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[Music]

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I am Jade really happy to be closing

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this awesome meeting I'm seeing a lot of

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faces down which must means the co2 in

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this room is getting pretty high but

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let's just try to get through 15 more

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minutes and we can all go eat but today

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I'd like to discuss how we could

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potentially test the concept of the

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habitable zone so in the near future new

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and powerful instruments will allow us

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to characterize exoplanets like never

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before so what you're looking at here

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are a few instruments that are or have

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been at least partially involved in

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detecting and characterizing exoplanets

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now so far we have not yet been able to

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directly observe earth-sized habitable

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terrestrial planets however as we look

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to the future we can look forward to

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instruments dedicated to observing these

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kinds of exoplanets which we think may

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host life so in particular I'll be

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focusing on highbacks in the war right

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here which are both direct imaging

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instruments that are in the running to

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become NASA's next flagship mission and

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so they would directly image earth sized

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terrestrial exoplanets in the habitable

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zones of stars like the Sun Fuji stars

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and because for the first time in

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history we'll actually finally be able

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to observe these earth sized habitable

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exoplanets we may also be able to test

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some habitability hypothesis so to do

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that we could use a statistical

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comparative planetology approach which

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essentially just means that we'd be

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taking quick and cheap measurements on a

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large sample of exoplanets to test a

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particular hypothesis so in doing that

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we really want to take the number and

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the diversity of exoplanets as an

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advantage and a kind of real-life

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example of this is as on this cartoon

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here where we essentially just be taking

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quick and somewhat imprecise u2

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measurements on say 50 exoplanets in the

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habitable zones of their stars now a

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somewhat recent example of this approach

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is by Leslie Rogers IU Chicago and so

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this is for eggs

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and Leslie took very low precision

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measurements of match radius

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measurements for a large sample of

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planets to infer the radius at which

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planets are likely to become rocky so

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this is a really great example of this

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kind of approach because if we look at

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any individual point here the error bars

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are huge they're almost the entire size

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of the flat so it'd be really difficult

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to infer anything significant from any

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one or two of these points but by

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putting all of this low precision data

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together

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Leslie was actually able to get a

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procedure probability distribution on

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the thresholds at which planets are

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likely to become rocky so she found here

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that occurs at about 1.5 Earth radius

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now what I'd like to do with this kind

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of statistical approach is to test that

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concept of the habitable zone we've

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heard it quite a lot this week the

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habitable zone of course is defined as

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the possibility of surface we could

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water between two orbital separations

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and whenever a new planet or a new

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system of exoplanets is discovered the

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discovery usually comes with whether or

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not the orbit within the habitable zone

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however in habitable zone theory there's

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a lot of predictions and assumptions

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that we just have not yet tested

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observational now here's a slightly more

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scientific illustration of the habitable

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zone so it's distance and width varies

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as a function of cellar type and usually

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the inner edge is taken to be this

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yellow curve here which is the limits at

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which planets are likely to go into a

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moist greenhouse state so they're going

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to start using their water to space now

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within this bluish region right here we

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make an important assumption so this is

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the habitable zone we assume that the

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silicate weathering feedback functions

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to regulate the climate of this planet

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so the entire concept of the habitable

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zone relies on this climate feedback so

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what what is the silicate weathering

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feedback well it's a um negative climate

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feedback that relies on the cycling of

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co2 in and out of a planet to regulate

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its surface temperature so an easy way

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to think of it is that if we have a

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terrestrial exoplanet orbiting in the

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habitable zone but slightly further away

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from its star so closer to the outer

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edge technically its surface temperature

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could drop to below freezing now luckily

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when surface temperature decreases the

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weathering rate so the intake of co2 by

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the planets right here also starts to

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slow down and because the outgassing

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rate is usually constant co2 is going to

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be able to build it the atmosphere of

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the planet and bring the surface

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temperature back to habitable condition

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so we have pretty good geological

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evidence that this feedback has been

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functioning Earth rotates history but we

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have no idea whether or not it works on

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exoplanets we just assume it does

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because it does on earth okay so let's

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just come back to this plot right here

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what would happen if the silicate

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weathering feedback did not in fact

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function well the outer edge would be

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found much more close in so the

