Perhaps you have experienced your family members, significant other, or friends behaving rudely in front of you. This is exactly what happened to Nancy. Meet Nancy.  Her close friends describe her as a glass-half-full kind of girl, hard-working, extremely courteous, and polite. But her friends worry. They say her extreme politeness can take a toll on her emotional well-being. Rude people can sometimes take advantage of her strength and behave improperly in her presence. Oh no. So how does she respond to these rudely behaving fellows? Let's find out, shall we? One fine afternoon while working her part-time job in the convenience store of her college, a young lady walks up to the counter. She plops a can of energy drink and tuna sandwiches onto it, all the while frantically looking for something in her sling bag. Excuse me. Did you forget to bring your card? You can stand using the college app if you've downloaded it inside your phone. Nancy said politely. The woman rolls her eyes. And what makes you think I brought my phone? The customer raises her voice. Nancy is taken aback by her snarky remark. She then remembers what her mother has always taught her. To be empathetic towards people, even if they might seem rude to you. So this is the time she can use her power of empathy. She decides not to take the rudeness personally, and just let it go. The woman storms off, leaving the drink and sandwiches on the counter unpaid. Maybe she's having a bad day and is projecting that upset feeling to the world. Nancy thought to herself. She feels quite calm and assured when she does not let the negative behavior affect her emotion. As they say, rudeness begets rudeness and is contagious. So yes, dear psych-to-goers, one tip when encountering a rude person is to break the cycle of rudeness by choosing to empathize and be kind. Moving along, do you know what happened when Nancy had to prepare a presentation along with two other groupmates the other day? Meet Will and Amber, the school's hotshot couple. They were Nancy's groupmates. Unfortunately, both of them contributed very little to their preparations. Nancy was the one always arranging a meeting to discuss what they should do regarding the presentation, and most of the time, the couple would bail out. They said they're too busy with their other classes, so they always postponed the discussion. The class presentation was in two days, so Nancy decided to send the couple one last text in the group chat, inviting them to complete the slides together with her in the library. They ignored her invitation, so Nancy proceeded to looking for information and doing the slides all by herself. And that is how she spent the whole weekend. Finally, after finishing up the slides, she logs onto her Instagram only to find it filled with pictures of the star couple's Saturday. Outrage, she then remembered reading an article a while ago on how to behave when someone is rude towards you. It said, one of the ways is to count to 10 and take a few deep breaths. So, she did that. Nancy counted taking a few deep breaths in between. She asked herself, Nancy decided that it's a waste of her emotional energy to let this get under her skin. She lets it go, since she doesn't want the situation to take up too much room in her life. Two days later, the group presentation turns out quite well. The professor compliments the slide presentation stating that the designs and bullet point information is very engaging to the audience. Hearing the compliment, Nancy is elated and feels appreciated. However, her bubble of joy bursts when Will says, thanks to my dearest Amber working very hard for the presentation. Without her, these slides would be super dull.  Here's another tip. When you're dealing with disrespectful people, you need to summon up your courage. Always trust your gut instincts and intellect.  This is unfair. Nancy thought to herself, I spent a whole lot of time finding the information and making the slides all by myself and now someone else is going to take the credit for it. They're being rude and disrespectful towards myself and the time that I spent making the presentation. So that's what made Nancy stand up in the lecture hall. Dr. James. She addresses her professor. I am their groupmate. I'm the one who spent my whole Saturday making the presentation. Leaving Will and Amber shocked. Nancy continued. I designed everything and even edited the video that was played at the beginning of the presentation. The only thing that they were involved in is to attend the class and present from the notes I made on what to say and highlighted during the presentation. She also wanted to spill the beans about them lying to her and ignoring her when she asked for a discussion regarding the presentation and having fun instead. But she thought that what she'd said was already enough to let people know that it was her doing the gritty work behind the scenes and she won't let people like Amber or Will take away the appreciation from her. Okay Nancy, thank you for letting me know. Dr. James then continues. Will, Amber, I'll need to see you after class. Nancy, I'll see you separately and we'll let you know. Dr. James asked to meet Nancy two days later. He asked her some questions and clarified things with her. Dr. James said that this will not affect their carry marks in any way since the presentation is judged collectively as a group. I appreciate you standing up for yourself. Dr. James said. I hope this experience will teach you more about yourself and how to deal with others and you did a really good job with the presentation. Thank you Nancy. Nancy feels appreciated. She feels ever so grateful to have a supporting lecturer like Dr. James. She walks back home with a light heart and a skip in her step. After all, there is a way to stand in the face of rudeness without resorting to it yourself. Have you ever encountered a person behaving rudely towards you? How did you respond to them? Now that you have some tips and advice from Nancy, let us know in the comments below.


