Planetary systems

arXiv:2601.16253v2 Announce Type: replace Abstract: This letter reports statistically significant changes in the equivalent widths of MgII and CaII lines in the dusty and polluted white dwarf WD 0106-328, based on six epochs of spectroscopy using the VLT and Keck spanning 25 yr. Furthermore, the ratio of these two equivalent widths may also vary, with a 7% probability of being constant. Between 2000 and 2025, both Mg and Ca have experienced decreases in accretion rates, of approximately 20 and 60%, respectively, but with individual variation during the interim. These metal abundance decreases are the first empirical corroboration of diffusion theory in white dwarfs, which predict sinking timescales on the order of days for this star. However, the persistent atmospheric metals require a more gradual, circumstellar process, where one possibility is viscous spreading in an ionized disk of metals, consistent with $\alpha\approx0.1$ within that formalism. The combination of optical and ultraviolet spectroscopy with the Hubble Space Telescope detects all the major rock-forming elements (O, Mg, Si, Fe), and demonstrates that Fe dominates the accreted material by mass, and that it is delivered mostly as pure metal from within a differentiated parent body. This inference is consistent with the possibility that chemically-segregated accretion may result from a combination of planetary assembly, fragmentation, disk evolution, and be observed on relatively short timescales.

arXiv:2602.09553v1 Announce Type: new Abstract: K2-18b, a sub-Neptune exoplanet located in the habitable zone of its host star, has emerged as an important target for atmospheric characterization and assessments of potential habitability. Motivated by recent interpretations of JWST observations suggesting a hydrogen-rich atmosphere consistent with Hycean-world scenarios, we conducted a coordinated, multi-epoch search for narrowband radio technosignatures using the Karl G. Jansky Very Large Array equipped with the COSMIC backend and the MeerKAT telescope with the BLUSE backend. Our observations span frequencies from 544MHz to 9.8GHz and include multiple epochs that cover at least one full orbital period of the planet. In this work, we outline, create, and apply a comprehensive post-processing framework that incorporates observatory-informed RFI masking, drift-rate filtering based on the expected dynamics of the K2-18 system, multibeam spatial discrimination, primary and secondary transit filtering (when applicable), and SNR-based excision of weak and strong spurious signals. Across all bands and epochs, no signals consistent with an astrophysical or artificial origin were identified at a limit of 10^12 to 10^13W. These non-detections allow us to place upper limits on the presence of persistent, isotropic narrowband transmitters within the K2-18 system, providing the first interferometric technosignature constraints for a Hycean-planet candidate. Our results demonstrate the efficacy of coordinated multiepoch interferometric searches and establish a methodological framework for future technosignature studies of nearby potentially habitable exoplanets.

arXiv:2601.18965v1 Announce Type: new Abstract: The MIRI Excess Around Degenerates (MEAD) Survey is a cycle 2 JWST program designed to image nearby white dwarfs with MIRI at 10 and 15 microns. This survey targeted 56 white dwarfs within 25 pc to search for mid-infrared excesses, flux deficits from collision-induced absorption, and resolved substellar companions. In this paper we present our analysis of WD 0644+025, an unusually massive white dwarf (0.95 Msun) and the MEAD target exhibiting the most significant mid-infrared excess. The observed JWST MIRI photometry shows a 7.3 sigma excess at 15 microns and a 3.6 sigma excess at 10 microns, which may be associated with either a planetary companion or a circumstellar dust disk. This excess corresponds to a companion mass of 6.8 Mjup (Teff=261 +/- 9 K) with orbital distance <11.8 au, although substantially lower masses are possible if we consider a closely orbiting insolated companion. No spatially resolved sources are detected within 200 au, with contrast curve analysis excluding planets more massive than 2 Mjup beyond ~12 au. Metal pollution is confirmed in both archival Keck HIRES spectra from 1999 and new observations from 2025, with no evidence suggesting the accretion rate has substantially changed over the decades. We explore possible dust disk morphologies to describe the observed IR excess, and find that traditional debris disks struggle to fit our data. WD 0644+025 thus represents a compelling case study in the growing population of white dwarfs with cold infrared excesses, and highlights JWST's ability to probe planetary system remnants inaccessible to prior infrared observatories.

