A&A 423, 33-47 (2004)
DOI: 10.1051/0004-6361:20035856
E. Pointecouteau 1 - M. Arnaud 1 - J. Kaastra 2 - J. de Plaa 2
1 - Service d'Astrophysique du CEA, L'Orme des Merisiers,
Bât. 709, 91191 Gif-sur-Yvette, France
2 - SRON, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
Received 12 December 2003 / Accepted 5 March 2004
Abstract
We present an XMM-Newton
mosaic observation of the hot ( keV) and nearby (z=0.0881)
relaxed cluster of galaxies A478. We derive precise gas density, gas
temperature, gas mass
and total mass profiles up to
(about half of the virial
radius R200). The gas density profile is highly peaked towards
the center and the surface brightness profile is well fitted by a sum
of three
-models.
The derived gas density profile is in excellent agreement, both in
shape and in normalization, with the published Chandra density
profile (measured
within
of the center). Projection
and PSF effects on the temperature profile determination are thoroughly
investigated.
The derived radial temperature structure is as expected for a cluster
hosting a cooling core, with a
strong negative gradient at the cluster center. The temperature rises
from
2 keV up to a plateau of
6.5 keV beyond
(i.e.
,
R200=2.08 Mpc being the virial radius).
From the temperature profile
and the density profile and on the hypothesis of hydrostatic
equilibrium, we derived the total mass profile of A478 down to 0.01 and
up to 0.5 times the virial radius. We tested different dark matter
models against the observed mass profile. The Navarro et al.
(1997) model is significantly preferred to other models.
It leads to a total mass of
for
a concentration parameter of
.
The gas mass
fraction increases slightly with radius. The gas mass fraction at a
density contrast of
is
,
consistent
with
previous results on similar hot and massive clusters. We confirm the
excess of absorption in the direction of A478. The derived absorbing
column density exceeds the 21 cm measurement by a factor of
2,
this excess extending well beyond the cool core region. Through the
study of this absorbing component and a cross
correlation with infrared data, we argue that the absorption excess
is of Galactic origin, rather than intrinsic to the cluster.
Key words: galaxies: clusters: individual: A478 - galaxies: intergalacic medium - cosmology: observations - cosmology: dark matter - X-rays: galaxies: clusters
As nodes of large scale structure and thus places of dark matter concentration, galaxy clusters can be used as powerful tools to test theories of structure formation. The basic hierarchical scenarios based on gravitation make the population of galaxy clusters a homologous population of sources. Their physical properties follow scaling laws depending only on their redshift and mass, and their internal structures are similar.
The exceptional capabilities of XMM-Newton in terms of sensitivity and of Chandra in term of spatial resolution allow us to characterize the gas density and temperature profiles with unprecedented accuracy. For a relaxed cluster, the hydrostatic equations can be used to derive the underlying dark matter distribution, from the very central part of clusters up to nearly the virial radius (David et al. 2001; Allen et al. 2001b; Arabadjis et al. 2002; Allen et al. 2002a; Pratt & Arnaud 2002, 2003; Lewis et al. 2003; Buote & Lewis 2003). The observed clusters seem to have a cusped dark matter profile as predicted by numerical simulations (Navarro et al. 1997, hereafter NFW; Moore et al. 1999, hereafter MQGSL). However, the central slope of the dark matter profile and the possible dispersion of the concentration parameter remain open issues. Larger samples of high quality mass profiles are needed to further assess these points.
In this paper we present the XMM-Newton spectro-imaging observation of A478,
a massive, relaxed nearby cluster (z=0.0881 - Struble & Rood 1999).
Detected in surveys (UHURU, HEAO-1, Ariel-V), this cluster is well
known in X-rays and its physical properties have been carefully
studied with previous X-ray observatories: EXOSAT (Edge &
Stewart 1991), Einstein and Ginga (Johnstone
et al. 1992), ROSAT (Allen et al. 1993; White
et al. 1994) and ASCA (Markevitch 1998; White et al.
2000). All those previous studies converge for what
concerns the overall temperature of the cluster,
keV.
Recently, Sun et al. (2003) performed a high angular resolution
study of the central part of the cluster with Chandra. They pointed
out the presence of an X-ray cavity in the very central part of the
cluster which is anti-correlated with the radio lobes.
Here we focus on the characterization of the gas and dark matter distribution of A478. In a companion paper de Plaa et al. (2004) present a detailed spectroscopic study of the metal abundances and their distribution within A478's core based on EPIC and RGS data. We present the observation and the different data processing steps in Sect. 2. In Sect. 3 we briefly discuss the cluster morphology. In Sect. 4 we analyze the surface brightness profile and derive the gas density profile. Spatially resolved spectroscopic analysis is presented in Sect. 5, where we also discuss the temperature and absorption profiles. In Sect. 6, we present the resulting total mass and gas mass fraction profiles of A478 and we discuss the shape of the dark matter profile according to our observational results.
Throughout this paper, we use H0=70 km Mpc-1 s-1,
and
.
In such a cosmological framework, at the cluster
redshift (z=0.0881)
kpc.
In this work, we only kept events with pattern 0 to 12 from EMOS data, pattern 0 from EPN data and flag equal 0 for both detectors.
First the event list for each camera and each observation was
filtered for periods of high background due to soft proton flares.
Visual inspection of the light curve in a source-free energy band
(
for EMOS and
for EPN) revealed long
periods of high background. These were excluded. We then
fine-tuned the flare cleaning by using a "3
clipping''
selection of good time intervals as described in Pratt & Arnaud
(2003). The Poisson fit of the light curve histogram
provides a 3
threshold above which corresponding frames are
discarded. To excise all flaring periods, this clipping method was
applied in different energy bands:
,
and
for EMOS;
,
,
and
for EPN. This quite
conservative choice was made to avoid any low energy flares that are
present in some observations (Pratt & Arnaud 2002).
The remaining exposure times after cleaning are 48.0 ks, 40.9 ks and 37.3 ks for the central pointing and the EMOS1, EMOS2 and EPN camera respectively. The corresponding times for the offset pointing are 13.1 ks for the EMOS camera and 11.0 ks for the EPN camera.
