Constraints on turbulent velocity broadening for a sample of clusters, groups and elliptical galaxies using XMM-Newton

Abstract

Using the width of emission lines in XMM-Newton Reflection Grating Spectrometer spectra, we place direct constraints on the turbulent velocities of the X-ray emitting medium in the cores of 62 galaxy clusters, groups and elliptical galaxies. We find five objects where we can place an upper limit on the line-of-sight broadening of 500 km/s (90 per cent confidence level), using a single thermal component model. Two other objects are lower than this limit when two thermal components are used. Half of the objects examined have an upper limit on the velocity broadening of less than 700 km/s. To look for objects which have significant turbulent broadening, we use Chandra spectral maps to compute the expected broadening caused by the spatial extent of the source. Comparing these with our observed results, we find that Klemola 44 has extra broadening at the level of 1500 km/s. RX J1347.5-1145 shows weak evidence for turbulent velocities at 800 km/s. In addition we obtain limits on turbulence for Zw3146, Abell 496, Abell 1795, Abell 2204 and HCG 62 of less than 200 km/s. After subtraction of the spatial contribution and including a 50 km/s systematic uncertainty, we find at least 15 sources with less than 20 per cent of the thermal energy density in turbulence. Comment: 17 pages, 17 figures, accepted by MNRAS. Includes minor edits to proof

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Mon. Not. R. Astron. Soc. 000, 000–000 (0000)Printed 16 September 2010(MN LATEX style file v2.2)
Constraints on turbulent velocity broadening for a sample of
clusters, groups and elliptical galaxies using XMM-Newton
J. S. Sanders1, A. C. Fabian1and R. K. Smith2
1Institute of Astronomy, Madingley Road, Cambridge. CB3 0HA
2MS 6, 60 Garden Street, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA
16 September 2010
ABSTRACT
Using the width of emission lines in XMM-Newton Reflection Grating Spectrometer spectra,
we place direct constraints on the turbulent velocities of the X-ray emitting medium in the
cores of 62 galaxy clusters, groups and elliptical galaxies. We find five objects where we can
place an upper limit on the line-of-sight broadening of 500kms−1(90 per cent confidence
level), using a single thermal component model. Two other objects are lower than this limit
when two thermal components are used. Half of the objects examined have an upper limit on
the velocity broadening of less than 700kms−1. To look for objects which have significant
turbulent broadening, we use Chandra spectral maps to compute the expected broadening
caused by the spatial extent of the source. Comparing these with our observed results, we find
that Klemola44 has extra broadening at the level of 1500kms−1. RXJ1347.5-1145 shows
weak evidence for turbulent velocities at 800kms−1. In addition we obtain limits on turbu-
lence for Zw3146, Abell 496, Abell 1795, Abell 2204 and HCG 62 of less than 200kms−1.
After subtraction of the spatial contribution and including a 50kms−1systematic uncertainty,
we find at least 15 sources with less than 20 per cent of the thermal energy density in turbu-
lence.
Key words: intergalactic medium — X-rays: galaxies: clusters
1 INTRODUCTION
Measurements of the velocity structure of the intracluster medium
(ICM) are of great interest. They are important for measuring the
turbulence predicted to be injected into clusters from mergers or the
accretion of material, tracing how the central nucleus injects energy
into its surroundings, examining ICM transport properties, such as
looking at metal diffusion or sound waves, and for the determi-
nation of cluster gravitational potentials using X-ray observations.
However, there are few observational constraints on the amount of
bulk flow or random motions within the intracluster medium.
Theoretical models of the intracluster medium have predicted
that the fraction of pressure support in gas motions is typically 5
to 15 per cent (e.g. Lau et al. 2009; Vazza et al. 2009). Three-
dimensional hydrodynamic simulations typically include at most
numerical viscosity, and most do not attempt to examine the ef-
fects of magnetic fields on gas motions. Some simulations do
however attempt to model the effect of the central active nu-
cleus on the gas motions. Br¨ uggen et al. (2005) predict motions
in the range 500−1000kms−1around the central nucleus. Heinz
et al. (2010) finds cluster-wide turbulent line-of-sight velocities of
∼ 500kms−1in their simulations of clusters containing AGN jets,
examining how easily these signals would be detected by IXO.
