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The investigation of the behaviour for geometric functionals of random fields on manifolds has drawn recently considerable attention. In this paper, we extend this framework by considering fluctuations over time for the level curves of general isotropic Gaussian spherical random fields. We focus on both long and short memory assumptions; in the former case, we show that the fluctuations of $u$-level curves are dominated by a single component, corresponding to a second-order chaos evaluated on a subset of the multipole components for the random field. We prove the existence of cancellation points where the variance is asymptotically of smaller order; these points do not include the nodal case $u = 0$, in marked contrast with recent results on the high-frequency behaviour of nodal lines for random eigenfunctions with no temporal dependence. In the short memory case, we show that all chaoses contribute in the limit, no cancellation occurs and a Central Limit Theorem can be established by Fourth-Moment Theorems and a Breuer-Major argument.

We point out that conservation of information implies that remnants produced at the end of black hole evaporation should radiate in the low-frequency spectrum. We model this emission and derive properties of the diffuse radiation emitted by an otherwise dark population of such objects. We show that for early universe black holes the frequency and energy density of this radiation, which are in principle measurable, suffice to estimate the remnant density., Comment: 8 pages, 4 figures

We study the behaviour of the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam amplitude with homogeneous boundary data, under a graph refinement going from five to twenty boundary tetrahedra. This can be interpreted as a wave function of the universe, for which we compute boundary geometrical operators, correlation functions and entanglement entropy. The numerical calculation is made possible by adapting the Metropolis-Hastings algorithm, along with recently developed computational methods appropriate for the deep quantum regime. We confirm that the transition amplitudes are stable against such refinement. We find that the average boundary geometry does not change, but the new degrees of freedom correct the quantum fluctuations of the boundary and the correlations between spatial patches. The expectation values are compatible with their geometrical interpretation and the correlations between neighbouring patches decay when computed across different spinfoam vertices., Comment: 34 pages, 18 figures

Inspired by the recent work [MRT21], we prove a non-universal non-central Moderate Deviation principle for the nodal length of arithmetic random waves (Gaussian Laplace eigenfunctions on the standard flat torus) both on the whole manifold and on shrinking toral domains. Second order fluctuations for the latter were established in [MPRW16] and [BMW20] respectively, by means of chaotic expansions, number theoretical estimates and full correlation phenomena. Our proof is simple and relies on the interplay between the long memory behavior of arithmetic random waves and the chaotic expansion of the nodal length, as well as on well-known techniques in Large Deviation theory (the contraction principle and the concept of exponential equivalence)., Comment: 26 pages

The propagation of Galactic cosmic rays is well understood in the context of the solar system but is poorly studied for M dwarf systems. Quantifying the flux of cosmic rays reaching exoplanets is important since cosmic rays are relevant in the context of life. Here, we calculate the Galactic cosmic ray fluxes in AU Mic and Prox Cen planetary systems. We propagate the Galactic cosmic rays using a 1D cosmic ray transport model. We find for Prox Cen b, AU Mic b and AU Mic c that the Galactic cosmic ray fluxes are strongly suppressed and are lower than the fluxes reaching Earth. We include in our models, for the first time for a star other than the Sun, the effect of radial particle drift due to gradients and curvatures in the stellar magnetic field. For Prox Cen we find that the inclusion of particle drift leads to less suppression of Galactic cosmic rays fluxes than when it is excluded from the model. In the case of AU Mic we explore two different wind environments, with a low and high stellar wind mass-loss rate. For AU Mic, the particle drift also leads to less suppression of the Galactic cosmic ray fluxes but it is only significant for the high mass-loss rate scenario. However, both wind scenarios for AU Mic suppress the Galactic cosmic rays strongly. Overall, careful modelling of stellar winds is needed to calculate the Galactic cosmic ray fluxes reaching exoplanets. The results found here can be used to interpret future exoplanet atmosphere observations and in atmospheric models., Comment: 10 pages, 7 figures, accepted for publication in MNRAS

Spectropolarimetric data allow for simultaneous monitoring of stellar chromospheric $\log{R^{\prime}_{\rm{HK}}}$ activity and the surface-averaged longitudinal magnetic field, $B_l$, giving the opportunity to probe the relationship between large-scale stellar magnetic fields and chromospheric manifestations of magnetism. We present $\log{R^{\prime}_{\rm{HK}}}$ and/or $B_l$ measurements for 954 mid-F to mid-M stars derived from spectropolarimetric observations contained within the PolarBase database. Our magnetically active sample complements previous stellar activity surveys that focus on inactive planet-search targets. We find a positive correlation between mean $\log{R^{\prime}_{\rm{HK}}}$ and mean $\log|B_l|$, but for G stars the relationship may undergo a change between $\log{R'_{\rm{HK}}}\sim-4.4$ and $-4.8$. The mean $\log{R^{\prime}_{\rm{HK}}}$ shows a similar change with respect to the $\log{R^{\prime}_{\rm{HK}}}$ variability amplitude for intermediately-active G stars. We also combine our results with archival chromospheric activity data and published observations of large-scale magnetic field geometries derived using Zeeman Doppler Imaging. The chromospheric activity data indicate a slight under-density of late-F to early-K stars with $-4.75\leq\log{R'_{\rm HK}}\leq-4.5$. This is not as prominent as the original Vaughan-Preston gap, and we do not detect similar under-populated regions in the distributions of the mean $|B_l|$, or the $B_l$ and $\log{R'_{\rm HK}}$ variability amplitudes. Chromospheric activity, activity variability and toroidal field strength decrease on the main sequence as rotation slows. For G stars, the disappearance of dominant toroidal fields occurs at a similar chromospheric activity level as the change in the relationships between chromospheric activity, activity variability and mean field strength., Comment: 20 pages, 15 figures, 3 tables

