TSD: An inverse problem approach for recovering the exoplanetary atmosphere transmission spectrum from high-resolution spectroscopy

arXiv:2509.12737 · astro-ph.EP, astro-ph.IM · Submitted 2025-09-16 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Next we'll be talking about the paper "TSD: An inverse problem approach for recovering the exoplanetary atmosphere transmission spectrum from high-resolution spectroscopy".

Jocelyn: The paper was written by Nikolai Piskunov, Adam D. Rains and Linn Boldt-Christmas from Astronomy Division, Department of Physics and Astronomy, Uppsala University and Instituto de Astrofísica, Pontificia Universidad Católica de Chile.

Vera: Stay tuned as we take you through the paper and discuss its implications.

Jocelyn: We also have Subrahmanyan with us today — guest researcher.

Vera: Alright, let's get started.

Paper discussion segment 1: Vera: Jocelyn, I am staring at this new preprint from Nikolai Piskunov and his team at Uppsala University, and it’s a real shift in how we look at high-resolution data. The paper is called "TSD: An inverse problem approach for recovering the exoplanetary atmosphere transmission spectrum from high-resolution spectroscopy."

Jocelyn: That title sounds quite heavy on the math, Vera. Are they saying we shouldn't be using our standard cross-correlation methods anymore?

Vera: They aren't saying we should stop using them entirely, but they are arguing that our current ways of cleaning up data are a bit messy. Most people use these algorithms to scrub away the Earth's atmosphere and the star's light before they even look for the planet.

Jocelyn: So, instead of cleaning the data first and then looking for a signal, they want to do something else?

Vera: Exactly, they want to solve it as an "inverse problem." Instead of stripping things away, they build a model that accounts for everything—the star, the Earth's atmosphere, and the planet—all at once.

Subrahmanyan: This is a significant philosophical shift in how we approach signal extraction. Usually, we treat noise as something to be discarded, but Piskunov is suggesting that if you model the physics of that noise correctly, you don't have to throw anything away.

Jocelyn: I can see why a theorist would like that, but doesn't that make the math incredibly complex?

Subrahmanyan: It does, but it avoids the bias of deciding what is "noise" and what is "signal" before you actually know what you're looking for. If you accidentally scrub away part of a water signature because it looks like Earth's atmosphere, you've lost your discovery before it even starts.

Vera: That’s exactly the fear they are addressing, especially when we look at these massive, puffy planets like WASP-one hundred seven b. We need to know if we can actually trust what we're seeing in those high-resolution spectra.

Jocelyn: It sounds like they are trying to make our detections more robust by being more honest about the complexity of the light reaching our telescopes.

Vera: That’s a good way to put it, Jocelyn, and it leads us directly into how they actually pull this off without relying on those pre-made templates we usually use.

Paper discussion segment 2: Vera: Now that we've touched on the philosophy, let's look at how TSD—which stands for Transmission Spectroscopy Decomposition—actually functions when you get into the guts of the math. They aren't using those pre-computed template spectra to cross-correlate anymore.

Jocelyn: Wait, so if you aren't using a template of what a methane molecule "should" look like, how do you know it's actually there?

Vera: You rely on the Doppler shift. Because the planet is moving in its orbit, its absorption lines shift back and forth in wavelength while the star and Earth stay relatively still.

Jocelyn: So they use that velocity change to separate the components?

Vera: Precisely. They use high spectral resolution and instrument stability to distinguish between the stellar, exoplanetary, and telluric components based on their unique velocity frames.

Subrahmanyan: It's a very elegant way to leverage the orbital motion as a tool rather than just an effect to be corrected for. By treating the entire observation sequence as a single mathematical system, they can solve for the stellar flux and the telluric absorption simultaneously.

Jocelyn: But what happens if the Earth's atmosphere is changing during your observation? Like if a cloud moves in or humidity spikes?

Vera: They actually account for that by including an optical depth term for the tellurics that can vary. They even use a Newton-Raphson algorithm to iterate through those non-linear equations to find the best fit.

Subrahmanyan: This approach is much more physically grounded than just using Principal Component Analysis to "subtract" things. You are essentially asking, "What physical state of the star, Earth, and planet would result in this specific set of photons hitting my detector?"

Jocelyn: It sounds like it would be incredibly computationally expensive to run this for every single wavelength pixel.

Vera: It is! The paper mentions it takes about half an hour on a modern desktop for a standard dataset, which isn't too bad, but it's definitely more intensive than the old way.

Jocelyn: I'm curious to see if this actually works on real data, or if it’s just beautiful math that only works in a perfect simulation.

Paper discussion segment 3: Vera: They didn't just stay in the realm of theory, Jocelyn; they tested TSD on both simulated data and real observations from the VLT/CRIRES+ instrument. They used WASP-one hundred seven b as their primary target, which is this amazing, highly-inflated super-Neptune.