Of course, being from here, I've always been interested at some point to make a wine here in Romania. Marc Hezma, who's our HATES World Consultant, I call him our spiritual advisor, but from the beginning I chose to work with Marc because we like and we think about wine in a very similar term. So we're acid junkies, we like fresh wines, elegant wines with finesse, relatively low in alcohol. You know, 12 and a half, 13 for the whites, not really more than 14 for the reds. Wines that can be drunk relatively quickly that you don't necessarily need to wait for forever to mature and open them. We do a lot of experimentation, we like to try a lot on your things. That's why we do small batch modifications. We also, right from the beginning, wanted to focus on the local grape varieties, Fates Canega and for the white Fates Calbus. Frankly, we do as little as possible. We want, by the time the grapes arrive in the vineyard, we have 8-9% of quality wine right there. We just have a press, we have a destemmer and a pump, and that's pretty much it. We ferment naturally, so without any additives at all, no selected yeast, no enzyme, no additives of any kind. In 2016, we were able to make our first estate wine, which is a sandwich. Sandwiches actually, in true Burgundian fashion, is an actual piece of land that is a sandwich, in essence. In particular, it's a reserve because it happens to be a barrel that we thought is quite exceptional. It's a very pure expression of the grape of our ancestral grape. It goes to show that here in Romania, we can make well-class wines that can stand near any other in the world.


In this presentation, we will continue on with our statements of cash flows. We're not going to enter the final adjustments that we will need to finalize the statement of cash flows to bring those last few numbers to the correct balances. In order to do that, we're going to use this information. We've got our comparative balance sheet support accounting instruction by clicking the link below, giving you a free month membership to all of the content on our website, broken out by category, further broken out by course. Each course then organized in a logical, reasonable fashion, making it much more easy to find what you need than can be done on a YouTube page. We also include added resources such as Excel practice problems, PDF files, and more like QuickBooks backup files when applicable. So once again, click the link below for a free month membership to our website and all the content on it. Our income statement and additional information, we put together most of our information so far with the comparative balance sheet, which we made into a worksheet. Now we're going to use some of these other resources, the income statement, the additional resources to make those final adjustments, those fine tunings that are needed to get those a few numbers that we have left and noted into balance. And this is going to be part of the normal practice where once we get this information set up, we can then make some comparisons such as net income, does it tie out, such as depreciation, does it tie out on the cash flow statement to what we see here on the income statement. Then we can have this other information which will be given in book problems in practice, of course, we'll just go to the general ledger and we'll get this information in a book problem. We don't want to give all the detail of a general ledger or just when we're going over an example. So we have to just kind of give this other information in practice. We go to the GL and we can see that information, then we'll pull any documents we need, including if we purchased the equipment and we took a loan out or any of that kind of stuff, we'll purchase that, we'll pull that out. We'll talk a little bit about that process as we go through here. So now what we want to do is look through these journal entries related to this additional information. And if we think about what we've had so far, we noted that there's going to be a couple areas we need to go back to and fix. One, we noted that net income didn't tie out to the income statement. We noted that depreciation didn't tie out. And we noted that the equipment that we put on the books probably something more happened. That's always something we need to go back to. And we noted that the notes payable is probably something more to it than just taking the difference between notes payable. It could be more activity. In practice, we would look at the GL again. Here, they're just going to give us that more activity and we're going to try to figure out, okay, what types of journal entries is this added activity given related to? Now, obviously, if they're giving this information in like a book type problem, then we're going to, it's useful just to go through that and think about it. Okay, what is the journal entry related to these? In practice, we would always pretty much do this for a cash flow statement for the equipment accounts and the loan account. If there's any activity, we would naturally go through there, figure out the few transactions related to it and what the journal entries would be. And note that these types of accounts don't have a lot of activity. So it shouldn't be too difficult to do that, meaning we're not going to buy equipment every day. It's not like inventory. So whatever activity is there, there should be fairly few of it. And we can figure out what happened and make these types of adjustments as needed. We're going to start here with E because that's actually going to be a smaller journal entries. That's where we will start. We'll pick off that one first and move it from there. It says we declared and