Searcharxiv⌕ Search

arXiv subjects

Joanna K. Barstow

Publications and source records attributed to Joanna K. Barstow.

At least 19 recordsLinked to original sources

K-dwarf starspot hunters: how to directly characterize spot and faculae properties with UV-IR panchromatic transit spectra

Transmission spectroscopy of exoplanets provides an important window into their atmospheric composition, structure and dynamics, especially in the JWST era. As the quality of the observational data and therefore the precision of our constraints improves, we become increasingly sensitive to sources of systematic bias in our models and observations. One significant example of this is the Transit Light Source Effect, in which heterogeneous features in the stellar photosphere - spots and faculae - imprint additional spectral signatures onto exoplanet transmission spectra. The effects of this stellar contamination must be accounted for or removed in order to accurately recover the planet's atmospheric properties. Including parameterized models of spots and faculae within spectral retrieval analysis is increasingly adopted as a solution to this problem, but is limited by the accuracy of models of stellar spectra. In this paper, we outline an observational strategy combining simultaneous data from JWST and the Hubble Space Telescope that would enable us to further constrain these models. We perform synthetic retrievals to demonstrate how we could constrain starspot and faculae parameters; we test the impact of using different model spectra in the retrieval; and we consider the impact of variable stellar activity on coadding transits to achieve the desired signal-to-noise. We find that ultraviolet and optical wavelengths are key for breaking degeneracies between stellar contamination and planetary parameters.

astro-ph.EP↗

Early Exploration of the Scientific Discovery Space for the Habitable Worlds Observatory

The Habitable Worlds Observatory (HWO) is a future NASA flagship mission concept identified by the Astro2020 Decadal Survey as the highest priority for large space missions. HWO should conduct "transformative astrophysics" and search for biosignatures in the atmospheres of approximately 25 potentially Earth-like planets. To further the early-stage development of HWO, NASA formed the Science, Technology, Architecture Review Team (START). In turn, START invited the scientific community to join working groups to explore the potential discovery space. In this paper, we present 70 science cases that resulted from this process. The cases address four scientific pillars: growth of galaxies (15 cases), evolution of the elements (13 cases), solar systems in context (32 cases), and living worlds (10 cases). Combined, they would address 27 of the 30 science questions and discovery areas identified by Astro2020. The 140 observing programs needed for the 70 investigations encompass a rich variety of spectroscopic (for 87% of science cases) and photometric (for 30%) observations extending from the UV to the NIR. Additionally, high-contrast and polarimetric capabilities would be needed for 34% and 27% of science cases, respectively. Access to UV wavelengths is critical: 83% of science cases need data at wavelengths <400 nm, and 26% extend to <100 nm. In the NIR, 26% of science cases need observations at wavelengths >=2000 nm. Pursuing the full portfolio of science would also necessitate precise astrometry for planet mass measurement, rapid response capabilities, a large instantaneous field of regard, non-sidereal tracking, saturation mitigation strategies, and high dynamic range.

astro-ph.IM↗

On the synergetic use of Ariel and JWST for exoplanet atmospheric science

This paper explores the potential for strategic synergies between the JWST and the Ariel telescopes, two flagship observatories poised to revolutionise the study of exoplanet atmospheres. Both telescopes have the potential to address common fundamental questions about exoplanets-especially concerning their nature and origins-and serve a growing scientific community. With their operations now anticipated to overlap, starting from 2030, there is a unique opportunity to enhance the scientific outputs of both observatories through coordinated efforts. In this report, authored by the Ariel-JWST Synergy Working Group, part of the Ariel Consortium Science Team, we summarise the capabilities of JWST and Ariel; we highlight their key differences, similarities, synergies, and distinctive strengths. Ariel is designed to conduct a broad survey of exoplanet atmospheres but remains highly flexible, allowing the mission to integrate insights from JWST's discoveries. Findings from JWST, including data from initiatives shaped by NASA's decadal survey priorities and community-driven research themes, will inform the development of Ariel's core survey strategy. Conversely, Ariel's ability to perform broad-wavelength coverage observations for bright targets provides complementary avenues for exoplanet researchers, particularly those interested in time-domain observations and large-scale atmospheric studies. This paper identifies key pathways for fostering JWST-Ariel synergies, many of which can be initiated even before Ariel's launch. Leveraging their complementary designs and scopes, JWST and Ariel can jointly address fundamental questions about the nature, formation, and evolution of exoplanets. Such strategic collaboration has the potential to maximise the scientific returns of both observatories and lay the foundation for future facilities in the roadmap to exoplanet exploration.

