2 The spatial correlation of galaxy clusters with unidentified EGRET gamma-ray sources

Motivated by the previous arguments, we analyzed the available data for the gamma-ray sources in the Third EGRET catalog (Hartman et al. 1999) and we looked for a correlation between the position of unidentified gamma-ray sources with |b|>20 $\deg$ and the positions of galaxy clusters in the Abell catalogue (Abell et al. 1989). We further looked for the X-ray information about the selected clusters in the ROSAT all sky survey and pointed observations and in the BeppoSAX cluster catalogue. We also looked for radio sources associated with galaxy clusters in the NVSS radio survey, in the VLA and SUMSS surveys as well as in the available literature.

We first studied such a spatial correlation within a fixed radius (1 $\deg$) from the center of each EGRET source and subsequently we refined our analysis considering the actual $95 \%$ confidence level position error contours of each EGRET source found in the previous step.

We found that 50 EGRET sources at high galactic latitude, |b|>20 $\deg$, are spatially correlated - within 1 degree from the center of the EGRET source - with the position of 70 galaxy clusters in the Abell catalogue (Abell et al. 1989). We choose a correlation radius of 1 $\deg$ because this is the angular distance at which EGRET cannot distinguish two separate point-like sources (Hartman et al. 1999). We performed a Monte Carlo simulation to check if such a spatial association can be understood as a simple random projection effect. Specifically, we built 10³ random distributions of galaxy clusters extracted from the Abell catalogue and taking into account their clustering properties and we cross-correlated their positions with the EGRET source positions within 1 $\deg$ radius. We find that, on average, 33 EGRET sources can be randomly associated with simulated cluster positions. Based on a Kolmogorov-Smirnov test, the probability that all of the remaining 17 EGRET unidentified sources are still randomly associated with galaxy clusters is $\la$$0.5\%$. This indicates that the confidence level of the spatial association is about $2.96 \sigma$ (assuming a Gaussian statistics which is justified for $\ga$20 spatial associations).

For a more detailed analysis, we correlated the positions of the Abell clusters with the exact position error contours given for each EGRET source found in the Third EGRET catalogue. In this procedure we consider also the spatial extent of the galaxy clusters. We find that the coordinates of the optical centers of 52 Abell clusters fall within the contour containing the $95 \%$ confidence level error region for the positions of 39 EGRET sources. In this analysis we consider a positive correlation also for those clusters whose optical centers are close to the border of the $95 \%$ confidence level error contours of the EGRET sources and whose spatial extent is found within the $95 \%$ confidence level EGRET position error contour. We then simulated, as before, 10³ random distributions of galaxy clusters extracted from the Abell catalogue preserving their clustering properties and we cross-correlated their positions with the EGRET source positions within their $95 \%$ confidence level contours, finding that, on average, 26 EGRET sources can be randomly associated with simulated cluster positions. Based on a Kolmogorov-Smirnov test, the probability that all of the remaining 13 EGRET unidentified sources are still randomly associated with galaxy clusters is $\la$$1 \%$ (or, in other words, the significance of the probable correlation between galaxy clusters and EGRET sources is at more than $2.5 \sigma$ confidence level).

Since a substantial fraction of the sky observed by EGRET has a low sensitivity (where it would be difficult to observe any faint source), the previous estimate of the significance level of the correlation can be safely considered as a lower limit of the true one. In fact, the cluster - EGRET source correlation we found here is suffering from a lack of other possible EGRET-cluster associations coming from those gamma-ray sources which are not detected in the low-exposure region of the EGRET sky. Assuming that the number of additional EGRET sources detectable with a uniform sky coverage, $N_{\rm x} \propto A_{\rm low-exp.}$ (where $A_{\rm low-exp.}$ is the area of the gamma-ray sky with low-exposure), is correlated with galaxy clusters in the same ratio of our previous estimates, and assuming that the fraction of random correlation is again similar to what previously estimated (i.e. $\sim$2/3 of the correlations are random and ${\sim} 1/3$ are probable), the statistical confidence level of the correlation found after correcting for the non-uniform exposure of EGRET increases with increasing value of $N_{\rm x}$ and scales like $\sim$ $\sqrt{N_{\rm x}} \propto \sqrt{A_{\rm low-exp.}}$, for high values of $N_{\rm x}$. So, in conclusion, we believe that the previous estimate of the statistical significance of the cluster-EGRET source correlation given above can be reliably considered as a lower limit to the actual significance level of the spatial correlation between galaxy clusters and unidentified EGRET sources.

