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so as you said i'm tyler this work was

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done with my advisor rob garrett at

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cornell

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this is going to be again modeling so

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not as many pretty pictures

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but some plots

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the work is

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going to be looking at the effects that

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a grain size distribution would cause to

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a model

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i'm going to explain a lot i have plenty

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of warm-up slides as well so plenty of

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background to get through first

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so let's just get on to that um the

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major background questions that this

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work is going to try and address

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is where and how could chemical

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complexity thrive and again coming from

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an astronomy department we're not

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talking about

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things like you know rocks

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or atmospheres even

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but molecular clouds so these molecular

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clouds or interstellar clouds are the

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places where stars are forming and

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eventually planets will form around

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those stars

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so to look at those regions you want to

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think about what environmental

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parameters you need to think about

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densities temperatures uv field

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strengths

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you need to look at chemical pathways

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this is where the laboratory chemists

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come in they need to tell us what

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reactions we should be thinking about

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what barriers they have what rate

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constants we need to put into our models

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for

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um

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we're i'm going to be looking at the

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building blocks for complex species so

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this is kind of breaking it down to the

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very beginning like brett showed in the

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warm-up talk this will be looking at

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things closer to methane and water and

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methanol rather than methyl formator

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anything more complex than that

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and then the model parameters that i

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need to put into my model to make this

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thing work so again plenty of rate

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constants plenty of barriers and plenty

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of chemical species

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so

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applying this model to a quiescent dark

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cloud

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quiescent just means it's static it's

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not yet collapsing it's not entering the

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protostellar phase so it's it's fairly

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boring as you might

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want to say

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but it is a large region region of over

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density um the density here is around 10

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to the four particles per cubic

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centimeter um

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i think most people could realize that's

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a fairly low number it's a pretty good

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vacuum

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but it's still more dense than your

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average interstellar space um an average

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dark cloud uh interstellar cloud has a

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total mass of uh 10 000 to a million

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solar masses solar mass again

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you know the mass of the sun 10 to the

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30 kilograms so it's a lot of a lot of

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mass

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and the places i'm looking at uh have a

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temperature of around 10 kelvin so the

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low end of these spectra that have been

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shown in the terahertz

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we're going to assume some elemental

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abundances for this model with respect

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to total hydrogen um showing that i have

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a pseto ratio of about 0.5 that can vary

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it depends on what stars you're around

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or what stars are affecting the

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environment

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but this is just what i've used

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and the model will involve more elements

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but these are the only ones that really

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matter

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you can see that i list atomic hydrogen

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as 5

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times 10 to the minus 3 with respect to

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total hydrogen because most hydrogen in

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this dark cloud is locked up in

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molecular form

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okay so i'm not sure how well this is

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going to translate i think you can you

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can see it there are these dark clouds

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here this is just a picture of the night

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sky

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with a fairly good camera and you can

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actually see these dark clouds imprinted

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uh on the background field stars so

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these are very large regions and you

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can't really tell that it's there apart

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from the fact that it obscures the stars

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behind it

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the easiest way to observe what's in

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these clouds is to find a reference star

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near the edge of one of these clouds and

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take spectra of that star and notice how

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the stars spectra maybe compare it to an

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average star that's not being obscured

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and see how that cloud is affecting the

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spectra of the background star

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so doing this um mostly in the seven

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millimeter or the radio

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looking at that one i just showed which

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is the taurus molecular cloud is kind of

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the archetypal molecular cloud

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this is just showing you a list of the

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gas species greater than some arbitrary

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cut off

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just to show you that there is a diverse

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amount of gas species

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there's plenty of aliphatics and or

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other just carbon bearing species

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there's plenty of nitrogen bearing

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species

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there's some interesting oxygen variant

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species and even one that contains

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sulfur although

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i generally neglect sulfur because it

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doesn't do anything interesting in my

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models

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and then here is just a large table that

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has more information i needed but it was

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a good reference so this is for ice

