XMM-NEWTON OBSERVATIONS OF THREE LOW X-RAY LUMINOSITY GALAXY CLUSTERS

The cleaned MOS1 and MOS2 data were exposure-corrected and added together to create a combined image to investigate the X-ray surface brightness profiles of the clusters. The exposure map used was normalized to the maximum exposure value to maintain the number of counts in the final image. A two-dimensional surface profile was fit to the sources using the SHERPA tool found in CIAO. Due to the small number of counts, even after binning the images over 64 pixels (32 × 32), the C-statistic (Cash 1979) was used to determine the maximum likelihood statistic for minimization. The fitted model includes a circular beta profile (Cavaliere & Fusco-Femiano 1976) of the form

$$\begin{equation} S(r)=S_0\left[ 1+ \left(\frac{r}{r_{\rm core}}\right)^2\right]^{-3\beta +0.5} \end{equation} \tag{ 1 }$$

plus a constant background. This fit function is typical of the X-ray surface brightness profiles of the inner regions of many X-ray clusters. Given the small number of counts, using such a function to estimate aperture corrections is our only option. The β parameter was fixed to 2/3 (Jones & Forman 1984) for all clusters. The best-fit value of r_core for each X-ray source can be found in Table 2.

Because the mean surface brightnesses of these sources are low, choosing an aperture that maximized the signal-to-noise ratio of our spectra was essential for the best temperature estimate. To determine the best aperture size for spectral extraction, we first fit a radial profile to the cluster emission. The radius of the aperture was then selected to be the radius at which the background noise began to dominate the total counts. The spectral extraction aperture used for each cluster can be found in Table 2. The spectra were binned such that each bin contained at least 20 total counts (25 in the case of KDCS112) to improve the signal-to-noise ratio in each bin. The average percentage of the total counts that are signal counts after background subtraction is 21.7%, 26.8%, and 27.8% for RX J0110, RX J1011, and KDCS112, respectively. The redistribution response functions and ancillary response functions were generated using the rmfgen and arfgen SAS tasks, respectively. The background was estimated from an annulus of width ∼60'' around the region of interest in all cases. In order to minimize chip-to-chip differences, the background region was chosen to completely lie on the same chip as the cluster was.

For each cluster, the spectra from the MOS1 and MOS2 detector were fit simultaneously to an absorbed APEC emission spectrum model from 0.5–5.0 keV using XSPEC (Arnaud 1996). Since the net number of counts in each cluster was of order 100, the absorbing N_H column density was fixed to the galactic level determined by Kalberla et al. (2005) and can be found in Table 1. The metallicity was fixed to 0.3 solar relative to Anders & Grevesse (1989) for all the clusters. The temperature and normalization parameters were allowed to vary and the best-fit model was found. Our results are found in Table 2. The given luminosities are unabsorbed bolometric luminosities (in practice, 0.01–16 keV) of the best-fit model and the errors cited are those given by XSPEC, which includes the uncertainty in the temperature. The luminosity measured from within the region of spectral extraction is labeled as L_Detected in Table 2. In order to compare our measured values of luminosity to previous works, we also include an estimated value of the bolometric luminosity within r₅₀₀, the projected radius at which the interior density is 500 times the critical density (=3H(z)²/8πG). We estimated the size of r₅₀₀ via its relationship with the spectral temperature given by Willis et al. (2005):

$$\begin{equation} r_{500} = 0.391T_x^{0.63} h_{70}(z)^{-1} \rm {Mpc}. \end{equation} \tag{ 2 }$$

The X-ray luminosity at r₅₀₀ (L_X(r < r₅₀₀)) was estimated by extrapolating from the luminosity measured within our X-ray aperture using the best-fit radial profile found in the previous section out to r₅₀₀. Typical aperture correction factors from detected flux to total flux lie between 1.2 and 1.3 for these clusters. Uncertainties in r₅₀₀, r_core, and the detected luminosity were propagated to derive an uncertainty in L_X(r < r₅₀₀). While we fixed β = 2/3 when fitting the surface brightness profile (Section 3.1), this parameter has been observed to vary in clusters of similar temperature and redshift (Willis et al. 2005; Jeltema et al. 2006). To properly account for this uncertainty, we refit the surface brightness profiles with β = 0.5 and β = 0.75 to determine how much this affects our estimation. This resulted in an uncertainty of ∼10% which has been included in the uncertainties listed in Table 2. However, it should be noted that the uncertainties in the best fit r_core dominate the uncertainty due to the specific choice of β. We also note that both the slope and the normalization of the Willis et al. (2005) relation is different from more recent results obtained with Chandra and XMM-Newton (e.g., Sun et al. 2009). However, this difference changes our estimate of both r₅₀₀ and L(r < r₅₀₀) very little. We can compare our estimates against those given by Sun et al. (2009), if we assume that the temperature we measure within our aperture is the same as that at r₅₀₀. The comparisons can be found in Table 2. As can be seen, both relationships produce statistically indistinguishable results. We will use the Willis et al. (2005) relationship throughout this paper as their measurement procedure most closely matches the procedure used in this paper.

