β-model and cooling flows in X-ray clusters of galaxies

The spatial emission from the core of cooling-flow clusters of galaxies is inadequately described by a β -model. Spectrally, the central region of these clusters is well approximated with a two-temperature model, where the inner temperature represents the multiphase status of the core and the outer temperature is a measure of the ambient gas temperature. Following this observational evidence, I extend the use of the β -model to a two-phase gas emission, where the two components coexist within a boundary radius r _cool and the ambient gas alone fills the volume shell at a radius above r _cool. This simple model still provides an analytic expression for the total surface brightness profile     (Note in the first term the different sign with respect to the standard β -model.) Based upon a physically meaningful model for the X-ray emission, this formula can be used (i) to improve significantly the modelling of the surface brightness profile of cooling flow clusters of galaxies when compared to the standard β -model results, (ii) to constrain properly the physical characteristics of the intracluster plasma in the outskirts, like, e.g., the ambient gas temperature.     

Note on a polytropic β-model to fit the X-ray surface brightness of clusters of galaxies

I suggest that the β -model used to fit the X-ray surface brightness profiles of extended sources, like groups and clusters of galaxies, has to be corrected when the counts are collected in a wide energy band comparable to the mean temperature of the source, and a significant gradient in the gas temperature is observed. I present a revised version of the β -model for the X-ray brightness that applies to an intracluster gas with temperature and density related by a polytropic equation and extends the standard version that is strictly valid for an isothermal gas. Given a temperature gradient observed through an energy window of 1–10 keV typical for the new generation of X-ray observatories, the β parameter can change systematically by up to 20 per cent from the value obtained under isothermal assumption, i.e. by an amount larger than any statistical uncertainty obtained from the present data. Within the virial regions of typical clusters of galaxies, these systematic corrections affect the total gravitating mass estimate by 5–10 per cent, the gas mass by 10–30 per cent and the gas fraction value up to 50 per cent, when compared with the measurements obtained under the isothermal assumption.     

ROSAT PSPC observations of the outer regions of the Perseus cluster of galaxies

We present an analysis of four off-axis ROSAT Position Sensitive Proportional Counter (PSPC) observations of the Perseus cluster of galaxies (Abell 426). We detect the surface brightness profile to a radius of 80 arcmin (∼2.4 h⁻¹₅₀ Mpc) from the X-ray peak. The profile is measured in various sectors and in three different energy bands. First, a colour analysis highlights a slight variation of N _H over the region, and cool components in the core and in the eastern sector. We apply the β-model to the profiles from different sectors and present a solution to the, so-called, β-problem. The residuals from an azimuthally-averaged profile highlight extended emission both in the east and in the west, with estimated luminosities of about 8 and 1 ×10⁴³ erg s⁻¹, respectively. We fit several models to the surface brightness profile, including the one obtained from the Navarro, Frenk &38; White potential. We obtain the best fit with the gas distribution described by a power law in the inner, cooling region and a β-model for the extended emission. Through the best-fitting results and the constraints from the deprojection of the surface brightness profiles, we define the radius where the overdensity inside the cluster is 200 times the critical value, r ₂₀₀, at 2.7 h⁻¹₅₀ Mpc. Within 2.3  h⁻¹₅₀ Mpc (0.85 r ₂₀₀), the total mass in the Perseus cluster is 1.2 × 10¹⁵ M_⊙ and its gas fraction is about 30 per cent.     

Galaxy cluster masses without non-baryonic dark matter

We apply the modified acceleration law obtained from Einstein gravity coupled to a massive skew symmetric field,   F _μνλ  , to the problem of explaining X-ray galaxy cluster masses without exotic dark matter. Utilizing X-ray observations to fit the gas mass profile and temperature profile of the hot intracluster medium (ICM) with King 'β-models', we show that the dynamical masses of the galaxy clusters resulting from our modified acceleration law fit the cluster gas masses for our sample of 106 clusters without the need of introducing a non-baryonic dark matter component. We are further able to show for our sample of 106 clusters that the distribution of gas in the ICM as a function of radial distance is well fitted by the dynamical mass distribution arising from our modified acceleration law without any additional dark matter component. In a previous work, we applied this theory to galaxy rotation curves and demonstrated good fits to our sample of 101 low surface brightness, high surface brightness and dwarf galaxies including 58 galaxies that were fitted photometrically with the single-parameter mass-to-light ratio ( M / L )_stars. The results obtained there were qualitatively similar to those obtained using Milgrom's phenomenological Modified Newtonian Dynamics (MOND) model, although the determined galaxy masses were quantitatively different, and MOND does not show a return to Keplerian behaviour at extragalactic distances. The results obtained here are compared to those obtained using Milgrom's phenomenological MOND model which does not fit the X-ray galaxy cluster masses unless an auxiliary dark matter component is included.     

