 in this lecture and focus on, I'll show some actual data. So I'll be mixing simulations and real data. And the focus will be on the most massive halos and the baryon structure within them. And also towards the sort of two thirds of the way through, I'll describe a project that involves creating what I call synthetic catalogs and images for to support survey science analysis. Often in the community, they're called MOCs. And maybe you've heard the term MOC catalogs, MOC images. I think MOC is a bit harsh. So I tend to try to use a bit softer tone with synthetic. But at the same time, one can think of this as Monte Carlo realizations. Essentially, one has underlying physics, astrophysics, physics associated with cosmology, physics associated with astrophysics, especially the astrophysics part involves an ensemble of parameters. Of course, there are parameters on the cosmological side. And what ideally in the far future we will have are essentially laboratories that will create in a Monte Carlo sense, randomly sample in that parameter space and provide detailed imaging and catalogs for expectations in say optical wavelengths or x-ray wavelengths or millimeter wavelengths, whatever. So the ideal goal, like hundreds of years from now, will be to create spectrophotometric maps with the kind of fidelity that matches or exceeds that of observational capability, of what the state of the art observations. We are far from that goal right now, but that is the ultimate goal of this kind of work. And I'm showing you a very baby step here because one of these images is real and one of these images is simulated. And then about halfway through, I'm gonna ask you to raise your hand as to which is which. So study it carefully now and think about which is real and which is not. Okay, I'll show this again. Rough outline, what we'll do today, I'll tell you a little bit about galaxy clusters, the phenomenology associated with massive halos. I'll tell you about how we can constrain cosmological parameters through counting clusters as a function of redshift, very briefly. We'll talk a little bit more about what's going on in terms of astrophysics in the cluster core and essentially the focus will be, we need to control the star formation rate in the very center so that the brightest central galaxy doesn't get too bright and too big. We have to constrain the top end mass of the galaxy stellar mass function. Then I'll launch into a little bit about synthetic surveys and close with some thoughts on the future. Okay, so a brief overview of clusters. This is from a review, this image is a set of images, this is from a review that I wrote with Steve Allen and Adam Manson 2011 in annual reviews of astronomy and astrophysics. If you wanna know about cluster cosmology, pick up that review and read through it for more details. But when you look at halos above, say, 10 to the 14 solar masses at low redshift, what you see are tens of very luminous galaxies, the luminosity is greater than or of order of that of the Milky Way, at least 10. And it turns out that most of the baryonic material, however, as we already know, doesn't get converted into stars. It remains as a plasma. Now, in most of the universe, the plasma temperature is low and it's very hard to observe. In galaxy clusters, because of the deep potential well, the densities are high and the temperatures are high. And so you can observe this baryonic phase through a couple of different channels. One is that the plasma emits X-rays. So just sheer bremstrawling and line emission from a thermal plasma. And this is an X-ray image of Abel 1835 sitting at a redshift of 0.25. Here is an optical image. These are the stars in our galaxy in the foreground, but what you see is kind of a big fat galaxy in the center and a bunch of other galaxies. They look yellow in this diagram, but really we call them red in the sense that they contain old stellar populations that emit mostly in the redward, towards the redward side of the optical bands, as opposed to young stellar populations which are very blue. And then when you look in the cosmic microwave background, the hot electrons that are also, that are producing the X-ray emission interact with cosmic microwave background photons and essentially upscatter them through inverse Compton scattering. And when you point your CMB telescope and look at low frequencies, what you see is kind of a hole in the microwave background in the sense that the temperature, effective temperature is decreased, the flux is decreased, so the antenna temperature is decreased. And that's called, that effect was first predicted by Senyayev Zoldovich in 1972. So again, you know, pebbles, Zoldovich, here we have Zoldovich coming in from 1972. And it was, this effect was first observed relatively recently. I mean, it was only until the 80s that the radio astronomy was sensitive enough to be able to detect this because it's a relatively small effect. The optical depth in these systems for the microwave background photons is of order 10 to the minus three. So the effect on the Planck spectrum is relatively modest. It shifts upward a little bit in temperature, so at low frequencies you see a diminution in flux, but now it's very easily observable because of the sensitivities of CMB experiments that you've heard about already in this school. Okay, so, you know, and then most of the baryons you see, so there's no missing baryons problem in clusters. You see them all, which is really one of the benefits of working with clusters. Now as a simulator, there's a couple of ways that you can think about modeling clusters and we've kind of gone over this. This was lecture one. You can just ignore baryons completely and do collisionless dark matter and look at how the merging accretion creates a structure that contains subhalos and maybe paint those subhalos with luminosity, et cetera. You can play those games and there's literature that does that. Then you can recognize that they're two fluid systems at least and you can say, okay, we're gonna couple the baryonic fluid and do hydrodynamics, gas dynamics, okay? And then that allows you to look at this hot gas phenomenology at least and possibly if you include radiative cooling and star formation, you can also look at galaxies, okay? So sorry, in the simplest possible gas dynamic models, you ignore cooling so you can't see these but you can address this phenomenology here and here. Then when you include star formation and black holes, et cetera, now you can address the phenomenology associated with all these wavelengths. Let me show you a level one image. Well, first of all, okay. Now, here we go, we're being empirical. This is real data. In the next slide, we'll show you simulated data. Here are real, here's a rogues gallery, as we say, of a bunch of local clusters from what's called the REXS sample, a Pratt et al. 2009. The surface brightness is shown in the color contours and what you can see is, again, these systems are fairly round and many of them are fairly relaxed. They look to be very close to hydrostatic equilibrium, although there are some isophodal shifts going on, say this system here, the center of the isophod in the outer parts is maybe here, the center of the isophod in the inner parts is displaced a little bit with respect to that. So there's some evidence of merging even in these images. Now let me show you a rogues gallery from the level one, just looking at the simple shock heating of baryons inside a dark matter potential. Yes, question? Oh, sorry, yes, let me go back. Indeed, these are just different clusters. The phone number, if you will, of the cluster is listed here. These are all relatively low redshift systems. They'll be between, say, redshift 0.05 and maybe redshift 0.3 or 0.4, that's the highest redshift here. These are fairly bright nearby clusters. And the scale here you can see is about three arc minutes. So they subtend a fraction of the size of the full moon on the sky. They're extended systems, but not wildly extended systems, unless those are for the most nearby clusters of which there's only a few. Any other, thank you. And then here's a rogues gallery of, we don't name our clusters in the simulation. So here's a rogues gallery of just a collection. And again, you see kind of the similar morphology here. The scales are similar to the observed images before. Maybe a little bit more. This is a recent merger where you can see, and I'll show you actually another real cluster that has a very complex morphology like this. And it's a very recent merger event occurring in the plane of the sky. In fact, such systems and the simulation technology is such that we're starting to see in the literature papers that are kind of designer simulations trying to model a single cluster. So for example, here, from recent work by a group in Brazil, here are images of a real cluster of galaxies, ABEL 3376. This is an