Okay. It's a little after four, so I guess we'll get started here. Thanks for joining today's space and Astro seminar. We've been having several talks this month on people who work on various aspects of massive stars. Last week we heard about binary mergers, but we have some slots open in November, if anybody has any suggestions. I think the week after the election is open and then I think there's two slots and November open in one slot in December still. So anybody who has any suggestions for seminar, please contact me and we'll get you on the schedule or we'll pencil and the person on schedule. And anyway, let's go ahead and get started then. Today we have a person I've met just a few minutes ago, William Schultz. I met him at a conference in Ireland on massive stars and he's working. He basically will got his PhD from UC Berkeley. I'm sorry, he got his undergraduate at UC Berkeley. And now as a graduate student at UC Santa Barbara, he works with Lars built-in who believe you know, is the director of the Kavli Institute of theoretical physics where they have these great symposia that, well, I don't know if they're supposedly there's group meetings lasting two or three programs that are focused topics. And he's also working a lot with John Jay Jane, who is the person who radiation hydrodynamic expert, who is currently at the platyrrhines Institute in New York. Today, William is going to teach us about our talked to us about turbulent and massive star envelopes. And you can read the subtitle, understand the dynamics of near-surface convection. So under impact on photometry and photospheric line broadening taken away. Well, thanks Dan. Thank you all for joining me. Sorry. Thanks for being on Zoom for such a long time. I'm sorry, I can't be there in person. But I hope hope you enjoyed this talk Today. I want to talk to you about basically turbulence and your surface convection zones. This is the work of my PhD and I'm happy to share it with you. So this talk will be broken into five main parts. First one and motivated massive stars and explain what near-surface conduction zones are. Then I want to talk about the 3D radiation hydrodynamic models that I've been used analyzing and my thesis work. And then I want to talk to about the impacts of these nearest surface convection zones, both on the seller structure, but also on synthetic observations and highlighting and photometry from recent tests observations and some synthetic Spectroscopy. Focusing on what are massive stars and why are they interested in? Massive stars shape the entirety of the ISM. They have strong winds that are bright in the both UV and the x-ray. They're often in binaries, which can be quite interesting. They die in these explosive deaths that are supernova and they create gravitational wave sources. There are fusion. Their core also generates all the elemental abundances throughout the universe and they were thought to be the first objects in the universe with very hydrogen-rich stars at low metallicity being the first ours and thought that they were quite massive and then populated the universe with elemental abundances. So the massive stars I'm talking about, which are greater than around 20 solar masses, are quite high, hot and bright. With it affects the temperatures are surface temperature is being greater than around 10,000 kelvin. They're really bright. The luminosity is very close to the ancient limit, meaning that the radiation from their luminous fluxes are supporting against gravitational collapse. Which is quite an interesting regime to explore. The nominal description of the structure of a massive star is that it has a convective core where you have hydrogen or helium or other heavier elements fusion happening. Then you have this large radiative envelope shown in the blue, kinda in this kind of schematic. Often not talked about is what I want to talk about all of today. And this is kinda small convective zone that appears the surface. And so kinda going to hopefully going to convince you that this surface convection zone is one of the more important parts and should be understood. And people should care more about it when they deal with massive stars. So as you go towards the surface of these massive stars, the temperature decreases. So we're going in this plot of opacity, brush temperature are going to the left. As you go to the left and temperature, you can see the opacity increases. These are lines of constant density and the first peak is associated with iron. You have a whole bunch of iron lines at these temperatures that will cause this opacity bump. This opacity peak. As you go to lower and lower temperatures, you have recombination of helium, which can give you this huge increase in opacity, many orders of magnitude. If you take the engine luminosity, which is the luminosity you needed to match gravity and solve for the opacity needed. You can then compare for these different stars, like a 35 solar-mass model on the zeros main sequence or a sequence or in the hearts of a solar mass and Hertzsprung gap. You can see that the stars become super Eddington or these out these opacities becomes super editing, meaning that the flux is then stronger than gravitational collapse. You'd expect something crazy to happen or you need something else to carry the flux other than just radiative diffusion. As nobody expected. From the stellar structure equations. These surface convection zones are kinda ubiquitous to all massive stars. They appear down at five or six solar masses and with the helium to opacity peak. But the one I'm gonna focus on today is this iron opacity peak, which becomes the dominant opacity peak and convection zone as you propagate up to higher and higher solar masses. I want to emphasize that we're really close to the surface right on the y-axis on this plot is a radial extent of the star with one being the surface. So really we're probing the outer fiber. So percent less than 5% of the cellular surface, which doesn't really affect the core evolution at all. So it's not going to affect, not going to drastically affect the amount of heavy elements that you're developing, but it's going to entirely affect your observational. But what you can observe from the star, because we can only really see the photosphere or the wins from these stars. When you have these really large opacity peaks exciting this vigorous convection in 1D stellar evolution models, you can get some interesting things happening. So this is, this is plotting current engine ratio versus the gas pressure. And each point is a location, radial location in a 1D model. And you can see that there are points for this 30 solar mass model where you get these density inversions, where the density starts to rise towards the surface and you have this kind of bump in density that is thought to be unphysical. And you can even get to the point where the gas pressure itself has this inversion as the density gradient can surpass the temperature gradient. These are all thought to be non-physical and these environments. And so people have come up with engineering solutions, e.g. in Mesa, the 1D stellar evolutionary code that I use most MLT plus plus, which is like an enhancement to the current mixing length theory, has been proposed, but it's not really physically motivated. It's just a solution so that this doesn't happen in your models and you can run them throughout their evolution. But these kinda density inversions and this desire to have a more physically motivated prescription kinda started this whole work in 2015. Dan pay ransom parallel plane, parallel model is, and it's kind of gotten to the point where my thesis work. I've published several papers using these models and trying to, proposing some note, some novel prescriptions for these Wendy's Don't evolution codes. And so I want to focus on is these later, this latter work to play in parallel models were great, but they were just a starting point. And now we're using much more sophisticated models. Before I get to the models, I want to talk a bit about conductive efficiency, because I think this is quite interesting. So you can kind of think of how efficient convection transport is by comparing the convective flux to the radiative flux, right? How much energy is being moved by this turbulent dynamic convection versus how much is being diffused through Ready to diffusion. Then you can write that as a convective velocity. This VC times the pressure of the thermal pressure divided by the radiation pressure times the photon diffusion time, which is c over Tau, where Tau is the optical depth and c is the speed of light. So obviously if this is much larger than one, then it cannot just fluxes dominating and you're carrying a lot of the energy through convection. And if it's much less than one, then the radiation pressure is dominating. A radiative flux, excuse me, is dominated and you're not having much convective flux whatsoever. You can take this equation in the upper left, upper right, and solve for a critical optical depths such that below that are for tau less than that critical optical depth, you're going to have radiated leakage. So as the plume moves up in this convection is going to lose a lot of heat due to radiation and you're going to have weaker, a less efficient convection. Whereas if you're deeper than this critical optical depths, where tau is much larger than this dark red. The photons can't escape the plumes as they rise. And so you're, you're gonna have more efficient convection. In most situations. This tau create is about order unity. So for the Sun It's about one. For most red giants It's about too. But for a massive stars on the main sequence and across the Hertzsprung gap. It can be ten to the three, or 1,000 to 10,000 tau credit. So you get these optically thick diffusive regimes where you have this inefficient convection in this rate of leakage. And again, this is, this is kind of can be shown across the HR diagram. So here's some spectroscopic HR diagram. So basically you have brightness, effective brightness on the y-axis and temperature on the left. These are stellar at Wendy's taught evolutionary tracks from mesa. And