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>> It was a welcome to our business cloth them it's a great pleasure to help as there are rules America visiting us today. In her fashion degree from Harvard University and then she went home to u.c. Berkeley and up came her Ph d. degree. Afterwards she was came back to Howard University and she became one of our favorite And the most popular electorate that tourists on campus and world was this that you could understand the only chair professor at u.c. center troops.

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Is that's the thing expert in planetary science and she has been there isn't an elected as that heavy fallow after that in the past and she's also obviously awarded the hull on what they're prized by her significant contribution in understanding the formation and evolution of planetary systems the Today he was with us the excited puzzles and the mechanisms involved in forming this in their planetary systems Thank you.

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Thank you go. Hi everyone and I'm so happy to be here today I'm going to be telling you about some new ideas that we've had in our group got the origins of structure and our planetary system and I'll start with the question is Earth rare now of course there are many things that could mean by that I could be in either early in that they are shooting each other with a very sort of I'd like to know the answer to that question but of course we're not there yet so there how many approaching That's what I'm there approach that we're taking is thinking about it's related question is the solar system rare so our systems that are similar to that environment that the earth forms and a common outcome of planet formation.

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This is something that we can't address observationally right now. Even in spite of the fact that our current observations of planetary systems suffer from a large amount of selection bias and that's really the key thing that we have to get past right now and are standing planet formation and how theories are related to the planetary system that we see.

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So this is a compilation of known planets from various techniques on the left we have masses as a function of orbital period so as a function of distance from the planet star These are mostly measured with the radial velocity technique on the right we have radio as a function of orbital period again as a function of distance from the star and these are mostly planets discovered through the transit method so these are not the same set of planets the transit planets are mostly coming from the Kepler space satellite that looked for the dips and light as planets past in front of their stars staring at a patch of sky for for several years the radial velocity planets are mostly from ground based observations looking for the Doppler shifts and stellar absorption lines due to the gravitational pull of the planets as they orbit their stars so there's some overlap in the 2 plots but it's not one to one right so if we look at these plots there are a ton of selection biases in them but let's take a look at what we can see here at the top we have gas giant planets and will notice that we can see it yesterday and planets that are and the radial velocity data the mass data but still the majority of the detections are an orbital periods smaller than that of Jupiter so we're not seeing giants in the outer regions of planetary systems that we might consider if we thought about the solar system to be the giant planet formation region.

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But we do have a large population of quite massive gas giants in our systems quite a bit mass more massive than Jupiter in fact these things go up to 20 Jupiter masses will come back to that later talk. Tristrem planets we still can't see very well they're just beyond the limits of our current detection techniques though there are a few exceptions like the traffic's planets.

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And then in the middle here we have this population of super earths that have no analogs in the solar system but you can see on the right hand plot form the best majority of the planets that are. Discovered by the couple are settling so that it's just about a 3rd of stars in the sky host a system of close and Super Earth so these are not only common in the data but they're actually a very common.

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Planet formation in the universe and of course it's not what happened in the solar system so we'd like to know why why do we not have super Earths How does the solar system fit in to this very common outcome. Ok so I'm going to start by revealing some of the standard model of planet formation and then I'm going to go into some of the ideas that we've been having in our group lately and that are very related to the standard model but in some ways question Ok so planet formation of course occurs and start forming regions Here's the classic Orion star forming region and you can see in the ins that it's baby stars with discs of gas and dust that are forming around them.

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In that environment gas from the surrounding nebulous forming the star is processed through a desk in order to get rid of its angular momentum as it falls onto the star and what you end up with in there during that process is a gas a star is a desk a gas just ice and then as you get closer to the star that.

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The mates because it's too hot you just have gas and dust so in this desk is where we form planets the debris of the star formation process that we take a look at that disk the dust in it starts at something like Micron sizes and if we want to form planets out of that so you have to grow through many orders of magnitude to get a large planetary bodies that we see so there are a few basic principles that we'll go through so the 1st one is that if you have a bunch of solid stuff it has to collide with its neighbors to grow then the growth time scale increases as the orbital timescale increases so as you're closer to the star you're dynamical time scale is shorter you orbit more quickly and all of the motions happen faster and so that and that meaning that collisions happen more frequently and growth happens more quickly grow kind skills are shorter close to your star and also if you have more material that means faster growth because you have more stuff to go faster.

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Right. So if you take that principle and you sort of overlay it on the solar system you get the pretty exoplanets explanation for why the solar system structure looks the way it does so basically in the inner system you don't have very much material you collided as much as you can but you don't have a lot of stuff to work with you end up with puny planets like the earth.

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If you go out a little bit farther to the shaded region of the desk you have more material there to reasons for that one is it gets colder so you have a snow in addition to sell it means that when you're farther from the star but also it's just that if you look at the area of the shaded region it's just a bigger area than than the part so there's just more material out there because there is this more area.