paid cash dividends of $53,600. So anytime we get this added information, I would think about the journal entries related to them. And then we'll go back to our worksheet and say, okay, what are we going to do with our cash flows, David, based on this information? So if we declared and paid cash dividends, we could think of that as two journal entries where we declare the dividend and have a payable and then we pay it. But if we combine those two out, if they both happen in the same time period, then in essence, we had retained earnings and cash. In other words, cash went down, we paid cash, the debit's going to go to retained earnings, bringing down retained earnings. So and this is similar to like if a withdrawal for a partnership or a sole proprietor. So we gave money from the company to the owners in the form of dividends, cash went down, and we debited the equity account in this case, retained earnings for a corporation. So what does that do? If we think about that journal entry, what are we going to do to our cash flow statement? Well, on the cash flow statement, we can think, well, net income is going to be affected here on because of this retained earnings. Why? Because remember when we made this net income, what is it from? It's from the difference in our worksheet between the retained earnings. So we made the assumption. We said, okay, we didn't pull this from the income statement. We said, what would it be represented as on the difference between the balance sheet accounts? And typically it would be the difference in retained earnings because we closed out the retained earnings or the net income to retained earnings. So the major difference between retained earnings between two accounting periods should be net income. And that's what we used here. We noted that it wasn't the amount that's on the income statement said, hey, we're going to go back and fix that. Now we're going to go fix that. We're going to say, okay, net income is one of those areas that this hopefully will bring us now in balance with the income statement. But there's got to be something else happening here because we're already where we want to be. So there's got to, we got to do something equal and opposite, kind of like a journal entry somewhere else. So note, I set this up kind of like a journal entry where we're increasing and decreasing. If we do something to net income here to make it correct, then the other side we can put here to cash dividend, cash paid for dividends. So that's going to be down here in the financing. So we paid cash for dividends. That's what happened here. So we're going to make net income correct, basically. And then we're going to post the difference here to cash paid for dividends. Note that if we didn't do it this way. So let's see what that happens. If we do that, then we're going to say, okay, here's net income went from 104 500. I'm kind of putting this like as if it's an adjusting worksheet for adjustments in terms of adjusting entries. And here's our ending adjusted cash flow. The other side of it's going to go down here. And that, of course, should keep us in balance. So we're not talking about debits and credits, but we're using kind of a similar system. We're saying, Hey, we tied out to the 61 900 already using the numbers that we get from our worksheet. If we make any adjustments, we want to do it systematically, we want to say, okay, if we're going to adjust net income to what is on the income statement, hopefully, then we also want to adjust something else so that that difference that we got from the difference in retained earnings is still there. If we did not do it this way, in other words, if we took this number, which is the amount on the income statements working, here's the income statement, here's this number, that's the number we wanted. If we started out just pulling this number and saying that's going to be our first number that we work with, and our first number that we're working with is not on our worksheet that we're using, then it's very likely that we wouldn't understand what what the differences are and be able to figure out why we're not in balance. If we use this number, which is not net income, but then go through this whole process, then we can now figure it out in a systematic way. And note also that we have to do this whole thing basically to have the space down here, to have it built out to be able to break this number out between the two. So now we can go down here and say, okay, the other side of it's going to go to cash paid for dividends, and it's going to be a financing activity. And that'll put us back in balance. So cash went out because we paid it for dividends, it's financing because we're dealing with the owner. It's not it's not an income statement activity. So it's not in the operating activities, we didn't buy anything for the company. So it's not in the investing activities, we're dealing with financing the company and paying back the owner, therefore it's in financing. So that's going to be our first adjustment that we'll have. And that of course makes net income tie out. So that worked. So that looks good. Now we're going to do our next adjustment. And we're going to say that we're going to have the sales sold equipment. We sold the equipment and it says we received 26,050. So if we think about the journal entry first, and then kind of think about what we're going to do in terms of increases and decreases to our cash statement, we can say, okay, the cash went up, equipment must have gone down. And then the accumulated depreciation is going to be a debit because remember it's on the books as a credit, we have to debit it to make it go away. The