LHS 1140 b is a potentially habitable water world

Abstract: LHS 1140 b is a small planet orbiting in the habitable zone of its M4.5V dwarf host. Recent mass and radius constraints have indicated that it has either a thick H$_2$-rich atmosphere or substantial water by mass. Here we present a transmission spectrum of LHS 1140 b between 1.7 and 5.2 $\mu$m, obtained using the NIRSpec instrument on JWST. By combining spectral retrievals and self-consistent atmospheric models, we show that the transmission spectrum is inconsistent with H$_2$-rich atmospheres with varied size and metallicity, leaving a water world as the remaining scenario to explain the planet's low density. Specifically, a H$_2$-rich atmosphere would result in prominent spectral features of CH$_4$ or CO$_2$ on this planet, but they are not seen in the transmission spectrum. Instead, the data favors a high-mean-molecular-weight atmosphere (possibly N$_2$-dominated with H$_2$O and CO$_2$) with a modest confidence. Forming the planet by accreting C- and N-bearing ices could naturally give rise to a CO$_2$- or N$_2$-dominated atmosphere, and if the planet evolves to or has the climate-stabilizing mechanism to maintain a moderate-size CO$_2$/N$_2$-dominated atmosphere, the planet could have liquid-water oceans. Our models suggest CO$_2$ absorption features with an expected signal of 20 ppm at 4.2 $\mu$m. As the existence of an atmosphere on TRAPPIST-1 planets is uncertain, LHS 1140 b may well present the best current opportunity to detect and characterize a habitable world.

• The paper presents evidence from spectral and transit analyses indicating LHS 1140 b's potential to harbor liquid water.
• It employs multi-wavelength observations and atmospheric modeling to assess the planet's habitability.
• The results suggest that LHS 1140 b is a strong candidate for future exoplanet habitability studies.

An Examination of AAS and AMS Math Symbols in LaTeX

The paper under analysis provides a comprehensive inventory of mathematical symbols and accents available within the American Astronomical Society (AAS) and American Mathematical Society (AMS) document classes for LaTeX. This inventory is structured through a series of tables categorizing these symbols and accents according to their respective functionalities in document preparation.

Structure and Content

The primary body of the paper is presented as a collection of tables, each designated to classify symbols into relevant categories such as binary operators, variable-sized symbols, delimiters, function names, Greek and Hebrew letters, text-mode and math-mode accents, national symbols, and arrows, among others. Each table pairs specific symbols with their respective LaTeX command representations, offering a direct mapping for researchers intending to leverage these functionalities in document preparation.

Numerical Results and Discussions

While the paper itself does not inherently present empirical results or hypotheses subject to traditional informatics evaluation, the comprehensive listing serves a numerical purpose by cataloging extensive symbol usage options. This taxonomy provides a vital reference point for those in computational mathematics or related fields, streamlining the process of document encoding and symbol deployment in mathematical and scientific manuscripts.

Theoretical and Practical Implications

From a theoretical perspective, the paper enhances the understanding of symbol representation in LaTeX, which is widely utilized across research disciplines for document preparation due to its robust handling of complex typographical elements. Practically, this catalog functions as an essential tool for document authors by ensuring consistent, accurate representation of mathematical notation, crucial for effectively conveying complex concepts in scholarly publications.

Speculations on Future Developments

The continued development and refinement of LaTeX packages and symbol libraries seem inevitable as computational needs evolve, potentially incorporating more symbols to cater to emerging fields requiring specialized notation. Future enhancements might also focus on user-friendly interfaces that facilitate symbol integration, reducing the need for manual reference and improving accessibility for users with varying proficiency in LaTeX.

In conclusion, while the paper under analysis is ostensibly straightforward, serving primarily as a reference, its contribution to the field cannot be understated. The precise classification and enumeration of symbols enable researchers to maintain consistency and rigor in symbolic representation, an essential component of effective scientific communication.