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you

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[Music]

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so if we look at the planets in the

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solar system we see we have the

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terrestrial planets on the smaller side

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we have Mars and Venus and Earth and so

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on these planets the atmosphere

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represents a negligible fraction of the

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bulk mass of the planet and if we go up

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to size scale the next largest planets

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that we see are the ice giants Neptune

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and Uranus and in the solar system we

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have nothing in between these two bodies

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that's not the case around other stars

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and so we'd like to know it's how big

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can a planet like the earth be before it

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becomes something more like Uranus or

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Neptune where it has that very thick

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atmosphere that is an important factor

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in the both mass of the planet to answer

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that question we first have to consider

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how atmospheres form on planets and so

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there are three main ways you could form

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an atmosphere on a planet the first

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being volatile delivery which we see

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here where you could have comments or

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volatile richa meteorites that come in

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you impact on the surface and over time

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you can build up oceans in an atmosphere

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via these impacts the second option is

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this outgassing and if we look at the

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earth today we see that volcanoes

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outguess lots of gases like co2 and

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water vapor and on young planets this

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can be much more efficient where you can

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have magma oceans that cover the entire

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surface of these rocky planets and you

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could out get oceans and atmosphere on

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very short timescales and so this is

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probably how the earth formed its

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atmosphere of shortly after formation

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and the third option is this disk

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accretion and so this is where you have

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the disk from which the star on the

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planets are forming and you have planets

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that are able to accrete hydrogen and

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helium directly from that disk when they

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form so Jupiter and Saturn likely formed

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via this process and were able to

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accrete large quantities of hydrogen and

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helium from the disk before it

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dissipated even Neptune and Uranus

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likely accreted a fairly substantial

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amount of this gas but it turns out that

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even the smallest planets can accrete

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this hydrogen and helium from the disk

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before it dissipates and you only need

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to be about one-tenth the mass of the

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earth which is about the mass of Mars

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and you can start a creating hydrogen

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and helium directly from the disk before

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it dissipates

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and so we call these atmospheres proto

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atmospheres

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on rocky planet and they could be

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thousands of bars at the surface so

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these would be very hot atmospheres

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which could be very puffy and and light

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and extended and if you think about the

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modern earth as being the size of an

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apple the Earth's atmosphere would be as

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thick as just the skin on that Apple so

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very small but if you think about an

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earth-like planet with a proto

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atmosphere like this the atmosphere

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could extend many times the radius of

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the planet outwards so if you were an

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observer of one of these planets and you

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were to look at say an earth-like planet

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with a proto atmosphere you wouldn't see

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a rocky planet what you would see is

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something that looked more like Jupiter

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in terms of density but it would just be

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much less massive and since we're

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focused on habitability these planets

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are not habitable and any way that I

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could imagine the temperature at the

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surface would be much too hot for liquid

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water to exist in to exist and so if we

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look at the available exoplanet data if

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we if we look at these these planets

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these small mass planets that we see

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down here on the lower portion what

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we're seeing in this plot is mass versus

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radius so each of these dots represents

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an exoplanet and if we make the

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assumption that all planets initially

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formed with proto atmospheres and we

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said there's no real barrier for them to

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form so if we assume that all planets

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form with those atmospheres then we

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would expect all planets to form along

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this hydrogen line here or close to it

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and each of these lines you can think of

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as a contour of constant density so

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planets that are on this hydrogen line

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have a lot of hydrogen and helium in

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them water is the blue line and planets

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which you see right here is the earth

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and Venus on this rocky line right here

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those are the rocky planets and so we

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see here is that we only have these

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low-mass planets that are falling off of

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this hydrogen line towards this rocky

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composition and if we look at the zoomed

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in version which is just a low match the

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low mass region of this same plot down

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here the largest rocky planet that we

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see is this 55 Cancri E and that's about

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eight to ten Earth masses and the radius

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on that planet is in a 1.6 1.7 Earth

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radii and this plot is a little bit

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dated but even if you were to put the

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latest exoplanet data on here the same

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trend is visible or this entire portion

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of this plot is empty we don't see these

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large mass rocky planets that just don't

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exist so then why is it that these small

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planets don't have atmospheres

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these stick proto atmospheres while

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these larger mass planets are able to

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retain those and so one way that that

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we've found that can explain that is

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through atmospheric escape via

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hydrodynamic escape and so hydrodynamic

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escape is a pressure driven thermal loss

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process where your atmosphere becomes

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heated and in this case we're

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considering heating by XUV where the XUV