Turbulent motions have been used to explain the lack of cool
X-ray emitting gas in the cores of galaxy clusters. Random mo-
tions of 50−150kms−1could randomize the magnetic field direc-
tion, enhancing conduction and helping suppress central cooling
(Ruszkowski & Oh 2010). Turbulence should trigger plasma in-
stabilities, giving thermally stable local heating rates comparable
to the cooling rates in the intracluster medium (Rosin et al. 2010;
Kunz et al. 2010).
Observational constraints on random turbulent motions in
galaxy clusters are mostly indirect in nature. In the elliptical galaxy
NGC4636, Xu et al. (2002) examined the strength of the resonantly
scattered 15˚ A Fe XVII line relative to the line at 17.1˚ A. The ICM
can be optically thick in the light of resonant lines given correct
temperaturesandsufficientdensities.Randommotionsdecreasethe
effect of resonant scattering because the resonant lines are velocity-
broadened. Xu et al. (2002) observed the consequences of resonant
scattering, inferring that the turbulent velocity dispersion is less
than 10 per cent of the sound speed. Werner et al. (2009) also ex-
amined this object, concluding a maximum of 5 per cent of energy
is in turbulent motions.
Random motions contribute to nonthermal ICM pressure.
Churazov et al. (2008) derived the the gravitational mass profiles
from optical and X-ray data in M87 and NGC1399. Stars act as
collisionless particles, so comparing their potentials from that de-
rived from X-ray data can measure or place limits on the nonther-
mal pressure. They obtained an upper limit on the nonthermal pres-
sure of ∼ 10 per cent of the thermal gas pressure.
One of the few constraints on turbulence in an unrelaxed
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2J.S. Sanders et al
galaxy cluster was made by Schuecker et al. (2004), who examined
the power spectrum of pressure fluctuations in the Coma cluster.
They deduced that a minimum of 10 per cent of the total pressure
in Coma is in the form of turbulence.
The shape of X-ray emission lines provides information about
velocity structure in clusters (Inogamov & Sunyaev 2003). The low
resolution spectra from CCD instruments can be used to look for
changes in bulk velocity as a function of position, if the gain of
the instrument is stable enough. Such flows were reported using
ASCA and Chandra in Centaurus (Dupke & Bregman 2001, 2006)
and other clusters (Dupke & Bregman 2005). However, Ota et al.
(2007) placed an upper limit on bulk flows of 1400kms−1in the
Centaurus cluster using Suzaku.
The only direct limit on turbulence in the X-ray waveband
came from our recent work examining the XMM-Newton Reflec-
tion Grating Spectrometer (RGS) spectra from a long observation
of the X-ray bright galaxy cluster Abell 1835 (Sanders et al. 2010).
Since this cluster is at z = 0.2523 and has a compact cool core,
the line emission is concentrated in a small region on the sky. The
broadening of the emission lines by the slitless RGS spectrometers
is therefore small. We were able to place an upper limit on the to-
tal broadening, including the turbulent component, of 274kms−1,
at the 90 per cent level. The ratio of turbulent to thermal energy
density in the core of Abell1835 is less than 13 per cent.
In this paper, we continue this work by examining RGS spec-
tra of the most point-like clusters, groups and elliptical galaxies in
the XMM-Newton archive, to obtain the best current direct limits on
turbulent velocity broadening of emission lines.
All uncertainties are at the 1σ level, unless stated otherwise.
We use the Solar relative abundances of Anders & Grevesse (1989).
2 ANALYSIS
In the first part of our analysis we measure conservative upper lim-
its on the turbulence in our sample by assuming that the objects
are point sources. We measure the total line width of the sources in
kms−1, which includes the turbulent component.
As the RGS instruments are slitless spectrometers and the ex-
amined objects are not point sources, the spectra are broadened be-
cause of the spatial extent of the source in the dispersion direction.
The effect of the broadening of the spectrum by the spatial extent
of the source is given by
∆λ ≈0.124
m
where m is the spectral order and ∆θ is the half energy width of
the source in arcmin (Brinkman et al. 1998). This broadening is be-
cause when we measure a particular dispersion angle on the detec-
tor for an X-ray photon, we cannot differentiate between a change
in wavelength and a change in position along the dispersion direc-
tion. However, there is a low resolution measurement of the energy
of each event by the CCD detector which is used to differentiate
the multiple spectral orders, also removing noise and signal from
the calibration sources.
The observed broadening of emission lines is the sum of this
spatial broadening, the thermal broadening of the ICM and any tur-
bulent motions within the observed region. If we determine what
the upper bound is to the broadening of the emission lines, beyond
the instrumental point source broadening, subtracting the thermal
broadening, we can place an upper limit on the turbulent broaden-
ing of the source. In addition we can obtain measurements of the
redshift of the objects by measuring the emission line centroids.