difference then is going to be 2,100. And that's going to be a loss. So that's what we need to be in balance. That's the plug. So if we took this plus this minus this, we'd need 2,100 in order to remain in balance. So we know that this is going to be a loss, we can think of it a couple different ways. One, it's a debit. And that's kind of like an expense. Expenses are debit balance accounts. Therefore, it's probably a loss, not a gain. And two, if we looked at the book value, which would be the 51,000 minus the 22,850, that would be greater than the cash we got. And therefore, it's a loss. So that's why we're going to name it a loss here. And then that's not the only thing that happened to equipment though. So notice the equipment, of course, is more messy than we would just assume like we just got cash and sold equipment. So the other side of this is that we bought equipment. And how would we know this, you might be asking, we would look at the GL, we'd look at the two accounts that made the difference up in the general ledger, then we would find the journal entries related to it and the documents possibly for those purchases. So then the equipment, it went up by 113,250 cash, we paid 43,250 and we financed it 70,000. So that's common because we buy an equipment and we didn't have the cash for it's common to finance the equipment. So we have this debt now. So these two then are going, this is where the most complicated component is of these journal entries of these types of cash flow statements generally to figure out the equipment because notice all these accounts, it's, it's affecting. Now, if you do everything up to this point, the way we've looked at it, even if you can't figure out this last step, if it's a book problem, you will have picked up a lot of points. If it's a problem in practice, you'll be able to go to your supervisor or whoever and say, look, I know exactly what the difference is. I know exactly what's going on. I know exactly how this thing ties out and it has to do with equipment. And you can start from there and not have to start the whole thing over again. That's, that's the point of this process. Now, our goal now is to take these journal entries and look at our cash flow and try to say, okay, how are we going to apply these in terms of an increase and decrease, convert this into kind of like an increase, decrease to our cash flow accounts, so that we're still in balance. So we're going to use those same kind of balancing concept to adjust these out so that we're still in balance here. So whatever we do with these journal entries, we got to find a home for them in kind of like an increase and decrease mode so that we're still in balance. That's going to be our goal. Now, that's again, a little bit difficult, a little bit more difficult to do this. Now, we noted that we saw when we built this cash flow that depreciation was not right because it didn't match what was on the income statement. We know that we saw a sale, a loss on the income statement, and we didn't put the number here. So there's probably something there. And we noted that cash paid for equipment was probably too simplistic when we put that on there. And we noted that the cash pay for the long-term note, again, probably too simplistic. So we noted that all these things could have more detail to it. However, because they're all tied together with each other, the equipment, the loan, it would have been very difficult for us to do that as we construct. So it's better for us to put these numbers there and now go back to it and say, okay, here's the puzzle. We've got these journal entries and we have to fix these accounts. Now, there's a couple of things we know. We know what the loss is because it's on the income statement and we know what the depreciation is because it's on the income statement. And now we know these journal entries. So let's take this information and try to see how we can adjust these accounts. So first, the depreciation. We're going to say we adjusted depreciation. That's going to be basically this number we're picking up. And we can verify that by saying, okay, if we adjusted depreciation, if we increase depreciation by 15,750, will that come out to the depreciation on the income statement? And we'll see that it will, we'll have to check that. And then we're going to say that the cash received from equipment, we're going to basically say that that's coming from this account. Now, that might not be as intuitive. We're going to say, well, why is that? Well, this is debit and cash. And we, that's our cash flow statement over here. And we just need to know where did that cash come from? That's, we're looking at cash flow here. Well, that cash flow came from equipment that that we sold. So, and then we're going to ask ourselves, well, is that operating investing or financing? It's not going to be operating because it's not really an income statement account. This accounts income statement. But the bulk of this isn't really an income statement transaction. Really, it has to do with us buying or selling an asset, which is an investing activity. So we're going to be dealing with cash received, we're going to say it's an investing activity. We sold property, plant and equipment. Anytime we deal with property, plant and equipment, it's typically going to be dealing investing activity when we're working with a cash flow statement. And then we got cash paid for the purchase of equipment. That's going to be the 51 here. So the 51 and so why would that be? Well, cash paid for the purchase is where we put the entire thing, the entire difference between that's really a result of kind of these two journal entries. So we're