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Figure 1:
Left panel: total (EMOS+EPN) XMM-Newton mosaic
image of A478 in the
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For each camera, we merged the cleaned event lists of the two
observations into a single event list. We only selected events
falling within a
circular region centered on the detector
optical axis.
The sky pixel coordinates of each event of the offset pointing were
re-projected onto the sky pixel grid of the central pointing.
Scientific products (spectra, images, surface brightness profiles) can thus be extracted in a single step from the merged events list, simplifying the analysis. However, the exposure time can vary strongly in a given extraction region and this has to be taken into account in estimating count rates. The extraction method we used is fully described in Appendix A. All the products are corrected for vignetting in this extraction process. The vignetting correction is based on the photon weighting method described in Arnaud et al. (2001), the weight coefficients being tabulated in the event list with the SAS task EVIGWEIGHT.
For each camera, a clean background event list was extracted from the
corresponding blank-field data using the same filtering criteria
(pattern and flag selection, 3 flare clipping) as for the
observations. Cast-background files were then generated for each
pointing by applying the aspect solution of the observation to the
background dataset. The correct exposure time was computed for each
blank field event list.
To estimate the difference of particle background level
between each observation and the corresponding blank field data, we
computed the ratio of the total count rates in the high energy band
(
and
respectively for EMOS and EPN data).
As
the expected average temperature of this bright cluster is quite high (
)
we excluded a circular central region
to avoid any contamination due to the cluster.
Blank field products have to be normalized by this ratio, when used as a background for the corresponding observation products. The normalizations are slightly different from one pointing to the other. To take that normalization into account, we multiplied the weight coefficients in each cast background file by the corresponding normalization factor. Vignetting-corrected blank field counts are then automatically "normalized''. These cast background files of the two pointings are then merged as for the observations. Product extraction is then the same (see Appendix A).
For the EPN data, we generated a list of out-of-time events (OoT hereafter) to be treated as an additional background component. An OoT event occurs when a photon is detected during the read-out process. The current observing mode (Extended Full Frame) minimizes the effect of OoT to 2.3%. The OoT event list was processed similarly to the observation EPN event files.
The background subtraction (for spectra and surface brightness
profiles) is performed as described in full detail in Arnaud
et al. (2002). It is a two-step procedure, which insures a
correct cosmic X-ray background (CXRB) subtraction, even when the
local CRXB is different from the average CRXB in blank field data. In
a first step, for each product extracted from the merged observation
event list, an equivalent product is extracted from the corresponding
merged blank-field file and subtracted from it. For EPN the
OoT data are also subtracted. This first step allows us to remove the
particle background. However, it may over (under) subtract the CRXB if
the CRXB in the observation region is smaller (larger) than the average
value in the blank field observation. The residual CXRB (i.e. the
difference between the CXRB in the A478 field and in the blank field)
is then estimated by using blank field subtracted data in the region
free of cluster emission (
from the cluster center
- the cluster is significantly detected in the background subtracted
surface brightness profile up to 12-13
). This residual CRXB is
subtracted in a second step from each EMOS and EPN product. In our
case the residual is negative in the
energy band. The
residual count rate summed over the three detectors is -0.68 counts/s/arcmin2, which represents 23% of the total
background count rate in this energy band. Beyond 3 keV the residual
background (
)
spectrum is consistent with zero. Therefore
the double subtraction beyond 3 keV will only contribute increasing
the noise level in each channel. To minimize errors, the double
subtraction is thus applied only to data in the energy band
.
We nevertheless check (on the global spectrum) that
the best fit values remain the same if a full double subtraction is
applied.
Starting from the output of the SAS detection source task, we made a visual selection on a wide energy band EMOS & EPN image (extracted from the merged event lists) of point sources in the FOV. Events from these regions were excluded directly from each merged event list. We generated corresponding mask mosaic images, which were then used to compute the surface of each extraction region.
The mosaic count rate image (EMOS+EPN) in the
energy
band is
presented in Fig. 1, together with the hardness ratio map
computed from the ratio of the images in the
and
energy bands. The images in various energy bands are
vignetting corrected and background subtracted using the corresponding
blank field image and the OoT image in case of EPN. To generate the
hardness ratio map, the hard band image was first adaptively smoothed
(with the task ASMOOTH). The soft band image was then smoothed using
the same smoothing template as was created for the hard band image. The
cluster morphology is regular and the hardness ratio map does not
exhibit any peculiar feature, reinforcing the assessment that A478 is
a very relaxed cluster.
A478 has an elliptical shape. From optical and ROSAT/PSPC and HRI data White et al. (1994), derived an ellipticity varying
between 1.2 and 1.4 within the central
region.
We fitted a 2D
-model to the EMOS1+EMOS2 image in the
energy band, within the
region. We derived a
consistent value of the ellipticity,
.
The quality of
the fit is poor, however: the residual image shows a strong excess at
the cluster center position, as expected for a strong cooling flow
cluster.
Despite its slightly elliptical shape, in the remainder of this work we
assume spherical symmetry and use circular annuli to extract the surface
brightness profile and spectra. Pratt & Arnaud (2002)
showed in
the case of A1413, a cluster of a higher ellipticity of
,
that this has negligible impact on the derived
temperature and mass profiles.
We computed a background-subtracted vignetting-corrected radial surface
brightness profile for each detector in the
energy band. The width of the radial bins was
.
The
profiles for the three detectors were added into a single profile,
which was rebinned to reach a significance level of at least 3
in each radial bin. The cluster emission is detected up to
.
The emissivity in the considered energy band varies slightly with
radius, due to the radial gradients in the hydrogen column density
along the
line of sight (
), temperature (
)
and metallicity (Z)
(see Sect. 5.2). The
,
and Z values were extrapolated at each radius of the surface brightness
profile by fitting the observed
,
and Z profiles (see
Sect. 5.2) with a 3 degree polynomial, an empirical
temperature profile as described in Allen et al. (2001b) and
a lognorm law respectively. The corresponding emissivity profile
(with errors) was estimated using an absorbed redshifted MEKAL model,
convolved with the instrument response. Its radial variation is
mainly dominated by the variations of
.
