arXiv subjects

Jacob Lustig-Yaeger

Publications and source records attributed to Jacob Lustig-Yaeger.

At least 37 records · Page 2Linked to original sources

arXiv2026

Oxygenated False Positive Biosignatures in Mars-like Exoplanet Atmospheres

Oxygen is a well-studied biosignature. Studying potential abiotic pathways for O2 build-up in exoplanet atmospheres is essential for evaluating whether the detection of O2 would constitute a biosignature detection on other worlds. Previous modeling efforts in the literature demonstrated that detectable abiotic O2 and O3 can be produced through CO2 photolysis for rocky planets around M dwarf stars. Building on modeling approaches from previous studies, we use photochemical simulations to reassess the conditions under which O2 and O3 may accumulate through similar photochemical mechanisms. Using a Mars-like atmospheric composition and planetary parameters, we vary the hydrogen mole fraction to assess how changes in HOx chemistry can affect the resulting accumulation of abiotic O2 and O3. Across the range of hydrogen mole fractions explored, we obtain a maximum O2 abundance of ~2.7% for H = 0.0065 ppm, about an order of magnitude lower than reported in the literature. This reduction is consistent with the elevated water vapor abundance adopted in our simulations, which enhances HOx-driven recycling of CO and O and thereby suppresses the accumulation of O2 and O3. Our improved understanding of how this cycle results in atmospheric false positive biosignatures in crucial towards developing future exoplanet characterization strategies.

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arXiv2026

High Tide or Riptide on the Cosmic Shoreline? A Water-Rich Atmosphere or Stellar Contamination for the Warm Super-Earth GJ~486b from JWST Observations

Planets orbiting M-dwarf stars are prime targets in the search for rocky exoplanet atmospheres. The small size of M dwarfs renders their planets exceptional targets for transmission spectroscopy, facilitating atmospheric characterization. However, it remains unknown whether their host stars' highly variable extreme-UV radiation environments allow atmospheres to persist. With JWST, we have begun to determine whether or not the most favorable rocky worlds orbiting M dwarfs have detectable atmospheres. Here, we present a 2.8-5.2 micron JWST NIRSpec/G395H transmission spectrum of the warm (700 K, 40.3x Earth's insolation) super-Earth GJ 486b (1.3 R$_{\oplus}$ and 3.0 M$_{\oplus}$). The measured spectrum from our two transits of GJ 486b deviates from a flat line at 2.2 - 3.3 $σ$, based on three independent reductions. Through a combination of forward and retrieval models, we determine that GJ 486b either has a water-rich atmosphere (with the most stringent constraint on the retrieved water abundance of H2O > 10% to 2$σ$) or the transmission spectrum is contaminated by water present in cool unocculted starspots. We also find that the measured stellar spectrum is best fit by a stellar model with cool starspots and hot faculae. While both retrieval scenarios provide equal quality fits ($χ^2_ν$ = 1.0) to our NIRSpec/G395H observations, shorter wavelength observations can break this degeneracy and reveal if GJ 486b sustains a water-rich atmosphere.

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arXiv2026

GEMS JWST: Transmission spectroscopy of TOI-5205b reveals significant stellar contamination and a metal-poor atmosphere

Recent discoveries of transiting giant exoplanets ($R_p\gtrsim8\mathrm{~R_\oplus}$) around M dwarfs (GEMS) present an opportunity to investigate their atmospheric compositions and explore how such massive planets form around low-mass stars contrary to the prediction from formation models. We present the first transmission spectra of TOI-5205b, a short-period ($P=1.63~\mathrm{days}$) Jupiter-like planet ($M_p=1.08~\mathrm{M_J}$ and $R_p=0.94~\mathrm{R_J}$) orbiting an M4 dwarf ($M_\star=0.392~\mathrm{M_\odot}$, $R_\star=0.394~\mathrm{R_\odot}$). We obtained three transits using the PRISM mode of the JWST Near Infrared Spectrograph (NIRSpec) spanning $0.6-5.3$ um. The data reveal significant stellar contamination that is evident in the light curves as spot-crossing events and in the transmission spectra as a larger transit depth at bluer wavelengths. Atmospheric retrievals demonstrate that stellar contamination from unocculted starspots and faculae is the dominant component of the transmission spectrum at wavelengths $λ\lesssim3.0$ um, reducing the sensitivity to the presence of clouds or hazes in our models and preventing detection of $\mathrm{H_2O}$. The wavelength coverage enabled a robust detection of $\mathrm{CH_4}$ and $\mathrm{H_2S}$, which have detectable molecular features between $3.0-5.0$ um. For both clear or cloudy atmospheres, Bayesian retrievals consistently favored an atmosphere with sub-solar metallicity ($3σ$ upper limit of $\log\mathrm{[M/H]}\lesssim-1.24$) and super-solar C/O ratio ($3σ$ lower limit of $\log\mathrm{[C/O]}\gtrsim0.09$), although this may partly be driven by the non-detection of water due to stellar contamination. Planetary interior models predict a bulk metallicity of 10--20\%, which is larger than the atmospheric metallicity and suggests that the interior of TOI-5205b is decoupled from its atmosphere.