The nearby M dwarf WX UMa has recently been detected at radio wavelengths with LOFAR. The combination of its observed brightness temperature and circular polarisation fraction suggests that the emission is generated via the electron-cyclotron maser instability. Two distinct mechanisms have been proposed to power such emission from low-mass stars: either a sub-Alfv\'enic interaction between the stellar magnetic field and an orbiting planet, or reconnection at the edge of the stellar magnetosphere. In this paper, we investigate the feasibility of both mechanisms, utilising the information about the star's surrounding plasma environment obtained from modelling its stellar wind. Using this information, we show that a Neptune-sized exoplanet with a magnetic field strength of 10-100 G orbiting at ~0.034 au can accurately reproduce the observed radio emission from the star, with corresponding orbital periods of 7.4 days. Due to the stellar inclination, a planet in an equatorial orbit is unlikely to transit the star. While such a planet could induce radial velocity semi-amplitudes from 7 to 396 m s$^{-1}$, it is unlikely that this signal could be detected with current techniques due to the activity of the host star. The application of our planet-induced radio emission model here illustrates its exciting potential as a new tool for identifying planet-hosting candidates from long-term radio monitoring. We also develop a model to investigate the reconnection-powered emission scenario. While this approach produces less favourable results than the planet-induced scenario, it nevertheless serves as a potential alternative emission mechanism which is worth exploring further., Comment: 15 pages, 12 figures. Accepted for publication in MNRAS

Magnetic interactions between stars and close-in planets may lead to a detectable signal on the stellar disk. HD 189733 is one of the key exosystems thought to harbor magnetic interactions, which may have been detected in August 2013. We present a set of twelve wind models at that period, covering the possible coronal states and coronal topologies of HD 189733 at that time. We assess the power available for the magnetic interaction and predict its temporal modulation. By comparing the predicted signal with the observed signal, we find that some models could be compatible with an interpretation based on star-planet magnetic interactions. We also find that the observed signal can be explained only with a stretch-and-break interaction mechanism, while that the Alfv\'en wings scenario cannot deliver enough power. We finally demonstrate that the past observational cadence of HD 189733 leads to a detection rate of only between 12 to 23%, which could explain why star-planet interactions have been hard to detect in past campaigns. We conclude that the firm confirmation of their detection will require dedicated spectroscopic observations covering densely the orbital and rotation period, combined with scarcer spectropolarimetric observations to assess the concomitant large-scale magnetic topology of the star., Comment: 16 pages, 8 figures, 4 tables, accepted for publication in MNRAS

We present a spectroscopic analysis of a 1-year intensive monitoring campaign of the 22-Myr old planet-hosting M dwarf AU Mic using the HARPS spectrograph. In a companion paper, we reported detections of the planet radial velocity (RV) signatures of the two close-in transiting planets of the system, with respective semi-amplitudes of 5.8 $\pm$ 2.5 m/s and 8.5 $\pm$ 2.5 m/s for AU Mic b and AU Mic c. Here, we perform an independent measurement of the RV semi-amplitude of AU Mic c using Doppler imaging to simultaneously model the activity-induced distortions and the planet-induced shifts in the line profiles. The resulting semi-amplitude of 13.3 $\pm$ 4.1 m/s for AU Mic c reinforces the idea that the planet features a surprisingly large inner density, in tension with current standard models of core accretion. Our brightness maps feature significantly higher spot coverage and lower level of differential rotation than the brightness maps obtained in late 2019 with the SPIRou spectropolarimeter, suggesting that the stellar magnetic activity has evolved dramatically over a $\sim$1-yr time span. Additionally, we report a 3-$\sigma$ detection of a modulation at 8.33 $\pm$ 0.04 d of the He I D3 (587.562 nm) emission flux, close to the 8.46-d orbital period of AU Mic b. The power of this emission (a few 10$^{17}$ W) is consistent with 3D magnetohydrodynamical simulations of the interaction between stellar wind and the close-in planet if the latter hosts a magnetic field of $\sim$10 G. Spectropolarimetric observations of the star are needed to firmly elucidate the origin of the observed chromospheric variability., Comment: Accepted for publication in MNRAS (15/03/2022); 19 pages including 6 pages of appendices; 14 figures including 5 in appendices

We report the detection and characterization of the transiting sub-Neptune TOI-1759 b, using photometric time-series from TESS and near infrared spectropolarimetric data from SPIRou on the CFHT. TOI-1759 b orbits a moderately active M0V star with an orbital period of $18.849975\pm0.000006$ d, and we measure a planetary radius and mass of $3.06\pm0.22$ R$_\oplus$ and $6.8\pm2.0$ M$_\oplus$. Radial velocities were extracted from the SPIRou spectra using both the CCF and the LBL methods, optimizing the velocity measurements in the near infrared domain. We analyzed the broadband SED of the star and the high-resolution SPIRou spectra to constrain the stellar parameters and thus improve the accuracy of the derived planet parameters. A LSD analysis of the SPIRou Stokes $V$ polarized spectra detects Zeeman signatures in TOI-1759. We model the rotational modulation of the magnetic stellar activity using a GP regression with a quasi-periodic covariance function, and find a rotation period of $35.65^{+0.17}_{-0.15}$ d. We reconstruct the large-scale surface magnetic field of the star using ZDI, which gives a predominantly poloidal field with a mean strength of $18\pm4$ G. Finally, we perform a joint Bayesian MCMC analysis of the TESS photometry and SPIRou RVs to optimally constrain the system parameters. At $0.1176\pm0.0013$ au from the star, the planet receives $6.4$ times the bolometric flux incident on Earth, and its equilibrium temperature is estimated at $433\pm14$ K. TOI-1759 b is a likely gas-dominated sub-Neptune with an expected high rate of photoevaporation. Therefore, it is an interesting target to search for neutral hydrogen escape, which may provide important constraints on the planetary formation mechanisms responsible for the observed sub-Neptune radius desert., Comment: Accepted for publication in the 10. Planets and planetary systems section of Astronomy & Astrophysics