arXiv:2601.16253v1 Announce Type: new Abstract: This letter reports statistically significant changes in the equivalent widths of MgII and CaII lines in the dusty and polluted white dwarf WD 0106-328, based on six epochs of spectroscopy using the VLT and Keck spanning 25 yr. Furthermore, the ratio of these two equivalent widths may also vary, with a 7% probability of being constant. Between 2000 and 2025, both Mg and Ca have experienced decreases in accretion rates, of approximately 20 and 60%, respectively, but with individual variation during the interim. These metal abundance decreases are the first empirical corroboration of diffusion theory in white dwarfs, which predict sinking timescales on the order of days for this star. However, the persistent atmospheric metals require a more gradual, circumstellar process, where one possibility is viscous spreading in an ionized disk of metals, consistent with $\alpha\approx0.1$ within that formalism. The combination of optical and ultraviolet spectroscopy with the Hubble Space Telescope detects all the major rock-forming elements (O, Mg, Si, Fe), and demonstrates that Fe dominates the accreted material by mass, and that it is delivered mostly as pure metal from within a differentiated parent body. This inference is consistent with the possibility that chemically-segregated accretion may result from a combination of planetary assembly, fragmentation, disk evolution, and be observed on relatively short timescales.

arXiv:2601.15285v1 Announce Type: new Abstract: The A1V star $\gamma$ Oph, at a distance of 29.7 pc, is known from Spitzer imaging to host a debris disk with a large radial extent and from its spectral energy distribution to host inner warm dust. We imaged $\gamma$ Oph with JWST/MIRI at 15 and 25.5 microns, which reveal smooth and radially broad emission that extends to a radius of at least 250 au at 25.5 microns. In contrast to JWST findings of an inner small-grain component with distinct ringed substructures in Fomalhaut and Vega, the mid-infrared radial profile combined with prior ALMA imaging suggests a radially broad steady-state collisional cascade with the same grain size distribution throughout the disk. This further suggests that the system is populated by a radially broad planetesimal belt from tens of au or less to well over 200 au, rather than a narrow planetesimal belt from which the observed dust is displaced to appear broad. The disk is also found to be asymmetric, which could be modelled by a stellocentric offset corresponding to a small eccentricity of $\sim$0.02. Such a disk eccentricity could be induced by a mildly eccentric $<$$10\,M_\mathrm{Jup}$ giant planet outside 10 au, or a more eccentric companion up to stellar mass at a few au, without producing a resolvable radial gap in the disk.

arXiv:2505.01512v2 Announce Type: replace Abstract: The discovery of inhabited exoplanets hinges on identifying biosignature gases. JWST can reveal biosignature gases, though current discoveries have yet to evidence life. The central challenge is attribution: how can we confidently identify biogenic sources while ruling out, or deeming unlikely, abiotic explanations? Attribution is particularly difficult for individual planets, especially given the stochastic abiotic processes that can set atmospheric conditions. To address this, we propose a comparative multi-planet approach centred on systemic retrievals: the analysis of multiple planets within a system to empirically define the `abiotic baseline'. This baseline, constructed from obligate uninhabited planets, serves as a local reference point. Systemic retrievals enable marginalisation over inaccessible, latent, shared abiotic parameters within planet evolution models. This is possible because planets within a system are linked by their birth in the same natal disk, have been irradiated by the same evolving star, and have a linked dynamical history. Observations aligning with the abiotic baseline, where the locally-informed abiotic planet evolution models demonstrate high out-of-sample predictive accuracy, are likely non-biological. Potentially biological anomalies are identified as statistical outliers from the abiotic baseline using Bayesian leave-one-out cross-validation. A comparative biosignature is thus defined: an anomaly where a biotic planetary evolution model provides a superior fit than its abiotic counterpart. Where both abiotic and biotic models yield poor predictive accuracy, the anomaly is flagged as an ``unknown unknown"; a signature of either unconstrained abiotic processes, or life as we don't yet know it.

arXiv:2601.14254v1 Announce Type: new Abstract: The internal composition of sub-Neptunes remains a prominent unresolved question in exoplanetary science. We present a technique to place constraints on envelope mean molecular weight that utilises observations of escaping hydrogen or helium exospheres. This method is based on a simple timescale argument, which states that sub-Neptunes require a sufficiently large hydrogen or helium reservoir to explain on-going escape at their observed rates. This then naturally leads to an upper limit on atmospheric mean molecular weight. We apply this technique to archetypal sub-Neptunes, namely GJ-436 b, TOI-776 b and TOI-776 c, which have all been observed to be losing significant hydrogen content as well as relatively featureless transit spectra when observed with JWST. Combining constraints from atmospheric escape and transit spectroscopy in the case of TOI-776 c allows us to tentatively rule out the high mean molecular weight scenario, pointing towards a low mean molecular weight atmosphere with high-altitude aerosols muting spectral features in the infra-red. Finally, we reframe our analysis to the hycean candidate K2-18 b, which has also been shown to host a tentative escaping hydrogen exosphere. If such a detection is robust, we infer a hydrogen-rich envelope mass fraction of $\log f_\text{env} = -1.67\pm0.78$, which is inconsistent with the hycean scenario at the $\sim 4\sigma$ level. This latter result requires further observational follow-up to confirm.