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arXiv2026

Exomoons and Exorings with the Habitable Worlds Observatory II: Finding Endor with Lunar Eclipses

Giant planets in the habitable zone may host exomoons with conditions conducive to life. In this paper we describe a method by which the Habitable Worlds Observatory (HWO) could detect such moons: broadband reflected-light lunar eclipses (e.g., the moon passing into the shadow of the planet). We find that an Earth-like moon orbiting a Jovian-size planet at 1au can outshine its host planet near 1 micron, producing frequent (days time-scale) lunar eclipses with depths of order 50%. We determine that single eclipse events out to $\sim$12pc may be detectable for Earth-like moons around giant planets, down to $0.9R_\oplus$. Detection of smaller moons, $\sim$0.5$R_\oplus$ (corresponding to about the size of Mars or Ganymede), may be possible, but would generally require multiple events for most systems. These several-hour events provide a clear pathway to detecting habitable moons with HWO, given sufficient stare-time on each system to detect lunar eclipses. The occurrence rate of habitable exomoons remains unconstrained, however, making the ultimate yield uncertain. HWO will be capable of placing the first meaningful constraints on the frequency of habitable exomoons around giant planets; if it is non-negligible, HWO could also search for life on these worlds, possibly with lunar eclipse spectroscopy.

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arXiv2026

Habitable Worlds Observatory (HWO): Living Worlds Community Working Group: The Search for Life on Potentially Habitable Exoplanets

The discovery of a biosphere on another planet would transform how we view ourselves, and our planet Earth, in relation to the rest of the cosmos. We now know Earth is one planet among eight circling our sun; our sun is part of a swirling galaxy of over one hundred billion other suns; and our galaxy is one of untold billions in the universe. While we do not yet know how many, if any, other biospheres exist on the countless worlds orbiting countless other suns, we stand at the precipice of a new era of discovery, enabled by powerful new facilities able to peer across the light years into the atmospheres of planets similar to our own. This article is an adaptation of a science case document (SCDD) developed for the NASA Astrophysics Flagship mission the Habitable Worlds Observatory (HWO) Science, Technology, and Architecture Review Team (START) Living Worlds Community Working Group.

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arXiv2026

NASA Decadal Astrobiology Research and Exploration Strategy (NASA-DARES 2025) White Paper -- Habitable Worlds Observatory Living Worlds Science Cases: Research Gaps and Needs

Executive Summary: The Habitable Worlds Observatory (HWO) is the first astrophysics flagship mission with a key cross-divisional astrobiology science goal of searching for signs of life on rocky planets beyond our solar system. The Living Worlds Working Group under the Science, Technology, and Architecture Review Team (START) was charged with investigating how HWO could characterize potentially habitable exoplanets orbiting stars in the solar neighborhood, search for signs of life, and interpret potential biosignatures within a false positive and false negative framework. In particular, we focused on (1) identifying biosignatures that have spectral features in the UV-Vis-NIR wavelength range and defining their measurement requirements, (2) determining additional information needed from the planet and planet system to interpret biosignatures and assess the likelihood of false positives, and (3) assembling current knowledge of likely HWO target stars and identify which properties of host stars and systems are most critical to know in advance of HWO. The Living Worlds atmospheric biosignatures science case is considered one of the key drivers in the design of the observatory. An additional 10 astrobiology science cases were developed that collectively revealed key research gaps and needs required to fully explore the observatory parameter space and perform science return analyses. Investment in these research gaps will require coordination across the Science Mission Directorate and fall under the purview of the new Division-spanning astrobiology strategy.