Vikhlinin et al. (1998) give ROSAT fluxes of RX J0110 and RX J1011 of (7.8 ± 1.6) and (4.7 ± 1.2) × 10⁻¹⁴ erg cm⁻² s^-1, respectively, from 0.5 to 2.0 keV. Converting these fluxes to luminosity at the redshift of the clusters measured by Mullis et al. (2003), the ROSAT measured luminosity is (2.6 ± 0.5) × 10⁴³ erg s⁻¹ and (1.7 ± 0.4) × 10⁴³ erg s⁻¹, respectively. Applying a bolometric correction from the APEC model within XSPEC at the cluster redshift and XMM-Newton temperature gives an estimated bolometric luminosity of (3.71 ± 0.7) and (2.92 ± 0.7) × 10⁴³ erg s⁻¹, respectively. Our measured X-ray luminosity of RX J0110 of (2.52 ± 0.7) × 10⁴³ erg s⁻¹ is consistent with the previous ROSAT measurement. However, our measurement of the X-ray luminosity of RX J1011, at (0.8 ± 0.4) × 10⁴³ erg s⁻¹, is much lower than the previous ROSAT measurement. The ROSAT measurement was likely contaminated by a point source that is ∼10 from the center of the cluster emission. The FWHM of the point-spread function (PSF) of the PSPC detector is ∼05 for photons of 1.0 keV when detected on-axis, and ∼10 for photons of 1.0 keV when detected far off axis (Gunther et al. 1993; Hasinger et al. 1992). (In contrast, the XMM-Newton PSF FWHM is 4''–6'', which makes distinguishing between the arcminute-scale extended emission of a cluster from a point source relatively straightforward.) Because the survey of Vikhlinin et al. (1998) was a serendipitous survey, the galaxy cluster was not observed on axis, but instead 84 from the center of the field. The FWHM of the Gaussian fit to the PSF is ∼15'' (Gunther et al. 1993) at this distance from the center of the field. As a result of the overlap, the emission of the two objects overlapped around the 2σ ROSAT surface brightness contour. This overlap may have been enough to contaminate the flux estimation by Vikhlinin et al. (1998). If we include the point source in the flux measurement region, we infer a bolometric luminosity of (2.5 ± 0.4) × 10⁴³ erg s⁻¹ which is consistent with the previously measured value by Vikhlinin et al. (1998). The revised luminosity of RX J1011 makes it one of the lowest luminosity X-ray clusters with a known X-ray temperature at z > 0.3.

The central electron density was estimated by using the spectra normalization parameter in the best-fit model within XSPEC and the emission integral–central density relation for a self-consistent, isothermal gas having a beta-model distribution given by Sarazin (1986):

$$\begin{eqnarray} \rm {EI} & = & 3.09\times 10^{66}\ \rm { cm}^{-3}\\ &&\times \left(\frac{n_0}{10^{-3} \,\rm { cm}^{-3}} \right)^2 \left(\frac{r_c}{0.25 \,\rm {Mpc}} \right)^3 \frac{\Gamma \left(3\beta - \frac{3}{2}\right)}{\Gamma (3\beta)}, \nonumber \end{eqnarray} \tag{ 3 }$$

where n₀ is the proton density, r_c is the core radius of the beta-model distribution, and

$$\begin{equation} {\rm EI} \equiv \int n_e n_0 \,dV. \end{equation} \tag{ 4 }$$

The normalization parameter for the APEC model found in XSPEC is

$$\begin{equation} \frac{10^{-14}}{4\pi \left(D_A [1+z]\right)^2} \int n_e n_0 \,dV, \end{equation} \tag{ 5 }$$

where D_A is the angular diameter distance in units of cm, n_x has units of cm⁻³, and dV has units of cm³. Combining Equations (3) and (5) via Equation (4) allows the calculation of n₀ given the best-fit surface brightness model found in Section 3.1 and the normalization of the best-fit spectral model. We assumed that n_e/n₀ = 1.2. Estimated central electron density for each cluster is provided in Table 2. The uncertainty was estimated by propagating the spectral and spatial fit uncertainties throughout the calculation, including the uncertainties in the normalization parameter and r_c. This central electron density estimate assumes spherical symmetry, but past studies have shown that assuming more general ellipsoidal gas distributions would not affect our estimate or our error budget, which is dominated by statistical noise (e.g., Donahue 1996).