LoCuSS: the connection between brightest cluster galaxy activity, gas cooling and dynamical disturbance of X-ray cluster cores

We study the distribution of projected offsets between the cluster X-ray centroid and the brightest cluster galaxy (BCG) for 65 X-ray-selected clusters from the Local Cluster Substructure Survey, with a median redshift of   z = 0.23  . We find a clear correlation between X-ray/BCG projected offset and the logarithmic slope of the cluster gas density profile at  0.04 r ₅₀₀(α  ), implying that more dynamically disturbed clusters have weaker cool cores. Furthermore, there is a close correspondence between the activity of the BCG, in terms of detected Hα and radio emission, and the X-ray/BCG offset, with the line-emitting galaxies all residing in clusters with X-ray/BCG offsets of ≤15 kpc. Of the BCGs with  α < −0.85  and an offset <0.02 r ₅₀₀, 96 per cent (23/24) have optical emission and 88 per cent (21/24) are radio active, while none has optical emission outside these criteria. We also study the cluster gas fraction ( f _gas) within r ₅₀₀ and find a significant correlation with X-ray/BCG projected offset. The mean f _gas of the 'small offset' clusters (<0.02 r ₅₀₀) is  0.106 ± 0.005 (σ= 0.03  ) compared to  0.145 ± 0.009 (σ= 0.04  ) for those with an offset >0.02 r ₅₀₀, indicating that the total mass may be systematically underestimated in clusters with larger X-ray/BCG offsets. Our results imply a link between cool core strength and cluster dynamical state consistent with the view that cluster mergers can significantly perturb cool cores, and set new constraints on models of the evolution of the intracluster medium.     

Structural parameters of Mayall II = G1 in M31

Mayall II = G1 is one of the most luminous globular clusters (GCs) known in M31. New deep, high-resolution observations with the Advanced Camera for Surveys on the Hubble Space Telescope are used to provide accurate photometric data to the smallest radii yet. In particular, we present the precise variation of ellipticity and position angle, and of surface brightness for the core of the object. Based on these accurate photometric data, we redetermine the structural parameters of G1 by fitting a single-mass isotropic King model. We derive a core radius,   r _c= 0.21 ± 0.01  arcsec (= 0.78 ± 0.04  pc)  , a tidal radius,   r _t= 21.8 ± 1.1  arcsec (= 80.7 ± 3.9  pc)  , and a concentration index   c = log ( r _t/ r _c) = 2.01 ± 0.02  . The central surface brightness is 13.510 mag arcsec⁻². We also calculate the half-light radius, at   r _h= 1.73 ± 0.07  arcsec (= 6.5 ± 0.3  pc)  . The results show that, within 10 core radii, a King model fits the surface brightness distribution well. We find that this object falls in the same region of the   M_V   versus  log   R _h  diagram as ω Centauri, M54 and NGC 2419 in the Milky Way. All three of these objects have been claimed to be the stripped cores of now defunct dwarf galaxies. We discuss in detail whether GCs, stripped cores of dwarf spheroidals and normal dwarf galaxies form a continuous distribution in the   M_V   versus  log   R _h  plane, or if GCs and dwarf spheroidals constitute distinct classes of objects; we present arguments in favour of this latter view.     