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arXiv2025

What's Inside Matters: The Effect of Oxygen Fugacity and Initial Volatile Abundance on the Atmospheres of the TRAPPIST-1 Planets

The TRAPPIST-1 planets have become prime targets for studying the atmospheric and geophysical properties of planets around M-dwarf stars. To effectively identify their atmospheric composition, we first must understand their geological evolution. For this study, we focus on enhancing an existing atmosphere-interior exchange model by incorporating additional geological processes relevant to rocky planets. We have extended the model to include the carbon cycle, which enables the model to track four key gas species - CO$_2$, CO, H$_2$O, and H$_2$ - across four planetary reservoirs: the mantle, plate, ocean, and atmosphere. Major features added include surface temperature calculations which are crucial for the carbon cycle, oxygen fugacity as a planetary interior parameter in the model, and oxidation reactions and diffusion-limited escape calculations to the atmosphere portion of the model. We successfully validated the model for Earth and applied this model to study the effect of oxygen fugacity and initial water abundance on TRAPPIST-1 d, e and f. Our results for present-day abundances show that oxygen fugacity significantly affects the partial pressures of H$_2$ and CO$_2$ for all three planets with minor effects for CO on two of the planets. We also found that H$_2$ is strongly dependent on water mass fraction (WMF). The addition of atmospheric processes produced a significant difference in the H$_2$ and CO abundances at present-day. These results highlight the importance of considering interior parameters to be able to further constrain the geological evolution of these planets and effectively put atmosphere observations into context.

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arXiv2025

JWST-TST DREAMS: The Nightside Emission and Chemistry of WASP-17b

Theoretical studies have suggested using planetary infrared excess (PIE) to detect and characterize the thermal emission of transiting and non-transiting exoplanets, however the PIE technique requires empirical validation. Here we apply the PIE technique to a combination of JWST NIRSpec G395H transit and eclipse measurements of WASP-17b, a hot Jupiter orbiting an F-type star, obtained consecutively (0.5 phase or 1.8 days apart) as part of the JWST-TST program to perform Deep Reconnaissance of Exoplanet Atmospheres through Multi-instrument Spectroscopy (DREAMS). Using the in-eclipse measured stellar spectrum to circumvent the need for ultra-precise stellar models, we extract the first JWST nightside emission spectrum of WASP-17b using only transit and eclipse data thereby performing a controlled test of the PIE technique. From the WASP-17b nightside spectrum, we measure a nightside equilibrium temperature of $1005 \pm 256$ K and find tentative evidence for nightside SO2 absorption ($\ln B = 1.45$, $2.3σ$). In context with the dayside, the temperature of the nightside is consistent with (1) previous eclipse mapping findings that suggest relatively inefficient day-night heat transport, and (2) a non-zero bond albedo of $0.42^{+0.06}_{-0.10}$. SO2 on the nightside, if confirmed, would represent the first direct evidence for transport-induced chemistry, matching previous model predictions, and opening a new door into the 3D nature of giant exoplanets. Our results suggest that PIE is feasible with JWST/NIRSpec for two epochs separated in time by significantly less than the rotation period of the host star.

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arXiv2025

Identifying rocky planets and water worlds among sub-Neptune-sized exoplanets with the Habitable Worlds Observatory

Astronomers are debating whether the plentiful "sub-Neptune" exoplanets -- worlds a bit larger than Earth but smaller than Neptune -- are predominantly rocky planets, water-rich "ocean worlds," or gas-enshrouded mini-Neptunes. This question is crucial because such sub-Neptune-sized planets are among the most common in our galaxy, yet we have no analog in our own solar system, making them a key to understanding planet formation and diversity. It also directly impacts the search for habitable worlds: larger-than-Earth planets with solid surfaces or oceans could support life, whereas gas-rich mini-Neptunes likely cannot. However, distinguishing these types using only a planet's mass and radius is very challenging, because different compositions can produce similar densities, leaving a world's nature ambiguous with current data. The proposed Habitable Worlds Observatory (HWO), a future NASA flagship telescope, offers a solution. HWO could directly image and spectroscopically analyze starlight reflected from 50~100 sub-Neptunes around nearby stars, aiming to reveal their atmospheric compositions and potential surfaces. Using visible and near-infrared spectroscopy along with sensitive polarimetry, HWO would detect atmospheric gases (such as water vapor, methane, and carbon dioxide) and search for telltale surface signatures, including rock absorption features and the characteristic reflectivity patterns of oceans. By analyzing these signals, we could determine whether sub-Neptunes are large rocky planets or water worlds rather than gas-dominated mini-Neptunes. Crucially, expanding the search beyond Earth-sized planets to include these abundant sub-Neptunes may uncover entirely new classes of potentially habitable worlds, directly advancing HWO's mission to identify and characterize planets that could support life.