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habitable zone would be super tiny so

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it's clearly super important when we

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talk about the habitability of any given

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planet and whether or not it's actually

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in the habitable zone but in addition to

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bring the outer edge much more further

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out it also regulates the surface

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temperature of of planets within the

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habitable zone so instead of having

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their surface temperature go from 270

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here to 373 Kelvin here it's going to

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regulate the surface temperature to be

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more closely to that of the earth around

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290 Kelvin faster - a pretty narrow

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uncertainty range now the outer edge

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right here is usually defined by the

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point at which tier 2 is going to

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condense out of the atmosphere of the

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planet

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so therefore the silicate weathering

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feedback can no longer function and the

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planets found here are likely to be in a

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globally glaciated state so in a

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snowball state ok so we want to test

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whether or not the silicate weathering

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feedback actually functions on

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terrestrial planets and if it does and

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we observe a number of them and takes

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you to measurements on each of them at

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different orbital separation from their

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stars what we should see that there

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should be a drop of co2 with increasing

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irradiation so to illustrate why that is

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let's take this point right

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here it's a planet orbiting further away

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from its stars where they nor value of

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your radiation and because of that if

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the feedback function it should have a

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higher amount of co2 to maintain

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habitability in comparation this point

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right here is much closer to its star

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and because of that it should require

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less u2 to maintain similar surface

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conditions so if the feedback functions

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we're going to get a downward slope

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right here now of course there is going

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to be a lot of uncertainties with this

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with what exact amount of co2 we can

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expect as a function of your radiation

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so for example the exact surface

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temperature the surface pressure other

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greenhouse gases clouds and a first

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instrumental uncertainties all of these

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are going to make it more difficult for

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us to see this downward slope but the

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idea here is that the more planets we

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observe the easier it will be to

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marginalize over these uncertainties and

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so to be able to detect the downward

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slope despite our big error bars now of

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course well probably if we observe

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thousands of thousands of exoplanets we

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may detect a downward slope if the

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feedback functions but even a crazy

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expensive futuristic instruments such as

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the war won't be able to see that many

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planets so we want to know whether or

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not this test is at all feasible so the

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big question I'm asking in my work right

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now is how many planets would we have to

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observe to detect a downward slope if

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the feedback functions so to answer that

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question first at to understand how

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these downward slope changes as we vary

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our parameters so here I'm just going to

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show you some examples of the kind of

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data I get so this is using Klima

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a radiative convective model and smart a

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radiative transfer model and this is the

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same axis as you just saw YouTube versus

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irradiation and everything else is held

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fixed except surface temperature so if

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we pick a value of your radiation say

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here and we go from green to black so

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from lower to higher surface

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temperatures we see that we gradually

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need more and more co2 to maintain these

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higher surface temperatures which makes

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sense if the feedback function

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I wanted you to realize from this flood

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right here if that surface temperature

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is going to be a pretty important

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uncertainty parameter that when we vary

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it always within habitable bounds here

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we see that the shape of the curves

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changes quite a bit so this will make it

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more difficult for us to resolve over

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these error bars it adds a lot of

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uncertainty now in comparation here's

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the similar example this time for

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different amounts of methane and we see

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that this time when we go from green to

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no methane to blue so current Earth

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levels of methane and then to red torque

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in Earth levels of methane we see that

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the shape of the curve this time doesn't

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change quite that much so this is just

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to illustrate that some parameters even

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though there are certain keys they may

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not matter why that much and other thing

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such as surface pressure and temperature

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are going to really matter in this okay

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so these were just some examples of the

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kind of data we're going to be using now

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I'd like to lead you through a

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simplified explanation of the

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statistical method I used to enter the

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question of how many planets we need to

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observe to detect the downward slope and

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so prove whether or not the feedback

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function but first we had to make some

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kind of assumptions under uncertainty

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parameters we don't yet know that much

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about terrestrial exoplanets but we had

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to decide on how much we're going to for

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example at surface pressure surface

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temperature cloud opacities and so forth

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vary so here is an example for surface

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temperature here so it's a normal

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distribution centered around the value

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of the earth plus or minus is pretty

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limited range the reason we're using

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this in a bit of an optimal optimistic

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manner here is because previous work has

