F547M band (see Table 6)
instead of the derived F and got only a slightly tighter correlation.
![\begin{figure}
\par\includegraphics[width=85mm, angle=270, clip]{0499fi10.eps}\par\end{figure}](/articles/aa/full/2004/39/aa0499-04/img98.gif) |
Figure 10:
Spectral index
versus
optical flux, log (F), in the
Hz range
for the different areas of the PWN marked according to
Fig. 5.
The thick solid line shows the best fit linear model given by
Eq. (4). The point marked by bold errorbars shows the parameters for
the full PWN rescaled to a 7-pixel aperture (cf. Fig. 8). The gray area
shows the 1
uncertainty area for possible linear fits to the data
points using the method described in Sect. 2.5. A zero slope correlation
is excluded at the 1.4
level.
|
| Open with DEXTER | |
Therefore, deeper observations of the PWN are needed to probe a
correlation between the brightness and the spectral index
which is indeed only marginally indicated by the current
optical data. A study of the index-flux distribution in X-rays
would also be useful for the PWN of PSR B0540-69.3, as has recently been done for the
Crab PWN (Mori et al. 2004). The study of Mori et al. shows that for brightnesses
above 0.7 counts s-1 arcsec-2
there is a hint that (cf. their Fig. 3) the spectral index of the
torus region increases with the surface brightness, as marginally
indicated also in our case for PSR B0540-69.3. However, including brightnesses down
to 0.4 counts s-1 arcsec-2,
the spectral index - surface brightness distribution appears flat.
The indices of the Crab jet are generally
smaller compared to those of peripheral PWN regions although their
surface brightnesses are comparable (Mori et al. 2004).
In the case of PSR B0540-69.3 the correlation may be enhanced
by a larger brightness asymmetry of the PWN. We note that such
a correlation, as well as a flat index versus flux distribution,
contradicts simple expectations from synchrotron cooling of relativistic
particles which suggest a softening of the underlying electron
spectrum toward the PWN boundary. In this picture, the fainter outer regions
of the nebula would emit softer spectra. However, this simple picture
does not work even for the much better studied Crab,
where the PWN torus does not change its size significantly from
radio to hard X-rays, whereas the respective cooling times
differ by many orders of a magnitude implying much larger extents
in the radio and optical than in X-rays. The same appears to be true
for PSR B0540-69.3 (Caraveo et al. 2000). This is not yet explained, neither by the
classical isotropic pulsar-wind model of a PWN by Kennel & Coroniti (1984),
nor by modern MHD versions of it (Bogovalov & Khangoulyan 2002; Komissarov & Lubarsky 2004;
Del Zanna et al. 2004) despite the fact that these also include anisotropy of
the wind along the pulsar rotation axis, and can qualitatively explain
the observed torus-jet structure invoking a complicated axisymmetric
picture of the wind termination shock in the internal region
of the PWN.
The position of PSR B0540-69.3 is defined on the HST PC chip frames with an accuracy
of better than 0.17 PC pixels which corresponds to 0
0077.
This is only a factor of 1.5 larger than the yearly proper
motion value reported by Manchester et al. (1993b), see Table 1.
This allows a direct estimate of the proper motion of the pulsar using accurate
superposition of the F555W and F547M images taken at
epochs separated by 4 years (see Sect. 2.3).
We used the positions of 9 reference stars to construct
the coordinate transformation between the two images with the IRAF routines
geomap and gregister.
The rms errors of the transformation fit were
0.078 and
of the PC pixel size in RA and Dec,
respectively, with residuals being 
0.156 pixels in RA and
pixels in Dec.
Using imcentroid for measuring the coordinates of the pulsar
we find a shift of
pixels between
its positions for a time difference of 3.995 years, where the error
accounts for the centroid and transformation uncertainties.
This corresponds to a proper motion
mas y-1
in the South-East direction at a position
angle of 108
7
(along the southern jet).
The significance of this result is low and can be considered
only as an attempt to make a first direct measurement of the proper motion.
Based on the displacement between the pulsar optical position and
the center of the PWN, as seen in radio,
Manchester et al. (1993b) argued for a similar value of the proper
motion but in the South-West direction (in the plane of the torus).
We note that the proper motion of the Crab
pulsar is aligned with the symmetry axis of the inner Crab nebula, as
defined by the direction of the X-ray jet discovered by
ROSAT (Caraveo et al. 1999), and that a similar situation applies
to the Vela pulsar (De Luca et al. 2000; Caraveo et al. 2001; Dodson et al. 2003).
If our estimates are close to reality,
we have the intriguing situation that all these three young pulsars
appear to move along the jet axis.
A difference is, however, that while the Crab and
Vela pulsars both have transverse velocities of
,
our
results for PSR B0540-69.3 indicate
a higher transverse velocity
,
assuming a distance
to the LMC of 51 kpc (Panagia 2004).
