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Atmospheric characterization is key to understanding exoplanetary systems, offering insights into the planets current and past conditions. By analyzing key lines like H alpha and the He I triplet, we can trace the evolution of planets through atmospheric photo-evaporation. While ultra-hot Jupiters have been the focus for years, attention is shifting toward smaller, colder planets, which are more challenging to study due to weaker signals, requiring more precise techniques. This study aims to characterize the atmosphere of TOI-5398 b, a warm Saturn with a 10.59-day orbit around a young (650 Myr) G-type star. The system also hosts a smaller inner planet, TOI-5398 c, with a 4.77-day orbit. Both planets are ideal for atmospheric studies due to their proximity to the host star, which drives strong photo-evaporation, especially in planet b, whose high transmission spectroscopy metric (288) makes it a prime target. We analyzed data from a transit observed with the HARPS-N and GIANO-B high-resolution spectrographs, using cross-correlation and single-line analysis to search for atomic species. During this observation, planet c was also transiting, so we investigated the source of the signals. Based on photo-evaporation models, we attribute the signal mainly to planet b, which is expected to lose more mass. We detected H alpha and He I triplets, key markers of photo-evaporation, corresponding to atmospheric heights of 2.33 Rp and 1.65 Rp, respectively. The ATES models supported our observations, predicting a similar He I absorption for planet b and suggesting an He/H ratio of 1/99. Additionally, we detected an Na I doublet via single-line analysis, though cross-correlation did not reveal other atomic species., Comment: Accepted to A&A

Context. Stellar activity consists of different phenomena, mainly spots and faculae, and it is one of the main sources of noise in exoplanetary observations because it affects both spectroscopic and photometric observations. If we want to study young active planetary systems we need to model the activity of the host stars in order to remove astrophysical noise from our observational data. Aims. We modelled the contribution of stellar spots in photometric observations. Through the use of multiband photometry, we aim to extract the geometric properties of the spots and constrain their temperature. Methods. We analyzed multiband photometric observations acquired with the 80 cm Marcon telescope of the Osservatorio Polifunzionale del Chianti of V1298 Tau, assuming that the photometric modulation observed in different bands should be due to cold spots. Results. We constrained the effective temperature of the active regions present on the surface of V1298 Tau, which is composed by the contemporary presence of spots and faculae. We tested our hypothesis on solar data, verifying that we measure the size of the dominant active region and its averaged effective temperature.

We investigate the choice behavior of a decision maker (DM) who harms herself, by maximizing some distortion of her true preference, in which the first $i$ alternatives are moved to the bottom, in a reversed order. The deterministic declination of our pattern has no empirical power, but it allows to define a degree of self-punishment, which measures the extent of the denial of pleasure adopted by the DM in her decision. We analyze irrational choices that display the lowest degree of self-punishment, and a characterization of them is provided. Moreover, we characterize the choice behavior that exhibits the highest degree of self-punishment, and we show that it comprises almost all choices. We also characterize stochastic self-punishment, which collects all the Random Utility Models (RUMs) whose support is restricted to the harmful distortions of some preference. Full identification of the DM's preference and randomization over its harmful distortions is allowed if each alternative is selected from the ground set with probability greater than zero. Finally, the degree of self-punishment of harmful stochastic choices is characterized.