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So you have more materials you can grow more larger solid bodies and if they get big enough then they can actually create the gas in the net below around them into their gravitational well and if you can a create a mass of enough gas below that it doubles your mass now suddenly you're twice as massive so you can create another gas on below that doubles your mass and so on and so forth and that you get exponential runaway into a gas giant like Jupiter you know go further yet in the disk and you can grow these giant cores like you're innocent Neptune but it takes you a long time because again as you said the growth kind of gets longer as you go out in the desk and it takes you a long time then maybe it takes you so long that most of the gas disk has dissipated over its humility in your lifetime by the time you've grown big enough to accrete gas and so you end up with much less gas to a pretty diets are about 10 percent gas by mass as compared of course to Earth which is kind of the minus 6 I guess and as biomass and and the gas giants which are 95 percent Ok.

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So their strengths are really something quite in between so as the pretext exoplanets explanation it all fits together very nice. And I'll just add in another piece of physics that's important for understanding that explanation and that is. As related to the title radius of the planet otherwise no it's still radius or it's Roshi lobe radius and that's the the hill radius here is the radius within which planetary gravity is total acceleration from the star.

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Within the hill radius you can have a stable moon orbiting and if you were to go outside the whole radius then you couldn't have a stable in order to become orbiting because title gravity from the star. Would pull it off though if we take the idea of the color radius stick it into a proto planetary disk and then say how much material can you accrete your region within a few killer radio.

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Without replenishment then you get something called the isolation mass of the planet so it's isolation mass because it's isolated itself by eating all of the material and it's the city in that desk and it can't gravitationally reach anything else. Though if we go back to this picture here.

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It's important an important part of this picture is that in the inner solar system you have a small isolation so I just said well there was a very much stuff do you get. And I'm being a little more specific now its isolation masses small and so and in fact isolation masses in the inner solar system are star much smaller than the mass of the earth well not much smaller a little bit smaller than the mass of the earth and we think that the growth of the earth's thinnest in a giant impact is completed its growth so neighboring oligarchs their car collided with each other and including the collision that was the moon forming impact to finish the final growth in their solar system.

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Meanwhile in the outer solar system a solution that is just small enough that runaway gas accretion takes a long time so it's not just that that that growth slow out there you don't have to have a very fine tuning to time scale for growth compared to gas dissipation The idea is that these are about isolation masses and so they had trouble growing any more.

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At the very end they were only able to create a little bit of. All right so that is. That's the sort of standard structure of planetary systems argument. If we take that and try to extend it to across different planetary systems one way we could do it would be with a diagram kind of like this and I have no numbers on the axes intentionally This is just supposed to be a cartoon so you know we think about our distance from the star and this mass going up and down and I'm being a little fuzzy about what I mean by just master I mean solid I mean the whole gas plus dollars.

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Not quite sure let's just let's just let's just say just math but the idea is in the middle here you have a structure where just how we describe you know rocky planets in the inner part like the earth and have some gas giants and then I stance and I feel comfortable putting the solar system on the spot because it exists comparable with that assumption.

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And then the other assumption that goes into the squad is that it's not a super weird outlier that may or may not be true but I'm assuming that and. The idea is that if you go too low or just masses maybe you will never have enough to make a gas giant you'll always be small if you go to higher disk masses it might start becoming easier to make gas giants to making those big solid cores is just more material it's easier to do it and if you go really massive.

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Then you can make so many gas giants that you'll start having league giant dynamical interactions mixing everything up into a big now it's not guaranteed that this mass is the key to trolling for embitter in the structure of planetary systems but there are going to be a few controlling parameters and that's one of the things that I'd like to understand what is the key controlling parameter that sets the range of structures planetary systems.

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There are question. Since this is Holmes I have I have a question about that this schematic but it's a phrase diagram folks for me call it so you have one data point which is the solar system roughly based on what we know so what all the data points do you have you know how to construct something like this I know it's very rough but.

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So so I have to end quick to answer that one of them is that we do have systems from Kepler and we do have systems from radial velocity studies and if you were to go ahead and decide that this mass is correlated with dollar metallicity which is yet another leap so the amount of solid material that's in your star then you can actually put a number of systems you know on this plot and have it come out Ok so it's not immediately falsifiable that's not a proof of anything but it's just it's not immediately falsifiable so there isn't only one data point that works and here.

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However what I find useful about this is not so much that it is that it's coming from the data that I'm plenty useful as a way to conceptualize what is what are the basic hypotheses that sort of standard planet formation models would. Would raise like you know people working in planet formation assume even when it's not stated that the amount of solid material you have around is an important primitive for the kind of system that you make is that true or is that not true so you can try to you can use these sorts of.