A third
epoch of HST imaging to confirm the large value and direction for the
transverse velocity is clearly needed to establish this result
at a higher significance level. Based on our proper motion estimates
a level of 3
can be achieved starting from the beginning of 2005.
We also determined the coordinates of the
pulsar in the F547M image using seven GSC-II stars visible within
the PC chip frame and the IRAF routines ccmap, cctran,
and ccsetwcs. The formal rms errors of the astrometric
fit are 0
423 and 0
472 in the RA and Dec, respectively.
Combined with the nominal GSC-II catalog accuracy
of 0
5, this gives an accuracy of
the position of the pulsar of 0
655 and 0
688
in RA and DEC, respectively.
In Table 7 we compare our astrometry
with previous results. We note the good agreement between our measurement
and the latest Chandra result (Kaaret et al. 2001).
Table 7: Coordinates of PSR B0540-69.3.
with
within the photon energy range
E = 0.6-10.0 keV range,
provided that the foreground photoelectric absorption is caused by gas with
Milky Way (MW) abundances and a column density
of
cm-2. A similar number
(
cm-2) was estimated
by Finley et al. (1993) analyzing ROSAT X-ray data.
However, the use of MW abundances is obviously a simplification for PSR B0540-69.3.
As a matter of fact, only a fraction of the photoelectric absorption is
likely to occur in the Milky Way. The recent Parkes 21 cm multibeam survey
of the LMC (2003) shows that the MW contribution to the
column density in the direction to PSR B0540-69.3 is
just
cm-2.
This survey also shows that the maximum value of
in the LMC
is
cm-2, and that this occurs close to the
position of PSR B0540-69.3. This is consistent with the hydrogen column density found
by fitting the wings of the Ly
absorption profile for the neighboring
LMC star Sk -69 265,
cm-2(Gordon et al. 2003). It is quite likely that PSR B0540-69.3 could have a similarly high
column density, especially since its dispersion measure (see Table 1)
is 50% higher than for any other pulsar in the LMC (Crawford et al. 2001).
A rough estimate of the LMC part of
for PSR B0540-69.3 can be obtained
from scaling of the estimated column density for SNR 1987A and its neighboring
star, "Star 2''. Michael et al. (2002) used LMC abundances to derive
cm-2 for
SNR 1987A, and Scuderi et al. (1996)
obtained
cm-2
for Star 2 allowing for a foreground MW contribution
of
cm-2. We
adopt
cm-2 for
SNR 1987A and Star 2. Assuming that SNR 1987A and PSR B0540-69.3 suffer similar
amounts of LMC absorption in proportion to the LMC 21 cm emission
(2003) along their respective lines of sight, we
obtain
cm-2,
where
Jy/beam and
Jy/beam
are the line flux densities toward the pulsar and SNR 1987A, respectively,
according to the Parkes survey data
base.
The assumptions used to obtain this result
for
are of course uncertain, but the result points in
the same direction as the estimates from the 21 cm emission, Sk -69 265
and the pulsar dispersion measure discussed above, i.e., the column
density for PSR B0540-69.3 is high. Assuming that the
21 cm emission at the position of PSR B0540-69.3 marks an upper limit to
its
,
we can limit the range
to
cm-2. This is
similar to what was used by Kaaret et al. (2001), but with the important
difference that the X-ray absorption is not mainly Galactic,
but arises in the LMC.
To illustrate the effect of LMC abundances we show in Fig. 11 the ratio of
photoelectric cross sections (per hydrogen atom) in the LMC and MW for the
energy range 0.1-10 keV. We will refer to this ratio as f(E). The drop
in f(E) at E > 0.28 keV (the K-shell edge of carbon) just reflects the
lower metal content in the LMC compared to the Galaxy. For the MW we have
used the abundances in Morrison & McCammon (1983, henceforth MM83), and for
LMC we have adopted the abundances of He, C, N, O, Mg, Si and Fe from Korn et
al. (2002). We have also included the elements Ne, Na, Al, S, Ar and Ca
for which we have assumed that the LMC abundances are 0.4, 0.4, 0.5, 0.4,
0.5 and 0.5 times the solar values in MM83, respectively. The exact numbers
for these elements are not important for our analysis
since the absorption is dominated by C, N, O and Fe in the
energy range we are most interested in. We assume that the interstellar
gas is neutral, and we disregard dust. Photoionization cross sections were
taken from the code used in Lundqvist & Fransson (1996) with further
updates for Na, Mg, Al, Ar, & Ca using the TOPbase archive (Cunto & Mendoza
1993), as well as for He (Samson et al 1994; Pont & Shakeshaft 1995).
We have tested this code against the results of MM83 for solar abundances,
and the cross sections agree to the same level of accuracy as the
recent cross sections compiled by Wilms et al. (2000). The comparison
against MM83 is relevant as Kaaret et al. (2001) did their analysis using
XSPEC Ver. 10.0 which uses data fully compatible with MM83. Figure 11
shows that LMC abundances strongly suppress the photoelectric absorption,
and that C and O are particularly important constituents at the energies
for which Kaaret et al. (2001) claim photoelectric absorption is most
important for the observed pulsar spectrum, i.e., at 1 keV.
