ner_tags: O O B-Wavelength O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject B-Wavelength O O B-Wavelength O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O B-Software I-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O
tokens: produced synthetic NIR light curves based on GRMHD models that incorporate a model for accelerating electrons from a thermal distribution into a power-law tail. A control model, which contains only thermal electrons, produces no significant NIR emission. A simple non-thermal model that places a constant fraction of the electrons into a non-thermal (κ distribution) component is able to produce the correct spectral slope and flaring flux density but not the variability. The next simplest model is based on the idea that electrons are accelerated due to resistive dissipation in reconnecting current sheets and, therefore, sets the fraction of electrons in the non-thermal distribution proportional to J 2 , where J is the 3-current density measured in the plasma frame. This model matches the spectral slope and flaring emission but also matches the flux density distribution fairly well. A final model fares similarly in matching observations but is both better motivated physically and more computationally expensive. It advects the non-thermal electrons with the fluid, accelerates electrons into the non-thermal component at a rate proportional to J 2 , and allows them to cool using a constant cooling time model. Because these last two models agree with each other relatively well, future work will focus on the simpler one. No model shows substantial NIR centroid wander or any correlation between the NIR flux density and image centroid. These models are the first to accurately produce the observed Sgr A* mm mean flux, mm image size NIR spectral slope, flare duration, and flux distribution at the same time. Future work will adapt these models to 3D and will include Compton scattering in order to examine X-ray flares. APPENDIX A: DISSIPATION IN RELATIVISTIC MHD Here, we prove that heating rate per unit volume due to resistive dissipation (the dissipation function) is J 2 /σ if we adopt the simplest covariant model for Ohm’s law. Maxwell’s equations are Project this into the space normal to the plasma four-velocity u μ using the projection tensor and define the projected current If we then write a simple model for Ohm’s law as where σ is the conductivity, it is easy to show that this reduces to the familiar form of Ohm’s law for a scalar conductivity. To evaluate the dissipation function, observe that since then For an ideal fluid stress-energy tensor, this implies where u is internal energy and p is pressure. This is just the internal energy equation as derived from the first law assuming the dissipation function ρ T d s /dτ = ρ Tu μ s ; μ = 0. Here, the scalars s ≡ entropy and T ≡ temperature. Now consider a magnetized fluid and break the stress-energy tensor into an ideal fluid and electromagnetic piece, . Then From MTW, Misner et al. ( 1973 ), exercise 22.10 (which uses a symmetry argument and Maxwell’s equations) Combining, Then Ohm’s law implies This is positive definite because J μ is spacelike by construction and, therefore, the second law is