Luminosity function of low-mass X-ray binaries in the globular cluster system of NGC 1399

<BR /> Aims We present a study of the faint end of the X-ray luminosity function (XLF) of low-mass X-ray binaries (LMXBs) in the Globular Cluster (GC) system of the cD galaxy <ASTROBJ>NGC 1399</ASTROBJ>. <BR /> Methods We performed a stacking experiment on 618 X-ray undetected GCs, in order to verify the presence of faint LMXBs and to constrain the faint-end slope of the GC-LMXBs XLF below the individual detection threshold of 8 10<SUP>37</SUP> erg s<SUP>-1</SUP> in the 0.5 - 8 keV band. <BR /> Results We obtain a significant X-ray detection for the whole GC sample, as well as for the red and blue GC subpopulations, corresponding to an average luminosity per GC < L<SUB>X</SUB> > <SUB>GC</SUB> of (3.6 1.0) 10<SUP>36</SUP> erg s<SUP>-1</SUP>, (6.9 2.1) 10<SUP>36</SUP> erg s<SUP>-1</SUP>, and (1.7 0.9) 10<SUP>36</SUP> erg s<SUP>-1</SUP>, respectively, for all GCs, red GCs, and blue GCs. If LMXBs in red and blue GCs have the same average intrinsic luminosity, we derive a red/blue ratio ~=3 of GCs hosting LMXBs (2.5 1.0 or 4.1 2.5 depending on the surveyed region); alternatively, assuming the fractions observed for brighter sources, we measure an average X-ray luminosity of L<SUB>X</SUB> = (4.3 1.3) 10<SUP>37</SUP> erg s<SUP>-1</SUP> and L<SUB>X</SUB> = (3.4 1.7) 10<SUP>37</SUP> erg s<SUP>-1</SUP> per red and blue GC-LMXBs, respectively. In the assumption that the XLF follows a power-law distribution, we find that a low-luminosity break is required at L<SUB>X</SUB> <= 8 10<SUP>37</SUP> erg s<SUP>-1</SUP> both in the whole, as well as in the color-selected (red and blue) subsamples. Given the bright-end slopes measured above the X-ray completeness limit, this result is significant at >3sigma level. Our best estimates for the faint-end slope are beta<SUB>L</SUB> = -1.39/-1.38/-1.36 for all/red/blue GC-LMXBs. We also find evidence that the luminosity function becomes steeper at luminosities L<SUB>X</SUB> ≳ 3 10<SUP>39</SUP> erg s<SUP>-1</SUP>, as observed in old ellipticals. <BR /> Conclusions If most GCs host a single X-ray binary, we conclude that in <ASTROBJ>NGC 1399</ASTROBJ> the XLF flattens at low luminosities as observed in other nearer galaxies, and we discuss some consequences of this flattening on LMXBs formation scenarios.