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shown that if a planet has a functioning

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liquid weathering feedback and it's in

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the habitable zone it should really

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maintain its surface temperature around

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that of the earth that's 4 minus about

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20 Kelvin now if you're worried if this

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is raising a red flag in your head

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already it's okay this is all really

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optimistic case for each parameter we've

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also considered a much more pessimistic

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case where for example for surface

277
00:11:04,870 --> 00:11:00,890
temperature we considered a uniform

278
00:11:06,820 --> 00:11:04,880
distribution from 270 to 373 Kelvin but

279
00:11:07,670 --> 00:11:06,830
anyway for now let's take it as it is

280
00:11:10,460 --> 00:11:07,680
and

281
00:11:13,010 --> 00:11:10,470
go through the statistical method so

282
00:11:14,930 --> 00:11:13,020
first we choose a number of model planet

283
00:11:16,880 --> 00:11:14,940
say three so were inventing we're

284
00:11:19,519 --> 00:11:16,890
creating planets that may or may not

285
00:11:21,260 --> 00:11:19,529
exist then for each of them we're going

286
00:11:23,510 --> 00:11:21,270
to draw a surface temperature values

287
00:11:25,820 --> 00:11:23,520
here from the distribution I just showed

288
00:11:28,310 --> 00:11:25,830
you so this is where these distributions

289
00:11:30,560 --> 00:11:28,320
are going to come into play they help us

290
00:11:31,970 --> 00:11:30,570
create our imaginary planet so if we

291
00:11:34,639 --> 00:11:31,980
were considering all of the parameters

292
00:11:36,860 --> 00:11:34,649
that in real life we are we'd be drawing

293
00:11:38,510 --> 00:11:36,870
values for them right here so we draw a

294
00:11:40,970 --> 00:11:38,520
surface pressure value from its

295
00:11:42,620 --> 00:11:40,980
distribution and so forth then for each

296
00:11:45,769 --> 00:11:42,630
of them we of course also draw a

297
00:11:47,510 --> 00:11:45,779
radiation values from a uniform

298
00:11:51,550 --> 00:11:47,520
distribution because the planet can be

299
00:11:54,380 --> 00:11:51,560
anywhere in the habitable zone and then

300
00:11:56,210 --> 00:11:54,390
based on these values that we've drawn

301
00:11:59,540 --> 00:11:56,220
we're going to compute the corresponding

302
00:12:01,550 --> 00:11:59,550
amount of co2 so this is where our data

303
00:12:03,820 --> 00:12:01,560
that I showed you earlier comes into

304
00:12:06,650 --> 00:12:03,830
play it's essentially a big

305
00:12:09,170 --> 00:12:06,660
multi-dimensional matrix of co2 as a

306
00:12:11,240 --> 00:12:09,180
function of a bunch of other uncertainty

307
00:12:12,949 --> 00:12:11,250
parameters okay

308
00:12:14,780 --> 00:12:12,959
so now we have co2 for all of our

309
00:12:16,370 --> 00:12:14,790
planets then we're going to add some

310
00:12:18,350 --> 00:12:16,380
instrumental noise to these values

311
00:12:21,140 --> 00:12:18,360
because we're pretending we're really

312
00:12:23,180 --> 00:12:21,150
only measuring co2 for this planet and

313
00:12:25,970 --> 00:12:23,190
then we're going to compute the

314
00:12:28,790 --> 00:12:25,980
irradiation versus co2 slope for these

315
00:12:31,460 --> 00:12:28,800
three points so here I've Illustrated

316
00:12:33,800 --> 00:12:31,470
the slope as being negative which it

317
