ERRATUM: "CONSTRAINING THE QUADRUPOLE MOMENT OF STELLAR-MASS BLACK-HOLE CANDIDATES WITH THE CONTINUUM FITTING METHOD" (2011, ApJ 731, 121)

In the published version of the paper, Equation (6) should have g³ in the integral, where g is the redshift factor

$$\begin{eqnarray}&&{\rm{g}}=\displaystyle \frac{\nu }{{\nu }_{e}}=\displaystyle \frac{{k}_{\mu }{u}_{o}^{\mu }}{{k}_{\mu }{u}_{e}^{\mu }},\end{eqnarray} \tag{ 1 }$$

${u}_{o}^{\mu }=(1,0,0,0)$ is the 4-velocity of the observer, and ${u}_{e}^{\mu }=({u}_{e}^{t},0,0,{\rm{\Omega }}{u}_{e}^{t})$ is the 4-velocity of the emitter. The correct formula is thus

$$\begin{eqnarray}&&L(\nu )=\displaystyle \frac{8\pi h}{{c}^{2}}\mathrm{cos}i{\displaystyle \int }_{{r}_{{\rm{in}}}}^{{r}_{{\rm{out}}}}{\displaystyle \int }_{0}^{2\pi }{{\rm{g}}}^{3}\displaystyle \frac{{\nu }_{e}^{3}\sqrt{-G}{dr}\;d\phi }{\mathrm{exp}\left[h{\nu }_{e}/({kT})\right]-1}.\end{eqnarray} \tag{ 2 }$$

Indeed, from Liouville's theorem we have ${I}_{e}({\nu }_{e})/{\nu }_{e}^{3}={I}_{o}(\nu )/{\nu }_{}^{3},$ where I_e(ν_e) and I_o(ν) are, respectively, the specific intensity of the radiation in the rest frame of the emitter and in that of the distant observer.

This typo is also present in our code, but we have verified that the corrections to the disk's thermal spectrum are small and that the conclusions of our paper do not change. This can be understood qualitatively as follows. First, in our analysis we only compare theoretical predictions with theoretical predictions, without involving real data. The correction affects thus all the spectra in a similar way. Second, the thermal spectrum of the disk is not very informative: it is mainly sensitive to the position of the ISCO radius and therefore to the value of r_in.

We acknowledge support from the European Union's Seventh Framework Programme (FP7/PEOPLE-2011-CIG) through the Marie Curie Career Integration Grant GALFORMBHS PCIG11-GA-2012-321608 (to E.B.)