the points or observations, which I'll, I'll touch again on later. But you can see these vertical lines kinda show you these tau over tau of iron past the peak to these top grit boundaries where all these main sequence stars or should have very inefficient conduction at an opacity p and not carry very much the flux. Whereas you go across the Hertzsprung gap here. Over to the red giant branch, you'd expect to conduction beam become more and more efficient. And therefore you just select the turbine dynamics to become or the conductive dynamics to become stronger and stronger and stronger. Okay, So I know that was kind of a whirlwind, but hopefully we're all still we're all still together. Oh, and I should say it, please. If you have any questions, don't hesitate to ask. Just pop your hand up or just interrupt me. Both are fine. And so now I want to kind of briefly describe to you the hydrodynamic models that I've been using. We've been using the thena plus plus, which was developed by n Fe and several others at Princeton. Basically what we do is we take Mason models, these 1D stellar evolution models. We take the average temperature, average density, luminosity, and internal mass at a given point on the H-R diagram where we kinda wanna model. Now you plug it out into Athena extrapolated. So it's a 3D simulation domain. And we use Yan phase prescription for implicitly solving the time dependent radiation transport equations. This is not a variable and its intensity, this is not SLD. This is a novel way to solve radiation transport. It assumes local LTE or local thermal equilibrium. So you don't have different chain. You don't have some changes in ionization state and the source function. And it also only use this gray Opacity use. And in doing that, we also make several other assumptions. We have a constant mean, molecular weight or constant composition. All the models I'll show today, or it's solar metallicity. We are investigating lower metallicity models because that's interest. Because we are only modeling this outer region of the star. We're only capturing around less than 0.1% of the stellar mass. So we are safe and making the assumption that the gravity is just the core mass, or basically the mass of the star was one over r-squared potential to it. There's no self-gravity for the material outside of that core mass. Recent Grey opacities that are solely a function of temperature and density there from opal which are commonly used. Another two assumptions we're making it so there are no magnetic fields for these velocities were seen in our models, you would need a ten kilocalorie magnetic field to really affect the transport source thing. We think we're pretty safe for most massive stars that you're not going to have that strong of a magnetic field. Then for the rotation. Some stars have been seen to be working quite quickly. But even for very fast rotating stars, the rotation period compared to Eddie turnover time of these convection zones, that the turnaround time is much smaller so you don't have, we don't expect rotation to play a significant role in these, in these simulations. We have run two different classes of models based on where they are on the HR diagram. We run these kind of global simulations which cover a third of the stellar surface shown by this visualization down here. And this is because the scale height and these models is quite large compared to the stellar re-use. So you really need to capture a whole us significant part of the solid angle two, make sure you're resolving enough plumes that they are, your boundary conditions aren't really affecting the dynamics because of their size and their extent. These take hundreds of millions of CPU hours. And if you're using a reasonable number of cores, like a few thousand cores on a supercomputer. They take real-time timesteps. So 1 s of using 1,000 cores models of star for once, for 1 s of stellar life. So we can't feasibly run these 3D simulations for a huge region of the lifetime that takes billions and billions years, the computers wouldn't last that long, nor would we. But we can run these first four different snapshots and run them for about a model, model of a time itself. And you can kind of start to understand a snapshot in the stellar life, if you will. The other models we're doing is he's much models, same exact idea. They're just smaller because these are hotter stars. So the scale height as much lessee the plumes or there's much more plumes per surface area. As a way to think about it. You don't need to resolve as much of the solid angle as needed. And these run a little bit faster. So you can hopefully run more of them, which are slightly less computationally expensive, although they are still quite expensive. So putting these on an HR diagram, this is kinda the current suite of models we have. In particular, I'm going to emphasize for this talk, the most massive ones. And so kind of going through them into papers I published, I've given them these names which are a function that the effect of temperature and the luminosity. But in practice, this orange squares and a solar mass model and the Hertzsprung gap here, kind of an LD50 life model. Like luminous blue variable, this red square also this red square is a 56 molar mass model than the kinda this LV outburst phase. And these two stars are both 35 solar-mass models. The purple is that the zeros main sequence and the blues in the middle of the main sequence. And you can see the kind of straddle, this barrier of the tau creative about 0.1, which I'll get to a little bit later. So now I want to share with you a movie of the ADA solar mass model. So you can see that this is the density contours. And so we're starting in a stratified condition. And as the 3D model runs were kind of evolving more and more and more, it's trying to reach a steady-state. You'll see some things get expelled here in the first kinda outburst as we see here. And then it kinda starts to quiesce and we're, we're almost getting into a steady-state now. And then finally right around here is where the Energy, the energy, radial energy flux is roughly constant with time. So this is what we call a steady-state solution. Although you can see it's anything but you have these huge plumes and this huge dynamic range of densities. And this begs the question of where is the photosphere, right? Where, where's the last scattering event happening? And the stars? Well, if you used a 1D approximation of saying Where's the average scattering location and the spherical average sense. Because something like the orange line. So you can see that this is not really a 1D problem. You have really large overdensities here with a lot of things and you have almost nothing in this region. And again, you have more density is here. So this is the first, this is one of the first things we saw in 2018 paper of that there is something inherently 3D about these dollars surfaces. And that was the motivation for, for all of this work. And it still continues to this day. But if we stick with optical depths for a moment where the, how ought to be thick, this material is at the surface. We can plot profiles to see how, what the variety of the radially into integrated optical depth is basically looking at single radial lines of sight. You integrate inwards. I'm going to plot how that quantity changes as a function of radius. So that's what's plotted here for the same, safer, a snapshot of the same model. The color here is the probability of that given value at that given time. So basically, if you summed all the colors along vertical lines, you would get to one. So the lighter colors are more probable values, the darker colors are less probable values. But that being said, you can see that at the photosphere, which is this black dashed line, or the average tau is one and the orange line on my previous movie, there's like 55 or six orders of magnitude variability in the optical depth, meaning that some lines of sight see an optical depth of 100, which is very optically thick. And some lines upside seen optical depth of ten to the minus three, which you would expect if photon to not even C and it would just travel right through. So obviously this notion that there's a single photosphere is flawed. And in fact, when you compare it to the area fraction of tau less than one, we have these two red lines where the area fraction is around 5% and tell us the one in 20% of tablet has to be less than one. And again, the variety is quite striking. You have five or six orders of magnitude variability in this optical depth at a single radius. Implying that there really isn't a single surface, you have to single radius, That's the service. There is a surface that is topography is quite, quite complicated. Quick quick quick question. Yes, please do. This is all LTE, but this allowing for then lateral radiation transport to come out of the places where the optical depth is less. Yeah, so ration, so that's a great question. I skipped over that. So each cell has 100, has roughly 100 different directions that radiation transport and kinda flow, flow. So it covers the whole four pi of that cell. So there is a strong tangential radiation fields as well as vertical radiation fields. So we are truly modeling how the, how the radiation field will flow through this inhomogeneous plasma basically dream. So the optical depth is a function of density and opacity. So if you see the optical depth, is this much, then you would expect those two great, substantially as well. So here I show for the same model, this AT solid mass model, the variety of density in the upper left, the ready to flux, and the upper right, and the opacity and temperature in the bottom, bottom-left. Looking at the bottom-left really quickly, despite the large variety, you can see that if the factors of fiber, so and the opacity, the majority of the values are quite confined to within 50% or so of the mean. So the opacity is actually not changing all that drastically and the temperature is quite confined as well. It's really just the rate, the density in the radiative flux that are very end by orders of magnitude. So this is telling us is