A 3x109 M⊙ black hole in the quasar SDSS J1148+5251 at z=6.41

We present near-infrared H- and K-band spectra of the z = 6.41 quasar SDSS J114816.64 + 525150.3. The spectrum reveals a broad Mg II lambda2799 emission line with an FWHM of 6000 km s(-1). From the peak wavelength of this emission line, we obtain a more accurate redshift than is possible from the published optical spectrum and determine a redshift of z = 6.41 +/- 0.01. If the true peak of the Lyalpha emission is at the same redshift, then a large fraction of the flux blueward of the peak is absorbed. The equivalent width of the Mg II emission line is similar to that of lower redshift quasars, suggesting that the UV continuum is not dominated by a beamed component. Making basic assumptions about the line-emitting gas, we derive a mass estimate of 3 x 10(9) M. for the central black hole in this quasar. The very high luminosity of the quasar shows that it is accreting at the maximal allowable rate for a black hole of this mass, adopting the Eddington limit criterion.