$\begin{figure} \par\includegraphics[width=4.5cm,clip]{MS1576f1.eps}\hspace*{3mm} \includegraphics[width=4.5cm,clip]{MS1576f2.eps}\end{figure}$

Figure 1: Relative positions of the mid-IR and X-ray surveys. On the left, on the full-band (0.5-10 keV) XMM image of the Lockman Hole we superimpose the contours of the area deeply surveyed by ISOCAM and the circle from inside which Hasinger et al. (2001) sources have been extracted. The area considered in the paper results from the intersection of these two regions. On the right, on the full-band (0.5-8 keV) Chandra image of the Hubble Deep Field and flanking fields we draw: the field observed with the Hubble Space Telescope, the field surveyed with ISOCAM (irregular contour) and the Caltech area (square).

A region of $20 \times 20$ square arcminutes in the Lockman Hole, centred on the sky position 10:52:07+57:21:02 (J2000), which corresponds to the centre of the ROSAT HRI image (Hasinger et al. 1993, 1998), has been surveyed by ISOCAM, the mid-IR camera on board ISO (Fadda et al. 2002). The field was observed for a total of 45 ks at 15 $\mu$ m and 70 ks at 6.75 $\mu$ m. Moreover, a shallow survey has been done at 15 $\mu$ m on a region of $40 \times 40$ arcmin² with the same centre for a total exposure time of 55 ks. Combining the two surveys, ISOCAM observed at 15 $\mu$ m the central region for a total of 60 ks.

If we compare this observation with the deepest ISOCAM surveys performed in the HDF-N region (24.3 square arcminutes for 22 ks at 15 $\mu$ m and 10.4 square arcminutes for 23 ks at 6.75 $\mu$ m, Aussel et al. 1999), the Lockman Deep Survey is 16 times more extended and $\sim$ 4 times shallower at 15 $\mu$ m than the HDF-N survey (the sensitivity depending on the integration time and on the redundancy of the observations). ISOCAM data have been reduced using the PRETI pipeline (see Starck et al. 1999) with a few improvements as described by Fadda et al. (2000).

The XMM-Newton observation of the Lockman Hole has been done during the verification phase of the satellite (Hasinger et al. 2001) and is centred on the sky position 10:52:43+57:28:48 (J2000) which was the centre of the PSPC ROSAT image (Hasinger et al. 1998). The total exposure time of this observation was 190 ks, but only 100 ks are usable because of bad space weather (solar activity) during the observations. The limiting fluxes of these observations are $3\times 10^{-16}$ erg cm^-2 s^-1 in the 0.5-2 keV band and $1.4 \times 10^{-15}$ erg cm^-2 s^-1 in the 2-10 keV band.

To match X-ray and mid-IR sources we considered X-ray sources detected at the 4 $\sigma$ level inside an off-axis angle of 10 arcmin (Hasinger et al. 2001).

Due to the different centre of the ISOCAM and XMM-Newton observations, the size of the overlapping region is 218 square arcminutes (see Fig. 1), which corresponds to 70% of the XMM-Newton region. In this region, a total of 76 sources was detected in the various X-ray bands excluding clusters and stars (68, 42 and 19 in the 0.5-2 keV, 2-10 keV and 5-10 keV energy bands, respectively). In the same area, 184 and 65 extragalactic sources were detected by ISOCAM at the 3 $\sigma$ level in the LW3 band and at 4 $\sigma$ level in the LW2 band which have central wavelenghts of 15 $\mu$ m and 6.75 $\mu$ m, respectively (Fadda et al. 2002). As shown in Fig. 1, the region centred on the Hubble Deep Field observed by ISOCAM (Rowan-Robinson et al. 1997) has been completely covered by deep 1 Ms Chandra observations (Brandt et al. 2001a). The Chandra observations are one order of magnitude deeper than the XMM-Newton observations in the 0.5-2 keV band (flux limit of $3\times 10^{-17}$ erg cm^-2 s^-1) and 2-8 keV band (flux limit of $2\times 10^{-16}$ erg cm^-2 s^-1). On the contrary, Chandra is less sensitive than XMM-Newton in the ultra-hard band (>5 keV). In the X-ray-LW3 common area, Chandra detects a total of 59 sources in the full X-ray band (0.5-8 keV) and 50, 40 and 23 sources in the 0.5-2 keV, 2-8 keV and 4-8 keV bands, respectively. Aussel et al. (1999) list a total of 93 LW3 sources, 42 of which have a flux greater than 0.1 mJy (completeness flux limit of the survey, Aussel et al. 2002). In the X-ray-LW2 common area (10.4 square arcminutes with 10 ISOCAM detections), Chandra detects a total of 24 sources in the full band and 22, 12 and 7 sources in the soft, hard and ultra-hard bands, respectively.