arXiv:2601.12128v1 Announce Type: new Abstract: Debris disks -- collisionally sustained belts of dust and sometimes gas around main sequence stars -- are remnants of planet formation processes and are found in systems ${\gtrsim}10$ Myr old. Millimeter-wavelength observations are particularly important, as the grains probed by these observations are not strongly affected by radiation pressure and stellar winds, allowing them to probe the dynamics of large bodies producing dust. The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) is analyzing high-resolution observations of 24 debris disks to enable the characterization of debris disk substructures across a large sample for the first time. For the most highly inclined disks, it is possible to recover the vertical structure of the disk. We aim to model and analyze the most highly inclined systems in the ARKS sample in order to uniformly extract the vertical dust distributions for a sample of well-resolved debris disks. We employed both parametric and nonparametric methods to constrain the vertical dust distributions for the most highly inclined ARKS targets. We find a broad range of aspect ratios, revealing a wide diversity in vertical structure, with a range of best-fit parametric values of $0.0026 \leq h_{\rm HWHM} \leq 0.193$ and a median best-fit value of $h_{\rm HWHM}=0.021$. The results obtained by nonparametric modeling are generally consistent with the parametric modeling results. We find that five of the 13 disks are consistent with having total disk masses less than that of Neptune (17 $M_{\oplus}$), assuming stirring by internal processes (self-stirring and collisional and frictional damping). Furthermore, most systems show a significant preference for a Lorentzian vertical profile rather than a Gaussian.

arXiv:2601.11732v1 Announce Type: new Abstract: Dusty discs detected around main-sequence stars are thought to be signs of planetesimal belts in which the dust distribution is shaped by collisional and dynamical processes, including interactions with gas if present. The debris disc around the young A-type star HD 131835 is composed of two dust rings at ~65 au and ~100 au, a third unconstrained innermost component, and a gaseous component centred at ~65 au. New ALMA observations show that the inner of the two dust rings is brighter than the outer one, in contrast with previous observations in scattered light. We explore two scenarios that could explain these observations: the two dust rings might represent distinct planetesimal belts with different collisional properties, or only the inner ring might contain planetesimals while the outer ring consists entirely of dust that has migrated outwards due to gas drag. To explore the first scenario, we employed a state-of-the-art collisional evolution code. To test the second scenario, we used a simple dynamical model of dust grain evolution in an optically thin gaseous disc. Collisional models of two planetesimal belts cannot fully reproduce the observations by only varying their dynamical excitation, and matching the data through a different material strength requires an extreme difference in dust composition. The gas-driven scenario can reproduce the location of the outer ring and the brightness ratio of the two rings from scattered light observations, but the resulting outer ring is too faint overall in both scattered light and sub-millimetre emission. The dust rings in HD 131835 could be produced from two planetesimal belts, although how these belts would attain the required extremely different properties needs to be explained. The dust-gas interaction is a plausible alternative explanation and deserves further study using a more comprehensive model.

arXiv:2601.11712v1 Announce Type: new Abstract: CO gas is detected in a significant number of debris discs, but its origin and evolution remains unclear. Key constraints are its mass and spectro-spatial distribution, which are coupled through optical depth and have only been analysed at low to moderate resolution so far. The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) is the first ALMA large program to target debris discs at high spectro-spatial resolution. We used $^{12}$CO and $^{13}$CO J=3-2 line data of 18 ARKS debris belts, 5 of which were already known to host gas, to analyse the spectro-spatial distribution of CO, constrain the gas masses, and to search for gas in the remaining systems. We developed a line-imaging pipeline and produced line cubes for each disc, with a spatial resolution down to $\sim$70 mas and spectral resolution of 26 m s$^{-1}$. Using spectro-spatial shifting and stacking, we produced high signal-to-noise maps, and radial and spectral profiles that reveal the distribution and kinematics of gas in 5 gas-bearing discs. For these discs, we constrained the inner radius of the $^{12}$CO, and found the radial brightness profile of CO peaked interior to the dust ring, but that CO was more radially extended than the dust. We present the first radially resolved $^{12}$CO/$^{13}$CO isotopologue flux ratios in gas-bearing debris discs, which are constant with radius for the majority of systems, indicating $^{12}$CO and $^{13}$CO are both optically thick or thin throughout the discs. We report CO line fluxes/upper limits for all systems and optical depth dependant masses for the 5 gas-bearing systems. Finally, we analysed the $^{12}$CO J=3-2 line luminosities for the ARKS debris discs and discs from the literature. We confirm that gas is mostly detected in young systems. However, the high scatter seen in young/high fractional luminosity systems indicates no trend within the systems with detected gas.