The surface brightness
profile was then divided by the emissivity profile normalized to its
value at large radii. The errors on the emissivity were propagated to
the corrected surface brightness profile.
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Figure 2:
A478
XMM-Newton (EMOS+EPN) surface brightness profile in the
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The corrected surface brightness profile (presented in
Fig. 2) is proportional to the emission measure profile,
EM(r), and
can be fitted directly using various parametric models of the gas
density profile,
.
The corresponding emission measure models
were convoluted with the XMM-Newton PSF (Ghizzardi
et al. 2001, 2002) and binned in the same
way as the observed profile.
As expected, a standard -model provides an unacceptable fit, the
data showing a strong excess in the center compared to the model.
Progressively cutting the central region decreases the reduced
.
The fit becomes acceptable (
)
for a
cut-out radius of
with a best fit
value of
(
errors). The reduced
keeps decreasing with increasing
until
it stabilizes to a value of
for
.
There is an indication that
increases with increasing
,
but the effect is
marginally significant: for instance we obtained
for
.
We then considered the alternative parametrisations of the gas
density profile
proposed by Pratt & Arnaud (2002) for cases where a central
excess is seen. We fitted the entire profile with a cusped model,
similar to
the NFW profile (their AB model) and a double isothermal -model (their BB model). Both models fail to account for the data, although
formally the latter provides a better fit than the former: the reduced
are respectively 5.5 and 4.2. We then tried a
generalized double
-model (their KBB model). This model allows a
more centrally peaked gas density profile in the core than the BB model and is defined by:
This model provides an excellent fit to the data, but only if the very
central part is excluded from the fit (see Fig. 2).
Fitting the
region gives a
reduced
of
for
,
,
,
and
.
A clear excess is observed when extrapolating this
model in the central part (see Fig. 2).
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Figure 3: Same as Fig. 2 with the best fit BBB model (Eq. (2)) fitted over the full radial range. |
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Figure 4: Comparison between the Chandra gas density profile derived by Sun et al. (2003) and the XMM-Newton best fit BBB gas density model (as plotted in Fig. 3). Bottom panel: ratio between the Chandra data and this model. |
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We then tried a 3 component model. We went back to direct
parametrisation of the emission measure profile (rather than the
density profile) for simplicity. We considered the sum of three
-models (hereafter BBB model).
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(3) |
This BBB model provides an excellent fit to the data over the whole
radial
range: the reduced
is
for 56 d.o.f. This best fit model is plotted in Fig. 3, together
with the ratio between data and model. The best fit parameters are
,
,
,
(
errors). The best fit central
density is
,
with a relative normalization
of the second and
third components of
and
,
respectively.
We further compared this best fit density profile with the profile
obtained by Sun et al. (2003) from a deprojection of the
Chandra ACIS-S3 surface brightness (see Fig. 4). The
Chandra profile is determined out to
.
There is a good
agreement between the two profiles, both in shape and in
normalization. Simply adjusting the overall normalization of the XMM-Newton
best fit model
to the Chandra data gives already a reduced
of 1.3 with residuals between model and data less than
.
The
normalization is
lower than the XMM-Newton value, corresponding to
discrepancy in X-ray
flux, well within the discrepancy of
between the two
instruments found by Snowden (2002). Although the
best fit XMM model does not fit perfectly the Chandra profile shape,
slightly adjusting the parameters provides an acceptable fit. We kept
the
and outer core radius values to their best fit XMM values,
as the external shape of the density profile is not well constrained
by Chandra data. We obtained a reduced
of 1.0 for
and
,
consistent with the XMM
confidence range. The relative
normalizations of the three components are marginally inconsistent.
Nevertheless, taking into account that the effect of the Chandra PSF
is negligible, the good agreement between XMM and Chandra central core
radius indicates that the PSF modeling we have used to fit the XMM-Newton
data is basically correct.
The XMM best fit BBB model is thus used in the following to
estimate the cluster gas and total mass profiles and to correct the
temperature profile for PSF and projection effects. The total mass
profile depends on the logarithmic slope of the density profile. To
estimate the systematic uncertainties in the mass estimates we will
also consider the density logarithmic slopes derived from the BBB model best fitting the Chandra profile. The differences are small
however, in the range
.
Finally we would like to
emphasize that the BBB model functional form must only be viewed as a
convenient parametric representation of the gas density profile. It
has no particular physical ground and must not be over-interpreted
(e.g. in terms of three distinct gravitational systems in the cluster).
Throughout the analysis, the spectra are binned to reach a
significance level of at least 3
in each bin. We used XSPEC
to fit the data with an absorbed redshifted thermal model
( WABS ( MEKAL)). Due to larger calibration uncertainties in the
instrument response below the O edge we only fitted the spectra above
.
We used the following response matrices:
m1_thin1v9q20t5r6_all_15.rsp (EMOS1),
m2_thin1v9q20t5r6_all_15.rsp (EMOS2) and epn_ef20_sY9_thin.rsp
(EPN, created in December 2002). Unless otherwise stated, the
relative normalizations of the EPN and EMOS spectra were left free when
fitted simultaneously.
We first extracted the cluster EMOS1, EMOS2 and EPN spectra within a
circular region of
.
Fitting simultaneously the EMOS and
EPN spectra, we obtained a redshift of
.
This value is significantly smaller than the optical value
(
). An investigation of the variation of
with z revealed two local minima, one at the optical
redshift location and one at z= 0.079. Independent spectral fits
of EMOS and EPN spectra clarify the issue. The EMOS best fit value is
,
perfectly consistent with the optical
value. On the other hand, the EPN best fit redshift is
and corresponds to the second minimum.
The redshift difference from the optical value corresponds to an
energy shift of
with respect to
the expected iron line position.
We thus checked for a possible gain problem in the EPN data. The
non-background subtracted spectrum shows strong Al-K, Ni-K and Cu-K
fluorescence lines, which can be used for this purpose. We fitted the
spectrum extracted in the
region in a
restricted energy range around these lines with a power law plus
Gaussian line(s). The fitted Ni-K and Cu-K line energies are
significantly higher than expected:
and
respectively, to be compared to the expected
values of
and
.
