 Okay, I think we are live Welcome everyone. Thank you for joining us for today's low physics webinar. My name is Alejandro and I'm going to be your host Today we are presenting the medical models of astrophysical black hole accretion flows by professor James Stone Jim obtained his bachelor and master from Queens University in Kingston, Canada, and then his PhD from the University of Illinois Then he was a professor at Maryland then he went to Cambridge for a little bit then moved to Princeton and Currently he is at the Institute for Advanced Studies. He are also at Princeton, New Jersey His research interests and fluid dynamics particularly Magneto hydrodynamics for which he has developed some of the most powerful and use codes in astrophysics Remember you can ask questions over email through our YouTube channel or Twitter And then the questions would be read at the end of the talk now without further ado We will turn it down over professor Stone. Thank you for joining us and thank you James for accepting our invitation Thank you Alejandro. It's a pleasure to be here Maybe I should share my screen. Yes Okay, hopefully you can see that now perfect. Thank you great So it's a pleasure to be here. Welcome everybody. I Thought I would tell you a little bit about some research. We've been doing actually mostly pre-pandemic This is mostly results that we've obtained in the last five years or so on I'm trying to understand accretion onto compact objects like black holes I apologize if some of you may have seen some of these results at various Presentations because they are over the last few years being published And so there's been some presentations made by many of my collaborators here, which I like to acknowledge Omar Blase, Shane Davis, Carl Thelker, Yanfei Zhang now at the CCA Can't go to meet a Chris White. So it's been a it's a it's an effort that's involved many people and over many years to get to the point where we are beginning to calculate these models with with Full physics that we think is important So I wanted to just you know, I introduced these results and tell you what you know, why this important important problems and well I mean in fact begin by My slides are not I I think I might be sharing the wrong screen my slides are not advancing here. So Let me try sharing that screen Yes, we see now the outline So So I thought I would first motivate, you know why this is an interesting problem to study tell you a little bit about the numerical methods Which are absolutely essential for studying this problem and then again talk about some of these results. We've had over the last five years So basically why is everyone so interested in accretion flows and the answer is very really very simple accretion onto compact objects is by far the most energetic Process in the universe. It leaves it releases far more energy Program then then say nuclear fusion in stars And so if accretion powers all of the most luminous sources that we know in the universe This includes quasars an active galactic nuclei And in the stellar context when we have close binary stars X-ray binaries for example are powered by accretion onto a Neutron star or white dwarf in a close binary system And so we'd really like to understand this gas dynamical process of accretion to understand these very luminous sources And more over more recently, I'm sure many of you know We've obtained the first image of accretion flows onto black holes through the event horizon telescope This is a millimeter interferometer with a baseline essentially the diameter of the earth It's a attained very high resolution images Of the black hole and and in the galaxy m87. It's elliptical galaxy Supermassive black hole at the center And we've known about this black hole for a very long time because it produces Relativistic jets which were seen in optical images taken of the galaxy more than 100 years ago this bright white filament here And now with the ht we could actually resolve The center You know with with multiple resolution elements across the event horizon scale for this black hole And we see this bright ring of emission in the millimeter wavelengths Which is coming from an accretion disc from an accretion flow On the scales of the vent horizon in the system and we like to understand You know Exactly how this flow is being fed and its dynamics So while the ht is a wonderful instrument for observing black holes It's also a fabulous instrument for understanding accretion It's really a wonderful experiment to understand relativistic plasma physics because that's what we're actually observing It's the plasma as it's accreting into the black hole So these these observations really motivate, you know, what we want to do but The accretion comes in many different forms and the physics you need to include really depends on what mode of accretion you're in There's a so-called radiation dominated accretion involving dense collisionless plasmas Where there a strong radiation field and strong cooling by strong radiation I mean the radiation pressure is comparable to the thermal pressure And typically that involves eddington ratios and i'll explain exactly what that is in a minute The eddington ratio bigger than say 10 to the minus two 10 to the minus three And the kind of objects that we observe in this state are quasars and x-ray binaries in the so-called soft high state Also, tds or tidal disruption events are thought to be super eddington accretion flows There's also low luminosity accretion disks or accretion flows where it involves accretion a very diffuse plasma Plasma in which the collisional mean free path is typically bigger than the event horizon itself So the plasma is essentially collision less It's very inefficient at producing radiation. It doesn't cool at all. It's essentially Adiabatic as it falls in and this this typically occurs when the eddington ratio is very very very small Say 10 to the minus four or less And it turns out the galactic center in m 87 the two sources that the eht is observing is in this low Luminosity state and the physics there is very different because it's really collisionless plasma physics And my focus today will be on the radiation dominated case where we need to include the radiation field Along with the plasma physics and that's really aimed towards these high luminosity sources Despite the interest in these low luminosity sources. I won't say too much more But I have to say something now. There's sort of an industry in modeling that in them now there's a A large number of groups that are Studying eht like flows or flows observed by eht and involves doing full general relativistic mhd simulations i'll explain explain why mhd is so important in a minute And basically this movie shows the accretion flow around the black hole is sort of an A ploidal slice of the density showing the time evolution of the plasma as it creates inwards And then you can ray trace that or make images including all the general relativistic ray tracing effects all of the light bending effects Due to the curved spacetime of the black hole to make images of what that would look like at various orientations from 40 degrees To fully face on at 90 degrees and many of these images are strikingly similar to what the eht observes And so we think that we at zerith level understand what the eht is observing is one of these accretion flows around a black hole But again, this is in this low luminosity Limit where the radiation field is really not very very important And I really want to focus on the high luminosity state Where there's sort of many more observations and many more observationally motivated questions Of these high luminous accretion systems. So for example recent x-ray satellite new star has unambiguously identified ultra