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Diagrams as you called it to to generate positive particle predictions about some of the basic predictions of planet formation so I'm not trying to argue that this is necessarily correct I'm just trying to to to get us thinking in a way of how could what is one way we could organize these systems and are there ways that we could think of to test that I'll give you one last example if if you were if this were correct right then if super earths are rock then they should be associated with gas giants because you make a big earth you should make a gas chamber.

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That they should go together and there is actually some data that indicates that that is the case now whereas Alternatively if you said that super Earths were ice giants that were sort of the failed gas giants that never made it and so then they ended up migrating and you might expect super Earth to be intact.

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That's a sort of. That answer question yeah I think so I was just trying to have an idea where all their systems might might be but. That's just going to get going I think your security I don't think it's in this talk unfortunately maybe it'll show up later without me remembering but there are you can put more systems on this and it does it's again not immediately falsifiable.

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All right Ok so another one of the. Survey tional facts about these systems is the early results from exit planet science which is this is from Fisher and Valentin 2005 shilling that the frequency of Jupiter's increases with stellar metallicity So this is stellar iron over hydrogen but this is a proxy for just the amount of solid material in the host star and here you can see this very clear trend where the percentage of stars with planets increases with stellar metallicity.

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What I'd also like to point out that in 2005 the the planets that were in the sample were typically hot Jupiters their Jupiter mass planets very close to their stars that was what was available to observe. Here's another way. Of looking at this metallicity data this is some a major axis the distance from the star versus one minus eccentricity squared this is just to pull out the really high so low on this plot are really high eccentricity things of the red and this will be true for several So I think this is low metallicity stars stars without much solid material compared to hydrogen and the blue is high in the list stars and you can see that in this sort of intermediate point one a huge 2 about the orbit of Earth the really high eccentricity planets tend to be around that list the stars and that becomes less true at larger distances.

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Ok so I said that Fisher and Valentina result was mostly about. About how Jupiter is the let's take this as inspiration this distinction between sort of this intermediate regime and this more distant regime as inspiration to look again at distance from our star versus mass to look at these giant planets around low and high metallicity stars so this is and this this is low and higher cut compared to the solar metallicity it doesn't really matter that much exactly where you put the cut there was I'd be worried about this statement but you can see that around little metal is a star is most of the giants that are observed are actually at about the orbit of Earth a little bit interior or farther out but if you look at the high metallicity stars and that's no longer the case these are all the planets that were on that high metallicity stars have more planets but there's these giants that are interior to.

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To this orbit these orbits where you might expect it to be easier to form a gas giant So if you ask the question. Given that there are more planets around higher metallicity stars are you more likely to is it going to be a better chance to look for an Earth like planet around a high metallicity star or not.

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You might just say well more planets around have it with the Stars means yes but if you look at this these system structures in more detail at are you that the answer is no because you really don't want a giant planet these things tend to have high eccentricity orbits sweeping through this whole space in your system if you want to have a surviving Earth mass planet so this is actually arguing that let's.

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But them together that systems with high level a city where there are more easily observable planets might be the less favorable environments for making something that's like the earth their environments where you have these highly eccentric highly massive destructive destabilizing planetary orbits Ok so. So those are the sort of dynamically next orbits that are up here maybe if you want to try to put them on the star Ok so so what I've been thinking about lately.

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Recently in the last you know several several years now the basic idea is that I described about planet formation have become suspect for. For one sort of philosophical reason and that is this idea of isolation mass and isolation is suspect due to gas drag and proto planetary disks so the idea is that gas drag causes drifts if you have this particle in a disk it wants to orbit at a Keplerian velocity but the disk has a radial pressure gradient pushing outward That means that from the disk gasses perspective it's orbiting a slightly lower mass star orbiting a slightly lower mass star beings are orbiting a little more slowly so the gas is going a little bit less than the cup Larry Bossidy and that means that the particle moving through the gas field ahead and as with all gas drag prophecies.

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Smaller things feel a larger acceleration from gas drag because they have a larger surface area to mastership. So. So particles so small particles in these disks which are observed to exist in the regions of proto planetary dest are expected to drift through the nebula and if your solid material is drifting with respect to your gas that you're not then our fundamental assumption that you're you're only creating material from your isolation region is not necessarily correct and and a follow on to this.

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Is that. Gas drag can also help to capture small planets has small. Growing planets so captured so gastritis is called Pebble publication or gas assisted growth and the idea is that if you have a core in your desk then without gas you'd you to create on some you know gravitational focusing cross-section but with gas if you if your planet testable gets into that hill radius that we talked about the radius where you're stable and then you remove all of the energy.

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That relative motion the now suddenly are gravitationally bound to the core and you can spiral and then accrete on to your core and the hill radius of a growing planet tends to be dramatically larger than the classical gravitationally focused. Accretion radius so this can cause planets to grow dramatically faster Ok so now we don't have isolation anymore and we have a way to make things grow dramatically faster even in the outer parts.

