[ExI] Life must be everywhere!

[Kelly Anderson]

On Sun, Apr 15, 2012 at 2:23 AM, Anders Sandberg <anders at aleph.se> wrote:
> (Summary: Panspermia is fun! So many different factors interacting, so much
> cool physics, mathematics and biology! Introduce your family to the joys of
> trying to estimate whether it works or not today! Oh, and big rocks are
> likely *much* more viable vehicles for spores than small ones. )

I would have to agree, this is highly interdisciplinary. Don't forget
the computer science in the monte carlo simulations... :-)

> On 2012-04-15 08:13, Kelly Anderson wrote:
>>
>> On Sat, Apr 14, 2012 at 4:26 PM, Anders Sandberg<anders at aleph.se>  wrote:
>>>
> You can check some of the physics in Collins, Melosh and Marcus' *excellent*
> paper describing their calculator:
> http://www.purdue.edu/impactearth/Content/pdf/Documentation.pdf

My brother works at the University of Arizona... should we need, I'm
sure he could run over and ask these fine gentlemen questions for
us... :-)

> The real issue for us is sequential breakups, since we are interested in the
> conditions that produce pieces that have cores that are not too hot; whether
> they get deposited on the ground with a bang or just float down as dust
> doesn't matter.

By sequential breakups, do you mean big rocks that get broken into
littler pieces later?

>>> A simple problem: a spherical granite pebble of radius R starts out with
>>> a
>>> core temperature ~300 K and a surface that is molten, ~1500 K. How long
>>> will
>>> it take for the core to become 500 K hot, and is this time shorter than
>>> the
>>> time it takes to cool the surface in a space environment down to around
>>> 300
>>> K?
>>
>>
>> And why would we assume that the entire surface is molten? And how
>> thick would that molten layer be? Wouldn't it make a difference if a
>> lot of the surface was melted vs just a little bit?
>
>
> We have to start somewhere with the calculations. We can be fairly confident
> that the interior of a major impact is going to be a fireball, so a thin
> molten layer is likely not a bad approximation.

There will clearly be a molten portion nearest the impact site.

> In fact, for doing the calculation properly the thickness of the molten
> layer matters a lot. Obviously the initial amount of hot rock vs cold rock
> matters for estimating the end temperatures.

That was just intuition on my part, but it makes sense. Seems it could
be rather thin if the event happens fast enough. Looking at the stuff
scattered around meteor crater in Arizona, some is clearly
resolidified glass, and other is just broken up rock, it varies a lot.

> But then there is this: the
> surface is radiating away P = 4*pi*R^2sigma*epsilon*T^4 Watts of heat. This
> will decrease its temperature as P/(4*pi*R^2*t*K) = sigma*epsilon*T^4/(t*K)
> Kelvin/second (ignoring heating from the inside), where t is the thickness
> of the IR-optically transparent outer layer and K is the thermal capacity. A
> thick layer of melt means that it will cool quicker since it can move heat
> out faster (also, it might shed droplets, a far more potent cooling
> mechanism than radiation). However, I don't know how much t should be in
> this estimate - any thermal physicist or hot material scientist around?

Not me.

>> You're amazing Anders. If I'm reading right though, there is a bigger
>> size that works better... I'm sure you'll figure out how big it has to
>> be to work in your sleep, and will just awaken with the right answer
>> on your pillow.. :-)  I love hanging around with smart people!
>
> Me too! Unfortunately my dreams tonight were about running a restaurant at
> the Cote d'Azure (involving noneuclidean geometry and some minor plot for
> world domination), so I will still have to do the calculations while awake.

Can I be the Pinky to your Brain? LOL

> But the basic point you made is right: big boulders will not be fried as
> easily as pebbles. They also have the benefit that they are less likely to
> be ablated to nothing when passing through a terrestrial atmosphere on
> impact. On the downside, and this could be major, there will be fewer of
> them.

I think that it would be safe to estimate boulder size with a Poisson
distribution. The other really big problem is that smaller stuff seems
likely to travel faster (F=ma and all) and thus have a better chance
of escaping the solar system.

> I suspect the size distribution is a power-law, with far more small
> pieces than bigger ones.