However, the
discrepancies,
and
respectively, are smaller than observed for the cluster iron line.
Furthermore we cannot simply add a constant offset to the energy
scale: the centroid energy of Al-K,
,
is consistent with the expected value of
.
Any linear
gain correction based on the position of these fluorescence lines
would thus be insufficient to bring the EPN redshift determination into
agreement with the optical value.
We thus did not try to define and apply a gain correction
In principle, the EPN gain
uncertainty could affect our results. To assess this point, we fitted
the EPN spectrum both fixing the redshift at the optical value and
letting this parameter free. The derived
values are the same,
the best fit temperatures differ by
,
similar to the
statistical uncertainty. As expected the main impact is on the
derived abundance: for a free redshift
,
only marginally consistent with the value,
,
obtained fixing the redshift at the
optical value. When the EPN spectrum is fitted simultaneously with
the EMOS spectrum, these discrepancies are even smaller. The
abundance difference is two times less and the temperature is the same.
As we are mostly interested in the temperature information, we can
neglect the gain uncertainty and choose to fix the redshift to the
optical value, in all the following
analysis. The overall cluster parameters are:
cm-2,
keV and
(
confidence level).
We extracted background-subtracted, vignetting-corrected spectra in 13 concentric annuli centered at the peak of the X-ray emission. The annuli were defined to have about the same number of counts per bins (except the outermost annulus).
The EMOS1, EMOS2 and EPN spectra of each annulus were simultaneously
fitted with a WABS ( MEKAL) model. The resulting
,
,
and abundance profiles are plotted in Fig. 5. The definition
of the annuli and the best fit parameters are gathered in
Table 2. We also checked that the temperature profiles
obtained by fitting the EMOS and EPN spectra independently are
consistent within the error bars.
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Figure 5:
Result of the radial spectral fitting. From top to
bottom the temperature (kT), Galactic absorption (
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Table 1: A478 global properties from previous studies.
The temperature profile shows a clear drop towards the center. It is
well fitted by the analytical formula proposed by Allen et al.
(2001b):
The temperature profile shows a strong gradient towards the center,
whereas we
recall that the surface brightness profile is very peaked. This
temperature profile is thus likely to be affected by both PSF and
projection effects. These effects will be analyzed in
Sect. 5.5. However, the overall
value is
significantly
higher than the 21 cm value and its radial profile is not flat. As
the
and
determination are not independent, we will first
discuss our absorption results.
Our best fit overall value for the Galactic absorption,
cm-2, is nearly two
times the 21 cm value of
cm-2 (Dickey
& Lockman 1990). Such an excess absorption was found in
all previous X-rays studies of A478 and our derived value is only
marginally higher than the value derived from ROSAT/Ginga and Chandra
data (see Table 1).
The radial
profile that we obtained
exhibits a clear gradient ranging from
cm-2 in
the central regions to
cm-2 at
.
This gradient is consistent with the
Chandra gradient measured by Sun et al. (2003): from a
central value of
cm-2 down to
cm-2 for the last bin at
(perfectly consistent with the XMM-Newton value, see
Table 2).
Table 2: Radial spectral fitting - best fit values and associated error bars (90% confidence level).
This excess of absorption seen in A478 and other cooling flow clusters was interpreted in previous studies (e.g., Allen et al. 1993, 2001a) in terms of intrinsic absorption by very cold gas related to the strong cooling flow. However our vision of cool cluster cores has dramatically changed due to XMM-Newton observations. The standard cooling flow model predicts low energy emission lines which are simply not seen in the RGS spectra (Peterson et al. 2001, 2003). This standard model is also inconsistent with EPIC data (e.g., Molendi & Pizzolato 2001; Matsushita et al. 2002; Böhringer et al. 2002; Kaastra et al. 2003). No evidence of intrinsic absorption was found with XMM-Newton in the center of the cooling flow regions in M 87 and the Perseus cluster, and Böhringer et al. (2002) argued that the excess absorption measured by previous missions is an artifact of fitting standard cooling flow models. The low energy emission over-predicted by this model can be artificially suppressed by adding an extra absorption component when fitting spectra obtained with instruments like ASCA, which have relatively low sensitivity at low energies.
Although the absorption excess in A478 is confirmed by XMM-Newton data, it
is more likely, in view of our current knowledge of cooling cores in
clusters, that all the absorption is of Galactic origin. This
hypothesis is reinforced by the spatial distribution of the excess
absorption: the excess extends well beyond the cool core region.
We also note that if cold gas has indeed now been detected in the core
of clusters, like A478, through CO measurements (Edge 2001), there is
still a large mismatch, by an order of magnitude, between the inferred column
densities and the absorption excess (see Edge 2001, for full
discussion). Finally the local CXRB that we measure with XMM-Newton is
lower than the
average blank field value (see Sect. 2.4). The Rosat All
Sky Survey (RASS)
maps (see Snowden 1997) also
clearly show a deficit of CXRB in that region. This again points
towards a high Galactic absorption.
To further test the origin of the absorption and the robustness of
our
estimates, we considered other indicators of the Galactic gas
column
density. We recall that the column density derived from X-ray data is
actually the total hydrogen column density (assuming standard
abundances). We considered the IRAS 100
m cleaned map of
Schlegel et al. (1998). The Galactic hydrogen is
correlated with
the Galactic dust responsible for the IR emission, as shown by
Boulanger et al. (1996) and Schlegel et al.
(1998), who
correlated COBE/DIRBE and IRAS data with the Leiden/Dwingeloo survey
(Hartmann & Burton 1997). The correlation between the
IR emission and the atomic hydrogen column density is determined from
low
data (
cm-2). Above this
threshold an increasing dispersion is observed with higher IR/HI ratio
on average. Boulanger et al. (1996) argued that this
excess IR emission is due to dust associated with molecular hydrogen. The IR emission
could thus actually be a tracer of the total hydrogen content.