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abundances and this is generally done

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with infrared band absorption

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and the interesting ones i've tried to

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highlight you can see this is just

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listed as a percentage of water ice and

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this ice is forming on dust greens so

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this large cloud is mostly gas but it

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does contain about a hundredth of its

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mass in in dust and this dust is usually

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either silicates or carbonaceous

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and as this cloud just sits there the

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gas species will collapse or collide

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with the grain surface you assume some

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some sticking parameter and things just

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started creating onto the the dust

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surfaces and as these things accrete you

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know we call them ice

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and you can see that uh the first five

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uh columns here are protos or stars or

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protostars allia 16 is a background

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field star for the molecular cloud

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whereas these four here are protostars

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so that's past the point of quiescence

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that's started to collapse and it's the

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center has started to heat up

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and it started to thermally process the

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ice and so co is the most volatile ice

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species so it's its uh composition is

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decreased the composition of the ice as

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co is decreasing you can notice that the

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co2 is relatively constant which implies

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that it's

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a relatively robust mechanism must be

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forming co2 in this in these regions

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and then the rest that i've highlighted

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are just kind of interesting things that

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we'll be looking at later in my plots

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one particular thing to note is methanol

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in the least processed ices there's not

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too much methanol

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in the kind of intermediate processing

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stage there's quite a bit of methanol

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it's actually the second most abundant

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ice in some protostars and then in the

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highly processed protostars where the

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the the

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cartilage disc is starting to be

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evacuated by the heat of the the inner

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star

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this just points to

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high processing either

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evacuating the ice off or

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supplying sublimating the ice off of the

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dust surface or even just

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decomposing some of the more complex

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species the last column here besides

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comets sahaja star is the center of the

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galaxy where there is just a large very

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interesting molecular cloud that's being

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irradiated by many different sources and

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so it's kind of an outlier and hard to

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model

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something that you've probably all done

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in say a high school chemistry course

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you just have a couple

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rate equations for a chemical species to

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evolve or to react with some other

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chemical species to form another one

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and then you have you know instead of

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one of those you have 12 000 reactions

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now and they're all coupled

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with 1200 separate chemical species

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reacting using 12 elements

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you have to specify those in local

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environmental parameters again and you

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evolve what's initially an atomic gas

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with the exception of molecular hydrogen

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generally just through time just letting

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the reaction network do its thing so you

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know most reactions here are not going

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to have a barrier because there's enough

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reactions that if anything has a barrier

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it's probably just going to be safely

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ignored all gas phase reactions

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essentially are barrier-less the

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solid-state reactions can have a barrier

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and that gets a little more complex

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it is a three-phase model so we

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worry about gas species we worry about

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the accretion of the gas species onto a

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grain surface you have grain surface

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reactions and then you have an ice

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mantle where more reactions can occur

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but you can also just sequester species

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you can kind of imagine how this model

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works it is not spatial whatsoever it is

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a 0d model it is just essentially a

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chemistry accounting model

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but you can imagine how we treat the

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grain surface is kind of just like a

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golf ball um you we assign the dust

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grain to have a certain amount of

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binding sites in this case roughly a

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million for a typical grain size of 0.1

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micron

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and as a species of creates onto the

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surface it sticks into a dimple of the

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golf ball and then it has two barriers

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to either diffuse around the surface

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through the dimples or a barrier to just

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pop off the grain and desorb back into

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the gas phase

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and then as things accrete you

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essentially just layer things on top of

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each other and the ice mantle grows

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and i just have a list of included

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reactions if people like chemistry um

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but it's essentially just out of those

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12 000 reactions you're going to have

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some cosmic ray

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interesting reactions some

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photoionization ions neutrals etc etc

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so all that's kind of the background the

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thing that i'm adding to to the field or

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attempting to um maybe modifying some

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other work is to add this grain size

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distribution um so the almost all prior

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models the exception of one has assumed

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a canonical grain size um it's just kind