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arXiv2025

K2-18b Does Not Meet The Standards of Evidence For Life

K2-18b, a temperate sub-Neptune, has garnered significant attention due to claims of possible biosignatures in its atmosphere. Low-confidence detections of dimethyl sulfide (DMS) and/or dimethyl disulfide (DMDS) have sparked considerable debate, primarily around arguments that their absorption features are not uniquely identifiable. Here, we consider all five questions from the astrobiology standards of evidence framework, starting with: Have we detected an authentic signal? To answer this, we analyzed publicly-available JWST observations of K2-18b using independent data reduction and spectral retrieval methodologies. Our comprehensive set of reductions demonstrates that the MIRI transit spectrum is highly susceptible to unresolved instrumental systematics. Applying different wavelength binning schemes yields a potpourri of planet spectra that then lead to a wide assortment of atmospheric interpretations. Consequently, we offer recommendations to help minimize this previously-underappreciated instrument systematic in future MIRI reductions of any exoplanet. While the MIRI binning scheme adopted by Madhusudhan et al. (2025) favors the presence of DMS/DMDS in K2-18b, we find that 87.5% of retrievals using our preferred MIRI binning scheme do not. When considering the full, 0.7 - 12 micron transit spectrum, we confirm the detection of CH4 and favor CO2, and find the presence of DMS and C2H4 to be interchangeable. Moreover, we find that the tentative presence of large features in the MIRI transit spectrum is in tension with the more robust, yet smaller, features observed in the near IR. We conclude that red noise -- rather than an astrophysical signal -- plagues the mid-IR data and there is, as yet, no statistically significant evidence for biosignatures in the atmosphere of K2-18b.

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arXiv2025

First JWST thermal phase curves of temperate terrestrial exoplanets reveal no thick atmosphere around TRAPPIST-1 b and c

We report JWST/MIRI 15 $μ$m phase curves of TRAPPIST-1 b and c, revealing thermal emission consistent with their irradiation levels, assuming no efficient heat redistribution. We find that TRAPPIST-1 b shows a high dayside brightness temperature (490 $\pm$ 17 K), no significantly detectable nightside emission ($F_{\rm b, Night, max}$ = $39_{-27}^{+55}$ ppm), and no phase offset -- features consistent with a low-albedo, airless ultramafic rocky surface. TRAPPIST-1 c exhibits a lower dayside brightness temperature (369 $\pm$ 23 K), and a nightside flux statistically indistinguishable from that of TRAPPIST-1 b ($F_{\rm c, Night, max}$ = $62_{-43}^{+60}$ ppm). Atmosphere models with surface pressures $\geq$1 bar and efficient greenhouse effects are strongly disfavoured for both planets. TRAPPIST-1 b is unlikely to possess any substantial atmosphere, while TRAPPIST-1 c may retain a tenuous, greenhouse-poor O$_2$-dominated atmosphere or be similarly airless with a more reflective surface. These results suggest divergent evolutionary pathways or atmospheric loss processes, despite similar compositions. These measurements tightly constrain atmosphere retention in the inner TRAPPIST-1 system.

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arXiv2025

Additional JWST/NIRSpec Transits of the Rocky M Dwarf Exoplanet GJ 1132 b Reveal a Featureless Spectrum