The ESO public survey VISTA Variables in the V\'ia L\'actea (VVV) surveyed the inner Galactic bulge and the adjacent southern Galactic disk from $2009-2015$. Upon its conclusion, the complementary VVV eXtended (VVVX) survey has expanded both the temporal as well as spatial coverage of the original VVV area, widening it from $562$ to $1700$ sq. deg., as well as providing additional epochs in $JHK_{\rm s}$ filters from $2016-2023$. With the completion of VVVX observations during the first semester of 2023, we present here the observing strategy, a description of data quality and access, and the legacy of VVVX. VVVX took $\sim 2000$ hours, covering about 4% of the sky in the bulge and southern disk. VVVX covered most of the gaps left between the VVV and the VISTA Hemisphere Survey (VHS) areas and extended the VVV time baseline in the obscured regions affected by high extinction and hence hidden from optical observations. VVVX provides a deep $JHK_{\rm s}$ catalogue of $\gtrsim 1.5\times10^9$ point sources, as well as a $K_{\rm s}$ band catalogue of $\sim 10^7$ variable sources. Within the existing VVV area, we produced a $5D$ map of the surveyed region by combining positions, distances, and proper motions of well-understood distance indicators such as red clump stars, RR Lyrae, and Cepheid variables. In March 2023 we successfully finished the VVVX survey observations that started in 2016, an accomplishment for ESO Paranal Observatory upon 4200 hours of observations for VVV+VVVX. The VVV+VVVX catalogues complement those from the Gaia mission at low Galactic latitudes and provide spectroscopic targets for the forthcoming ESO high-multiplex spectrographs MOONS and 4MOST., Comment: 17 pages, 11 figures (+ appendix). Accepted for publication in Astronomy and Astrophysics in section 14: Catalogs and data

MHD kink instability can trigger the fragmentation of a twisted magnetic flux tube into small-scale current sheets that dissipate as aperiodic impulsive heating events. This instability propagates as an avalanche to nearby flux tubes and leads to a nanoflare storm. Our previous work was devoted to related 3D MHD numerical modeling with a stratified and realistic atmosphere. This work addresses predictions for the EUV imaging spectroscopy of such structure and evolution of a loop, with an average temperature of 2.5 MK in the solar corona. We set a particular focus on the forthcoming MUSE mission. From the output of the numerical simulations, we synthesized the intensities, Doppler shifts, and non-thermal line broadening in 3 EUV spectral lines in the MUSE passbands: Fe IX 171A, Fe XV 284 A, and Fe XIX 108 A, at 1 MK, 2 MK, and 10 MK, respectively, according to the MUSE expected pixel size, temporal resolution, and temperature response functions. We provide maps showing different view angles and realistic spectra. Finally, we discuss the relevant evolutionary processes from the perspective of possible observations. We find that the MUSE observations might be able to detect the fine structure determined by tube fragmentation. In particular, the Fe IX line is mostly emitted at the loop footpoints, where we track the motions that drive the magnetic stressing and detect the upward motion of evaporating plasma from the chromosphere. In Fe XV, we see the bulk of the loop with increasing intensity. The Fe XIX line is very faint within the chosen simulation parameters; thus, any transient brightening around the loop apex may possibly be emphasized by the folding of sheet-like structure. In conclusion, we show that coronal loop observations with MUSE can pinpoint some crucial features of MHD-modeled ignition processes, such as the related dynamics, helping to identify the heating processes.

Context. Traditionally, Globular Clusters (GCs) have been assumed to be quasi-relaxed non-rotating systems, characterized by spherical symmetry and orbital isotropy. However, in recent years, a growing set of observational evidence is unveiling an unexpected dynamical complexity in Galactic GCs. Indeed, kinematic studies show that a measurable amount of internal rotation is present in many present-day GCs. Aims. The objective of this work is to analyse the APOGEE-2 Value-Added Catalogs (VACs) DR17 data of a sample of 21 GCs to extend the sample showing signatures of systemic rotation, in order to better understand the kinematic properties of GCs in general. Also, we aim to identify the fastest rotating GC from the sample of objects with suitable measurements. Methods. From the sample of 23 GCs included in this work, the presence of systemic rotation was detected in 21 of the GCs, using three different methods. All these methods use the radial velocity referred to the cluster systemic velocity. Using the first method, it was possible to visually verify the clear-cut signature of systemic rotation. Whereas, using the second and third methods, it was possible to determine the amplitude of the rotation curve and the position angle of the rotation axis. Results. This study shows that 21 GCs have a signature of systemic rotation. For these clusters, the rotation amplitude and the position angle of the rotation axis have been calculated. The clusters cover a remarkable range of rotational amplitudes, from 0.77 km/s to 13.85 km/s.

The super-Earth LHS 1140 b is an interesting target for atmospheric observations since it is close to the habitable zone of its star and falls in the gap of the radius distribution of small exoplanets, in the region thought to correspond to the transition between planets with and without atmospheres. Observations of the primary transit with WFC3 on board of the Hubble Space Telescope (HST) revealed a modulation in the planet transmission spectrum compatible with the presence of water; however this modulation may be also due to stellar activity-related phenomena. Here we present a detailed analysis of the WFC3/HST observations to probe the nature of this modulation and to understand if it can be attributable to the presence of unocculted spots on the stellar surface. Our analysis strongly suggests that LHS1140 is a rather quiet star with subsolar [Fe/H] and enriched in alpha elements. Therefore, we rule out the possibility that the planetary spectrum is affected by the presence of spots and faculae. This analysis shows the importance of a proper modelling of the stellar spectrum when analyzing transit observations. Finally, we modelled the planetary atmosphere of LHS1140 b to retrieve its atmospheric composition. However, the low resolution and the narrow spectral range of HST observations prevented us from definitively determining whether the spectral features are attributable to the presence of water or of other molecules in the planetary atmosphere., Comment: 12 pages, 10 figures

Atmospheric escape plays a fundamental role in shaping the properties of exoplanets. The metastable near-infrared helium triplet at 1083.3 nm (HeI) is a powerful proxy of extended and evaporating atmospheres. We used the GIARPS (GIANO-B+HARPS-N) observing mode of the Telescopio Nazionale Galileo to search for HeI absorption in the upper atmosphere of five close-in giant planets hosted by the K and M dwarf stars of our sample, namely WASP-69b, WASP-107b, HAT-P-11b, GJ436b, and GJ3470b. We focused our analysis on the HeI triplet by performing high-resolution transmission spectroscopy. When nightly variability in the HeI absorption signal was identified, we investigated the potential influence of stellar magnetic activity by searching for variations in the H$\alpha$. We spectrally resolve the HeI triplet and confirm the published detections for WASP-69b (3.91$\pm$0.22%, 17.6$\sigma$), WASP-107b (8.17$^{+0.80}_{-0.76}$%, 10.5$\sigma$), HAT-P-11b (1.36$\pm$0.17%, 8.0$\sigma$), and GJ3470b (1.75$^{+0.39}_{-0.36}$%, 4.7$\sigma$). We do not find evidence of extra absorption for GJ436b. We observe night-to-night variations in the HeI absorption signal for WASP-69b, associated with variability in H$\alpha$, which likely indicates the influence of stellar activity. Additionally, we find that the HeI signal of GJ3470b originates from a single transit, thereby corroborating the discrepancies in the existing literature. An inspection of the H$\alpha$ reveals an absorption signal during the same transit. By combining our findings with previous analyses of GIANO-B HeI measurements of planets around K dwarfs, we explore potential trends with planetary/stellar parameters that are thought to affect the HeI absorption. Our analysis is unable to identify clear patterns, emphasising the need for further measurements and the exploration of additional potential parameters that might influence HeI absorption., Comment: 23 pages, 13 figures, accepted for publication in A&A. v3 includes language editing

High-energy radiation from stars impacts planetary atmospheres deeply affecting their chemistry, providing departures from chemical equilibrium. While the upper atmospheric layers are dominated by ionizations induced by extreme ultraviolet radiation, deeper into the atmosphere molecular abundances are controlled by a characteristic X-ray dominated chemistry, mainly driven by an energetic secondary electron cascade. In this work, we aim at identifying molecular photochemically induced fingerprints in the transmission spectra of a giant planet atmosphere. We have developed a numerical code capable of synthesizing transmission spectra with arbitrary spectral resolution, exploiting updated infrared photoabsorption cross sections. Chemical mixing ratios are computed using a photochemical model, tailored to investigate high energy ionization processes. We find that in case of high levels of stellar activity, synthetic spectra in both low and high resolutions show significant, potentially observable out-of-equilibrium signatures arising mainly from CO, CH$_4$, C$_2$H$_2$, and HCN., Comment: The paper has been accepted for publication in The Planetary Science Journal (PSJ)

Several studies suggest that the emission properties of a star can be affected by its interaction with a nearby planet. However, the actual observability of these effects remains a subject of debate. An example is the HD189733A system, where some characteristics of its emissions have been interpreted as indicative of ongoing interactions between the star and its planet. Other studies attribute these characteristics to the coronal activity of the star. In this work, we investigate whether the observed stellar X-ray flare events, which appear to be in phase with the planetary period in the HD189733A system, could be attributed to the accretion of the planetary wind onto the stellar surface or resulted from an interaction between the planetary and stellar winds. We developed a 3D MHD model that describes the system HD189733A, including the central host star and its hot Jupiter, along with their respective winds. The effects of gravity and the magnetic fields of both star and planet are taken into account. In the cases examined in this study, the accretion scenario is only viable when the stellar and planetary magnetic field strengths are at 5 G and 1 G, respectively. In this case, the Rayleigh-Taylor instabilities (RTIs) lead to the formation of an accretion column connecting star and planet. Once formed the column remains stable for the entire simulation. The accretion column yields an accretion rates of about 1e12 g/s and shows a mean density of about 1e7 cm^-3. In the other cases, the accretion column does not form because the RTI is suppressed by the stronger magnetic field intensities assumed for both the star and the planet. We synthesized the emission resulting from the shocked planetary wind and, its total X-ray emission ranges from 5e23 to 1e24 erg/s. In the case of accretion, the emission originating from the hot spot cannot be distinguished from the coronal activity., Comment: Accepted for publication in Astronomy and Astrophysics. 11 pages, 10 figures

Context. The Galactic centre is hazardous for stellar clusters because of the strong tidal force. Supposedly, many clusters were destroyed and contributed stars to the crowded stellar field of the bulge and the nuclear stellar cluster. However, it is hard to develop a realistic model to predict the long-term evolution of the complex inner Galaxy, and observing surviving clusters in the central region would provide crucial insights into destruction processes. Aims. Among hitherto-known Galactic globular clusters, VVV CL002 is the closest to the centre, 0.4 kpc, but has a very high transverse velocity, 400 km s$^{-1}$. The nature of this cluster and its impact on Galactic astronomy need to be addressed with spectroscopic follow-up. Methods. Here we report the first measurements of its radial velocity and chemical abundance based on near-infrared high-resolution spectroscopy. Results. We found that this cluster has a counterrotating orbit constrained within 1.0\,kpc of the centre, as close as 0.2 kpc at the perigalacticon, confirming that the cluster is not a passerby from the halo but a genuine survivor enduring the harsh conditions of the Galactic mill's tidal forces. In addition, its metallicity and $\alpha$ abundance ([$\alpha$/Fe] $\simeq +0.4$ and [Fe/H]$=-0.54$) are similar to some globular clusters in the bulge. Recent studies suggest that stars with such $\alpha$-enhanced stars were more common at 3 - 6 kpc from the centre around 10 Gyrs ago. Conclusions. We infer that VVV CL002 was formed outside but is currently falling down to the centre, exhibiting a real-time event that must have occurred to many clusters a long time ago., Comment: Contains 6 pages with 6 figures. Accepted for publication in Astronomy & Astrophysics

The intrinsic variability due to the magnetic activity of young active stars is one of the main challenges in detecting and characterising exoplanets. We present a method able to model the stellar photosphere and its surface inhomogeneities (starspots) in young/active and fast-rotating stars, based on the cross-correlation function (CCF) technique, to extract information about the spot configuration of the star. Within the Global Architecture of Planetary Systems (GAPS) Project at the Telescopio Nazionale Galileo, we analysed more than 300 spectra of the young planet-hosting star V1298 Tau provided by HARPS-N high-resolution spectrograph. By applying the SpotCCF model to the CCFs we extracted the spot configuration (latitude, longitude and projected filling factor) of this star, and also provided the new RVs time series of this target. We find that the features identified in the CCF profiles of V1298 Tau are modulated by the stellar rotation, supporting our assumption that they are caused by starspots. The analysis suggests a differential rotation velocity of the star with lower rotation at higher latitudes. Also, we find that SpotCCF provides an improvement in RVs extraction with a significantly lower dispersion with respect to the commonly used pipelines, with consequent mitigation of the stellar activity contribution modulated with stellar rotation. A detection sensitivity test, by the direct injection of a planetary signal into the data, confirmed that the SpotCCF model improves the sensitivity and ability to recover planetary signals. Our method enables the modelling of the stellar photosphere, extracting the spot configuration of young/active and rapidly rotating stars. It also allows for the extraction of optimised RV time series, thereby enhancing our detection capabilities for new exoplanets and advancing our understanding of stellar activity., Comment: 18 pages, 20 figures, accepted by A&A

Over the past decade, millions of smart meters have been installed by electricity suppliers worldwide, allowing them to collect a large amount of electricity consumption data, albeit sampled at a low frequency (one point every 30min). One of the important challenges these suppliers face is how to utilize these data to detect the presence/absence of different appliances in the customers' households. This valuable information can help them provide personalized offers and recommendations to help customers towards the energy transition. Appliance detection can be cast as a time series classification problem. However, the large amount of data combined with the long and variable length of the consumption series pose challenges when training a classifier. In this paper, we propose ADF, a framework that uses subsequences of a client consumption series to detect the presence/absence of appliances. We also introduce TransApp, a Transformer-based time series classifier that is first pretrained in a self-supervised way to enhance its performance on appliance detection tasks. We test our approach on two real datasets, including a publicly available one. The experimental results with two large real datasets show that the proposed approach outperforms current solutions, including state-of-the-art time series classifiers applied to appliance detection. This paper appeared in VLDB 2024., Comment: 10 pages, 7 figures. This paper appeared in VLDB 2024

Understanding how humans explore the world in search of novelties is key to foster innovation. Previous studies analyzed novelties in various exploration processes, defining them as the first appearance of an element. However, innovation can also be generated by novel association of what is already known. We hence define higher-order novelties as the first appearances of combinations of two or more elements, and we introduce higher-order Heaps' exponents as a way to characterize their pace of discovery. Through extensive analysis of real-world data, we find that processes with the same pace of discovery, as measured by the standard Heaps' exponent, can instead differ at higher orders. We then propose to model the dynamics of an exploration process as a random walk on an evolving network of the possible connections between elements. The model reproduces the empirical properties of higher-order novelties, revealing how the space of possibilities expands over time along with the exploration process., Comment: 14 pages, 5 figures

In recent years, smart meters have been widely adopted by electricity suppliers to improve the management of the smart grid system. These meters usually collect energy consumption data at a very low frequency (every 30min), enabling utilities to bill customers more accurately. To provide more personalized recommendations, the next step is to detect the appliances owned by customers, which is a challenging problem, due to the very-low meter reading frequency. Even though the appliance detection problem can be cast as a time series classification problem, with many such classifiers having been proposed in the literature, no study has applied and compared them on this specific problem. This paper presents an in-depth evaluation and comparison of state-of-the-art time series classifiers applied to detecting the presence/absence of diverse appliances in very low-frequency smart meter data. We report results with five real datasets. We first study the impact of the detection quality of 13 different appliances using 30min sampled data, and we subsequently propose an analysis of the possible detection performance gain by using a higher meter reading frequency. The results indicate that the performance of current time series classifiers varies significantly. Some of them, namely deep learning-based classifiers, provide promising results in terms of accuracy (especially for certain appliances), even using 30min sampled data, and are scalable to the large smart meter time series collections of energy consumption data currently available to electricity suppliers. Nevertheless, our study shows that more work is needed in this area to further improve the accuracy of the proposed solutions. This paper appeared in ACM e-Energy 2023., Comment: 11 pages, 7 figures. This paper appeared in ACM e-Energy 2023

Context. Massive substellar companions orbiting active low-mass stars are rare. They, however, offer an excellent opportunity to study the main mechanisms involved in the formation and evolution of substellar objects. Aims. We aim to unravel the physical nature of the transit signal observed by the TESS space mission on the active M dwarf TOI-5375. Methods. We analysed the available TESS photometric data as well as high-resolution (R $\sim$ 115000) HARPS-N spectra. We combined these data to characterise the star TOI-5375 and to disentangle signals related to stellar activity from the companion transit signal in the light-curve data. We ran an MCMC analysis to derive the orbital solution and apply state-of-the-art Gaussian process regression to deal with the stellar activity signal. Results. We reveal the presence of a companion in the brown dwarf / very-low-mass star boundary orbiting around the star TOI-5375. The best-fit model corresponds to a companion with an orbital period of 1.721564 $\pm$ 10$^{\rm -6}$ d, a mass of 77 $\pm$ 8 $M_{\rm J}$ and a radius of 0.99 $\pm$ 0.16 $R_{\rm J}$. Conclusions. We derive a rotation period for the host star of 1.9692 $\pm$ 0.0004 d, and we conclude that the star is very close to synchronising its rotation with the orbital period of the companion., Comment: Accepted for publication in Astronomy & Astrophysics

The chromatic contamination that arises from photospheric heterogeneities e.g. spots and faculae on the host star presents a significant noise source for exoplanet transmission spectra. If this contamination is not corrected for, it can introduce substantial bias in our analysis of the planetary atmosphere. We utilise two stellar models of differing complexity, StARPA and ASteRA, to explore the biases introduced by stellar contamination in retrieval under differing degrees of stellar activity. We use the retrieval framework TauREx3 and a grid of 27 synthetic, spot-contaminated transmission spectra to investigate potential biases and to determine how complex our stellar models must be in order to accurately extract the planetary parameters from transmission spectra. The input observation is generated using the more complex model (StARPA), in which the spot latitude is an additional, fixable parameter. This observation is then fed into a combined stellar-planetary retrieval which contains a simplified stellar model (ASteRA). Our results confirm that the inclusion of stellar activity parameters in retrieval minimises bias under all activity regimes considered. ASteRA performs very well under low to moderate activity conditions, retrieving the planetary parameters with a high degree of accuracy. For the most active cases, characterised by larger, higher temperature contrast spots, some minor residual bias remains due to ASteRA neglecting the interplay between the spot and the limb darkening effect. As a result of this, we find larger errors in retrieved planetary parameters for central spots (0 degrees) and those found close to the limb (60 degrees) than those at intermediate latitudes (30 degrees)., Comment: 34 pages, 20 figures, accepted for publication in ApJ

We show that many bounded rationality patterns of choice can be alternatively represented as testable models of limited consideration, and we elicit the features of the associated unobserved consideration sets from the observed choice. Moreover, we characterize some testable choice procedures in which the DM considers as few alternatives as possible. These properties, compatible with the empirical evidence, allow the experimenter to uniquely infer the DM's unobserved consideration sets from irrational features of the observed behavior.

We use a combinatorial approach to compute the number of non-isomorphic choices on four elements that can be explained by models of bounded rationality.

Active region evolution plays an important role in the generation and variability of magnetic fields on the surface of lower main-sequence stars. However, determining the lifetime of active region growth and decay as well as their evolution is a complex task. We aim to test whether the lifetime for active region evolution shows any dependency on the stellar parameters. We identify a sample of stars with well-defined ages via their kinematics. We made use of high-resolution spectra to compute rotational velocities, activity levels, and emission excesses. We use these data to revisit the activity-rotation-age relationship. The time-series of the main optical activity indicators were analysed together with the available photometry by using Gaussian processes to model the stellar activity of these stars. Autocorrelation functions of the available photometry were also analysed. We use the derived lifetimes for active region evolution to search for correlations with the stellar age, the spectral type, and the level of activity. We also use the pooled variance technique to characterise the activity behaviour of our targets. Our analysis confirms the decline of activity and rotation as the star ages. We also confirm that the rotation rate decays with age more slowly for cooler stars and that, for a given age, cooler stars show higher levels of activity. We show that F- and G-type young stars also depart from the inactive stars in the flux-flux relationship. The gaussian process analysis of the different activity indicators does not seem to provide any useful information on active region's lifetime and evolution. On the other hand, active region's lifetimes derived from the light-curve analysis might correlate with the stellar age and temperature. Although we caution the small number statistics, our results suggest that active regions seem to live longer on younger, cooler, and more active stars., Comment: Accepted by A&A

We describe a context-sensitive model of choice, in which the selection process is shaped not only by the attractiveness of items but also by their semantics ('salience'). All items are ranked according to a relation of salience, and a linear order is associated to each item. The selection of a single element from a menu is justified by one of the linear orders indexed by the most salient items in the menu. The general model provides a structured explanation for any observed behavior, and allows us to to model the 'moodiness' of a decision maker, which is typical of choices requiring as many distinct rationales as items. Asymptotically all choices are moody. We single out a model of linear salience, in which the salience order is transitive and complete, and characterize it by a behavioral property, called WARP(S). Choices rationalizable by linear salience can only exhibit non-conflicting violations of WARP. We also provide numerical estimates, which show the high selectivity of this testable model of bounded rationality.

We present the complete Bayesian statistical analysis of the HArps-n red Dwarf Exoplanet Survey (HADES), which monitored the radial velocities of a large sample of M dwarfs with HARPS-N at TNG, over the last 6 years. The targets were selected in a narrow range of spectral types from M0 to M3, $0.3$ M$_\odot < M_\star < 0.71$ M$_\odot$, in order to study the planetary population around a well-defined class of host stars. We take advantage of Bayesian statistics to derive an accurate estimate of the detectability function of the survey. Our analysis also includes the application of Gaussian Process approach to take into account stellar activity induced radial velocity variations, and improve the detection limits, around the most-observed and most-active targets. The Markov chain Monte Carlo and Gaussian process technique we apply in this analysis has proven very effective in the study of M-dwarf planetary systems, helping the detection of most of the HADES planets. From the detectability function we can calculate the occurrence rate of small mass planets around early-M dwarfs, either taking into account only the 11 already published HADES planets or adding also the 5 new planetary candidates discovered in this analysis, and compare them with the previous estimates of planet occurrence around M-dwarf or Solar-type stars: considering only the confirmed planets, we find the highest frequency for low-mass planets ($1$ M$_\oplus < m_p \sin i < 10$ M$_\oplus$) with periods $10$ d$ < P < 100$ d, $f_\text{occ} = 85^{+5}_{-19}\%$, while for short-period planets ($1$ d$ < P < 10$ d) we find a frequency of $f_\text{occ} = 10.3^{+8.4}_{-3.3}\%$, significantly lower than for later-M dwarfs. These results, and their comparison with other surveys focused on different stellar types, confirms the central role that stellar mass plays in the formation and evolution of planetary systems., Comment: 21 pages, 14 figures, 8 table. Accepted by A&A