Both RX J1011.0+5339 and KDCS112 (XMMU J101119.6 +533436) are nearly identical in their X-ray properties and are separated by ∼6', yet each one was missed in the survey that discovered the other. In this section, we solve this mystery. We note that the ability to deal with point-source contamination is essential for accurate luminosities of clusters, particularly faint clusters, and therefore spatial resolution is essential for faint-cluster counts and luminosity functions.

KDCS112 was not detected in the 160 Square Degree Survey (Vikhlinin et al. 1998), an X-ray-selected sample. In this survey, the useful exposure length of the observation and the location of the cluster in the focal plane determine how luminous an object would have to be detected. The ROSAT exposure (RP700264N00) that included RX J1011.0 and KDCS112 was 14.8 ks in length. For an exposure of this length, the limiting flux of the 160SD Survey was ≈1.5 × 10⁻¹³ erg cm⁻² s⁻¹ in the 0.5–2.0 keV energy band (Vikhlinin et al. 1998). We measured the flux of KDCS112 to be 6.80(±1.63) × 10⁻¹⁴ erg cm⁻² s⁻¹ in the same energy band, which is below the detection threshold. KDCS112 was previously identified in the WARPS Survey (as WARPS J1011.3+5333) by Horner et al. (2008) who noted its proximity to a point source. It was not included in the WARPS cluster catalog because after correction for the point source, the estimated flux of the cluster was fainter than the flux limit of the survey (6.5 × 10⁻¹⁴ erg cm⁻² s⁻¹). Our measurement of the flux of the cluster is consistent with the point-source-corrected flux estimate made by Horner et al. (2008). Ironically, RX J1011.0 has an even lower X-ray luminosity than KDCS112. As discussed in Section 3.1, the ROSAT luminosity of this source was overestimated because of an unresolved point source. With XMM-Newton's spatial resolution we were able to exclude this contaminating source from the L_x estimate.

RX J1011 was not detected in the KPNO/DEEPRANGE Distant Cluster Survey (Postman et al. 2002), an optically selected sample that used the matched filter technique to locate clusters. This technique looks for locations in a galaxy catalog that best matches the pre-defined filter. This filter includes such properties as cluster core radius, the characteristic galaxy magnitude, and the cluster luminosity function. If a location maximizes the likelihood function of matching the filter in two different filters (V and I in the case of Postman et al. 2002), then the routine says that there is a galaxy cluster at that location.

The first method we used to determine if the cluster should have been detected in the survey exploits the X-ray luminosity–optical luminosity relationship observed by Donahue et al. (2001). Correcting for the cosmology used in that paper, it was observed that

$$\begin{eqnarray} \log L_{44} &=& (-3.6 \pm 0.7) + (1.6 \pm 0.4) \log \Lambda _{\rm cl} \nonumber\\ &&- 2 \log h_{70} - 0.059, \end{eqnarray} \tag{ 6 }$$

where L_x = L₄₄ × 10⁴⁴ ergs⁻¹ and Λ_cl is the total optical luminosity of the cluster divided by L^⋆, the location of the knee of the luminosity function (Schechter 1976). Accounting for the large intrinsic scatter in the relationship, an estimate of Λ_cl = 40(±20) is reasonable based on the projected r₅₀₀ luminosity of 0.80^+0.77_−0.42 × 10⁴³ erg s⁻¹. At the redshift of this cluster, if the true value of Λ_cl is at the lower end of the uncertainty, then the survey only claims to be approximately 60% complete. As a result, it is not surprising that the survey failed to find the cluster.