that this, this, this clumpy media we're seeing is really, is really just clumpy. It's not some weird opacity effect, but it's really just there. You have these overdensities and he's under densities that are causing this large discrepancy. And what we're seeing. Now, a fair critic would be like, okay, cool, Well you're showing me the biggest model. What about the other models? We do see this the same kind of thing as we go to lower-mass and hotter models, where tau is less than Tau crit and the efficiencies of convection is less. And so this is the mid main sequence model, the blue star here. And you see that we still have several orders of magnitude variation in density and OPAT and the opacity looks quite different as well. However, when we go to the direct sequence model, this purple star, which is much hotter, we do recover a 1D life model like a spherically symmetric model, because there's just not significant enough convection to really alter the variability we're seeing. For reference this, this shaded region is where the entropy gradient is negative, which is the typical definition of the extent of the convection zone in these N12 and stellar evolution and in cellular models. And you can see the entropy in this, in this bottom plot. So that's kind of a sense of these models. They're very poorest, they're very clumpy. The radiation fields are quite intricate, both radially and tangentially. And there's a whole bunch of turbulence throughout, throughout them. So how is this? This is how basically the first question that, that is begged to ask is how is this going to affect the stellar structure? Or how, how can we improve 1D models based on what we're seeing in the 3D. The first thing we looked at is we know that these models are radiation pressure dominated. The flux is so strong that that's what supporting against gravitational collapse. And so we can first look at the radiation pressure gradient, which is again the switches, the structure in which is fighting gravity to see if there's, if there's any impact from these large variability we're seeing. So we can write the, define the radiation pressure gradient as in two different ways. You can have this, basically it's one or minus one over c kappa reflux. But you can have different correlations between the kappa and the row and the flux. In the 3D model, all these cells are correlated. So when we do the average, we're taking a correlated average. Whereas in the 1D model, you only have a single value for opacity. You only have the spherically average rate Ready to flux and you only have a spherically average density. So you're inherently doing this separate multiplication of these, of these averages. And if we look at our 3D model and one d of phi it to extract this, taking spherical averages, we see a large discrepancy mean it looks small and these axes, but these acts is span many, many orders of magnitude between the 1D version and the blue and the 3D expected value in black again. And so what we can do is we can say, okay, as in the previous slides I showed, the opacity was only order unity variations with the flux and the density we're grain by many, many orders of magnitude. So let's pull out the opacity just to make our problem, our problem a little bit easier to solve. Then we define this new site parameter. And by 2020 paper, which is literally just defined such that if you multiply the 1D radiation pressure gradient by it, you would approximate the 3D radiation pressure gradient. The correlated average are pretty to flux and density over there, uncorrelated average. It's pretty basic. But the impact was kinda profound. When we looked at this, at the side parameter versus an independent variable, which is called the pseudo Mach number. I can talk about it later, but it's really just analogous to radius. It's monotonic with radius, and it just allows you to plot all the, all the stellar models on top of each other. So you can only see, you only have to use a single independent variable. When they're radii chain vary from like ten solar radii to hundreds of solar radii. So that's not really a good you're able to use. But the main takeaway of this plot is that near the surface of the star, around ten to the 310 to the four ish and pseudo Mach number space, we see an 80% reduction or the sine value goes to point to or less than point to. The radiation pressure gradient. Meaning that you would expect these stars to be much more compact than you would nightly thing. Because if this radiation pressure gradient is supported against gravity and you reduce that radiation pressure gradient by almost, almost entirely. Something has to collapse. The equation is not balanced. So that begs the question of what, what, why aren't we seeing these collapse stars? And so that is the check hydrostatic balance. So in steady-state, like I've been saying this whole time, but I'll now write it as an equation. We have these pressure gradients and they match gravity or the density times gravity. So you can just trivially rewrite this equation to kinda get a fractional deviation from hydrostatic balance, which is what I've plotted here on the y-axis. And sure enough, when I use the thermal pressure from the 3D models to gas flows radiation, we see this 80% discrepancy from hydrostatic balance like we would normally expect from the side parameter that I discussed. But we were thinking about it and we have this vigorous turbulence that's been excited cause of all these variations. And the cause of all this turbulence is when these, these turbulent dynamics in the near surface convection zones, because that's going to lead to some sort of turbulent pressure. Which if you solve the, if you expand some of the terms in the momentum equation for 3D spherical transport, you get that should be equal to the density times the radial velocity squared. And sure enough, if you implement that and you add that into your hydrostatic balance, you see a market reduction in this discrepancy from hydrostatic balance to then around 10% of variations, which is about all we can expect from from 1D models with current, current implementations. This is showing that this turbulent pressure is essential if you want to have hydrostatic balance and accompany, and accompany the effects from the turbulence of the reduction in the radiation pressure gradient. And it recovers it quite well. Can I ask another question? Sorry to interrupt you. Please do so. What's the, what are the speeds of this turbulent flow speed? Is it supersonic to the gas pressure, the gas sound speed? Yeah, So in all the models except the zeros, meaning signals model, we see transatlantic turbulence to the isothermal gas sound speed. To put numbers on it. The 35 solar mass model, and in blue here is roughly seems like 8,000/s velocities, whereas the orange and the red C, two to 300 400/s velocity. Okay? So, but these are all, what are the ratio of the width ratio, the radiation pressure, gas pressure in these models. So they really strongly radiation dominated. So for, again, for the orange and the red, it's about, it's basically just radiation pressure by order, by, over an order of magnitude. Okay, for the 35, it's about a factor of two or three. For the blue and for the purple, It's order unity thereabout comparable. So radiation pressure is a dominant support mechanism in all of these models. It's the only support mechanism in these cooler, larger models, but it is still very important in the other two main sequence models. Okay, so then the other thing, if we have this turbulent dynamics that's setting hydrostatic balance and in fact in hydrostatic balance, then other parts of the stellar structure are likely to be affected. And so a very brief introduction and a service level injection of stellar structure. You basically can determine what's happening in the star by comparing temperature gradients defined as these grads, which is the derivative of the log of the temperature to the log of the pressure. And if you compare this temperature gradient to the same temperature gradient but held at constant entropy or the adiabatic temperature gradient. You can kinda get these three different regions if grads less than grad add. It's not convective. Meaning that radiation diffusion is carrying all the energy. If they're approximate, then you have efficient convection. Because the temperature gradient can carry energy at roughly the adiabatic temperature gradient, allowing for very efficient convective transport. If the temperature getting is much larger than the adiabatic temperature gradient, the conductor is quite inefficient and doesn't actually carry pretty much at the flux despite conduction being present. And if we look at these in our 3D models, again, we see all of them kinda lie in this last regime where we have inefficient convection. As the temperature gradient shown in solid colors is quite different from the adiabatic temperature gradient shown here, which is this black dashed line. But this is the temperature gradient that's currently used in 1D stellar evolution models. And I kinda alluded to the problem here is this is still comparing just the thermal pressure. It's not accounting for this turbulent pressure dynamics that were I showed as crucial, the hydrostatic balance is really important in these stars. So back in 1965, HENI at all proposed that you should actually modify this adiabatic temperature gradient with his granddad prime by chain ruling in the turbulent pressure to be included in this total pressure term. And sure enough, when we do that using the values in our 3D models, we see for the two more massive models where convection is much larger and towels much large, larger than Tau cred at the convection zone. We see much better agreement between this new modified adiabatic gradient and the actual temperature gradient itself, implying that the conduction is now very efficient there. And as we, as we have seen in 3D models, that connection does actually carry a significant fraction of energy transport compared to the radiative flux. Whereas in these two hotter models, it's still quite inefficient because the optical depth is much less than