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Now we have to re-evaluate. Some of the parts of the story that I told you at the beginning of the talk. So. So I'm going to just talk a little in a little bit more detail about this growth process so again if you have a plan a testable that is orbiting inside the hill radius without gas that's where your satellites can be stable now let's add gas drag into the system so this whole this core is is moving through some gas that's going it a little bit of a different velocity if you have small particles in there they can actually be pulled off by that gastric headwind the gas drag acceleration is larger than the acceleration due to gravity from the core it would just be pulled off of the you know by the head but.

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So depending on the particle size if it's small enough so if it has like a large enough surface area to mass ratio that can make your stable radius smaller than the radius. And when that happens we call it the wish radios or for wind sharing but also for whoosh.

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So so now you have a different stable radius and if your pebble comes in to that which radius and now it has its relative energy removed by gas drag damping and it can be captured in this is essentially a binary capture process and this is again called publication.

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Right so here is a numerical simulation. Led by as you know as you. Undergraduate and graduate student working on this and you can see that we have a number of pebbles coming by and in this 3 d. hydro simulation with an h.d. not ideal m.h.d. going on you can see this publication process happening.

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Or growing so most of what I'm going to talk about in this talk is order of magnitude but you can see it having a numerical simulation that helps you make it feel like it's real they got. Ok so what does this mean for a super well we said and a classic Tresco planet formation.

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The mass of the planets are limited by the available mass the local isolation mass and that gets enhanced by crossing orbits in a joint impact but with public creation you're not limited by your local mass because drift a small solids provides a large source of material and it's a large source of material over a 1000000 years you know with some reasonable numbers you can get 100 if not drifting through the inner desk.

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There does this mean so so here are some examples of pebble accretion in the growth timescales calculated by. The state of mind recently graduated Mickey Rosenthal and this is at 38 you know but it's even faster in the inner disk and this shows that blue here what I want you to take away from this is growth time scales are short they're like less than 10 of the 5 years.

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This is blue and this is just the last several 1000000 years if you have it and I The other thing I want you to take away from this is that it's extremely particle size dependent this is these are these small pebble sizes if you have the right pebble sizes.

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Growth is and if your core mass is big and you have growth happening on an extremely fast time so don't let me repeat that again so there are 2 conditions 1st you have to have the right couple sizes if you don't have the right couple sizes and you don't need to worry about the exact numbers on this but if you don't have to republish rises it won't happen fast it's size dependent and the 2nd thing is that unlike that of classic planet formation models there's a minimum planet mass you have to reach before this kicks in the once you've reached that minimum asked growth happens dramatically quickly All right so what do we do why don't these things just drove forever to gas giants Why is it everything you got happened those minimal masses you have to reach are well under an Earth mass in most cases.

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And and the answer to that perhaps there been to answer that have been recently suggested they're called Pebble isolation and flow a solution and in the energy ask both of these products and I'll go through them in a 2nd but and it's both of these prophecies limit growth at about the thermal mass which is.

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The mass where you're particles Hill radius are your plans to raise is about equal to the scale of the disk. And I just want to point out that the thermal mass is given by the ratio of the scale. To the radius of the desk times kid turns the stellar mass this is determined by the disk temperature and it is not determined by how much solid material is there it doesn't matter the surface density of your just go just to matters how hot it is.

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And I just know that there's been a suggestion that this characteristic mass killer appears in the thermal in the couple of data Ok so so the suggestion here is that you have a really fast growth. At about the thermal that and this is politically quite different from what I said before we're not this is not isolation mass due to the amount of material available it's very fast growth with lots of material coming through limited by a scale set by the disk temperature All right so what are these 2 processes.

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Head lice elation happens when a growing planet. Generates an over density in the disk gas that prevents pebbles from flowing out to the planet so there's a there's a pressure in the disk Yes that essentially captures puddles as they're trying to filter through on to the planet. And this happens at about the thermal mass this is a very nice model and you know I kind of wonder whether once you capture enough pebbles at that have a mass comparable to the mass of the planet whether that's going to be stable that's still ongoing work that needs to be done but but it's nice model at this at this mass scale because the whole radius is comparable to the disk scan height you see a substantial change in the surface density and you can get the structure to.

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I'm going to talk about the low isolation mass and at a little more length just because it's the one that we've been working on but either of them could be going on here and perhaps both. So I'm going to go back to this this diagram that we had before about this wish radius where if a particle is small and and this field this gas drag force from just this whole planet and anything orbiting it as part of the gas it.

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You know if you like a strike force that pulls it off of the planet then it can create a group publication Well what happens. And again we're going to capture in that which radius what happens if that wish radius is actually interior to the size of the planet's atmosphere when the planets in the disk and its atmosphere is set by what's called the body radius that is where the state velocity from the planet is equal to the sound speed in the surrounding to get discussed that's essentially where you know the disk gas moving at its Thermopylae city can't just escape from the gravitational pull of the planet but you can just think that as the atmosphere size so so what if you can't actually accrete interior to the atmosphere size Well the gas will actually flow around the atmosphere and if you're one of the small particles as well coupled to the gas not only will you not a cream by publication but you'll actually be coupled to the gas on a scale low around the planet and have no opportunity to create a doll even if you would have a created gas was not present and We call this flow isolation because you're coupled to the flow and you're you're not able to accrete these pebbles because the pebbles are couple to the flow around the planet's atmosphere.