X-ray image. Here's a temperature map of the inner part where the photon count is large. And then here is a synthetic X-ray map done from an SPH simulation that was just shock heating and that's all. And it was a simple two-body problem that wasn't even done in a cosmological setting. There was a blob set up over here in hydrostatic equilibrium, a smaller one over here. The two merged. Maybe I'm doing it in the wrong direction. The bigger one here, the smaller one here, they merge. And you can see that the morphology in terms of the X-ray mission, the bright areas here, but the merging kind of temporarily blows out the gas to one side. And there's a temperature map that is in rough consistent agreement with the temperature map observed. One more system to look at with a high degree of complexity. There's a lot going on in this image. This is real data. Yes. Yes, so the question is, how do they capture shocks in SPH? And the answer is artificial viscosity, as I mentioned in lecture two. I'm sorry? Well, the entropy is raised at the shock location, right? Because the density will go up. So the temperature will go up much more than the density goes up. So T over root of the two thirds typically goes up at the location of a shock. So that will generate entropy. Okay, so this is a complex image. Let me try to walk you through it. The background grayscale is an optical image in a single band, in a red band. And the red is an X-ray image from the XMM satellite. And the blue is radio from the very large array. And there's, in the optical, there's a large galaxy here and a second large galaxy here. And essentially there's been a merger occurring basically on the plane of the sky between two systems that had each as a big central galaxy. And now they're temporarily displaced from one another. Ultimately they'll come back and merge in a few billions of years. Now the X-ray mission has a peak here and an extended tail out in the direction of the post merger. And out here, this part of the radio diagram, there are radio point radio sources shown in the image. But the radio emission associated with the cluster is the interesting part is located here and here. And that is non-thermal emission that is generated by the shocks. So in the process of merging, the shock heating occurs in the post merger phases out on the edges of the system. And that shock heating can amplify any seed non-thermal population of electrons. And there's gonna be magnetic fields there. So basically you're seeing synchrotron emission from a non-thermal component of electrons that will die away on the order of a half a gig a year or so. Okay, now looking at a collection of clusters. Again, this is real data. This is, there's funny things going on in the core of clusters. So what I'm showing you here, K is that pseudo entropy. So K is proportional to natural log of T over root of the two thirds. This you get from X-ray spectroscopy, and this density you get from X-ray imaging, all right? And you can do that with very high resolution data. You can do that as a function of radius. Estimate the temperature as a function of radius and the density as a function of radius. Put that together to get an entropy as a function of radius. And this is work done by Ken Cavagnolo and folks at Michigan State bearing your bye to me back home. And there's essentially a way, when you look at clusters of two different temperature bins, here's four to eight keV, here's greater than eight keV. At large radius, they tend to line up in a very kind of self-similar way. But at small radius, there's a lot of variety. And in fact, there are some systems that have very high elevated central entropies and some that have very low central entropies. And in fact, some that seem to apparently not converge, the entropy continues to drop all the way in. Question? The x-axis is just a radius. Yeah, it's just, you know the redshift of the system and so essentially this is an angular scale converted into a physical distance given the redshift of the cluster. Thank you, yes. It's the straight line is the expectation that comes out of simple adiabatic heating of the entropy scaling as R to the 1.1. And the details of that you can find listed in this paper, Mark Voight, for example, has written papers about this. And so shock heating will kind of drive you to this line and you see that indeed at large radius, the effects of shock heating are the most important part of the physics. But at low radius, at the very, the inner part of the cluster, there's more physics going on. And that's what I wanna focus on. It's what physics we think is going on there. Well, and one more observational picture and then we'll get going with other things. This is kind of a relatively old image but still very pretty and one of the most, one of the deepest x-ray images of a galaxy cluster. The Perseus cluster is a relatively nearby cluster. Chandra, the Chandra X-ray satellite has a very high resolution imager on it. And if you stare at it for a while and they stared at it for a order several hours, so a mega-second exposure, which is a lot of observing time on an x-ray telescope orbiting the Earth, what you see is this image. And over here is that image kind of with features highlighted. What you can see is that there are just void regions here, empty regions, bubbles. They're empty of thermal plasma. They're not literally empty because otherwise the pressure of the surrounding thermal plasma would collapse them but they're filled with relativistic plasma that provides pressure support and is basically blowing, it's blowing a bubble into the surrounding thermal plasma and pushing it out of the way. And here's a recent episode. So the idea is you've got a central galaxy here that's not shown in this image but it's located right here. That central galaxy is occasionally a creating gas. It's got a supermassive black hole at the center of it. Some of that gas will drain down on the supermassive black hole and through mechanisms that are still kind of non-understood but Blanford and Narayan and company, Cretian disks occur, MHD phenomenon occurs, you've got a deep gravitational potential well to tap the energy from. Some of that material will escape carrying energy from the supermassive black hole and feeding it back into the surrounding medium generating the holes. And what you see over here are kind of past episodes of that. So a bubble over here and a bubble over here occurred from a Cretian event that occurred earlier compared to the inner bubbles here. And then it creates these sonic disturbances that basically you can see as ripples in the intercluster medium. It's a beautiful image that helps guide us as to what physics we need. Okay, so what I've kind of told you about so far is listed here to some extent. But why should you care about clusters? Here's some more reasons. There's a host of multi-wavelength features too. So if whatever wavelength you're a fan of there's, you can point a telescope at the cluster and learn something. And what I won't go into a detail today on but hopefully you'll get some in other lectures maybe Shirley Ho and large scale structure will talk about this. Clusters provide the universe's largest telescopes. The gravitational lensing power of the gravitational potential wall of a cluster is such that in the inner few arc seconds of some of the richest clusters in the universe you can get magnifications that approach maybe a factor of 10 and thereby you can see into the background universe much deeper than you can in some arbitrary part of the sky. Okay, all right let's just do a quick look at how we do cosmology from clusters. Whoops, back up. This is an image from a set of simulations that I was involved in in 2002 called the Hubble volume simulations which helps set the stage for doing cluster cosmology through counting halos as a function of redshift. There are two simulations, a lambda CDM and a standard what was then called the standard CDM scenario with omega matter equal one on this side. The observer, this is a map that was generated using what are called light cone outputs from the simulation. These simulations were a Hubble length large so C over H 3000 megaparsecs large on a side that was the box size. And when you have a box that big the standard method of looking at simulation output is to essentially take snapshots that fixed proper times and just output them to disk and then analyze them. But instead of doing that or along with doing that what we decided to do was if this is a cross section of the box, y and x, we set an observer here and then we output shells of particles. So this might be at some z one. We'll output this shell and collapse that shell in an appropriate way. Given the behavior of the metric distance as a function of redshift as z. When we look at another redshift z two, less than z one will be outputting the particles here and we collect up