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Young protostellar discs are likely to be both self-gravitating, and to support grain growth to sizes where the particles decoupled from the gas. This combination could lead to short-wavelength fragmentation of the solid component in otherwise non-fragmenting gas discs, forming Earth-mass solid cores during the Class 0/I stages of Young Stellar Object evolution. We use three-dimensional smoothed particle hydrodynamics simulations of two-fluid discs, in the regime where the Stokes number of the particles St>1, to study how the formation of solid clumps depends on the disc-to-star mass ratio, the strength of gravitational instability, and the Stokes number. Gravitational instability of the simulated discs is sustained by local cooling. We find that the ability of the spiral structures to concentrate solids increases with the cooling time, and decreases with the Stokes number, while the relative dynamical temperature between gas and dust of the particles decreases with the cooling time and the disc-to-star mass ratio, and increases with the Stokes number. Dust collapse occurs in a subset of high disc mass simulations, yielding clumps whose mass is close to linear theory estimates, namely 1-10 Earth masses. Our results suggest that if planet formation occurs via this mechanism, the best conditions correspond to near the end of the self-gravitating phase, when the cooling time is long and the Stokes number close to unity., Accepted for publication in MNRAS, 20 pages

The stability of young planetary systems is strongly influenced by multiple factors, both internal and external. In this paper, we investigate the link between the environment in which young stars form and the possibility of having stable planetary systems around them. We analyze the robustness of such systems after an encounter with another star within the same stellar cluster. We employ a model for the star cluster to extract the encounter properties, such as the mass of the perturber star and its velocity. We perform numerical simulations on systems with a single planet perturbed by an external star, in order to calculate the emission probabilities of the planet. We also calculate analytically the stellar encounter rates in the cluster. We find that such probabilities are strongly dependent on the thermal velocity of the cluster. We also notice that these probabilities are generally quite small, below 3% for the systems tested by us.

We investigate the mechanism of polar alignment for accretion discs in hierarchical systems (HSs) with more than two stars. In eccentric binary systems, low mass discs that are sufficiently tilted to the binary orbit align in a polar configuration with respect to the binary plane by aligning their angular momentum to the binary eccentricity vector. In HSs, secular evolution of the orbital parameters makes the eccentricity vector of the system precess with time. This precession undermines the stability of the polar orbit for accretion discs hosted in HSs. We analytically show that the binary criteria for polar alignment derived in the literature are necessary but not sufficient conditions for polar alignment in HSs. Then, we derive an analytical criterion for polar alignment in HSs. In general, we find that discs orbiting the innermost level of a HS can go polar. Conversely, radially extended discs orbiting the outer levels of a HS cannot polarly align and evolve as orbiting around a circular binary. We confirm our findings through detailed numerical simulations. Also, our results are compatible with the observed distribution of disc-orbit mutual inclination. Finally, we compare the observed distribution of disc inclinations in the binary and in the HS populations. Binaries host mainly coplanar discs, while HSs show a wide range of disc inclinations. We suggest that the wider range of inclinations in HSs results from the secular oscillation of their orbital parameters (such as Kozai-Lidov oscillations), rather than from a different initial condition or evolution between HSs and binaries., 11 pages, 9 figures, accepted for publication on MNRAS

Recent observations show that planet formation is already underway in young systems, when the protostar is still embedded into the molecular cloud and the accretion disc is massive. In such environments, the role of self gravity (SG) and gravitational instability (GI) is crucial in determining the dynamical evolution of the disc. In this work, we study the dynamical role of drag force in self-gravitating discs as a way to form planetesimals in early protoplanetary stages. We obtain the dispersion relation for density-wave perturbations on a fluid composed of two phases (gas and dust) interacting through the common gravitation field and the mutual drag force, and we find that the stability threshold is determined by three parameters: the local dust-to-gas density ratio, the dust relative temperature and the relevant Stokes number. In a region of parameters space, where young protoplanetary discs are likely to be found, the instability can be dust driven, occurring at small wavelengths. In this regime, the Jeans mass is much smaller than the one predicted by the standard gravitational instability model. This mechanism can be a viable way to form planetary cores in protostellar discs, since their predicted mass is about 10 Earth masses., 14 pages, 8 figures, 1 appendix, accepted for publication on MNRAS

A key problem in protoplanetary disc evolution is understanding the efficiency of dust radial drift. This process makes the observed dust disc sizes shrink on relatively short timescales, implying that discs started much larger than what we see now. In this paper we use an independent constraint, the gas radius (as probed by CO rotational emission), to test disc evolution models. In particular, we consider the ratio between the dust and gas radius, $R_{\rm CO}/R_{\rm dust}$. We model the time evolution of protoplanetary discs under the influence of viscous evolution, grain growth, and radial drift. Then, using the radiative transfer code RADMC with approximate chemistry, we compute the dust and gas radii of the models and investigate how $R_{\rm CO}/R_{\rm dust}$ evolves. Our main finding is that, for a broad range of values of disc mass, initial radius, and viscosity, $R_{\rm CO}/R_{\rm dust}$ becomes large (>5) after only a short time (, 17 pages, 14 figures

Many stars are in binaries or higher-order multiple stellar systems. Although in recent years a large number of binaries have been proven to host exoplanets, how planet formation proceeds in multiple stellar systems has not been studied much yet from the theoretical standpoint. In this paper we focus on the evolution of the dust grains in planet-forming discs in binaries. We take into account the dynamics of gas and dust in discs around each component of a binary system under the hypothesis that the evolution of the circumprimary and the circumsecondary discs is independent. It is known from previous studies that the secular evolution of the gas in binary discs is hastened due to the tidal interactions with their hosting stars. Here we prove that binarity affects dust dynamics too, possibly in a more dramatic way than the gas. In particular, the presence of a stellar companion significantly reduces the amount of solids retained in binary discs because of a faster, more efficient radial drift, ultimately shortening their lifetime. We prove that how rapidly discs disperse depends both on the binary separation, with discs in wider binaries living longer, and on the disc viscosity. Although the less-viscous discs lose high amounts of solids in the earliest stages of their evolution, they are dissipated slowly, while those with higher viscosities show an opposite behaviour. The faster radial migration of dust in binary discs has a striking impact on planet formation, which seems to be inhibited in this hostile environment, unless other disc substructures halt radial drift further in. We conclude that if planetesimal formation were viable in binary discs, this process would take place on very short time scales., 18 pages, 11 figures; accepted for publication in MNRAS

Young multiple systems accrete most of their final mass in the first few Myr of their lifetime, during the protostellar and protoplanetary phases. Previous studies showed that in binary systems the majority of the accreted mass falls onto the lighter star, thus evolving to mass equalisation. However, young stellar systems often comprise more than two stars, which are expected to be in hierarchical configurations. Despite its astrophysical relevance, differential accretion in hierarchical systems remains to be understood. In this work, we investigate whether the accretion trends expected in binaries are valid for higher order multiples. We performed a set of 3D Smoothed Particle Hydrodynamics simulations of binaries and of hierarchical triples (HTs) embedded in an accretion disc, with the code Phantom. We identify for the first time accretion trends in HTs and their deviations compared to binaries. These deviations, due to the interaction of the small binary with the infalling material from the circum-triple disc, can be described with a semi-analytical prescription. Generally, the smaller binary of a HT accretes more mass than a single star of the same mass as the smaller binary. We found that in a HT, if the small binary is heavier than the third body, the standard differential accretion scenario (whereby the secondary accretes more of the mass) is hampered. Reciprocally, if the small binary is lighter than the third body, the standard differential accretion scenario is enhanced. The peculiar differential accretion mechanism we find in HTs is expected to affect their mass ratio distribution., Comment: Accepted for publication in MNRAS, 15 pages, 13 figures, 1 tables, 2 appendices

Extreme mass ratio inspirals (EMRIs) are compact binary systems characterized by a mass-ratio $q=m/M$ in the range $~10^{-9}-10^{-4}$ and represent primary gravitational wave (GW) sources for the forthcoming Laser Interferometer Space Antenna (LISA). While their standard formation channel involves relaxation processes deflecting compact objects on very low angular momentum orbits around the central massive black hole, a number of alternative formation channels has been proposed, including binary tidal break-up, migration in accretion disks and secular and chaotic dynamics around a massive black hole binary (MBHB). In this work, we take an extensive closer look at this latter scenario, investigating how EMRIs can be triggered by a MBHBs, formed in the aftermath of galaxy mergers. By employing a suite of relativistic three-body simulations, we evaluate the efficiency of EMRI formation for different parameters of the MBHB, assessing the importance of both secular and chaotic dynamics. By modelling the distribution of compact objects in galaxy nuclei, we estimate the resulting EMRI formation rate, finding that EMRI are produced in a sharp burst, with peak rates that are 10-100 times higher than the standard two-body relaxation channel, lasting for 10$^6$--10$^8$ years. By coupling our results with an estimate of the cosmic MBHB merger rate, we finally forecast that LISA could observe ${\cal O}(10)$ EMRIs per year formed by this channel., 18 pages, 15 figures, accepted for publication in MNRAS

In order to understand which mechanism is responsible for accretion in protoplanetary discs, a robust knowledge of the observed disc radius using gas tracers such as $^{12}$CO and other CO isotopologues is pivotal. Indeed, the two main theories proposed, viscous accretion and wind-driven accretion, predict different time evolution for the disc radii. In this Letter, we present an analytical solution for the evolution of the disc radii in viscously evolving protoplanetary discs using $^{12}$CO as a tracer, under the assumption that the $^{12}$CO radius is the radius where the surface density of the disc is equal to the threshold for CO photo-dissociation. We discuss the properties of the solution and the limits of its applicability as a simple numerical prescription to evaluate the observed disc radii of populations of discs. Our results suggest that, in addition to photo-dissociation, also freeze out plays an important role in setting the disc size. We find an effective reduction of the CO abundance by about two orders of magnitude at the location of CO photo-dissociation, which however should not be interpreted as the bulk abundance of CO in the disc. The use of our analytical solution will allow to compute disc sizes for large quantities of models without using expensive computational resources such as radiative transfer calculations., Comment: 5 pages, 3 figures

The evolution of protoplanetary discs and the related process of planet formation is regulated by angular momentum transport and mass-loss processes. Over the past decade, the paradigm of viscosity has been challenged and MHD disc winds appear as a compelling scenario to account for disc accretion. In this work, we aim to construct the equivalent of the widely used analytical description of viscous evolution for the MHD wind case. The transport of angular momentum and mass induced by the wind is parameterized by an $\alpha$-like parameter and by the magnetic lever arm parameter $\lambda$. Extensions of the paradigmatic Lynden-Bell and Pringle similarity solutions to the wind case are presented. We show that wind-driven accretion leads to a steeper decrease in the disc mass and accretion rate than in viscous models due to the absence of disc spreading. If the decline of the magnetic field strength is slower than that of the gas surface density, the disc is dispersed after a finite time. The evolution of the disc in the $\dot{M}_*-M_D$ plane is sensitive to the wind and turbulence parameters. A disc population evolving under the action of winds can exhibit a correlation between $\dot{M}_*$ and $M_D$ depending on the initial conditions. The simplified framework proposed in this work opens to a new avenue to test the effectiveness of wind-driven accretion from the observed disc demographics and constitutes an important step to include wind-driven accretion in planet population synthesis models., Comment: Accepted for publication in MNRAS

Binaries and multiple systems are common among young stars (Reipurth et al. 2014). These stars are often surrounded by discs of gas and dust, formed due to the conservation of angular momentum of the collapsing cloud, thought to be the site of planet formation.In the case of binary systems, three discs can form: an outer disc surrounding all the stars (called circumbinary disc), and two inner discs around the stars. As circumbinary planets have recently been discovered by Kepler (see e.g., Martin 2018, Bonavita & Desidera 2020), it is crucial to understand the dynamics and evolution of circumbinary discs to better understand the initial conditions of planet formation in multiple systems.The GG Tau A system is an example of a young multiple T Tauri star. The binary is surrounded by a bright disc, observed in the continuum emission at different wavelengths (see e.g., Guilloteau et al. 1999; Dutrey et al. 2014; Phuong et al. 2020b) and in scattered light (e.g., Duchene et al. 2014, Keppler et al. 2020). The disc extends in the dust from 180 to 280 au from the center of mass, and in the gas up to 850 au. The inner (Two different configurations are possible fitting the proper motion data for the system: a co-planar case with a low eccentricity binary with a semi-major axis of 34 au, explored by Cazzoletti et al. 2017 and Keppler et al. 2020, and a misaligned case (i=30) with an eccentric binary (e=0.45) and a wider semimajor axis of 60 au (Aly et al.2018). At the state of the art, all these analyses focused on the gas dynamics only.We will show the results of new 3D SPH simulations of dust and gas performed with the code PHANTOM, devised to test the two possible scenarios. We will describe the dynamics of the system in the two cases, comparing our models with observational results in order to better constraint the orbital parameter of the GG Tau A system. Our predictions will guide future observing campaigns and shed light on the complex evolution of discs in triple stellar systems.

The recently discovered exoplanets in binary or higher-order multiple stellar systems sparked a new interest in the study of proto-planetary discs in stellar aggregations. Here we focus on disc solids, as they make up the reservoir out of which exoplanets are assembled and dominate (sub-)millimetre disc observations. These observations suggest that discs in binary systems are fainter and smaller than in isolated systems. In addition, disc dust sizes are consistent with tidal truncation only if they orbit very eccentric binaries. In a previous study we showed that the presence of a stellar companion hastens the radial migration of solids, shortening disc lifetime and challenging planet formation. In this paper we confront our theoretical and numerical results with observations: disc dust fluxes and sizes from our models are computed at ALMA wavelengths and compared with Taurus and $\rho$ Ophiuchus data. A general agreement between theory and observations is found. In particular, we show that the dust disc sizes are generally smaller than the binary truncation radius due to the combined effect of grain growth and radial drift: therefore, small disc sizes do not require implausibly high eccentricities to be explained. Furthermore, the observed binary discs are compatible within $1\sigma$ with a quadratic flux-radius correlation similar to that found for single-star discs and show a close match with the models. However, the observational sample of resolved binary discs is still small and additional data are required to draw more robust conclusions on the flux-radius correlation and how it depends on the binary properties., Comment: 20 pages, 10 figures; accepted for publication in MNRAS

