🔭 astrophysics

Present-day stellar constraints leave multiple high-energy histories for TOI-700 and LHS 1140

This study demonstrates that for temperate exoplanets TOI-700 and LHS 1140, present-day stellar observations are insufficient to uniquely determine their high-energy evolutionary histories, as multiple distinct cumulative X-ray, EUV, and wind exposure tracks can converge to identical current stellar states.

Original authors: Yuzhan Zhang

Published 2026-08-18

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CC BY 4.0

Original authors: Yuzhan Zhang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

To understand the fate of a planet, we must first understand the life of its star. Stars are not static beacons; they are dynamic engines that change as they age. When a star is young, it spins rapidly and acts like a stormy, energetic parent, bombarding its nearby planets with intense bursts of high-energy radiation and stellar winds. As the star ages, it slows its spin, and this violent activity settles down into a calmer, more predictable state. Scientists have long known that a planet's atmosphere is shaped by the total amount of this energy it receives over billions of years, not just by what the star is doing right now. This creates a difficult puzzle for astronomers studying temperate worlds around small, red stars. They can measure how fast a star spins today and how active it is in the present moment, but they cannot directly see the star's past. Two stars might look identical today, yet one could have spent its youth as a raging beast while the other was a gentle giant. If we cannot tell the difference between these two histories, we cannot accurately calculate how much energy a planet has endured, which is essential for knowing if it could still hold an atmosphere or support life.

A recent study by independent researcher Yuzhan Zhang tackles this problem by focusing on two specific planetary systems: TOI-700 and LHS 1140. Both systems host Earth-sized planets in the habitable zone, the region where liquid water could exist. The researcher asked a simple but profound question: If we only know the current spin and activity of these stars, how much can we really know about their violent youth? To answer this, the study did not try to guess the single most likely history for each star. Instead, it used computer models to generate thousands of possible pasts for each star that all end up looking exactly like the stars we see today. By comparing these different paths, the study revealed a surprising truth: knowing a star's current state leaves a huge amount of uncertainty about its past.

For the star TOI-700, the analysis found 194 different possible histories that all match its current rotation speed. While these histories agree on the star's current energy output to within a very small margin, they tell wildly different stories about the past. The total amount of high-energy radiation the planet TOI-700 d would have received over its lifetime varies by a factor of 2.65 across these different scenarios. In some histories, the planet was bathed in intense radiation for a long time; in others, the exposure was much lower. The total amount of stellar wind hitting the planet varies by a factor of 2.73. This means that even with perfect knowledge of the star today, we cannot pin down the total energy dose the planet received without knowing more about its specific past. The same pattern appeared for the star LHS 1140, though the uncertainty was slightly smaller. Among 97 possible histories that match its current slow spin, the total radiation exposure varied by a factor of 1.57, and the wind exposure varied by a factor of 1.54.

The study also tested whether other pieces of information could solve this puzzle. For LHS 1140, astronomers have a direct measurement of its current X-ray brightness. The researchers checked if this measurement could help distinguish between the different possible histories. They found that it could not. All 97 of the possible pasts predicted almost the exact same X-ray brightness for the star today. This means that measuring the X-rays again would not help us figure out which of the many possible histories actually happened; it would only tell us if the computer models used to predict the X-rays are accurate. The study suggests that the X-ray measurement is useful for checking the model, but it is useless for narrowing down the star's history.

The only way to significantly reduce this uncertainty, the study shows, is to know the star's age with much greater precision than we currently do. The researchers simulated what would happen if we knew the age of these stars within a range of 100 million years. For the LHS 1140 system, this small window of time would shrink the uncertainty in the total radiation exposure down to a factor of just 1.06, effectively solving the problem. For TOI-700, it would reduce the uncertainty significantly as well, though some ambiguity would remain because the star could be slightly more or less massive, and each mass has its own set of possible histories. This highlights a critical gap in our knowledge: we need better ways to measure the ages of these old, quiet stars. Without that information, the total energy budget of these potentially habitable worlds remains a matter of guesswork.

The findings serve as a caution against assuming we can simply look at a star today and work backward to its past. The path a star takes to reach its current state is not unique. A star that is calm now could have been a fierce source of radiation for billions of years, or it could have been relatively mild. This uncertainty matters deeply for understanding the atmospheres of planets like TOI-700 d and LHS 1140 b. If we assume a single, smooth history for these stars, we might be calculating the wrong amount of atmospheric loss, leading us to incorrect conclusions about whether these worlds are truly habitable. The study concludes that to truly understand these planets, we must stop treating the star's current state as a complete record of its life. Instead, we must acknowledge that multiple, very different high-energy histories are compatible with the stars we see today, and we need new observations to tell them apart.

Technical Summary: Present-day stellar constraints leave multiple high-energy histories for TOI-700 and LHS 1140

Problem Statement
The atmospheric evolution of temperate exoplanets is driven by the time-integrated X-ray, extreme-ultraviolet (XUV), and stellar-wind forcing from their host stars. However, host stars are typically characterized only by present-day measurements. Because stellar rotation and magnetic activity are coupled, stars of the same mass can follow divergent XUV trajectories during their youth before converging to similar states as they spin down. This convergence creates an inverse problem: distinct cumulative high-energy histories can result in indistinguishable present-day stellar states. Previous work suggests that while planetary atmospheres in close-in H/He-rich systems might retain a record of this integrated exposure, temperate terrestrial planets (like TOI-700 d and LHS 1140 b) do not necessarily offer a monotonic record of past XUV exposure due to complex atmospheric and surface processes. Consequently, treating such planets as calibrated "chronometers" risks replacing stellar-history uncertainty with unconstrained planetary model assumptions. This study isolates the stellar component of the problem to determine what present-day stellar constraints alone reveal about the cumulative forcing experienced by these two systems.

