Dust and the intrinsic spectral index of quasar variations: hints of finite stress at the innermost stable circular orbit

TL;DR

This study analyzes quasar spectral variations to determine the intrinsic spectral index, revealing evidence for a steeper temperature profile in accretion discs possibly caused by finite stress at the innermost stable orbit.

Contribution

It introduces a method to decompose quasar spectra into variable and non-variable components and finds the spectral index supports a modified accretion disc model with finite stress.

Findings

Best-fit spectral index α=0.71±0.02

Supports a steeper temperature profile T∝r^{-7/8}

Evidence for finite stress at the innermost stable orbit

Abstract

We present a study of 9242 spectroscopically-confirmed quasars with multi-epoch ugriz photometry from the SDSS Southern Survey. By fitting a separable linear model to each quasar's spectral variations, we decompose their five-band spectral energy distributions into variable (disc) and non-variable (host galaxy) components. In modelling the disc spectra, we include attenuation by dust on the line of sight through the host galaxy to its nucleus. We consider five commonly used attenuation laws, and find that the best description is by dust similar to that of the Small Magellanic Cloud, inferring a lack of carbonaceous grains from the relatively weak 2175AA absorption feature. We go on to construct a composite spectrum for the quasar variations spanning 700 to 8000AA. By varying the assumed power-law $L_{\nu}\propto\nu^\alpha$ spectral slope, we find a best-fit value $\alpha=0.71\pm0.02$, excluding at high confidence the canonical $L_{\nu}\propto\nu^{1/3}$ prediction for a steady-state accretion disc with a $T\propto r^{-3/4}$ temperature profile. The bluer spectral index of the observed quasar variations instead supports the model of Mummery & Balbus in which a steeper temperature profile, $T\propto r^{-7/8}$, develops as a result of finite magnetically-induced stress at the innermost stable circular orbit extracting energy and angular momentum from the black hole spin.