tau cred. And so we don't expect very much conductive transport to happen here. And we expect that conduction to be quite efficient, inefficient. So both of these, both the hydrostatic balance and workers, are currently being written up in a paper. I'm trying to implement them in Mesa currently. So hopefully that will be, that will be out in the world in the near future. Then really quickly I want to talk about my favorite part of the stellar structure, which is the actual shape of the convection zone. This what I'm showing you here is for the 35 mid-May signals on the bottom, this arithmetic sequence on the top. This is what mesa would tell you the convection zone should look like. So the x-axis here is the radius centered on the iron opacity peak, radius or the radius of the center that aren't opacity peak. The brown line is the conductive velocity that Mason will tell you. Its extent shows you the size of the convection zone. These scale bars here show you the scale height at that location, which is, which coincides with theory that the conventional theory that the conduction zone is roughly a scale header two and width because you have basically one or two convected Eddie turnovers in your radial extent of the near surface convection zone. However, when we look at the connective velocity is from our determinant velocities from our 3D simulations. We get the average RMS velocity is these yellow dashed lines and the kind of the error bars, if you will up those are the shaded regions. We see much more extended velocity fields with significant velocity use even propagating through this dotted black line, which is the photosphere, the definition of the photosphere, the tau upon location. So from this, we would predict that the photospheric velocity is even if the zeros sequence model, which doesn't have very much, very strong convection would still be 10 km/s. And for the remaining segments are getting up to 100 km/s with these photospheric velocity. This is all despite the entropy gradient definition of where the, where the conduction zone should be. Still a green quite, quite well with the 1D models. So really the notion is that these velocities aren't just confined to a convection zone unlike 1D model and predict there's nothing to stop these turbulent eddies from propagating up to the photosphere. And this is going to impact photospheric observables in a way that was not previously seen, are predicted from 1D stellar evolution models. And so this plot alone kind of motivated taking, making synthetic observations at these models. Especially with the advent of many spectroscopic surveys and the test photography that was coming in. And specifically this SLS variability that was being ubiquitously discovered. So test was looking at all these massive stars. And in 2020, several papers, 2,019.20, 20, several papers came out quantifying this kinda low frequencies stochastic variability. An example like curve is shown in the upper left that seemed to be kind of ubiquitous to all these massive stars and the upper part of the HR diagram. And it was kinda characterized by if you take a temporal power spectrum of this light curve, you get this characteristic knee with a high amplitude and low frequencies. And this power law slope down to some floor. Dumped stochastic low-frequency variability. And originally, the proposed theory for it was that the core, the convective core that an index and the conductive core excited G modes are gravity waves that propagate through the rate of radiative envelope and manifest as this variability on the surface. With many works explaining, showing that this could be representative of what we're seeing in this photometric variability. Others, along a similar timeline proposed that these near-surface convection zones could actually be the hypothesis. And I'm, I'm in that group myself, and that's what I'll be talking about in this section. And several others also proposed that wind interactions. So above the photosphere, you can have wind plumes combining together and interacting and produce similar photometric variability that is seen in these light curves. So in order to compare my models with these light curves as I have the luminosity variability as a function of time, but I needed to compare them. So first I want to define the fitting parameters because it's no use telling you what parameters are unless I explain them. So this is kinda the fitting function. There's a red noise component and there's a white noise floor. This is basically the detector noise from either tests or any other instrument that's used. And this is kinda just the read noise of your instrument, if you will. And then this alpha naught is the main amplitude. So it's kinda set by this large flat amplitude up here, the characteristic frequency. And this nominator sets this where this knee is and the power loss Lopez, this gamma. Despite what you might read some papers, this game is basically to sum, There's a lot of significant figures after the two, but it's basically two. And that's why this has been referred to as red noise. Because that's the characteristic function for the spectral shape of red nodes. And the other work that's been done for near somebody conviction zones was by Mateo County yellow at CCA. The flight aren't Institute. And he took a whole array of mesa models and just saw if if the near surface convection zones could match the trend of observations. So in the left he compared the amplitude of variability, this alpha naught to the convective flux ratio. Basically you saw that the observations shown in these points, with larger points being larger amplitudes, was consistent with the fraction of the conductive flux, that is profit carried in these convection zone. So the strength of this convection, basically, with large values being in the upper right and smaller values being in the lower level. You also compared the characteristic frequency of these observations to the ATP turnover time of the iron opacity P convection zone and perform the same analysis and found the same thing. You add the zeros main sequence and the upper left, you have longer turnover times, bigger. As you go to the right, you see the characters frequency or the turnover time. The frequency of turnover decrease. But it was time. It seemed that you're sort of confessions tones in 1D model is could recreate these trends. But we were hoping to do one veteran and do an actual apples-to-apples comparison. Luckily, some of the tests observations matched one of our 3D models, this series, this mid main sequence 35 solar mass model. I've highlighted three stars I'll compare to. And blue that were taken from tests from Dominic's Bowman's paper, 2020 paper. And then we can go ahead and get started with the process. So here's the light curve from the 35 maybe and secretes model ID trended it just using a third order polynomial fit. And took the temporal power spectrum, which is shown in the second panel. Then the third panel shows the cumulative power distribution. Basically the sum, the integral of the power or divide a normalized so that the maximum is one. Just as a different way to represent the power spectrum. One thing you might notice right away is that there's these characteristic peaks about these. There's about three of them. These are Nazi and observations. But there are solely a function of the periodic boundaries of our simulation domain. If we change the extent of our simulation, we see these peaks change frequency. So we don t think there are physical, they're just quasi-periodic oscillation is from inherent GMOs and PMOS that are excited from our convection zones. Unfortunately, we can't really get rid of them without doing a complicated pre widening scheme. So instead I just kinda remove them by eye and did a smoothing, smoothing fit, which kinda fit this this yellow line. And I did my, and then I use the MCMC method to fit this yellow line to the same shape as I showed in a few slides ago. And that gives us this pink dot dash line with some error bar shown in the shaded region. Then we can compare this to the observations. So the blue dashed lines are the same or from the stars that I showed on the previous HR diagram. And you can see this looks quite bad. We're quite a lot. We're off by about a factor of two in the characteristic frequency. But I can't help but think that these cute quasi periodic oscillations caused our characters in pregnancy to shift to higher frequencies. And if we could effectively removed these clouds of periodic oscillations with the proper pre whitening technique, which is really, really hard to do and would need collaboration with observers to extrapolate. We might see a better agreement. However, the amplitude, if I extrapolate our small patch to you, the entire star, the amplitude of variability is extremely similar between the two and quiet consistent. And again, the power loss lobe is also very consistent with red noise, which is seen in both our simulation and the observations. Okay? So hopefully, hopefully you're still with me and you're not you're not asleep. And I hope you're enjoying it so far because because this is actually my favorite part of what I've been working on. What I've been working on most recently is making synthetic spectra of our simulations. So first, what do we see observationally? Basically, when you look at a photospheric lion, shown here is as extra from surgery estimated Jesus paper. You see three main velocity field. You see the projected rotational velocity, which is v Sinai, which gives you this kind of large trough shown by the red dash and the green line, but doesn't have this wing that seems characteristic to almost all photospheric spectra, spectral lines. And that's explained by macro turbulent velocities, which are velocities moving on scales larger than the median regional scale is larger than roughly a scale height is then there's a nomenclature. And they are comparable velocity in order of magnitude to the rotational velocity. But when you combine these two together, you get this purple line that models the spectral profiles quite well. The third velocity field that's also in here, but