luminous x-ray sources These are Point sources and external galaxies which have very high lute x-ray luminosities They've been unambiguously identified to be neutron stars with the luminosity greatly exceeding the eddington luminosity You know thought to be the highest luminosity you can sustain for an accretion flow So how does super eddington accretion occur? It clearly occurs in nature We we now have an unambiguous proof that super eddington accretion occurs. And how is that possible? Moreover A slightly below an eddington ratio of one sub eddington accretion discs Have a ubiquitous x-ray spectrum that involves not just a thermal spectrum from an accretion disc So Observed as the spectrum of sickness x1 a very famous x-ray source creating close binary system And the observed spectrum is this black line and it can be fit by multiple components including a thermal accretion disc But it essential is also a corona Made up of non-thermal emission from very very hot plasma And a very significant fraction of the total luminosity from the source comes from this corona So how do accretion discs produce these very hot plasma? Which produces this coronal emission that we observe it's a very significant part of sub eddington accretion discs Then finally, you know one way to measure mass and spin a black hole Is by spitting the fitting the spectra, especially the so-called iron k line profile Assuming a theoretical model a so-called alpha disc model for the emission from the disc And can we really compute synthetic spectra from first principles going beyond alpha discs? and try to test these continuum fitting models because If there is an error in our spectrum, it will mean that the mass and spin that we're inferring from the spectrum is incorrect We really need to calibrate these spectral fitting models to make sure they're really working And so this is just a sampling of all kinds of questions that have emerged about luminous secreting sources That theoretical models would hope to try to address and that's really our goals to try to address these questions And so what are we going to need to try to? investigate these questions and the first thing we're going to need is mhd And that's because we now know that The accretion flow itself is driven by magnetic processes so-called magnetorotational instability So this is a local linear instability with a very large growth rate that occurs in a keplerian rotation field in plasma magnetized plasma orbiting around a compact object or indeed any plasma in any keplerian flow And you know the the the instability itself can be you know Discovered analytically if you like you can get the dispersion relation But to study the non-linear regime of the instability really requires numerical methods And so this little uh, this little movie that was playing here Was showing you a small little piece of an accretion disc And it was showing you the evolution of the angular velocity fluctuations generated by the magnetorotational MRI the magnetorotational instability see the linear modes emerge and then they go fully non-linear and generate turbulence And so if we want to understand this turbulence Which indeed sets the mass accretion rate and sets the angular momentum transport rate in the flow We need to use mhd methods. You have to incorporate magnetic fields directly You can't just model this with a viscosity. It needs to be modeled with full mhd And so mhd is essential for modeling black hole accretion flows And we can either use so-called global simulations, which I'll talk about mostly today in which we model the entire accretion flow over many decades in radius Or we've learned a lot about the MRI from so-called local simulations where you study a small little patch Of an accretion flow using appropriate boundary conditions to focus all your computational effort on a smaller area So both local and global simulations have taught us about the MRI and and these are going to be required mhd is going to be required to model these these black hole accretion flows in the luminous state But in addition, we're going to need to incorporate radiation fields And that's Straightforward from from the so-called endington limit. I've already mentioned a few times So basically spherical accretion is clearly only possible when the outward force from the radiation field Exceeds the or is smaller than the the inward pull of gravity If the radiation exceeds gravity, you'll just blow away all the plasma the radiation force will exceed gravity And you'll you'll produce a wind and not an accretion flow So these two forces balance when the radiation forces, which is just a Intensity specific intensity luminosity over the area at some radius r Times the electron scattering opacity is equal to just a you know far away from the black hole You can just use the Newtonian gravitational force on on the protons But the electrons and protons are tightly coupled by electrostatic forces So while the photons interact with the electrons the mass is all on the protons And so you put this the proton mass to compute the gravitational force and the electron scattering opacity to compute the radiation force So very simple formula Which gives you the so-called endington luminosity if l is bigger than this endington luminosity You should not be able to get spherically symmetric accretion because the Radiation pressure on the electrons and indeed the plasma would exceed the inward pull of gravity and you should get a wind And indeed whenever the luminosity is close to eddington In fact, even just 10 to the minus 2 eddington Then you're going to need to incorporate these radiation forces because they're very very important in producing the accretion flow itself And so we need to include both radiation and magnetic fields into these calculations So If we're not studying the flow close to the black hole if we're say 10 or 20 or more rgoa We can just write down the Newtonian equations of radiation mhd, which I've done here So while this talk is about black hole accretion flows, I'm going to write down the Newtonian equations for mhd the black and blue terms and equations represent the Flu dynamics mass conservation momentum conservation energy conservation And maxwell's equations to evolve the magnetic field For a magnetized fluid And then in addition we need to add in the radiation forces and the momentum equation this minus g representing the radiation force and the Net heating cooling rate due to photon material interaction This is source term in the energy equation and then to compute these terms They're just moments of the specific intensity of the radiation field that requires integrating the radiation Over all angles and frequencies at all positions in space using the rate of transfer equation written in red on the bottom So in principle, we have a straightforward well posed closed system of pds Where the source terms and the fluid equation just become come from angular quadratures of the specific intensity To calculate the heating cooling and radiation forces in the lab frame And there's no missing physics no subgrid needed here And so I always say this in many ways is an easier computational problem than many others in astrophysics For example in galaxy formation where there's small scale processes that are unresolved on the computational mess Feedback from star formation and turbulence and so on that have to be included through some kind of subgrid prescription And here there are no subgrid models No subgrid physics needed in principle These equations describe the dynamics of the plasma And we just need to solve them as accurately as we can and understand the resulting solutions and that will tell us About black hole accretion flows and if the solutions don't match the observations We're