To select out of the full list previously found the more probable associations of galaxy clusters with the unidentified EGRET sources, we superposed the optical cluster positions and their X-ray images onto the maps containing the probability distribution for the spatial position of the 50 EGRET sources found in our spatial correlation analysis.

We found that 18 of the original 50 EGRET sources associated with galaxy clusters have also an AGN (with confirmed identification) whose position falls within the $95 \%$ confidence level position error contours of the gamma-ray source. We also found that a Gamma Ray Burst is found in association with the EGRET source 3EG J2255-5012 and the clusters Abell 1073S and Abell 1074S. Also a SN remnant is found in the field of the source 3EG J1235+0233 associated to the cluster Abell 1564. We then excluded these 20 EGRET sources and the associated 30 clusters from the list of probable physical associations.

We also excluded 12 EGRET sources with a possible, but not confirmed, AGN contamination in the Third EGRET catalog (see Hartman et al. 1999). Note that also this procedure is very conservative since there are 4 cases out of the 12 listed in which the possible AGN source is found beyond the $95 \%$ confidence level position error contours of the associated EGRET sources, while the galaxy clusters spatially associated with the EGRET sources fall within their $95 \%$ confidence level position error contours.

Finally, we conclude that, in our conservative analysis, 24 galaxy clusters are associated to 18 unidentified EGRET sources with |b|>20 $\deg$ for which there is no firmly established counterpart at other wavelengths, neither extragalactic (AGN or "active'' galaxy) or galactic (Supernova remnant, pulsar, neutron star). All of these galaxy clusters have their optical and X-ray centers falling within the $95 \%$ confidence level position error contours of the EGRET sources. We show in Table 1 the list of the 18 EGRET sources and the 24 clusters which are spatially correlated within the $95 \%$ confidence level position error contours of each EGRET source. This is the initial sample of likely associations between galaxy clusters and EGRET gamma-ray sources on which we performed a more detailed analysis, as discussed in the following.

 

 

Table 1: List of probable cluster - EGRET source association. Shown are the coordinates (J2000) of the EGRET unidentified sources (Cols. 2 and 3) together with those of the associated galaxy clusters (Cols. 5 and 6). The cluster optical redshifts (Col. 7), their richnesses R (Col. 8) and optical radii $r_{\rm opt}$ (Col. 9) are extracted from the NED archive, unless otherwise specified (the redshift references are: ^a Andernach 2002, priv. comm.; ^k Kowalski et al. 1984). The most probable associations are marked with an asterisk (see text for details).