breaking this out in a sense to its components now. So that's going to be that's why this has got to be a component and it's got to go down. And then we've got the loss. And the loss is something we can see here. We knew it was on the income statement. So we're going to pick up that loss and put it here. So of these, you can probably figure these out. And then you got to go, okay, that's this is where the difference is going to go to because that's where we put everything too. So that's, that's the other side of it. And then we've got this journal entry. Now the major thing with this journal entry is that we've got this loan, this financing amount here. So the financing amount is going to be the issue because the financing amount is not cash related. So we're going to be dealing with the 70,000. So we're going to say that cash paid for long term note here is going to have to be adjusted because that's going to be the note payable. The other side of it's going to go to cash paid for the purchase of equipment, which is where we put everything. That's the other side of this transaction. So you might want to spend some time with something like like these journal entries and try to figure out why that, you know, mull it over a few times. If we were to post this out then in terms of this kind of increase and decrease, not really a journal entry, but a similar kind of concept to our worksheet, we're going to say, okay, here's where we were at before we're in balance. This matches what's on our balance sheet. We need to do increases and decreases here in such a way that we don't affect the bottom line. So they have to equal in some way. So if we do our adjustments that we had, we're going to say depreciation, we'll record that gets us to 38. So it was at 15, 750 plus 22, 850 brings us to 386. The loss, we didn't have one before it's going to go up by 2100, 2100. We had the cash paid for equipment was at 62,250. There were two transactions. So this is the net of those two transactions bringing us to 43,250. And then we had the cash received from the sale of equipment, 2650 bringing us to 2650. And then we have the cash paid for long-term debt that kind of flipped this one. This we would have thought it was a receivable. And now it flipped at 70,000 paid. So now it's really paid, right? 47,500. So this is going to be the activity we have. Now if we look at all that, then here's our adjustments we just had. They add up to zero. The additions and the subtractions add up to zero. So we end up in the same spot is the point. So we got to this amount by doing a simplified method, just looking for the differences in our two in our balance sheet accounts so that we know we tied out. Then we went back and looked at those problem cases and figured out our ending numbers made these adjustments in such a way that they're going to be in balance so that we're still in balance here. And now we can tie out these numbers. We can say, does net income work? Does depreciation work? Well, if we go here, net income 158,100. Depreciation 38,600 should be on the income statement. So it looks like those are going to be good. And of course, when we go to the loans, we want to be able to say, does that tie out to actual loan documents that we got when we look at the GL, the amount we borrowed in the short term loan? In this case, cash paid on long term notes. Does that add up to the cash we paid when we financed the equipment or the cash we actually paid on the notes? And then cash received from issuing stock, 45, and the dividends. We can see that we have some of the additional information we checked these amounts on here on the income statement. Then we have it says that we borrowed short term loan 5,000. That looks good. Paid to reduce the long term loan, 47,500. And that now 47,500 is where we're at there. So that's going to be another one of our major kind of check figures to look through that. So it looks like everything ties out. Now we're going to take this, and we're just basically going to eliminate the adjustments and be left with just this. So we're just going to say, okay, now we can hide this information and be left with our ending numbers, which would look like something like this. So again, this is more of a kind of a worksheet because we could go through here and fix up and trim up the terminology and whatnot. But that's a kind of a worksheet process that can get us through this through this process in such a way that we can do it in a step by step basis. And the cash flow statement is similar to like a balance sheet where when we get to the end of it, oftentimes it's not in balance and no one knows how to fix it except to start all over again. Well, this process will hopefully give us a process that we can not have to start over again and have some check figures along the way.


Many colorful stars are packed close together in this image of the globular cluster NGC 1805 taken by Hubble. This tight grouping of thousands of stars is located near the edge of the Large Magellanic Cloud. In the dense center, stars are 100 to 1000 times closer together than the nearest stars are to our Sun. This makes planetary system formation around them highly unlikely. The striking difference in star color is illustrated beautifully in this image, which combines two different types of starlight. Blue stars shining brightest in near ultraviolet light and red stars illuminated in red and near infrared. Usually globular clusters contain stars which are born at the same time. However NGC 1805 is unusual as it appears to host two different populations of stars with ages of the older red stars being millions of years older than the blue young stars.