∆θ˚ A,
(1)
It would be useful to be able to remove the broadening due to
the source extent. To do this we need to know how the high reso-
lution spectrum of the source varies along the dispersion direction,
which is not known. We can estimate how it varies by examining
maps of the source properties (temperature, metallicity and abun-
dance) constructed using spatially-resolved spectroscopy of Chan-
dra data. These data have much lower spectral resolution than the
RGS data, so cannot remove the degeneracies completely. As the
RGS gratings and Chandra detectors are fundamentally different
kinds of instrument, with potential calibration uncertainties, a joint
analysis is difficult.
We therefore construct synthetic RGS spectra from Chandra
spectral maps of several of the sources in the sample. These spec-
tra do not contain any turbulent emission line broadening, but do
include spatial and thermal broadening. By measuring the width of
the emission lines in these theoretical spectra, and comparing them
with the width of the lines in the real spectra, we can identify ob-
jects in which there is likely to be significant turbulent velocities.
2.1 Sample selection
The objects we examined were selected on the basis of strong emis-
sion lines in order to get good limits on broadening. We examined
by eye all the clusters in the XMM-Newton archive which came
under the category ‘groups of galaxies, clusters of galaxies, and su-
perclusters’ and ellipticals in ‘galaxies and galactic surveys’. We
looked for those clusters, ellipticals or groups which had a bright
central peak in the EPIC images and emission lines in the pre-
view RGS spectra or when displayed with the XMM-Newton online
BiRD (Browsing Interface for RGS Data) interface, or gas tempera-
tures where there should be emission lines. The sample is therefore
not statistically complete or rigorous and is biased towards bright
relaxed objects.
We list the objects in Table 1 and their redshifts taken from the
NED database. As the absolute energy calibration for the RGS in-
struments depends on the source position being correct, we use the
X-ray position measurements using Chandra if possible. We use
the centroid position from the ACCEPT cluster archive (Cavagnolo
et al. 2009) if available, verifying the position from Chandra data
manually to find the X-ray peak. For those clusters without Chan-
dra observations we used the XMM EPIC peak position.
2.2Spectral extraction
We downloaded the datasets for each of the clusters listed in Ta-
ble 1 from the XMM archive. We ignored some datasets which
were very short or where the lightcurve showed strong flaring. The
datasets were processed individually through the RGS RGSPROC
pipeline (version 1.28.3, part of SAS 10.0.0). We excluded time pe-
riods where the count rate for events with flag values of 8 or 16, on
CCD 9, and an absolute cross-dispersion angle of 1.5×10−4(the
parameters used in Tamura et al. 2003), was greater than 0.2s−1.
Foreground spectra were extracted from within 90 per cent of
the PSF (point spread function) of a point source, including 90 per
cent of the peak of the pulse-height distribution (this is the CCD
measurement of energy). The selection region roughly corresponds
to a 50 arcsec wide strip across the centre of the cluster. We created
spectra for background subtraction from the region outside of 98
per cent of the PSF. Shown in Table 1 are the total cleaned exposure
times (summing the RGS1 and RGS2 exposure times) and average
foreground and background count rates.
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Turbulence in galaxy clusters3
Figure 1. Views of the NGC4261 0502120101 RGS2 dataset. The bot-
tom panel shows the X-ray events, plotting the CCD-measured energy (PI)
against the the dispersion angle on the detector. Shown are the first and sec-
ond order selection regions (corresponding to 90 per cent of the pulse height
distribution)andtheregionsforthecalibrationsources.Thetoppanelshows
those events in the first order spectrum, as a function of dispersion angle
and cross-dispersion angle. Within the solid lines are the source extraction
region (corresponding to 90 per cent of the width of a point source) and
outside the dashed lines are the background extraction region.
The wavelength binning option was used to enable spectral
binning by wavelength so that the spectra from the two RGS in-
struments could be combined. For a particular spectral order and
object, we combined the the RGS1 and RGS2 spectra, responses
and background files from the appropriate datasets.
We show in Fig. 1 the spectral extraction regions for a line-
rich bright source, NGC 4261. The bottom panel shows the dis-
persion angle of each X-ray event on the RGS2 detector plotted
against the PI (pulse invariant) value, which is a measure of the en-
ergy of the X-ray photon. The two spectral orders are split up by
the pulse height distribution selection. Also seen are the calibra-
tion source events, excluded using the rectangles shown. The top
plot shows the distribution of the first order events as a function of
cross-dispersion direction and dispersion angle.