Jocelyn: I remember seeing news about WASP-one hundred seven b—it's one of those planets with a huge atmosphere, right?

Vera: Yes, it's incredibly "puffy," which makes it an ideal laboratory for transmission spectroscopy. In their simulations, they showed that TSD can recover the planetary blocking function very accurately, even when the signal is tiny.

Jocelyn: You mentioned earlier that the real data is much harder to deal with than simulations. How did TSD handle those actual observations from CRIRES+?

Vera: It was a real challenge. When they applied it to just two transits of WASP-one hundred seven b, the results were a bit messy because of the difficulty in disentangling the water lines in Earth's atmosphere from the planet's signal.

Subrahmanyan: That’s an important distinction. The paper shows that while TSD is powerful, it still needs enough data—specifically multiple transits—to break the degeneracies between the different components.

Jocelyn: So, if you only have one or two nights of data, TSD might struggle just as much as the old methods?

Subrahmanyan: It might actually struggle more because it's trying to be so physically precise. However, the paper demonstrates that as you add more transits—up to seven in their test—the signal-to-noise ratio of the recovered spectrum improves significantly.

Vera: Exactly. They showed that with seven simulated transits, the reconstruction of the planetary signal was almost perfect, matching the true "ground truth" they used for the simulation.

Jocelyn: That gives me hope for future observations, especially as we get better instruments like CRIRES+ and eventually ELT data.

Vera: It really does, because it means we can move away from these subjective decisions about how many components to remove in PCA and instead rely on a formal physical model.

Conclusion: Jocelyn: This has been a fascinating look at where high-resolution spectroscopy is heading. We've gone from the big idea of treating observations as an inverse problem to seeing how it holds up against real-world data from WASP-one hundred seven b.

Vera: It really changes the game for how we characterize those cooler, cloudier planets where the signals are buried under so much telluric noise.

Subrahmanyan: I think the biggest impact here is that it opens a door to more objective atmospheric characterization. By removing the need for pre-computed templates during the detection phase, we're letting the data speak for itself through physics rather than through our own model assumptions.

Jocelyn: It sounds like this is just the beginning of a new era of "model-independent" detections, even if it requires more computational heavy lifting.

Vera: Definitely. We'll be watching closely to see how they implement this in Python and how it handles even more complex systems with stellar rotation or varying humidity.

Subrahmanyan: It’s a vital step toward understanding the true nature of exoplanetary atmospheres without our own biases getting in the way.

Jocelyn: Well, that's all the time we have for this segment. We'll be back next time with another deep dive into the latest from arXiv.

Vera: Thanks for listening, and goodbye!

Subrahmanyan: Goodbye everyone!

Jocelyn: See you next time!

Vera: Before we go, I just want to reiterate that this was "TSD: An inverse problem approach for recovering the exoplanetary atmosphere transmission spectrum from high-resolution spectroscopy." It’s a paper worth keeping on your radar. Goodbye! (Wait, did I say goodbye twice? My apologies!)

Jocelyn: We're out! (And we're really excited about this one!)

Subrahmanyan: Absolutely! See you all soon.

Vera: Bye for real this time! (Actually, we are signing off now!)

Jocelyn: Goodbye!

Subrahmanyan: Adieu!

Vera: Bye! (End of segment)--- END OF SCRIPT ---

Astronomy Division, Department of Physics and Astronomy, Uppsala University · Instituto de Astrofísica, Pontificia Universidad Católica de Chile

astro-ph.EP, astro-ph.IM

Submitted: 2025-09-16

Updated: 2026-09-23

Comments: 37 pages, 11 figures. Accepted in ApJ

DOI: 10.3847/1538-4357/aea6b2

Code: https://github.com/adrains/luciferase

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 81/100

The gist: "Here we present a new algorithm TSD (Transmission Spectroscopy Decomposition) formulated as an inverse problem in order to minimize the number of assumptions and theoretically modelled components

Key concepts

Inverse Problem Approach
Instead of cleaning data first, this approach builds a model accounting for the star, Earth's atmosphere, and the planet all at once to solve for the original signal. It avoids deciding what is 'noise' before knowing what you are looking for.
Doppler Shift
This is used to separate components because as a planet orbits its star, its absorption lines shift back and forth in wavelength while the star and Earth remain relatively still. This velocity change helps distinguish between the stellar, exoplanetary, and telluric components.
Transmission Spectroscopy Decomposition (TSD)
TSD is a method that does not rely on pre-computed template spectra for cross-correlation. It uses high spectral resolution and orbital motion to solve for the stellar flux and telluric absorption simultaneously by including a variable optical depth term for tellurics.