astro-ph.IM↗

The power of polarimetry for characterising exoplanet atmospheres, clouds, and surfaces with NASA's Habitable Worlds Observatory

The Habitable Worlds Observatory (HWO), planned for launch in the 2040s, represents the next major step in exoplanet characterisation. HWO will, for the first time, enable detailed studies of the atmospheres and surfaces of Earth-like exoplanets through high-contrast reflection spectroscopy across the UV, optical, and near-infrared. These wavelength ranges provide access to key molecular absorption features, including O2, O3, H2O, CO2, and CH4, as well as potential surface biosignatures such as the vegetation red edge or ocean glint, making HWO a cornerstone mission for assessing planetary habitability. Clouds are a dominant factor in determining planetary climate and observability, yet their properties remain highly degenerate when constrained using reflected flux alone. Spectropolarimetry, a measure of the polarisation state of reflected light as a function of wavelength and orbital phase, provides a powerful complementary diagnostic. Polarisation is highly sensitive to cloud particle size, composition, shape, vertical distribution, and surface type, enabling degeneracies between atmospheric and surface models to be broken. Numerous studies have demonstrated the value of polarimetry for characterising a wide range of exoplanets, from hot Jupiters to cooler potentially habitable worlds. HWO's proposed instrument suite includes a coronagraph, a high-resolution imager, and a candidate high-resolution spectropolarimeter, offering multiple pathways to exploit polarimetry across diverse planetary regimes. This white paper argues that incorporating polarimetric capability into HWO instruments would significantly enhance the mission's scientific return. We highlight the unique opportunity for UK leadership in both instrument development and theoretical modelling, and advocate for a strong UK role in shaping HWO's polarimetric capabilities to maximise its impact on exoplanet science.

astro-ph.IM↗

Exoplanet characterization with NASA's Habitable Worlds Observatory

Exoplanet atmosphere characterization has seen revolutionary advances over the last few years, providing us with unique insights into atmospheric chemistry, dynamics and planet formation mechanisms. However, true solar system analog planets remain inaccessible. A major goal for exoplanet science over the coming decades is to observe, and characterize, temperate rocky planets and cool gas giants in orbit around solar-type stars, with the prospect of detecting signs of habitability or even life. Characterization and categorization of these planets relies on direct spectroscopic observations capable of identifying molecular species in their atmospheres; however, these observations represent a substantial engineering challenge due to the extreme contrast between a temperate, Earth-sized exoplanet and its parent star. NASA's next flagship mission, the Habitable Worlds Observatory (HWO) - planned for launch in the mid-2040s - will boast a coronagraphic instrument capable of reaching the needed 10$^{-10}$ contrast, on an ultrastable platform enabling long integration times to achieve the required signal to noise. HWO will cover near-ultraviolet to the near-infrared wavelengths, enabling detections of key biosignature molecules and habitability indicators such as ocean glint and a vegetation `red edge'. Via early involvement in this groundbreaking observatory, including a potential UK instrument contribution, the UK exoplanet community now has an important opportunity to influence the telescope's design. To maintain our international competitiveness, we must be at the forefront of observational campaigns with HWO when it eventually launches, and this comes with the need for parallel development in laboratory astrophysics and computational modelling. Maximising our exploitation of this transformative NASA mission requires consistent financial support in these areas across the next two decades.

astro-ph.IM↗

Transiting exoplanets as the immediate future for population-level atmospheric science