all those particles. So we're looking at the simulation the same way that we as observers look at the universe. As you go higher in redshift you're going out in distance and back in time. All right, so the back in time part is what's important here. So in this map, this is a joint map from the two simulations in the sense that the observer sits here in one simulation we look out in this direction and we see that universe. In the other sector we look out in this direction and we see this universe. And both of these simulations were tuned meaning the power spectrum amplitude were chosen such that you'd get the same number of halos above 10 to the 14, 10 to the 14.5 and 10 to the 15 solar masses in the local fields because we can observe that locally. We kind of normalize to the observations that we see at low redshift. Now the interesting thing is as you go back in time in the Lambda CDM universe there still retains a very healthy population of high mass halos. Why? Because the growth of structure is shut down when Lambda kicks in, right? A, if Lambda is truly a vacuum energy density then we're entering a new decider phase of expansion and exponentially A going as E to the HT and H is approximately constant. So once Lambda starts taking over the Hubble constant and driving the dynamics of the overall expansion, the growth of structure shuts down and as I mentioned I think yesterday it's a very lonely future in Lambda CDM universe. So that means in the Lambda CDM universe you have to form your structure earlier compared to a case of omega matter equal one where structure forms continuously all throughout cosmic time. So that's shown, we can just show the effect of Lambda by actually counting the cumulative number greater than some mass scale and greater than some redshift and then plot up as a function of redshift what that number looks like. Here's the number on the whole sky. You see we're getting up to a million galaxies, sorry a million halos above 10 to the 14 solar masses. The solid symbols here are the Lambda CDM universe and the triangles are omega matter equal one and essentially what you can see is especially at the very high mass end, omega matter equal one, the number density tails off very rapidly. These are very accessible redshifts to observation now. Redshift's zero to 1.5 for galaxy clusters. Of course for galaxies themselves we're looking at redshift six and eight and 10 for galaxy population but for clusters the most massive, sorry the most distant and massive cluster known is about a redshift of two, two and a half now but there's one of them so you can't do statistics on one. However we're getting a good handle on what the population of clusters is out to redshift of one through surveys that I'll mention in a minute. Okay so that kind of sets this, the general idea of what cluster cosmology through counts is all about and I told you yesterday, well I told you two days ago that the mass function, i.e. the space density as a function of mass and redshift is calibrated by N-Buddy experiments very well. So we have that component pretty well nailed down. That's gravity and cosmology gives us the space density but we count clusters not as a function of total mass and free dimensions, we can't go do that, we can't measure that. Instead we need to go measure some quantity like a temperature or a X-ray luminosity or a galaxy number and we measure what's called a mass proxy and essentially we have to think about how that mass proxy scales with mass so we need to take this function, convolve it with a function that describes the likelihood of some observable given mass and redshift and then we can predict the counts in that observable. And this is the current bottleneck is a weak understanding of these scaling laws. These are observations where the mass has been inferred from assuming hydrostatic equilibrium and using the X-ray data to infer a mass given hydrostatic assumption. Let me show you a, compendium of current constraints on sigma eight is the normalization of the power spectrum on eight megaparsec scales in omega matter is omega matter and the constraints are shown from three different samples, a 10,000 cluster optical sample, a 50 cluster X-ray sample and a 450 Suniai-Ozol doberch sample of clusters of various redshifts. This tends to be fairly high mass, all these tend to be fairly high mass systems. But what you can see, I hope, is that the range of the, first of all, there's rough consistency with omega matter close to point three, sigma eight equal to something like point eight something. This is a little high, point eight five. This is a little low, point seven five. But the point is that the error bars here are about the same size, even though this sample is 200 times larger than the sample. So we're limited by, and why is that? It's because we have to marginalize over the uncertainties in those scaling relations in order to get constraints in the cosmological parameters. And that marginalization, that admission of, I don't fully understand how mass relates to optical counts of galaxies. Okay, this richness is a number of galaxies within R200. Here's X-ray temperature and KEV. This is a redshift diagram here. So we can do this counting, but we're kind of limited by uncertainties in these scaling laws. And recent work done from the Planck Satellite since 2015 demonstrates this explicitly. These two graphs don't use the same color scheme. They're from the same paper, so it's not my fault. The Planck team should have maybe thought about the consistent color scheme across figures. But what you can do is you can say, well, suppose my estimates of mass are biased and we'll write a bias as one minus B, okay? Yet another B parameter, but whatever. So if one minus B is one, you're unbiased with respect to the truth. And so you can think that maybe if you put, so you can look at different ways of different teams who have used gravitational lensing to calibrate masses. And one team here is blue, one team here is green, one team here is red. There's inconsistencies now at the level of about 0.3 in the absolute mass scale of clusters. So we don't know the absolute masses to about 30%. And what happens there is that depending on who you believe about this bias, you can float the constraints in sigma 8 and omega matter up and down, all right? There's a banana that kind of goes this direction in the plane, but you can float it up and down depending on how you want to handle the estimate of total mass. And we are just beginning to see the full halo population on the sky. In our lifetimes, including my lifetime, we will be universally complete with above say 10 to the 15 solar masses, but this is just a historical plot from this review that shows you catalogs that have been published either through X-ray identification, optical identification, or from the Alvizel Dovich, compared to the theoretical estimate for the whole sky. So the whole sky above 10 to the 15 solar masses in a lambda CDM with kind of current cosmological parameters should have about 2000 halos above 10 to the 15 solar masses. That's a decent amount, but you'd like more. Well, you can get more by just going to lower masses because it's a steep mass function. So you go to 10 to the 14 and you've got close to a million. And the median redshift to this sample will be about 0.4. The median redshift of 10 to the 14 is about 0.8. So you have to go deeper to get them, but you can get them if you just go deeper. And you can see that the current catalogs, the largest catalog published before we wrote this review was this optical catalog from the Sloan called MaxBCG. It had over 10,000 systems. Now there's been publications from Sonja Alvizel Dovich, SBT and ACT, with about 2,500 systems in 2015. And then soon to come out of Dark Energy Survey, which I'll mention in a minute, and later E. Rosita will be pushing up to hundreds of thousands of objects in our samples. So we're getting close to being complete with respect to these masses. In fact, Euclid and WFIRST, et cetera, will certainly be universally complete, meaning it's like, think about the early explorers of the Earth in the 16th Magellan and Ponce de Leon, those guys. They were figuring out where the continents, where the mountain ranges on the Earth, et cetera. We're going to get the mountain ranges. The highest mountains tend to 15 solar masses in the universe very soon. And it'll be it. That's all we'll have to study until we figure out ways to see another universe. If the multiverse is right, and we can find some ways to channel through the eighth dimension to see. But as I said, I'm a real guy working on real things. I don't think we're going to get through the eighth dimension to see another universe anytime soon. What we can do is put a telescope on our own sky and look out and see our own universe. And that's what's happening for the Dark Energy Survey. Just a