SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


Astron. Astrophys. 351, 413-432 (1999)

Previous Section Next Section Title Page Table of Contents

2. Cluster sample and its X-ray data

2.1. Cluster sample and its X-ray observations

Selecting 16 distant and rich clusters with [FORMULA] and [FORMULA]) from a complete sample of distant rich clusters selected from the EMSS, LF94 performed a medium-deep [FORMULA] and I imaging for a GLA survey and found 6 GLAs.

X-ray observations for all the 16 clusters in the LF94 sample were performed by ROSAT HRI . The HRI data of 11 clusters were taken from the ROSAT Archive at Max-Planck-Institut für Extraterrestrische Physik (MPE). The HRI data of remaining clusters were obtained by our own proposals. The instrument HRI had [FORMULA] FWHM resolution and was sensitive for an energy range of [FORMULA] keV (Trümper 1984), which makes HRI the best instrument to date to perform detailed observation of the ICM distribution in distant clusters. In Table 1, we list the log of the ROSAT HRI observations. The column density of the galactic hydrogen in 6th column in the Table 1 is calculated using EXSAS  1 command `CALCULATE/GALACTIC_NH' which calculates the galactic hydrogen column density toward the specified direction and is based on Dickey & Lockman (1990). Our observation revealed that MS 1333.3+1725 was not a cluster but an X-ray point source.


[TABLE]

Table 1. The log of ROSAT HRI observations of the sample clusters.


2.2. ROSAT HRI data reduction

We used EXSAS and XSPEC  2 analysis packages to reduce the data. The position of point sources higher than [FORMULA] is determined via standard source detection pipeline for HRI data in EXSAS . The cluster center was determined as the brightest X-ray peak. Accuracy of ROSAT HRI pointing was checked with both Hambrug RASS Catalog of Optical ID (HRASSCAT) and ROSAT SIMBAD identifications (ROSID) 3. Positions of sources higher than [FORMULA] were compared with positions of objects cataloged in HRASSCAT or ROSID. The vignetting of the ROSAT HRI was less than 5% within a radius of 5 arcminutes (i.e. 600 pixels) from the detector center at all energy range of [FORMULA] keV for which the ROSAT HRI was sensitive. Thus we restricted our analysis to the inner 600 pixels of each image, where the background can be regarded as flat.

2.3. Data analyses

Photon event tables were binned into radial rings to make azimuthally averaged surface brightness profiles. The width of each ring was determined in order that the number of photons in each bin become greater than or equal to 25 to ensure that [FORMULA] fitting could be performed, and that the size of each bin become greater than or equal to [FORMULA]. A radial surface brightness profile was then constructed by summing up the counts in each bin. Note that all the contaminating point sources which were higher than [FORMULA] were excluded from the photon counting.

The radial surface brightness profile was fitted via [FORMULA]-minimization routine to (Cavaliere & Fusco-Femiano 1976)

[EQUATION]

where [FORMULA] is the central surface brightness, [FORMULA] is the angular core radius, and B is the background. It was physically interpreted that [FORMULA] described the ratio of the kinetic energy per unit mass of the member galaxy to that in the ICM if cluster galaxy and the ICM distributions are isothermal and galaxy velocity dispersion is isotropic. Therefore, the surface brightness distribution described by the Eq. (1) was called isothermal [FORMULA] model. However, it seems that such a situation is far from the reality (Lubin & Bahcall 1993; Bahcall & Lubin 1994). Therefore, Eq. (1) has no meaning more than a conventional fitting model. We call the [FORMULA] model described by the Eq. (1) `standard [FORMULA] model ' in this paper. The background value was first determined via the above fitting. Removing the background from the image we then checked that the radial source photon counts remained constant outside the cluster source region, if not we modified the background value accordingly, and we re-did the standard [FORMULA] model fitting. In Table 2, we list the standard [FORMULA] model fitting result. The bracketed numbers in 6th column is the edge within which source photon numbers are counted.


[TABLE]

Table 2. The result of standard [FORMULA] model fitting.
Notes:
[FORMULA] Fixed. See Sect. 2.4.
[FORMULA] Assumed to estimate the upper limit of [FORMULA].