The transit method, during which a planet's presence is inferred by measuring the reduction in flux as it passes in front of its parent star, is a highly successful exoplanet detection and characterization technique. During transit, the small fraction of starlight that passes through a planet's atmosphere emerges with the fingerprints of atmospheric gases, aerosols and structure. During eclipse, the relatively small contribution of light from the planet itself may be observed as the planet is occulted by the star. For planets in near-edge-on, short-period orbits, observing the system throughout an entire orbit allows the varying flux from the planet to be extracted as the illuminated `dayside' rotates in and out of view. With spectroscopic observations, we can characterize not only the overall composition of the atmosphere, but also glean insights into atmospheric structure and dynamics. With over 6,000 transiting planets now discovered, such observations are currently our only window into a consistent sample of planetary atmospheres large enough to attempt a population-level study, a critical next step for our understanding of atmospheric science. The vast exoplanet population provides a laboratory for atmospheric physics, including chemistry, dynamics, cloud processes and evolution; extending these results to a larger number of targets will allow us to explore the effects of equilibrium temperature, gravity, mass and parent star type on atmospheric properties, as well as map observable trends to formation scenarios. These findings are critical for addressing STFC's Science Vision Challenge B: how do stars and planetary systems develop and how do they support the existence of life?. Here we outline how the UK must fit within this strategic context, suggest approaches and development for the future, and outline the unique capabilities and leadership of scientists across the UK.

astro-ph.IM↗

Data availability and requirements relevant for the Ariel space mission and other exoplanet atmosphere applications

The goal of this white paper is to provide a snapshot of the data availability and data needs primarily for the Ariel space mission, but also for related atmospheric studies of exoplanets and brown dwarfs. It covers the following data-related topics: molecular and atomic line lists, line profiles, computed cross-sections and opacities, collision-induced absorption and other continuum data, optical properties of aerosols and surfaces, atmospheric chemistry, UV photodissociation and photoabsorption cross-sections, and standards in the description and format of such data. These data aspects are discussed by addressing the following questions for each topic, based on the experience of the "data-provider" and "data-user" communities: (1) what are the types and sources of currently available data, (2) what work is currently in progress, and (3) what are the current and anticipated data needs. We present a GitHub platform for Ariel-related data, with the goal to provide a go-to place for both data-users and data-providers, for the users to make requests for their data needs and for the data-providers to link to their available data. Our aim throughout the paper is to provide practical information on existing sources of data whether in databases, theoretical, or literature sources.

astro-ph.IM↗

BOWIE-ALIGN: Weak spectral features in KELT-7b's JWST NIRSpec/G395H transmission spectrum imply a high cloud deck or a low-metallicity atmosphere

Hot Jupiters and their atmospheres are prime targets for transmission spectroscopy due to their extended atmospheres and the corresponding large signal-to-noise, providing the best possible constraints for the atmospheric carbon-to-oxygen (C/O) ratio and metallicity of exoplanets. Within BOWIE-ALIGN, we aim to compare JWST spectra of a sample of orbitally aligned and misaligned hot Jupiters orbiting F-type stars to probe the link between hot Jupiter atmospheres and planet formation history. Here, we present a near-infrared transmission spectrum of the aligned planet KELT-7b using one transit observed with JWST NIRSpec/G395H. We find weak features, only tentative evidence for H$_2$O and CO$_2$ in the atmosphere of KELT-7b. This poses a challenge to constrain the atmospheric properties of KELT-7b and two possible scenarios emerge from equilibrium chemistry and free chemistry retrievals: a high-altitude cloud deck muting all features or an extremely low metallicity atmosphere, respectively. The retrieved C/O ratios from our data reductions range from $0.43 - 0.74$, while the atmospheric metallicity is suggested to be solar to super-solar ($1-16 \times$ solar). Although these wide constraints prevent detailed conclusions about KELT-7b's formation history, a solar-to-super-solar metallicity would imply the accretion of solid material during its formation, which is valuable information for the survey's wider goals of understanding the relative importance of gaseous to solid accretion.

astro-ph.EP↗

Characterizing the Dynamics and Chemistry of Transiting Exoplanets with the Habitable World Observatory

The primary scientific objective of this Habitable Worlds Observatory (HWO) Science Case Development Document (SCDD) is to measure planetary rotation rates of transiting exoplanets to determine the structure, composition, circulation, and aerosol properties of their planetary atmospheres. For this analysis, HWO would obtain spectroscopic phase curves for planets with orbital periods of 5 - 20+ days, to assess tidal locking radius assumptions. Extending phase curve studies out to longer orbital periods than accessible with current and near-future telescopes will enable detailed investigation of atmospheric structure, composition, and circulation for planets that are much cooler than the more highly irradiated planets accessible with JWST phase curve observations (i.e., Teq < 500 K for HWO versus 1400 K <= Teq <= 2600 K for JWST). Broad wavelength coverage extending from the UV to the NIR would capture both reflected light and thermal emission, enabling HWO to conduct comprehensive characterization of planetary atmospheres. UV observations would probe high altitudes, thereby providing valuable insights into atmospheric (dis)equilibrium, aerosol properties, and the effects of photochemical processes on atmospheric composition. We also discuss the role of polarimetry in the classification of aerosols and the associated role they play in the atmospheric energy budget that directly ties them to the chemistry and circulation structure of the atmosphere.