little advertisement. It's an ongoing survey. It's finished its third year of observations this year. It will go on for another few years to complete 5,000 square degrees of imaging and essentially 5,000 square degrees in five bands, optical bands, GRIZY. And then another set of images that will go deeper in 10 supernova fields of totaling 30 square degrees. And so those data are coming in. And let me just show you a little preview of work that actually is published recently by Eli Rykoff. Here are some Dark Energy Survey decam images of known clusters. Here's what's the famous bullet cluster at redshift.3 and other cluster at redshift.4, a very high mass system called Ilagordo at redshift.78. And then here are some new systems that Dark Energy Survey found at high redshift. And these colors indicate that, again, the stellar populations in the galaxies of these systems are old and very red. There are other surveys going on at other wavelengths. I'll just have two slides to advertise an ongoing project called the XMM XXL Survey, led by Marguerite Pierre in Saclay. And what's shown here is what you've done is taken the XMM satellite and made multiple tiled pointings of 225 square degree regions. So this is a several megasecond project and here is a map of one of those fields. This full moon is shown for comparison of angular size. It's a pretty decent, you know, about the size of, like that on the sky, right? And what you see here are the first 100 brightest clusters circled in red. And most of them have redshifts now, either spectroscopic redshifts or so-called photometric redshifts, where you use the location of the 4000 extra break to assign redshifts through photometry. And you can see as a function of redshift we're getting out close to redshift of one. Okay, now one thing that we need to keep in mind, and now we're gonna kind of shift back into the simulation world, is be very careful when you talk about clusters versus halos, right? In the sense that clusters are phenomenon that live in the space of the sky. So they live in RA deck and redshift or RA deck and photometric bands, you know, they live in that space. Halos live in a 6D phase space, right? That's what we've been talking about for the last two days. So there's complexity, sometimes you get a very clean sight line to a cluster and these two things are in good correspondence. And sometimes you don't. Remember, galaxy clusters have a scale of about a megaparsec in size. The sight line distance out to a redshift to half is about a gigaparsec. So you're looking along a thousand times, you know, you're looking along a little sight line that's a thousand times the size of the system you look and there's a lot of stuff in between us and the cluster and behind it. So it's easy to get confused due to projection. And let me show you probably the most spectacular version of this, which is a Planck cluster known as Planck 510. So this magenta circle is what Planck said, there's a cluster here. And, you know, it's in our sample. It's one object. Then you can follow up with that detection in millimeter wave radiation right in the CMB. So it's, again, a hole was punched in the CMB at that location. That's a cluster, all right? So we follow it up an optical and, lo and behold, what do we find? We find that there are two systems, shown by red and cyan circles here. One hosts about, hosts 88 galaxies at a spectroscopic redshift of about 0.26 and the other hosts 84 galaxies lying at a spectroscopic redshift of 0.37. That distance is many hundreds of megaparsecs between those two redshifts. And they just happen to line up, you can see they line up within, this scale here is of order, you know, an arc minute, a few arc minutes. So they line up almost perfectly on the sky. Stuff happens, right? I mean, yeah. Okay, let's go now back to physics and simulations. A cartoon version of what's going on with respect to the difference between the population of halos versus the population of galaxies as defined by their stellar mass is shown by this diagram here from a recent review by Joe Silk and Gary Mamal. If you take the mass function in CDM and just kind of scale it by some ratio of say omega-baryon to omega-m and use that to predict what the galaxy stellar mass function would look like, whether galaxy stellar mass function here is defined as number of galaxies per unit stellar mass in the galaxy, you know, you would get this red line. The physics we talked about yesterday can explain why you don't see all of the halos at low mass, right? It's because you've blown out baryons and you haven't converted all the material into stars. So that assumption that m star is equal to omega-b over omega-m times m halo is just wrong. However, you need to do something here too because observations say that there's a very steep knee in the galaxy mass function or stellar mass function or luminosity function. So you need to do something. And what you do is you, what we think you do is to blow out the gas or keep the gas heated near these big galaxies through AGN feedback. And that's what I wanna focus on for a little while here in the next few slides. Why do we think that that might be realistic? Well, you can make very high resolution images and spectroscopy of elliptical galaxies and see that there's a cusp-y thing going on in the cores of galaxies. And the, i.e., the stellar velocity dispersion rises very rapidly towards the center. And that's the sign of a deep potential well. And in fact, you can infer the, so there's something very massive there. And the thing that's very massive is presumably a supermassive black hole. And by now, all other explanations are essentially ruled out. So there are these bad-ass, big-ass black holes, 10 to the 10 solar masses in the black hole sitting in these galaxies. And these are mostly BCGs, bright central galaxies lying at the center of groups and clusters of galaxies. So you have this deep potential well to tap and work with. So in 2006, Darren Croton and collaborators in the Virgo Consortium used the millennium simulation that I talked about yesterday. They used the merger trees from that simulation to apply what are called semi-analytic techniques, I'll say a little bit more about that in a minute, to essentially try to build a model for this kind of feedback, feedback from what's called the radio mode of AGN. I almost thought I would just, this is a really well-written abstract. Abstracts sometimes are crappy. This one's good. I give this one two thumbs up. I invite you to look at the slides later and read this carefully. But essentially, blah, blah, blah, blah, blah, we supplement previous treatments of the growth and activity of central black holes with a new model for radio feedback from these active nuclei that lie at the center of quasi-static X-ray emitting atmosphere in a galaxy group cluster. We show that for energetically and observationally plausible parameters, such a model can simultaneously explain the low mass dropout rate from cooling flows, the exponential cutoff of the bright end of the galaxy luminosity function and the fact that the most massive galaxies tend to be both dominated system in clusters and to contain some systematically older stars than lower mass galaxies. A lot of phenomenology there, really good. In a nutshell, what they've done is to take the merger trees from millennium and then write down, when you're doing hydro simulations, you're doing partial differential equations for the fluid. That's a pain. I mean, it's hard. It's computationally expensive. They've turned the PDEs into ODEs, ordinary differential equations. I have a halo, it's moving along. I'm gonna say DM star, literally DM star DT is something, something that's related to other halo properties that I can measure and calculate and keep track of over time. And you just integrate these ODEs, which is way simpler. Goes thousands of times faster on a computer. And then you just write scaling laws. So you know the virial velocity of the halo. You know how much hot gas is supposed to be there. You have seeded black holes there, so you know a black hole mass. And then you introduce a parameter and you say, I'm gonna let that black hole swallow some material from the surrounding medium. And I'm gonna write down a rate at which it swallows. That's M black hole dot. That's an ODE, right here, right? Then I'm gonna allow that M dot to basically some of that mass is gonna come back out in the form of energy. So I'm gonna write a luminosity. I'm gonna take M dot C squared. That's a heat, that's a energy input, right? And I'm gonna multiply by another parameter, eta. And these two things become free parameters in my model that I can tune and play with. So you do that. And when you do that, what you get is the following shown here. These are observations of the galaxy luminosity function in the K-band. This is astronomy, so it's crazy. Magnitude