kinda under the hood is the microtubule and velocity, or velocity zone scale is smaller than the limiting reagent. This is kind of hidden ranges typically go 1-10 km/s. And it's found using curve of growth analysis, which is also really interesting. But it basically gets added editing quadrature to the thermal velocity in the backend. So you don't really see that in this fitting method here. In addition to this, we see temporal variability and variability in the skewness. How anti-symmetric it is. Both of which could be explained by pulsations or turbulence or many other things. But one thing that I think is most interesting is this was all developed for solar like stars. Both all of these velocity fields are developed for the large scale turbulent velocities. We see where we have these kind of big granulations like we see on the Sun. It's not clear how these, how these work with nasa stars, other than they seem to fit the spectral lines quite well. But that being said, there's also some surprising correlations that arrives. So here's a recent paper by suggesting Medea's where the size of each point represents the value of macro terminal velocity. So you see larger macro turbulent velocity for these more massive stars that I'm interested in. If we take this sample and plot it in the macro turbulence on the y-axis and V Sinai projected rotational velocity on the x-axis. We see this kinda strange order unity correlation between the macro terminal velocity and the B Sinai projected rotational velocity. Which is kinda surprising because the Sinai should be a random number 0-1. So you would expect this whole area from this line of unity to kinda just expect this whole area to be filled in with red and orange points for these massive stars, although, but instead we're just kinda almost confined to this order unity correlation. We're just kinda, kinda of a red flag. In my mind. This, this, this has been extracted and understood as kinda some limitations of the observable, observables. So basically suggesting Medea's took 1D spectrum models with different velocity field values and try to extrapolate and see. What he could get from the given velocity fields. So e.g. he had chose to macro terminal velocity is 20 coulombs per second to 5 km/s. For a given input velocity, despite the input macro turbulent velocity here, to be zero, he gets non-zero narrative and velocities hours. So obviously there seems to be some correlation and his fitting method, rotational velocity in macro turbulent velocity. Sorry, The same thing is true if he tries to extract the V Sinai itself. Again, if micro turbines wasn't important, you'd expect a flatline. But it seems like micro turbulence sets a lower limit to what the rotational velocity could be as extracted from his models. Lastly, if you kinda combine these two together and you then pick up the Sinai, but then vary the Rotate macro turbulent velocity. Again, when you have these two micro turbulent velocities, you get different estimations than order unity when you extract an academic velocity. So all this, all this to say that I really want to use the 3D turbulence we see in our near surface convection zones on our stellar surfaces. To better understand how these velocity fields manifest and what these actually mean in terms of the spectral broadening. I think this is a very, very poorly understood field that I think I could hopefully assist with. But how do we do that? All of our rat hydro models currently have in gray. So I did was I used Sedona, which is a Monte Carlo 3D Monte Carlo radiation transport code to post-process the Athena Plus Plus models. And to do this kind of spectroscopic analysis. So I did a few things that are wedge geometry, which wasn't there before Athens at a customer meeting region, which basically just means like I found a way to avoid doing really high optical depth Monte Carlo transport, which is very expensive computationally. To prove as a proof of concept that did a great transport using the same exact opacity Standards, Act density and temperature, same exact input flux. And I can showed in this comparison where FA is Athena FSS, Sedona, that they basically match. Equivalently. The point of this plot is not that there are small discrepancies, but the point is in all the different components, the radial Theta and Phi, all the fluxes kind of agree quite accurately. So I knew that after checking the fluxes agreed, after checking my methods worked, I was very excited. And so I decided to try and understand how the spectral lines are generated by looking at the angular variability in spectral lines. I use this kind of customer muddied region is shown as this gray, this gray blacked out region, and just propagated Monte Carlo particles through this, these models, these RhD models with the provost spectral profile, I was interested in calculating the opacities thoroughly. And so then when I extract Wendy's want to call it particles leave the simulation domain, kinda shown by these green lines. They can have any sort of direction they choose. And so I just bend that direction relative to the pole of the simulation domain as a function of cosine theta. So here's the 700s humans that I chose to use. So e.g. these two have the same mu value relative to the pole, so there'll be banded to the same location despite them being from different locations on the surface are despite them having different normals to their elastic scattering location and whatnot, this is the most realistic towards observations that I think I can do with the current limitations of Monte Carlo transport. But that being said, every, everything seemed to go well. So I looked at the oxygen three line for the mid main sequence stars low-mass model. And so I, I, here in panel B, plotted the average number of Monte Carlo particles per frequency bin. And this is basically just showing you that blend darkening that you would expect from from stellar observations as a function of Mu. And more importantly, here's what the spectral lines look like as a function of mu, with lighter colors being towards the pole. And the darker colors that are more noisy because of a photon count being near the equator of the hemisphere. And these are just off to offset for viewing purposes. When I don't offset them, you can see the proper overlapping in panel E. And so this is just one model. I then took the zero age main sequence. If I solo mass model on 80 solar mass model and did the same thing for two different snapshots, which can be seen in this figure. And so this is kind of a lot. So let's just focus on one panel on at a time. For the zero sequence model that we have quite narrow spectral velocities, It's basically just thermal velocity is moving around. So that's what kind of setting this width basically there's not much turbulence or much Service dynamics. Contrast those in the similar T effective. We're saying much broader lines for the auction, for the mid-May sequence model implying that they're insignificant, turbulent broadening at around 100 km/s. And we see some slight temporal variability. If we look at three-and-a-half days later, we see a little bit more of a narrow peak. But it'd be quite hard to observe this difference with current spec, spectrographs. But more and more interestingly, when we look at 80 solar mass model, we see huge temporal variability is with this huge redshift and blue shifts. And we see spatial variability as individual plumes are now affecting the mu dependence of this spectrum or observing. So this is all good, but this is just one, this is just one snapshot and this is looking at new dependence. This isn't actually a realistic stellar profile. So to kind of get around that, I took this mu dependence and predicted it onto this stellar hemisphere or the stellar disk to try and see if I could get more realistic spectral lines. Excited that in two ways that had single snapshot projections where I just took the mu dependence of each snapshot and force it onto his daughter. Did is kind of replicating and replicating the profile, if you will, and waited it by the surface area of the solar disk and vice versa. You can do this alternating dual snapshot method where you just alternate humans for different snapshots that you're using. When you do this, you get the resulting spectral lines shown here, solid, solid lines with a single snapshot, dashed lines and the dual snapshot, it's not all that different. What is interesting to do is to compare it to the actual thermal velocity only. So I re-ran these simulations with no cell velocity, just having the intrinsic thermal velocity of the plasma as the excitation mechanism. And that's what gives you this dotted line. Here you can explicitly see that the zeros main sequence model on the left doesn't have very much of a deviation from just a thermal broadening. Whereas the mid main sequence model in the middle has significant turbulent broadening. That should that will affect the spectral profiles. And then the daily solar mass model. Obviously it has a whole bunch going on with many different types of broadening and a whole bunch of interesting skewness variability and depth variability. And it'd be very interesting to see if we can resolve these kind of this variability observationally. Unfortunately, no stars have currently been observed in this region to HR diagram. So we're, we're still, we're still waiting on future observations, hopefully. So thank you for that whirlwind of the talk. Thank you for listening to that whirlwind of the talk. My main takeaways or surface turbulence and he's nearest to the convection zones are really important for both the structure of the models in 1D and 3D, as well as extrapolating observables and understanding the light we're actually seeing from the surface of these stars. I'm hopeful that further spectroscopic analysis could help the whole field of massive stars photospheric spectroscopy. And they try and really understand what these velocity fields are and how they can be interpreted from our extracted from these spectral profiles. Then thank you again for listening my talk. I'm sorry again, this had to be over Zoom. But I'm on the