![\begin{figure}
\par\includegraphics[width=60mm,clip,angle=90]{0499fi11.eps}\end{figure}](/articles/aa/full/2004/39/aa0499-04/img128.gif) |
Figure 11: Ratio of photoelectric absorption per hydrogen atom in the LMC and Milky Way for the energy range 0.1-10 keV. Arrows mark at which energy each element starts to contribute to the photoelectric absorption. The absorbing gas is assumed to be neutral. The gradual changes of f(E) across absorption edges are due to moderate zoning of the photon energy in the code used for the cross section calculations. See text for further details. |
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We have used the function f(E) in combination with the results of MM83
to see how LMC abundances may affect conclusions about the derived
spectrum of PSR B0540-69.3. If we assume that the pulsar emits a pulsed power-law
spectrum with slope
in the range 0.6-10.0 keV, as
argued for by Kaaret et al. (2001) and marked in Fig. 12 as a straight
dotted line, the attenuated spectrum should look like the solid line in
Fig. 12 after passage through a column density of neutral hydrogen in the
Milky Way with a value of
cm-2.
If we disregard possible effects of an accurate treatment for the response
matrix of Chandra, we can deabsorb this spectrum with a more
likely composition for the photoelectrically absorbing gas. For this
we have chosen
cm-2and
cm-2. The
deabsorbed spectrum is marked by the upper dashed line in Fig. 12.
At the lower energy limit of the fit by Kaaret et al. (2001), i.e.,
at 0.6 keV, the deabsorbed spectrum undershoots by a factor of 2.9
compared to the power-law, but on the other hand overshoots by orders
of magnitude at energies below the K-shell edge of carbon. The latter can
be fixed by just lowering
to
cm-2, i.e., still consistent with the likely
range argued for earlier in this section. The spectrum would in that case
undershoot by a factor of 3.8 at 0.6 keV compared to the power-law.
The assumption of a power-law spectrum at energies below a few keV, where
the photoelectric absorption sets in, is of course uncertain.
Our results could indicate that the intrinsic spectrum is not a power-law, but
actually falls below the power-law at 0.6 keV. However, before jumping
to such a conclusion we need to check another possible source of X-ray
absorption, namely the supernova ejecta.
![\begin{figure}
\par\includegraphics[width=60mm,clip,angle=90]{0499fi12.eps}\par\end{figure}](/articles/aa/full/2004/39/aa0499-04/img133.gif) |
Figure 12:
Soft X-ray spectrum of the pulsed emission from PSR B0540-69.3. The dotted
line shows the intrinsic power-law spectrum argued for by Kaaret et al. (2001),
and the solid line shows the attenuated spectrum after passing through a
column of gas with MW
abundances,
cm-2. The
lower dashed line shows deabsorption using a more realistic value for the MW
contribution,
cm-2, and the
upper dashed line shows further deabsorption with the
value
cm-2 for LMC,
which is close to the maximum value found for the LMC as a whole
according to Staveley-Smith et al. (2003). The vertical bar at 0.6 keV
marks the energy above which Kaaret et al. (2001) fitted their power-law
to the deabsorbed spectrum.
|
| Open with DEXTER | |
![\begin{figure}
\par\includegraphics[width=60mm,clip,angle=90]{0499fi13.eps}\par\end{figure}](/articles/aa/full/2004/39/aa0499-04/img134.gif) |
Figure 13:
Same as Fig. 12, but with a lower value for the LMC
deabsorption,
cm-2.
Deabsorption due to supernova ejecta has also been included,
assuming the same structure as in SN 1987A.
The structure of SN 1987A on day 118 (Blinnikov et al. 2000) was
expanded homologously until 500 years (model "A'', long-dashed) or 750 years
(model "B'', short-dashed) after the explosion. Note that the age-parameter
in these models do not necessarily relate to the same age for
SNR 0540-69.3 as it depends on the explosion energy, the envelope mass
and the density structure. See text for further details.
|
| Open with DEXTER | |
,
and the results of Serafimovich et al.
(2004) show that a likely range is 15-22 .
To check the
importance of supernova ejecta for possible X-ray absorption,
the well-studied SN 1987A therefore serves as a good template.
We have used the mixed model 14E1 displayed in Figs. 2 and 6 in Blinnikov et
al. (2000), which has 
2 of pure oxygen spread out over
the innermost 5 of supernova ejecta. We assume that the
post-explosion structure expands homologously. At an age
of 1000 years after explosion, the hydrogen column density through the
ejecta, from the center, is
only
cm-2, i.e., far
less than even the MW contribution in the direction toward LMC. However,
the very high metal content in the supernova ejecta, and its concentration
toward the center of the ejecta,
boosts the X-ray absorption at energies above 300 eV. Above
the K-shell ionization edge of oxygen, i.e. at 600 eV, the cross section per
hydrogen atom is 40 times higher than for the MW absorption in
MM83. Because
scales with the time since explosion
as 
t-2, a less evolved supernova remnant can make a significant
contribution to the X-ray absorption of emission from the pulsar and
its PWN.