system. And sorry, astronomers in the audience, I apologize. But I've never got, I've been in the business 30 years. I've never gotten used to the magnitude system. It still drives me nuts. Bigger is to the left, negative numbers. Oh, it makes my brain hurt, you know? Anyway, so this is brighter, this is dimmer. And when you don't include this AGM feedback and you run the same analytic models, this is the prediction for the number of galaxies you get as a function of K-band magnitude. You see it works well at low masses, at low velocity, low mass systems, but it's crazy at high masses. When you bring in this AGM radio mode, you move the line back to here and this is the observations, the blue points. So it matches the observations perfectly. Of course, you had those free parameters to tune, right? So it's certainly an existence proof, if nothing else, that this is important physics. Okay, so the people who do semi-analytic modeling talk to the people who do hydrodynamic modeling, you know, we're friends, we're not, we are in competition somewhat, but you know, it's all about complementarity. All right, you learn something, tell me what you learned. I learned, no, I'm gonna take that, I like that, I'm gonna take it and run with it. So people take it and run with it. I'm gonna show you a bunch of simulations, recent simulations with AGM feedback put in. I'm not gonna tell you the details there. You can look it up in these papers. So Johann Dubois using the Ramseys code, which I mentioned yesterday, here's models without AGM feedback of central galaxies and group scale halos, 10 of the 13 solar masses. These are synthetic optical images. And what you see is, yeah, there's red stars and stuff, but there's these blue sensually disks, like we don't see those in the real universe. What's going on? Okay, that's not a fire alarm, that is a car alarm I'm going to assume. Okay, okay, then you include AGM feedback and basically all of this cold gas just disappears because any cold gas that forms rains down into the black hole and the black hole says, get out, all right? And I'll show you, we have two movies today and you'll see that. And then here are statistics now. That was kind of a small number of systems. Here's better statistics. Worked by W. De Martiz using Ramseys. Here's the stellar mass, halo mass relation shown without AGM feedback in black, with AGM feedback in red, and the observational range is shown in blue here. This is Andre Kratzoff work. So you can reduce the stellar masses to become consistent with observations using AGM feedback. Illustras, the Arapo simulation. Illustras is a simulation from a few years ago led by Mark Vogelsberger, Volker-Springel and company. Here's, they have AGM feedback. Here are elliptical galaxies formed and various other types of galaxies formed in that simulation. And here is our second to last movie, the formation of an elliptical galaxy in illustras. So redshift is up here. The amount of stars in this image, in logarithm is shown here. The star formation rate in solar masses per year is shown here. The specific star formation rate, which is defined as m star divided by m star dot divided by m star, so dm star dt divided by m star, which is an inverse timescale is shown here. When that specifics, okay, and occasionally what happens is you evolve and then freeze frame and then rotate. The stars are shown over here. The gas temperature is shown over here. And what we're gonna see is episodes in which the black holes are being fed and the gas will be blown out like there. All right, and there. And you can see the gas, some of the cold gas is entrained and lifted out. And now fireworks are really going off at around a redshift of one and a half, or sorry, one. You have a small group of galaxies which are interacting. Every time the galaxies interact, the gas within them gets stirred up. Some of it drizzles onto the black hole. Boom, off go the fireworks. Off go the fireworks. And we're left with, despite all the activities seen in the gas phase, you see that if you looked an optical, you wouldn't really notice very much. Kind of a boring pile of stars, right? Yet, if you had sensitive enough H-alpha, for example, measurement, you might see this trail of gas. You do in some systems. So that is observed. Okay, let's keep going with some simulations with AGN feedback. Now we're onto gadget. So we've had Ramsey's or Arapo, Ramsey's two versions, Arapo, now Gadget. This is work by Stefano Borgani's group here in Trieste. A little bit busy here, but let me just say the non-radiator runs are solid black and what's shown here is a temperature mass relation. What's shown here is an X-ray luminosity temperature relation. And the observations are shown in green and orange. The simulations with AGN are shown in red and the point is to see that the red lines up nicely with the green and the orange here and also with the green and the orange here. So again, when you put this physics in, it helps simulations get the correct properties, not just, and the important thing here is this is not looking at the galaxy properties, this is looking at the hot gas properties. This is what's left over outside of galaxies. So it helps, it helps you both make galaxies and also agree with X-ray observations of the hot plasma. Now we're back to Ramses simulations, Albert Hahn, a so-called Rhapsody sample of halos. These are 10 halos with a final mass of around 10 to the 15 solar masses. Looked at at various red shifts, that's the different lines here. We're showing entropy profiles for the halos and it turns out that there's kind of two different populations. There's populations which have a high entropy core and a sub-population that has a low entropy core. And that's basically these systems, the gas cooling is dominating and starting to rain down on the AGM. These systems, the gas cooling is ineffective and the AGM has already done its job to heat up the gas. And observations from the accept sample, which I showed you earlier are shown as the black lines. And you can see that the models don't quite match. There's a little too low an entropy here, but these are observations so we're getting close. We just have to tune, it's all about tuning parameters. These are hard things to get right. And you can see time scales here of freefall times, gravitational time versus cooling times. And these low entropy systems have relatively short cooling times comparable to their freefall times or a few times their freefall times. Okay, then a couple more plots from that work, from Rhapsody G work, I've been collaborating with Oliver on this, so I'm on these papers. Here's the stellar mass halo mass relation once again. Seeing Davide Martizia is also involved here. The central galaxies are shown in orange from the simulation. And then Andrei Kratsov's constraints from observations are shown as black lines. The solid black symbols are just a binned versions of the orange points and you can see that the stellar mass halo mass relation is a good match. And then the hot gas phase is also a good match over here. This is the Sonyaievs-Odovich magnitude called Y500 as a function of mass for the simulations in color and the observations of Planck are in black and they're well lined up. Now, not everything works in this simulation. Even though the pressure profiles appear to be correct, there's too much gas in the centers of these systems. So the AGM feedback isn't doing quite the right thing yet. There's more work to be done. And the way you can tell that is because the X-ray luminosity mass relation for the simulations shown here in colored points lies fairly well above, a factor two, above the observational constraints which are shown again as black points. So there's still more tuning, more work to be done. One little side note I'd like to point out that's somewhat intriguing is that even with all this fireworks, the depth of the potential well of these very massive halos is so deep, so great, that you can't drive baryons out of the system easily. There's not enough energy to drive baryons out to very large radius. So in the language of the chemical evolution modelers of the 1970s, galaxy clusters appear to be closed boxes. That is to say all the baryons that were associated with the dark matter mass that was involved in the halo at low redshift are still there inside that halo. As opposed to the Milky Way galaxy where maybe something on the order of 30 to 50% of the baryons associated with the dark matter of the halo of the Milky Way will be living at larger radius somewhere between us and Andromeda instead of inside that. So, and you can see that by basically plotting the hot gas fraction versus cold and stellar mass fraction. And if we had a closed box, the sum of those two would have to be equal which means they would lie along this line. And indeed the points really do lie along this line. And for cluster