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of a necessary thing especially earlier

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with you know numerical models in the

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70s 80s 90s you can't do too much and so

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an easy simplification was assume all

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grains are the same size and that they

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don't grow so you just leave it at 0.1

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micron but of course in reality that's

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not true and we want to investigate what

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might change if we were to uh involve

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this or invoke this distribution so how

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do we find it well again we just use our

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extinction curve we find this background

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field star we find a model spectra for a

283
00:09:10,630 --> 00:09:08,640
star like that uh for a star of similar

284
00:09:13,430 --> 00:09:10,640
character and then we find how it's

285
00:09:15,110 --> 00:09:13,440
extincted by this cloud

286
00:09:17,509 --> 00:09:15,120
and most of this this extinction is just

287
00:09:20,150 --> 00:09:17,519
occurring due to dust and an individual

288
00:09:22,310 --> 00:09:20,160
dust grain of a given size will remove

289
00:09:23,829 --> 00:09:22,320
will absorb light of given wavelengths

290
00:09:25,990 --> 00:09:23,839
in a certain pattern there's plenty of

291
00:09:27,430 --> 00:09:26,000
theory for this me theory or just if

292
00:09:29,990 --> 00:09:27,440
your grain is small or large enough you

293
00:09:32,550 --> 00:09:30,000
get into rayleigh limit or just

294
00:09:34,710 --> 00:09:32,560
black body limits

295
00:09:35,990 --> 00:09:34,720
someone did this in 1977 and i just used

296
00:09:37,350 --> 00:09:36,000
his model because it's the most

297
00:09:39,030 --> 00:09:37,360
straightforward it's the easiest way to

298
00:09:40,470 --> 00:09:39,040
just throw it in my chemical model and

299
00:09:42,710 --> 00:09:40,480
see what happens

300
00:09:44,070 --> 00:09:42,720
and his model just uses a power law for

301
00:09:45,750 --> 00:09:44,080
the distribution

302
00:09:48,389 --> 00:09:45,760
of how how many grains you expect for a

303
00:09:50,550 --> 00:09:48,399
given size here a is the radius so the

304
00:09:53,509 --> 00:09:50,560
number of grains per given radius

305
00:09:55,190 --> 00:09:53,519
goes as the radius to the minus 3.5

306
00:09:57,269 --> 00:09:55,200
this is um

307
00:09:58,790 --> 00:09:57,279
i guess what this tells you is that if

308
00:10:00,710 --> 00:09:58,800
you were to plot the total amount of

309
00:10:02,310 --> 00:10:00,720
cross-sectional area for a given size of

310
00:10:04,150 --> 00:10:02,320
grain that the total amount of