The importance of the supernova ejecta is illustrated in Fig. 13. Here we have
used the same value for
as in Fig. 12, but
lowered the LMC contribution
to
cm-2.
We have also included deabsorption due to supernova ejecta, assuming
a homologously expanding SN 1987A at an age of 500 years (model "A'',
long-dashed) and 750 years (model "B'', short-dashed).
The increased oxygen column density compared to that in Fig. 12 makes it
possible to retrieve the initial power-law spectrum above 0.6 keV
for a supernova similar to SN 1987A at an age of 500 years, but it is
also clear that a remnant with an age closer to the spin-down age of PSR B0540-69.3
will not contribute significantly to the X-ray absorption. Although the
ejecta of SNR 0540-69.3 could expand more slowly than those of SN 1987A,
could contain more oxygen (and/or having it more concentrated to the center),
could have a clumpy and asymmetric structure (as is indicated for SN 1987A,
Wang et al. 2002), or could have a lower age than the pulsar spin-down age,
it seems that we have to stretch the parameters to claim that the X-ray
absorption along the line of sight to the pulsar is largely affected by
the supernova ejecta. A possible way to test this is to check the spatial
variations of the X-ray absorption over the larger PWN. The low metal
content of LMC, and the low MW foreground absorption, make such tests
sensitive to any supernova ejecta contribution. X-ray spectral fits to data
obtained with Chandra of the Crab pulsar have recently highlighted the
importance of the abundance factor (Willingale et al. 2001; Weisskopf et al. 2004).
Using various abundances
it was found that the line of sight to the Crab is significantly
underabundant in oxygen.
To summarize this section, it is evident that the X-ray spectral analysis
of PSR B0540-69.3 needs a revision. Contrary to previous assumptions,
the metal abundance of
the X-ray absorbing gas must clearly be sub-solar, unless the supernova ejecta
contribute significantly. The latter, however, appears to be less likely.
While a full analysis of the X-ray spectrum, i.e., a detailed reduction
of the Chandra data including various abundance combinations in XSPEC,
is beyond the scope of this paper, we have argued that
the power-law spectrum, which seems to be appropriate to use at energies
above 1 keV, may experience a depression below 1 keV (cf.
Sect. 3). This can be tested by how the X-ray spectrum connects to that in
the optical. We will discuss that in Sect. 3.
,
and this agrees with the value
found for SN 1987A (Scuderi et al. 1996) and that used by Gordon et al. (2003).
The value used for the parameter R in these works is the standard
value 3.1.
The extinction parameters E(B-V) and R(V) for LMC along the line of
sight to SNR 0540-69.3 and the pulsar have not yet been investigated in
detail in the same way as for SN 1987A (Scuderi et al. 1996).
However, in Serafimovich et al. (2004) we studied SNR 0540-69.3 and H II
regions close to it. The reduced spectra were analyzed using the total
value
and
R(V) = 3.1, i.e., the same numbers
we used in Sect. 2, and we found that the
H
/H
/H
line ratios are in good agreement with
Case B recombination theory (Baker & Menzel
1938; Hummer & Storey 1987). Allowing for higher extinction would
boost H
and H
relative to H
causing a disagreement
with the Case B theory, which for these lines normally explains
the observations of supernova remnants well (e.g., Fesen & Hurford 1996).
Looking at the projected pulsar neighborhood, Gordon et al. (2003) obtain
the average value
for the LMC2 supershell,
and it seems reasonable that this could be used also for PSR B0540-69.3.
Out of the eight stars forming this average, six of them can accommodate
the standard value of 3.1 within .
The spread in
ranges between 0.12-0.24 (including
errors), so the values we
have used for PSR B0540-69.3 and its PWN in Sects. 2.4 and 2.5 seem reasonable also
from this comparison. However, to check the effect of a different extinction
curve on E(B-V), and still being compatible with Case B line ratios for
SNR 0540-69.3, we have compared
(cf. Sect. 2.4) for the extinction
used in Sect. 2.4 (we call that case "C1'') to a case (called "C2'')
with
(
R(V) = 2.76, Gordon et al. 2003)
and
(
R(V) = 3.1, Cardelli et al. 1989). We
formed the ratio
for
both cases, and found
that
does not exceed 2% within the interval 2620-8480 Å. Only at the very
blue end of the FOS spectrum of Hill et al. (1997), i.e.,
at 2500 Å, does the ratio approach 5%. This justifies
the use of
(assuming
)
regardless of whether we choose to use extinction combinations like C1 or
C2. The absolute flux level of the dereddened spectrum of course depends
on the exact value of R(V) being used. Further direct extinction studies
of the pulsar and its neighborhood in the UV and optical bands are
needed to pin down the detailed extinction corrections.