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.  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


Welcome back. So far we have seen what is mastery learning, how we at Khan Academy implemented on our platform and how you can use master reports to provide personalized learning to all your students. In this video, we will go through the student experience while they work on achieving mastery. This will help you to guide your students through the platform. In order to begin their mastery journey, students need to log into the Khan Academy platform using their ID and password. After logging in, the students can see the course mastery tab on the left side of the screen. When they click on it, they can view the goal assigned along with the due date set by the teacher. Students can also see the progress bar indicating the percentage of goals attempted by them. On clicking the goal, the students reach the course home page and they see a blue box that says get started. By clicking on this box, they start their course mastery journey. Smartphone users will be able to get the complete view by scrolling down. If you want the students to be accountable for their learning, they must know how to track their own progress. Every course has mastery points and the students can see these above the course summary at the top left corner. On the course home page, the student can see all the units and their mastery points. Every unit has a progress bar next to it. The bar turns purple only when the student starts his mastery journey and shows the progress your students are making. Encourage them to check their progress on the purple bar. In order to teach your students about the level of mastery, you can request them to click on any one unit. You will be able to see a skills summary section which shows the level of mastery attained by the student in a particular skill. Students can click on the question mark right next to the skills summary. You will be able to see a brief summary of different levels. We have already covered these levels in our previous videos. We recommend you take your students through these levels and explain to them the meaning of each of these levels at the start. This will help you in empowering students to take control of their learning and thus improve the skill mastery of your students. As your students start putting in efforts towards their mastery goal, you must stay connected with them and support them to push their levels up. Here are three ideas for you to play this role effectively. Idea 1. Remember that the course mastery goal is a long-term goal set by you. Students can't complete this goal in one go. They need to take small steps and keep leveling up. The secret to leveling up is consistency and a fixed routine. Fix days and times for reviewing the progress of your students. For example, you could check progress every Friday and decide the appropriate steps you want to take on the basis of the reports. You can have time allocated in your class on Monday to communicate with students and celebrate their progress. You can also train your students to check their mastery points and the mastery crown. Idea 2. Remember to share with your students that they can retry as many times till they earn a score they are happy with. They can level up their skills and scores by practicing the exercises, quizzes and unit tests again and again. Your role is to keep them motivated so that they keep trying. Idea 3. If you see that some of the students are getting stuck and need extra support, encourage them to read articles, watch the videos and use hints. You may need to take these students through the steps involved in using hint and accessing videos or articles. Now that we have covered how you can implement course mastery in your class, let's start using it in a classroom. Here are two quick tasks for you. First, in case you haven't already done so, please assign a course mastery goal to your class. Second, please check how many mastery points you have earned so far in this course.


One example is Kahoot. During some lectures we used it and they used it to test our knowledge. Most of the time it was at the end of the course and the exams were coming up and they would just use it to see how much we already knew and how much we could still learn or where the difficult points were. So I really liked that because it was also a reflection for myself to see how much I already knew and on which points I still had to work on some more to get a good grade for my tests. Some of the times we used quizzes or you could just get a sheet of paper yourself or from the teacher and he would just ask questions and you could write down your answer and afterwards we would discuss it. I also really liked that because it's an interactive way which for me is a really good way to remember the things that I was taught. I had a quiz in English analysis where we had to use for bonus points. I liked the quizzes on the mobile phone. Also in the stats we had I think. It just makes you think about how to interpret questions and how to look at it because you always get it on the exam in the same form. There's completely no, with us at least there's no any form. There's no form of technology in there. It's only all papers on paper. I would wish there was a bit more involvement with computers. It's really inefficient. If you would integrate technology to it it would be a lot faster. Currently the pop quizzes and the voting of things just takes a huge portion of the time. If the teacher has to hand out like a class of 150 people he has to hand out papers and using a website would make it awesome. No, I don't have any experience in that kind of quizzes or digital testing. I think that they could be good to have some interaction in class. I think it's also useful in order to have a vision about something.