A statistically selected Chandra sample of 20 galaxy clusters – II. Gas properties and cool core/non-cool core bimodality

We investigate the thermodynamic and chemical structure of the intracluster medium (ICM) across a statistical sample of 20 galaxy clusters analysed with the Chandra X-ray satellite. In particular, we focus on the scaling properties of the gas density, metallicity and entropy and the comparison between clusters with and without cool cores (CCs). We find marked differences between the two categories except for the gas metallicity, which declines strongly with radius for all clusters  ( Z ∝ r ^−0.31)  , outside  ∼0.02 r ₅₀₀  . The scaling of gas entropy is non-self-similar and we find clear evidence of bimodality in the distribution of logarithmic slopes of the entropy profiles. With only one exception, the steeper sloped entropy profiles are found in CC clusters whereas the flatter slope population are all non-CC clusters. We explore the role of thermal conduction in stabilizing the ICM and conclude that this mechanism alone is sufficient to balance cooling in non-CC clusters. However, CC clusters appear to form a distinct population in which heating from feedback is required in addition to conduction. Under the assumption that non-CC clusters are thermally stabilized by conduction alone, we find the distribution of Spitzer conduction suppression factors, f _c, to be lognormal, with a log (base 10) mean of  −1.50 ± 0.03  (i.e.   f _c= 0.032  ) and log standard deviation  0.39 ± 0.02  .     

Two serendipitous low-mass LMC clusters discovered with HST1

We present V and I photometry of two open clusters in the LMC down to V ∼26. The clusters were imaged with the Wide Field and Planetary Camera 2 (WFPC2) on board the Hubble Space Telescope ( HST ), as part of the Medium Deep Survey Key Project. Both are low-luminosity ( M_V ∼−3.5), low-mass ( M ∼10³ M⊙) systems. The chance discovery of these two clusters in two parallel WFPC2 fields suggests a significant incompleteness in the LMC cluster census near the bar. One of the clusters is roughly elliptical and compact, with a steep light profile, a central surface brightness μ _V (0)∼20.2 mag arcsec⁻², a half-light radius r _hl∼0.9 pc (total visual major diameter D ∼3 pc) and an estimated mass M ∼1500 M⊙. From the colour–magnitude diagram and isochrone fits we estimate its age as τ∼(2–5)×10⁸ yr. Its mass function has a fitted slope of Γ=Δlogφ( M )/Δlog M =−1.8±0.7 in the range probed (0.9≲ M /M⊙≲4.5). The other cluster is more irregular and sparse, having shallower density and surface brightness profiles. We obtain Γ=−1.2±0.4, and estimate its mass as M ∼400 M⊙. A derived upper limit for its age is τ≲5×10⁸ yr. Both clusters have mass functions with slopes similar to that of R136, a massive LMC cluster, for which HST results indicate Γ∼−1.2. They also seem to be relaxed in their cores and well contained in their tidal radii.     

Correlations of near-infrared, optical and X-ray luminosity for early-type galaxies

The relation between X-ray luminosity and near-infrared (NIR) luminosity for early-type galaxies has been examined. NIR luminosities should provide a superior measure of stellar mass compared to optical luminosities used in previous studies, especially if there is significant star formation or dust present in the galaxies. However, we show that the X-ray–NIR relations are remarkably consistent with the X-ray–optical relations. This indicates that the large scatter of the relations is dominated by scatter in the X-ray properties of early-type galaxies, and is consistent with early-types consisting of old, quiescent stellar populations.
We have investigated scatter in terms of environment, surface brightness profile, Mg₂, Hβ, Hγ line strength indices, spectroscopic age and nuclear Hα emission. We found that galaxies with high Mg₂ index, low Hβ and Hγ indices or a 'core' profile have a large scatter in L _X, whereas galaxies with low Mg₂, high Hβ and Hγ indices or 'power-law' profiles generally have   L _X < 10⁴¹ erg s⁻¹  . There is no clear trend in the scatter with environment or nuclear Hα emission.     

The intragroup medium in loose groups of galaxies

We have used the ROSAT PSPC to study the properties of a sample of 24 X-ray-bright galaxy groups, representing the largest sample examined in detail to date. Hot plasma models are fitted to the spectral data to derive temperatures, and modified King models are used to characterize the surface brightness profiles.
In agreement with previous work, we find evidence for the presence of two components in the surface brightness profiles. The extended component is generally found to be much flatter than that observed in galaxy clusters, and there is evidence that the profiles follow a trend with system mass. We derive relationships between X-ray luminosity, temperature and optical velocity dispersion. The relation between X-ray luminosity and temperature is found to be L _X∝ T ^4.9, which is significantly steeper than the same relation in galaxy clusters. These results are in good agreement with pre-heating models, in which galaxy winds raise the internal energy of the gas, inhibiting its collapse into the shallow potential wells of poor systems.     