Table 1: Number of X-ray sources detected at 15 $\mu$ m and 6.75 $\mu$ m in the Lockman Hole-centred region and percentage with one-sigma errors of common detections relative to the total number of X-ray and mid-IR sources in the different XMM-Newton bands. Poissonian errors are computed according to Gehrels et al. (1986).
XMM LW3 LW2

band # X% IR% # X% IR%

Soft 20 29 ⁺¹²_-10 11 ⁺³_-3 6 9 ⁺⁶_-5 9 ⁺⁷_-5

Hard 16 38 ⁺¹⁹_-15 9 ⁺⁶_-4 5 12 ⁺¹⁰_-7 8 ⁺⁶_-4

U-hard 12 63 ⁺⁴²_-32 7 ⁺³_-2 5 26 ⁺²⁵_-17 8 ⁺⁶_-4

Full 22 29 ⁺¹¹_-9 12 ⁺⁷_-5 7 9 ⁺⁶_-4 11 ⁺⁷_-5

**Table 1:** Number of X-ray sources detected at 15 $\mu$ m and 6.75 $\mu$ m in the Lockman Hole-centred region and percentage with one-sigma errors of common detections relative to the total number of X-ray and mid-IR sources in the different XMM-Newton bands. Poissonian errors are computed according to Gehrels et al. (1986).
XMM	LW3	LW2
band	#	X%	IR%	#	X%	IR%
Soft	20	29 ⁺¹²_-10	11 ⁺³_-3	6	9 ⁺⁶_-5	9 ⁺⁷_-5
Hard	16	38 ⁺¹⁹_-15	9 ⁺⁶_-4	5	12 ⁺¹⁰_-7	8 ⁺⁶_-4
U-hard	12	63 ⁺⁴²_-32	7 ⁺³_-2	5	26 ⁺²⁵_-17	8 ⁺⁶_-4
Full	22	29 ⁺¹¹_-9	12 ⁺⁷_-5	7	9 ⁺⁶_-4	11 ⁺⁷_-5

Table 2: Number of X-ray sources detected at 15 $\mu$ m and 6.75 $\mu$ m in the Hubble Deep Field-centred region and percentage with one-sigma errors of common detections relative to the total number of X-ray and mid-IR sources in the different Chandra bands. Poissonian errors are computed according to Gehrels et al. (1986).
Chandra LW3 LW2

band # X% IR% # X% IR%

Soft 20 40 ⁺¹⁸_-15 21 ⁺⁸_-7 5 23 ⁺²¹_-15 50 ⁺⁵⁵_-37

Hard 12 30 ⁺¹⁷_-13 13 ⁺⁶_-5 2 17 ⁺¹⁰_-6 20 ⁺³⁵_-19

U-hard 7 30 ⁺²⁴_-18 8 ⁺⁵_-4 2 29 ⁺⁶_-4 20 ⁺³⁵_-19

Full 22 37 ⁺¹⁵_-13 24 ⁺⁹_-7 5 21 ⁺¹⁹_-13 50 ⁺⁵⁵_-37

**Table 2:** Number of X-ray sources detected at 15 $\mu$ m and 6.75 $\mu$ m in the Hubble Deep Field-centred region and percentage with one-sigma errors of common detections relative to the total number of X-ray and mid-IR sources in the different Chandra bands. Poissonian errors are computed according to Gehrels et al. (1986).
Chandra	LW3	LW2
band	#	X%	IR%	#	X%	IR%
Soft	20	40 ⁺¹⁸_-15	21 ⁺⁸_-7	5	23 ⁺²¹_-15	50 ⁺⁵⁵_-37
Hard	12	30 ⁺¹⁷_-13	13 ⁺⁶_-5	2	17 ⁺¹⁰_-6	20 ⁺³⁵_-19
U-hard	7	30 ⁺²⁴_-18	8 ⁺⁵_-4	2	29 ⁺⁶_-4	20 ⁺³⁵_-19
Full	22	37 ⁺¹⁵_-13	24 ⁺⁹_-7	5	21 ⁺¹⁹_-13	50 ⁺⁵⁵_-37

Tables 1 and 2 summarise the percentages of X-ray and mid-IR sources which emit in the mid-IR and X-ray bands, respectively. It appears clear that a large fraction of X-ray sources have an LW3 counterpart. In particular, in the case of the Lockman Hole, the percentage of X-ray sources emitting in the 5-10 keV band with LW3 counterpart is greater than 60%. The same does not occur in the case of the Chandra deep field, probably because the 4-8 keV ultra-hard band of Chandra is not so sensitive as the similar band of XMM-Newton. On the other hand, only around 10% of the LW3 sources are detected in the various X-ray bands except for the soft X-ray band in the HDF-N, where the extremely deep Chandra observations are able also to detect normal galaxies.

$\begin{figure} \par\includegraphics[width=9cm,clip]{MS1576f3.eps}\end{figure}$

Figure 2: Finding charts of the common X-ray and mid-IR sources in the Lockman Hole region (see Table 3). X-ray and mid-IR isocontours are plotted on optical images (I-band) with grey and black lines, respectively. X-ray contours come from the 0.5-7 keV image, while mid-IR contours refer to the 15 $\mu$ m image, except for sources #104 and #121 which have been detected only in the 6.75 $\mu$ m image. The size of each image is $25''\times 25''$ .

$\begin{figure} \par\includegraphics[width=9cm,clip]{MS1576f4.eps}\end{figure}$

Figure 3: Finding charts of the common X-ray and mid-IR sources in the Hubble Deep Field and Flanking Fields (see Table 4). X-ray and mid-IR isocontours are plotted on optical images (I-band, Barger et al. 1999) with grey and black lines, respectively. X-ray contours come from the 2-8 keV Chandra image, while mid-IR contours refer to the 15 $\mu$ m image except for sources #176 and #183 which have been detected only in the 6.75 $\mu$ m image. The size of each image is $15''\times 15''$ . Sources #161 and #175 correspond to blank fields in the I-image.

In the case of LW2 observations, we have less detections with respect to LW3and a similar trend of detections as a function of the energy band in the Lockman Hole. The case of the Hubble Deep Field is not very constraining because of the bad quality of the LW2 observations (only 10 extragalactic sources have been detected).

2 Observations