Some of the most extended objects have background spectra
which are contaminated by cluster emission. Fig. 2 shows the back-
ground subtraction for Abell 2029 with template backgrounds gen-
erated using the SAS RGSBKGMODEL tool and with backgrounds
derived from the observation itself. For these extended objects the
spectrum from the background region is smoother than the line
emission from the centre. This is because this background emis-
sion comes from a large part of the cluster, much larger than the
core, and is highly broadened.
For Abell 2029 the line width is identical when using a tem-
Template background
Data (1st order)
Model (1st order)
Background (1st order)
Data (2nd order)
Model (2nd order)
Background (2nd order)
10-2 counts s-1 Å-1
0
0.5
1
1.5
2
2.5
3
3.5
Observation-derived background
10-2 counts s-1 Å-1
0
0.5
1
1.5
2
2.5
3
3.5
Wavelength (Å)
1015 2025
Figure 2. Comparison of background-subtracted data using backgrounds
generated from templates (top panel) and from backgrounds from the ob-
servation itself (bottom panel) for the extended cluster Abell 2029.
NGC 4261
Observation-derived background
Template background
10-3 counts s-1 Å-1
0
4
1
2
3
4
Hercules A
10-3 counts s-1 Å-1
0
1
2
3
E 1455+2232
10-3 counts s-1 Å-1
0
2.5
5
7.5
10
12.5
15
Wavelength (Å)
510152025 3035
Figure 3. Comparisons of template and observation-derived backgrounds
for three observations.
plate background or a background derived from the observation.
For some other objects, for example Centaurus, the line width
is narrower by ∼ 100kms−1using an observation-derived back-
ground because the broader component of the emission lines has
been subtracted.
We note that our background spectra for several compact ob-
jects do not match the template backgrounds generated by the SAS
RGSBKGMODEL program, even at wavelengths where the RGS in-
struments have little effective area. Although some objects such as
NGC 4261 (Fig. 3) match the template backgrounds well, others
such as Hercules A and E1455+2232 show substantial mismatches
between the templates and observed background at short wave-
lengths.
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4J.S. Sanders et al
2.3Spectral fitting
For each object we simultaneously fit the spectra with an APEC
1.3.1 spectral model (Smith et al. 2001). In the spectral model we
fit the temperature, Galactic absorbing column density, emission
measure and abundances for O, Ne, Mg, Si, Fe and Ni. All other
elemental abundances were fixed to the have the same ratio relative
to Solar as Fe, as their emission lines were weak in the wavelength
range examined. The lines in the spectral model were given Gaus-
sian line widths. The width of the lines were the appropriate ther-
mal line widths for an ion at the model temperature, plus an addi-
tional velocity width added in quadrature, which was a free param-
eter in the fits. This additional velocity parameter is of most interest
here, as it includes the turbulent broadening and spatial broadening
of the object. The redshift of the thermal model is also a free pa-
rameter in the spectral fitting.
We simultaneously fit the first order spectra between 7 and
28˚ A and second order spectra between 7 and 17˚ A, minimising the
XSPEC modified Cash statistic when fitting. We used XSPEC ver-
sion 12.6.0. Using C statistics rather than χ2allows us to not bin or
group the spectra, helping preserve the energy resolution.
The spectral fitting results are shown in two tables. Table 2
lists the best fitting temperature, column density and metallicities.
Table 3 shows the best fitting redshift and 90 per cent upper limit
on the line broadening, in kms−1.
Some of the cooler objects are extremely line dominated. For
these objects the continuum and emission measure are hard to
determine. This leads to large uncertainties on the metallicities,
which are measured relative to the continuum. Where the metal-
licity uncertainties are large, we fix the Fe metallicity to Solar. The
other metallicites and emission measures become much better de-
termined when this is done. These objects are listed as having Fe
equal to 1 in Table 2.
We show the 90 per cent upper bound on the broadening of
the emission line in Fig. 4. These were calculated with the XSPEC
error command, which examines how the fit quality changes when
a model parameter is stepped over a range of values.
