Aims: We present a spectral analysis of a deep (220 ks) XMM-Newton observation of the Phoenix cluster (SPT-CL J2344-4243). We also use Chandra archival ACIS-I data that are useful for modeling the properties of the central bright active galactic nucleus and global intracluster medium. Methods: We extracted CCD and reflection grating spectrometer (RGS) X-ray spectra from the core region to search for the signature of cold gas and to finally constrain the mass deposition rate in the cooling flow that is thought to be responsible for the massive star formation episode observed in the brightest cluster galaxy (BCG). Results: We find an average mass-deposition rate of Ṁ = 620 (-190 + 200)stat (-50 + 150)syst M⊙ yr-1 in the temperature range 0.3-3.0 keV from MOS data. A temperature-resolved analysis shows that a significant amount of gas is deposited at about 1.8 keV and above, while only upper limits on the order of hundreds of M⊙ yr-1 can be placed in the 0.3-1.8 keV temperature range. From pn data we obtain Ṁ = 210 (-80 + 85)stat (-35 + 60)syst M⊙ yr-1 in the 0.3-3.0 keV temperature range, while the upper limits from the temperature-resolved analysis are typically a factor of 3 lower than MOS data. No line emission from ionization states below Fe XXIII is seen above 12 Å in the RGS spectrum, and the amount of gas cooling below ~3 keV has a formal best-fit value Ṁ = 122-122+343 M⊙ yr-1. In addition, our analysis of the far-infrared spectral energy distribution of the BCG based on Herschel data provides a star formation rate (SFR) equal to 530 M⊙ yr-1 with an uncertainty of 10%, which is lower than previous estimates by a factor 1.5. Overall, current limits on the mass deposition rate from MOS data are consistent with the SFR observed in the BCG, while pn data prefer a lower value of Ṁ ~ SFR/ 3, which is inconsistent with the SFR at the 3σ confidence level. Conclusions: Current data are able to firmly identify a substantial amount of cooling gas only above 1.8 keV in the core of the Phoenix cluster. At lower temperatures, the upper limits on Ṁ from MOS and pn data differ by a factor of 3. While the MOS data analysis is consistent with values as high as Ṁ ~ 1000 within 1σ, pn data provide Ṁ < 500 M⊙ yr-1 at 3σ confidence level at a temperature below 1.8 keV. At present, this discrepancy cannot be explained on the basis of known calibration uncertainties or other sources of statistical noise.
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