Variability Timescale and Spectral Index of Sgr A* in the Near Infrared: Approximate Bayesian Computation Analysis of the Variability of the Closest Supermassive Black Hole

Sagittarius A* (Sgr A*) is the variable radio, near-infrared (NIR), and X-ray source associated with accretion onto the Galactic center black hole. We present an analysis of the most comprehensive NIR variability dataset of Sgr A* to date: eight 24-hour epochs of continuous monitoring of Sgr A* at 4.5 $\mu$m with the IRAC instrument on the Spitzer Space Telescope, 93 epochs of 2.18 $\mu$m data from Naos Conica at the Very Large Telescope, and 30 epochs of 2.12 $\mu$m data from the NIRC2 camera at the Keck Observatory, in total 94,929 measurements. A new approximate Bayesian computation method for fitting the first-order structure function extracts information beyond current Fast Fourier Transformation (FFT) methods of power spectral density (PSD) estimation. With a combined fit of the data of all three observatories, the characteristic coherence timescale of Sgr A* is $\tau_{b} = 243^{+82}_{-57}$ minutes ($90\%$ credible interval). The PSD has no detectable features on timescales down to 8.5 minutes ($95\%$ credible level), which is the ISCO orbital frequency for a dimensionless spin parameter $a = 0.92$. One light curve measured simultaneously at 2.12 and 4.5 $\mu$m during a low flux-density phase gave a spectral index $\alpha_s = 1.6 \pm 0.1$ ($F_\nu \propto \nu^{-\alpha_s}$). This value implies that the Sgr A* NIR color becomes bluer during higher flux-density phases. The probability densities of flux densities of the combined datasets are best fit by log-normal distributions. Based on these distributions, the Sgr A* spectral energy distribution is consistent with synchrotron radiation from a non-thermal electron population from below 20 GHz through the NIR.