These values are only upper limits because we do not know
the effect of the extent of the source in the measurements, which
may be the dominant contribution. To show whether the the upper
limit is primarily due to the quality of the spectrum or whether the
width of the emission line well determined, we also plot the best
fitting broadening and its 1σ error bars in Fig. 5. The cumulative
distribution of broadening upper limits is shown in Fig. 6. Seven
of the objects have upper limits less than 500kms−1. We show
rebinned spectra of these objects in Fig. 7 with their best fitting
spectral models. There are also two objects which give limits better
than 500kms−1for a second temperature component added to the
model (NGC 4636 and Abell S1101).
To demonstrate how we measure our limits, plotted in Fig. 8
is the change in fit quality as a function of broadening velocity for
Zw3146. The plot shows that for this object we are able to very
good limits using either of the spectral orders, or both combined.
For some objects (Abell 262, 2A 0335+096, NGC 4636, Cen-
taurus, Abell 3581, Abell 1991, Abell 2052 and Abell S1101), sin-
gle component models are poor fits to the spectra. The models do
not properly fit the Fe XVII emission lines in the spectrum. For
those objects we added a second thermal component to account for
the lower temperature gas in the core of the cluster. This cooler
component was tied to the same metallicities and redshift as the
hotter one. We allowed the cooler component to have a different
line broadening. As this cooler material is concentrated in the cores
of these objects it is likely to have a smaller line width because the
spatial broadening effect is lower. We show the upper limits for the
velocity broadening for the cooler component separately in Table 3
and plot them in Fig. 4.
We looked for other second thermal components in the re-
maining sample of objects by automatically fitting models. We did
not find any objects where the parameters for a second thermal
component were distinct from the first component, or where the
new line width was well constrained.
2.4Markov Chain Monte Carlo
Conventional spectral fitting and error estimation can sometimes
underestimate the likely range of model parameters which can fit
data. An alternative way to determining the model parameter space
probability distribution is to use a Markov Chain Monte Carlo
(MCMC) method.
We applied the MCMC routine built into XSPEC, which uses
the Metropolis-Hastings algorithm to sample parameter space, con-
structing a chain of parameter values. The algorithm starts from
a particular point in parameter space. A new set of parameters is
selected by adding values from a proposal distribution (here a N-
dimensional Gaussian) to the current parameters. If the quality of
fit is better for the new parameters, they are ‘accepted’ and become
the next point in the chain. If they have a worse fit, they are ac-
cepted randomly with a probability which depends on the increase
in the fit parameter. The parameters are otherwise rejected and the
next point on the chain is the existing point.
Such a method explores parameter space around the best fit.
The fraction of chain values in a particular parameter space region
should be related to the likelihood of those model parameters un-
der certain conditions. These include that the proposal distribution
should be big enough to explore parameter space (it will take too
long to converge if it is too small), but not so large that few points
are accepted in a chain. The length of the chain required to sam-
ple parameter space depends on factors such as the proposal width
and how complex the parameter space is. Unfortunately it is diffi-
cult to tell when a chain has sufficiently converged. We manually
examined the results of the chain over its run to check that it was
covering parameter space randomly and we also checked that the
repeat fraction of the chain was close to the rule-of-thumb value of
0.75, which indicates the proposal distribution is correct.
We used the XSPEC MCMC routines to examine the uncer-
tainties on the the broadening of the emission lines for a number of
objects. We imposed the following priors on the acceptable range
of parameter values:
(i) The redshift of the object should not vary from the NED
value by more than 1500kms−1.
(ii) The Galactic column density to the object should not vary
from the average values of Kalberla et al. (2005) by more than 20
per cent.
(iii) Elemental abundances should lie between 0.2 and 1Z?.
Although these were not necessary for most objects, for some ob-
jects the chain wandered into very unlikely regions of parameter
space and could not move back. For three objects, Abell 2667,
E 1455+2232 and Kelmola 44, we had to impose a fixed redshift
on the chain because of the data quality.