Assuming that the correlation determined at low
values (where the
H2 fraction is expected to be small) is representative of this IR - total
correlation, we converted the IR brightness map into a total
map. We used both the Boulanger et al. (1996)
and
Schlegel et al. (1998) results, these two groups having
derived slightly different correlation coefficients. We then derived
radial profiles which are compared with the XMM-Newton derived
profile
in Fig. 7. Interestingly, the IR and X-ray derived
profiles are indeed found to be consistent up to about
.
Beyond that radius the XMM-Newton
profile starts to become significantly
lower than the expected values from the IR emission. However, the IR emission shows a strong gradient over the cluster area in
the north-east/south-west direction (see Fig. 6). There is
a drop by a factor of
two between the north-east sector of our mosaic and the south-east
sector. Obviously the azimuthal average tends to smooth the gradient
effects. Keeping the previous definition of annuli, we then divided
each
annulus in four sectors separated by a North-South and an East-West
axis (see Fig. 6). In each sector, we ran a spectral fit
for each annulus. The
resulting
profiles are presented in Fig. 7. All four
profiles are compatible with the azimuthally averaged profile within a
3
limit. One can notice, however, that the South-East
measurements are systematically lower than the azimuthal values whereas
the North-West values are systematically larger.
In summary, both X-ray and IR data indicate a higher Galactic hydrogen
column density than the 21 cm value. Both X-ray and IR
estimates agree remarkably well in the cluster center, suggesting that
the excess absorption is indeed of Galactic origin. Moreover, FIR observations from the ISO satellite at 90 and 180
m show a color
ratio favoring a cold temperature structure (Pointecouteau & Giard,
in preparation), which is more likely to be due to a Galactic
structure than to an intracluster dust component. Indeed, the
expected temperatures for the intracluster dust according to the current
models are >20 K (Montier & Giard 2003). However, the radial
variations of the X-ray and IR derived hydrogen column density differ.
This could be due to variations in gas to dust ratio and/or
metallicity for instance.
To probe the foreground structure on the cluster scale toward A478,
FIR observations with a higher spatial resolution would be extremely
useful. For instance, soon the ASTRO-F mission (Shibai 2002) will
survey the whole sky at FIR wavelengths and will provide observations
up to 200
m that will reveal the galactic cold component
structure. These upcoming observations on the whole cluster scale will
certainly help to clarify this issue.
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Figure 6:
IRAS 100 ![]() ![]() |
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Figure 7:
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In view of the discrepancy between the IR and X-ray derived
values beyond
,
we further checked the
robustness of our
and thus
measurements in that region
(two outer annuli). We ran again the individual spectral fit on the
annuli, fixing the value of the Galactic absorption to
cm-2. The derived temperature drops from
down to
.
However, the fit is significantly worse.
Indeed, the F-test probability, given the
value and the one
obtained previously by letting free the
,
is 10-8.
Furthermore, if we still fix the
value to
cm-2, but fit the spectra for
E>1.5 keV, avoiding the low energy band that is sensitive to the
Galactic absorption, the derived temperature profile is fully
compatible with the nominal one. Therefore, we can be reasonably
confident that the derived radial column density and temperature
profiles are real.
The best fit values we derived for the overall physical properties of A478 are in agreement with the previous results for the
Galactic absorption and the metallicity (see Table 1).
Moreover, their radial profiles match
closely those derived by Sun et al. (2003) using the
Chandra data. However, our overall temperature value is
marginally compatible with the temperature values from ROSAT/Ginga
and ASCA.
A478 does not exhibit an overall isothermal plasma (presence of a cool
core). The temperature derived from an isothermal fit is actually an
emission weighted temperature, which depends on the instrument response.
Due to its higher sensitivity at low energies, XMM is more sensitive to
the presence of a cool component. This would explain the slightly
lower temperature derived from our data with respect to Ginga and ASCA results.
To further check this point, we fixed the absorption value to
cm-2 (the value derived from the ROSAT/Ginga
analysis) and we fitted the overall spectrum over the [1-10] keV energy
band. The best fit temperature value is then
,
a
value compatible with ROSAT/Ginga value, as well as ASCA value.
Despite this agreement, some important discrepancies appear between
the temperature
profiles obtained from XMM-Newton and Chandra. If we focus on the average
value of the temperature
excluding the cool core region, the Chandra value (
)
is significantly higher than the XMM-Newton value (
).
Similar discrepancies appear for the luminous X-ray cluster
PKS 0745-191. Indeed, the temperature derived from the
Chandra analysis (Hicks et al. 2002) outside the cool core
(
1.5'<r<2.3'),
,
is significantly higher than the value
derived from XMM-Newton data (Chen et al. 2003) in the same
region,
.
In this case, the XMM-Newton result compares better
with the
value of
by BeppoSAX (De Grandi & Molendi 1999). However, it must
be noted that
the BeppoSAX temperature measurement includes the
cold core region which is likely to induce a bias toward lower
temperatures.
We have failed to explain the discrepancy between XMM-Newton and Chandra.
Apart from calibration related problems, we thought that it could be
due to background subtraction problems. For both PKS 0745-191 and A478, the CXRB was found with XMM-Newton to be different from the CXRB of a typical blank field. The higher
observed in the direction of the
A478 cluster certainly contributes to this difference for this
cluster, but we cannot exclude a contribution from some intrinsic
spatial variation in the soft X-ray Galactic emission. This
difference was taken into account in the XMM-Newton background subtraction
procedure (in the second subtraction step - see Sect. 2.4).
On the other hand, Chandra analysis had to rely on a simple blank
field background subtraction, by lack of data at large radii. In the
Chandra analysis of A478, the CRXB is a priori oversubtracted and this could
bias the temperature determination, especially in the outer cluster
region where the CXRB count rate is no longer negligible with respect to
the cluster count rate. To test this hypothesis for A478, we perform
a single blank field subtraction for each XMM annular spectrum and
re-ran the spectral isothermal fit. The resulting absorption and
temperature profiles become significantly different beyond
(the upper limit of the Chandra profile). However, below
,
the profiles are not significantly affected and remain
inconsistent with Chandra values
. Although
the Chandra blank field observations are not the same as those of XMM-Newton,
it is thus unlikely that the background subtraction issue is an
explanation of the discrepancies. Furthermore the agreement between
the XMM-Newton and Chandra profiles for the Galactic absorption would be
puzzling if that was the explanation, since the
determination is
particularly sensitive to the subtraction of the residual CXRB, which
affects the low energy part of the spectrum most.