To estimate Λ_cl directly, we used data from the SDSS Data Release 7 (Abazajian et al. 2009). We selected objects within a projected radius of 0.5 Mpc from the coordinates of the X-ray emission centroids. To ensure that we were looking at cluster members, extremely bright stars were removed as well as all objects that were more than 0.4 mag in g' − r' color away from the observed red sequence of each cluster. Because L_Cluster = Λ_clL^⋆ (Donahue et al. 2001), we can obtain an estimate of Λ_cl by summing the total luminosity of cluster members and dividing by L^⋆, the knee in the commonly used Schechter luminosity function (Schechter 1976). Hansen et al. (2005) analyzed the composite luminosity function of galaxy clusters in the redshift range of our clusters and found that for clusters with the same number of galaxies as our clusters, M^⋆ = −20.7 ± 0.04. Converting M^⋆ to L^⋆ at the redshift of each cluster allows us to estimate Λ_cl. For KDCS112, we find 90 ± 22, while RXJ1011 and RXJ0110 are poorer optically, at 34 ± 13 and 43 ± 11, respectively (Table 2). Our measurement of KDCS112 is consistent with the previous measurement by Postman et al. (2002), where they found Λ_cl = 79.2. Our direct measurement of Λ_cl in RX J1011 is consistent with our estimate via the X-ray luminosity, supporting the idea that RXJ1011 is indeed optically too poor to have been detected in the KPNO/DEEPRANGE Distant Cluster Survey.

In some sense, RXJ1011 should no longer be considered a proper member of the 160SD sample, because its inclusion was an accident of its proximity to an X-ray point source. On the other hand, it represents one of the poorest and lowest L_x clusters with a known T_x at moderate redshift, and therefore is a cluster of interest to us.

To be sure, the scatter in the relationship between Λ_cl and L_X is enormous (Donahue et al. 2001). Subsequent studies show similar results. For example, Bahcall et al. (2003) found eight clusters with X-ray measurements from the NORAS X-ray cluster catalog (Böhringer et al. 2000) in the early Sloan commissioning data. Six of those clusters have Λ_cl similar to the clusters in our sample (42–50), but the X-ray luminosities were significantly higher than our sample (L_x ∼ 0.83–8.65 × h⁻²10⁴⁴ erg s⁻¹). Lopes et al. (2006) compare X-ray galaxy clusters from a heterogeneous list (BAX) to an optical galaxy cluster catalog extracted from analysis of the Digitized Palomar Sky Survey. In comparison to this sample, the three clusters have typical X-ray and optical properties. The T_x-richness comparison suggests that the three clusters in our study are all a little cool (low T_x) compared to their optical richness. However, this feature could be a selection bias, in that very few of the BAX clusters in this study have T_x < 2 keV in any case.

We see very little difference between the X-ray properties of these clusters and clusters at low redshift. In Figure 4, we compare the L and T measurements for these clusters to the GEMS low-redshift group sample (Osmond & Ponman 2004), the ASCA/ROSAT low-redshift cluster sample of Markevitch (1998), the low-redshift (z < 0.3) clusters from the XMM-Newton Large Scale Structure (XMM-LSS) Survey (Pacaud et al. 2007), and the REXCESS sample (Pratt et al. 2009). In Figure 5, we show only groups and clusters with z > 0.3 from the intermediate-redshift groups of Jeltema et al. (2006), the AEGIS catalog (Jeltema et al. 2009) and the XMM-LSS Survey (Pacaud et al. 2007; Willis et al. 2005). The luminosities of all of the plotted clusters are bolometric and extrapolated to r₅₀₀, which allows for direct comparison to the clusters presented in this paper. In both of these figures, a scale factor of E(z)⁻¹, based on the assumption of self-similarity, has been applied to the luminosities of the clusters, a customary choice of past workers. (E(z) = H(z)/H₀ = (Ω_Λ +  Ω_M(1 +  z)³)^0.5). The scaled luminosities and temperatures of the three clusters reported here are consistent with those at lower redshift and with those at similar redshift.

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The L_x–T_x relation may evolve with redshift, although exactly whether and how it evolves are yet matters of debate. Using observations of 10 galaxy clusters with 0.4 < z < 0.7 by XMM-Newton, Kotov & Vikhlinin (2005) observed that L ∝ (1 + z)^1.8±0.3 for a fixed temperature. This trend has been supported with other observations as well, such as by Jia et al. (2008), Lumb et al. (2004), and Vikhlinin et al. (2002). However, the WARPS sample observed by Maughan et al. (2006) shows evolution of L ∝ (1 + z)^0.8±0.4 in their 11 galaxy clusters with 0.6 < z < 1.0. Evolution similar to Maughan et al. (2006) was also seen by Ettori et al. (2004) in a study of 28 galaxy clusters ranging from 0.4 < z < 1.3.