It seems, however, that the steep spectral
slopes we obtain for the pulsar and its PWN in the optical in Sects. 2.4 and
2.5 cannot be corrected by some extreme reddening corrections as this is
neither justified by our observations of the supernova remnant nor by the
study by Gordon et al. for supposedly neighboring objects.
![\begin{figure}
\par\includegraphics[height=180mm, clip, angle=270]{0499fi14.eps}\par\end{figure}](/articles/aa/full/2004/39/aa0499-04/img151.gif) |
Figure 14:
Multiwavelength unabsorbed spectrum of PSR B0540-69.3. The data
were obtained with the different telescopes and instruments marked in the plot.
The optical data are from this paper. Phase-averaged (upper polygon) and pulsed
(lower polygon) X-ray emission spectra with their uncertainties
are shown for the 0.6-10 keV range (Kaaret et al. 2001).
The pulsed emission spectra obtained with ROSAT and RXTE
are from de Plaa et al. (2003), and the radio and -ray data are
from Manchester et al. (1993a) and Thomson et al. (1994), respectively.
All upper limits are defined at 
level.
The unabsorbed spectrum of the total pulsed emission of the Crab pulsar
is shown for comparison, where the high energy and optical data are from
Kuiper et al. (2001) and Sollerman (2003), respectively.
The dotted line for the Crab pulsar indicates a possible connection
between the optical/X-ray regions through the EUV. The same
line (shifted to overlap with the soft X-ray spectrum) is overlaid on the optical/X-ray
region of PSR B0540-69.3. Note how the blue band fluxes of
PSR B0540-69.3 undershoot by a factor of 3 compared to this
overlay while it fits well in the X-ray band. |
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To connect the optical pulsar emission to the emission at other
wavelengths, we have compiled results for the radio (Manchester et al. 1993a),
X-ray (Kaaret et al. 2001; de Plaa et al. 2003) and -ray (Thomson et al. 1994)
spectral regions. The unabsorbed spectrum is displayed in
Fig. 14. In comparison with previous
compilations (e.g., Hirayama et al. 2002; de Plaa et al. 2003) the accuracy is
significantly improved due to the new high spatial resolution data
obtained in the optical with HST and in X-rays with Chandra.
This reveals new features in the spectrum of the pulsar.
Table 8:
Comparison of the optical and X-ray spectral indices
(
,
),
luminosities (
,
), efficiencies (
,
),
and a weighted ratio (
)
of the two young pulsars, Crab and PSR B0540-69.3,
and the older Vela pulsar. Here
and
are
the energy intervals in the opticala and X-raysb, respectively, used for
the frequency integration to obtain
and .
Information on the period P, dynamical age
,
spindown
luminosity 
,
and distance d for each pulsar is included.
The optical and X-ray parts of the spectrum can be fitted with power-laws
(for specific assumptions about the intervening extinction and photoelectric
absorption discussed in Sects. 2.7 and 2.8), which would suggest a non-thermal
nature of the emission in both domains, likely to be formed in the
magnetosphere of the rotating neutron star. However, the connection between
the emission in X-rays and in the optical seems far from trivial, especially
if the slope for the optical spectrum derived from the archival
HST/WFPC2/F336W data is correct (spectral indices and other emission
parameters for PSR B0540-69.3, as well as for the Crab and Vela pulsars,
in the optical and X-rays are presented in Table 8).
The data for PSR B0540-69.3 suggest at least two spectral breaks
between the optical and X-ray spectral bands. For a comparison,
Fig. 14 also shows the multiwavelength spectrum of the total
pulsed emission from the Crab pulsar (Kuiper et al. 2001; Sollerman 2003).
For the Crab, it seems that a smooth turn-over can be possible (dotted line)
between the X-ray band and the optical. This is in contrast to spectra
of the middle-aged pulsars Vela and PSR B0656+14, whose optical fluxes are
generally compatible with the low-frequency extrapolation of a power-law
spectral tail for 
keV (Koptsevich et al. 2001;
Shibanov et al. 2003).
In Sect. 2.7 we noted that PSR B0540-69.3 could have a non-powerlaw spectrum
below 1-2 keV, and inspired by this we tried to use the
shape of the Crab optical/X-ray turn-over to fit the spectrum of PSR B0540-69.3. This,
however, fails for the WFPC2/F336W band where the flux falls below such
a fit. As we pointed out in Sect. 2.8, the depression in U is unlikely to be
caused by insufficient dereddening; to reach the Crab pulsar spectral
slope (
,
cf. Table 8) one has to
apply
,
which is at least twice as high as the most likely value (cf. Sect. 2.8).
Does this mean that PSR B0540-69.3 experiences
a spectral dip in the F336W band? While future deep and well-calibrated data
in U and UV should reveal this, we note that such an
explanation is not farfetched. As a matter of fact, the broad-band
optical spectra of middle-aged pulsars (Vela, PSR B0656+14, and Geminga,
cf. Shibanov et al. 2003) do show a dip in the U and B bands, which could
indicate a multicomponent continuum spectrum, or the presence of unresolved
emission/absorption features, possibly related to electron/ion cyclotron
lines originating in the magnetospheres of the neutron stars
(Mignani et al. 1998; Jacchia et al. 1999).