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is x-ray and UV photons from the host

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star so that comes in and heats the

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atmosphere of your planet the atmosphere

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starts to expand and it expands so

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rapidly that the atmosphere just sort of

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puffs off into space so you can remove

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the entire proto atmosphere from small

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planets very quickly via this process on

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timescales of just a few million years I

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borrowed a an animation of this from the

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LPO where you can see this hydrodynamic

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escape happening to a planet orbiting a

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sun-like star and what you're seeing

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with that light blue that's atmosphere

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being blown off from the star and this

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is similar to what happens on comets

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that enter the inner solar system where

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they shed mass to remain an energy

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balance so we took the equations that

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describe this hydrodynamic escape and we

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put together a simple energy limited

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hydrodynamic escape model where we

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assumed that all these rocky planets are

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forming with those stick proto

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atmospheres and we put them very close

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to a sun-like star at point 1 au and

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we're putting them close in since the

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goal is to figure out how big a rocky

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planet can be and sort of what will what

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will it take to evolve it to a rocky

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planet status and so putting them close

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in will make them very hot and expose

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them to a lot of that UV radiation which

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will drive off their atmosphere then to

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calculate the loss rate from the planet

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we have to specify 7 model parameters

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which are shown in this table which

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specify the temperature the XUV flux the

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initial atmospheric mass fraction we

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need to know the escape efficiency which

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you can think of as just being the

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fraction of that incoming x UV radiation

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that goes into driving the atmospheric

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escape then the pressure at the base of

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the thermosphere is where that X UV

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radiation is absorbed in the atmosphere

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you need to know the specific gas

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constant for the atmosphere which you

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can think of as just telling you how

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light the atmosphere is and then the XUV

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saturation time and so the XUV

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saturation time is the period during

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which the host star remains at a peak

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XUV emissions and so forth unlike stars

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this is about a hundred million years

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and so during that time the XUV flux is

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maximal and then after

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of that period it dips off exponentially

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so most of the mass loss is going to

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occur during this time so we can select

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from the you know these seven parameters

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for our model and if we run it we

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generate something that looks like this

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so we're seeing here again as the mass

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versus radius and this - contour here

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represents an earthlike density so any

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planet that falls below that is a rocky

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planet and any planet above it is a low

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density planet that we would consider

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guest enveloped and so we see here is

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that the small mass planets very quickly

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lose their atmospheres and fall below

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this line well the larger mass planets

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are able to retain them for extended

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periods and this is dependent on what

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parameters we select from that table so

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we took our model and we ran it for

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10000 parameter combinations and

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calculated where that cutoff between

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those rocky and gas envelope planets

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occurred and so that's what we see in

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this histogram here and so the mean for

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our model is that this 1.6 1.7 Earth

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radii with the error bar showing the 1

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sigma confidence interval on that

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calculation the red dot is from the

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Rogers at all 2015 paper where they

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looked at exoplanet data and found that

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there was a transition between rocky and

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gas and below planets at about 1.6 Earth

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radii was there 95% confidence interval

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on that measurement so what we see here

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is that there's this strong agreement

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between what our simple model would

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predict for the cutoff between rocky

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planets and what actually observed in

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the exoplanet data and just if we look

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back in at the end of data here again we

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can see that it does agree right around

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that 1.6 1.7 cutoff and just to give

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this a little bit of context of why this

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is important and why we should care

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about these rocky planet sizes well

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rocky planets can be habitable so it's

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interesting just to know how big they

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could possibly be and it's also helpful

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for future observations since we often

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detect exoplanets through a transit

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which is shown on this cartoon here and

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the thing that you measure in that is

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often the dip in the planet the

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Starlight as the planet passes in front

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and the amount of solid that's blocked

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tells you of the radius of the planet so

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often that's all you'll know is just the

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radius so being able to determine

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whether or not a planet is worthy of

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follow-up studies could be helped in

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this manner of looking for earth-like

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planets so put up a summary and take any

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questions thank you

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I think we have lots of time for

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questions so please come up to the

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microphone if you have questions thanks

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that I talk that are really interesting

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I'm going to ask you the question that

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is not supposed to be asked which is

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what about magnetic fields because what

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I mean is that they're the atmospheric

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loss from pressure because I noticed a

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lot of your plots are as a function of

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radius mass but not there's a function

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of distance or insulation flux and I

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would imagine that under many

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circumstances the the atmospheric loss

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from from the from the stellar winds

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will be larger than that from the XUV