going to learn some very interesting physics because that would say there's something missing here But what could be missing there would be some other very interesting physics going on And so in some ways these direct ab initio models are possible in these flows So despite this being a complicated system of equations, I admit that solving these equations is not easy At least at the end of the day, we're not missing something else and I think that's something to be said So solving these equations As you might guess analytically in full three dimensions and time dependent flows Is just not possible and so computational methods have emerged as being absolutely crucial And and why are they so useful and important partially because of faster computers Mostly because of better software. So I wanted to say a couple of words about those or the computational approaches used here The faster computers If you're not aware or if you're not seen this before you might find this of interest this So-called top 500 list is a list of the world's fastest computers The red line is the number one computer at any given date at time the blue line is the Some of all the computers in the top 500 list Um, and the yellow line is the slowest computer on the list Uh, and the performance is measured in gigaflops. So a teraflop is this line here petaflop Exaflop and the list is created in 1993 and has continued to today And so what's amazing about this result is this exponential growth Moore's law, which has shown you the growth of the fastest computers Moore's law has not stopped the power law may have broken around 2012 or so, but it's still continuing as an exponential growth Uh, that's because the uh technology changed them previously. It was faster processors Nowadays, it's more parallel process and that the growth rate is slightly different and you can also see trends of Technological advances that make the number one computer suddenly jump up very quickly And then the technology doesn't change for a while and it jumps up again We're about to jump into the exaflop error this year as more than one exaflop computer is installed around the world Uh in this coming 2022 and so, uh, obviously this drives, uh, a huge expansion in computation It's analogous to my observ observational colleagues having their telescopes You know expand in aperture, you know exponentially in time, which for them would be, you know, absolutely amazing But that's what's happening in computation. What we can do is is exponentially, uh, you know getting faster And that's pretty amazing. But in fact the number one driver of Computation and the importance of computation is not the increase in computers. It's the increase in And uh improvements in software You know a better algorithm always beats a faster computer And so nowadays we have very sophisticated algorithms for doing Uh computational fluid dynamics in curved spacetime with radiation transport There are many such codes available and have been implemented. I've been working with one in particular called Athena plus plus This is just the one code that we've been working on but there are You know, literally dozens of groups around the world developing these application codes and many other codes around Athena plus plus implements so-called constrained transport algorithm for mhd Adaptive and static mesh refinement. I'll say a few more words about some of these features Includes gr and stationary spacetimes and most importantly full transport Uh radiation uh transport for doing these calculations So the sort of things that are really important for what i'm talking about today are the red highlighted things this mhd as I mentioned and radiation transport along with adaptive mesh refinement and good scaling and and performance Are all what enable the kind of calculations if you just gave us The world's biggest computer, but without the software to to run on it It's pointless you have to have the software that can take advantage of that And and the software is really the intellectual effort that that's required for these to make progress in this field So the important ingredient. This is adaptive mesh refinement Uh for those who are not working computational fluid dynamics Let me just explain quickly what that what that is And basically your computational domain is broken up into blocks Here this domain is broken up into three by three blocks. It's two-dimensional domain And if there's some region of space where you would like to resolve it better with smaller cells finer resolution Then you just divide the blocks into smaller blocks and keep subdividing those smaller blocks into yet smaller blocks And so you can concentrate very small Spatial grid cells and regions in the volume of the domain that you need them and you don't waste a lot of Resolution or fine resolution areas where you don't need it And so this adaptively it changes the spatial resolution to the flow to resolve small scales where you need it And this block based refinement is what we've implemented in in Athena plus plus Very similar to what in another code called flash but quite different from Codes like Pluto and Enzo for those again who are familiar with astrophysical fluid dynamics. You may know some of these codes This block based amr really works well on modern parallel computers because Communication is only required through the boundaries It's very very efficient on very large parallel systems with large core counts And indeed I think this block based amr is becoming sort of the de facto standard now for large scale computing systems Another feature to get good performance on parallel systems is the ability To interleave calculations and communications and this can be done through something called dynamical execution Where each processor is assigned many many blocks if you go back I mentioned these mesh blocks in the previous Slide here these you know the domain is divided into these blocks Release processor on the computer can be assigned many many many of these blocks And the integration of each of those blocks is independent And so the blocks are organized into a dynamical execution Procedure called a task list So part of the execution requires communication between processors through something called the message passing interface And the calculations and communications Can be overlapped some you can be communicating on one block while you're computing on another And that allows you to hide all the communication on the computer Behind calculations and allows you to run a very very large core counts at very very high efficiency. So again Through the evolution of algorithms and software that you know has emerged this dynamical execution model And again, it's important for being able to run in very very large core counts And again, this is implemented in Athena plus plus and then finally We need to know that our algorithms are accurate that they're calibrated that we they're really giving you the right solution that our approximations That we implement in the methods are giving you and converging to the correct solutions for the equations of fluid dynamics You can do that by comparing to analytic solutions And you can also doing it by comparing to other numerical solutions for fixed test problems And a very popular test problem is studying nonlinear regime of instabilities fluid dynamical instabilities For example the kelvin helmholtz instability that occurs when two fluids are Shearing past each other through an interface then that interface is unstable to the development of roles and Substructure and this is so-called kelvin helmholtz instability and what's shown here Is the results from a calculation using Athena at different resolutions And a spectral code called deadless Each row here is the solution at