Observations of the Sunyaev–Zel'dovich effect in the z=0.78 cluster MS 1137.5+6625

We have observed the   z =0.78  cluster MS 1137.5+6625 with the Ryle Telescope (RT) at 15 GHz. After subtraction of contaminating radio sources in the field, we find a Sunyaev–Zel'dovich flux decrement of  -421±60 μJy  on the ≈0.65 k λ baseline of the RT, spatially coincident with the optical and X-ray positions for the cluster core.
For a spherical King-profile cluster model, the best fit to our flux measurement has a core radius   θ _C=20 arcsec  , consistent with previous X-ray observations, and a central temperature decrement  Δ T =650±92 μK  .
Using this model, we calculate that the cluster has a gas mass inside a     radius of  2.9×10¹³ M_⊙  for an  Ω _M =1  universe and  1.6×10¹³ M_⊙  for  Ω _M =0.3  ,  Ω_Λ=0.7  . We compare this model with existing measurements of the total mass of the cluster, based on gravitational lensing, and estimate a gas fraction for MS 1137.5+6625 of ≈8 per cent.     

Measurement of the Sunyaev–Zel'dovich increment in massive galaxy clusters

We have detected the Sunyaev–Zel'dovich (SZ) increment at 850 μm in two galaxy clusters (Cl 0016+16 and MS 1054.4−0321) using the Submillimetre Common User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope. Fits to the isothermal β model yield a central Compton y parameter of  (2.2 ± 0.7) × 10⁻⁴  and a central 850-μm flux of  Δ I ₀= 2.2 ± 0.7 mJy beam⁻¹  in Cl 0016. This can be combined with decrement measurements to infer   y = (2.38 ±^0.36_0.34) × 10⁻⁴  and   v _pec= 400±¹⁹⁰⁰₁₄₀₀ km s⁻¹  . In MS 1054 we find a peak 850-μm flux of  Δ I ₀= 2.0 ± 1.0 mJy beam⁻¹  and   y = (2.0 ± 1.0) × 10⁻⁴  . To be successful such measurements require large chop throws and non-standard data analysis techniques. In particular, the 450-μm data are used to remove atmospheric variations in the 850-μm data. An explicit annular model is fit to the SCUBA difference data in order to extract the radial profile, and separately fit to the model differences to minimize the effect of correlations induced by our scanning strategy. We have demonstrated that with sufficient care, SCUBA can be used to measure the SZ increment in massive, compact galaxy clusters.     

Lithium depletion in G and K dwarfs

We present deep wide-field (16.4×16.4 arcmin²) Washington CT ₁ CCD surface photometry of the giant elliptical galaxy NGC 4472, the brightest member of the Virgo cluster. Our data cover a wider and deeper field than any previous CCD photometry. A single King model does not give a good fit to the surface brightness profiles of NGC 4472, but they can be fitted approximately using two King models: with the separate models representing the inner and outer regions . Surface brightness profiles for the outer region can also be fitted approximately by a de Vaucouleurs law. There is clearly a negative colour gradient within 3 arcmin of NGC 4472, in the sense that the colour gets bluer with increasing radius. The slope of the colour gradient for this region is derived to be Δ μ ( C − T ₁)=−0.08 mag arcsec⁻² for Δ log  r =1, which corresponds to a metallicity gradient of Δ[Fe/H]=−0.2 dex. However, the surface colour becomes gradually redder with increasing radius beyond 3 arcmin. A comparison of the structural parameters of NGC 4472 in C and T ₁ images has shown that there is little difference in the shapes of ellipses observed using isochromes or isophotes. In addition, photometric and structural parameters of NGC 4472 have been determined.     