If the depression in U is of more general character, the multiwavelength
spectrum of PSR B0540-69.3 suggests a double break "knee'' in the spectral region
between the optical and soft X-ray bands. Observations in the UV and
reanalysis of the Chandra X-ray data with accurate corrections for
extinction and photoelectric absorption, as discussed in Sect. 2.7,
will help us constrain the position of the breaks and to understand whether
they are located just blueward of the U band and below 0.6 keV, or occur
in the EUV range.
Taking into account the difference in distance to the Crab pulsar (2 kpc)
and PSR B0540-69.3 (51 kpc), as well as the spectral energy distributions for
both pulsars (see Fig. 14), we note that the overall intrinsic flux
from PSR B0540-69.3 is almost as high as that from the Crab pulsar in the radio
(while its slope is possibly steeper in this range), but that it is 1.4
and 3 times higher in the optical and X-ray ranges, respectively. This
is also shown in Table 8. At the same time, the spindown luminosity, ,
of PSR B0540-69.3 is 3 times lower than for the Crab. Therefore, the
efficiency of producing nonthermal optical and X-ray photons in the
magnetosphere of the rotating neutron star from its spindown
power,
,
is a factor 4 and 10 higher
for PSR B0540-69.3 in the optical and X-rays, respectively (Table 8). For a
comparison we show also in Table 8 the parameters for the 10 times
older Vela pulsar, which is much less luminous and a less efficient optical
and X-ray emitter, but still capable of powering a weak and less extended
PWN around it. The Vela pulsar
has also a peculiar optical spectrum in comparison with the Crab pulsar
with a possible excess in the near-IR and a dip in the U band
(Shibanov et al. 2003). Based on the available data it is not yet clear
whether these spectral peculiarities in the pulsar optical emission do
indicate a spectral evolution with pulsar age (PSR B0540-69.3 has a spin-down age
which is 400 years higher than the Crab pulsar) or whether they
are connected to the pulsar optical efficiency, or just reflects specific
parameters (e.g., viewing angle and magnetic field geometry) of each pulsar.
Detecting PSR B0540-69.3 in the near-IR would allow us to understand to which
extent its spectrum is similar to that of the Vela pulsar and other
middle-aged pulsars detected in the optical range. We also note that the
ratio of optical to X-ray luminosity, weighted by the observed spectral
ranges (cf. the last column in Table 8), is for PSR B0540-69.3 about half the value
for the Crab pulsar, but comparable with that of the Vela pulsar.
![\begin{figure}
\par\includegraphics[width=100mm, clip, angle=270]{0499fi15.eps}\par\end{figure}](/articles/aa/full/2004/39/aa0499-04/img170.gif) |
Figure 15:
Spatially averaged multiwavelength spectrum of the PSR B0540-69.3 PWN obtained
with the different telescopes indicated in the plot. The optical data are
from the present work, whereas the radio and X-ray data are from Manchester
et al. (1993b) and Kaaret et al. (2001), respectively. The filled regions
(for the HST and Chandra data) show 1
uncertainty regions around
the best-fit power laws indicated by thick lines. We have also included
similar data for the Crab PWN, where the data are from Velusamy et al.
(1992), Veron-Cetty & Woltjer (1993) and Kaaret et al. (2001) for
the radio, optical and X-ray bands, respectively. The dotted curved line is
a cubic spline fit for the multiwavelength spectrum of the Crab PWN, and
the dashed-dotted line is a linear fit for the optical/X-ray region of the
Crab PWN. These fits have been shifted to the level of the X-ray emission of
the PSR B0540-69.3 PWN for a comparison. Note how the fits overshoot for PSR B0540-69.3 in both
the optical and the radio.
|
| Open with DEXTER | |
Unfortunately, there is no data of similar quality on the spatially
averaged optical spectrum of the Crab PWN, but spectra of specific
signatures of the Crab PWN (knots, wisps etc.) are significantly steeper
than the pulsar spectrum (Sollerman 2003).
On a larger scale, the continuum optical emission of the whole Crab Nebula,
at 10
spatial resolution (Veron-Cetty & Woltjer 1993), shows a
similar spectral behavior. In particular, a bright area roughly
overlapping in position and morphology with the Crab X-ray PWN was resolved.
Its spatially averaged spectrum is steeper than the spectrum of the
pulsar.
We see the same behavior for the whole
PWN of PSR B0540-69.3 and for some parts of it (cf. Figs. 6 and 7), whereas the
much fainter Vela PWN has not yet been detected in the optical
(Mignani et al. 2003). However, some hints of specific structures in the Vela
case, clearly detected in X-rays (Helfand et al. 2001; Pavlov et al. 2001),
may have been detected also in the near-IR JH bands (Shibanov et al. 2003).