While measuring an L_x–T_x relation does not require a complete sample, it is best done with a representative sample, particularly given the high scatter seen in the low-redshift relation. At high redshift, the highest-luminosity representatives for clusters of a given temperature may be the only ones to make it into the sample. This Malmquist bias can be accounted for, but the scatter and the selection function must be well defined. Selection biases can induce effects that look like evolution in the direction that has been claimed, and therefore claims of L_x–T_x evolution need to be examined in the context of how the basis sample was assembled. Pacaud et al. (2007) notes that while these previous studies claimed relations fit well over the redshift range over which they are derived, they are not consistent with other observations over the full redshift range. They then suggest that the apparent evolution in the L_x–T_x relationships reported in these works is mostly due to selection bias. In their own survey of 29 clusters out to z = 1.05, they show that when selection bias is taken into account, the evidence for evolution is minimal. They find that the evolution they measure in their sample favors self-similar evolution only, and note that no evolution at all is still marginally consistent with their data.

As we have shown, the L_x–T_x data for all three clusters presented in this paper are consistent with the z ≈ 0 L_x–T_x data as well as with the z ≈ 0.3 galaxy groups observed by Jeltema et al. (2009), Jeltema et al. (2006), Pacaud et al. (2007), and Willis et al. (2005). We note that these clusters have very similar temperatures but exhibit a factor of ∼5 in the luminosity range. Local galaxy groups observed by Osmond & Ponman (2004) showed larger intrinsic scatter, especially toward the less luminous/higher temperature side of the L_x–T_x relationship. We see no evidence for strong evolution perpendicular to the z ≈ 0.0 L_x–T_x relation in these higher redshift, z ≈ 0.3 clusters. As noted above, the X-ray properties of the optically selected cluster KDCS112 turn out to be consistent with those of the X-ray-selected clusters.

The scatter of the L_x–T_x relationship may change with redshift. Comparing high- and low-luminosity galaxy clusters at low redshift (Markevitch 1998; Osmond & Ponman 2004, for example) there is a significant difference in the inherent scatter of the points about the best-fit relationships of clusters compared to groups. This increase in intrinsic scatter of groups may be due to the larger relative effect of feedback process on group gas properties. The intrinsic scatter may vary as a function of mass of the system, although quantifying this is difficult with standard statistical analysis packages.

Stanek et al. (2006) fit the L_x–T_x data of Reiprich & Böhringer (2002) and obtained σ_ln T|Lx = 0.25. In log₁₀ space this translates to σ_log T ∼ 0.25log e = 0.11. We explore here whether the current state of the data for moderate redshift clusters is sufficient to show evidence for intrinsic scatter of this order.

We fit these points using the WLS_REGRESS program (Akritas & Bershady 1996), which allows the estimate of a intrinsic scatter, from a data set with a varying level of measurement errors, with a measurement error in the independent variable (luminosity) that is much less than that of the dependent variable (temperature). Using the same z > 0.3 galaxy clusters as in Section 4.1 (Figure 5), we found the best fit of log₁₀T_x = A + Blog₁₀Lx (T_x is in keV and L_x in erg s⁻¹.) We obtain best-fit parameters of A = −12.2 ± 2.9 and B = 0.289 ± 0.065, errors estimated from 10,000 bootstrap simulations. This analysis indicates very little evidence for intrinsic scatter (consistent with none), beyond what is expected from the stated measurement errors, which are considerable.

More typically, the L_x–T_x relation is described as L ∝ T^α (α = 1/B, for the fitting function defined in the previous paragraph). We found somewhat higher values for α (∼2.8–4.4) than are typically estimated for low-redshift samples. Pratt et al. (2009) find a BCES (L|T) slope of 2.70 ± 0.23 for 31 z = 0.05–0.15 clusters in the REXCESS sample, consistent with previous determinations (see reference in Pratt et al. 2009). For direct comparison, we perform a similar BCES fit which weights errors in both parameters, using the BCES_REGRESS routine (Akritas & Bershady 1996). We obtain a similar fit to the weighted LS (WLS) result, with BCES(L|T) of 3.8 ± 0.5, and an even steeper orthogonal fit of 4.5 ± 0.9. Ordinary LS (OLS) fits which weight all points equally find a range of acceptable slopes: OLS(L|T) slope is 2.4 ± 0.3 and OLS(T|L) is 3.7 ± 0.5 while the bisector approach splits the difference, 2.9 ± 0.3. The larger measurement errors and any preference toward higher luminosity at the higher redshifts of this heterogeneous sample would tend to steepen the fit of the raw relation. Either way, the slopes we obtain here do not differ much from other cluster L_x–T_x determinations, and we see no strong evidence for dispersion beyond the measurement error.