arXiv:2601.11708v1 Announce Type: new Abstract: The outer regions of planetary systems host dusty debris discs analogous to the Kuiper belt (exoKuiper belts), which provide crucial constraints on planet formation and evolution processes. ALMA dust observations have revealed a great diversity, and that some belts contain CO gas, whose origin and implications are uncertain. Most of this progress, however, has been limited by low-resolution observations. We conducted the first ALMA large programme dedicated to debris discs: the ALMA survey to Resolve exoKuiper belt Substructures (ARKS). We selected the 24 most promising belts to constrain their detailed radial and vertical structure, and to characterise the gas content. We constrained the radial and vertical distribution of dust, as well as the presence of asymmetries. For a subset of six belts with CO gas, we constrained the gas distribution and kinematics. To interpret these observations, we used a wide range of dynamical models. The first ARKS results are presented as a series of ten papers. We discovered that up to 33% of our sample exhibits multiple dusty rings. For highly inclined belts, we found that non-Gaussian vertical distributions are common and are indicative of multiple dynamical populations. We also found that 10 of the 24 belts present asymmetries. We find that the CO gas is radially broader than the dust, but this could be an effect of optical depth. At least one system shows non-Keplerian kinematics due to strong pressure gradients, which may have triggered a vortex that trapped dust in an arc. Finally, we find evidence that the micron-sized grains may be affected by gas drag in gas rich systems. ARKS has revealed a great diversity of structures in exoKuiper belts that may arise when they are formed in protoplanetary discs or subsequently via interactions with planets and/or gas. We encourage the community to explore the reduced data and data products.

arXiv:2601.11709v1 Announce Type: new Abstract: Debris discs were long considered to be largely gas-free environments governed by collisional fragmentation, gravitational stirring, and radiative forces. Recent CO detections show that gas is present, but its abundance and origin remain uncertain. The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) revealed a narrow gas and dust ring in the disc HD 121617 with an asymmetric arc 40% brighter than the rest of the ring. We aim to constrain the total gas mass in HD 121617 assuming the dust arc is produced by hydrodynamical gas-dust interactions. We used the Dusty FARGO-ADSG code, modelling dust as Lagrangian particles, including radiation pressure and dust feedback, and varying the total gas mass. Simulations were compared to observations using radiative transfer. An unstable gas ring creates a size-dependent radial and azimuthal dust trap whose efficiency depends on gas mass. Two models, with 50 and 5 Earth masses of gas, reproduce both the ALMA band 7 arc and the outward offset of the VLT/SPHERE scattered-light ring via gas drag and radiation pressure. We infer a conservative gas-mass range of 2.5 to 250 Earth masses. If the ALMA asymmetry is caused by gas drag, the required gas mass compared with the observed CO implies substantial H2, consistent with primordial gas. HD 121617 would then be a hybrid disc between protoplanetary and debris stages. Since a planet could also create an arc, future observations are needed to distinguish these scenarios.

arXiv:2601.11711v1 Announce Type: new Abstract: ExoKuiper belts around young A-type stars often host CO gas, whose origin is still unclear. The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) includes 6 of these gas-bearing belts, to characterise their dust and gas distributions and investigate the gas origin. As part of ARKS, we observed the gas-rich system HD121617 and discovered an arc of enhanced dust density. In this paper, we analyse in detail the dust and gas distributions and the gas kinematics of this system. We extracted radial and azimuthal profiles of the dust (in the millimetre and near-infrared) and gas emission ($^{12}$CO and $^{13}$CO) from reconstructed images. To constrain the morphology of the arc, we fitted an asymmetric model to the dust emission. To characterise the gas kinematics, we fitted a Keplerian model to the velocity map and extracted the azimuthal velocity profile by deprojecting the data. We find that the dust arc is narrow (1-5 au wide at a radius of 75 au), azimuthally extended, and asymmetric; the emission is more azimuthally compact in the direction of the system's rotation, and represents 13% of the total dust mass (0.2$M_\oplus$). The arc is much less pronounced or absent for small grains and gas. Finally, we find strong non-Keplerian azimuthal velocities at the inner and outer wings of the ring, as was expected due to strong pressure gradients. The dust arc resembles the asymmetries found in protoplanetary discs, often interpreted as the result of dust trapping in vortices. If the gas disc mass is high enough ($\gtrsim20M_\oplus$, requiring a primordial gas origin), both the radial confinement of the ring and the azimuthal arc may result from dust grains responding to gas drag. Alternatively, it could result from planet-disc interactions via mean motion resonances. Further studies should test these hypotheses and may provide a dynamical gas mass estimate in this CO-rich exoKuiper belt.

