We have studied an ultra-luminous X-ray source ( ULX ) in the dwarf galaxy NGC 5408 with a series of XMM-Newton observations , between 2001 July and 2003 January .
We find that its X-ray spectrum is best fitted with a power law of photon index \Gamma \approx 2.6 – 2.9 
and a thermal component with blackbody temperature kT _ { bb } \approx 0.12 – 0.14 keV .
These spectral features , and the inferred luminosity \approx 10 ^ { 40 } 
erg s ^ { -1 } in the 0.3 – 12 keV band , are typical of bright ULXs in nearby dwarf galaxies .
The blackbody plus power-law model is a significantly better fit than either a simple power law or a broken power law ( although the latter model is also acceptable at some epochs ) .
Doppler-boosted emission from a relativistic jet is not required , although we can not rule out this scenario .
Our preliminary timing analysis shows flaring behaviour which we interpret as variability in the power-law component , on timescales of \sim 10 ^ { 2 } s. The hard component is suppressed during the dips , while the soft thermal component is consistent with being constant .
The power density spectrum is flat at low frequencies , has a break at \nu _ { b } \approx 2.5 mHz , and has a slope \approx - 1 
at higher frequencies .
A comparison with the power spectra of Cyg X-1 and of a sample of other BH candidates and AGN suggests a mass of \sim 10 ^ { 2 } M _ { \odot } .
It is also possible that the BH is at the upper end of the stellar-mass class ( M \sim 50 M _ { \odot } ) , in a phase of moderately super-Eddington accretion .
The formation of such a massive BH via normal stellar evolution may have been favoured by the very metal-poor environment of NGC 5408 .