The Size of Accretion Disks from Self-consistent X-Ray Spectra and UV/Optical/NIR Photometry Fitting: Applications to ASASSN–14li and HLX–1

Abstract We implement a standard thin disk model with the outer disk radius ( R out ) as a free parameter, integrating it into a standard X-ray fitting package to enable self-consistent and simultaneous fitting of X-ray spectra and Ultraviolet (UV), Optical, and Near-infrared (NIR) photometry. We apply the model to the late-time data (Δ t ≈ 350–1300 days) of the tidal disruption event (TDE) ASASSN–14li. We show that at these late times, the multiwavelength emission of the source can be fully described by a bare compact accretion disk. We obtain a black hole mass ( M BH ) of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>7</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>×</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> , consistent with host-galaxy scaling relations, and an R out of 45 ± 13 R g , consistent with the circularization radius, with possible expansion at the latest epoch. We discuss how simplistic models, such as a single-temperature blackbody fitted to either X-ray spectra or UV/optical photometry, lead to erroneous interpretations of the scale/energetics of TDE emission. We also apply the model to the soft/high state of the intermediate-mass black hole candidate HLX–1. The model fits the full spectral energy distribution (from X-rays to NIR) without needing an additional stellar population component. We investigate how relativistic effects improve our results by implementing a version of the model with full ray tracing calculations in the Kerr metric. For HLX–1, we find <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">BH</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>×</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> and R out ≈ few × 10 3 R g , in agreement with previous findings. The relativistic model can constrain the inclination ( i ) of HLX–1 to be 10° ≤ i ≤70°.