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processes if the stellar wind could be

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could be very effective especially these

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close distances distances and that's not

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something that we've put into the model

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although if it became sufficiently rapid

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than you'd be removing materials so

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quickly that it would actually be a

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hydrodynamic eventually you sort of

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reach that cutoff if you were removing

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material so quickly so I'm not sure how

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exactly adding magnetic fields in would

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impact our model I imagine you may slow

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down a little bit and that's definitely

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an area for future research but it's not

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included at all in this model which

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we're just looking at the energy limited

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for thermally driven escape but that

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it's very of an excellent point and we

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did only look at one orbital distance we

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put them at that point one au which is

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sort of an inner limit where you can

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have a hydrostatic rebound lower

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atmosphere for these planets around

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sun-like stars okay thanks yeah there

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you go in a nice talk I was just

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wondering if you've tested how sensitive

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your results are at the exact escape

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efficiency that you assumed and if you

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assume some kind of prior and notice the

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range is like point one to point six for

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a de to do something like a flat prior

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did you play around with it I'm just

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wondering aside what we just significant

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it is a linear dependence on what we

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assumed for that escape efficiency and

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so we just looked at a uniform

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distribution across that which there's

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probably a better distribution to

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consider when looking at escape but for

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this model it was just uniform and so

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the linear dependence on that with

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and yeah I think that there are papers

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showing that for the Kepler population

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something like point one matches the

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population at the population level

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median Valley point one matches it so I

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wonder if that would make your histogram

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even more consistent with the Rogers

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video when I play around with that thank

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you what about impacts knocking off the

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atmosphere climate ID hits the planet

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and blows the whole atmosphere away yes

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so that it could definitely happen if

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you had two planets collide you could

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probably remove an atmosphere very

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quickly impacts do tend to be less

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important for the larger mass planet so

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by the time you reach six to seven Earth

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masses it seems less likely that you

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could have impacts that are removing the

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entire atmosphere so then this

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hydrodynamic escape becomes more

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important which is where we see sort of

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that final cut off but for those lower

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mass planets especially then having

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impacts could remove your atmosphere

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very quickly thanks great awk I think

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there it seems parent that this is sort

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of an upper limit as in there are many

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other ways to remove atmospheres but I'm

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actually more interested in the other

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question is a number of the planets that

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are quite low mass seem to have very

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puffy atmospheres I mean a number of

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them that have been detected clearly

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within the error bars fit above that

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range not all I mean it's only a few but

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I guess have you guys thought about ways

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to actually preserve even for low-mass

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planets that puffy atmosphere actually

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we haven't looked at how to preserve

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those atmospheres at this point and what

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actually motivated this work was looking

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at some of those very low-mass planets

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and trying to figure out why they still

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had atmospheres since some of them have

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densities you know that are less than

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point zero five grams per cubic

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centimeter or something I'm from these

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planets so we're trying to model

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initially how those plans could have

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atmospheres and that's what we ended up

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with these escape models that are

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showing this cutoff between the rocky

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and gas envelope worlds but that's a

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really good question that I think

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definitely deserves future study is how

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you can have these really low density

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low-mass planets that are retaining

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their thick atmospheres

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do we have so following up on obvious

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question does that preservation of

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atmosphere depend upon the age of the

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star or radio system because it takes up

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00:13:38,670 --> 00:13:36,040
100 million years for you to remove

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00:13:40,200 --> 00:13:38,680
atmosphere right right so it does depend

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00:13:42,540 --> 00:13:40,210
on the age of the stars so we're using

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00:13:45,390 --> 00:13:42,550
the XUV flux which on these sun-like

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00:13:46,950 --> 00:13:45,400
stars is really in that peak for about a

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00:13:48,870 --> 00:13:46,960
hundred million years and after that

387
00:13:50,640 --> 00:13:48,880
it's going to drop off exponentially so

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00:13:52,470 --> 00:13:50,650
your your mass whilst driven by that

389
00:13:53,910 --> 00:13:52,480
flux is going to drop off with it so if

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00:13:55,530 --> 00:13:53,920
a planet were to form further out and

391
00:13:57,270 --> 00:13:55,540
migrated inwards after that that

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00:13:59,070 --> 00:13:57,280
actually be saturation then it would

393
00:14:01,290 --> 00:13:59,080
definitely not be subjected to the same

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00:14:03,300 --> 00:14:01,300
level of mass loss and that's something

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00:14:04,710 --> 00:14:03,310
that we could consider in this model as

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well in the future