As an archetypal M-dwarf rocky exoplanet, GJ 1132 b has a varied history of atmospheric measurements. At 1.13 $\rm R_{\oplus}$, 1.66 $\rm M_{\oplus}$, and 580 K, it orbits a bright, slowly rotating M dwarf in a 1.6-day period, making it a prime target for characterization. In this study, we combine two JWST NIRSpec/G395H transits previously reported by May and MacDonald et al. 2023 with two new NIRSpec/G395M transits to constrain the presence of an atmosphere. This marks the first time the G395H and G395M modes have been combined for a single target, and we report no difference in the quality of data between the two modes. For rocky M-dwarf studies, G395H may still be preferred if stacking transits to utilize the high-resolution flux-calibrated stellar spectra and assess evolving stellar heterogeneity. GJ 1132 b's co-added transmission spectrum is best-fit with a flat line. A thin steam atmosphere is also consistent with the data, but this interpretation is driven almost entirely by the first transit, which suggests an increase in cool spot coverage-fraction derived from the flux-calibrated stellar spectra. This demonstrates the importance of always considering stellar heterogeneity evolution in multi-visit transits, and also the importance of a "leave-one-transit-out" approach in modeling efforts of co-added transits. We combine these results with MIRI/LRS emission data (Xue et al. 2024) to show that together, transmission and emission are consistent with only the thinnest of atmospheres. Given GJ 1132 b's age and distance from the star, a thin atmosphere is not likely stable. Therefore, the simplest explanation is that GJ 1132 b is indeed a bare rock.

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arXiv2025

Detecting Surface Liquid Water on Exoplanets

Planets with large bodies of water on their surface will have more temperate and stable climates, and such planets are the ideal places for life-as-we-know-it to arise and evolve. A key science case for the Habitable Worlds Observatory (HWO) is to determine which planets host surface liquid water. Aside from its implications for planetary climate and astrobiology, detecting surface water on terrestrial exoplanets would place important constraints on our theories of planet formation and volatile delivery. Rotational variability in the reflectance of an exoplanet may reveal surface features rotating in and out of view, including oceans. Orbital changes in reflectance and polarization, meanwhile, are sensitive to the scattering phase function of the planetary surface, including specular reflection from large bodies of water. Although these techniques are applicable to all temperate terrestrial exoplanets, we focus in this document on the directly-imaged planets that are more likely to drive the HWO coronagraph design. Identification of water oceans relies on detecting a liquid, and using other lines of evidence to narrow that liquid down to being water. Liquids have smoother surfaces than most solids, and hence exhibit specular reflection instead of diffuse reflection. In practice, this makes lakes and oceans look dark from most illumination angles, but mirror-like at glancing angles. HWO is uniquely capable of identifying surface liquid oceans via their optical properties. Given that discovering an ocean on an exoplanet would confirm its status as a habitable world, this science case is literally the raison d'etre of the Habitable Worlds Observatory.

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arXiv2025

The Magnetically Induced Radial Velocity Variation of Gliese 341 and an Upper Limit to the Mass of Its Transiting Earth-sized Planet

The Transiting Exoplanet Survey Satellite (TESS) mission identified a potential 0.88 REarth planet with a period of 7.577 days, orbiting the nearby M1V star GJ 341 (TOI 741.01). This system has already been observed by the James Webb Space Telescope (JWST) to search for presence of an atmosphere on this planet. Here, we present an in-depth analysis of the GJ 341 system using all available public data. We provide improved parameters for the host star, an updated value of the planet radius, and support the planetary nature of the object (now GJ 341 b). We use 57 HARPS radial velocities to model the magnetic cycle and activity of the host star, and constrain the mass of GJ 341 b to upper limits of 4.0 MEarth (3 sigma) and 2.9 MEarth (1 sigma). We also rule out the presence of additional companions with M sin i > 15.1 MEarth, and P < 1750 days, and the presence of contaminating background objects during the TESS and JWST observations. These results provide key information to aid the interpretation of the recent JWST atmospheric observations and other future observations of this planet.

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arXiv2024

Updated forecast for TRAPPIST-1 times of transit for all seven exoplanets incorporating JWST data

The TRAPPIST-1 system has been extensively observed with JWST in the near-infrared with the goal of measuring atmospheric transit transmission spectra of these temperate, Earth-sized exoplanets. A byproduct of these observations has been much more precise times of transit compared with prior available data from Spitzer, HST, or ground-based telescopes. In this note we use 23 new timing measurements of all seven planets in the near-infrared from five JWST observing programs to better forecast and constrain the future times of transit in this system. In particular, we note that the transit times of TRAPPIST-1h have drifted significantly from a prior published analysis by up to tens of minutes. Our newer forecast has a higher precision, with median statistical uncertainties ranging from 7-105 seconds during JWST Cycles 4 and 5. Our expectation is that this forecast will help to improve planning of future observations of the TRAPPIST-1 planets, whereas we postpone a full dynamical analysis to future work.