arXiv:2601.10635v1 Announce Type: new Abstract: We present spatially resolved spectroscopic observations of the planetary nebula NGC 6720, the Ring Nebula, taken during the science verification phase of WEAVE, a new instrument mounted on the William Herschel Telescope on La Palma. We use the instrument's Large Integral Field Unit (LIFU) to obtain spectra of the Ring Nebula, covering its entire optically bright inner regions as well as parts of its much fainter outer molecular halo. We report the discovery of emission from [Fe~{\sc v}] and [Fe~{\sc vi}] confined to a narrow ``bar'' extending across the central regions of the nebula. No lines of other elements share this morphology or, at the spectral resolving power used ($R \sim 2500$), the same radial velocity. The extent to which iron in this bar is depleted is presently unclear; comparison with JWST-detected dust continuum emission suggests that some dust grain destruction may be occurring in the region, but there is currently no observational evidence for the $>$ 50~km\,s$^{-1}$ shock waves or $T > 10^6$~K X-ray emitting gas needed to enable this. Where the bar is located along the line of sight through the nebula, and how it was created, are new puzzles to be solved for this iconic planetary nebula.

arXiv:2601.10508v1 Announce Type: new Abstract: Planet population synthesis is an integral tool for linking exoplanets to their formation environments. Most planet population synthesis studies have focused on the carbon-to-oxygen ratio (C/O) in gas or solids, yet more insight into planet formation may be afforded by considering a wider suite of elements. Sulfur is one such key element. It has been assumed to be entirely refractory in population synthesis models, restricting it to being a tracer of accreted rocky solids. However, sulfur also has a volatile reservoir dominant at the onset of star and planet formation. We investigate sulfur's wider potential as a formation history tracer by implementing the first multi-phase treatment of S in a planet population synthesis model. We present the planet formation module of \textsc{sponchpop} and its first predicted planet growth tracks and populations. We explore the diversity of planet compositions in terms of their sulfur budget, including both refractory and volatile components, and apply a novel gas-grain conversion of sulfur to study how formation trajectories of giant planets relate to final core and envelope compositions. We show that planets inherit a wide range of core and envelope sulfur content related to accretion history while considering late-stage planetesimal infall, providing a new diagnostic tool for planet formation. The diverse sulfur content of planet cores suggests some rocky planets may be born sulfur-poor, with implications for their geochemistry and habitability. Enhanced sulfur abundances in gas-giant atmospheres can be attributed to formation beyond the H2S iceline, such as the giants in our Solar System.

arXiv:2601.00057v1 Announce Type: new Abstract: A population of free-floating planets is known from gravitational microlensing surveys. None have a directly measured mass, owing to a degeneracy with the distance, but the population statistics indicate that many are less massive than Jupiter. We report a microlensing event -- KMT-2024-BLG-0792/OGLE-2024-BLG-0516, which was observed from both ground- and space-based telescopes -- that breaks the mass-distance degeneracy. The event was caused by an object with 0.219^{+0.075}_{-0.046} Jupiter masses that is either gravitationally unbound or on a very wide orbit. Through comparison with the statistical properties of other observed microlensing events and predictions from simulations, we infer that this object likely formed in a protoplanetary disk (like a planet), not in isolation (like a brown dwarf), and dynamical processes then ejected it from its birth place, producing a free-floating object.

arXiv:2512.15861v1 Announce Type: new Abstract: The nearby star Fomalhaut is orbited by a compact source, Fomalhaut b, which has previously been interpreted as either a dust-enshrouded exoplanet or a dust cloud generated by the collision of two planetesimals. Such collisions are rarely observed but their debris can appear in direct imaging. We report Hubble Space Telescope observations that show the appearance in 2023 of a second point source around Fomalhaut, resembling the appearance of Fomalhaut b twenty years earlier. We interpret this additional source as a dust cloud produced by a recent impact between two planetesimals. The positions and motion of two impact-generated dust clouds over twenty years provide constraints on the collisional dynamics in the debris belt.