Cool main-sequence stars, such as the Sun, have magnetic fields which are generated by an internal dynamo mechanism. In the Sun, the dynamo mechanism produces a balance between the amounts of magnetic flux generated and lost over the Sun's 11-year activity cycle and it is visible in the Sun's different atmospheric layers using multi-wavelength observations. We used the same observational diagnostics, spanning several decades, to probe the emergence of magnetic flux on the two close by, active- and low-mass K dwarfs: 61 Cygni A and Epsilon Eridani. Our results show that 61 Cygni A follows the Solar dynamo with a regular cycle at all wavelengths, while Epsilon Eridani represents a more extreme level of the Solar dynamo, while also showing strong Solar-like characteristics. For the first time we show magnetic butterfly diagrams for stars other than the Sun. For the two K stars and the Sun, the rate at which the toroidal field is generated from surface poloidal field is similar to the rate at which toroidal flux is lost through flux emergence. This suggests that the surface field plays a crucial role in the dynamos of all three stars. Finally, for Epsilon Eridani, we show that the two chromospheric cycle periods, of ~3 and ~13 years, correspond to two superimposed magnetic cycles., Comment: 8 pages, 5 figures: Accepted by A&A

Quantum theory can be understood as pointing to an ontology of relations. I observe that this reading of quantum mechanics is supported by the ubiquity of relationality in contemporary fundamental physics, including in classical mechanics, gauge theories, general relativity, quantum field theory, and the tentative theories of quantum gravity., Comment: To appear in the volume "Quantum Mechanics and Fundamentality: Naturalizing Quantum Theory between Scientific Realism and Ontological Indeterminacy", edited by Valia Allori, Springer Nature

We study numerically the first order radiative corrections to the self-energy, in covariant loop quantum gravity. We employ the recently developed 'sl2cfoam-next' spinfoam amplitudes library, and some original numerical methods. We analyze the scaling of the divergence with the infrared cutoff, for which previous analytical estimates provided widely different lower and upper bounds. Our findings suggest that the divergence is approximately linear in the cutoff. We also investigate the role of the Barbero-Immirzi parameter in the asymptotic behavior, the dependence of the scaling on some boundary data and the expectation values of boundary operators., Comment: 16 pages, 13 figures

The two planetary systems TOI-942 and TOI-421 share many similar characteristics, apart from their ages (50~Myr and 9~Gyr). Each of the stars hosts two sub-Neptune-like planets at similar orbits and in similar mass ranges. In this paper, we aim to investigate whether the similarity of the host stars and the configuration of the planetary systems can be taken as proof that the two systems were formed and evolved in a similar way. In paper I of this series, we performed a comparative study of these two systems using 3D modeling of atmospheric escape and its interaction with the stellar wind, for the four planets. We demonstrated that though the strong wind of the young star has a crucial effect on observable signatures, its effect on the atmospheric mass loss is minor in the evolutionary context. Here, we use atmosphere evolution models to track the evolution of planets in the younger system TOI-942 and also to constrain the past of the TOI-421 system. We demonstrate that despite all the similarities, the two planetary systems are on two very different evolutionary pathways. The inner planet in the younger system, TOI-942, will likely lose all of its atmosphere and become a super-Earth-like planet, while the outer planet will become a typical sub-Neptune. Concerning the older system, TOI-421, our evolution modeling suggests that they must have started their evolution with very substantial envelopes, which can be a hint of formation beyond the snow line., Comment: 9 pages, 4 figures; Accepted for publication in MNRAS

At young ages, when radiation from the host star is high, and the planet is hot and inflated after formation, planetary atmospheric mass loss can be extremely strong compared to older planets. In turn, stellar winds are faster and denser for young stars compared to evolved main-sequence stars. Their interaction with escaping planetary atmospheres can substantially affect atmospheric mass loss rates, as well as the observable signatures of escaping atmospheres, with both effects expected to occur differently for young and evolved planets. We perform a comparative study of two systems around stars of similar masses but very different ages (50~Myr and 9~Gyr): TOI-942 and TOI-421. Both stars host two sub-Neptune-like planets at similar orbits and in similar mass ranges, which allows a direct comparison of the atmospheric escape and interactions with the stellar winds in the young and old systems. We perform the 3D atmospheric modeling of the four planets in TOI-942 and TOI-421 systems and make the theoretical predictions of possible observational signatures in Ly-alpha absorption. We find that accounting for the stellar wind interacting with planetary atmospheres is crucial for the interpretation of the observations for young planets. Additionally, we show that a particular energy distribution along the XUV spectra has a minor effect on the atmospheric mass-loss rates, but it is of crucial importance for modeling the Ly-alpha absorption and therefore for interpretation of observations., Comment: 19 pages, 9+3 Figures (including Appendix); Accepted for publication in MNRAS