astro-ph.EP↗

The HUSTLE Program: The UV to Near-IR Transmission Spectrum of the Hot Jupiter KELT-7b

The ultraviolet and optical wavelength ranges have proven to be a key addition to infrared observations of exoplanet atmospheres, as they offer unique insights into the properties of clouds and hazes and are sensitive to signatures of disequilibrium chemistry. Here we present the 0.2-0.8 $μ$m transmission spectrum of the Teq = 2000 K Jupiter KELT-7b, acquired with HST WFC3/UVIS G280 as part of the HUSTLE Treasury program. We combined this new spectrum with the previously published HST WFC3/IR G141 (1.1-1.7 $μ$m) spectrum and Spitzer photometric points at 3.6$μ$m and 4.5$μ$m, to reveal a generally featureless transmission spectrum between 0.2 and 1.7 $μ$m, with a slight downward slope towards bluer wavelengths, and a asymmetric water feature in the 1.1-1.7 $μ$m band. Retrieval models conclude that the 0.2 - 1.7$μ$m spectrum is primarily explained by a high H- abundance ($\sim 10^{-5}$), significantly above the equilibrium chemistry prediction ($\sim 10^{-12}$), suggesting disequilibrium in KELT-7b's upper atmosphere. Our retrievals also suggest the presence of bright inhomogeneities in the stellar surface, and tentative evidence of CO2 at the Spitzer wavelengths. We demonstrate that with the UV-optical coverage provided by WFC3 UVIS/G280, we are able to confirm the presence and constrain the abundance of H-, and obtain evidence for bright stellar inhomogeneities that would have been overlooked using infrared data alone. Observations redward of 1$μ$m with JWST should be able to further constrain the abundance of H-, as well as confirm the presence of CO2 inferred by the two Spitzer datapoints.

astro-ph.EP↗

SiO and a super-stellar C/O ratio in the atmosphere of the giant exoplanet WASP-121b

Refractory elements such as iron, magnesium, and silicon can be detected in the atmospheres of ultrahot giant planets. This provides an opportunity to quantify the amount of refractory material accreted during formation, along with volatile gases and ices. However, simultaneous detections of refractories and volatiles have proved challenging, as the most prominent spectral features of associated atoms and molecules span a broad wavelength range. Here, using a single JWST observation of the ultrahot giant planet WASP-121b, we report detections of H$_2$O (5.5-13.5$σ$), CO (10.8-12.8$σ$), and SiO (5.7-6.2$σ$) in the planet's dayside atmosphere, and CH$_4$ (3.1-5.1$σ$) in the nightside atmosphere. We measure super-stellar values for the atmospheric C/H, O/H, Si/H, and C/O ratios, which point to the joint importance of pebbles and planetesimals in giant planet formation. The CH$_4$-rich nightside composition is also indicative of dynamical processes, such as strong vertical mixing, having a profound influence on the chemistry of ultrahot giant planets.

astro-ph.EP↗

WASP-121b's transmission spectrum observed with JWST/NIRSpec G395H reveals thermal dissociation and SiO in the atmosphere

WASP-121b has been established as a benchmark ultrahot Jupiter, serving as a laboratory for the atmospheric chemistry and dynamics of strongly irradiated extrasolar gas giants. Here, we present and analyze WASP-121b's transmission spectrum observed with NIRSpec G395H on board the James Webb Space Telescope and find evidence for the thermal dissociation of H$_2$O and H$_2$ on the planet's permanent dayside. Additionally, we detect SiO at a statistical significance of $5.2σ$ which is compatible with chemical equilibrium in the atmosphere. Constraining the abundance of SiO and abundance ratios between silicon and volatile atoms in WASP-121b's atmosphere could help discriminate between possible migration histories of the planet. The three-dimensional nature of thermal dissociation on WASP-121b's dayside and of recombination on its nightside, however, poses a challenge to constraining molecular abundances and elemental abundance ratios from the transmission spectrum. To account for this, we implemented an atmospheric model in the NEMESIS framework that splits the planet's atmosphere into dayside and nightside. A retrieval applying our atmospheric model to WASP-121b's transmission spectrum favors a higher H$_2$O abundance on the nightside than on the dayside, demonstrating the impact of hemispheric heterogeneity when attempting to constrain WASP-121b's bulk H$_2$O inventory.