West Coast or if you just e-mail me, I'm more than happy to meet anytime on Zoom. And I'll leave you here with an image from an AI Artist of what they think the surface of a turbulent massive star could look like after some manipulation. But thank you for your time and please ask any questions you have. Okay, Thanks a lot. Well, I tried to just hitting the applause button there. That was a whirlwind talk. I think there was a lot of really great information in there. I I certainly have some questions, but I know that they're probably better to go ahead, Jim. Yeah. So I just have a question that's relatively easy to answer. If we wanted to improve my 1D steady evolution code, would it be sufficient just to turbulent velocity has suggested in your slides, or is there more to it than that? That's, that's a good question. So you need to have a correct way to predict the turbulent velocities as well. So like the, the value that MLT gives you. If I go back really quickly to this slide, right? If you look at this, at this slide that the value of the turbulent MLT predicted velocity for mesa is about right to within an order of magnitude or so, but it's just so confined that if you use this, if you use this predicted terminal velocity wouldn't really give you the right value. You need to, you need to extend this region somehow to get a larger turbulent pressure inflation region. Yeah, So just by adding the turbulent pressure would not expand the convection zone is what you are basically saying? Correct? Because it, because the connection zones in the 3D models are still defined by these kinda narrow entropy gradients that are negative. It's really like it. I think the way to think about is you have this turbulent overshooting at the surface, right? So the convection zone is still quite confined. But we wait to implement. It might be to have some sort of overshooting where you just have those velocities manifest all the way to the surface. And then you have this kind of turbulent velocities that you could then use as a turbulent pressure. Yeah, okay, so you need to develop some sort of model for overshooting. Include it in the energy transport, not just for mixing, right? Exactly n to n to modify the adiabatic temperature gradient. Yeah, well, yeah, there's a lot of places that it comes into play and they all don't talk to each other very well. So it's, it's hard to do 1D implementations of this stuff, but yeah, good question. Thank you. Thank you. Are there any further questions? I think a guest Well, go ahead. Are there any other questions before I go into my own inquiry here? A break. I'm sorry, it looks like the main sequence models and the blue one showed that it was not that much increase compared in the turbulence compared to the thermal speed. Was that right? Did I see this right? Yeah. You mean in terms of like the in terms of the line profile is sorry. Yeah. Let's get back there. Yeah. So I mean, I don't really know what you would refer to as a lot of broadening. But then they may sequence does see like 100 or so kilometers per second broadening. Okay. Sorry, I was looking at the left one. That's why. Yeah. Yeah. So yeah, Although zero would mean sequence that there's almost nothing because it's, so, it's so hot. And it's, the convection is so inefficient that you only have a few clock per seconds service velocities. When you were talking about the correlation between macro turbulence and the VI cyanide that was derived with the Fourier method of Sergio. So something interesting is that magnetic stars have known rotation period. Because the magnetic measurements gives you kind of an ambiguous period measurements that you cannot really have four other normal stars. There's a star that has a longest period is HD want to wait? It's quite massive star and it has the spectral lines are about 50 km/s rod, give or take. The Zemin broadening is negligible. In this case, the period is 50 years, which means that the visa and I should be zero. But then when you use the measured the Fourier method, it predicts half and half V Sinai and macro turbulence. Oh, interesting. Yeah. Which kinda send other thing pointing towards that dichotomy between the walnut, another dichotomy, but the point towards this correlation that we see and your observations, right, exactly. But it's kind of a fitting effect more than a real correlation, probably. But that would be an entrance thing. Star, of course there's a magnetic field. But I would be an interesting start to model and see whether you can recover the same broadening. Because it's one of the few stars for which you know, the visa and I should be practically exactly zero. Yeah. So that was 108. Is that correct? Yes, That's cool. Yeah. I'll definitely look into that. That's sounds really interesting. Thank you. That was a good point. Yeah, so even want to wait, normally the magnetic fields are, don't seem to have that much effect on the macro turbulence unless you to very, very strong magnetic fields. And so I would say the first crack is just to go ahead and model it without putting any magnetic field. Just have to figure out where it is on the HR diagram and see Bryce, you take yeah. Right. Anybody else? Okay. It's about just about five o'clock now. If anybody wants to know if anybody wants to leave, that's fine. I'm going to sit and chat a little bit with William, anybody who wants to join the post closed seminar chat as welcomed to stay on. I have several questions that I'd like to ask 1 min. Anybody who wants to join in that discussion as welcome to do that. But otherwise, let's just think with the reaction button there again. Well, for a great talk. And anybody who wants to stick around and go ahead and we'll just give you a chance to leave and continue the discussion. So first of all, I was a little bit confused. Anybody have any questions chime in whenever you want? I was little bit confused why he spent so much time on the Angular profile, for the broad, for the lime profiles. Because after all, when you look at stars, you only have access to the flux. So I like this stuff because I spent a lot of time talking about that. I was just curious about. Why, why that was? I mean, basically you once you, once you have some from different perspectives, then you're just taking a flux average, right? When the going from this specific intensity to the specific angle, of course, you're assuming that that the main change is only with mu. But if you have 3D model, obviously there's that some beautiful variation as well. But your average, I guess you're averaging over that. That was your friend circles, I guess were. But anyway, it just seemed to me that that's an immediate step that you can't it doesn't give you any information that you can test with a star because we don't have angular except for a very few exceptions. We don't want to have any resolution resolution information. So that's a good plan. So it is it is a good way to check a few things, right? So if I go back to my previous slide, you know, checking this flux per mu e.g. I. Can make a prediction for limb darkening. And again, because our simulation patches so small, I was worried about making a full synthetic observation based solely on this small patch of like a 50th of the stellar surface, right? That's, that's not exactly a good representation of what's happening across the entire star, right? So you want to make sure that you're not, you're raised, not slicing through unknown territory. You're basically able to see enough of the star. I mean, you can do of course is just replicate that patch different angles and then take the slice through, right? Yeah, so that's the next step is to kinda collage a whole bunch of these patches together and make a, make a full hemisphere of a star and go through it that is currently not memory. It's very memory intensive because these are quite high resolution stipulations and extrapolate that across would be quite, quite a large run, even if it would be kinda fast. Yeah, I currently don't have their computational ability to do that. That is something I hope to do as a postdoc to do that. And so that's kinda why I did this, did this all mu dependence so that I can extrapolate with these projections that kinda of like us make an assumption, a prediction of what the dependence would look like. Okay. You're still on Doherty. Did you have any questions or you just want to listen it? Oh, I guess I had one question. Hey, wellness see again spend so I guess my question was really just about, I guess, yeah. In terms of handling the subsurface convection zone, surface effects like in 1D. So in terms of like how it manifests in the US and how it manifests in like these small contributions to spectral line like your micro turbulence. Sorry, treating it just like something that's propagating from the edge of the convection zone. Kinda like extended overshoot or yeah. So I think the interplay yeah. How how how this turbulence is affecting micro turbulence is not well understood in my mind. Currently. Okay, So, so that's what actually one thing that I want to do that I hope to do in the future is to perform a full curve of growth analysis on these models and see what micro turbines I extract from it because that's how they do it. They, you look at a whole bunch of spectral lines, right? And you see how you then know what the shape should be and you fit a two parameters, one being the abundance and one being the micro turbulence. And that, that's how they extract these migratory and y values. And so it'd be very interesting if I could do that same analysis with these 3D models and see if I get 10 km a second or if I get 50 km/s, I don't know what that would result in. One thing I do know is that just the temperature variation on the surface deviates the thermal broadening profile from the Lorenz, from a void profile. So the thermal profile isn't even, isn't even void because you have factors are three different variations along this tau of one scattering surface. Now how important that is? An unknown question again, but it is worth noting that there's this dynamic turbines at the surface affects all aspects of spectral line fitting. And