cosmology purposes, the good thing is that if you can make both of these measurements and sum them, then you're gonna get basically a 4.7% mass scatter estimator as opposed to either 8% or 34% by measuring either alone. So that's good news for cosmological applications. Okay, that was a little aside. Let me just come back to the core physics. And I'm gonna show you our last movie. This is a movie made by Yuan Li when she was a graduate student at Columbia working with Greg Bryan. This is Enzo simulations. When I turn it on, what we're gonna see, this is kind of a specialized simulation that wanted to go to very high resolution, something on the order of 100 parsecs or less in the gas. There's a supermassive black hole at the center of a potential well that's modeled in a static way. So it's like a cluster that's formed and it's not undergoing any major mergers. It's just sitting there. There's a supermassive black hole there and it's got this hot atmosphere surrounding it. That atmosphere can cool and can rain. That cooling, cooled gas can then sink down to the bottom of the potential and the creed onto the black hole. There are then rules like what Darren Croton wrote down to provide feedback in jet form. So there's directed momentum and energy back in two opposite directions, bipolar directions, to drive jet driven feedback. So enough talking, let me just play. You see the feedback happens and it drives the jets are oriented vertically in this diagram. And what's shown here is temperature, 10 to the sixth, 10 to the seventh. You see gas cool. When it rains down, there's a little disc that forms here creeding onto this central supermassive black hole. That feedback heats up, heats up, heats up. And occasionally you get these quiet periods where the feedback does its job and the cluster can just sit there and that would be a core profile that would be constant, right? And then as the gas cools, that core entropy profile will start to decline and create another episode of feedback. Okay, and here's the time scale up here operating in giga-years. Here's the quiet period. There was a soundtrack with this movie, by the way. It's classical. Yes. Sorry, can you say that again? This is not what we should have the AGN feedback. Yeah, so the question is whether the AGN feedback actually kind of promotes or demotes star formation. And that's a really good question. And the answer is a little bit of both. I mean, mostly what you're doing is preventing the gas, because you're heating the gas, you're preventing it from cooling and forming a lot of stars. So that's true. On the other hand, the turbulence, why don't I just run the movie one more time. The turbulence that you generate out here, some of that local turbulence will condense and cool. And that's where the cool gas emerges, actually, from essentially vortices that are driven by the jets, those instabilities that occur on the edges of the jet will occasionally, gas will occasionally condense out and you'll get local star formation happening there. So that's absolutely true. Yes. So I think the question is whether there's shock-driven star formation. Generally speaking, that doesn't seem to happen in these codes. You might need extremely high resolution to be able to see that phenomenon. The shocks are just relatively poorly resolved here. So you don't see any star formation associated with shocks in these simulations. It's usually associated, and I'll show you in a minute, actually. You anticipated the next slide that the star formation occurs inside the galaxy. So yeah, you're talking about, I think, as a galaxy, a gas-rich galaxy passes through a shock, some of the interstellar medium in the galaxy can be agitated and that can promote star formation. Yes, you're absolutely right about that. But if you just have plasma not inside a galaxy, it doesn't promote, the shock won't promote star formation in that plasma. Right, good, we're on the same page. Yeah, let me, these are good questions. You anticipated the next couple of slides. These are observations, Hubble Space Telescope observations of H-alpha emission, which H-alpha is an indicator of star formation in galaxies, it's a UV line. And what you see is these complex morphologies where it looks like star formation is happening sometimes in disks, but often in these kind of complex filaments, right, that come in and out. These are very high resolution, 30 kiloparsecs, right, is the scale shown here. And then you can take Yuan Li's simulation and you can look at where the cold gas is. And in fact, she has versions with star formation now, the original movie there didn't have star formation in it. Here's what you would see, and this is courtesy Mark Voight, who's really been pushing this along with Megan Donahue. So this is the HSD image, and here's like a synthetic image of what you would see from Yuan Li's simulation. Really compelling in the sense of, again, kind of the morphologies are similar. This is probably what's going on. Okay, now that's core physics, let's set that aside. I'm gonna open up one last box for our lectures. To give you an example of what I and my graduate student, Arya Farahi, are currently doing to support science survey analysis for the Dark Energy Survey. I'll show you an application to the Sloan Digital Sky Survey, but we're gonna be employing this on the DES data as it becomes available. So what have we done? We've done what's called spectroscopic mass estimates of optically selected redmapper clusters. So let me unpack that a little bit. But to give you some context, first thing I'm gonna show you is a synthetic sky image. So what the future holds for us, I think, and I'll come back to this at the very end, is we spend billions of dollars on projects like LSST, Euclid, WFIRST, right? They're multi-billion dollar efforts, right? And they get data, and we all love data. Everybody loves data. Data is truth with a capital T, right? Meaning, you go into the sky, you get photons. Those photons don't lie. Nobody generated those photons from a, actually that's a pretty weird thought, I'm sorry. It's too early in the morning. So I think that there are extraterrestrials out there creating the synthetic, Max Tegmark might appreciate that. Max, if you're watching on YouTube, Max Tegmark has written papers demonstrating that the entire universe could be a simulation. Lemmas, theorems and lemmas, 98 equations, it's like, oh man, Max, calm down, dude. Anyway, I love you, Max, by the way. All right, so what we can do is we can create, with these simulations, lowercase T truth catalogs, right? We're God, with the lowercase G, in our little synthetic universe, and we can do whatever we want. We can make galaxies shaped like pencils, or pretzels or something, you know. Why don't, why, you wouldn't wanna do that, but you could do that, right? But at least you can then say, okay, what if you observed that synthetic universe? So you can do things like predict what are the observable features would be, calculate signal covariance, all this good stuff, right? And how do we do that? Well, for Dark Energy Survey, we applied for time on Exceed resources in the US. Exceed is a big computational, set of computational centers with the largest supercomputers that you can get on the planet, right? And we have a kind of a flow that works like this. Take the power spectrum, generate initial conditions, run your in-body, the in-body produces light cone output and snapshots. The light cone outputs are the versions that we know, the synthetic universe that we see, but we have to dress them up with galaxies. So how do we do that? Well, we measure our local density, we measure halo properties with this thing called rock star, and then that all drops into methods to add galaxies to lens them, which creates a lensed galaxy catalog or an un-lensed galaxy catalog, from which you can produce imaging, and that's your synthetic sky, and that's what's the previous picture. There's a few more steps in there because you'll notice if we take a step back, there are stars here, right? Well, those are stars that were pulled from the USNO catalog. I mean, they're really stars in our galaxy, whereas this little galaxy cluster sitting back here is the part of the fake universe, right? Okay, and furthermore, we do that, we had a little fun with some of the computer scientists. We used a very early, this is a Aravada, as a workflow system that's part of the Apache, incubator, it was an Apache incubator project at the time, and what it means is you can kind of have, really build out this workflow using these kinds of tools, you know? You can run your in-body simulation, and then we got to the stage where we were actually launching these jobs, not just in a single supercomputer, but on multiple supercomputers, separated by thousands of miles, you know? So run some in Texas, run some in San Diego, right? And then move the data to