astro-ph.EP↗

Atmospheric retrievals suggest the presence of a secondary atmosphere and possible sulfur species on L 98-59 d from JWST NIRSpec G395H transmission spectroscopy

L 98-59 d is a Super-Earth planet orbiting an M-type star. We performed retrievals on the transmission spectrum of L 98-59 d obtained using NIRSpec G395H during a single transit, from JWST Cycle 1 GTO 1224. The wavelength range of this spectrum allows us to detect the presence of several atmospheric species. We found that the spectrum is consistent with a high mean molecular weight atmosphere. The atmospheric spectrum indicates the possible presence of the sulfur-bearing species H$_2$S and SO$_2$, which could hint at active volcanism on this planet if verified by future observations. We also tested for signs of stellar contamination in the spectrum, and found signs of unocculted faculae on the star. The tentative signs of an atmosphere on L 98-59 d presented in this work from just one transit bodes well for possible molecular detections in the future, particularly as it is one of the best targets among small exoplanets for atmospheric characterization using JWST.

astro-ph.EP↗

Hints of a sulfur-rich atmosphere around the 1.6 R$_{\oplus}$ Super-Earth L98-59 d from JWST NIRSpec G395H transmission spectroscopy

Detecting atmospheres around planets with a radius below 1.6 R$_{\oplus}$, commonly referred to as rocky planets (Rogers_2015, Rogers_2021), has proven to be challenging. However, rocky planets orbiting M-dwarfs are ideal candidates due to their favorable planet-to-star radius ratio. Here, we present one transit observation of the Super-Earth L98-59d (1.58 R$_{\oplus}$, 2.31 M$_{\oplus}$), at the limit of rocky/gas-rich, using the JWST NIRSpec G395H mode covering the 2.8 to 5.1 microns wavelength range. The extracted transit spectrum from a single transit observation deviates from a flat line by 2.6 to 5.6$σ$, depending on the data reduction and retrieval setup. The hints of an atmospheric detection are driven by a large absorption feature between 3.3 to 4.8 microns. A stellar contamination retrieval analysis rejected the source of this feature as being due to stellar inhomogeneities, making the best fit an atmospheric model including sulfur-bearing species, suggesting that the atmosphere of L98-59d may not be at equilibrium. This result will need to be confirmed by the analysis of the second NIRSpec G395H visit in addition to the NIRISS SOSS transit observation.

astro-ph.EP↗

Sulphur dioxide in the mid-infrared transmission spectrum of WASP-39b

The recent inference of sulphur dioxide (SO$_2$) in the atmosphere of the hot ($\sim$1100 K), Saturn-mass exoplanet WASP-39b from near-infrared JWST observations suggests that photochemistry is a key process in high temperature exoplanet atmospheres. This is due to the low ($<$1 ppb) abundance of SO$_2$ under thermochemical equilibrium, compared to that produced from the photochemistry of H$_2$O and H$_2$S (1-10 ppm). However, the SO$_2$ inference was made from a single, small molecular feature in the transmission spectrum of WASP-39b at 4.05 $μ$m, and therefore the detection of other SO$_2$ absorption bands at different wavelengths is needed to better constrain the SO$_2$ abundance. Here we report the detection of SO$_2$ spectral features at 7.7 and 8.5 $μ$m in the 5-12 $μ$m transmission spectrum of WASP-39b measured by the JWST Mid-Infrared Instrument (MIRI) Low Resolution Spectrometer (LRS). Our observations suggest an abundance of SO$_2$ of 0.5-25 ppm (1$σ$ range), consistent with previous findings. In addition to SO$_2$, we find broad water vapour absorption features, as well as an unexplained decrease in the transit depth at wavelengths longer than 10 $μ$m. Fitting the spectrum with a grid of atmospheric forward models, we derive an atmospheric heavy element content (metallicity) for WASP-39b of $\sim$7.1-8.0 $\times$ solar and demonstrate that photochemistry shapes the spectra of WASP-39b across a broad wavelength range.