so understanding how these 3D models can help with that is what I'm hoping to look for more in the future. I think. Yeah. Okay. So this is a okay, so there's a several several directions here. So one of the things of course is that the ideas, the concept of macro turbines and micro turbulence or are based on this idealization that one is small compared to the mean free path and one is large. And you said, well, it's kinda characterized by the scale height or the scale lanes. But for line transfer, that's not completely true because the opacity in the line is very, very strong. And what actually constitutes micro turbulence can be very, very stringent because line mean free path are very, very short. Okay, I have a backup slide for that. One cool thing about the Monte-Carlo transport is I can actually see where the last scattering region is, right? I can see where the last interaction for the Monte Carlo particles were before they propagate outwards. If you look down at this bottom region, this is kinda what it's showing is that the scale head is roughly the width of the scale bar, and the emitting region is shown in the purple contours. So for the 235 cell mass models like the contours are basically a scale height and width, meaning that the immediate region is basically a scale height wide. Muscle mass model is quite more extended, but that's always the case at any given frequency. Where you go from being transparent to being brought to being free. Just that when you are looking at in the middle of a line, you're looking high or up. When you look in the center of the line, you're looking at Wayne's the line you're looking deeper down. That's why, because source functions tend to decline with height, that's why you get an absorption profile, right? But I'm trying to say is that when you talk about the actual turbulence that are moving the light profile around that thing that constitutes micro turbulences when to scale length of that turbulence is small compared to the mean free path. I guess what you're saying is that by definition, the mean free, where the protons are escaping the mean free path is always on the order of the scale height because that's one of the protons go from being trapped. And maybe, I guess, alright, So to that extent, maybe the scale height is probably as good. But of course, one of the questions, one of the nice things. So if you have a simulation of real velocity field, a real physical model, is that you don't have to make this idealization. You just kinda calculate the full, the full radiative transfer for that line profile. And there was, this goes back to when I was a solar physicist, back when I was a grad student. Goes back to the whole question of the whole question of whether he's called Mezzo turbulence. What scales is that transfer between micro turbines to macro turbulence. And because you have a flow velocity field, do you have the, you have the option now to see when did the line profile, because as you talked about, main way of doing this is to curve of growth because macro turbulence doesn't affect the equivalent with whether micro turbulence does. And so that goes into the whole business. I guess the other thing, I mean, if you have any more questions, just feel the break-in. I'm just going to keep drilling. I guess we only have like one last question. Then I can let you take around. Yeah. Yeah. Because I guess I'm wondering are positive, it's quite interesting how you kind of had the mat, that extent of the subsurface convection zones. And I've noticed those and look them on my models with Meza. I'm wondering what do you like? Just like the spatial resolution, like in your implementation of mesa. Until I get a full mapping of like that sounds like you have you can map that entity is mapped the velocity field if necessary, convective velocity is or sorry, are you referring to this plot? Are you referring to like this one? The fly you would just add the first one. Okay. Cool. Yeah. Yeah. I'm just curious, like if you were just like the facial resolution of the zones that made the tracks when you try to isolate this. That's actually a very good point. I haven't done a resolution study on this to the extreme high edition, but I, but I haven't seen anything that seems to change it very much. Okay. Basically, it's the extent of the connection zone, no matter what you're doing. Changes like the extent changes as you go across the main sequence and across the Hertzsprung gap. And if you go up in massive without a mask changes everywhere. But it seems to be confined regardless. One thing I did notice when I recently money and running new models with TDC, you can get much more extended convection zones in Mesa, which lies towards the terminal adenine sequence. For an easel or mass model, you can get the whole envelope, the whole surface to be conducted, which I have not seen before. I'm currently looking into that more with this trying to implement this turbulent pressure into Mesa. But that could be resolution thing that I'm just not resolving at high enough or something. Oh, no. I was just curious because I didn't know there was like a way to do that. That's something I've been trying to do for awhile. Yeah. I mean, I I'm not the best 1D modeler and I consider myself a good 3D modeler, but I'm not the best 1d1d modeling. Many, many people only care about what you give them a recipe for it, because obviously, you know, putting 3D models and everything is very hard to do. So if you have a one description them modified mixing length or whatever. Yeah. So the thing that it's the holy grail, everybody wants you to give it. Reality. 3d is different than one day and you can't always mock it up. So I get back a little bit also to the magnitude through these turbulent velocities. So like when people talked about this macro turbulence that you've seen ubiquitously and hot stars. They always have. I think Barrow mentioned the HD 108. But almost every one of these stars has macroeconomists. The only exception is this. Dash two. Dash two. Yeah. What is it What's the phone number for it? I always end V6, 60, 24 dash two or something like that. Yeah, that's the strongest magnetic star and that's the one which we think magnetic fields have succeeded in inhibiting. And so I think it's really interesting to think about it because you see most people when they think about convection, they think about it in a language of buoyancy. The material gets to the point where if you lift it up, it's less dense in its surroundings and so it just continues to effect. But when you have convection that's driven at the limit of the Eddington limit, it really is radiation forces that are lifting. The only problem is the radiation forces cannot. Well, they radiation forces and sustained enough to actually make the material escape. Once you have buoyancy, if you think about gas pressure, how can a gas pressure make a turbulence that's more than Mach ten or something or 55. Buoyancy is driven by gas pressure. So it's very, very hard to see how buoyancy you can ever make something go faster than the isothermal sound speed. But in this case, if it's radiation for us is it doesn't care about that. It just accelerates it until it continuing to accelerate it. And if it doesn't have enough acceleration to lift it out of the gravitational potential, the material reaches a height and falls back down. And so I believe that the way one should think about convection in the context of radiation dominated, for the radiation pressure dominating over gas pressure is more in term of like almost like a wind driving a failed wind, then it buoyancy. And so the point being is that you're seeing velocities that are 100, maybe 100, even 200 km/s. And of course that's still below the escape velocity of your star. And so you don't actually, whatever opacity is driving this doesn't get, doesn't persist, and so forth stops and then the material coast and then eventually comes back down and you'd get this very bright. But of course, that exactly means that, that does change the whole way. One thinks about both the, both the, well, first of all, it changes the energy transport idea, right? Because now you're lifting things that are much higher velocity. And so you can't really use a mixing length picture as it were. You have to think about it in terms of. Then the other thing I think is that when you have radiation pressure dominating, what you're actually exacting. Even carry transport is your advection radiation. The energy, right? That means the radiation has to stay trapped and they effective. So of course that has to do with your optical depth. Now, the other point being here that So, but, but going back to this issue between macro and micro turbulence, if you started directing things on a, on a very small-scale and an only have small cells. Then they, you know, then you're going to get gas dynamic type of shocks and you get dissipation. So I think the point is, is that when people tried to understand this macro term is that one sees in these very massive stars, it's often described in terms of gravity waves or something like that, which have the ability to be, in principle, they can be driven faster than sound because they don't run in, because they're circulations. It's hard to make them very supersonic. And so I think a lot of it is driven by radiation for us, this is what I would say. Anyway, so that's one factor and then the other factor, I guess it's coming back to this slide that you talked about in terms of the effective radiation, go back a few slides where you have the gradient of the radiation pressure averaged over kappa rho V, I think it was. Or if kappa kappa rho F. Yeah. Yeah. Yeah. We're gonna have that ticket head home, but excellent. You recording this, right, Stan? Recording and I'll you can listen to as much as you want. And I'll probably reach out over Zoom will definitely have it answered questions in chat. Yeah. Anyway, of course, what we're looking at here is just the standard porosity effect, right? Yeah, yeah. Especially when you pull out the variation in opacity, right? Model for, for porosity is to think in terms of the capacity doesn't