To investigate how much the measurement uncertainties limit our sensitivity to an intrinsic dispersion, we created 24 mock catalogs of cluster luminosity and temperature, based on the luminosities and temperature measurement errors for 29 out of the 32 clusters (including the three reported here) with z ∼ 0.3 and error in log T < 0.5. The clusters that were excluded from the analysis due to large uncertainty in the temperature were RX J1648 (Jeltema et al. 2006), CXOU J1422, and CXOU J1423 (Jeltema et al. 2009). Each catalog was generated using temperature errors drawn randomly from the actual temperature errors and luminosities smoothly sampled from 10⁴³–3 × 10⁴⁵ erg s⁻¹. Temperature points were generated using the exact temperature based on the fit above. We then added two random Gaussian errors, the measurement error (scaled by either 1.0 or 0.5 to investigate the effect of smaller measurement errors), and an intrinsic scatter of δlog T(keV) of 0, 0.05, 0.1, and 0.25. We generated cluster catalogs of three different sizes for each combination of intrinsic and experimental errors. We then used WLS_REGRESS from Akritas & Bershady (1996) to estimate the slope, intercept, and intrinsic dispersion for each catalog, and compare that result to the known slope, intercept, and dispersion used to generate the catalog. Estimates of the scatter, slope, and intercept with δlog T = 0.25 can be found in Table 3.

For catalogs with 50 clusters, we found that the slope B(=1/α) was estimated to within 20%–30% and the intercept A was estimated ±1 (log keV): the mean properties are not very well estimated even with 50 clusters. This situation was improved by halving the experimental error (in log T): under those circumstances B is estimated within 10–15%, and A to ±0.5 (log keV). Interestingly, if one simply doubled the sample to N = 100, but obtained measurements of a similar quality, the situation is not much improved over that of an N = 50 cluster sample. In contrast, the result for intrinsic dispersion was more encouraging, although partly a consequence of the ideal Gaussian nature of the simulated errors and scatter in the catalog. Fits to a small sample of 50 predicted an intrinsic dispersion of δlog₁₀T < 0.1 for catalogs with no intrinsic dispersion, even with a random sampling of the measurement errors in the current sample. If the intrinsic simulated scatter were 0.05 or 0.10 in δlog₁₀T, the resulting fits identified similar dispersions, the estimates of which improved to within 40% of the true dispersion when the experimental error was halved.

If we took the results of this mock catalog exercise at face value, we might suggest that the dispersion in the L_x–T_x relation for these moderate redshift clusters is similar to the dispersion seen in HIFLUGCS clusters, and possibly even less. In reality, estimates of the magnitude of the scatter depend on the accuracy and nature of the temperature uncertainties. An inspection of temperature estimates would show that temperatures are not symmetric, particularly large uncertainties (although this effect is not so bad in log space). Therefore, lower quality X-ray temperature probability distributions are only approximately Gaussian. We conservatively assigned the larger (positive) error bar in our fits, but an overestimate of the measurement error leads to an underestimate of the intrinsic scatter. A simple experiment of running WLS_REGRESS and assigning 1/2 the measurement error to each point resulted in an intrinsic scatter estimate in δlog T ∼ 0.05 ± 0.02, beyond the measurement error.

Nevertheless, we conclude that improvement over the current state of L_x–T_x characterization is possible, if some of the larger measurement uncertainties of existing temperature estimates were reduced, and analyzed with compensation for possible Malmquist bias of flux-limited samples. Large numbers of clusters from one or more well-understood cluster samples are optimal, but temperature uncertainties that are somewhat smaller than the intrinsic dispersion would improve the reliability of the mean parameter estimates as well as that of any intrinsic dispersion. Future wide field surveys such as eROSITA (Predehl et al. 2007) and the Wide Field X-ray Telescope (Murray & WFXT Team 2010) of sufficient sensitivity to make accurate temperature measurements and sufficient sky coverage to include a large number of clusters with a wide range of luminosities are required. We note that more sophisticated Monte Carlo techniques will be required to test models that predict a variation of scatter with the relation. Standard statistical fitting routines usually assume the intrinsic scatter is not a function of the dependent variable.