astro-ph.EP↗

Simultaneous retrieval of orbital phase resolved JWST/MIRI emission spectra of the hot Jupiter WASP-43b: evidence of water, ammonia and carbon monoxide

Spectroscopic phase curves of hot Jupiters measure their emission spectra at multiple orbital phases, thus enabling detailed characterisation of their atmospheres. Precise constraints on the atmospheric composition of these exoplanets offer insights into their formation and evolution. We analyse four phase-resolved emission spectra of the hot Jupiter WASP-43b, generated from a phase curve observed with the MIRI/LRS onboard the JWST, to retrieve its atmospheric properties. Using a parametric 2D temperature model and assuming a chemically homogeneous atmosphere within the observed pressure region, we simultaneously fit the four spectra to constrain the abundances of atmospheric constituents, thereby yielding more precise constraints than previous work that analysed each spectrum independently. Our analysis reveals statistically significant evidence of NH3 (4$σ$) in a hot Jupiter's emission spectra for the first time, along with evidence of H2O (6.5$σ$), CO (3.1$σ$), and a non-detection of CH4. With our abundance constraints, we tentatively estimate the metallicity of WASP-43b at 0.6-6.5$\times$solar and its C/O ratio at 0.6-0.9. Our findings offer vital insights into the atmospheric conditions and formation history of WASP-43b by simultaneously constraining the abundances of carbon, oxygen, and nitrogen-bearing species.

astro-ph.EP↗

A warm Neptune's methane reveals core mass and vigorous atmospheric mixing

Observations of transiting gas giant exoplanets have revealed a pervasive depletion of methane, which has only recently been identified atmospherically. The depletion is thought to be maintained by disequilibrium processes such as photochemistry or mixing from a hotter interior. However, the interiors are largely unconstrained along with the vertical mixing strength and only upper limits on the CH$_4$ depletion have been available. The warm Neptune WASP-107 b stands out among exoplanets with an unusually low density, reported low core mass, and temperatures amenable to CH$_4$ though previous observations have yet to find the molecule. Here we present a JWST NIRSpec transmission spectrum of WASP-107 b which shows features from both SO$_2$ and CH$_4$ along with H$_2$O, CO$_2$, and CO. We detect methane with 4.2$σ$ significance at an abundance of 1.0$\pm$0.5 ppm, which is depleted by 3 orders of magnitude relative to equilibrium expectations. Our results are highly constraining for the atmosphere and interior, which indicate the envelope has a super-solar metallicity of 43$\pm$8$\times$ solar, a hot interior with an intrinsic temperature of T$_{\rm int}$=460$\pm$40 K, and vigorous vertical mixing which depletes CH4 with a diffusion coefficient of Kzz = 10$^{11.6\pm0.1}$ cm$^2$/s. Photochemistry has a negligible effect on the CH$_4$ abundance, but is needed to account for the SO$_2$. We infer a core mass of 11.5$_{-3.6}^{+3.0}$ M$_{\odot}$, which is much higher than previous upper limits, releasing a tension with core-accretion models.

astro-ph.EP↗

Nightside clouds and disequilibrium chemistry on the hot Jupiter WASP-43b

Hot Jupiters are among the best-studied exoplanets, but it is still poorly understood how their chemical composition and cloud properties vary with longitude. Theoretical models predict that clouds may condense on the nightside and that molecular abundances can be driven out of equilibrium by zonal winds. Here we report a phase-resolved emission spectrum of the hot Jupiter WASP-43b measured from 5-12 $μ$m with JWST's Mid-Infrared Instrument (MIRI). The spectra reveal a large day-night temperature contrast (with average brightness temperatures of 1524$\pm$35 and 863$\pm$23 Kelvin, respectively) and evidence for water absorption at all orbital phases. Comparisons with three-dimensional atmospheric models show that both the phase curve shape and emission spectra strongly suggest the presence of nightside clouds which become optically thick to thermal emission at pressures greater than ~100 mbar. The dayside is consistent with a cloudless atmosphere above the mid-infrared photosphere. Contrary to expectations from equilibrium chemistry but consistent with disequilibrium kinetics models, methane is not detected on the nightside (2$σ$ upper limit of 1-6 parts per million, depending on model assumptions).

astro-ph.EP↗