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Slow isolation requires you to be at about the thermal mass that I told you about pebbles that are that are marginally coupled to the discounts are present for aficionados that Stokes number one. In the disk for smaller particles that are well couple of to the disgust the flow isolation mass can actually be quite a bit smaller.

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But in any regions of planetary systems we think that relatively large puddles are probably available and so so it's going to be about the thermal mass similar to the puddle isolation which is the other process I told you about before now in the outer disk that's not true in these 2 processes actually behave very differently but we're focusing on the inner just right so so there's all right so what happens if we put that mass scale and a physical system.

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Here is an example here is just since from our host star. The flow isolation mass. On the y. axis and the different lines are for different math accretion rates the reason that's relevant is because they actually affect the temperature of the disk in the in a region but the key thing is that this Ray region here is about Super Earth masses and you can see that a lot of these reasonable lines flow right through the great region so super Earths could be stopping their growth the flow isolation another thing that I would like you to notice about this is that these lines in a region are pretty flat like mass does is not very dependent on the distance from the host star it just turns out that.

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That the dependence cancels out when you take into account the thermal pressure of the desk and this is actually consistent with recent observations work showing that super Earth may have similar sized. This could be an explanation for why you end up with a series of similar sized planets.

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Right so in case they're anything if you're not is around I'm happy to talk lately later about. The difference between slow and published lation but I'll just say again that in the outer desk they behave very differently but in the inner region where we're talking about Super they both get similar answers right so.

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That leads me to the question of gas giants and I'm going to pas there in case there are questions before. All seems to answer the question from the chart. She. Wants to know contemplated by which time thing that's why we talk about this though. Paul needs plentiful us almost time to start up company and test component.

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So sorry the cartoon about it. To some structures. The difference is some structure on the y. axis instead of these commands Yeah yeah I haven't made a cartoon for a binary system but but how challenging to make when I think that it's I think it's a useful way to sort of organize your thinking and.

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I again I don't see those cartoons as being results but rather a sort of like thought organization tools and I would be excited to see what you had where you're thinking about binary systems and how they differ. It is interesting to see you have this to start a company but they're from the tenets of the planets are going to source Yeah I'll kill titles for the banners Yeah you have to think about what are they going to keep.

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As you're sort of alluding to going to whether what are they parameter so when I'm making those things and thinking about like there are probably a lot of important transit areas you know for for making that structure like stellar mass you know certainly by near 80 that disk mass maybe something about you know.

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Early formation environment and whether you had y. buys or you know a large and the station environments your desk like I'm sure you could come up with a lot of things but still it's going to be many fewer than the knobs we have to turn in planet formation models which is a Brazilian So the the key parameter is the number of them is not going to be huge or at least the number of them that are really important it's not going to be huge so I so I'd like to understand what are those key perimeter so in a binary system you know the binary separation might actually be much more important than than some of the other you know parameters since you guys are thinking a lot about binary is that it might be nice to think about what are the key what should be on the y. axis of the system.

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These commands. Yeah yeah what's the most important so yeah I think that's a great point and then the problem was just you want us to Tim No. I can't I can answer a couple more now but also post something on the coast to the under go home polls.

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I'm just asking if I was curious to make a connection between the. The graph that you show before with the mass versus distance in which you have a maximum. There was a parameter that you were very there yes so how does that connect back to what you just the last slide that you just showed that this this message to be flipped.

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I not sure where the alphabet is but this is this part I don't know if you for that this is a tough couple slides before. Over here you know. Thank you Ok so. It is. You know one dimensional ised premature is ation a disk that's got to be because we don't know what's causing the disguise to be in this disc so so higher Alpha means more turbulent disc this is no turbulence this is.

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Extremely turbulent this is probably a more realistic high turbulence pretty planetary disk and this may be a more reasonable number and I think. In the plot is that for a higher turbulence level the minimum mass that you need to reach before publication kicked higher but once you've actually reached whatever the minimum that.

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It was your question you know I was trying to understand so if I wouldn't connect to the very last slide that you have what kind of use causative you have on the under that situation. Though there is instead of fixing the viscosity we have fixed accretion rate. So the accretion rate in the distant least a simple model and it is the surface density times was $3.00 to $3.00 pious times the surface since the times of the sky city that the sky city would be Alpha times the sound speed scale head of the disk so you can choose to keep Alpha constant throughout the disk or to keep.