Revisiting the baryon fractions of galaxy clusters: a comparison with WMAP 3-yr results

The universal baryonic mass fraction  (Ω_b/Ω_m)  can be sensitively constrained using X-ray observations of galaxy clusters. In this paper, we compare the baryonic mass fraction inferred from measurements of the cosmic microwave background with the gas mass fractions ( f _gas) of a large sample of clusters taken from the recent literature. In systems cooler than 4 keV, f _gas declines as the system temperature decreases. However, in higher temperature systems, f _gas( r ₅₀₀) converges to  ≈(0.12 ± 0.02)( h /0.72)^−1.5  , where the uncertainty reflects the systematic variations between clusters at r ₅₀₀. This is significantly lower than the maximum-likelihood value of the baryon fraction from the recently released Wilkinson Microwave Anisotropy Probe ( WMAP ) 3-yr results. We investigate possible reasons for this discrepancy, including the effects of radiative cooling and non-gravitational heating, and conclude that the most likely solution is that Ω_m is higher than the best-fitting WMAP value (we find  Ω_m= 0.36^+0.11_−0.08  ), but consistent at the 2σ level. Degeneracies within the WMAP data require that σ₈ must also be greater than the maximum likelihood value for consistency between the data sets.     

The evolution of the cluster X-ray scaling relations in the Wide Angle ROSAT Pointed Survey sample at 0.6 < z < 1.0

The X-ray properties of a sample of 11 high-redshift  (0.6 < z < 1.0)  clusters observed with Chandra and/or XMM–Newton are used to investigate the evolution of the cluster scaling relations. The observed evolution in the normalization of the   L – T , M – T , M _g– T   and M – L relations is consistent with simple self-similar predictions, in which the properties of clusters reflect the properties of the Universe at their redshift of observation. Under the assumption that the model of self-similar evolution is correct and that the local systems formed via a single spherical collapse, the high-redshift L – T relation is consistent with the high- z clusters having virialized at a significantly higher redshift than the local systems. The data are also consistent with the more realistic scenario of clusters forming via the continuous accretion of material.
The slope of the L – T relation at high redshift  ( B = 3.32 ± 0.37)  is consistent with the local relation, and significantly steeper than the self-similar prediction of   B = 2  . This suggests that the same non-gravitational processes are responsible for steepening the local and high- z relations, possibly occurring universally at   z ≳ 1  or in the early stages of the cluster formation, prior to their observation.
The properties of the intracluster medium at high redshift are found to be similar to those in the local Universe. The mean surface-brightness profile slope for the sample is  β= 0.66 ± 0.05  , the mean gas mass fractions within   R _{2500( z )}  and   R _{200( z )}  are  0.069 ± 0.012  and  0.11 ± 0.02  , respectively, and the mean metallicity of the sample is  0.28 ± 0.11 Z_⊙  .     

Constraints on dark matter physics from dwarf galaxies through galaxy cluster haloes

One of the predictions of the standard cold dark matter model is that dark haloes have centrally divergent density profiles. An extensive body of rotation curve observations of dwarf and low surface brightness galaxies shows the dark haloes of those systems to be characterized by soft constant-density central cores. Several physical processes have been proposed to produce soft cores in dark haloes, each one with different scaling properties. With the aim of discriminating among them we have examined the rotation curves of dark-matter-dominated dwarf and low surface brightness galaxies and the inner mass profiles of two clusters of galaxies lacking a central cD galaxy and with evidence of soft cores in the centre. The core radii and central densities of these haloes scale in a well-defined manner with the depth of their potential wells, as measured through the maximum circular velocity. As a result of our analysis we identify self-interacting cold dark matter as a viable solution to the core problem, where a non-singular isothermal core is formed in the halo centre surrounded by a Navarro, Frenk & White profile in the outer parts. We show that this particular physical situation predicts core radii in agreement with observations. Furthermore, using the observed scalings, we derive an expression for the minimum cross-section ( σ ) which has an explicit dependence with the halo dispersion velocity ( v ). If m _x is the mass of the dark matter particle: σ m _x ≈4×10⁻²⁵ (100 km s⁻¹  v ⁻¹) cm² GeV⁻¹.     