![]() |
Figure 8: Temperature profiles corrected for the PSF effect ( left panel), deprojected ( middle panel), PSF corrected and deprojected ( right panel). The data points are the temperatures derived from simultaneous fitting of the annular spectra. The open points are the temperatures obtained by fitting each annular spectrum individually with an isothermal model (Same as in Fig. 5). The dotted line is the analytical model fitted to these data (Eq. (4)). The full lines are the PSF corrected model ( left panel), the deprojected model ( middle panel) and the PSF corrected deprojected model (see Sect. 5.5.3 for details). |
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The central drop in the temperature profile emphasizes the need to perform a deprojection analysis and to take into account the PSF effect. For such a highly peaked cooling flow cluster, PSF effects are important in the center where we have chosen narrow bins for the temperature computation to recover the best temperature profile.
The incident emission of each annulus, i, is the projected sum of
the emission from various shells, .
This emission is then
redistributed among various annuli due to the finite PSF. In principle,
we should apply an absorption model to each incident annular spectrum
(i.e.
after the projection and before the PSF convolution). However the
profile derived from the annular spectra fit does not show strong
gradients in the central region (where the PSF effect is significant).
We thus used a single absorption model for each observed annular
spectrum, fixing the
value to the best fit value obtained from
individual annular fits (see Table 2).
We thus model the observed annular spectra,
,
with a linear combination of isothermal MEKAL models (normalized to
the unit emission measure), multiplied by a WABS model:
Similarly we assess the projection effects, neglecting the PSF blurring. We used the same formula with the ai,j redistribution factors being now the emission measure contribution of the shell jto the ring i and Tj the temperature of the shell j (assumed to be isothermal).
Finally we took into account both effects, using as ai,j the emission measure contribution of the shell j to the ring i after convolution with the PSF.
The fitting was done with XSPEC. We have to take into account that
XSPEC can only handle 1000 parameters (even if most of them are
frozen). The EMOS1, EMOS2 and EPN spectrum of each annulus was loaded
into XSPEC as a data group. The same model parameters are applied to
each spectrum of a given group. Therefore, EMOS and EPN spectra have
to be normalized in order to be fitted with the same normalization.
Furthermore the ai,j coefficients are computed without taking into
account flux loss due CCD gaps, bright pixels, etc. We therefore first
renormalized each spectrum by the ratio of the annular geometrical
area to the actual extraction region surface ( BACKSCALE value).
After this correction, the ratio of the EMOS and EPN normalizations
obtained from the annular fits (Sect. 5.2) were found to be
consistent with the ratio obtained by fitting the overall EMOS and EPN spectra:
.
We thus applied this factor to all
EPN spectra. Finally, we checked that the annular fit results
indeed remain the same: the differences in derived kT are negligible
compared to the statistical errors.
Fitting simultaneously n annular spectra with a sum of n MEKAL
models, multiplied by a WABS model, gives a total number of
parameters of (6n + 1)n. We thus have to limit n to 12. To
overcome this problem, we have used two different sets of 12 annular
spectra. The first set is obtained by grouping the last two annuli
into a single annulus and the second set by grouping the first two
annuli. We then combined the first set results for annuli
to
with the second set results for annuli
to
.
For each set, the free parameters are the 12 temperatures, 12 normalizations, one per data group (annulus), the other normalizations being linked according to Eq. (6). In practice we ignore all contributions less than 1%. We have frozen the abundance of each MEKAL model to the annular best fit value, except for the 4 innermost components corresponding to the r <1' region. Beyond that region the annular abundance profile is flat. PSF and projections effects are unlikely to affect the abundance determination in such a way that it has a significant impact on the temperature determination. To further check this point, we also fixed all the abundances to the best fit annular value. Only the central temperature is changed significantly.
The resulting corrected temperatures are plotted versus effective radius (defined in Eq. (5)) in Fig. 8. These data are compared to the temperature profile derived in Sect. 5.2 (hereafter the raw temperature profile).
We also considered the best fit model
(Eq. (4)) of the raw temperature profile (dotted line in
Fig. 8). It can also be corrected for PSF and/or
projection effects, assuming that the annular temperatures
are emission-weighted temperatures:
First, it is instructive to consider the PSF correction (Fig. 8, left panel) and the deprojection (Fig. 8, middle panel) separately. In both cases, the corrected model fits reasonably well the corresponding corrected temperature profile derived from the spectral fit. However, while the former remains a smooth function of radius, the later is more noisy. A comparison of the observed and model profiles before and after correction shows that the correction process amplifies any variation of the raw temperature profile compared to the smooth model (see in particular the temperatures of annuli # 3, #10 #11 and #12). This is probably linked to the well known problem of noise amplification when deconvolving or deprojecting noisy data (see also Kaastra et al. (2003) for a discussion on PSF/projection effects).
The PSF-corrected projected temperatures and the deprojected temperatures are consistent, within the error bars, with the raw temperatures in the external part of the cluster (nearly isothermal region, R > 100 kpc). Significant deviations are seen for the first four annuli. The general effect of the PSF blurring and of the projection are best seen by comparing the corrected and uncorrected models. The PSF affects mostly the central bin (the temperature of which is increased due to contamination by the higher temperatures of the external bins). In turn the other bins are contaminated by the low temperature central bin, and their observed raw temperatures are slightly lower than the incident ones. The effect is small however and consistently tends to zero with increasing radius. The main effect is the projection effect. As expected it damps down the gradient in the central region. The deprojected temperatures are always smaller than the projected ones, the effect increasing with decreasing radius.