a given time And each vertical column is the Athena solution at either 4096 squared 8192 squared or a deadless At 4096 squared spectral elements And you can see as As you increase the resolution with Athena Pixel by pixel the solution is identical to the deadless 4096 solution At at Athena 4096 squared. There are some slight subtle differences between the secondary k h rolls a deep in the nonlinear regime But at 8192 squared the Athena solution is basically pixel by pixel identical and you can be much more quantitative you can calculate the L1 error norm between the two solutions is a function of time And you can show how the solution converges to the deadless solution And indeed at 8192 the error you know maximum Integrated L1 error is at 10 to the minus 5 so a single precision On a computer which you basically converge to the spectral solution And so with these finite volume methods implemented in modern codes You can get spectral resolution at half the cost because these even at 8192 squared Athena runs much much faster than spectral codes because they're much more expensive requiring all all communications and ffts And so you know you you're able to calibrate your methods and confirm They really are giving you as good accuracy as sort of the the best algorithms We have for fluid dynamic spectral methods and it gives you confidence that your methods are working So let me say also about the radiation transport methods because again, this is crucial for studying radiation dominated Problems where we simply discretize and evolve the frequency integrated radiation transport equation as I wrote down earlier typically using roughly 100 angles at each grid point Then we can take angular moments of that specific intensity to calculate the heating rate in force Because you know this this greatly increases the complexity because we have 100 more variables per grid point 100 angles specific intensity to 100 angles but The cost to integrate the radiation transport equation at any given angle is much less than the cost to integrate in mhd equations And therefore we can roughly afford to do 100 angles at the same computational cost as doing the full mhd And so this makes the problem tractable Because we're solving the time-dependent transport equation. It's suitable for relativistic problems We're following their dynamical evolution on the light crossing time by solving the time-dependent transport equation Currently we have a frequency-dependent version is working as well and we're currently doing new calculations with frequency-dependent transport And these full transport methods are are really quite important because current generation of modeling radiation transport typically involves approximate methods for example flex-limited diffusion or fld Which involves simply reducing the transport equation into a two-temperature diffusion problem Or so-called m1 methods which assume an analytic closure For the moments of the radiation field without actually solving the transport equation directly And uh through various test problems You know you can find differences between direct solution of the transport equation using so-called Variable-ending-contensor methods like the et versus m1 versus fld So here's a test problem where you have a hot plate emitting photons into an optically thin medium the hot plate Extends from minus one to one in this domain here and you just simply calculate what the radiation energy density is above this hot plate as photons emerge And the solution from this variable-ending-contensor m1 and fld methods are shown In this panel here the analytic solution the exact solution is the black lines And the red is again the v et solution repeated. And so clearly these Direct transport methods converge to the correct solution. They are consistent with the underlying pds. You're solving Whereas m1 and fld does not converge to the solution of the transport equation For simple test problems like this and this is a relevant test problem because our cretion disc In the low luminosity cases will be a thin disc which would be like a hot plate And we want to know what the radiation field is above The disc and so you know these full transport methods potentially will be important We need to you know, it's important in the future to be able to calculate these flows using these full transport methods While early solutions using other methods are certainly warranted and are very important Ultimately we want to study these flows using these full transport methods And without belaboring again, we can test that our full transport radiation is working Again through both analytic and numerical problems So a great analytic problem is the dispersion relation for linear waves So these are just basically sound waves and radiating dominating plasma You can calculate the phase velocity and damping rate due to the emission absorption and radiation For the sound waves and the analytic solution are the red blue and black lines computed for different ratios of the radiation to gas pressure So it's a parameter in the problem And then the stars are the numerically measured phase velocity and damping rates from our code Using different optical depths per wavelength That's the x-axis here And so you can see excellent agreement between the numerically measured dispersion relation for these waves and the analytic solution over a wide range of parameter space Optical depth and radiation to gas pressure radio ratio And again, you can be more quantitative and calculate the l1 error norms for one of these points and show that they converge With numerical resolution in regions where it's not radiation pressure dominated You get second order convergence because we're using a backward oil or implicit scheme There's first order convergence where radiation pressure dominates and that's these two curves here And by the way, this convergence demonstrates the importance of algorithms Because notice that second order algorithms give you you know up to two orders of magnitude lower air Than a first order algorithm does for the same problem And so you would need a computer or you would need a resolution 100 times higher per dimension in a first order algorithm to get the same accuracy And 3d that's 10 to the uh, uh, you know two to the four that's 10 to the eight times more expensive So no computer advancement is ever going to beat A second order algorithm compared to a first order algorithm No improvement in computer speed is ever going to make a first order method Be more accurate than a second order method And so this is a you know demonstration of why it's so important to have accurate algorithms And why it's really the improvement in algorithms, not the faster the computers That's been the most important advancement and being able to do computational problems accurately and robustly That problem is linear So we want to say nonlinear evolution of turbulent flows and so you want a nonlinear test problem And that can be provided by radiation dominated shocks Again, this is just a one-dimensional plane parallel steady state shock for which there's a semi-analytic solution shown in the red dotted line And again, you can set this solution up with a numerical code and you get excellent agreement between the two Again, you can compute l1 errors now they converge at first order because there's a discontinuity in the problem And everything is first order for discontinuities But nonetheless you repeat you you recover all of the structure of the radiation dominated shock including this This uh radiative precursor which heats the temperature upstream of the shock wave and the so-called zeldovich spike Which is a post shock cooling region due to the emission of radiation And so again, we can confirm these methods are working well