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Constant and for the temperature structure all you need to assert is that we we've used this for a printer here but you could you could translate that back into an alpha one or 2 I don't have it off the top of my head Ok if he does not know critical mass in this case this I mean if you're already above the critical mass then I'm going to get to that in a sec this isn't necessarily If you mean for gas transmission.

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Yeah I will get to that in one moment thank you for that question this is 2345 this is like 5 Earth masses that's not the critical mass necessarily It could be if your opacity in your planet's atmosphere is low but we actually see super Earths with those masses so.

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You know somehow they have to. Exist and not because gas giants so but some of them at the tail appear to become go at the high attrition rates do go about the critical mass for gas giant formation so just for reference when when you look at the accretion rates of observed creating proto planetary desks.

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You see rates that range all the way through all of these numbers these are very high accretion rates they're probably more indicative of like early stages of accretion you see all the way and of minus 7 to 10 to the minus 9 accretion rate in the observations so so this whole range is a reasonable range just from the observations of.

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Your whatever process is. Determining there they're pretty Ok but some of them are about the critical mass with there another question or should I continue with that. Then there are a couple of quick questions also one cookie and then some move to move the others to the end of the call but basically.

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The lesson is home is the more the field the right the status. In that in the desk commuter in the planet. This is the question well I'll do my own tools I suppose. Always whining about. Yeah thanks so the stellar magnetic field. Could certainly be. Could certainly be very important and in later stages like atmosphere evolution that sort of thing but most of the disk that we're talking about here the mid plane is shielded from the stellar magnetic field assistance.

[00:42:51]
That the stellar field isn't that important but that said if the dismaying that actually has connected to the stellar magnetic field we really don't understand the structure of these tests and what's causing the accretion rates whether it be disk winds or you know m.r.i. turbulence and. And that actually does matter for these results because it depends a lot on the temperature in that plane and these temperatures are calculated assuming that the disk is a creating through the mid plate and so they can get the potential energy of the disgust is being dissipated into heat as a decrease and so if the magnetic structure of the system is such that disk winds or something are allowing accretion without that much heating that would change the result but in terms of the stellar field itself I think that the plate is mostly shielded and that's going to become more important for the atmospheres later Ok Ok I'm going to go on and I'll answer other questions that they get Ok great so some of these things some Yeah yeah most of this is below that.

[00:44:02]
So the critical core mass for creation of a gas giant atmosphere the standard number people say is 10 Earth masses it's not exactly 10 or masses it depends on the opacity of your atmosphere because you have to be able to dump a lot of heat in order to be able to create.

[00:44:21]
A giant gas giant on a bloke. And it depends on some other things too but the opacity is a big one. So so I'm not going to go into that in this talk we could talk about it but just for the sake of having a number to point at the plots let's just say 10 or masses the critical court mass for making it.

[00:44:41]
Ok most of this great region is below that but yes some of it is above that in this red line certainly Ok so I would consider that potentially not a bug but a feature of the and that's what you know talk about for for the 2nd for the last part of the talk so it was somewhat more than interject broken.

[00:45:12]
All right so. So if you were just talking about the disk temperature structure on the left here we have a plot that's just a very simple temperature structure from accretion heating in the interior and then radiative heating of your debt disc in the exteriors so once you get far enough away then accretion doesn't hear just that much and you're just passively heated by radiation from the star and that affects the thermal mass of your planet because again it depends on your just temperature flat and then it a certain point it goes up and if you look at a wide range of parameters for these systems then in some of the cases you end up with a relatively small thermal mass and you can get terrestrial or super planets in this scenario but in other cases as was just pointed out you are masses might be above the critical mass and you could get a string of gas giant planets.

[00:46:09]
So if this were to happen then making gas giants could be rare which we know it is they can guess that it's rare compared to other planets but when they form it would be possible to make it come in for multiple gas giants in the inner system to be a common outcome of gas transformation in her system.

[00:46:30]
Ok so why do I say that this is a feature and that comes to. The other last part of my talk which I just think is really fun I don't know if it's right but I think it's one that I hope you'll enjoy Ok what if there is a giant impacts for gas right there remember we said in the standard model.

[00:46:53]
Restaurant planets go through a gas giant impact is like the moon for me and to finish their growth. And. We know that planet so planet Planet scattering. Is another outcome. Dynamical interactions in planetary systems so here is. A movie by Eric Ford and collaborators you've got some of the giant planets and you know loops they're starting to interact and it's going to go badly for one of them.

[00:47:24]
And you end up with a scattering situation with an eccentric orbit left behind and one of them is objective and at least for me when I think about standard planet formation models this is what I think of as happening to guess trends not collisions but instead ejection events and that I would say is based on you know essentially our prejudiced big coming from the solar system because in the solar system all of our trust your planets are in the inner part and all of our gas giants are in the outer part and actually whether you get giant collisions or ejections has less to do with how big you are as a planet and more to do with whether you're deep in the stars potential well or you know larger distances in the shallower part of the.