I don't recall if Poisson is a power law, but it's close.

> So even if the probability of life surviving in
> small pebbles is much lower the sheer number of pebbles might outweigh the
> boulders in terms of viable cells lofted into space. More calculations are
> needed...

There is clearly a sweet spot... where the chance of survival and
transport are both optimal... :-) It might not be that either is
totally satisfied in any given event, and that in and of itself would
be an interesting thing to ponder.

If you're talking about a life bearing planet other than earth, the
mass of that planet probably also figures into the calculations quite
a bit. That is, the more massive the planet, the less likely for life
bearing rocks to escape.

>>> Now, how fast is radiative cooling of ejecta? I am too sleepy to solve
>>> that
>>> differential equation right now. But I bet it is slower than 20 seconds.
>>
>>
>> No doubt.
>
>
> I did find this excellent little page:
> http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/cootime.html

Looks promising. Been a long time since I did any physics at all, and
I don't know if I ever did heat stuff.

> Running the numbers likely for a small pebble suggests that it does indeed
> take more than a minute for it to cool down below temperatures that would
> denaturate life. A bit of a caveat: this assumes the pebble is all a uniform
> temperature and conducts heat instantly, so it will be somewhat wrong. But
> it still shows that the timescale is not in favor of life.

So how big does it have to be? Depends on how hot it initially is, and
the cooler areas farther from the impact site are going to be blown
out with a much lower velocity, as energy is lost as it gets farther
from the impact zone.

However, If you look at the computer models they make of these things,
it looks like planting an onion... there is a puncture in the skin of
the planet, then a huge powerful explosion from inside, down below, (I
think more deeply for iron than rock impactors, but that's from
memory) and then the skin of the planet above that is pushed out with
fantastic velocity without being severely heated. So a significant
amount of ejecta, and in fact some of the stuff that would be going
the fastest would not be heated at all. I can't find the animation
that I was looking for that showed this... but you can imagine what
I'm talking about... especially when (as is most common) the asteroid
comes in at an angle.

There's just so many variables in all this. Monte carlo does seem like
the only way to go.

> *************
>
> The real problem to solve is this:
>
> Solve the spherical heat equation
> r^2 dT/dt = alpha*d/dr(r^2 dT/dr) + r^2 q'/rho c_p
> where the thermal diffusivity = k/rho c_p is alpha, k is the thermal
> conductivity, rho is the density, c_p is the specific heat capacity and q'
> is the rate of addition/removal of heat.
>
> Boundary conditions:
> r<R, t>0
> T(r,0) = T0 (say 300 K) for r < R-thickness (where thickness might be 1 mm)
> R(r,0) = T1 (say 1200 K) for R < thickness < r < R
> q' = 0 for r<R
> q' = - sigma*pi*T(R,t)^4 / c_p rho thickness
>
> What conditions on R, T1 and thickness will guarantee that T(0,t) always
> remain under a critical denaturation temperature T_d(say 500 K)?

Or side step that problem entirely, and just figure out that a lot of
stuff gets shot out really fast without heating up all that much...
but that requires modelling the impact very carefully. However a
number of people have done that sort of thing to great specificity.

> *************
>
> A quick mathematician's look at the problem and borrowing a bit from
> http://www.ewp.rpi.edu/hartford/~ernesto/S2006/CHT/Notes/ch03.pdf
> suggests that core temperatures will change roughly like Tx -
> (Tx-T0)exp(-alpha*lambda^2*t), where Tx is some hot temperature and lambda
> is the smallest eigenvalue, ~pi/R. So if that is true, the time to serious
> heating of the core will scale roughly as R^2. But again, this ignores the
> radiative cooling issue and the shape of the Fourier spectrum.
>
>
>
>> One of the most interesting factoids dancing around in my Ken Jennings
>> type mind is that water bears can survive in outer space. If a water
>> bear can do that, then why not a bacteria? It could just go into a
>> state of suspended animation... no need to reproduce, or keep extra
>> junk around. One worry is the degradation of DNA in the radiation of
>> space over thousands of years. That one is probably worthy of some
>> math by someone smarter than me. :-)
>
>
> Yup, DNA degradation is likely the big problem. To be honest, I think launch
> due to big impacts is less of a problem: if it is possible at all, the
> amount of mass launched and the number of cells are going to be large. But
> then they will drift around for potentially millions of years.