The PSF-corrected deprojected temperature profile is shown in Fig. 8 (right panel). When both PSF and projection effects are taken into account the noise amplification is dramatic. The temperature profile derived from the spectral fit shows strong discontinuities (e.g. bins #3, 4, 5, bin #10). On the other hand, the corrected model remains smooth. Although the corrected temperatures derived from the spectral fit are not consistent with the corrected model within the statistical errors, they are distributed around it. The largest deviations correspond to the discontinuities mentioned above and are again clearly located around the bins which originally deviate most from the smooth model profile. These discontinuities are thus very likely non-physical and the corrected model is probably a better representation of the true cluster temperature profile than the profile derived from the spectral fit. As discussed in Sect. 6, we will use this corrected model as a reference in our computation of the mass profile.
The PSF-corrected deprojected model profile is consistently intermediate
between the PSF-corrected model profile and the deprojected model
profile for bins
to
.
As shown above, the PSF and
projection have opposite effects in that region. The model temperature
of the central bin is however extremely low. The PSF correction and
deprojection was done assuming that the annular temperatures are
emission-weighted temperatures. This assumption is probably less and
less valid with decreasing temperature and the low value we derive
might be an artifact of our assumption. Furthermore the gas may be
multiphase in that region (r<20 kpc) due to the interaction of the
intracluster medium with the central cD galaxy (see also below).
At large radii, the errors on the derived mass profile are dominated by
the statistical
errors on the temperature profile. However
we have to consider possible systematical errors, specially in the
central
(R<100 kpc) region, where the PSF and deprojection corrections
introduce noise in the derived temperature profile (see Sect. 5.5). Only data beyond
are considered:
the temperature of the central bins is highly uncertain (see Sect. 5.5.4). Furthermore, Chandra data have clearly revealed
sub-structure in the central
region. Below that radius, the hot thermal gas might interact with the
radio halos, producing a non-thermal population of electrons, and
therefore the hydrostatic equilibrium might be disturbed locally
producing possible multiphase states for the gas at this spatial scale
(see previous work on M 87: Böhringer et al. 1995; Belsole et al. 2001; and on
PKS 0745-191: Chen et al. 2003).
![]() |
Figure 9:
Integrated total mass
distribution. Filled circle: the reference total mass profile
obtained from the best fit BBB model for the gas density profile and
the PSF-corrected deprojected model of the temperature profile (errors
are ![]() |
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We first derived a reference mass profile. It was computed using our
best fit BBB model for the gas density profile. For the temperature
profile we used the PSF-corrected deprojected model profile. The
profile derived from the spectral fit is too noisy to be used: the
strong fluctuations observed are inconsistent with any underlying mass
profile. It is difficult to assess the statistical errors on this
model profile in an objective way. We used the errors derived from
the spectral fit, which is probably a conservative approach. For bin
we also add as an error the difference between the fitted
temperature and the model value (the latter might be affected by the
too low value derived for bin #1).
We then computed the mass profiles obtained using alternative temperature and density data, to assess the systematic uncertainties. For the gas density profile, we considered the best fit BBB model of the Chandra profile (crosses in Fig. 9). The differences between the derived mass profile and the reference profile are much smaller than the statistical uncertainties.
We then considered systematic uncertainties due to the temperature profile determination. We have shown that PSF effects in the region considered here are less important than projection effects and that pure deprojection introduces much less noise. We thus also computed the mass profile derived from the deprojected temperature profile (neglecting the PSF blurring). We used both the profile derived from the spectral fit (triangles in Fig. 9) and the deprojected model profile (open circles in Fig. 9). The latter is well within the error bars of the reference profile, but the former differs significantly (see for instance the first point). Considering that these differences are likely to be representative of the systematic uncertainties due to the PSF correction treatment, we add them quadratically to the statistical errors on the reference mass profile.
In the following, we will thus consider the reference mass profile with these errors bars.
![]() |
Figure 10: Modelling of the integrated total mass distribution. Filled circle: total mass profile as in Fig. 9. The errors now include systematic errors due to the PSF correction (see text). The solid line is the best fit NFW profile (c=4.18), the dotted line is the best MQGSL profile and the dashed line is the best fit King model. |
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We first tried to fit the data with a King model, where the mass
density profile is given by:
.
This model (dashed line in
Fig. 10) is inconsistent with our data, the
is
for 10 d.o.f.
The total mass profile was then fitted using cusped density
distributions: the Navarro et al. (1997) profile
and the
Moore et al. (1999) profile
.
These models have
two free parameters, the central density and the scaling radius, or
equivalently the total mass M200 (corresponding to a density
contrast of 200, as compared to the critical density of the Universe
at the cluster redshift) and the concentration parameter
.
All useful formulae relating these quantities can
be found in Pratt & Arnaud (2002).
The NFW profile provides a good fit to the data:
for 10 d.o.f. The best fit NFW parameters are:
and
,
corresponding to a concentration
parameter of
and a total mass enclosed within R200 of
.
The
previous errors are quoted at 68% confidence level. This best-fit
NFW model is shown overplotted on the mass profile of the cluster in
Fig. 9. The upper axis is the radius in units of the
derived R200. We are thus probing the dark matter shape on a
scale from
0.01 to
0.5 virial radius.
The alternative MQGSL profile is rejected by our data:
.
It must also be noted that the deviations from the data are
not only significant at low radii, where the mass estimate is most
sensitive to systematic errors. There is a general deviation at large
radius, where the model gives essentially a power law, while the
observed profile shows a significant curvature.
![]() |
Figure 11:
The integrated gas mass fraction as a function of the radius. The
1![]() |
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We derived the integrated gas mass fraction profile,
,
from
the ratio of the gas mass profile to the total mass profile. The gas
mass profile is computed from the integration of the best fit BBB model for the density profile (see Sect. 4.2). The errors
for the gas mass fraction are obtained from the propagation of the
total mass uncertainties, the gas mass uncertainties being negligible.
The resulting gas mass fraction profile is shown in
Fig. 11, together with the profile derived from the NFW best fit model. There is a general increase of
with radius,
although the effect is small over the [0.01-0.5] R200 range. The
gradient is most pronounced in the cool core region (about
),
beyond which there is only marginal evidence of a positive gradient (
from 0.1 to
0.5 R200).
Excluding the cool core region (e.g. r<2), the average value
for the gas fraction is
.
We interpolated the gas mass fraction
value at
,
the radius corresponding to a
density contrast of
(2500 times the critical density of
the Universe at the cluster redshift),
.