[00:48:11]
Right so in our solar system again we have these trust planets and they're expected to go under undergo giant collisions. But. But if we were to put gas giant planets in our systems that would happen to them too and actually people have done planets scattering models up there was you know and this always happens people don't really report on it that much but it always happens in their simulations it's just in that little result so the question is could in see chimp scattering plus coalitional growth of multiple gas giants in a population of discs reduce the features of the observed asteroid population and I'll show you that it can so if you're willing to make what I would say is one wacky assumption but maybe it's not so wacky which is that you can recreate multiple gas giants in a region of a system either through in situ formation with like I just suggested or you could just might get them in from the outside.

[00:49:10]
And have major scattering events that produced planet growth then. With almost no other fine tuning we can do some nice things and I'll show you the nice things you can see if you're if you're convinced that interest so. I'll just start by reminding you that the gastritis that we see and our planetary systems are much more massive than Jupiter remember I showed you that at the beginning they go to like 20 Jupiter masses so we can start with a bunch of little gas giants by which I mean Jupiter mass.

[00:49:45]
And have tracked Ok. I should show the visual that I just know in closing gas giants are up and much more massive than Jupiter so you know you could make these with a bunch of Jupiter's and you don't have to start with like really small things or anything.

[00:50:01]
Ok and their orbits are often eccentric there are a lot of differential. Pieces of work that have been done on this trying to understand why these things are eccentric and putting back on Cheney and this great and it's work in this area. We are going to be focusing right now on the planet Planet scattering family.

[00:50:25]
Of models of which there are many stars Ok but here's the data this is just a that this isn't a model at all so a major axis of the planet and its observed eccentricity and I'm going to be showing several counterplots now and they're all like this 90 percent contra level 80 percent contour 70 percent contour so they're just lines that are in closing that percentage of the plots and so you can see that as you go farther from the star you have more eccentric time.

[00:50:57]
And many of them are eccentric like these are this is a giant eccentricity you know Ok planet is getting leads to collisions for close in planet it's an ejection for distant planets so I just said that where it's not going to show it in pictures if you start with a relative velocity in an interaction less than the escape velocity from your planet you can have gravitational focusing this is sort of the standard growth process I mentioned before describe occasional forces will allow you to accrete from a slightly larger cross-section than your physical size.

[00:51:32]
But if you're eligible us use larger than your skin philosophy then there's no gravitational physics so you just have a cross-section that's that's that's your size and in this regime collisions prevent strong scattering So here I said that collisions happened at larger than your cross-section but scattering happens even larger cross-section though if you're in this regime the expected outcome is strong scattering if you're in this regime the expected outcome is collisions.

[00:52:04]
Ok so what a relative loss that is I'm not I don't think I have time to go through this but basic idea that you're going to play an orbit you haven't epicycle your velocity on your epicycles your eccentricity times or orbital velocity complaint epicycles work. So your collisions happen and if you're that velocity your eccentricity times get Larry is larger than the escape velocity of the planet that means that the maximum eccentricity you can get to before collision set in is described by this thing here the escape velocity from the planet divided by the Kepler and glossy which is essentially the Schiphol I see from the star so if that is but you can you'll see escape your system if the relative velocity is larger than the escape velocity so I mean it's large and kept Larry and the objections are suspect expected that the escape velocity from the planet is greater than the escape velocity from the star Ok so in other words if you're scared but also your planet which is what you can pick things up to is smaller than the escape velocity from the star then there ratio gets to your maximum eccentricity it can take things too and if it's larger regular Jack things and that means that it's harder to eject things if you're deeper in the potential Well Ok so.

[00:53:24]
In the interest on your Jeep or in the potential well you end up with collisions in the outer system more in more shallowly in the potential well escape from the star and if we look at our warm Jupiter's you can actually see that an eccentricity on a pillow given by that ratio of planets to star escape velocity is just the data decently well there are other things that can match this curve to this is that a super strong constraint but it matches pretty well in the outer system you have ejection So the eccentricity is go all the way up to one and you expect ejection right.

[00:54:01]
Here's the here's the key thing here though eccentricity Giants are also higher math isn't that funky you should be easier to take a lot of things to headaches interested in fact if you do a simulation of one system your small things will be kept to higher eccentricity but in this in observations the more massive things are higher eccentricity this looks like that other part that I should before but it's an entirely different plot this is mass versus eccentricity and that's why it's interesting all right and in these high mass headaches interesting things are also around her middle of the stars All right interesting ones.