And be subjected to the vicissitudes of interstellar radiation. I
would assume (big assumption???) that most of the radiation in our
vicinity actually comes from the sun. Most of the articles I could
find on the subject seemed to talk about solar behavior with respect
to radiation. So perhaps interstellar space is somewhat less
radioactive than close to stars. Though of course you could pass by
some really nasty neighbors in a few million years.

> In most papers I have read the idea is that bacteria on the surface of
> grains are going to get killed quickly, but bacteria inside are fairly safe.
> Of course, that might be biased because the papers are typically written by
> pro-panspermia people.

Well, yeah... who knows how this stuff really works.

> I guess the relation to look at is something like this: radiation will
> penetrate into the material with some decay length lambda, so over time T
> cells at depth d will have received a dose of D_0*exp(-lambda*d)*T. So a
> cell at the core will survive until its dose reaches D_max, at time T_max =
> D_max/(D_0*exp(-lambda*R)). D_max for Deinococcus radiodurans is 5,000 Gray,
> although I am uncertain that relates to spores or the living bacterium.
> Lambda depends on the type of radiation; UV mostly affects the surface (a
> few hundred microns in basalt,
> http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1101&context=star
> ), while cosmic rays go deeper (64 cm for typical rocks on Rarth, according
> to
> http://www.geo.cornell.edu/geology/classes/Geo656/656notes03/656%2003Lecture13.pdf
> ). D_0 in the solar system is on the order of 0.1 Gray per year
> http://en.wikipedia.org/wiki/Health_threat_from_cosmic_rays
> http://www.srl.caltech.edu/ACE/ASC/DATA/bibliography/ICRC2005/usa-mewaldt-RA-abs1-sh35-oral.pdf
> (I am here ignoring the difference between Grays and Sievert dose
> equivalents - Bad Anders! Bad Anders! - but I don't think I know how to
> estimate it properly for bacterial spores...)
> So, putting it all together: T_max = 5000/(0.1*exp(-R*0.64)) years. For
> R=0.01 pebbles T_max is 50,000 years. For R=0.1 rocks T_max is 53,000 years.
> For R=1 m boulders T_max is 95,000 years. For big R=10 m boulders T_max is
> 30 million years.

On the biology side of things though... Bacteria are MUCH less
susceptible to radiation damage than Eukaryotes. Our DNA has the
protection of the nuclear sack, and so it has lost some of the ability
that prokaryotic cells have for ongoing DNA repair. So the take home
message here is that prokaryotes are much more likely to have come
from outer space than eukaryotes. And since it did take a long time
for the eukaryotes to emerge on earth, that is consistent with the Law
of Accelerating returns whereas the sudden appearance of the
prokaryotes seems rather sudden.

> Conclusion: bigger is better.

Not so fast. Bigger is only better in terms of survival... but not
necessarily in terms of getting there. Bigger = slower.

> Especially since damage and cell death is a
> random (Poisson) process: more cells means that some are more likely to be
> lucky - expect to find some viable spores beyond a few multiples of T_max.

You only need to get one or just a few there...

> Since the number of cells likely scales as some power of volume (why a
> power? fractal distribution!) and the earlier discussion shows that surface
> heating is less likely to kill everything in big boulders, big is good.
>
> Of course, big is also likely to be rare, as the earlier power law argument
> pointed out. This might be another reason why relatively low velocity
> impactors on light icy moons produce more viable spores than hits on
> terrestrials. KT impactors are rare, hot and tend to spray short-lived
> vehicles for spores, while small impacts on tiny moons are common, cold and
> can launch big chunks.

But moons aren't very good for life, in general... And just because
big impactors are now rare here, remember they weren't always rare
here... and they might not be quite as rare in solar systems without
gas giants.

> OK, My work here is done. Time to run off and give a lecture. Wheeeee!
>
> (As you can tell, I got good morning coffee today :-) )

Yeah, I can tell you are into this. Sounds like fun stuff to send
students chasing off after... LOL  They could have fun with it. Maybe
a Panspermia seminar...

-Kelly