There is no reliable spectral information on them and their identification
still have to be confirmed by deeper observations both in the optical and IR.
The optical efficiency of the PWN of PSR B0540-69.3 is a factor of 30 higher
than for the pulsar. This is markedly different from the situation
in X-rays where the efficiency of the PWN is only 4 times higher
than for the pulsar (Kaaret et al. 2001).
If we assume that the bright optical areas of Veron-Cetty & Woltjer (1993)
are associated with the the optical emission of the whole Crab PWN,
we obtain a similar situation also for this pulsar with its 50
higher optical efficiency of the PWN compared to that of the pulsar, while
the efficiency ratio is only a factor of 2-3 in X-rays.
This may give a hint on the particle
energy distribution responsible for the synchrotron emission of the PWN.
To estimate the ratio of the efficiencies in the optical and X-rays
we normalized the luminosity in each domain to the respective energy range
for which the luminosity was calculated. The ranges are
3370-7870 Å (i.e., 1.58-3.68 eV) and 0.6-10 keV. As seen in
Tables 8 and 9, the normalized optical luminosity
(
,
where the
parameters are defined in Table 8) is 16 and 140 times higher than that in X-rays for the pulsar and its PWN, respectively.
The inferred values for the Crab are even higher
(35 and 870, respectively). This is natural since
the rotational loss of the Crab pulsar is 3 times higher and its
multiwavelength spectrum does not show a depression in the optical,
as PSR B0540-69.3 appears to have.
Table 9: Same as in Table 8 but for the PWNs of the same pulsars. Information on the PWN size and the ratios of the pulsar to PWN luminosities in the optical and X-rays for each pulsar is included.
The PWN of PSR B0540-69.3 has similar sizes in the optical (this paper) and in X-rays
(Gotthelf & Wang 2000; Kaaret et al. 2001) and extends up to 4
away from the
pulsar, which corresponds to 1 pc at 51 kpc. However, the brighter
emission is confined to
pc (cf. Fig. 5). This is a factor
of 2 smaller than the size of the Crab PWN which has also similar
sizes in the optical and in X-rays (Hester et al. 2002).
The smaller size of the PSR B0540-69.3 PWN is in rough agreement with the expected
(e.g., Kennel & Coroniti 1984)
PWN size scaling with pulsar spindown
luminosity,
.
A similar proportionality has been
found from the comparison of the Crab and Vela PWNs (Helfand et al. 2001;
Pavlov et al. 2001b).
The higher optical and X-ray efficiencies of PSR B0540-69.3, as compared with the Crab
pulsar, are not reflected in a simple way in its PWN efficiencies.
For instance, the X-ray efficiency of the PSR B0540-69.3 PWN is almost twice as high
as that of the Crab PWN, while its optical efficiency is 4 times lower
than in the Crab case. The reason for this is unclear and may be explained
either by the propagation effects discussed above, or by different pulsar
environments, or a combination of these effects. The pulsar contribution to
the total pulsar+nebula X-ray luminosity is 4.5%, 21%, and 25% for
the PSR B0540-69.3, Crab, and Vela pulsars, respectively. The contribution is smaller
in the optical and ranges from 0.17% for the Crab to 3% for PSR B0540-69.3.
The Vela PWN has not been detected in the optical range, but we note
that even for this much older and fainter pulsar, the PWN dominates
the total X-ray luminosity, and that its contribution is comparable
to that of PSR B0540-69.3, although
is an order of the magnitude smaller.
This cannot be explained by a simple scaling with the spindown luminosity,
as in case of the PWN sizes, and requires additional studies.
Our results do not reveal any significant variation
of the spectral index over the torus and jet like structures
of the PWN of PSR B0540-69.3, although a marginal inverse correlation between
the spectral hardness and brightness cannot be excluded
at 
level (cf. Fig. 10 and Sect. 2.5 for more details).
No significant variation of the spectral index was also found in
recent X-ray studies of the Crab PWN along its torus and the cores of the
PWN jets (Mori et al. 2004). This suggests that for both these PWNs
the energy spectra of the emitting electrons and positrons injected
in these two different directions by the shocked pulsar wind
are similar. This fact, as well as the similar sizes
of the these parts of PWNs in the optical and X-rays suggest
that the particle spectra in the bright, central parts of PWNs
are not affected by synchrotron cooling. In the Crab case
the spectral softening and hence the synchrotron losses
become significant only in the faint outermost regions
of the PWN detected in X-rays (Mori et al. 2004; Weisskopf et al. 2000)
and in the UV/optical ranges (Scargle 1969; Veron-Cetty & Woltjer 1993;
Hennessy et al. 1992). A similar dependence may be seen
in the Vela PWN (Pavlov et al. 2001b). This imposes important
constraints on the pulsar wind models.
