infrared Kishimoto et al. 2008, Nature spectropolarimetry. In Fig. 1 we show the spectra of linearly polarized light measured in the near-infrared broad-band imaging polarimetry, and optical spec- tropolarimetry, of the six quasars (including the one studied in the seen in Fig. 2, and we did not find dependen MBH or Eddington ratios L/LEdd derived fr Balmer line. This is expected if the near-in long-wavelength limit of the disk model, parameters such as black-hole mass and Edd by regarding each measurement as a measur ity, the weighted mean over the measurem meaningful. We note that if we formally c the radial temperature distribution for the disk, we obtain T / r20.78 6 0.03, consis dependence T / r23/4. The systematicbehaviourof thenear-infra as the constancy of the position angles over argues against there being any secondary po 1.0 0.1 0.2 1.0 14.4 14.2 14.6 14.8 15.0 2.0 Rest wavelength (µm) Log[rest frequency (Hz)] Total light Polarized light Scaled nF n (arbitrary units) F n ∝ n+1/3 1.5 1.0 0.5 0.0 a = +1/ Q0144-3938 CTS A09.36 Ton 202 PKS 2310-322 Spectral index, a In Fig. 1 we show the spectra of linearly polarized light measured in the near-infrared broad-band imaging polarimetry, and optical spec- tropolarimetry, of the six quasars (including the one studied in the seen in Fig. 2, and we did not find dependencies on black-hole masses MBH or Eddington ratios L/LEdd derived from the width of the Hb Balmer line. This is expected if the near-infrared spectrum is in the long-wavelength limit of the disk model, which is independent of parameters such as black-hole mass and Eddington ratio. In this case, by regarding each measurement as a measurement of the same quant- ity, the weighted mean over the measurements becomes physically meaningful. We note that if we formally convert the mean slope to the radial temperature distribution for the case of an optically thick disk, we obtain T / r20.78 6 0.03, consistent with the predicted dependence T / r23/4. The systematicbehaviourof thenear-infrared polarized light,aswell as the constancy of the position angles over all wavelengths, strongly argues against there being any secondary polarization contamination. 1.0 0.1 0.2 1.0 14.4 14.2 14.6 14.8 15.0 2.0 Rest wavelength (µm) Log[rest frequency (Hz)] Total light Polarized light Scaled nF n (arbitrary units) F n ∝ n+1/3 Figure 1 | Overlay of the polarized- and total-light spectra observed in six different quasars. We plot scaled nFn data: Q0144-3938 (redshift z 5 0.244), green; 3C 95 (z 5 0.616), blue; CTS A09.36 (z 5 0.310), light blue; 4C 09.72 (z 5 0.433), red; PKS 2310-322 (z 5 0.337), yellow. Plotted in purple are the data for Ton 202 (z 5 0.366) from a previous paper25. Total-light spectra, shown as bold traces in the optical and as squares in the near-infrared, are normalized at 1 mm in the rest frame, by interpolation (except that of 3C 95, which we normalized by nFn observed at 1.3 mm in the rest frame). Polarized- light spectra, shown as light points in the optical and as bold points in the near-infrared (vertical error bars, 1s), are separately normalized, also at 1 mm, by fitting a power law to the near-infrared polarized-light spectra. For both total-light and polarized-light data, horizontal bar lengths indicate bandwidth. The normalized polarized-light spectra are arbitrarily shifted downwards by a factor of three relative to the normalized total-light spectra, for clarity. The total-light spectra begin to increase in nFn at wavelengths around, or slightly greater than, 1 mm. In contrast, the polarized-light spectra all consistently and systematically decrease in nFn towards long wavelengths, showing a blue shape of approximately power-law form. 1.5 1.0 0.5 0.0 Weighted mean a = +1/3 0.15–0.95 µm (ref. 9) Q0144-3938 4C 09.72 3C 95 CTS A09.36 Ton 202 PKS 2310-322 0.15–0.51 µm (ref. 11) 0.13–0.50 µm (ref. 13) 0.10–0.55 µm (ref. 10) 0.11–0.22 µm (ref. 12) 1 10 nL n (1045 erg s–1) at 0.5 µm Spectral index, a –0.5 –1.0 Figure 2 | Spectral index of polarized light spectra. We plot a (in Fn / na) against nLn for total light at 0.51 mm. The index was measured using a power- law fit for each near-infrared polarized-light spectrum (note the different wavelength ranges covered depending on the redshift) and is shown with 1s error bars. A weighted mean of the spectral index measurements is shown dashed; the shaded area represents its deduced 1s uncertainty. The mean or median slopes of the ultraviolet–optical total-light spectra derived in various other studies9–13 are also shown. 493 ©2008 Macmillan Publishers Limited. All rights reserved