We used an initial proposal distribution based on the uncer-
tainties of each parameter using the XSPEC error command. We
started the chains from the best-fitting values, discarding the first
2000 values (the burn in period) and using a chain length of 40000
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Turbulence in galaxy clusters5
Velocity limit (km s-1)
100
1000
104
Abell 133
NGC 499NGC 533
Abell 262
NGC 777
Abell 383
NGC 1316NGC 1399
2A 0335+096
NGC 1404NGC 1550
RBS 540
Abell 496
RXC J0605.8-3518
NGC 2300
MS 0735.6+7421
PKS 0745-19
Hydra A
RBS 797
Zw3146
Abell 1068
RXC J1044.5-0704
NGC 3411
RXC J1141.4-1216
Abell 1413
MKW 4
NGC 4261NGC 4325NGC 4472NGC 4552NGC 4636NGC 4649
Centaurus
HCG 62
Abell 1650
NGC 5044
Abell 3558
RX J1347.5-1145
Abell 1795Abell 3581Abell 1991
E 1455+2232
NGC 5813
RXC J1504.1-0248
NGC 5846
Abell 2029Abell 2052
MKW 3s
Abell 2063Abell 2199Abell 2204
Hercules A
RX J1720.1+2638
RXC J2014.8-2430
RX J2129.6+0005
RXC J2149.1-3041
Abell S1101
Abell 2597Abell 2626
Klemola 44
Abell 2667Abell 4059
Single-component upper limitTwo-component upper limit
Figure 4. Upper limits (90 per cent) on the turbulent velocity broadening of the spectra. Shown are the limits for single thermal component modelling for all
objects, and two temperature modelling for selected objects.
Velocity (km s-1)
100
1000
104
Abell 133
NGC 499 NGC 533
Abell 262
NGC 777
Abell 383
NGC 1316NGC 1399
2A 0335+096
NGC 1404 NGC 1550
RBS 540
Abell 496
RXC J0605.8-3518
NGC 2300
MS 0735.6+7421
PKS 0745-19
Hydra A
RBS 797
Zw3146
Abell 1068
RXC J1044.5-0704
NGC 3411
RXC J1141.4-1216
Abell 1413
MKW 4
NGC 4261NGC 4325NGC 4472NGC 4552NGC 4636NGC 4649
Centaurus
HCG 62
Abell 1650
NGC 5044
Abell 3558
RX J1347.5-1145
Abell 1795 Abell 3581Abell 1991
E 1455+2232
NGC 5813
RXC J1504.1-0248
NGC 5846
Abell 2029Abell 2052
MKW 3s
Abell 2063Abell 2199Abell 2204
Hercules A
RX J1720.1+2638
RXC J2014.8-2430
RX J2129.6+0005
RXC J2149.1-3041
Abell S1101
Abell 2597Abell 2626
Klemola 44
Abell 2667Abell 4059
Upper limitNarrow LSF limitBroad LSF limit Best fitting valueMCMC limit
Figure 5. A comparison between the upper limits on the line widths obtained with the standard calibration, and responses in which the LSF is 10 per cent
narrower or 10 per cent broader than standard. The continuous line shows the upper limits derived from the MCMC analysis. Also plotted are the best fitting
line width and 1σ error bars, which include the spatial component of broadening.
steps. We took the parameter distribution from this chain and used
it to create a proposal distribution for a second chain with the same
length. We discarded the first chain (used to get a reasonable pro-
posal distribution) and used the second chain to calculate the re-
sults. In Fig. 9 are shown the temperature, velocity, redshift and fit
statistic as a function of chain step for Zw3146.
In Fig. 5 are plotted the 90 per cent upper limit from the chains
for the velocity broadening, marginalising over the other parame-
ters. We get good agreement between our upper limits and those
from conventional spectral fitting for most objects. There are ex-
ceptions to this, including RBS 797, RXJ2129.6+0005, Abell 2667
and Klemola 44. These objects appear to have a long tail in the
marginalised probability distribution for the velocity broadening,
often with an inner tighter core. In the case of Klemola 44, the
cluster occupies much of the region used to extract spectral back-
grounds. If a template background is used instead for this object,
the best fitting velocity broadening is 3200+950
the limit obtained using MCMC.
−600kms−1, close to
2.5 Response line spread function
Fitting the line shape of bright point-like objects such as Capella in-
dicates that systematic uncertainties remain in the line spread func-
tion (LSF) of the RGS instruments (den Herder, private communi-
cation). If the intrinsic spectral resolution is different from the cal-
ibrated value, this would lead to an incorrect determination of the
additional line width caused by the extent of the source or motions
within the object.
We have approached this problem by adjusting the calibration
of the RGS LSF to see the effect on our upper limits. The RGSRM-
FGEN response generation tool in SAS supports the use of an op-
tional FUDGE header keyword in the FIGURE part of the RGS1
and RGS2 LINESPREADFUNC 0004.CCF calibration files. This
parameter is used to adjust the width of the narrow part of the LSF.
We repeated our analysis using values where this width was in-
creased and decreased by 10 per cent, using fudge values of 1.1
and 0.9, respectively.
The upper limits derived using these manipulated line spread
functions are also shown on Fig. 4. The effect of this on many ob-
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