Deeper observations in the optical and X-rays are needed
to study the faint outer regions of the PWN of PSR B0540-69.3, and
to test the reality and magnitude of the inverse hardness/brightness
correlation. We note a significant surface brightness
asymmetry with the respect to the pulsar position along the major
axis of the torus structure of the PWN of PSR B0540-69.3 seen in both the
optical and in X-rays. This asymmetry can hardly be explained within
the framework of axisymmetrical pulsar wind models by simply
invoking Doppler boosting and relativistic aberration effects, as has been
done for the near and far sides of the Crab PWN torus.
The asymmetry is more likely to be caused by plasma instabilities
in the internal parts of the pulsar wind flow, or by asymmetry of
the SN ejecta. The latter is also discussed from another point of
view in Sect. 3.3.
,
and that the direction is consistent with the pulsar
moving along the southern jet axis. A pulsar velocity of 1000
is
high, but not exceptional. In a recent VLA study of pulsar proper motions,
Brisken et al. (2003) show that there is a relatively large fraction of
pulsars which have velocities in excess of
.
Peng et al. (2003)
quantify this number to be 16%.
Even if our results for the proper motion
of PSR B0540-69.3 have only a 
significance,
and a third epoch
of HST imaging is needed to test whether or not
PSR B0540-69.3 belongs to this
high-velocity class of objects, we cannot avoid connecting the origin
of the possibly large velocity of PSR B0540-69.3 to the origin of
the significant redshift of the inner part of SNR 0540-69.3 which has been
estimated to be several hundred
(Kirshner et al. 1989; Serafimovich
et al. 2004). The most straightforward interpretation of this is that the
0540-69.3 system could be the result of a very asymmetric explosion.
Evidence of asymmetric supernova ejecta in core-collapse supernovae is
abundant, and perhaps of specific interest for the 0540-69.3 system with
its asymmetric inner ejecta structure (e.g., Kirshner et al. 1989), is that
in general the asymmetry appears to increase with depth into the ejecta
(see Akiyama et al. 2003, and references therein). The prime example is
SN 1987A where the powering by radioactive nucleids in the center occurs along
bipolar jets that are likely to be aligned with the rotational axis of the
presupernova (Wang et al. 2002). Assuming that also the explosion in
core-collapse supernovae itself could be jet-induced,
Khoklov et al. (1999) find from 2D-modeling that pulsar kick
velocities of 1000
can be achieved. The pulsar would move along
the jet axis, consistent with our tentative finding for PSR B0540-69.3, but to
reach a velocity as high as
a large difference in momentum
between the two jets is required. As pointed out by Lai (2000), it is not
clear what could give rise to such a difference.
Lai et al. (2001) discuss various models how to produce large pulsar kick
velocities in the context of the aligned spin axis and pulsar proper motion
in Crab and Vela (cf. Sect. 2.6), and their discussion may now also apply
to PSR B0540-69.3. The conclusion is that spin-kick alignment requires fast, perhaps
close to break-up rotation, at the pulsar birth. There is
observational evidence pointing in the same direction at least for the Crab
pulsar (Atoyan 1999; Sollerman et al. 2001).
We note that among the various models reviewed by Lai et al. (2001), the
hydrodynamically driven kicks may face a problem in reproducing kick
velocities of the order we infer for PSR B0540-69.3, and Fryer (2004)
finds that even in his most asymmetric 3D-models of an exploding 15 star, the neutrino emission becomes asymmetrically emitted, thereby damping
out the hydrodynamical pulsar kick. Fryer suggests that one way to obtain fast
pulsars is to rely on them being produced by low-mass progenitors
(8-12 ). This is, however, not a likely explanation for the
0540-69.3 system, which most probably originates from a 20
progenitor. The recent models of Scheck et al. (2004) appear to be more
successful in producing pulsars with high kick velocities.
It could also be that models including rotation
will alter the results of the hydrodynamically driven kick models (cf.
Lai et al. 2001), perhaps providing a link to the results of
Khoklov et al. (1999). Further observations of the 0540-69.3 system will
show if it can add to Crab and Vela as a testbed for different kick scenarios.
Acknowledgements
We are grateful to Jelle de Plaa for sharing with us his reduced ROSAT and RXTE data of PSR B0540-69.3, to Lucien Kuiper for high energy data of the Crab pulsar, and to the referee, Patricia Caraveo, for useful comments allowing us to improve several important points in the text. Partial support for this work was provided by RFBR (grants 02-02-17668, 03-02-17423 and 03-07-90200), and support was also given by The Royal Swedish Academy of Sciences. The research of PL is further sponsored by the Swedish Research Council. PL is a Research Fellow at the Royal Swedish Academy supported by a grant from the Wallenberg Foundation. The work was initialized while NIS was supported by a stipend from The Swedish Institute.
![\begin{displaymath}\frac{S}{N}=\left[\frac{N_{\rm c}}{G} +
A\sigma_N^2(1+\frac{A}{A_{\rm sky}})\right]^{-1/2}N_{\rm c},
\end{displaymath}](/articles/aa/full/2004/39/aa0499-04/img55.gif)