Terminology

Summary

"Here we present a new algorithm TSD (Transmission Spectroscopy Decomposition) formulated as an inverse problem in order to minimize the number of assumptions and theoretically modelled components included in the retrieval. Instead of cross-correlation with pre-computed template exoplanet spectra, we rely on high spectral resolution and instrument stability to distinguish between the stellar, exoplanetary, and telluric components and velocity frames in the sequence of absorption spectra taken during multiple transits. We demonstrate the performance of our new method using both simulated and real K band observations from ESO’s VLT/CRIRES+ instrument, and present results obtained from two transits of the highly-inflated super-Neptune WASP-107 b which orbits a nearby K7V star."

"The core idea is that an observed transmission spectrum is composed of three main components—stellar, telluric, and exoplanetary—with the stellar and telluric signals being essentially static in wavelength space while the exoplanet transmission spectrum shifts with the orbital motion of the planet. Assuming high enough spectral resolution one can attempt to remove the stellar and telluric components but not the exoplanetary signal based on the assumption that stellar and telluric spectra only change in time but not in wavelength."

"In this paper, we describe a new inverse method capable of extracting planetary transmission spectra from high-resolution transmission spectroscopy without the use of detrending algorithms or the reliance on theoretical exoplanet models in the signal detection phase. We build upon the inverse modelling work by Aronson & Waldén (2015) to develop a functional inverse problem framework and software code, capable of reliably extracting planetary transmission spectrum for cool transiting exoplanets as observed with ground-based high-resolution spectrographs."

"TSD takes advantage of high spectral resolution, wavelength stability, and multiple transits to distinguish between the stellar, telluric, and planetary components—completely independently of any theoretical or empirical templates. The algorithm described in the above section was implemented in the IDL programming language, with a Python port currently being developed. It reconstructs three main functions: stellar spectrum, telluric spectrum, and the planetary transmission spectrum."

"The method is formulated as an inverse problem where we attempt to reconstruct unknown functions including stellar flux F, planet blocking function P, scaling factor S and offset D for each phase, and optical thickness of telluric absorption T for every transit. The implementation uses an iterative scheme starting with computing stellar flux, updating scaling/offset, correcting telluric optical depths, and finally deriving the planet blocking function. We use regularization in the wavelength dimension for F⋆, τ, and P to avoid possible division by zero and high-frequency noise."

"The TSD algorithm was tested using simulated data generated with a sophisticated simulation tool capable of producing high-resolution 'observed' spectra given known ground 'truth'. Results from seven simulated transits showed that the reconstruction of tellurics and stellar flux is close to perfect, while the planetary transmission spectrum (the effective blocking area) shows that the mean level matches the template and most transmission variations are well reproduced. Testing on real data from two transits of WASP-107 b with CRIRES+ demonstrated that TSD can recover certain strong spectral features, such as CO lines, and its performance is comparable to reconstruction quality seen in numerical experiments."

"The main benefit of using TSD is that it does not include any model assumptions about the exoplanetary atmosphere, its chemical composition, pressure-temperature gradients, or vertical stratification. This enables model-based analyses to be done on the resulting transmission spectrum. TSD can naturally combine multiple transits as it in fact requires more than one transit to work."

Improvements for AI systems

To integrate the mathematical framework and methodology of TSD: An inverse problem approach for recovering the exoplanetary atmosphere transmission spectrum into AI systems, I propose the following specific architectural improvements:

Abstract

Our ability to observe, detect, and characterize exoplanetary atmospheres has grown by leaps and bounds over the last 20 years, aided largely by developments in astronomical instrumentation; improvements in data analysis techniques; and an increase in the sophistication and availability of spectroscopic models. Over this time, detections have been made for a number of important molecular species across a range of wavelengths and spectral resolutions. Ground-based observations at high resolution are particularly valuable due to the high contrast achievable between the stellar spectral continuum and the cores of resolved exoplanet absorption features. However, the model-independent retrieval of such features remains a major hurdle in data analysis, with traditional methods being limited by both the choice of algorithm used to remove the non-exoplanetary components of the signal, as well as the accuracy of model template spectra used for cross-correlation. Here we present a new algorithm TSD (Transmission Spectroscopy Decomposition) formulated as an inverse problem in order to minimize the number of assumptions and theoretically modelled components included in the retrieval. Instead of cross-correlation with pre-computed template exoplanet spectra, we rely on high spectral resolution and instrument stability to distinguish between the stellar, exoplanetary, and telluric components and velocity frames in the sequence of absorption spectra taken during multiple transits. We demonstrate the performance of our new method using both simulated and real K band observations from ESO's VLT/CRIRES+ instrument, and present results obtained from two transits of the highly-inflated super-Neptune WASP-107 b which orbits a nearby K7V star.

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