EGRET source	RA	Dec	Cluster	RA	Dec	z	R	$r_{\rm opt}$	Notes
* 3EG J2219-7941	22 20 00.0	-79 41 24.00	Abell 1014S	22 24 10	-80 10 4	0.048	0	-	SUMSS
			Abell 1024S	22 27 32	-78 45 4	0.105a	0	-	SUMSS
3EG J1825-7926	18 25 02.4	-79 26 24.00	Abell 3631	18 34 08	-78 47 4	0.085a	0	-	SUMSS
3EG J0348-5708	03 48 28.8	-57 08 24.00	Abell 3164	03 45 49	-57 02 4	0.057	0	4.5$^\prime$	SUMSS
* 3EG J0159-3603	01 59 21.6	-36 03 36.00	Abell 2963	02 00 45	-35 59 3	0.113a	0	-	NVSS
			Abell 219S	02 02 03	-35 48 3	0.128a	1	15$^\prime$	-
3EG J0616-3310	06 16 36.0	-33 10 12.00	Abell 577S	06 15 18	-34 07 0	0.102a	2	7$^\prime$	NVSS
			Abell 575S	06 13 25	-33 40 5	0.098a	0	-	NVSS
			Abell 573S	06 12 02	-32 57 4	0.078a	0	-	NVSS
3EG J2034-3110	20 34 55.2	-31 10 48.00	Abell 886S	20 37 11	-31 38 3	0.095a	0	-	-
3EG J1234-1318	12 34 02.4	-13 18 36.00	Abell 1558	12 33 59	-13 34 3	0.116a	0	14$^\prime$	NVSS
			Abell 1555	12 31 59	-13 23 3	0.127a	1	14$^\prime$	NVSS
* 3EG J0038-0949	00 38 57.6	-09 49 12.00	Abell 85	00 41 37	-09 20 3	0.056	1	30$^\prime$	RH, RG, NVSS
* 3EG J1310-0517	13 10 24.0	-05 18 00.00	Abell 1688	13 11 29	-04 40 5	0.190k	0	-	NVSS
* 3EG J0253-0345	02 53 57.6	-03 45 36.00	Abell 388	02 51 36	-03 45 4	0.134	2	10$^\prime$	NVSS
* 3EG J0439+1105	04 39 14.4	11 05 24.00	Abell 497	04 36 51	10 38 0	0.140k	0	17.5$^\prime$	NVSS
* 3EG J0215+1123	02 16 00.0	11 22 48.00	Abell 331	02 15 35	11 21 5	0.186k	1	9$^\prime$	NVSS
3EG J2248+1745	22 48 57.6	17 46 12.00	Abell 2486	22 48 45	17 09 5	0.143k	0	18$^\prime$	NVSS
3EG J1212+2304	12 12 36.0	23 04 48.00	Abell 1494	12 13 14	23 56 1	0.159k	1	15$^\prime$	NVSS
3EG J1347+2932	13 47 12.0	29 32 24.00	Abell 1781	13 44 28	29 50 5	0.062	0	16$^\prime$	RG, NVSS
* 3EG J1424+3734	14 24 52.8	37 34 48.00	Abell 1902	14 21 46	37 17 2	0.160	2	15$^\prime$	RG, NVSS
			Abell 1914	14 26 02	37 49 3	0.171	2	13$^\prime$	RH, RG, NVSS
* 3EG J1337+5029	13 37 31.2	50 28 48.00	Abell 1758	13 32 32	50 30 3	0.279	3	11$^\prime$	RH, RG, NVSS
3EG J1447-3936	14 14748.0	-39 36 36.0	Abell 774S	14 49 23	-40 20 6	0.062a	0	-	-

Notes: RG: identified radio galaxies in the cluster; NVSS, SUMSS: radio sources found within the Abell radius, $\frac{1.7}{Z}$ arcmin, of the cluster; RH: radio halo or relic belonging to the cluster. The specific ID names of the identified radio galaxies and NVSS radio sources associated to the clusters are given in Sect. 3 of the text.

According to our selection procedure, the significance level of such a spatial association is $\approx$ $2.55 \sigma$ which corresponds to a probability ${\la} 1 \%$ for the null hypothesis that the two source populations are randomly associated. However, the point is still to determine how many of these spatial associations are due to random projection effects and which are the most probable physical associations. A rough estimate of the probability to have still random associations in the sample here selected (see Table 1) and to be not contaminated by either extra-galactic (AGN, GRB) or galactic (SNR, pulsars, ...) gamma-ray sources, yields that about 2/3 of the 18 selected EGRET sources are still random associations. This rough estimate would yield 6 most probable cluster-EGRET source associations with a confidence level of $1.73 \sigma$. Note, however, that this is again a lower limit to the true statistical confidence of the correlation since the effect of the non-uniform EGRET sky coverage has to be taken into account and would tend to increase the statistical significance level of the most probable association. If we correct for the number of correlations expected in the fraction of the EGRET sky ($\sim$$30 \%$ of the full sky) which has a flux limit below $F({>}100~{\rm MeV}) \leq 6 \times 10^{-8}~$cm^-2 s^-1, we obtain that the expected confidence level of the most probable associations increases from $1.73 \sigma$ to $2.12 \sigma$.