Atmospheric escape is considered to be one of the main channels for evolution in sub-Jovian planets, particularly in their early lives. While there are several hypotheses proposed to explain escape in exoplanets, testing them with atmospheric observations remains a challenge. In this context, high-resolution transmission spectroscopy of transiting exoplanets for the metastable helium triplet (He 2$^3$S) at $1\,083$ nm has emerged as a reliable technique to observe and measure escape. To aid in the prediction and interpretation of metastable He transmission spectroscopy observations, we developed the code p-winds. This is an open-source, fully documented, scalable Python implementation of the one-dimensional, purely H+He Parker wind model for upper atmospheres coupled with ionization balance, ray-tracing, and radiative transfer routines. We demonstrate an atmospheric retrieval by fitting p-winds models to the observed metastable He transmission spectrum of the warm Neptune HAT-P-11 b, and take into account the variation of the in-transit absorption caused by transit geometry. For this planet, our best fit yields a total atmospheric escape rate of approximately $2.5 \times 10^{10}$ g s$^{-1}$ and wind temperature of $7200$ K. The range of retrieved mass loss rates increases significantly when we let the H atom fraction be a free parameter, but the posterior distribution of the latter remains unconstrained by He observations alone. The stellar host limb darkening does not have a significant impact in the retrieved escape rate or outflow temperature for HAT-P-11 b. Based on the non-detection of escaping He for GJ 436 b, we are able to rule out total escape rates higher than $3.4 \times 10^{10}$ g s$^{-1}$ at 99.7% (3$\sigma$) confidence., Comment: 13 pages, 12 figures. Accepted for publication in Astronomy & Astrophysics. We encourage the community to send comments and test the code, which is openly available at https://github.com/ladsantos/p-winds

High-energy stellar irradiation can photoevaporate planetary atmospheres, which can be observed in spectroscopic transits of hydrogen lines. For the exoplanet HD189733b, multiple observations in the Ly-$\alpha$ line have shown that atmospheric evaporation is variable, going from undetected to enhanced evaporation in a $1.5$-year interval. Coincidentally or not, when HD189733b was observed to be evaporating, a stellar flare had just occurred 8h prior to the observation. This led to the question of whether this temporal variation in evaporation occurred due to the flare, an unseen associated coronal mass ejection (CME), or even the effect of both simultaneously. In this work, we investigate the impact of flares (radiation), winds, and CMEs (particles) on the atmosphere of HD189733b using 3D radiation hydrodynamic simulations of atmospheric evaporation that self-consistently include stellar photon heating. We study four cases: first- the quiescent phase of the star including stellar wind, second- a flare, third- a CME, and fourth- a flare that is followed by a CME. Compared to the quiescent case, we find that the flare alone increases the evaporation rate by only 25%, while the CME leads to a factor of 4 increase in escape rate. We calculate Ly-$\alpha$ synthetic transits and find that the flare alone cannot explain the observed high blueshifted velocities seen in the Ly-$\alpha$ observation. The CME, however, leads to an increase in the velocity of the escaping atmosphere, enhancing the transit depth at high blueshifted velocities. While the effects of CMEs show a promising potential to explain the blueshifted line feature, our models are not able to fully explain the blueshifted transit depths, indicating that they might require additional physical mechanisms., Comment: Accepted for publication in MNRAS, 14 pages, 9 figures

We simulate possible stellar coronal mass ejection (CME) scenarios over the magnetic cycle of $\epsilon$ Eridani (18 Eridani; HD 22049). We use three separate epochs from 2008, 2011, and 2013, and estimate the radio emission frequencies associated with these events. These stellar eruptions have proven to be elusive, although a promising approach to detect and characterise these phenomena are low-frequency radio observations of potential type II bursts as CME induced shocks propagate through the stellar corona. Stellar type II radio bursts are expected to emit below 450 MHz, similarly to their solar counterparts. We show that the length of time these events remain above the ionospheric cutoff is not necessarily dependent on the stellar magnetic cycle, but more on the eruption location relative to the stellar magnetic field. We find that these type II bursts would remain within the frequency range of LOFAR for a maximum of 20-30 minutes post-eruption for the polar CMEs, (50 minutes for 2nd harmonics). We find evidence of slower equatorial CMEs, which result in slightly longer observable windows for the 2008 and 2013 simulations. Stellar magnetic geometry and strength has a significant effect on the detectability of these events. We place the CMEs in the context of the stellar mass-loss rate (27-48 $\times$ solar mass-loss rate), showing that they can amount to 3-50% of the stellar wind mass-loss rate for $\epsilon$ Eridani. Continuous monitoring of likely stellar CME candidates with low-frequency radio telescopes will be required to detect these transient events., Comment: 17 pages, 11 figures. Accepted for publication in ApJ

Quantifying the flux of cosmic rays reaching exoplanets around M dwarfs is essential to understand their possible effects on exoplanet habitability. Here, we investigate the propagation of Galactic cosmic rays as they travel through the stellar winds (astrospheres) of five nearby M dwarfs, namely: GJ 15A, GJ 273, GJ 338B, GJ 411 and GJ 887. Our selected stars each have 1 or 2 detected exoplanets and they all have wind mass-loss rates constrained by Lyman-alpha observations. Our simulations use a combined 1D magnetohydrodynamic (MHD) Alfv\'en-wave-driven stellar wind model and 1D cosmic ray transport model. We find that GJ 411 and GJ 887 have Galactic cosmic rays fluxes comparable with Earth's at their habitable zones. On the other hand, GJ 15A, GJ 273 and GJ 338B receive a lower Galactic cosmic ray flux in their habitable zones. All exoplanets in our sample, with exception of GJ 15A c and GJ 411 c, have a significantly lower flux of Galactic cosmic rays than values observed at the Earth because they orbit closer-in. The fluxes found here can be further used for chemical modelling of planetary atmospheres. Finally, we calculate the radiation dose at the surface of the habitable-zone planet GJ 273 b, assuming it has an Earth-like atmosphere. This planet receives up to 209 times less 15 MeV energy cosmic ray fluxes than values observed at Earth. However, for high-energy cosmic rays (~ GeV), the difference in flux is only 2.3 times smaller, which contributes to GJ 273 b receiving a significant surface radiation dose of 0.13 mSv/yr (40% of the annual dose on Earth's surface)., Comment: 11 pages, 6 figures, accepted for publication in MNRAS