on on radiation dominated problems Again, I mentioned performance is important and we we get excellent scaling. So up to a thousand nodes, which is more than half a million cores on modern parallel computers So these are x of scale computers these finite volume methods Show performance which does not decrease with number of nodes being used that is the performance per core Out to half a million cores is roughly the same. It's sort of 95 percent The same as it was if you're just running on one processor So you have 95 efficiency running on the entire machine out to half a million cores So these finite volume methods show excellent scaling on modern computers And these large-scale computers therefore and these methods are are well suited for large-scale parallel computing um For these kind of problems Moreover, uh many computers nowadays are accelerated by devices like Graphical processor units like GPUs and again these methods port well to GPUs So here's an example of the implementation of Athena plus plus onto a GPU using the so-called cocos performance portability library On a single GPU For large enough, you know, this shows you the performance versus the size of the mesh on the GPU A 32 cube mesh is just not big enough to keep a GPU busy. And so the performance is low But on a 256 cube mesh on a single GPU You're getting over 100 million zone cycles or zone updates per per wall clock second on a single gpu Um on a comparison to the cpu It's more than 20 times faster. And so you get excellent performance and improved scaling or improved Performance on GPUs. In fact, I spent my pandemic Rewriting Athena plus plus into cocos and there's a new version On including full gr and full radiation transport that we've just finished. We're now currently running on Parallel systems to do a whole new series of grm hd calculations with radiation transport on GPU accelerated machines using this cocos library and so Again, these five volume methods scale and and uh, adapt extremely well to modern computing systems, including gpus So, let me let me uh, talk about some of these results now and I should first say Something about previous work. We're not the only group working on this and indeed for the last uh, five to seven years or so people have been Uh, pioneering studies of grm hd christian flows including radiation I think the first papers were by john mckinney and olex sadowski Um, you know more than six years ago where they did uh, similar to that eht model. I mentioned her very early on They've been doing grm hd calculations. This is a poloidal slice of the density Uh, and the uh flow streamlines are shown here and this is an equatorial slice of the same flow at some late time in the flow uh, where they've done a accretion from a torus including Radiation calculator using them m1 approximation. So again, these are pioneering calculations using an approximate method in full gr to try to understand the effects of radiation Um, and that one of the important results from these calculations is measuring the radiation efficiency What fraction of the energy released by accretion is released by radiation versus what fraction goes into the black hole And uh, they get a radiation efficiencies of 10 percent or so in these calculations, which are very intriguing And more recently, uh, I think, uh, matuliska and sasha jackasko. I have recently Published or presented a paper posted a paper in which they have Repeated these calculations using the same numerical methods But now on a gpu accelerated cluster. So at higher resolution and again are reporting Similar results, but with new, uh, new sort of thermal instabilities emerging new clumping produced at very high resolution And so again, these are very interesting and important calculations to to understand. Um, these accretion flows using these approximate methods And our goal is to try to repeat some of this using these full transport methods To a confirm the results and be understand Uh, the accretion flow at at higher luminosities using full transport methods We've been using time allocated to us from the doe insight program, which provides access to very very large computers like mira We have not been doing full gr, but have been using Newtonian calculations in a post Newtonian potential that means our calculations are only relevant say beyond 10 or 20 rg Uh, we've been using this full time dependent rate of transfer method 80 angles per grid cell Uh, you know a factor of a thousand in dynamic range and radius With, uh, amr to give us resolutions in the interregions of about a thousand cubed grid cells And what's shown below is a movie of the density and velocity Streamlines resulting from one of our calculations and you can see how MRI turbulence develops Generates all sorts of fine scale structure and it also most importantly produces an increase in flow inwards And uh, you know, then the radiation field is generated dynamically and self-consistency By this accretion flow as the plasma is heated by the accretion And we follow the feedback and cooling and the radiation forces By solving the ray of transfer equation simultaneously with the image The equations as the as the flow proceeds the calculation proceeds And so to show you the what what the radiation field is doing in that calculation this movie shows you the radiation flux on an equatorial sliced blue is outgoing radiation flux Red is in going and we're going to just move outwards the the sphere will slice the data at larger and larger radii the radii is uh uh shown somewhere At right here, this is rg where it's being sliced 150 rg You can see that there's mostly outgoing flux in the polar regions And in the midplane in the equator where there's mhg turbulence and the radiation is trapped in the plasma You see the turbulent eddies are generating both inflow and outflow as they drag the radiation field around Most of the radiation is escaping in the polar regions in this very big large wedge So already you see a hint as to how you get around the eddington limit You do it by having non-spherical accretion Accretions primarily occurring at the midplane at the equator and the radiation is escaping Along with matter and there's a powerful wind generated by the radiation forces The outflow is primarily occurring and the poles of the flow uh while accretion is proceeding at the equator This calculation generated super eddington accretion that is to say the mass accretion rate Compared to the eddington rate that is the eddington rate mass accretion rate is what would produce the eddington velocity at 10 efficiency So we're getting eddington ratios that are a hundred or more in these in these Calculations depending on what magnetic field Geometry assume which tries the accretion through the MRI and depending what the surface density of the disk is initially So the number at the end is the uh that labels the run is the accretion rate and the eddington At the the mass accretion rate of the eddington rate. So this is 150 33 25 and 52 so you see The accretion rate is highly variable But there's a long-term average value which can be in this case, you know 150 times eddington so very highly spreading to And you know, so some of the important results to come uh one is that Uh, mhd turbulence is very important for transporting radiation in the disk itself Uh, so these two images show you the Correlation function between the density and the magnetic energy b squared Black is negative. So they're anti correlated red positive. They're positive correlated You can see in the equatorial plane These two quantities are negatively correlated mostly black with meaning that the where the magnetic field is large The density is low meaning there's regions of there are bubbles of high magnetic field strength and