really change, but the mean free path does. Well, of course that's related to the density. And it's the flux correlation with the fact that the density is low as the flux wants to go out. And so this all started for me. I was referee in a paper by near should either the 1890s repacked about basically this effect. And I always learned when I, when I talk my radiative transfer class, well, when you have gray Opacity, the flux just pass to the node that has no place to block the flux. The flux has to come out. And therefore the oral pass that you put on, the stronger the radiation for us. And of course, when you have line transfer, you put it in a lot of opacity. The photons go around the line and you get a dark absorption lines. The anti-correlation between new where there's lots of opacity and flux. And that's why you have 50 difference between the Roslin mean and flux, the plot mean for radiation opacity. My point is that this is part and parcel to the porosity effect. And I think you realize that you had Hickey later on you actually cite cite your urine John's paper from that. And to me, that paper I think has a real potential and I keep wanting to encourage you. And also, I think we talked about this even in Ireland has already called delight. Try to use that formula because if you do that averaging, if you're structures, then you get a kind of porosity mean opacity. And you can model how that, how that reduction, that 80% that you're seeing here. You that the photons are really wanting to go out to places where there's the least density and therefore the flux. And that you're not trapping the photons the way you would if you had an ordinary passive photons are taking the easiest way out. And that's why your mean radiation pressure is less, the gradient is less because photons are leaking. And I'm trying to say is that, that formalism that allows you to take those, those pathways averages that's in that suddenly a wacky son quiz paper. Really. We did it for just a one simple case of wine. The shadowing driven opacity, but it can easily be applied here. It'd be very interesting if you could characterize this opacity in that language, it would be very interesting to me. And so maybe at some point we could document, I'm not sure I really understand this psi Mach number, the pseudo Mach number. What does that mean? That the sky is, is just what we got the flux. I would call that the well, in our language that would just be the reduced opacity over the actual atomic opacity, right? Right, yeah, Yeah, yeah, Exactly. So psi, psi could be thought of a reduced opacity. That's, that's how it's gonna be implemented in Mesa. I wanted to eventually implemented as just an opacity reduction because, because the only thing that cares about opacity is the radiation transport in 1D models, right? But in reality it's not really an opacity change, right? It's really, it's really a change. And this correlation, which is why I kept it as this as this. I mean, I understand. I understand. But let's put it this way. For instance, if you're asking what is the radiation force, right? Yeah. Then, then radiation, normally we think of radiation forces, opacity times flux divided by the speed of light, right? Ready acceleration, right, right. And, and, you know, so if you have a star that's getting close to the Eddington limit and you reduce the opacity by a factor of five, then your longer getting, tell him it, right? Of course this is the this is the whole idea behind the work that I've done with Chavez. Saying, you know, a star can go above the I didn't tell him. And if it starts, you know, you can if you start if you wait. In that paper, cited one of your papers, that review article on the very massive stars. There's the whole discussion about the iron bump Eddington limit when I call the RPA. But in there, There's a whole idea that what if a star, where to go above the only time I really can't come up. Everybody thinks, well, it just comes apart. Well it can't because there's not enough energy that they can star blow apart by just radiation for us is the photons just don't have it. You have to ask, well, where does the, where is it actually able to succeed and driving mass away from the star? I know the words when it comes down to wind mass loss, this is a really important parameter. Yeah, I agree. I agree that like above, above the surface and when mass losses is extremely important, I have a suspicion that all of the variability we're seeing here is also important. And when Maslov's as terms like driving mechanism, right? Another thing I want to look at it when I'm a postdoc is Dr. wins from these turbulent things and because if because we currently just have gray opacity, but if you add line driven effects to these plumes are gonna get launched further away actually. So that's the whole idea. That's how they do it. And move it and Johnson, right? They said, Okay, the iron bank can get the wind started and make all this turbulent atmosphere. But you've got a shadow. And of course, you know, I mean, we've talked about this when we were in Ireland. The problem is, is that you treat this as a pseudo, as a gray opacity, but it's really made up of thousands and toxins, those spectral lines. And we started cutting velocity field throughout those things are going to radiation transport. It's gonna be very different in that ensemble of lines. And then that's the whole idea that you're using the Roslin need opacity. But what happens is that line when you have windy shadowing, that tends to shift you not completely but towards the plunk mean because you're taking your deep desaturating the lines. So I don't know if you've got a chance or if I shared with you. But the talk I gave in the meeting and in Italy that Matteo went to that was listed by hosted by Steve shore and a couple of other people. That was all about these gap transients. But I gave this talk that basically span radiation during wins to the stuff that you're talking about here. And then I talked about super Eddington wins and then dry interruptions and all that. So as I was given a whole hour, so I read quite a bit of grounded that so I can send you the link to that. It's an hour and then Rebecca half an hour of questions. And Matteo Matteo also gave a talk at that meeting. And I know it's not easy to do. But we can't, you can't really go anywhere until you start taking into account the fact that it's not really continue them. It's, you know, that it's really, really a bunch of lines that you can, once you start putting in velocity fields that are going to desaturate. And that's essentially what you do with a lighter wind theory. So anyway, that's obviously one point and then the other point being here that they do, I do think that it's really nice to apply the formulas. I'm going to walk Ian son twist to your simulations and if you want to talk about that some more and talk about ways in which ones could do that. But I've been looking around. I've been trying to encourage John himself to do that. So busy. Yeah. But yeah. Anyway, so that's another point. I think. Yeah. So that's something if you want to continue, we can discuss some more. And to me that's the lowest lying fruit. Because then, then you have a formalism for telling you how radiation actually affected by the structure. The point is, is that you're making, you're doing this ensemble mean. And the neat thing about this is that if you look at that paper, the great, the great lucky thing is that the distribution of the structure would tend to, tends to follow sort of Pusan or something like that or, you know, but you can't really integrate over that. But if you make this approximation of the truncated power law, that's integrable and you get an analytic expression for this porosity reduction. And that's like the key idea in that paper. I think that is really very powerful. And potentially help you go from being just having a model where you compute the structure, having an analytic tool where you can analyze what its actual consequences are. And so, yeah, if you want to take a look at that and chat about it some more, maybe I'd be happy to do that. If I take a look at it and reach out if I have any questions on whichever I would really, really be. Something that I would be highly interested in to see that formalism applied to your, to your bottles and NT on phase models and the stuff that you're doing. John is talked about doing it. It's just that oh, I don't know. So I don t know that John got this big grant last six months ago or maybe a year ago now. Basically massive stars in 3D or something like that. And I'm pretty sure there's money there for a postdoc and I think you guys would be he's an amazing person to work with. He's really smart. I don't know if you have any interest in living in Europe, but unfortunately, I think I'm I'm trying to stay on the state side for my postdoc. I didn't hear that too. I didn't hear that John was done. This has a lot of money and would be I agree that he'd be a good fit, but my partner and I are going to try and stay stay on the East Coast, I think is what we're hoping to end up. You're going to be on the East Coast as that's the hope. Yeah. What about in New York? You can be able to is there anything that's flat irons? Yes. I'm applying to the CCA postdoc. I'm applying to Princeton postdocs, apply it to a CFA. Find a space telescope and nasa Goddard as well, because they have the observational aspect that I use. And I'll, I'll, I'll still be around for another year. So I'm in my final year of teaching, but there'll be another round of the year before actually go into full retirement. That point we might move to Colorado, but we'll be around here, so anyway, alright. Well, it's great having you. And thanks for, thanks for agreeing to give the talk and I learned a lot. I'll go ahead and let's see. I'll go ahead and stop the recording now.
Astroseminar 11Oct22 - William Schultz
From Stanley Owocki October 11, 2022
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Zoom Recording ID: 7874089078
UUID: U2IvaBdDQauPZ5iPxbHDyA==
Meeting Time: 2022-10-11 07:45:13pm
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