311
00:10:05,910 --> 00:10:04,160
cross-sectional area goes up as you go

312
00:10:07,990 --> 00:10:05,920
to smaller grains and this is going to

313
00:10:08,949 --> 00:10:08,000
be important because the grain surface

314
00:10:10,790 --> 00:10:08,959
is where a lot of the interesting

315
00:10:12,790 --> 00:10:10,800
chemistry occurs and for chemistry to

316
00:10:14,870 --> 00:10:12,800
occur on the grain surface gas species

317
00:10:16,389 --> 00:10:14,880
need to accrete onto that grain surface

318
00:10:17,750 --> 00:10:16,399
and if the small grains have the largest

319
00:10:19,509 --> 00:10:17,760
cross-sectional area they're going to be

320
00:10:20,710 --> 00:10:19,519
accreting the most gas and therefore

321
00:10:22,389 --> 00:10:20,720
will be affecting the chemistry the

322
00:10:23,990 --> 00:10:22,399
strongest

323
00:10:26,389 --> 00:10:24,000
okay so the goal now is to find the

324
00:10:27,190 --> 00:10:26,399
effect of this distribution

325
00:10:29,430 --> 00:10:27,200
so

326
00:10:31,030 --> 00:10:29,440
how do you at least initially might

327
00:10:33,509 --> 00:10:31,040
expect this grain distribution to affect

328
00:10:35,350 --> 00:10:33,519
the model well one you might expect as

329
00:10:36,710 --> 00:10:35,360
the grains grow

330
00:10:38,069 --> 00:10:36,720
and have different sizes you might

331
00:10:39,829 --> 00:10:38,079
expect that the total number of binding

332
00:10:41,430 --> 00:10:39,839
sites on the surface might play a role

333
00:10:43,829 --> 00:10:41,440
so the first model here is just a single

334
00:10:45,430 --> 00:10:43,839
grain size the control model and the

335
00:10:47,670 --> 00:10:45,440
next model that i ran is just five

336
00:10:49,590 --> 00:10:47,680
grains but with uniform temperature and

337
00:10:51,110 --> 00:10:49,600
so this is just to find the effect of

338
00:10:53,509 --> 00:10:51,120
how the different grain sizes might

339
00:10:55,590 --> 00:10:53,519
change the chemistry the next thing way

340
00:10:56,870 --> 00:10:55,600
you might expect the grains to matter

341
00:10:58,069 --> 00:10:56,880
the different grain sizes to matter is

342
00:10:59,350 --> 00:10:58,079
that

343
00:11:02,389 --> 00:10:59,360
if you have a different grain size you

344
00:11:03,750 --> 00:11:02,399
might absorb and emit uh absorb or emit

345
00:11:04,630 --> 00:11:03,760
energy in different manners and

346
00:11:05,670 --> 00:11:04,640
therefore might have different

347
00:11:07,430 --> 00:11:05,680
temperatures

348
00:11:08,870 --> 00:11:07,440
and a kind of a canonical estimate on

349
00:11:10,069 --> 00:11:08,880
how these different grains might have

350
00:11:11,829 --> 00:11:10,079
different temperatures is just another

351
00:11:13,430 --> 00:11:11,839
simple power law astronomers love power

352
00:11:14,949 --> 00:11:13,440
laws and this power realized that the

353
00:11:16,470 --> 00:11:14,959
temperature of a grain might go as the

354
00:11:18,150 --> 00:11:16,480
or should go as the radius of the grain

355
00:11:19,590 --> 00:11:18,160
to the minus one sixth so the smaller