2.1 Flux and spectral analysis

In addition to the spatial information contained in the Third EGRET catalog and in the Abell cluster survey, we can use more physical criteria to determine the number of spurious correlations in our selected sample of Table 1. Specifically, we first analyze the flux level, the flux variability and the spectral indices of the 18 EGRET sources in Table 1 compared to the same quantities of other gamma-ray sources more definitely identified in the Third EGRET catalogue (mainly AGN and Pulsars). Then we run Monte Carlo simulations of flux level and variability for the probable EGRET-cluster associations to determine the fraction of random correlations expected in our selected sample.

Figure 1: We show the gamma-ray flux of the EGRET sources in Table 1 as detected in the different viewing periods (VP) of the source detection. Data are from Hartman et al. (1999). The flux detected in the different VPs are reported here in the sequential order given in the Third EGRET catalog, being the correct observing time sequence irrelevant for our purposes. The fluxes of the EGRET sources are in units of 10-8 cm-2 s-1.

Figure 1 shows the flux variation in the viewing periods (hereafter VP) over which the EGRET sources reported in Table 1 have been detected. We notice that the flux variability for the probable cluster-EGRET source associations listed in Table 1 is, on average, $\la$$20 \%$ and only in a few cases (3EG J1825-7926, 3EG J1212+2304, 3EG J0616-3310, 3EG J2248+1745) it can be considered $\ga$$30 \%$ in some specific VP (see Fig. 1). The correspondingly associated clusters (see Table 1) are poorly studied, do not have X-ray information and do not have any identified bright radio galaxy or radio halo/relic emission. Hence, we also consider these cases as suspiciously due to projection effects. Beyond the positive detections with high statistical significance $({\it TS})^{1/2} \ga4$ (see Hartman et al. 1999 for a definition of the quantity (TS)^1/2) of the EGRET sources reported in Fig. 1, the Third EGRET catalog provides also upper limits on their fluxes in other independent VPs. Such upper limits have $({\it TS})^{1/2} < 2$ (i.e., a low statistical significance) and we verified that most of them are consistent with the positive detections of the EGRET sources we show in Fig. 1. In some cases, however, (see, e.g., 3EGJ0348-5708, 3EGJ1234-1318, 3EGJ0253-0345, 3EGJ0215+1123) there are upper limits which are well below the flux level found in other independent VP detections of the sources. Nonetheless, we noticed that these "quite low'' upper limits all have a very low statistical confidence level, $({\it TS})^{1/2} \sim 0$, and are hence extremely unreliable. Thus, due to their quite low statistical significance, the upper limits of the EGRET sources listed in Table 1 and shown in Fig. 1 do not strongly affect our conclusions on their overall flux variability. A few other sources with independent flux upper limits below the definite detections (see, e.g., 3EGJ0616-3310, 3EGJ2034-3110, 3EGJ1212+2304) show also a level of flux variability which does not justify to consider them as stationary sources. For the sake of completeness, we will discuss in Sect. 3 below the detailed analysis of each specific EGRET source listed in Table 1.

For comparison, we show in Fig. 2 the flux variation of the EGRET sources which are correlated with galaxy clusters and moreover contain also a confirmed AGN in the field. In these last cases, the flux of the EGRET sources not only show stronger and statistically significative variations, but also have a much higher value of their average gamma-ray flux.

Figure 2: The variation of the gamma-ray flux of the EGRET sources which are correlated with galaxy clusters and which have also an identified AGN in the field. Data are from Hartman et al. (1999). As in Fig. 1, the flux detected in the different VPs are reported in the sequential order given in the Third EGRET catalog, being the correct observing time sequence irrelevant for our purposes. The fluxes of the EGRET sources are in units of 10-8 cm-2 s-1.