We present the discovery and characterisation of two transiting planets observed by \textit{TESS} in the light curves of the young and bright (V=9.67) star HD73583 (TOI-560). We perform an intensive spectroscopic and photometric space- and ground-based follow-up in order to confirm and characterise the system. We found that HD73583 is a young ($\sim 500$~Myr) active star with a rotational period of $12.08 \pm 0.11 $\,d, and a mass and radius of $ 0.73 \pm 0.02 M_\odot$ and $0.65 \pm 0.02 R_\odot$, respectively. HD73583 b ($P_b=6.3980420 _{ - 0.0000062 }^{+0.0000067}$ d) has a mass and radius of $10.2 _{-3.1}^{+3.4} M_\oplus$ and$2.79 \pm 0.10 R_\oplus$, respectively, that gives a density of $2.58 _{-0.81}^{ 0.95} {\rm g\,cm^{-3}}$. HD73583 c ($P_c= 18.87974 _{-0.00074 }^{+0.00086}$) has a mass and radius of $9.7_{-1.7} ^ {+1.8} M_\oplus$ and $2.39_{-0.09}^{+0.10} R_\oplus$, respectively, this translates to a density of $3.88 _{-0.80}^{+0.91} {\rm g\,cm^{-3}}$. Both planets are consistent with worlds made of a solid core surrounded by a volatile envelope. Because of their youth and host star brightness, they both are excellent candidates to perform transmission spectroscopy studies. We expect ongoing atmospheric mass-loss for both planets caused by stellar irradiation. We estimate that the detection of evaporating signatures on H and He would be challenging, but doable with present and future instruments., Comment: Accepted for publication in MNRAS

A detailed investigation of the magnetic properties of young Sun-like stars can provide valuable information on our Sun's magnetic past and its impact on the early Earth. We determine the properties of the moderately rotating young Sun-like star kappa Ceti's magnetic and activity cycles using 50 years of chromospheric activity data and six epochs of spectropolarimetric observations. The chromospheric activity was determined by measuring the flux in the Ca II H and K lines. A generalised Lomb-Scargle periodogram and a wavelet decomposition were used on the chromospheric activity data to establish the associated periodicities. The vector magnetic field of the star was reconstructed using the technique of Zeeman Doppler imaging on the spectropolarimetric observations. Our period analysis algorithms detect a 3.1 year chromospheric cycle in addition to the star's well-known ~6 year cycle period. Although the two cycle periods have an approximate 1:2 ratio, they exhibit an unusual temporal evolution. Additionally, the spectropolarimetric data analysis shows polarity reversals of the star's large-scale magnetic field, suggesting a ~10 year magnetic or Hale cycle. The unusual evolution of the star's chromospheric cycles and their lack of a direct correlation with the magnetic cycle establishes kappa Ceti as a curious young Sun. Such complex evolution of magnetic activity could be synonymous with moderately active young Suns, which is an evolutionary path that our own Sun could have taken., Comment: 15 pages including appendices, accepted for publication in A&A

Using 3D radiative MHD simulations and Lyman-$\alpha$ transit calculations, we investigate the effect of magnetic fields on the observational signatures of atmospheric escape in exoplanets. Using the same stellar wind, we vary the planet's dipole field strength ($B_p$) from 0 to 10G. For $B_p<3$G, the structure of the escaping atmosphere begins to break away from a comet-like tail following the planet ($B_p=0$), as we see more absorbing material above and below the orbital plane. For $B_p\geq3$G, we find a ``dead-zone'' around the equator, where low velocity material is trapped in the closed magnetic field lines. The dead-zone separates two polar outflows where absorbing material escapes along open field lines, leading to a double tail structure, above and below the orbital plane. We demonstrate that atmospheric escape in magnetised planets occurs through polar outflows, as opposed to the predominantly night-side escape in non-magnetised models. We find a small increase in escape rate with $B_p$, though this should not affect the timescale of atmospheric loss. As the size of the dead-zone increases with $B_p$, so does the line centre absorption in Lyman-$\alpha$, as more low-velocity neutral hydrogen covers the stellar disc during transit. For $B_p<3$G the absorption in the blue wing decreases, as the escaping atmosphere is less funnelled along the line of sight by the stellar wind. In the red wing (and for $B_p>3$G in the blue wing) the absorption increases caused by the growing volume of the magnetosphere. Finally we show that transits below and above the mid-disc differ caused by the asymmetry of the double tail structure., Comment: Accepted for publication in MNRAS. 12 pages, 8 figures

Cosmic rays can penetrate planetary atmospheres driving the formation of prebiotic molecules, which are important for the origin of life. We calculate the Galactic cosmic ray fluxes in the habitable zone of five nearby, well-studied solar-type stars and at the orbits of 2 known exoplanets. We model the propagation of Galactic cosmic rays through the stellar winds using a combined 1.5D stellar wind and 1D cosmic ray transport model. We find that the habitable zone of 61 Cyg A has comparable Galactic cosmic ray fluxes to present-day Earth values. For the other four systems ($\epsilon$ Eri, $\epsilon$ Ind, $\xi$ Boo B and $\pi^1$ UMa), the fluxes are orders of magnitude smaller than Earth values. Thus, it is unlikely that any as-of-yet undetected Earth-like planets in their habitable zones would receive a higher radiation dose than is received on Earth. $\epsilon\,$Ind$\,$b, a Jupiter-like planet orbiting at $\sim$11au, receives higher Galactic cosmic ray fluxes than Earth. We find the suppression of Galactic cosmic rays is influenced by whether diffusion or advection dominates at GeV energies and at distances where the wind has reached its' terminal velocity. For advectively-dominated winds ($\sim$younger systems), varying the astrospheric size influences the suppression significantly. For diffusion-dominated systems ($\sim$older systems) the astrospheric size, and therefore knowledge of the ISM properties, are not very important. This reduces the Galactic cosmic ray flux uncertainties in the habitable zone for diffusion-dominated systems. Whether a system is advection- or diffusion-dominated can be determined from the stellar wind properties., Comment: 10 pages, 4 figures, accepted for publication in MNRAS

Energetic particles may have been important for the origin of life on Earth by driving the formation of prebiotic molecules. We calculate the intensity of energetic particles, in the form of stellar and Galactic cosmic rays, that reach Earth at the time when life is thought to have begun ($\sim$3.8Gyr ago), using a combined 1.5D stellar wind model and 1D cosmic ray model. We formulate the evolution of a stellar cosmic ray spectrum with stellar age, based on the Hillas criterion. We find that stellar cosmic ray fluxes are larger than Galactic cosmic ray fluxes up to $\sim$4 GeV cosmic ray energies $\sim$3.8Gyr ago. However, the effect of stellar cosmic rays may not be continuous. We apply our model to HR 2562b, a young warm Jupiter-like planet orbiting at 20au from its host star where the effect of Galactic cosmic rays may be observable in its atmosphere. Even at 20au, stellar cosmic rays dominate over Galactic cosmic rays., Comment: Proceedings of the 37th International Cosmic Ray Conference (ICRC 2021)

In this survey we collect some recent results regarding the Lipschitz-Killing curvatures (LKCs) of the excursion sets of random eigenfunctions on the two-dimensional standard flat torus (arithmetic random waves) and on the two-dimensional unit sphere (random spherical harmonics). In particular, the aim of the present survey is to highlight the key role of integration by parts formulae in order to have an extremely neat expression for the random LKCs. Indeed, the main tool to study local geometric functionals of random waves on manifold is to exploit their Wiener chaos decomposition and show that (often), in the so-called high-energy limit, a single chaotic component dominates their behavior. Moreover, reduction principles show that the dominant Wiener chaotic component of LKCs of random waves' excursion sets at threshold level $u\ne0$ is proportional to the integral of $H_2(f)$, f being the random field of interest and $H_2$ the second Hermite polynomial. This will be shown via integration by parts formulae., Comment: 19 pages

In recent years, thanks to new facilities such as LOFAR capable of sensitive observations, much work has been done on the detection of stellar radio emission at low frequencies. Such emission has commonly been shown to be coherent emission, generally attributed to electron-cyclotron maser emission, and has usually been detected from main-sequence M dwarfs. Here we report the first detection of coherent emission at low frequencies from T Tauri stars, which are known to be associated with high levels of stellar activity. Using LOFAR, we have detected several bright radio bursts at 150 MHz from two weak-line T Tauri stars: KPNO-Tau 14 and LkCa 4. All of the bursts have high brightness temperatures ($10^{13} - 10^{14}\ \mathrm{K}$) and high circular polarization fractions (60 - 90 \%), indicating that they must be due to a coherent emission mechanism. This could be either plasma emission or electron-cyclotron maser (ECM) emission. Due to the exceptionally high brightness temperatures seen in at least one of the bursts ($\geq 10^{14}\ \mathrm{K}$), and the high circular polarization levels, it seems unlikely that plasma emission could be the source and so ECM is favoured as the most likely emission mechanism. Assuming this is the case, the required magnetic field in the emission regions would be 40 - 70 G. We determine that the most likely method of generating ECM emission is plasma co-rotation breakdown in the stellar magnetosphere. There remains the possibility, however, it could be due to an interaction with an orbiting exoplanet., Comment: 16 pages, 9 figures, accepted for publication in A&A

Accompanying the mounting detections of planets orbiting white dwarfs and giant stars are questions about their physical history and evolution, particularly regarding detectability of their atmospheres and potential for habitability. Here we determine how the size of planetary magnetospheres evolve over time from the end of the main sequence through to the white dwarf phase due to the violent winds of red giant and asymptotic giant branch stars. By using a semianalytic prescription, we investigate the entire relevant phase space of planet type, planet orbit and stellar host mass (1-7Msun). We find that a planetary magnetosphere will always be quashed at some point during the giant branch phases unless the planet's magnetic field strength is at least two orders of magnitude higher than Jupiter's current value. We also show that the time variation of the stellar wind and density generates a net increase in wind ram pressure and does not allow a magnetosphere to be maintained at any time for field strengths less than 10^{-5} T (0.1 G). This lack of protection hints that currently potentially habitable planets orbiting white dwarfs would have been previously inhospitable., Comment: Accepted for publication in MNRAS