356
00:11:21,030 --> 00:11:19,600
grain should be warmer

357
00:11:22,870 --> 00:11:21,040
so this is a five grain plot

358
00:11:24,550 --> 00:11:22,880
distribution um with a distribution of

359
00:11:25,829 --> 00:11:24,560
both size and temperature i'll explain

360
00:11:27,350 --> 00:11:25,839
how these plots work real quick and then

361
00:11:29,190 --> 00:11:27,360
this last one is just a collapse model

362
00:11:30,630 --> 00:11:29,200
so it's not a quiescent cloud but

363
00:11:31,910 --> 00:11:30,640
collapse models generally try and

364
00:11:32,870 --> 00:11:31,920
represent

365
00:11:35,509 --> 00:11:32,880
actual

366
00:11:36,710 --> 00:11:35,519
physical conditions a bit more precisely

367
00:11:39,030 --> 00:11:36,720
so what i'm showing here is just the

368
00:11:41,030 --> 00:11:39,040
radius on the left and the radius is the

369
00:11:42,790 --> 00:11:41,040
dashed lines and the right is the

370
00:11:44,710 --> 00:11:42,800
temperature with the solid lines and so

371
00:11:47,509 --> 00:11:44,720
just how these evolve through my model

372
00:11:49,670 --> 00:11:47,519
time on the x-axis so we go from we

373
00:11:51,910 --> 00:11:49,680
essentially do a model for 10 million

374
00:11:53,990 --> 00:11:51,920
years and you can see that

375
00:11:56,389 --> 00:11:54,000
the grains grow in all models the dash

376
00:11:58,870 --> 00:11:56,399
lines do do increase the size is here

377
00:12:01,350 --> 00:11:58,880
this is a micron

378
00:12:03,910 --> 00:12:01,360
so for a single grain size the the mean

379
00:12:06,069 --> 00:12:03,920
grain size is is roughly a micron um

380
00:12:07,509 --> 00:12:06,079
whereas here we you can see that

381
00:12:09,350 --> 00:12:07,519
oh sorry this is in centimeters that's

382
00:12:11,430 --> 00:12:09,360
that's smaller than a micron that's uh

383
00:12:12,710 --> 00:12:11,440
it raises to about 0.1 micron

384
00:12:14,230 --> 00:12:12,720
but here you can see these grains are

385
00:12:17,030 --> 00:12:14,240
growing but i fixed the temperature this

386
00:12:19,030 --> 00:12:17,040
is just to kind of disentangle the

387
00:12:20,470 --> 00:12:19,040
the uh the number of great binding sites

388
00:12:22,310 --> 00:12:20,480
versus the temperature effects and here

389
00:12:24,069 --> 00:12:22,320
you can see that the temperatures are

390
00:12:25,990 --> 00:12:24,079
evolved through my static model they

391
00:12:28,550 --> 00:12:26,000
actually decrease and that's because as

392
00:12:29,829 --> 00:12:28,560
these ice mantles grow these grains are

393
00:12:31,990 --> 00:12:29,839
essential their effective area is

394
00:12:33,590 --> 00:12:32,000
increasing and because the temperature

395
00:12:34,790 --> 00:12:33,600
is determined by the size of the grain

396
00:12:36,389 --> 00:12:34,800
as the grains are growing their

397
00:12:37,910 --> 00:12:36,399
temperature is lowering and so you can

398
00:12:39,670 --> 00:12:37,920
see that for the smallest grains that

399
00:12:41,990 --> 00:12:39,680
start at roughly 15 and a half kelvin

400
00:12:42,790 --> 00:12:42,000
they end below 13.