low density And those bubbles of high magnetic field are positively correlated with outgoing velocity vz So the again, there's these red core positive correlation functions Between vz and b b squared meaning that these low density bubbles where b squared is large are moving outwards in the disk Carrying radiation with them. They're filled with low density low optical depth regions filled with radiation That are transporting energy out of the disk. So basically Turbulent convection is cooling down the radiation the cooling down the accretion disk and this actually exceeds the diffusion rate of Photons in the disk. It's not rate of diffusion that dominates cooling in these radiation dominated It's turbulence driven by the mri In the same way that you know convection can dominate over rate of diffusion inside stars In this case, it's turbulent Convection by the mri that dominates over a diffusion that was unexpected and is not incorporated in analytic models of radiation dominated disks And so but it's a very important contribution in the energy budget of the disk So that's something that emerges from these calculations We have radiative efficiencies that get small this eta rad Is the again the efficiency with a fraction of radiation fraction the energy released by radiation versus the fraction accreted And it's only 1 for this uh 150 times the eddington ratio calculation Um, and it's smaller than the values that the McKinney and Sadowski and others get using m one and that's interesting That's intriguing Is that something because of the numerics or something because we're doing something different in our initial conditions? We really need to understand that but what we find is that the eddington or the efficiency Drops as the eddington ratio gets larger Resulting in a total lunacy, which is roughly constant the actual total amount of energy released by the system is roughly You know 10 times the eddington and never gets larger than that because their efficiency drops to compensate the additional accretion energy released at higher accretion rates What about sub eddington disks? We can also use lower surface densities in the torus initially and study mass accretion rates that are therefore smaller and therefore produce sub eddington accretion So we've done calculations where the mass accretion rate is only 0.07 times the eddington mass accretion rates. So m dot or eddington saturates highly Variable but saturates at roughly 0.07 And we can actually calculate the luminosity as a function of time from the system. These are light curves so these are You know calculated ab initio light curves from recruiting compact objects What's interesting is that often them m dot is used as a proxy for the luminosity If you don't incorporate radiation transport, you only have the plasma often people use m dot to estimate what the Associated luminosity of the accretion flow would be and you can see there's not a very good Correspondence between m dot and the actual emergent intensity that comes when you do a full radiation to hydra calculation Therefore m dot really is not a very good proxy for the emission released In this accretion flow Uh, we've also done models which are 0.2. Uh eddington. So we've spanned Uh, you know about a factor of 10 in eddington ratio below one Again, we have mass accretion rates and light curves for those systems And they're very interestingly different. So this is kind of a rug's gallery snapshots of the time averaged and as emutely averaged structure of the accretion flow From super eddington. We're 150 times mass eddington mass accretion rate here All the way down to the lowest model 0.07 and spanning the full range 33.2 all the way down to 0.07 So you can see as the eddington ratio gets smaller The disc gets thinner and thinner it cools down and gets thinner. So the colors are the uh, density the Streamlines here are the velocity streamlines with the color measured in a fraction of speed of light you can see that The sub eddington ratio models produce very very thin discs The black dotted line is the photosphere the optical depth one Surface and the photosphere gets very very thin close to the disc surface You also see an outflow a strong outflow generated in these sub eddington discs And so the structure of the disc qualitatively changes as you go from super eddington Down to these sub eddington discs. These sub eddington discs is what we would think a normal agn seaford galaxy would look like This is the kind of uh parameter regime such discs would be in These discs are thermally stable. Uh, let me not say much more about that There's uh interesting predictions these radiation down a disc to be thermally stable It turns out that radiation pressure or sorry magnetic pressure probably stabilizes them Instead, let me say something about radiation stress because another resulting um surprising result that came from these calculations is that these low Uh luminosity so sub eddington results 0.07 the eddington ratio results Show that radiation stress is really important in the upper layer. So what's plotted here is again the time and as we've averaged Uh toroidal stress on the plasma Uh the rental stress that's the fluid stress due to Uh non-axis symmetric velocity fluctuations in the flow. That's rental stress There's the Maxwell stress due to magnetic torques on the flow That's produced by the mri And then finally there's the radiation stress because the radiation field can produce You know just like particle collisions can transport angle momentum then so can photon Collisions with electrons transport momentum and they can transport angle momentum. And so there's a non-axis Or a non-diagonal component to the radiation stress stress tensor Which is equivalent to radiation viscosity and that's what's plotted here the r5 component of the radiation viscous stress tensor You can see that in the mid-plane of the disk the mri dominates So it's magnetic torques that are driving the inflow In the optically thick mid-plane of the disk just as we have understood for many decades that magnetic fields drive the accretion But in the optically thin upper regions, it's viscous torques that are dominant and they actually drive A surface accretion layer Again, that was kind of unexpected and another difference with more approximate methods like m1 Is that m1 cannot capture the non The non-diagonal components of the stress tensor. There are they're assumed to be zero in m1 And so it's important to use these full transport methods Again to assess the importance of the viscous. Sorry the the radiation stress on angle momentum transport as well And then finally there's very interesting results about the thermodynamics of their Plasma and these subattington disks. So in particular For the 0.07 mass accretion rate. This is again a plot of the temperature In the time and as musically average flow That the temperature you can see is extremely high Above the surface layers of the disk Again, that's the formation of extremely hot plasma In the corona of the disk basically and the reason why is because this plasma is optically thin It's heated by magnetic dissipation of turbulence But it cannot cool because it's optically thin and so it just heats up to very very high temperatures And so we see spontaneous emergence of extremely hot corona at low eddington ratios from these radiation mhd calculations Again an agreement with observations of say seaford galaxies They don't appear and the super eddington flows because the photosphere Is confined to the polar regions and most of the flow is optically thick But at the low luminosity where the the photosphere is much much Closer to the equator. That's where we see the emergence of these of these corona We've tried spectral fitting of some of our