In Fig. 3 we compare the spectral index, $\gamma$, of the EGRET sources which are probably associated with galaxy clusters with those of the EGRET sources which are spatially correlated with galaxy clusters and moreover contain an AGN in the field. The EGRET sources correlated with clusters are not found to be brighter than $F({>}100~{\rm MeV}) \sim 2 \times 10^{-7}$ counts cm^-2 s^-1 and show spectral indices in a large range $\sim$ $2 \times 3.5$. With a remarkable difference, the EGRET sources identified with known AGNs span over a much higher gamma-ray flux range and have a much smaller range of spectral index values ( $\gamma \sim 2$-2.5) especially at very bright flux levels $F({>}100~{\rm MeV}) > 5 \times 10^{-7}$ counts cm^-2 s^-1. Pulsars also show very flat spectral indices $\gamma \la2$ and very high gamma-ray flux which cannot be compared with those of the EGRET sources associated with clusters.

The gamma-ray spectral indices for the probable associations listed in Table 1 have values which are consistent with those expected from the viable mechanisms for gamma-ray emission in clusters. Theoretical models for cluster gamma-ray emission predict in fact slopes in the range $\gamma \sim 1.8 {-} 3.2$, going from annihilation of dark matter neutralinos (Colafrancesco & Mele 2001) to non-thermal electron bremsstrahlung (Colafrancesco 2001a,b; Blasi 2000). Only the sources 3EG J2034-3110 (associated to Abell 886S) and 3EG J1424+3734 (associated to Abell 1902 and Abell 1914) have spectral indices $\ga$3, even though with large uncertainties. However, while the first source, 3EG J2034-3110, shows also some level of flux variability (see Fig. 1) and could then be contaminated by AGN-like sources, the gamma-ray source 3EG J1424+3734 has a very low flux variability ($\sim$$15 \%$) and is likely to be a probable association whose gamma-ray emission could be dominated by non-thermal electron bremsstrahlung, which shows typically a steep spectrum consistent with that of the parent cosmic-ray electrons (see, e.g., Longair 1993).

Figure 3: The gamma-ray spectral index $\gamma$ is plotted against the gamma-ray flux $F({>}100 ~{\rm MeV})$ of the EGRET sources found to be spatially correlated with galaxy clusters. In the top panel we compare the spectral indices for the EGRET sources which are more probably associated with clusters (filled circles) with the EGRET sources again correlated with clusters and in which an identified AGN is also found (open circles). In the lower panel the data from the EGRET sources contaminated by possible AGNs (gray triangles), GRB (open, light-gray triangle), SNR (open black triangle) and Pulsars (stars) are added to the previous data sets. Data are from Hartman et al. (1999).

We finally run Monte Carlo simulations of the flux variability level of the 18 EGRET sources of Table 1. For a uniform random distribution of their fractional flux change, $\Delta F/F$, we expect 4 EGRET sources with $\Delta F/F \la0.2$, while the remaining 14 EGRET sources possibly associated with galaxy clusters should have $0.2 \la\Delta F/F \la1$. The actual data reported in Fig. 1 show that there are about 11 EGRET sources with $\Delta F/F \leq 0.2$ and only 7 sources with $0.2 \la\Delta F/F \la1$. This indicates that the low flux variability shown by the EGRET sources found in association with clusters cannot be recovered by a simple random distribution at more than the $5 \sigma$ confidence level.

Based on these results we expect that about 10 EGRET sources out of the 18 listed in Table 1 are probable EGRET-cluster associations having $\Delta F/F \la0.2$, $F({>}100~{\rm MeV}) < (1 {-} 2)\times 10^{-7}~$cm^-2 s^-1 and $\gamma \sim 2 {-} 3.2$. However, only a detailed analysis of the spatial and spectral features of each EGRET source as well as a detailed analysis of their cluster counterparts can reveal the nature of the more probable physical association. We will present in the next section the detailed analysis of each one of the specific EGRET sources listed in Table 1 and of their possible astrophysical counterparts.