401
00:12:45,190 --> 00:12:42,800
so

402
00:12:46,790 --> 00:12:45,200
now we'll get into the actual chemistry

403
00:12:48,949 --> 00:12:46,800
this is just a representative plot of

404
00:12:50,389 --> 00:12:48,959
the single grain control model this is

405
00:12:52,389 --> 00:12:50,399
water at the top water is always the

406
00:12:55,829 --> 00:12:52,399
most dominant ice species so i know that

407
00:12:56,710 --> 00:12:55,839
that's getting that's doing a decent job

408
00:12:59,190 --> 00:12:56,720
here

409
00:13:01,350 --> 00:12:59,200
the magenta is methanol with blue as

410
00:13:03,269 --> 00:13:01,360
formaldehyde and methanol is a product

411
00:13:05,350 --> 00:13:03,279
of formaldehyde and so they should trail

412
00:13:06,949 --> 00:13:05,360
each other fairly well which they do

413
00:13:09,190 --> 00:13:06,959
red is carbon monoxide and green is

414
00:13:11,110 --> 00:13:09,200
carbon dioxide and the two dash species

415
00:13:12,230 --> 00:13:11,120
are just hydrogenated species which we

416
00:13:13,590 --> 00:13:12,240
don't like to care about because they're

417
00:13:14,949 --> 00:13:13,600
not interesting they don't do much other

418
00:13:17,430 --> 00:13:14,959
than just

419
00:13:19,350 --> 00:13:17,440
abstract hydrogen

420
00:13:21,750 --> 00:13:19,360
so here you can see that for a single

421
00:13:24,470 --> 00:13:21,760
grain i have mostly carbon monoxide of

422
00:13:25,990 --> 00:13:24,480
the two carbon and oxygen species

423
00:13:27,110 --> 00:13:26,000
now getting into the next model which is

424
00:13:28,710 --> 00:13:27,120
where it gets complicated to try and

425
00:13:30,470 --> 00:13:28,720
show this i essentially have an

426
00:13:32,710 --> 00:13:30,480
aggregate mantle this is for the five

427
00:13:34,310 --> 00:13:32,720
grains with the uniform temperature this

428
00:13:35,509 --> 00:13:34,320
is the aggregate ice mantle add up all

429
00:13:37,030 --> 00:13:35,519
the ice mantels off the five different

430
00:13:39,190 --> 00:13:37,040
grain sizes this is the mantle for the

431
00:13:41,509 --> 00:13:39,200
smallest grain the medium grain and the

432
00:13:43,509 --> 00:13:41,519
fifth grain and you can see if i flip

433
00:13:45,190 --> 00:13:43,519
back and forth here um just the general

434
00:13:46,790 --> 00:13:45,200
shapes of these of these plots look

435
00:13:48,710 --> 00:13:46,800
roughly the same

436
00:13:50,470 --> 00:13:48,720
and i can show that at the end that the

437
00:13:52,470 --> 00:13:50,480
the total chemistry doesn't change

438
00:13:53,829 --> 00:13:52,480
appreciably between those two models so

439
00:13:55,030 --> 00:13:53,839
the grain distribution doesn't really do

440
00:13:57,350 --> 00:13:55,040
much if i don't have a temperature

441
00:13:59,750 --> 00:13:57,360
distribution but now if i go from these

442
00:14:01,829 --> 00:13:59,760
plots to a distribution and temperature

443
00:14:02,870 --> 00:14:01,839
as you may expect just even naively that

444
00:14:04,069 --> 00:14:02,880
a temperature distribution probably is

445
00:14:05,509 --> 00:14:04,079
going to affect the chemistry because

446
00:14:06,550 --> 00:14:05,519
the temperature is what determines how

447
00:14:08,790 --> 00:14:06,560
my rates

448
00:14:09,990 --> 00:14:08,800
are how my reactions move right if a

449
00:14:10,790 --> 00:14:10,000
rate constant

450
00:14:12,629 --> 00:14:10,800
uh

451
00:14:14,470 --> 00:14:12,639
well generally you know chemical rates

452
00:14:16,150 --> 00:14:14,480
depend on the temperature and here the

453
00:14:19,350 --> 00:14:16,160
big chemical rate that's important here

454
00:14:21,670 --> 00:14:19,360
is the conversion of co2 co2 through

455
00:14:23,910 --> 00:14:21,680
various rates um is the most temperature

456
00:14:25,189 --> 00:14:23,920
sensitive in the region of 10 kelvin so

457
00:14:26,790 --> 00:14:25,199
for a temperature distribution that i

458
00:14:28,790 --> 00:14:26,800
showed earlier where the grains have a

459
00:14:30,150 --> 00:14:28,800
temperature between 9 and 15 kelvin

460
00:14:32,949 --> 00:14:30,160
there's a transitionary temperature

461
00:14:35,189 --> 00:14:32,959
around 10 around 12 kelvin where co