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arXiv2024

Toward Exoplanet Transit Spectroscopy Using JWST/MIRI's Medium Resolution Spectrometer

The Mid-Infrared Instrument (MIRI)'s Medium Resolution Spectrometer (the MRS) on JWST has potentially important advantages for transit and eclipse spectroscopy of exoplanets, including lack of saturation for bright host stars, wavelength span to longward of 20 microns, and JWST's highest spectral resolving power. We here test the performance of the MRS for time series spectroscopy by observing the secondary eclipse of the bright stellar eclipsing binary R Canis Majoris. Our observations push the MRS into saturation at the shortest wavelength, more than for any currently known exoplanet system. We find strong charge migration between pixels that we mitigate using a custom data analysis pipeline. Our data analysis recovers much of the spatial charge migration by combining detector pixels at the group level, via weighting by the point spread function. We achieve nearly photon-limited performance in time series data at wavelengths longward of 5.2 microns. In 2017, Snellen et al. suggested that the MRS could be used to detect carbon dioxide absorption from the atmosphere of the temperate planet orbiting Proxima Centauri. We infer that the relative spectral response of the MRS versus wavelength is sufficiently stable to make that detection feasible. As regards the secondary eclipse of this Algol-type binary, we measure the eclipse depth by summing our spectra over the wavelengths in four channels, and also measuring the eclipse depth as observed by TESS. Those eclipse depths require a temperature for the secondary star that is significantly hotter than previous observations in the optical to near-IR, probably due to irradiation by the primary star. At full spectral resolution of the MRS, we find atomic hydrogen recombination emission lines in the secondary star, from principal quantum levels n = 7, 8, 10, and 14.

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arXiv2024

A roadmap for the atmospheric characterization of terrestrial exoplanets with JWST

Ultra-cool dwarf stars are abundant, long-lived, and uniquely suited to enable the atmospheric study of transiting terrestrial companions with JWST. Amongst them, the most prominent is the M8.5V star TRAPPIST-1 and its seven planets. While JWST Cycle 1 observations have started to yield preliminary insights into the planets, they have also revealed that their atmospheric exploration requires a better understanding of their host star. Here, we propose a roadmap to characterize the TRAPPIST-1 system -- and others like it -- in an efficient and robust manner. We notably recommend that -- although more challenging to schedule -- multi-transit windows be prioritized to mitigate the effects of stellar activity and gather up to twice more transits per JWST hour spent. We conclude that, for such systems, planets cannot be studied in isolation by small programs, but rather need large-scale, jointly space- and ground-based initiatives to fully exploit the capabilities of JWST for the exploration of terrestrial planets.

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arXiv2024

Exomoons & Exorings with the Habitable Worlds Observatory I: On the Detection of Earth-Moon Analog Shadows & Eclipses

The highest priority recommendation of the Astro2020 Decadal Survey for space-based astronomy was the construction of an observatory capable of characterizing habitable worlds. In this paper series we explore the detectability of and interference from exomoons and exorings serendipitously observed with the proposed Habitable Worlds Observatory (HWO) as it seeks to characterize exoplanets, starting in this manuscript with Earth-Moon analog mutual events. Unlike transits, which only occur in systems viewed near edge-on, shadow (i.e., solar eclipse) and lunar eclipse mutual events occur in almost every star-planet-moon system. The cadence of these events can vary widely from ~yearly to multiple events per day, as was the case in our younger Earth-Moon system. Leveraging previous space-based (EPOXI) lightcurves of a Moon transit and performance predictions from the LUVOIR-B concept, we derive the detectability of Moon analogs with HWO. We determine that Earth-Moon analogs are detectable with observation of ~2-20 mutual events for systems within 10pc, and larger moons should remain detectable out to 20pc. We explore the extent to which exomoon mutual events can mimic planet features and weather. We find that HWO wavelength coverage in the near-IR, specifically in the 1.4 micron water band where large moons can outshine their host planet, will aid in differentiating exomoon signals from exoplanet variability. Finally, we predict that exomoons formed through collision processes akin to our Moon are more likely to be detected in younger systems, where shorter orbital periods and favorable geometry enhance the probability and frequency of mutual events.

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