00:12:35,900 --> 00:12:33,810
should be the feedback function but of

318
00:12:38,000 --> 00:12:35,910
course because of our uncertainties in

319
00:12:39,890 --> 00:12:38,010
here surface temperature and in

320
00:12:42,170 --> 00:12:39,900
instrumental noise in some of these

321
00:12:45,350 --> 00:12:42,180
cases the slope may end up being

322
00:12:47,210 --> 00:12:45,360
positive or very close to zero so when

323
00:12:49,250 --> 00:12:47,220
we repeat this whole process ten to the

324
00:12:51,199 --> 00:12:49,260
five times we're going to have a number

325
00:12:53,269 --> 00:12:51,209
of slopes that are negative and in

326
00:12:56,090 --> 00:12:53,279
number positive and of course the more

327
00:12:57,590 --> 00:12:56,100
planet we model the more slopes should

328
00:13:01,220 --> 00:12:57,600
be negative because we assumed the

329
00:13:03,290 --> 00:13:01,230
feedback function okay so this slide

330
00:13:05,510 --> 00:13:03,300
right here illustrates the point I just

331
00:13:07,639 --> 00:13:05,520
made so this is the distribution of

332
00:13:10,310 --> 00:13:07,649
slopes as a function of the number of

333
00:13:11,900 --> 00:13:10,320
planets that we would be observing until

334
00:13:14,540 --> 00:13:11,910
we see that for a low number of planets

335
00:13:16,550 --> 00:13:14,550
here in magenta a good fraction of the

336
00:13:18,890 --> 00:13:16,560
slopes and up being positive ratch is

337
00:13:20,490 --> 00:13:18,900
very close to zero but the more planets

338
00:13:23,170 --> 00:13:20,500
who observe the more slopes

339
00:13:24,490 --> 00:13:23,180
so this makes sense right the the more

340
00:13:26,440 --> 00:13:24,500
planets we're going to observe the

341
00:13:28,870 --> 00:13:26,450
easier it will be to detect a downward

342
00:13:30,910 --> 00:13:28,880
slope if the feedback functions but we

343
00:13:34,360 --> 00:13:30,920
had to decide on what's a good enough

344
00:13:36,699 --> 00:13:34,370
number of mother legs or planets so to

345
00:13:38,439 --> 00:13:36,709
do that we define the power as the

346
00:13:41,230 --> 00:13:38,449
fraction of slopes with a p-value less

347
00:13:44,079 --> 00:13:41,240
than zero point zero point zero five so

348
00:13:47,290 --> 00:13:44,089
this is just how many slopes are clearly

349
00:13:49,329 --> 00:13:47,300
negative enough and here to get a power

350
00:13:53,050 --> 00:13:49,339
of your point eight we see that in this

351
00:13:55,389 --> 00:13:53,060
case we need eleven model exoplanets so

352
00:13:57,879 --> 00:13:55,399
what this means in real life is that if

353
00:14:01,060 --> 00:13:57,889
the silicate weathering action feedback

354
00:14:03,579 --> 00:14:01,070
actually functions on exoplanet and we

355
00:14:05,579 --> 00:14:03,589
observed eleven of them then we'll have

356
00:14:08,410 --> 00:14:05,589
an eighty percent chance of actually

357
00:14:10,150 --> 00:14:08,420
detecting the feedback so if we want a

358
00:14:12,310 --> 00:14:10,160
higher chance of detecting it if it

359
00:14:17,290 --> 00:14:12,320
exists we'll just have to observe more

360
00:14:18,819 --> 00:14:17,300
planets now you may remember that I

361
00:14:21,759 --> 00:14:18,829
mentioned doing this for both an

362
00:14:23,620 --> 00:14:21,769
optimistic and a pessimistic case so

363
00:14:25,750 --> 00:14:23,630
this is friendly optimistic case 11

364
00:14:29,170 --> 00:14:25,760
planets and for the pessimistic case

365
00:14:31,540 --> 00:14:29,180
we'd have to after 51 exoplanet now some

366
00:14:33,610 --> 00:14:31,550
caution these are still early results in

367
00:14:35,500 --> 00:14:33,620
the sense that they're for a fixed

368
00:14:38,199 --> 00:14:35,510
amount of co2 now it's your upon five

369
00:14:40,389 --> 00:14:38,209
log unit I'm currently working with cat

370