This
value agrees with the average value of
at the same
overdensity derived by Allen et al. (2002b) from a sample of
six massive clusters observed by Chandra. Our value is also
consistent with the value derived from the analysis of A1413 (Pratt &
Arnaud 2002) when scaled to the chosen cosmology of this
paper:
f2500(A1413)=0.11. However, the A478 and A1413
profiles have different shapes, the latter decreasing more
strongly toward the center. This reflects differences in the
central gas density distribution, the total mass profile of both
clusters having similar concentration parameters. Such a difference
is probably linked to the different thermodynamical states of A1413
and A478, the latter hosting a strong cooling core, contrary to the
former.
In this paper we have analysed imaging and spatially resolved
spectral data of the galaxy cluster A478 obtained with the XMM-Newton
satellite. We obtained well constrained absorption, gas density and
gas temperature profiles up to 0.5 virial radius.
As in previous studies, we found an excess of absorption in the
direction of A478. The derived absorbing column density exceeds the
21 cm measurements by a factor of 2 in the center and the excess
extends well beyond the cooling core region. This excess of
absorption seen in A478 (and other cooling flow clusters) was
interpreted in pre-XMM and Chandra studies (e.g. Allen et al.
1993; Fabian 1994) as the signature of intrinsic cool absorbing
material, a consequence of the strong cooling flow in the cluster
center. From the absorption excess extent and a detailed comparison
with FIR data, we argue that the absorption excess is rather of
Galactic origin. We suggest it could be the effect of a Galactic
molecular/cold cloud type structure in the line of sight. The next
generation of FIR space missions will help to clarify this issue with
sensitive FIR mapping of the whole cluster area with a high spatial
resolution.
We fitted the surface brightness profile with various parametric
models of the gas density profile, taking into account the XMM-Newton PSF.
The gas density profile, derived on scales of
,
is highly peaked towards the center and is well fitted by
a quadratic sum of three
-model. The derived gas density profile is
in excellent agreement both in shape and normalization with the
Chandra density profile (measured up to
of the center).
This indicates that the PSF modeling we have used is basically correct
and that accurate density profiles in the very center of the cluster can be
derived with XMM data, in spite of the PSF blurring.
A raw temperature profile was obtained on scales of
by fitting isothermal models to spectra extracted in 13 concentric annuli. This profile shows a sharp negative gradient
measured toward the center (
), a signature of a cooling core.
Beyond that region the profile is essentially flat. We have thoroughly
investigated projection and PSF effects on the temperature profile
determination. The PSF effects beyond
are much less
important than projection effects, whereas both are important in the
very center. We discuss the noise introduced by the correction of these
effects and a way to overcome this problem. The derived deprojected
PSF-corrected temperature profile ranges from
2 keV in the
center up to an asymptotic value of
6.5 keV.
Using this temperature profile and the density profile, we have derived
the total mass profile
for this cluster from 0.01 up to 0.5 times the virial radius.
Systematic uncertainties due to the PSF and projection correction for
the temperature profile are taken into account. We have tested
different models for the dark matter profile distribution against the
observed mass profile. A mass distribution with a cusp in the center,
as predicted from numerical simulations, is clearly preferred.
An isothermal sphere model does not provide a good fit to the data.
In a second time we tested an MQGSL model and an NFW model. Those two
types of models have similar shapes at large radii (they both scale
like r-1.5) but differ significantly at small radii. Therefore to
discriminate those two models one needs data with a high statistic
quality over a wide range of radii (i.e. covering at least two
decades). Our data set nearly fulfilled this requirement and we were
indeed able to discriminate between the two models, the NFW model
being preferred to the MQGSL model. For the NFW model, we derived a
concentration parameter
.
This value is as expected from
numerical simulations:
(Navarro et al.
1997; Eke et al. 1998) with a typical
dispersion of
(Bullock et al. 2001). This work can
be compared with the similar work on the cluster A1413 by Pratt &
Arnaud (2002). In the case of A1413, if the NFW model was
acceptable, the MQGSL model was slightly preferred. Although this
cluster is detected out to 0.7 times the virial radius, the data are
limited in the center, a shortcoming, as emphasized above, for
discriminating between those two models. Moreover, data in the center
only are not sufficient (see the work on A1983 by Pratt & Arnaud
2003). On the other hand, our result agrees with the
analysis of A2029 by Lewis et al. (2003), which clearly
favors an NFW dark matter profile. To our knowledge, this is the only
other data set which covers a similar wide radial range (0.001 to 0.1 virial radius).
The key factors in fitting the mass profiles with different dark matter models, are the resolution in the center as well as the data at large radii. To date XMM-Newton is the best satellite to compute total mass profiles, especially through its capability to derive precise temperature profiles. Nevertheless, its spatial resolution limits the investigation at the very center of galaxy clusters. A direct combined analysis of XMM-Newton and Chandra data of very well relaxed clusters seems to be an ideal path to a full description of the dark matter profile in clusters. However, one has to keep in mind that this requires an excellent cross calibration between the two satellites, so that the temperature profiles derived at various scales can be combined.
Acknowledgements
The authors thank A. C. Edge, the referee, for his useful comments ans suggestions. We thank M. Sun for providing the Chandra density profile and useful discussion. E.P. and M.A. are grateful to G. W. Pratt for his help and fruitful discussions throughout this work. We thank A. Sanderson for useful discussion. E.P. acknowledges the support of CNES, the French Space Agency. This work is based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA member states and the USA (NASA). The Space Research Organization of the Netherlands (SRON) is supported financially by NWO, the Netherlands Organization for Scientific Research.
To correct for vignetting effects we used the photon weighting method,
described in Arnaud et al. (2001). An estimate of the
vignetting-corrected number of counts in a given sky region Reg and
in a given energy band
is the sum:
Count rate estimates are less straightforward, since the effective
exposure time can strongly vary in the extraction region (from 11 ks
in regions only observed with the offset pointings up to 60 ks in
the overlapping region). However, the total count rate in a given
region is simply the sum of the count rates in various sub-regions.
The count rate can be written as
In practice we used the following convenient procedure for each camera data set: