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We report on the detailed characterization of the HD 77946 planetary system. HD 77946 is an F5 ($M_*$ = 1.17 M$_{\odot}$, $R_*$ = 1.31 R$_{\odot}$) star, which hosts a transiting planet recently discovered by NASA's Transiting Exoplanet Survey Satellite (TESS), classified as TOI-1778 b. Using TESS photometry, high-resolution spectroscopic data from HARPS-N, and photometry from CHEOPS, we measure the radius and mass from the transit and RV observations, and find that the planet, HD 77946 b, orbits with period $P_{\rm b}$ = $6.527282_{-0.000020}^{+0.000015}$ d, has a mass of $M_{\rm b} = 8.38\pm{1.32}$M$_\oplus$, and a radius of $R_{\rm b} = 2.705_{-0.081}^{+0.086}$R$_\oplus$. From the combination of mass and radius measurements, and the stellar chemical composition, the planet properties suggest that HD 77946 b is a sub-Neptune with a $\sim$1\% H/He atmosphere. However, a degeneracy still exists between water-world and silicate/iron-hydrogen models, and even though interior structure modelling of this planet favours a sub-Neptune with a H/He layer that makes up a significant fraction of its radius, a water-world composition cannot be ruled out, as with $T_{\rm eq} = 1248^{+40}_{-38}~$K, water may be in a supercritical state. The characterisation of HD 77946 b, adding to the small sample of well-characterised sub-Neptunes, is an important step forwards on our journey to understanding planetary formation and evolution pathways. Furthermore, HD 77946 b has one of the highest transmission spectroscopic metrics for small planets orbiting hot stars, thus transmission spectroscopy of this key planet could prove vital for constraining the compositional confusion that currently surrounds small exoplanets., Comment: 19 pages, 13 figures, 5 tables. Published in MNRAS

Short-period giant planets are frequently found to be solitary compared to other classes of exoplanets. Small inner companions to giant planets with $P \lesssim$ 15 days are known only in five compact systems: WASP-47, Kepler-730, WASP-132, TOI-1130, and TOI-2000. Here, we report the confirmation of TOI-5398, the youngest compact multi-planet system composed of a hot sub-Neptune (TOI-5398 c, $P_{\rm c}$ = 4.77271 days) orbiting interior to a short-period Saturn (TOI-5398 b, $P_{\rm b}$ = 10.590547 days) planet, both transiting around a 650 $\pm$ 150 Myr G-type star. As part of the GAPS Young Object project, we confirmed and characterised this compact system, measuring the radius and mass of both planets, thus constraining their bulk composition. Using multidimensional Gaussian processes, we simultaneously modelled stellar activity and planetary signals from TESS Sector 48 light curve and our HARPS-N radial velocity time series. We have confirmed the planetary nature of both planets, TOI-5398 b and TOI-5398 c, alongside a precise estimation of stellar parameters. Through the use of astrometric, photometric, and spectroscopic observations, our findings indicate that TOI-5398 is a young, active G dwarf star (650 $\pm$ 150 Myr), with a rotational period of $P_{\rm rot}$ = 7.34 days. The transit photometry and radial velocity measurements enabled us to measure both the radius and mass of planets b, $R_b = 10.30\pm0.40 R_{\oplus}$, $M_b = 58.7\pm5.7 M_{\oplus}$, and c, $R_c = 3.52 \pm 0.19 R_{\oplus}$, $M_c = 11.8\pm4.8 M_{\oplus}$. TESS observed TOI-5398 during sector 48 and no further observations are planned in the current Extended Mission, making our ground-based light curves crucial for ephemeris improvement. With a Transmission Spectroscopy Metric value of around 300, TOI-5398 b is the most amenable warm giant (10 < $P$ < 100 days) for JWST atmospheric characterisation., Comment: 29 pages, Paper accepted for publication in Astronomy & Astrophysics

We define a local homomorphism $(Q,k)\to (R,\ell)$ to be Koszul if its derived fiber $R \otimes^{\mathsf{L}}_Q k$ is formal, and if $\operatorname{Tor}^Q(R,k)$ is Koszul in the classical sense. This recovers the classical definition when $Q$ is a field, and more generally includes all flat deformations of Koszul algebras. The non-flat case is significantly more interesting, and there is no need for examples to be quadratic: all complete intersection and all Golod quotients are Koszul homomorphisms. We show that the class of Koszul homomorphisms enjoys excellent homological properties, and we give many more examples, especially various monomial and Gorenstein examples. We then study Koszul homomorphisms from the perspective of $\mathrm{A}_\infty$-structures on resolutions. We use this machinery to construct universal free resolutions of $R$-modules by generalizing a classical construction of Priddy. The resulting (infinite) free resolution of an $R$-module $M$ is often minimal, and can be described by a finite amount of data whenever $M$ and $R$ have finite projective dimension over $Q$. Our construction simultaneously recovers the resolutions of Shamash and Eisenbud over a complete intersection ring, and the bar resolutions of Iyengar and Burke over a Golod ring, and produces analogous resolutions for various other classes of local rings., Comment: 47 pages; comments are welcome

One of the most ancient forms of life dating to ~3.5 billion years ago, cyanobacteria are highly abundant organisms that convert light into energy and motion, often within conjoined filaments and larger colonies. We study how gradients of light intensity trigger orderly phototactic motions and dense bacterial communities, which remained quantitatively unexplored despite being among the oldest forms of active living matter on Earth. The phototaxis drives a transition from initially polar motions of semiflexible long filaments along complex curved spatiotemporal trajectories confined within illuminated areas to their bipolar motility in the ensuing crowded environment. We demonstrate how simply shining light causes a spontaneous self-assembly of two- and three-dimensional active nematic states of cyanobacterial filaments, with a plethora of motile and static topological defects. We quantify light-controlled evolutions of orientational and velocity order parameters during the transition between disordered and orientationally ordered states of our photosynthetic active matter, as well as the subsequent active nematic's fluid-gel transformation. Patterned illumination and foreign inclusions with different shapes interact with cyanobacterial active nematics in nontrivial ways, while inducing soft interfacial boundary conditions and quasi-boojum-like defects. Commanding this cyanobacterial collective behavior could aid inhibiting generation of toxins or enhancing production of oxygen and biomaterials.

Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or age-and-size-structured models establish constraints on individual growth under which the age- or age-and-size- distribution stabilizes, even as the population continues to grow without bound. However, individuals in real-world populations exhibit far more structural features than simply age and size. Notably, cyanobacteria contain carboxysome organelles which are central to carbon fixation and can be older (if inherited from parent cells) or younger (if created after division) than the enveloping cell. Motivated by a desire to understand how carboxysome age impacts growth at the colony level, we develop a multi-structured model which allows for an arbitrary (but finite) number of structure variables. We then derive and solve the renewal equation for cell division to obtain an asymptotic solution, and show that, under certain conditions, a stable structural distribution is reached.

We explicitly present homological residue fields for tensor triangulated categories as categories of comodules in a number of examples across algebra, geometry, and topology. Our results indicate that, despite their abstract nature, they are very natural objects and encode tangent data at the corresponding point on the spectrum., Comment: 11 pages, minor updates, to appear in the proceedings of the Abel Symposium 2022, Triangulated categories in representation theory and beyond

Recently, a widely applicable system of hyperbolic partial differential equations has been derived that enables the deterministic computation of a full heterogeneous stress field from a measured deformation field, for example, from a strain field obtained via digital image correlation. This information enables the determination of material properties, making this approach an alternative to finite element model updating or the virtual fields method. This article focuses on developing a finite volume discretization of this system of equations to address instabilities that arise from violations of the Courant-Friedrichs-Lewy condition. The developed discretization enables the system of equations to be applied to irregular geometries and finite deformation. We determine how, in general, one may translate knowledge of the traction at the boundary into boundary conditions, so that the numerical method can be applied to a variety of loading conditions. We analyse the solution structure in the case of deformation discontinuities, and the results are applied to account for discontinuities at the interfaces between finite volumes (this has relevance to other applications such as composite materials). Interestingly, the discontinuities cause reflection and transmission of the principal stresses. The finite volume discretization is validated using data output from commercial finite element software. Furthermore, the discretization is applied to an experimental uniaxial tension test with plastic deformation and necking. The strain field is obtained using digital image correlation, and the stress field is computed using the developed finite volume discretization. Together, these give the stress-strain behavior for each material element.

55 Cnc e is a transiting super-Earth (radius $1.88\rm\,R_\oplus$ and mass $8\rm\, M_\oplus$) orbiting a G8V host star on a 17-hour orbit. Spitzer observations of the planet's phase curve at 4.5 $\mu$m revealed a time-varying occultation depth, and MOST optical observations are consistent with a time-varying phase curve amplitude and phase offset of maximum light. Both broadband and high-resolution spectroscopic analyses are consistent with either a high mean molecular weight atmosphere or no atmosphere for planet e. A long term photometric monitoring campaign on an independent optical telescope is needed to probe the variability in this system. We seek to measure the phase variations of 55 Cnc e with a broadband optical filter with the 30 cm effective aperture space telescope CHEOPS and explore how the precision photometry narrows down the range of possible scenarios. We observed 55 Cnc for 1.6 orbital phases in March of 2020. We designed a phase curve detrending toolkit for CHEOPS photometry which allows us to study the underlying flux variations of the 55 Cnc system. We detected a phase variation with a full-amplitude of $72 \pm 7$ ppm but do not detect a significant secondary eclipse of the planet. The shape of the phase variation resembles that of a piecewise-Lambertian, however the non-detection of the planetary secondary eclipse, and the large amplitude of the variations exclude reflection from the planetary surface as a possible origin of the observed phase variations. They are also likely incompatible with magnetospheric interactions between the star and planet but may imply that circumplanetary or circumstellar material modulate the flux of the system. Further precision photometry of 55 Cnc from CHEOPS will measure variations in the phase curve amplitude and shape over time this year., Comment: 15 pages, accepted by A&A

Context. Hot subdwarfs experienced strong mass loss on the Red Giant Branch (RGB) and are now hot and small He-burning objects. Aims. In this project we aim to perform a transit survey in all available light curves of hot subdwarfs from space-based telescopes (Kepler, K2, TESS, and CHEOPS), with our custom-made pipeline SHERLOCK, in order to determine the occurrence rate of planets around these stars, as a function of orbital period and planetary radius. Methods. In this first paper, we perform injection-and-recovery tests of synthetic transits for a selection of representative Kepler, K2 and TESS light curves, to determine which transiting bodies, in terms of object radius and orbital period, we will be able to detect with our tools. We also provide such estimates for CHEOPS data, which we analyze with the pycheops package. Results. Transiting objects with a radius $\lesssim$ 1.0 $R_{\Earth}$ can be detected in most of Kepler, K2 and CHEOPS targets for the shortest orbital periods (1 d and below), reaching values as small as $\sim$0.3 $R_{\Earth}$ in the best cases. Reaching sub-Earth-sized bodies is achieved only for the brightest TESS targets, and the ones observed during a significant number of sectors. We also give a series of representative results for farther and bigger planets, for which the performances strongly depend on the target magnitude, the length and the quality of the data. Conclusions. The TESS sample will provide the most important statistics for the global aim of measuring the planet occurrence rate around hot subdwarfs. The Kepler, K2 and CHEOPS data will allow us to search for planetary remnants, i.e. very close and small (possibly disintegrating) objects, which would have partly survived the engulfment in their red giant host., Comment: 22 pages, 7 figures, accepted to A&A

A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed equations that assume pure plastic behavior without elasticity. A method to numerically solve these equations is also presented. In addition to force balance, the equations are derived from the elastic-plastic decomposition of the deformation gradient, the assumption of isotropy, and the assumption that the function mapping the elastic strain to stress is known. The system of equations can be directly applied to complex geometries, finite deformation, non-linear elasticity and plasticity, compressible materials, rate dependent materials, and a variety of hardening laws. This system of PDEs is non-linear and time dependent. Furthermore, it overcomes an important prior limitation: it can be directly applied to cases where some regions of a body are elastically deforming while others are elasto-plastically deforming. A two-dimensional case study of necking in a uniaxial tensile specimen is investigated to illustrate and validate the method. The governing equations are numerically solved using strain fields output from a finite element simulation and validated against this same simulation showing accurate results.

Determining the architecture of multi-planetary systems is one of the cornerstones of understanding planet formation and evolution. Resonant systems are especially important as the fragility of their orbital configuration ensures that no significant scattering or collisional event has taken place since the earliest formation phase when the parent protoplanetary disc was still present. In this context, TOI-178 has been the subject of particular attention since the first TESS observations hinted at a 2:3:3 resonant chain. Here we report the results of observations from CHEOPS, ESPRESSO, NGTS, and SPECULOOS with the aim of deciphering the peculiar orbital architecture of the system. We show that TOI-178 harbours at least six planets in the super-Earth to mini-Neptune regimes, with radii ranging from 1.152(-0.070/+0.073) to 2.87(-0.13/+0.14) Earth radii and periods of 1.91, 3.24, 6.56, 9.96, 15.23, and 20.71 days. All planets but the innermost one form a 2:4:6:9:12 chain of Laplace resonances, and the planetary densities show important variations from planet to planet, jumping from 1.02(+0.28/-0.23) to 0.177(+0.055/-0.061) times the Earth's density between planets c and d. Using Bayesian interior structure retrieval models, we show that the amount of gas in the planets does not vary in a monotonous way, contrary to what one would expect from simple formation and evolution models and unlike other known systems in a chain of Laplace resonances. The brightness of TOI-178 allows for a precise characterisation of its orbital architecture as well as of the physical nature of the six presently known transiting planets it harbours. The peculiar orbital configuration and the diversity in average density among the planets in the system will enable the study of interior planetary structures and atmospheric evolution, providing important clues on the formation of super-Earths and mini-Neptunes.

We determine the homological residue fields, in the sense of tensor-triangular geometry, in a series of concrete examples ranging from topological stable homotopy theory to modular representation theory of finite groups., Comment: 9 pages

Some M-dwarfs around F-/G-type stars have been measured to be hotter and larger than predicted by stellar evolution models. Inconsistencies between observations and models need addressing with more mass, radius and luminosity measurements of low-mass stars to test and refine evolutionary models. Our aim is to measure the masses, radii and ages of the stars in five low-mass eclipsing binary systems discovered by the WASP survey. We use WASP photometry to establish eclipse-time ephemerides and to obtain initial estimates for the transit depth and width. Radial velocity measurements were simultaneously fitted with follow-up photometry to find the best-fitting orbital solution. This solution was combined with measurements of atmospheric parameters to interpolate evolutionary models and estimate the mass of the primary star, and the mass and radius of the M-dwarf companion. We assess how the best fitting orbital solution changes if an alternative limb-darkening law is used and quantify the systematic effects of unresolved companions. We also gauge how the best-fitting evolutionary model changes if different values are used for the mixing length parameter and helium enhancement. We report the mass and radius of five M-dwarfs and find little evidence of inflation with respect to evolutionary models. The primary stars in two systems are near the ``blue hook'' stage of their post sequence evolution, resulting in two possible solutions for mass and age. We find that choices in helium enhancement and mixing-length parameter can introduce an additional 3-5\,\% uncertainty in measured M-dwarf mass. Unresolved companions can introduce an additional 3-8\% uncertainty in the radius of an M-dwarf, while the choice of limb-darkening law can introduce up to an additional 2\% uncertainty., Comment: 36 pages, 29 Figures. Accepted for publication in Section 7. Stellar structure and evolution of Astronomy & Astrophysics

State of the art radial-velocity (RV) exoplanet searches are currently limited by RV signals arising from stellar magnetic activity. We analyze solar observations acquired over a 3-year period during the decline of Carrington Cycle 24 to test models of RV variation of Sun-like stars. A purpose-built solar telescope at the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) provides disk-integrated solar spectra, from which we extract RVs and $\log{R'_{\rm HK}}$. The Solar Dynamics Observatory (SDO) provides disk-resolved images of magnetic activity. The Solar Radiation and Climate Experiment (SORCE) provides near-continuous solar photometry, analogous to a Kepler light curve. We verify that the SORCE photometry and HARPS-N $\log{R'_{\rm HK}}$ correlate strongly with the SDO-derived magnetic filling factor, while the HARPS-N RV variations do not. To explain this discrepancy, we test existing models of RV variations. We estimate the contributions of the suppression of convective blueshift and the rotational imbalance due to brightness inhomogeneities to the observed HARPS-N RVs. We investigate the time variation of these contributions over several rotation periods, and how these contributions depend on the area of active regions. We find that magnetic active regions smaller than $60 \ \rm Mm^2$ do not significantly suppress convective blueshift. Our area-dependent model reduces the amplitude of activity-induced RV variations by a factor of two. The present study highlights the need to identify a proxy that correlates specifically with large, bright magnetic regions on the surfaces of exoplanet-hosting stars., Comment: 16 pages, 7 figures, accepted by ApJ

K2-36 is a K dwarf orbited by two small ($R_{\rm b}=1.43\pm0.08$ $R_\oplus$ and $R_{\rm c}=3.2\pm0.3$ $R_\oplus$), close-in ($a_{\rm b}$=0.022 AU and $a_{\rm c}$=0.054 AU) transiting planets discovered by Kepler/K2. They are representatives of two families of small planets ($R_{\rm p}$<4 $R_\oplus$) recently emerged from the analysis of Kepler data, with likely a different structure, composition and evolutionary pathways. We revise the fundamental stellar parameters and the sizes of the planets, and provide the first measurement of their masses and bulk densities, which we use to infer their structure and composition. We observed K2-36 with the HARPS-N spectrograph over $\sim$3.5 years, collecting 81 useful radial velocity measurements. The star is active, with evidence for increasing levels of magnetic activity during the observing time span. The radial velocity scatter is $\sim$17 \ms due to the stellar activity contribution, which is much larger that the semi-amplitudes of the planetary signals. We tested different methods for mitigating the stellar activity contribution to the radial velocity time variations and measuring the planet masses with good precision. We found that K2-36 is likely a $\sim$1 Gyr old system, and by treating the stellar activity through a Gaussian process regression, we measured the planet masses $m_{\rm b}$=3.9$\pm$1.1 $M_\oplus$ and $m_{\rm c}$=7.8$\pm$2.3 $M_\oplus$. The derived planet bulk densities $\rho_{\rm b}$=7.2$^{+2.5}_{-2.1}$ $g/cm^{3}$ and $\rho_{\rm c}$=1.3$^{+0.7}_{-0.5}$ $g/cm^{3}$ point out that K2-36\,b has a rocky, Earth-like composition, and K2-36\,c is a low-density sub-Neptune. Composed of two planets with similar orbital separations but different densities, K2-36 represents an optimal laboratory for testing the role of the atmospheric escape in driving the evolution of close-in, low-mass planets after $\sim$1 Gyr from their formation., Comment: Accepted for publication on Astronomy $\&$ Astrophysics

We investigated the discrepancy between planetary mass determination using the transit timing variations (TTVs) and radial velocities (RVs), by analysing the multi-planet system Kepler-9. Despite being the first system characterised with TTVs, there are several discrepant solutions in the literature, with those reporting lower planetary densities being apparently in disagreement with high-precision RV observations. To resolve this, we gathered HARPS-N RVs at epochs that maximised the difference between the predicted RV curves from discrepant solutions in the literature. We also re-analysed the full Kepler data-set and performed a dynamical fit, within a Bayesian framework, using the newly derived central and duration times of the transits. We compared these results with the RV data and found that our solution better describes the RV observations, despite the masses of the planets being nearly half that presented in the discovery paper. We therefore confirm that the TTV method can provide mass determinations that agree with those determined using high-precision RVs. The low densities of the planets place them in the scarcely populated region of the super-Neptunes / inflated sub-Saturns in the mass-radius diagram., Comment: 11 pages, 9 figures, 5 tables. Accepted for publication in MNRAS

Super-Earths belong to a class of planet not found in the Solar System, but which appear common in the Galaxy. Given that some super-Earths are rocky, while others retain substantial atmospheres, their study can provide clues as to the formation of both rocky planets and gaseous planets, and - in particular - they can help to constrain the role of photo-evaporation in sculpting the exoplanet population. GJ 9827 is a system already known to host 3 super-Earths with orbital periods of 1.2, 3.6 and 6.2 days. Here we use new HARPS-N radial velocity measurements, together with previously published radial velocities, to better constrain the properties of the GJ 9827 planets. Our analysis can't place a strong constraint on the mass of GJ 9827 c, but does indicate that GJ 9827 b is rocky with a composition that is probably similar to that of the Earth, while GJ 9827 d almost certainly retains a volatile envelope. Therefore, GJ 9827 hosts planets on either side of the radius gap that appears to divide super-Earths into pre-dominantly rocky ones that have radii below $\sim 1.5 R_\oplus$, and ones that still retain a substantial atmosphere and/or volatile components, and have radii above $\sim 2 R_\oplus$. That the less heavily irradiated of the 3 planets still retains an atmosphere, may indicate that photoevaporation has played a key role in the evolution of the planets in this system., Comment: 16 pages, 9 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society

Next-generation optoelectronic devices and photonic circuitry will have to incorporate on-chip compatible nanolaser sources. Semiconductor nanowire lasers have emerged as strong candidates for integrated systems with applications ranging from ultrasensitive sensing, to data communication technologies. Despite significant advances in their fundamental aspects, the integration within scalable photonic circuitry remains challenging. Here we report on the realization of hybrid photonic devices consisting of nanowire lasers integrated with wafer-scale lithographically designed V-groove plasmonic waveguides. We present experimental evidence of the lasing emission and coupling into the propagating modes of the V-grooves, enabling on-chip routing of coherent and sub-diffraction confined light with room temperature operation. Theoretical considerations suggest that the observed lasing is enabled by a waveguide hybrid photonic-plasmonic mode. This work represents a major advance towards the realization of application-oriented photonic circuits with integrated nanolaser sources., Comment: 24 pages, 4 figures

We present the discovery by the WASP-South transit survey of three new transiting hot Jupiters, WASP-161 b, WASP-163 b and WASP-170 b. Follow-up radial velocities obtained with the Euler/CORALIE spectrograph and high-precision transit light curves obtained with the TRAPPIST-North, TRAPPIST-South, SPECULOOS-South, NITES, and Euler telescopes have enabled us to determine the masses and radii for these transiting exoplanets. WASP-161\,b completes an orbit around its $V=11.1$ F6V-type host star in 5.406 days, and has a mass and radius of $2.5\pm 0.2$$M_{Jup}$ and $1.14\pm 0.06$ $R_{Jup}$ respectively. WASP-163\,b has an orbital period of 1.609 days, a mass of $1.9\pm0.2$ $M_{Jup}$, and a radius of $1.2\pm0.1$ $R_{Jup}$. Its host star is a $V=12.5$ G8-type dwarf. WASP-170\,b is on a 2.344 days orbit around a G1V-type star of magnitude $V=12.8$. It has a mass of $1.7\pm0.2$ $M_{Jup}$ and a radius of $1.14\pm0.09$ $R_{Jup}$. Given their irradiations ($\sim10^9$ erg.s$^{-1}$.cm$^{-2}$) and masses, the three new planets sizes are in good agreement with classical structure models of irradiated giant planets., Comment: 14 pages, 7 figures, Accepted for publication in Astronomical Journal

M-dwarf stars are promising targets for identifying and characterizing potentially habitable planets. K2-3 is a nearby (45 pc), early-type M dwarf hosting three small transiting planets, the outermost of which orbits close to the inner edge of the stellar (optimistic) habitable zone. The K2-3 system is well suited for follow-up characterization studies aimed at determining accurate masses and bulk densities of the three planets. Using a total of 329 radial velocity measurements collected over 2.5 years with the HARPS-N and HARPS spectrographs and a proper treatment of the stellar activity signal, we aim to improve measurements of the masses and bulk densities of the K2-3 planets. We use our results to investigate the physical structure of the planets. We analyse radial velocity time series extracted with two independent pipelines by using Gaussian process regression. We adopt a quasi-periodic kernel to model the stellar magnetic activity jointly with the planetary signals. We use Monte Carlo simulations to investigate the robustness of our mass measurements of K2-3\,c and K2-3\,d, and to explore how additional high-cadence radial velocity observations might improve them. Despite the stellar activity component being the strongest signal present in the radial velocity time series, we are able to derive masses for both planet b ($M_{\rm b}=6.6\pm1.1$ $M_{\rm \oplus}$) and planet c ($M_{\rm c}=3.1^{+1.3}_{-1.2}$ $M_{\rm \oplus}$). The Doppler signal due to K2-3\,d remains undetected, likely because of its low amplitude compared to the radial velocity signal induced by the stellar activity. The closeness of the orbital period of K2-3\,d to the stellar rotation period could also make the detection of the planetary signal complicated. [...], Comment: 14 pages, 15 figures, accepted for publication in A&A