Galactic cosmic rays are energetic particles important in the context of life. Many works have investigated the propagation of Galactic cosmic rays through the Sun's heliosphere. However, the cosmic ray fluxes in M dwarf systems are still poorly known. Studying the propagation of Galactic cosmic rays through the astrospheres of M dwarfs is important to understand the effect on their orbiting planets. Here, we focus on the planetary system GJ 436. We perform simulations using a combined 1D cosmic ray transport model and 1D Alfv\'en-wave-driven stellar wind model. We use two stellar wind set-ups: one more magnetically-dominated and the other more thermally-dominated. Although our stellar winds have similar magnetic field and velocity profiles, they have mass-loss rates two orders of magnitude different. Because of this, they give rise to two different astrosphere sizes, one ten times larger than the other. The magnetically-dominated wind modulates the Galactic cosmic rays more at distances < 0.2 au than the thermally-dominated wind due to a higher local wind velocity. Between 0.2 and 1 au the fluxes for both cases start to converge. However, for distances > 10 au, spatial diffusion dominates, and the flux of GeV cosmic rays is almost unmodulated. We find, irrespective of the wind regime, that the flux of Galactic cosmic rays in the habitable zone of GJ 436 (0.2 - 0.4 au) is comparable with intensities observed at Earth. On the other hand, around GJ 436 b (0.028 au), both wind regimes predict Galactic cosmic ray fluxes that are approximately $10^4$ times smaller than the values observed at Earth., Comment: 11 pages, 5 figures, accepted for publication in MNRAS

The space-weather conditions that result from stellar winds significantly impact the habitability of exoplanets. The conditions can be calculated from first principles if the necessary boundary conditions -- namely on the plasma density in the outer corona and the radial distance at which the plasma forces the closed magnetic field into an open geometry -- are specified. Low frequency radio observations ($\nu \lesssim 200$ MHz) of plasma and cyclotron emission from stars probe these magneto-ionic conditions. Here we report the detection of low-frequency ($120-167\,{\rm MHz}$) radio emission associated with the dMe6 star WX UMa. If the emission originates in WX UMa's corona, we show that the closed field regions extends to at least $\approx 10$ stellar radii, that is about a factor of a few larger than the solar value, and possibly to $\gtrsim 20$ stellar radii. Our results suggest that the magnetic-field structure of M dwarfs is in between Sun-like and planet-like configurations, where compact over-dense coronal loops with X-ray emitting plasma co-exist with a large-scale magnetosphere with lower plasma density and closed magnetic geometry., Comment: Accepted for publication in A&A, 10 pages, 7 figures, 2 tables

High resolution UV spectra of stellar H I Lyman-alpha lines from the Hubble Space Telescope (HST) provide observational constraints on the winds of coronal main sequence stars, thanks to an astrospheric absorption signature created by the interaction between the stellar winds and the interstellar medium. We report the results of a new HST survey of M dwarf stars, yielding six new detections of astrospheric absorption. We estimate mass-loss rates for these detections, and upper limits for nondetections. These new constraints allow us to characterize the nature of M dwarf winds and their dependence on coronal activity for the first time. For a clear majority of the M dwarfs, we find winds that are weaker or comparable in strength to that of the Sun, i.e. Mdot<=1 Mdot_sun. However, two of the M dwarfs have much stronger winds: YZ CMi (M4 Ve; Mdot=30 Mdot_sun) and GJ 15AB (M2 V+M3.5 V; Mdot=10 Mdot_sun). Even these winds are much weaker than expectations if the solar relation between flare energy and coronal mass ejection (CME) mass extended to M dwarfs. Thus, the solar flare/CME relation does not appear to apply to M dwarfs, with important ramifications for the habitability of exoplanets around M dwarfs. There is evidence for some increase in Mdot with coronal activity as quantified by X-ray flux, but with much scatter. One or more other factors must be involved in determining wind strength besides spectral type and coronal activity, with magnetic topology being one clear possibility., Comment: 40 pages, 11 figures, to appear in The Astrophysical Journal

There have recently been detections of radio emission from low-mass stars, some of which are indicative of star-planet interactions. Motivated by these exciting new results, here we present stellar wind models for the active planet-hosting M dwarf AU Mic. Our models incorporate the large-scale photospheric magnetic field map of the star, reconstructed using the Zeeman-Doppler Imaging method. We use our models to assess if planet-induced radio emission could be generated in the corona of AU Mic, through a mechanism analogous to the sub-Alfv\'enic Jupiter-Io interaction. In the case that AU Mic has a mass-loss rate of 27 times that of the Sun, we find that both planets b and c in the system can induce radio emission from 10 MHz to 3 GHz in the corona of the host star for the majority of their orbits, with peak flux densities of 10 mJy. Our predicted emission bears a striking similarity to that recently reported from GJ 1151 by Vedantham et al. (2020), which is indicative of being induced by a planet. Detection of such radio emission would allow us to place an upper limit on the mass-loss rate of the star., Comment: 4 pages, 3 figures. Proceedings of the 20.5th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun (CS20.5), March 2021. arXiv admin note: substantial text overlap with arXiv:2103.16318

There have recently been detections of radio emission from low-mass stars, some of which are indicative of star-planet interactions. Motivated by these exciting new results, in this paper we present Alfv\'en wave-driven stellar wind models of the two active planet-hosting M dwarfs Prox Cen and AU Mic. Our models incorporate large-scale photospheric magnetic field maps reconstructed using the Zeeman-Doppler Imaging method. We obtain a mass-loss rate of $0.25~\dot{M}_{\odot}$ for the wind of Prox Cen. For the young dwarf AU Mic, we explore two cases: a low and high mass-loss rate. Depending on the properties of the Alfv\'en waves which heat the corona in our wind models, we obtain mass-loss rates of $27$ and $590~\dot{M}_{\odot}$ for AU Mic. We use our stellar wind models to assess the generation of electron cyclotron maser instability emission in both systems, through a mechanism analogous to the sub-Alfv\'enic Jupiter-Io interaction. For Prox Cen we do not find any feasible scenario where the planet can induce radio emission in the star's corona, as the planet orbits too far from the star in the super-Alfv\'enic regime. However, in the case that AU Mic has a stellar wind mass-loss rate of $27~\dot{M}_{\odot}$, we find that both planets b and c in the system can induce radio emission from $\sim10$ MHz to 3 GHz in the corona of the host star for the majority of their orbits, with peak flux densities of $\sim10$ mJy. Detection of such radio emission would allow us to place an upper limit on the mass-loss rate of the star., Comment: 8 pages, 5 figures. Accepted for publication in MNRAS