462
00:14:36,710 --> 00:14:35,199
becomes efficiently converted into co2

463
00:14:38,230 --> 00:14:36,720
and so here for my smallest grain of

464
00:14:39,990 --> 00:14:38,240
distribution temperature you can see

465
00:14:42,629 --> 00:14:40,000
that the co2 is actually competing with

466
00:14:44,550 --> 00:14:42,639
water for um an immense amount of ice

467
00:14:46,629 --> 00:14:44,560
formation whereas co has dropped off the

468
00:14:49,269 --> 00:14:46,639
radar until the grain gets sufficiently

469
00:14:51,110 --> 00:14:49,279
large to cool off that co becomes uh

470
00:14:53,509 --> 00:14:51,120
competitive in the reaction rates again

471
00:14:54,949 --> 00:14:53,519
and even in the aggregate ice mantle co2

472
00:14:57,350 --> 00:14:54,959
is dominant because the smallest grain

473
00:14:58,470 --> 00:14:57,360
is excreting the most ice

474
00:15:01,110 --> 00:14:58,480
here's the collapse i'm just going to

475
00:15:02,550 --> 00:15:01,120
skip it because i'm running low

476
00:15:04,389 --> 00:15:02,560
so this is just the table that shows

477
00:15:05,910 --> 00:15:04,399
that the single grain model is very

478
00:15:07,189 --> 00:15:05,920
comparable to the five grain model with

479
00:15:08,629 --> 00:15:07,199
uniform temperature you can just compare

480
00:15:10,470 --> 00:15:08,639
all the numbers they're all about the

481
00:15:11,750 --> 00:15:10,480
same the difference here comes with the

482
00:15:13,990 --> 00:15:11,760
temperature difference there's less

483
00:15:15,189 --> 00:15:14,000
water ice because the the warmer grains

484
00:15:16,949 --> 00:15:15,199
essentially are

485
00:15:18,870 --> 00:15:16,959
allow water to more easily absorb off

486
00:15:21,350 --> 00:15:18,880
the surface and also the amount of co

487
00:15:22,949 --> 00:15:21,360
has dropped the amount of co2 has grown

488
00:15:24,310 --> 00:15:22,959
the amount of methanol has also dropped

489
00:15:25,110 --> 00:15:24,320
and that's kind of a curious thing

490
00:15:26,389 --> 00:15:25,120
because

491
00:15:27,990 --> 00:15:26,399
you might expect that

492
00:15:29,750 --> 00:15:28,000
methanol would grow just because warmer

493
00:15:31,910 --> 00:15:29,760
temperatures maybe is makes more complex

494
00:15:33,030 --> 00:15:31,920
species more easily formable but

495
00:15:35,350 --> 00:15:33,040
methanol generally requires

496
00:15:37,110 --> 00:15:35,360
hydrogenation of co and if cos being

497
00:15:39,509 --> 00:15:37,120
formed into co2

498
00:15:41,350 --> 00:15:39,519
the formation of methanol is inhibited

499
00:15:42,790 --> 00:15:41,360
so just a quick conclusion slide i guess

500
00:15:44,629 --> 00:15:42,800
i've probably talked about most of this

501
00:15:51,189 --> 00:15:44,639
so you can just read them out of time

502
00:15:51,199 --> 00:16:02,310
we have time for one quick question

503
00:16:05,990 --> 00:16:04,310
do you allow for bulk diffusion in your

504
00:16:07,189 --> 00:16:06,000
grain model and if so what's your bulk

505
00:16:09,110 --> 00:16:07,199
diffusion

506
00:16:11,189 --> 00:16:09,120
yes right yeah so

507
00:16:13,269 --> 00:16:11,199
as the ice species uh get sequestered

508
00:16:14,870 --> 00:16:13,279
into the mantle a lot of previous models

509
00:16:16,629 --> 00:16:14,880
would just say the ice is now completely

510
00:16:17,749 --> 00:16:16,639
dormant and nothing occurs and they just

511
00:16:19,749 --> 00:16:17,759
build up and then you can look at the

512
00:16:21,430 --> 00:16:19,759
ice at the end the small does include

513
00:16:23,110 --> 00:16:21,440
bulk diffusion and so you can allow

514
00:16:24,629 --> 00:16:23,120
these ice species even while in the

515
00:16:27,430 --> 00:16:24,639
mantle and not no longer on the surface

516
00:16:28,949 --> 00:16:27,440
to react with other ice species um it

517
00:16:30,790 --> 00:16:28,959
does ends up not playing a huge role in

518
00:16:32,550 --> 00:16:30,800
this model but if the temperature were

519
00:16:34,710 --> 00:16:32,560
say double to around 20 kelvin maybe in

520
00:16:36,629 --> 00:16:34,720
a warm-up stage of a protostar that can

521
00:16:38,550 --> 00:16:36,639
become very important um but for this