Slack at the end. So you can do that all in, you know, almost from your browser. All right, now back to the science. I'm gonna give you some motivation. This is real data. Here is a paper from colleagues, Eli, sorry, Eli Rykov and Eduardo Rozo, from Sloan Clustered Data. I'll tell you what Red Mapper is in a minute, but basically you take the Sloan catalog of galaxies, which has magnitudes in different colors, and in different photometric bands, and you identify clusters using a method called Red Mapper. Sloan also has spectroscopy for the brighter subset of galaxies. So for the central galaxy in a cluster, and any member of its satellites that are bright enough to get above the spectroscopic limit, you can get a velocity difference for that pair. If you do that for all the pairs, and Sloan Sample has a lot of galaxies, and therefore a lot of clusters, so it's 10,000 clusters of order 100,000 galaxy pairs in those clusters with relative velocities. So you can plot up the line-of-sight velocity magnitude here, this is the log scale magnitude, versus richness. This is kind of the number of galaxies in the system. We put a limit of it on 20 and go up. And what you see is kind of two populations. You see the population of systems that are associated with the main halo of the cluster, and then those that are projected along the line-of-sight, which have very large velocities, 10,000 and above kilometers per second. Typical velocity dispersions of 10 to the 15 solar masses you saw from the varial velocity analysis would be more like 1,000 kilometers per second, not 10. So this 1,000 is kind of a sweet spot of about 100 galaxies. Then you can fit this cloud, you can throw away all these, that's background. You can fit the cluster population to a line here, and then look at the deviations in the velocity direction about that line, and that's shown over here. So this is V over sigma V. On the next slide, I'll show you, or a couple of slides, I'll show you what sigma V is in particular. But it looks approximately Gaussian, but not quite. It's got a kurtosis that makes it more peeky in the center than a Gaussian, but only just a little. Let me tell you one slide about Red Mapper. Red Mapper feeds off of this red sequence, this red and dead population of galaxies to identify collections of galaxies that might be bound inside a single halo. Red sequence, Red Mapper stands for red sequence matched filter probabilistic percolation. Yes, anyway, I never remember that, so that's why I put it on the slide. But here's an example of red sequence from this famous El Gordo cluster at redshift 0.87. This is R minus C, R minus I, I minus C, and you can see that the galaxy members lie on a tight color magnitude relation. So back to the simulation, the simulation that we did in a Lambda CDM universe at low redshift has, if we just look at galaxies contained in 10 of the 14 solar masses halos and above, and look at their color magnitude diagram, there is a population of red galaxies, there's also some blue ones, but the bright ones tend to be red, and there's a strong red sequence that we see in the simulations. So it was kind of done by design. That AdGal's method uses an empirical approach to assigning galaxy magnitudes into particles in the simulation, and so it's kind of, by design, comes out with a red sequence. Now, we can run red bapper on the simulated world and compare the number as a function of redshift. This is the differential number above either 20 or 80, in terms of this Lambda richness, as a function of redshift, the observations are shown as the dashed lines, the simulation is shown as the black lines, the solid lines, there's pretty good agreement. And this was not, the simulations weren't tuned to produce this, this is an output, this is a prediction. Now we can do the same analysis, this spectroscopic analysis that was done two slides ago, we can do it in the synthetic world. And here I'm showing you now, this is the simulated version of the work that Eli and Eduardo did on Sloan. And again, here's the magnitude of the velocity for pairs as a function of Lambda. We get the same background foreground population. The line here is the same line, we actually didn't draw a new line, this is the line that came from them, their observational paper. We then fit this component with a model that looks like this, the characteristic square velocity or you know, characteristic velocity dispersion as a function of richness and redshift goes as a power law in both richness and redshift with some normalization. And then we look at the deviations around that power law behavior here. And here's the curve, it's peaky. And then we can write a likelihood of this functional, this PDF as a main Gaussian component plus a background. And this was the model that Redmapper for the paper, observational paper used. Okay, and we get parameters that are very, very similar, right in terms of, and this is the full sample, this is the correctly centered sub-sample of clusters in the simulation. We also applied our method to another simulation called Bolshoi, but let's not worry about that right now. I won't worry about the details for the moment. Instead, actually I think these slides are a little out of order, I forgot to move them before starting. I'm gonna go back to my opening slide. Here's the test. Yeah, this should have been right after the first slide that had the synthetic map. I meant to put this there, but we'll just take it where it is. Which one's real? Which one's not? How many of you think that the left-hand side is real? Yeah, raise your hand higher. I'm seeing about a third. How many of you think the right-hand side is real? I think the right-hand, well, okay, good. I'm seeing about the same number of hands. It's like a third of you think left, a third of you think right, and a third of you are asleep. So let me, yeah, just kidding. Let me tell you that this one's the simulated image and this one's the real image. And there was only, I've given a colloquia showing this now for a couple of years, and there's only one, maybe two places where somebody got it right for the right reason. And I'm gonna tell you why. When you look over here, you see these things. These are like satellite tracks that were put into the synthetic data. I mean, we actually put satellites in, we didn't put airplanes in, but we put that in. And we were so proud of having that that we left them in the image. Whereas a real observer would never leave that in the image. And somebody caught that in one of the talks I gave. It was great, it was brilliant. So that's how you can tell. Okay, sorry, back to what we did with simulations. Because we are lowercase g-god in our simulation world, we can do a little bit more than just the analysis that I showed you. We can tear apart cluster members into halo members. We can tell, okay, you think this is a cluster with so many members? Now I'm gonna tell you what halos contribute to that membership, right? And so, for example, here's redmapper membership probability. Here's one cluster and they're colored by redmapper probability, which is zero to one. And one is pretty blue and going to zero is getting pretty faint. So these guys are all thought to be the same. They're part of the same cluster. And they're also pretty much part of the same halo because they're all colored black, except for these two red guys. Now here's another case. Here's a big cluster. Redmapper thinks it's giant here. And it's made up of like six or seven or eight or nine different halos, okay? So again, this is projected. You have these filaments. And when the filament turns and points to you, you get confused, right? And that's what you're seeing there. It doesn't happen a lot. It's not the dominant effect, but it does happen. So it's nice to be able to tear it apart. So we can go into that distribution function and tear it apart. Here's the original one. Here's what you do. Here's what you find when you only look at pairs which are living in the matched halo to the halo that's matched to the cluster. And we match halos to clusters by maximizing this joint probability. For every galaxy alpha, you can multiply its membership probability in the cluster times the membership probability in a halo, maximize that joint probability. And that's your matched halo that is associated with the cluster, okay? So it looks much, first of all, you lose all the tails. All the high velocity tails come from non-match systems and you get a much more Gaussian looking thing. And then all the projected galaxies are shown here. So about 62% of the pairs lie in the top-ranked halo. It's just a number to take away. All right, and then finally, this is kind of getting towards the end of things here. Finally, you can compare the, so you can take the characteristic velocity, that sigma v. You can go back to lecture one and say, oh yeah, there's a virial scaling