[00:54:40]
This is data orbit high metallicity stars So here's the basic idea that I'm going to go through this quickly because I'm out of time but perhaps a little if the stars produce a larger number of mass of planets and then these disks all planets are excited hikes interest is their planet planets gathering and we go ahead and do a set of integrations I'm just going to tell you that we start things with massive equally distributed and logged in each in our desks one way we say the total amount mass in planets in the desk and it doesn't really matter how you distributed among the different masses of different planets it really turns out not to matter is such that we match the observed planet mass distribution so this is observations of the frequency of planet masses and we cheated in our initial disk masses to get that same distribution and then we go ahead and do some simulations and you can see that in our simulations on the right is the simulation on the left is the data disks with more mass and giant planets have more tonight impacts more giant planets and they get higher eccentricity So given that we really tuned very little.

[00:56:00]
In this in this in these simulations and our distribution of initial planets is extremely simplistic I consider this a really nice. We can look at this with eccentric with metallicity if we stay high in mass just you know high amounts of math and planets go with high dollar metal listening you can get that correlation as well that's not going to be a one to one correlation so I'm not surprised that in the data overlapping a little bit more that you can get.

[00:56:28]
These are the high mass disks that are producing these high mass high eccentricity joins that's part of the plot of looking at here and we can also see that in some i major axis Now this is eccentricity we can get this metallicity structure in our planet. So even if we've been able to match qualitatively again with very little tuning the really interesting observations of features that haven't really been I think pointed out in quite this way before all right planets are also more frequently larger distances Ok so what happens at larger scales.

[00:57:12]
Gathering dominates in the outer region collisions growth is dominating in the inner region what we project here is that higher mass planets are the result of collisions in the inner disk so this is the last thing I'm going to show and it's the observational prediction so you can make up for just one sec do you look at Justin's versus planet mass this is not Planet occurrence it's the mass of the planet we would predict that the most massive planets happen at a few a you which is where we're currently probing with the radial velocity data but if you go to larger distances we're going to go back to more normal Jupiter Massy planets and radial velocity is and direct imaging microlensing guy are all going to be able to to interrogate this predicted mass function peak at 3.

[00:58:05]
So we said making gas giants are rare but when they formed we could make multiple ones and we went ahead and did a proof of concept study to see whether we could get the distribution of gas giants that are observed if we you know using a range of just parameters.

[00:58:24]
And indeed just get that sorry indeed you can go for reasonable this population in critical mass as a function of stellar mass we can get gas giants super Earths in a mix we can get a comparable frequency of gas trying to make systems which is observed deeper it's $6.00 to $10.00 times more common than gas giants which is observed and gas giants more common around more massive stars search so this is their proposed story.

[00:58:54]
Planets grow to flow into a couple isolation mass of the inner disk cores are big enough to create gas multiple gas transform and then they scattering collide producing high mass eccentric Giants and I like all of these pieces but they can all live separately from each other. This.

[00:59:22]
Instance. Let's come. To. Think on this. Question I think. I want to start sure you have maybe I misunderstood but. It seemed like there was a dependence on the rate from the radius of the atmosphere well sort of very complex 10 times larger than some number then that's one floor solution can have to explain why.

[00:59:53]
Those that mysterious size is where. You know the the the gas that down to the planet. It separates the gases down to the planet from the gas that's flowing past the planet. You know that's the scale where you're either going to have pebbles either get into that atmosphere and now they're going to be bound to the planet that is your tent gets dense pretty quickly and so usually gas right will keep you down if you make it in there or whether you flow with the background gas around that atmosphere and again the atmosphere size order of magnitude is set by.

[01:00:32]
Comparison between the sound speed of the gas in the disk and the mass of the planet the escape velocity from the mass of the planet so it's so it's not an arbitrarily sized atmosphere it's an atmosphere that's sat by the mass of the planet and the temperature of the disk though it doesn't matter you know all of these scales matter in doing that calculation you're correct that's why it's a very size dependent process part one planet can be isolated from some particles but not from other particles so when you're flow isolated That's the mass where you're isolated from all different kettle sizes but even if you're smaller than that you can be isolated from some type of sizes so if there's a limit to how big that available totals are you can actually be a much smaller planet be isolated things are available I think it's actually kind of a nasty problem in all of the different scales.

[01:01:36]
Are there questions well you have a question about. Separation qual Thank you Ted So from the sketch through this seems that this can fall off the team particle of almost system probably depends on the stand almost something else mostly this trend shifts but the difference that wasn't so this well yeah yeah.

[01:02:02]
Yes this is for a solar mass and yeah exactly so it's all about how deep you are in the potential well so so the trend should sit shift if you have the seem like planet mass Well the peak should definitely shipped as you as you have a higher mass planet the peaks should shift outwards because you have a deeper potential well and so it's harder to escape from it and see if you have a low around a star the pic should shift inwards we did this 1st stellar Masters because the radial velocity survey shows are mostly for historical reasons around solar mass ish stars so that's why we chose that but you're quite right that that would be you know that would be an interesting prediction to look at.

[01:02:55]
All the questions that I think just students to ask. Ok so so we have already hit that home and that has all. The wonderful talk thank you for having me. Thank you.