arXiv:2512.15844v1 Announce Type: new Abstract: In recent years, JWST has facilitated detections of carbon-bearing molecules in the atmospheres of temperate sub-Neptunes orbiting M dwarfs, ushering in a new era in the characterization of this intriguing planetary regime. We report the transmission spectrum of the temperate sub-Neptune TOI-732 c, observed with JWST NIRISS, NIRSpec G395H and MIRI LRS between 0.9-12 $\mu$m. The observations provide evidence for methane (CH$_4$) in a H$_2$-rich atmosphere, at a volume mixing ratio of $\sim$1\%, and non-detection of NH$_3$ and HCN, along with nominal constraints on other prominent molecules H$_2$O, CO and CO$_2$, which are typically expected in H$_2$-rich atmospheres. We conduct a comprehensive survey of 250 chemical species and find moderate to strong evidence (up to $\ln B\sim 5.9$, $3.9\sigma$) for additional absorption due to one or more complex molecules including higher-order hydrocarbons and/or sulfur-bearing molecules. The spectral features are strongly degenerate among these molecules and with methane, which we find at $\ln B=3.2-8.8$ (up to $3.0-4.6$$\sigma$) significance. Two complex molecules are preferred with at least moderate evidence ($\ln B \gtrsim 2.5$) in both the near- and mid-infrared, while several others show such evidence in at least one of the two wavelength ranges. The preferred molecules are found in trace quantities on Earth, with no significant sources identified in other planetary atmospheres, requiring future work to assess their physical plausibility in this planet. Future observations are required to resolve the degeneracies and place more robust constraints on these species. We highlight the need for further theoretical and experimental work to robustly characterize the atmospheric and internal composition of TOI-732 c and similar sub-Neptunes.

arXiv:2512.14803v1 Announce Type: new Abstract: Debris discs reveal the architectures and dynamical histories of planetary systems. Sub-millimetre observations trace large dust grains within debris discs, revealing their bulk properties. Debris discs have so far only been detected around ~20% of stars, representing the bright end of the population. A new facility is required to reach fainter discs, overcoming the confusion limit, with multiwavelength capabilities for characterisation, sensitivity to large-scale emission for nearby targets and a large field of view for surveying distant populations. All of this is made possible with the Atacama Large Aperture Submillimetre Telescope (AtLAST).

arXiv:2512.09844v1 Announce Type: new Abstract: The Great Oxidation Event (GOE) was a $200$ Myr transition circa 2.4 billion years ago that converted the Earth's anoxic atmosphere to one where molecular oxygen (O$_2$) was abundant (volume mixing ratio $>10^{-4}$). This significant rise in O$_2$ is thought to have substantially throttled hydrogen (H) escape and the associated water (H$_2$O) loss. Atmospheric estimations from the GOE onward place O$_2$ concentrations ranging between 0.1\% to 150\% PAL, where PAL is the present atmospheric level of 21% by volume. In this study we use WACCM6, a three-dimensional Earth System Model to simulate Earth's atmosphere and predict the diffusion-limited escape rate of hydrogen due to varying O$_2$ post-GOE. We find that O$_2$ indirectly acts as a control valve on the amount of hydrogen atoms reaching the homopause in the simulations: less O$_2$ leads to decreased O$_3$ densities, reducing local tropical tropopause temperatures by up to 18 K, which increases H$_2$O freeze-drying and thus reduces the primary source of hydrogen in the considered scenarios. The maximum differences between all simulations in the total H mixing ratio at the homopause and the associated diffusion-limited escape rates are a factor of 3.2 and 4.7, respectively. The prescribed CH$_4$ mixing ratio (0.8 ppmv) sets a minimum diffusion escape rate of $\approx 2 \times 10^{10}$ mol H yr$^{-1}$, effectively a negligible rate when compared to pre-GOE estimates ($\sim 10^{12}-10^{13}$ mol H y$^{-1}$). Because the changes in our predicted escape rates are comparatively minor, our numerical predictions support geological evidence that the majority of Earth's hydrogen escape occurred prior to the GOE. Our work demonstrates that estimations of how the hydrogen escape rate evolved through Earth's history requires 3D chemistry-climate models which include a global treatment of water vapour microphysics.