00:14:43,300 --> 00:14:40,399
Fang from Santa Cruz right here on

371
00:14:45,970 --> 00:14:43,310
actually adding simulated habits and who

372
00:14:49,180 --> 00:14:45,980
were noise to this year to value so that

373
00:14:51,639 --> 00:14:49,190
will come later okay but are these

374
00:14:53,259 --> 00:14:51,649
values reasonable they already give us

375
00:14:56,079 --> 00:14:53,269
somewhat of an idea of what we can

376
00:14:58,660 --> 00:14:56,089
expect to ensure that we looked at some

377
00:15:00,490 --> 00:14:58,670
work from Chris dark who estimated the

378
00:15:03,250 --> 00:15:00,500
candidate field for eggs on earth using

379
00:15:06,309 --> 00:15:03,260
different future generation instruments

380
00:15:08,500 --> 00:15:06,319
so if we look here at havoc it's a

381
00:15:10,420 --> 00:15:08,510
pretty small mirror and because of that

382
00:15:13,329 --> 00:15:10,430
we likely only be able to detect about

383
00:15:15,519 --> 00:15:13,339
10-ish eggs or earth so that's not ideal

384
00:15:17,620 --> 00:15:15,529
to do any kind of statistical study in

385
00:15:19,689 --> 00:15:17,630
general which makes sense because habits

386
00:15:23,050 --> 00:15:19,699
isn't really being thought of in that

387
00:15:26,110 --> 00:15:23,060
way but in cooperation if we look at the

388
00:15:28,180 --> 00:15:26,120
war a here or even new war be we'd be

389
00:15:30,639 --> 00:15:28,190
able to observe up to about fifty five

390
00:15:31,990 --> 00:15:30,649
eggs or earth so that's really an ideal

391
00:15:33,670 --> 00:15:32,000
number two

392
00:15:36,310 --> 00:15:33,680
be able to do this kind of statistical

393
00:15:38,440 --> 00:15:36,320
study so to test the habitable zone in

394
00:15:40,300 --> 00:15:38,450
general and especially to test whether

395
00:15:44,050 --> 00:15:40,310
or not the silicate weathering feedback

396
00:15:47,260 --> 00:15:44,060
functions on exoplanets okay I'm going

397
00:16:01,920 --> 00:15:47,270
to leave my conclusions right here Thank

398
00:16:07,660 --> 00:16:05,710
Thanks so Robin Wordsworth Harvard I was

399
00:16:10,420 --> 00:16:07,670
wondering have you thought about if you

400
00:16:12,130 --> 00:16:10,430
had ancillary observations something

401
00:16:15,730 --> 00:16:12,140
like albedo that allowed you to rule out

402
00:16:18,310 --> 00:16:15,740
by the the parameter space that was

403
00:16:20,080 --> 00:16:18,320
caused you have a lot of dependence on

404
00:16:22,270 --> 00:16:20,090
certain parameters if you could if you

405
00:16:25,240 --> 00:16:22,280
could make other observations you had

406
00:16:30,340 --> 00:16:25,250
prior to your analysis with that help

407
00:16:33,460 --> 00:16:30,350
things maybe but I guess I mean if these

408
00:16:36,220 --> 00:16:33,470
observations were available sure I can't

409
00:16:37,930 --> 00:16:36,230
think of any right now in this spot but

410
00:16:39,850 --> 00:16:37,940
I think the whole point is that we

411
00:16:41,410 --> 00:16:39,860
really want it because we'd have to do

412
00:16:43,750 --> 00:16:41,420
this for a large number of planets like

413
00:16:46,810 --> 00:16:43,760
he maybe 50 we really want to make sure

414
00:16:49,810 --> 00:16:46,820
that we do this with only really quick

415
00:16:52,180 --> 00:16:49,820
and simple measurements so here in this

416
00:16:54,070 --> 00:16:52,190
case it's really advantageous because it

417
00:16:56,230 --> 00:16:54,080
would allow us to really only test for

418
00:16:58,480 --> 00:16:56,240
co2 to have an estimate of the amount of

419
00:17:00,480 --> 00:16:58,490
co2 and of course the distance to the

420
00:17:03,370 --> 00:17:00,490
star but if we want to add other

421
00:17:04,840 --> 00:17:03,380
parameters that may take longer although

422
00:17:07,569 --> 00:17:04,850
if they're available from like safe