relation between velocity, dispersion, and mass. So let me cube that velocity and turn it into a mass, okay? Why not? Because you're measuring a depth of the potential well that is associated with mass. So that's what we do. We take that calibrated velocity richness relation, cube it to get a mass richness relation. That's the black line, okay? And the parameters for the velocity fit are very well constrained because you've got 100,000 pairs. So the scatter here is tiny. It's about the width of the line. Then you can take the membership matching and that's the yellow point. So for every cluster here, we've put a point given the halo that's matched to it using that joint membership probability. And so you can see there's a large scatter because the projections happen, okay? And also because when lambda is 20, you have just Poisson's scatter in a halo. And so sometimes you have 20, sometimes you have 25, sometimes, right? So then we can take the log mean of the yellow points and we get the blue curve, okay? That's the matched mass relation. And you see that the black curve and the blue curves agree extremely well. In fact, that lambda of 30 or 35 or 40, they're basically overlapping. And so we can now say, oh, well, we've measured this velocity, characteristic velocity in the sky as well and the Sloan data. So now we can use this calibration to trust that what we can do is get an estimate of the log mean matched mass for Sloan clusters at a richness of 30 and a characteristic register of 0.2 and this is the number. We have to admit that the error bar here is associated with the fact that we don't understand how galaxies trace the dark matter in kinematically well enough yet. So we have a basically a fairly large uncertainty which is dominated by the fact that there's a velocity bias for galaxies that is a parameter that is poorly known. Lastly, before I get to closing thoughts, along with using the simulations for doing optical cluster identification and characterization, we can take those same simulations, take the halos in them and paint them with X-ray emission. And that's what I'm showing you here in this panel is the background gray scale is X-rays. The left-hand panel here, this is work by my student, Aria Farahi, that we're working on and we'll be going, I'm happy to say I'll be going to Mykonos next week to go to a conference and meet him there and we'll be presenting this work at a conference next week. We take the halo distribution in some one-square degree patch here and then we paint X-ray emission, that's the gray scale. We do red mapper galaxy identification, that's the yellow points, the galaxy is found by red mapper. And so we can start to tear apart the correspondence between halos found by X-ray emission and halos found by optical emission. And you don't always get the same thing, right? So shown over here is X-ray detections are black and green, higher or low signal to noise. And the optical is shown in red. So sometimes you see the same systems and sometimes you don't. And it's all about signal to noise. And this is a clean image, but we then take the image and process it in the same way X-ray observers would, meaning finite signal to noise, add point sources, add plus on statistics for the photon counts, et cetera. So we can go the full pipeline. That's the way of the future and the way of the present, we're doing it now. Yes, a question. This one? Yeah, that's, so, right. So there will be some, there is scatter in how you, we include scatter in the scaling relations between say X-ray luminosity and mass. So this is just one realization. We can make many realizations and do. The scatter in X-ray luminosity at fixed mass is approximately 40%. So it's considerable. And so yes, so it's all statistics game, but we can do the statistics in the sense that making these maps is not that expensive. So we can do many ensembles and make. The question is for the semi-analytic methods that Darren Crotan, that I mentioned from Crotan et al, how much tuning of parameters is involved and the answer is usually quite a bit. And I, that's all I'll say right now. The details are considerable and we can talk offline about that. Closing thoughts, just a couple of slides before I summarize. One is a slide that I've stolen from, stolen, that I, that was part of, that I borrowed. Thank you. Well, with attribution from Saman Habib, he gave a talk at the American Physical Society called Computational Cosmology at the Bleeding Edge. And Salman is a kind of well-known expert in high performance computing, has worked for a while at Los Alamos National Lab and is now at Argonne National Lab. And these national labs are the places where supercomputers, you know, that's where the supercomputers are. You know, all the people, the technical people who really know how to make these things work, live there. And he's harnessed both the technology and the people to write a series of codes that run at pediscale, intensive pediscale. And he was the runner up. Remember the Japanese group who won this Gordon Bell Prize? He was the runner up. And that's the second time he was the runner up for the Gordon Bell Prize. So, you know, Salman is frustrated. Hopefully he'll get it in his third time. But he's got this kind of complicated, you know, graph that I want to walk you through, right? So this is now going back to cosmology, right? And essentially what we're trying to do is to understand the dark universe, right? Well, okay, over here you have observations, right? Big telescopes, observational campaigns from which you basically take the imaging and you do high dimensional reduction, right? To get down to things like power spectra or, you know, endpoint correlation functions or whatever, right? You go from exabytes to, you know, megabytes or kilobytes of a plot, you know? Plot like this. But now you gotta, and then you gotta do some money, Markov chain Monte Carlo to understand how that relates back to cosmological parameters in your dark science. Well, how do you do that? Well, you take big HPC systems, you do simulation campaigns, you do what they're building out, these things called emulators. And I know at least one of you, I talked to you yesterday, is using the emulator. Eleanor, where are you? Are you here? Somewhere, maybe, maybe not. And oh, there you are, right here. And so, you know, instead of having these functional fits, you can just go and kind of say, give me the power spectrum in this universe with this set of parameters. And the emulator will interpolate between a set of simulations and give you the best estimate of what that power spectrum, for example, would be. Same thing with the mass function, okay? So this is, you know, likes to call a cosmic calibration framework. That's what we're after. So that's one direction that things are gonna go in, just to, you know, and then things are going in. But this can really only happen at big national labs in places with big ass HPC systems. Things that can happen at smaller scale are given, an example shown here. So, science gateways is a term that's becoming popular in the States. I don't know if it's so popular in Europe. Often the same thing happens in the, in two worlds and they're called different things. But a science gateway is this concept of, actually the iPlanet network is one of the more successful science gateways. Essentially, you know, in ecology and evolutionary biology, you have all sorts of people measuring all sorts of things. And sometimes what you'd like to do is just collect up a lot of different things about, let's say pine forests. Now, give me every piece of data that we know about pine forests in Mexico. Well, okay, you gotta collect all that up. Well, if you had a gateway where all that was collected and shared, that would be helpful, right? Now for us, we don't, you know, we don't have that much variety and we have observational data typically has been served by collaborations that LST will have a data management service and it will provide it to the world, right? But what about simulations? We don't really have good data management services yet for simulations. So here's a nice paper, recent paper from Swinburne that is trying to build this out. Like you as a user would come in and write a sequel query that would go and launch some job in the back end to make a mock catalog, to make a synthetic sky and feed it back to you, all right? So that I think is also, this is also the way of the future. And with these semi-analytic methods and other methods that are faster than pure hydro, you know, you don't necessarily need a national lab to build out one of these. Okay, I think that's pretty much all I wanted to say about that. I will sort of almost right on time today. So I'll let you read my summary. Thank you for your attention and thank you for everything. And I look forward to chatting with you at coffee and best of luck in your careers.