Methodology
The study utilizes the rotation, X-ray, EUV, and wind evolutionary tracks from Johnstone et al. (distributed via the MORS framework) as a finite set of deterministic model support. Rather than treating these tracks as samples from a population prior, the author conditions them on specific present-day constraints to identify admissible histories.

System Conditioning:
- TOI-700: The 0.40 and 0.45 $M_\odot$ grids are conditioned on a stellar rotation period ( $P_{rot}$ ) of approximately 54 days, occurring after a 1.5 Gyr age lower bound.
- LHS 1140: The 0.15 and 0.20 $M_\odot$ grids are conditioned on $P_{rot} = 131 \pm 5$ days, occurring after a 5 Gyr lower bound. The study notes a qualitative discontinuity in support: 0.15 $M_\odot$ tracks fail to reach the target rotation within the model limits, while 0.20 $M_\odot$ tracks succeed.
Identified Sets: For each system, the author defines "model-conditional identified sets" of histories ( $H$ ) that satisfy the present-day constraints. They calculate the multiplicative width ( $W$ ) of the resulting cumulative EUV fluence and integrated wind mass column ( $Q$ ) across these sets.
Leverage Audits:
- Age Information: A "worst-case" audit imposes a hypothetical independent age interval ( $\Delta t$ ) to quantify how much the historical forcing range contracts.
- Present Activity: For LHS 1140, an independent X-ray measurement ( $L_X$ ) is used to test whether present observables can discriminate among the retained histories or merely test the adequacy of the forward model.
- Observation Operator: The study compares native model predictions (0.1–2.4 keV) with observed XMM data (0.2–2.4 keV), highlighting bandpass mismatches that prevent a "hard" rejection of the model without matched spectral integration.

Key Results

Partial Identification of Cumulative Forcing: Present-day rotation constraints significantly narrow the range of current EUV flux but leave the cumulative history largely unconstrained.
- TOI-700: Among 194 rotation-matched tracks, current EUV flux varies by a factor of only 1.077. However, cumulative EUV fluence spans a factor of 2.65, and cumulative wind exposure spans a factor of 2.73. This spread persists even within fixed-mass grids (e.g., 0.40 $M_\odot$ ), indicating the degeneracy is not merely an artifact of mass uncertainty.
- LHS 1140: Among 97 rotation-matched tracks (all at 0.20 $M_\odot$ ), current EUV flux is nearly indistinguishable (factor 1.0085). Yet, cumulative EUV fluence varies by a factor of 1.567, and wind column by 1.543.
Limits of Age Constraints: Independent age information provides leverage but does not fully resolve the ambiguity.
- A 100-Myr age interval reduces the worst-case cumulative-EUV width to ~1.12 for fixed-mass TOI-700 grids and ~1.064 for LHS 1140.
- However, when pooling TOI-700 mass grids (0.40 and 0.45 $M_\odot$ ), a 100-Myr interval leaves a cumulative-EUV width of 1.731, demonstrating that structural ambiguity (mass-slice differences) persists even with precise timing.
Diagnostic vs. Discriminatory Power of X-ray Data: The independent X-ray measurement for LHS 1140 ( $L_X \approx 1.34 \times 10^{26}$ $L_{X} \approx 1.34 \times 1 0^{26}$ erg s $^{-1}$ $^{- 1}$ ) is largely uninformative for ranking the 97 retained histories. The native model predicts a narrow range of $L_X$ $L_{X}$ (spanning only 0.00382 dex) for all rotation-matched tracks, showing weak correlation with cumulative EUV (Pearson $r = -0.113$ $r = - 0.113$ ).
- The discrepancy between the model's predicted $L_X$ ( $\sim 3.5 \times 10^{26}$ erg s $^{-1}$ ) and the observation suggests a failure in the forward model (e.g., rotation-activity mapping or spectral integration) rather than a selection of a specific historical track.
- A "hard" rejection of all 97 tracks based on raw luminosity values is premature due to bandpass non-equivalence (0.1–2.4 keV vs. 0.2–2.4 keV) and the lack of a matched observation operator.

Significance and Claims
The paper argues for a conceptual separation of three distinct questions often collapsed into a single "best history" calculation:

Admissibility: Does a track reach the present state?
Model Adequacy: Does the forward model reproduce independent observables (like $L_X$ )?
Historical Identification: Is the integrated forcing uniquely identified?

The study demonstrates that satisfying the first two conditions does not guarantee the third. A measurement decisive for checking a model (like current $L_X$ ) may carry almost no leverage on the historical integral. Conversely, orthogonal information (like precise age) is required to contract the set of historical forcing scenarios.

The author concludes that current stellar data alone cannot uniquely determine the high-energy history of TOI-700 or LHS 1140. Propagating a single "convenient" stellar trajectory through planetary atmospheric models yields precise answers conditioned on histories that the stellar data did not uniquely select. Therefore, future observational goals should prioritize measurements that distinguish histories with different cumulative exposures or improve the forward models used to interpret them, rather than relying on simple scaling of present-day states. The study remains intentionally limited to two systems and one family of rotation-conditioned tracks, cautioning against generalizing the specific spread factors to all M dwarfs.

Technical Summary: Present-day stellar constraints leave multiple high-energy histories for TOI-700 and LHS 1140

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