results. So we've taken a snapshot of our calculation and we fed it into a monic harlow radiation transport code Which does full frequency and line dependent transport and then we used x spec to compute the opacities for that calculation And we've computed synthetic spectra and this black wiggly line is the spectrum from one of our our sorry, that's uh the the blue and green curves are Spectra computed from different regions of our calculation resulting in this in the red curve Which is the sum of the spectrum of over the entire radial range of our calculation And the black curve is an actual observed spectrum for an ultra luminous x-ray source Observed by new star and xm m newton With his phone number here ngc 13 13 x1 Uh, there's surprisingly few free parameters in this calculation. Basically, there's only one the mass accretion rate We don't know from the observation what the mass accretion rate is and that moves this curve Up and down vertically that sets the normalization. So we've chosen a mass accretion rate that fits The curve and we get an excellent agreement and the mass accretion rate that we choose is actually quite reasonable ends up being tens Of the eddington rate and we know this is a super luminous source And that agrees very very well with what we might expect and so These spectra are very promising and that we can reduce the or reproduce the broadband spectrum Of at least the ulx sources Uh from from these calculations So so let me wrap it up. I know i'm i'm running out of time here by returning to those observational questions How does super eddington accretion occur? Well, we think it occurs from these non-spherical geometries With cooling from turbulent transport being an important part of the agreement Our important ingredient to the flow. It's it's important for for cooling the disc And allowing photons to escape the system How do accretion discs form corona while we see any sub eddington discs That above the photosphere the plasma is unable to cool and that you can generate very very hot plasma In detail, we are not able to reproduce the spectra yet It needs a better model for cotton cooling in the in the coronal regions which dominates the What sets the temperature? It's the dominant physical process setting the temperature in the corona And so we have yet to We have more work to do in order to actually reproduce the spectrum observed in each corona But it's at least a promising step and the energetics and then finally We have some promising spectra And we're certainly working very hard to do a full frequency dependent transport To compute ab initio spectra and test this continuum fitting model that I mentioned at the very beginning So let me just summarize by saying, you know with modern Computational methods were able to do full radiation mhc calculations of these black hole accretion flows Other groups are doing these same kind of calculations in full gr With approximate methods and in the future we plan to also be doing full gr To study these super eddington and sub eddington accretion flows and I've I've got some bullets Summarizing some of the points I've made already and I'll just quit here and answer any questions if there are any Thank you. Thank you very much for this great talk. Let me yeah, there are a few questions Let me start with one that we have on our youtube channel I'm going to paste it here I think we can In case you also want to read it yourself So it says I'm interested in the study of the magnetic field and the behavior of turbulence in the accretion flow in sagittarius star Do you know some important numerical results to consider in this? Thank you. And this is from our youtube channel um, yes, uh So I mentioned this magnet or reticulants magnet or rotational instability first discovered more than 30 years ago in 1991 And in the intervening three decades there has been an awful lot of work in trying to understand Magnetic fields and mhd turbulence and accretion flows. There are a couple of excellent review papers by balbus and holly That I can that you that you can look up there's a paper from 2001 and one from 1999 So if you just search on the archive for for balus and holly There's a review of modern physics paper Which already now is almost 20 years old and somewhat dated but provides an excellent overview of Many of the numerical results on the mri There's to be honest probably by now hundreds to thousands of papers written on Numerical modeling of the mri. I certainly couldn't list them all. Um, that's why I would suggest starting with one of those review papers And then looking in from there I I hope that helps Thank you. We can see if there's a follow-up from that Uh, I have another question here here and it says like could you please comment a little bit more on the gpu implementation? And which part of the computations are more susceptible to be written for gpus? Sure, this is uh, this is uh, the latest stuff we've been doing. Um So I have I've been reluctant to adopt gpu computing for a very long time mostly because uh, it required special uh hardware dependent libraries like kuda Um, which meant that if you write your code in kuda, you can't run it on your laptop anymore And you can't run it on cpus anymore And I simply didn't have the resources to support multiple versions of a code to run on multiple different platforms But what's changed in the last five years is the emergence of a number of open source libraries that allow you To write code that runs on any architecture There's been a long interest in this using things like open mp and open cl Uh, however, the the challenge of those libraries is they require the vendor to implement Compilers that implement those standards Open cl and open mp are just a set of standards that requires the vendor to build a compiler that meets those standards And to be perfectly honest the vendors don't have a whole lot of motivation to write those compilers so instead Uh, this cocos library has emerged. It's spelled k o k k o s It's simply a c plus plus library It's basically a translator It turns whatever code you write in cocos into either standard c plus plus that can be compiled by any compiler gcc or clang into executable for a cpu Or it will turn it into kuda if you're running on an nvidia compiler Or it will turn it into sickle if you want to run on an intel gpu And so it takes away all of the work for you you write one code in one Language and it provides performance portability. So that's what we've done. We've rewritten athena and cocos It's just c plus plus. I mean you can't tell the difference. It's just c plus plus and it works exceptionally well We've been able to run on any kind of gpu and some of the key aspects are you have to move the entire calculation in the gpu so all of the data All of the calculation sits on the gpu. We only move data to the cpu to do outputs or to do control logic All the ribbon solvers reconstruction Everything is on the gpu all the amr logic is all on the on the gpu It runs on multiple nodes using mpi. There's kuda aware mpi that allows you to do gpu to gpu at mpi communication Um So so i've been very happy with how cocos works, you know, what the future is I don't know, you know five years from now Will cocos still be around? I don't know. I think what's going to happen is c plus plus is going to Embed some of the functionality that's in things like cocos You know, it's inevitable. You know computing has become heterogeneous There needs to be a way to program architectures that have different memory spaces devices and hosts different execution spaces And that needs to be embedded into the languages that we're using and so A future version of c plus plus is going to have to embed this in and therefore I don't care I'll I'll just use that