Spectral Model Components › KERRBB [4]: The thermal spectrum of the accretion disc around a Kerr (rotating) black hole. › SIMPL [5]: Converts soft disc photons to hard X-ray photons with a power-law spectrum expected for the disc corona. › RelXill [6]: The ionised disc reflection, with relativistic effects. › ISMabs [7]: Galactic absorption. Observations We use observations from March & September 2019: › 3 from XMM-Newton (blue): › rev3531, rev3533, rev3623 › 8.5 ks, 11.3 ks, 56.3 ks exposure times. › 2 from NuSTAR (orange): › Simultaneous with rev3533, rev3623 › 57.3 ks and 94.9 ks exposure times. rev3531 rev3533 rev3623 Fig 3. The Swift/BAT & XRT light curve of MAXI J1820+070. Fig 6. Mass posterior (grey) and prior (red). The Current Debate Different groups have reached very different conclusions, sometimes from the same data. These often correspond to the extreme cases: Model 1: › Zero or low spin and/or › A truncated disc (Rin ≥ 6 rg) Model 2: › High (near maximal) spin (a > 0.9) › Rin ~ 1 rg Fig 2. An overview of the two different, but extreme XRB models. Models like these are common in the literature, they all make implicit assumptions. Black hole Black hole Disc Disc Rin ≥ 6 rg Rin ~ 1 rg Where is the Inner Edge of the Accretion Disc? The location of the inner edge of the disc effects the spectrum in various ways: › The luminosity and temperature profile of the thermal emission from the disc. › The relativistic distortion on discrete features in the X-ray reflection spectrum, especially the Fe-Kline. It is theoretically possible to use the detailed shape of the spectrum to infer the location of the inner edge of the accretion disc. These spectral effects are subtle and modelling them is subject to several assumptions. A Bayesian analysis of X-ray spectra from the black hole LMXB MAXI J1820+070 using XMM-Newton and NuSTAR. Abstract We adopt a fully Bayesian approach with the best available prior information, making use of the latest spectral models and the most accurate models of ISM absorption, using XMM-Newton RGS data. Our test case is the recently confirmed black hole LMXB MAXI J1820+070. We fit data over the 0.8 – 70 keV range using XMM-Newton and NuSTAR observations. Fig 1. Structure of a low-mass X-ray Binary [1]. Sachin Dias, Simon Vaughan sdd9@leicester.ac.uk System Parameters Our modelling of MAXI J1820+070 includes proper priors on system parameters based on the best available radio through UV observations. System parameters are typically frozen or left entirely free, permitting other parameters to find unphysical values. › Distance: A gamma prior based on VLBI measurements [2]. › Inclination: A Gaussian prior from proper motion of ejecta [2] [3]. › Mass: The mass function (𝑓(𝑀)), mass ratio (𝑞) and inclination (𝑖) combine to give a shifted log-normal prior on the mass. 𝑴𝑩𝑯= 𝒇𝑴 𝟏+ 𝒒𝟐 𝒔𝒊𝒏𝟑(𝒊) › Mass Accretion Rate: A Jeffreys prior between 10−6 ṀEdd and ṀEdd, calculated based on the 10th and 90th percentile masses respectively, assuming a standard accretion disc. References: 1. Image Credit: NASA/R. Hynes 2. Atri et al., 2020, MNRAS, 493, 81 Fig 4. Distance posterior (black) and prior (red). Priors are broader due to effects of unknown errors. Additional Priors We adopt additional priors for the parameters: › Disc Colour Correction Factor (fcol): fcol is typically fixed at 1.7 [8]. Others argue the range could be broader [9] [10]. We assigned a gamma prior over the range [1, 10] with the highest density over [1.4, 2] [9]. › Reflection Emissivity Indices: A gamma prior over the range [0, 10] with a mode at 3 (near Euclidean case) and 10-6 lower density at 10. Ne K-edge Fe L2-edge Oi K-edge Fe L3-edge Fig 10. XMM-Newton RGS spectrum for rev3531 (black) and rev3533 (red). › ISM Column Densities: We fit XMM-Newton RGS spectra using ISMabs. H, O, Ne and Fe column densities were free parameters (having the largest effect in the 11 – 24 Å range) with other column densities fixed (relative to H) to the values given in