Decoding Alien Atmospheres & The Role Of Machine Learning

Is it really feasible that ten years from now,  data for the atmospheric physics  of other worlds will be available by the terabyte?   I am writing  about the spectra of alien atmospheres coming in by the hundreds of worlds, with the data of a higher quality than currently possible.   The answer is evidently  'yes' according to a recent report in EOS: Space Science Journal, p.7. 

The gist of it is fairly simple:An upcoming study in Monthly Notices of the Royal Astronomical Society documented a machine learning algorithm against the current gold standard process for decoding exoplanet atmospheres, i.e.  to see whether the algorithm could tackle this future big-data problem.

The current front-runner for best deciphering a planet’s atmospheric spectrum is called atmospheric retrieval. It uses statistical inference to calculate the likelihood that given an observed spectrum, an exoplanet’s atmosphere will possess a certain composition, temperature, level of cloud cover, and heat flow.   In the latter one would want to look at, for example, Rayleigh scattering in concert with radiative transport in standard gray atmosphere models, e,g.  looking at the applicable equation for radiative transport:

 -dI/dt (1/k r ) = I – J

Where k is a mass scattering coefficient, r  is the molecular density (e.g. in cloud cover) and J is the vector source function for a specific intensity I.

The technique has so far proven very reliable but can be computationally expensive.  (No wonder  considering what is demanded of it!)

The algorithm compares each artificial spectrum with the real one and chooses the closest match. This is a new and modified application of the random forest algorithm for exoplanetary atmospheres that was originally developed by astronomers at the University of Bern in Switzerland.

As exoplanet atmosphere research moves into the big-data era, machine learning will become an increasingly important research tool scientists should be trained to use, according to Nikku Madhusudhan.. Some graduate programs are already integrating more data science learning into students’ training. (Co-author Matthew Nixon also has doctorate work supported by one such program in the United Kingdom.)

This study adds to a growing effort by exoplanet scientists to find an efficient and more effective way to handle the upcoming deluge of atmospheric data.  In the words of Daniel Angerhausen, an astrophysicist at ETH Zürich in Switzerland who was not involved with this research:

 “It is great to see a growing group in the community using machine learning methods and cross-checking each other’s results and claims,”

Missions like JWST and ARIEL are first at bat, but Angerhausen is also thinking about missions that will come after those. Astronomers will need to strategize the most efficient ways to observe interesting targets. As   Angerhausen  added:

“This problem is predestined for a [machine learning] approach.  A random forest approach is just the “tip of the iceberg” for algorithms to try."


“On the other hand,” Madhusudhan added, “it also needs to be recognized that while machine learning is a great research tool in various areas, there are also important areas of research where other numerical, statistical, and analytic approaches are more suitable for some important problems. Therefore, I believe the right balance needs to be met while integrating machine learning into graduate programs in the right research areas.”

In the words of Ingo Waldmann - an astrophysicist at University College London:

"Perhaps unsurprisingly, the more detailed the model, the longer it takes to compute its results. Today we are rapidly reaching a stage where our traditional techniques become too slow to compute these increasingly complex models."

Adding:

“Machine learning may never replace an atmospheric expert,  but I’m certain that artificial intelligence will certainly play a role as a helping hand.”

Given human inputs will be inadequate to the task of recovering terabytes of data on extraterrestrial planetary atmospheres, this observation  can be said to be spot on.   What will be needed is the actual implementation of A.I. and its passing a number of major tests for analyzing exoplanet atmospheres.



See Also:
https://www.eurekalert.org/pub_releases/2020-02/uoc-lec022520.php

and:

https://arxiv.org/abs/1904.03190

And this lecture on exoplanet atmospheres::

https://www.youtube.com/watch?v=XaoceffJSKQ

Simple Solar Radiative Transfer (1)

In an earlier blog from two years ago, I examined some basic astrophysics applied to stellar atmospheres, especially the simplified model known as the "gray atmosphere", e.g.

http://brane-space.blogspot.com/2010/10/introducing-some-basic-astrophysics.html

It's now useful to see how we might apply some of this material to solutions of simple solar atmosphere problems. First, a bit of preparatory material-information to supplement that contained in the above link.

a)The flux F_o coming out of the stellar surface is equal to the source function at the optical depth τ = 2/3. This is the important ‘Eddington-Barbier’ relation that paves the way for the understanding of how stellar spectra are formed.

b) Thus, the energy distribution of F_o is that of a black body corresponding to the temperature at an optical depth τ= 2/3. From this, along with some simple substitutions and integrations one finds:

π( F_o ) = σ (Teff)^4 and Teff = T(τ = 2/3)

where σ (= 5.67 x 10^-8 W m^-2 K^-4) is the Stefan-Boltzmann constant. Thus, the temperature at optical depth 2/3 must equal the effective temperature!

c) The appropriate equation of transfer in a simple, plane-parallel atmosphere would be:

dI = j dx - σ I (Θ) dx = (j - σ I (Θ)) dx

or: dI/dx = j - σ I (Θ))

where I (Θ) is the specific intensity

Or, after some further manipulation, and replacing x with τ:

(cos Θ) dI/ dτ = I (Θ) – j/ σ

This is the important equation, in terms of emergent intensity I, that embodies the conservation of radiant energy (i.e. no more radiation can flow out of a star’s surface than can be generated within it and which approaches that surface).

d) To obtain an even more improved basis for calculations entails getting the moments of the intensity, leading to J (mean intensity), H (the “net flux” or the net energy breaching the stellar surface in units of net energy per second per unit area of that surface), and K, the energy density.

The "moments of intensity" are obtained by successive integrations over an element of solid angle - defined as (A/r^2) for a sphere, for example. Thus a sphere with surface area A = 4π r^2 has solid angle (4π r^2 / r^2 ) = 4π steradians. If we are only dealing with a sliver of emergent beam of area 0.01π r^2, say, then the element of solid angle(dw) is:

dw = (0.01π r^2 / r^2 ) = 0.01π sr

Thus: J = 1/4π INT I (Θ) dw

H = 1/4π INT I (Θ)cos Θ dw

K = 1/4π INT I (Θ)cos ^2 Θ dw

e) From the preceding a simplified set of differential equations appears relating H, J, and K, i.e.

dH/ dτ = J - j/ σ

dK/ dτ = H

(Recall, τ is optical depth, not time!)

Or, more simply, 4 πH = const. So, dH/ dτ = J - j/ σ = 0, and the equation of transfer now becomes:

(cos Θ) dI/ dτ = - I + J

e)In using the Eddington approximation (which will apply to the quantities J, H and K), we will also discriminate the radiation intensity I into two components: I1 (in the forward direction) and I2 (in the backward direction). We can then write as follows:

1) J = ½(I1 + I2)

2) H = ¼( I1 - I2)

3) K = J/3

f) Now, we focus on the boundary in Fig. 1, and note that here the optical depth τ= 0, and we must have I2 = 0 also.

Since I2 = 0 then:

H = ¼ I1 and

J = ½I1

so clearly: J = 2H.

Further, K = J/3 or (½I1)/3 so K = Hτ + const.

This follows, since we had:

dK/ dC = H or dK = H dτ and we know τ= 0, hence Hτ + const. on integration.

From this it follows that:

J = H(2 + 3 τ) and K = J/3 = 2H/3

At the boundary everywhere.

And since H = ¼( I1 - I2) = const. then:

I1 (τ) = H(4 + 3τ) and I1 (τ) = 3Hτ

f) A special case occurs if the mean intensity J = B (L), the Planck function, then (since B ~ σT^4/ π):

J = H(2 + 3 τ) = σ T^4/ π

Therefore, the boundary temperature (T_o) approaches the value of the effective (or surface) temperature when τ = 0. So we have the basic relationship:

T_o ^4/ π = 2H

And: σ T^4 = σ T_o ^4/ 2 [a + 3τ]

In the limit of this approximation, Teff ^4 = 2 T_o ^4
And hence:

Teff = (2)^¼ T_o = 1.189 T_o

A Problem:

Consider the solar half-sphere and the energy going into it each second. We know on average photons are absorbed after traveling a distance with optical depth τ =1 in the propagation direction. Averaged over all directions this corresponds to a vertical optical depth of τ= 2/3. Based on this find:

a) The energy going into the half sphere each second

b) The change in (a) over each absorption and re-emission over vertical optical depth.

c) The total absorption and total emission and the relationship between then over all space.

Solution:

(a) This is just: σ(Teff)^4 = π F = 2π S = 2πI

(b) Over a vertical optical depth one has τ = 2/3, then:

2π S/ τ = π F/ (2/3) = 3π F/ 2 or:

S/ τ = 3π F/ 2 (2π) = 3F/4

c) Over all space, the total emission = 4 πS and the total absorption = 4π J, and by radiative equilibrium: 4π S = 4π J so that S = J.


Problem for Ambitious Readers:

Find each of the above for the star Eta Ophiuchi which has a (B – V) color index of -0.30.

Hint: you will need to refer to this earlier blog -
http://brane-space.blogspot.com/2011/09/tackling-intermediate-astronomy_22.html