when it emerges and I think cocos You know if you write your code and cocos it will translate into whatever the syntax that c plus plus provides in the future seamlessly and so I have now become A gpu believer because you can now write portable code that can run on anything I develop it all on my laptop and then I run it on gpus in the office You know as when i'm ready to go for in the production mode and it works seamlessly I'll answer because I've been spending a lot of time working on this and so Awesome, I think I think that's that's that's what they we want actually. Thank you. Um, so I think there are A couple of questions also in you too. Let me see before I read those ones. Is someone here the coordinators have questions Yes, I have a very very nice question in the sense because of as far as I understood is the The the specter that you obtained to observe with xmas or no star It's is the kind of the Time independent specter. So my question is what would happen in the case if the Aggression flow changes in time. It's time dependent like you have a transient Is it possible to or it's going to be taken much longer to right because of the resolution that time right? right very good question. So so you're absolutely right that um We're computing the time evolution of the flow and so In reality the spectrum Is evolving in time Um, and in fact, it's well known that agn are highly variable You know, you look at them from night to night and they change from month to month. They change in fact There's so called changing look quasars. We're over the course of a few Are quit changing look agn where over the course of a few years it'll change completely from a seaford one to a seaford two And so the problem is that variation in time scales The variability that we capture in our calculations Is the variability associated with the flow at a few hundred rg Which is very very short. That's hours to days to months Uh, and the the year variation is occurring at much much larger radii Which is very hard to capture in these kind of numerical simulations because it requires a very very big box To follow the disc out to thousands or tens of thousands of rg And so to be honest Modeling the variability on long time scales through direct simulation like this is going to be very very challenging instead The kind of data sets that we can compare to are agn variability or Black hole variability from from these x-ray binaries You know again for a stellar mass black hole and x-ray binary There the variability is on millisecond time scales because that's the basically orbital time for a stellar mass black hole And indeed we have all these x-ray satellites for the last few decades that have been Timing missions to study the variability of x-ray You know for mission from black holes and stellar sources So we have all this amazing data set that we can compare to on orbital time scales at the event horizon And that's really what we should be doing And another related point for this question is very very important because it brings up many important things Another important point is that the spectrum we see is the total spectrum of the whole disc. It's an unresolved point source to our telescopes and so we see Emission not just from the black hole in the interregions. We see emission from far out. We see intervening plasma We see absorption from gas along the way in the galaxy And so how you'll correct for that? I mean our simulations don't include the whole galaxy So we also have to be very careful about how we actually compare the data What aspects of the observation are the black hole itself? What aspects are the intervening galaxy and how do we separate the two? That's going to be very challenging in many circumstances, but very important too Okay, thank you Thank you Okay, we have also from our youtube channel another question says that person says hi. Thank you for the talk Thank you advection dominates vertical transport only in super eddington accretion So far from the models we've computed It's dumb being dominant in a super eddington case where the disc is very thick geometrically And it's very very thick optically. So the photons are trapped and the diffusion time is very very long For these much much thinner discs The you know to be perfectly honest our spatial resolution is lower and we have much less dynamic range in the turbulence And that may be partially an issue. Maybe we're not really fully resolving all of the turbulent cascade in the the mid plane of these geometrically thin discs But even so it seems like the Turbulent transport of energy is sort of just less important for geometrical regions in these thinner discs than in these very thick sort of wedge like super eddington discs Thank you. We have another question here from the youtube said sorry if you mentioned this Could you comment on the super eddington accretion and the formation of supermassive black holes and what What is your opinion on primordial black holes at sea of supermassive black holes? Yeah, these these are excellent questions. I mean That's a very good point that I I failed to to mention yet another motivation of these calculations is understanding the growth of black holes in cosmic time It was this Very challenging issue that that we've we've discovered very massive black holes at very high red shifts Where there really isn't a whole lot of time to grow a black hole? Uh, and you really need super eddington accretion if you're going to do it You you have to accrete for a significant amount of cosmological time at super eddington rates to get to get that massive and These calculations point out that super eddington accretion is possible You can certainly do that and so you know, that's one feasible way Is it the way that black holes grow at early time? I'm not sure. I mean, that's related to a cosmological You know black hole formation question. What is the primordial seeds of these supermassive black holes? Is it direct collapse? Is it merger? That's a very challenging question that I don't know We have the definitive answer to right now But certainly these calculations are relevant to the growth of black holes in that regime I think that one of the I think the answer has to come from the cosmological context uh, what do I mean by that because A real challenge is is how you get the plasma all the way down to the black hole at a super eddington rate Over the whole dynamic range of radii The calculations we're studying again are still the interregents Somehow you got to get that plasma from parsecs or kill a parsecs away and get it all the way down to the To the event horizon and their feedback from the accretion itself the winds and the radiation field from a super eddington accretion flow If it interacts with that gas as it's falling in it can it can halt accretion at large radii Where it's only very weakly bound to the black hole And this is the process of agn feedback and that's very important to understand In order to know whether or not super eddington accretion really is viable for for long periods of time In other words, you need to start with a gas reservoir That's You know, or you need to supply gas over the whole range of radii for it to really be feasible and To to demonstrate that it's going to require a calculation that goes beyond what we're doing here That incorporates the feedback at large radii. It's a very important calculation to do I think Wonderful. Thank you. Thank you for your time for everyone. I think we are Already past the hour Thanks for joining us. Remember to all the people who will have more talks. This is our first talk of the year We have a lot of talks so you can just go to the whole calendar in in our webpage Thank you very much and stay tuned. Thank you Okay, I think we are not