How has the solar wind evolved to reach what it is today? In this review, I discuss the long-term evolution of the solar wind, including the evolution of observed properties that are intimately linked to the solar wind: rotation, magnetism and activity. Given that we cannot access data from the solar wind 4 billion years ago, this review relies on stellar data, in an effort to better place the Sun and the solar wind in a stellar context. I overview some clever detection methods of winds of solar-like stars, and derive from these an observed evolutionary sequence of solar wind mass-loss rates. I then link these observational properties (including, rotation, magnetism and activity) with stellar wind models. I conclude this review then by discussing implications of the evolution of the solar wind on the evolving Earth and other solar system planets. I argue that studying exoplanetary systems could open up new avenues for progress to be made in our understanding of the evolution of the solar wind., Comment: Living Reviews in Solar Physics, in press, 26 figures, 88 pages (invited review article)

Energetic particles, such as stellar cosmic rays, produced at a heightened rate by active stars (like the young Sun) may have been important for the origin of life on Earth and other exoplanets. Here we compare, as a function of stellar rotation rate ($\Omega$), contributions from two distinct populations of energetic particles: stellar cosmic rays accelerated by impulsive flare events and Galactic cosmic rays. We use a 1.5D stellar wind model combined with a spatially 1D cosmic ray transport model. We formulate the evolution of the stellar cosmic ray spectrum as a function of stellar rotation. The maximum stellar cosmic ray energy increases with increasing rotation i.e., towards more active/younger stars. We find that stellar cosmic rays dominate over Galactic cosmic rays in the habitable zone at the pion threshold energy for all stellar ages considered ($t_*=0.6-2.9\,$Gyr). However, even at the youngest age, $t_*=0.6\,$Gyr, we estimate that $\gtrsim\,80$MeV stellar cosmic ray fluxes may still be transient in time. At $\sim1\,$Gyr when life is thought to have emerged on Earth, we demonstrate that stellar cosmic rays dominate over Galactic cosmic rays up to $\sim$4$\,$GeV energies during flare events. Our results for $t_*=0.6\,$Gyr ($\Omega = 4\Omega_\odot$) indicate that $\lesssim$GeV stellar cosmic rays are advected from the star to 1$\,$au and are impacted by adiabatic losses in this region. The properties of the inner solar wind, currently being investigated by the Parker Solar Probe and Solar Orbiter, are thus important for accurate calculations of stellar cosmic rays around young Sun-like stars., Comment: 14 pages, 8 figures, accepted for publication in MNRAS

The evolution of the atmospheres of low and intermediate-mass planets is strongly connected to the physical properties of their host stars. The types and the past activities of planet-hosting stars can, therefore, affect the overall planetary population. In this paper, we perform a comparative study of sub-Neptune-like planets orbiting stars of different masses and different evolutionary histories. We discuss the general patterns of the evolved population as a function of parameters and environments of planets. As a model of the atmospheric evolution, we employ the own framework combining planetary evolution in MESA with the realistic prescription of the escape of hydrogen-dominated atmospheres. {We find that the final populations look qualitatively similar in terms of the atmospheres survival around different stars, but qualitatively different, with this difference accentuated for planets orbiting more massive stars. We show that a planet has larger chances of keeping its primordial atmosphere in the habitable zone of a solar mass star compared to M or K dwarfs and if it starts the evolution having a relatively compact envelope.} We also address the problem of the uncertain initial temperatures (luminosities) of planets and show that this issue is only of particular importance for planets exposed to extreme atmospheric mass-losses., Comment: 18 pages, 13 figures. Accepted for publication in MNRAS

We report on observations of the active K2 dwarf $\epsilon$ Eridani based on contemporaneous SPIRou, NARVAL, and TESS data obtained over two months in late 2018, when the activity of the star was reported to be in a non-cyclic phase. We first recover the fundamental parameters of the target from both visible and nIR spectral fitting. The large-scale magnetic field is investigated from polarimetric data. From unpolarized spectra, we estimate the total magnetic flux through Zeeman broadening of magnetically sensitive nIR lines and the chromospheric emission using the CaII H & K lines. The TESS photometric monitoring is modeled with pseudo-periodic Gaussian Process Regression. Fundamental parameters of $\epsilon$ Eridani derived from visible and near-infrared wavelengths provide us with consistent results, also in agreement with published values. We report a progressive increase of macroturbulence towards larger nIR wavelengths. Zeeman broadening of individual lines highlights an unsigned surface magnetic field $B_{\rm mono} = 1.90 \pm 0.13$ kG, with a filling factor $f = 12.5 \pm 1.7$% (unsigned magnetic flux $Bf = 237 \pm 36$ G). The large-scale magnetic field geometry, chromospheric emission, and broadband photometry display clear signs of non-rotational evolution over the course of data collection. Characteristic decay times deduced from the light curve and longitudinal field measurements fall in the range 30-40 d, while the characteristic timescale of surface differential rotation, as derived through the evolution of the magnetic geometry, is equal to $57 \pm 5$ d. The large-scale magnetic field exhibits a combination of properties not observed previously for $\epsilon$ Eridani, with a surface field among the weakest previously reported, but also mostly axisymmetric, and dominated by a toroidal component., Comment: A&A, in press, abridged abstract