The black hole mass–stellar velocity dispersion correlation: bulges versus pseudo-bulges

We investigate the correlation between the supermassive black holes (SMBHs) mass ( M _bh) and the stellar velocity dispersion  (σ_*)  in two types of host galaxies: the early-type bulges (disc galaxies with classical bulges or elliptical galaxies) and pseudo-bulges. In the form  log ( M _bh/M_⊙) =α+β log (σ_*/200 km s⁻¹)  , the best-fitting results for the 39 early-type bulges are the slope  β= 4.06 ± 0.28  and the normalization  α= 8.28 ± 0.05  ; the best-fitting results for the nine pseudo-bulges are  β= 4.5 ± 1.3  and  α= 7.50 ± 0.18  . Both relations have intrinsic scatter in  log  M _bh  of ≲0.27 dex. The   M _bh–σ_*  relation for pseudo-bulges is different from the relation in the early-type bulges over the 3σ significance level. The contrasting relations indicate the formation and growth histories of SMBHs depend on their host type. The discrepancy between the slope of the   M _bh–σ_*  relations using different definition of velocity dispersion vanishes in our sample, a uniform slope will constrain the coevolution theories of the SMBHs and their host galaxies more effectively. We also find the slope for the 'core' elliptical galaxies at the high-mass range of the relation appears steeper  (β≃ 5–6)  , which may be the imprint of their origin of dissipationless mergers.     

H 0 from an orientation-unbiased sample of Sunyaev–Zel'dovich and X-ray clusters

We have observed the Sunyaev–Zel'dovich (SZ) effect in a sample of five moderate-redshift clusters with the Ryle Telescope, and used them in conjunction with X-ray imaging and spectral data from ROSAT and ASCA to measure the Hubble constant. This sample was chosen with a strict X-ray flux limit using both the Bright Cluster Sample and the Northern ROSAT All-Sky Survey (RASS) cluster catalogues to be well above the surface brightness limit of the RASS, and hence to be unbiased with respect to the orientation of the cluster. This controls a major potential systematic effect in the SZ/X-ray method of measuring H ₀. Taking the weighted geometric mean of the results and including the main sources of error, namely the noise in the SZ measurement, the uncertainty in the X-ray temperatures and the unknown ellipticity and substructure of the clusters, we find   H ₀= 59⁺¹⁰₋₉ (random)⁺⁸₋₇(systematic) km s⁻¹ Mpc⁻¹  assuming a standard cold dark matter model with  Ω_M= 1.0, Ω_Λ= 0.0  or   H ₀= 66⁺¹¹₋₁₀ ⁺⁹₋₈ km  s⁻¹ Mpc⁻¹  if  Ω_M= 0.3, Ω_Λ= 0.7  .     

The early-type galaxies NGC 1407 and NGC 1400 – I. Spatially resolved radial kinematics and surface photometry

This is the first paper of a series focused on investigating the star formation and evolutionary history of the two early-type galaxies NGC 1407 and NGC 1400. They are the two brightest galaxies of the NGC 1407 (or Eridanus-A) group, one of the 60 groups studied as part of the Group Evolution Multi-wavelength Study.
Here, we present new high signal-to-noise ratio long-slit spectroscopic data obtained at the ESO 3.6-m telescope and high-resolution multiband imaging data from the Hubble Space Telescope /Advanced Camera for Surveys and wide-field imaging from Subaru Suprime-Cam. We spatially resolved integrated spectra out to ∼0.6 (NGC 1407) and ∼1.3 (NGC 1400) effective radii. The radial profiles of the kinematic parameters v _rot, σ, h ₃ and h ₄ are measured. The surface brightness profiles are fitted to different galaxy light models and the colour distributions analysed. The multiband images are modelled to derive isophotal shape parameters and residual galaxy images. The parameters from the surface brightness profile fitting are used to estimate the mass of the possible central supermassive black hole in NGC 1407. The galaxies are found to be rotationally supported and to have a flat core in the surface brightness profiles. Elliptical isophotes are observed at all radii and no fine structures are detected in the residual galaxy images. From our results, we can also discard a possible interaction between NGC 1400, NGC 1407 and the group intergalactic medium. We estimate a mass of  ∼1.03 × 10⁹ M_⊙  for the supermassive black hole in NGC 1407 galaxy.