423
00:17:10,500 --> 00:17:07,579
studies and such yeah that'd be great

424
00:17:10,510 --> 00:17:16,260
hmm Daniel here in front

425
00:17:23,710 --> 00:17:20,949
how much luar time IU is this gonna take

426
00:17:25,210 --> 00:17:23,720
overall like I'd I don't know I assume

427
00:17:27,280 --> 00:17:25,220
somebody has done some reference studies

428
00:17:29,680 --> 00:17:27,290
like to even detect like a crappy

429
00:17:31,510 --> 00:17:29,690
measurement of co2

430
00:17:36,490 --> 00:17:31,520
do you need like order of an hour or

431
00:17:38,470 --> 00:17:36,500
order weeks right I'm not sure yet I

432
00:17:40,570 --> 00:17:38,480
think we're going to take that into into

433
00:17:42,700 --> 00:17:40,580
consideration when actually computing

434
00:17:44,870 --> 00:17:42,710
the amount of co2 noise we're going to

435
00:17:48,490 --> 00:17:44,880
decide on an integration time

436
00:17:52,480 --> 00:17:48,500
we're not sure what yet yeah I don't

437
00:17:55,580 --> 00:17:52,490
probably a few hours means I don't know

438
00:17:57,020 --> 00:17:55,590
I'm not an observation there so there's

439
00:17:59,870 --> 00:17:57,030
a lot of people in this room would be

440
00:18:02,950 --> 00:17:59,880
able to say that much better than I

441
00:18:11,000 --> 00:18:08,420
secret yeah hi Sigurd ranch and MIT

442
00:18:12,680 --> 00:18:11,010
thank you for a really great talk just

443
00:18:14,930 --> 00:18:12,690
regarding the uncertainties how hard is

444
00:18:17,660 --> 00:18:14,940
it to differentiate co2 concentrations

445
00:18:20,060 --> 00:18:17,670
at very high co2 concentrations how hard

446
00:18:21,500 --> 00:18:20,070
is it to differentiate co2 concentration

447
00:18:23,210 --> 00:18:21,510
yeah I guess I'm wondering is there any

448
00:18:24,230 --> 00:18:23,220
risk of saturation of the co2 line so

449
00:18:26,390 --> 00:18:24,240
it's hard to tell if there's too much

450
00:18:28,790 --> 00:18:26,400
co2 or you always get it from the wings

451
00:18:31,310 --> 00:18:28,800
right yeah so like I'm not going to go

452
00:18:33,860 --> 00:18:31,320
back but as you saw on the plot if we're

453
00:18:36,860 --> 00:18:33,870
at lower values of irradiation

454
00:18:39,320 --> 00:18:36,870
the co2 kind of on the plot it starts

455
00:18:41,990 --> 00:18:39,330
being really straight so we definitely

456
00:18:43,550 --> 00:18:42,000
want to be able to simple enough of this

457
00:18:45,100 --> 00:18:43,560
thought that we're able to say downward

458
00:18:48,200 --> 00:18:45,110
slope because if we only looked at

459
00:18:49,850 --> 00:18:48,210
planets at which there's a lot of co2 we

460
00:18:51,560 --> 00:18:49,860
may not be able to get a slope at all

461
00:18:55,520 --> 00:18:51,570
because I don't know if you remember the

462
00:19:03,710 --> 00:18:55,530
plot kind of both like this right it's a

463
00:19:07,190 --> 00:19:03,720
good point Hannah Hannah wait good Space

464
00:19:10,160 --> 00:19:07,200
Telescope um how evenly distributed

465
00:19:12,350 --> 00:19:10,170
across the face face of stellar

466
00:19:15,530 --> 00:19:12,360
irradiance do you need these 50 planets

467
00:19:19,520 --> 00:19:15,540
to be and do we expect to be able to

468
00:19:22,270 --> 00:19:19,530
have such a distribution that's a really

469
00:19:27,260 --> 00:19:25,190
all I can say is again the same thing

470
00:19:30,890 --> 00:19:27,270
you definitely want to be able to sample

471
00:19:32,660 --> 00:19:30,900
enough of this plot that you have the

472
00:19:35,960 --> 00:19:32,670
the spot at which the downward slope is

473
00:19:39,790 --> 00:19:35,970
more obvious than rather at lower values

474
00:19:44,540 --> 00:19:39,800
of irradiation okay I'm not sure exactly

475
00:19:46,410 --> 00:19:44,550
that's a good point though all right