2.4. X-ray properties of the sample clusters

We list fluxes, luminosities and temperatures of the sample clusters calculated using the best-fit values of the standard [FORMULA] model fitting on the left side of each column in Table 2. Fluxes in the [FORMULA] keV band were calculated on the XSPEC using Raymond-Smith thermal plasma model assuming 30% of solar metallicity. The calculation of the flux requires the value of the temperature. For clusters who have no ASCA observation, the temperature of 6 keV was first assumed and the temperature was calculated iteratively using the 2-10 keV X-ray luminosity-temperature ([FORMULA]) relation of Arnaud & Evrard (1998, henceforth AE98) until the temperature converges. When ASCA temperature ([FORMULA]) was available, we used it to compute the X-ray flux and luminosity of the clusters. This luminosity was then used to compute the expected temperature from the [FORMULA] relation (we specify this in Table 4 by bracketing the temperatures with parentheses in column 6).


[TABLE]

Table 3. The result of ENF98 [FORMULA] model fitting.
Notes:
[FORMULA] Fixed. See Sect. 2.4.



[TABLE]

Table 4. Flux, luminosity and temperature of the sample clusters.
Notes:
[FORMULA] From standard [FORMULA] model (See Sect. 2.3) fitting results.
[FORMULA] From ENF98 [FORMULA] model (See Sect. 3.3) fitting results.
[FORMULA] From the luminosity-temperature relation in Arnaud & Evrard (1998). See Sect. 2.4.
[FORMULA] From ASCA observations.
[FORMULA] From Mushotzky & Scharf (1997).
[FORMULA] From Henry (1997).
[FORMULA] Power low model with photon index of 1.8.


Although the [FORMULA] relation of AE98 was derived from nearby cluster sample, we used it for our distant cluster sample assuming no evolution of [FORMULA] relation. David et al. (1993, henceforth D93) also derived 2-10 keV [FORMULA] relation in ([FORMULA],[FORMULA])=(0, 0) cosmology using Raymond-Smith thermal plasma model but they assumed 50% of solar metallicity which is too high value for the ICM. Since AE98 showed the [FORMULA] relation in ([FORMULA],[FORMULA])=(1, 0) cosmology, we re-plotted the [FORMULA] diagram in ([FORMULA],[FORMULA])=(0.3, 0.7) cosmology. The [FORMULA] relation we used is [FORMULA], where [FORMULA] is X-ray temperature in keV and [FORMULA] is 2-10 keV X-ray luminosity in [FORMULA], and where [FORMULA]. As AE98 discussed, their [FORMULA] relation has the slope of [FORMULA] steeper than D93 but the [FORMULA] relation of AE98 in ([FORMULA],[FORMULA])=(0.3, 0.7) cosmology is rather consistent with D93. Mushotzky & Scharf (1997) reported the [FORMULA] relation for distant clusters and showed that there was no evolution of [FORMULA] relation up to [FORMULA] comparing with the sample of D93. In Table 5, we list central electron number densities ([FORMULA]), central cooling times ([FORMULA]), ages of the universe at the cluster's redshift ([FORMULA]), cooling radii ([FORMULA]), and mass-flow rates ([FORMULA]) for sample clusters. The central electron number density was calculated using rest frame 0.5-2.0 keV HRI luminosity assuming the gaunt factor of [FORMULA] (Henry & Henriksen 1986), where h is the Plank constant, [FORMULA] is the frequency, [FORMULA] is the Boltzmann constant, and [FORMULA] is the X-ray temperature, and one-ninth of the hydrogen number density for the helium number density is assumed. The cooling radius is defined as the radius where [FORMULA]. The cooling mass-flow rate was calculated using Eq. (2) in Fabian (1994).


[TABLE]

Table 5. Central electron number density, cooling time, cooling radius and mass-flow rate of sample clusters.
Notes:
[FORMULA] From standard [FORMULA] model (See Sect. 2.3) fitting results.
[FORMULA] From ENF98 [FORMULA] model (See Sect. 3.3) fitting results.


Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999
helpdesk.link@springer.de