The evolution of young stars and disks is driven by the interplay of several processes, notably accretion and ejection of material. Critical to correctly describe the conditions of planet formation, these processes are best probed spectroscopically. About five-hundred orbits of the Hubble Space Telescope (HST) are being devoted in 2020-2022 to the ULLYSES public survey of about 70 low-mass (M, Comment: Accepted for publication on Astronomy & Astrophysics. 15 pages + appendix, language edited version

Tidal encounters in star clusters perturb discs around young protostars. In Cuello et al. (2019a, Paper I) we detailed the dynamical signatures of a stellar flyby in both gas and dust. Flybys produce warped discs, spirals with evolving pitch angles, increasing accretion rates, and disc truncation. Here we present the corresponding observational signatures of these features in optical/near-infrared scattered light and (sub-) millimeter continuum and CO line emission. Using representative prograde and retrograde encounters for direct comparison, we post-process hydrodynamical simulations with radiative transfer methods to generate a catalogue of multi-wavelength observations. This provides a reference to identify flybys in recent near-infrared and sub-millimetre observations (e.g., RW Aur, AS 205, HV Tau & DO Tau, FU Ori, V2775 Ori, and Z CMa)., 11 pages, 5 figures, accepted for publication in MNRAS

Tidal disruption events (TDEs) are among the brightest transients in the optical, ultraviolet, and X-ray sky. These flares are set into motion when a star is torn apart by the tidal field of a massive black hole, triggering a chain of events which is -- so far -- incompletely understood. However, the disruption process has been studied extensively for almost half a century, and unlike the later stages of a TDE, our understanding of the disruption itself is reasonably well converged. In this Chapter, we review both analytical and numerical models for stellar tidal disruption. Starting with relatively simple, order-of-magnitude physics, we review models of increasing sophistication, the semi-analytic ``affine formalism,'' hydrodynamic simulations of the disruption of polytropic stars, and the most recent hydrodynamic results concerning the disruption of realistic stellar models. Our review surveys the immediate aftermath of disruption in both typical and more unusual TDEs, exploring how the fate of the tidal debris changes if one considers non-main sequence stars, deeply penetrating tidal encounters, binary star systems, and sub-parabolic orbits. The stellar tidal disruption process provides the initial conditions needed to model the formation of accretion flows around quiescent massive black holes, and in some cases may also lead to directly observable emission, for example via shock breakout, gravitational waves or runaway nuclear fusion in deeply plunging TDEs., Comment: Review chapter in book: 'The Tidal Disruption of Stars by Massive Black Holes', Space Science Reviews, Springer. Comments welcome

Recent observations have shown that circumbinary discs can be misaligned with respect to the binary orbital plane.The lack of spherical symmetry, together with the non-planar geometry of these systems, causes differential precession which might induce the propagation of warps. While gas dynamics in such environments is well understood, little is known about dusty discs. In this work, we analytically study the problem of dust traps formation in misaligned circumbinary discs. We find that pile-ups may be induced not by pressure maxima, as the usual dust traps, but by a difference in precession rates between the gas and dust. Indeed, this difference makes the radial drift inefficient in two locations, leading to the formation of two dust rings whose position depends on the system parameters. This phenomenon is likely to occur to marginally coupled dust particles $(\text{St}\gtrsim1)$ as both the effect of gravitational and drag force are considerable. We then perform a suite of three-dimensional SPH numerical simulations to compare the results with our theoretical predictions. We explore the parameter space, varying stellar mass ratio, disc thickness, radial extension, and we find a general agreement with the analytical expectations. Such dust pile-up prevents radial drift, fosters dust growth and may thus promote the planet formation in circumbinary discs., Accepted for publication in MNRAS, 12 pages, 12 figures, 2 tables, 2 appendices

Recent claimed detections of tidal disruption events (TDEs) in multi-wavelength data have opened potential new windows into the evolution and properties of otherwise dormant supermassive black holes (SMBHs) in the centres of galaxies. At present, there are several dozen TDE candidates, which share some properties and differ in others. The range in properties is broad enough to overlap other transient types, such as active galactic nuclei (AGN) and supernovae (SNe), which can make TDE classification ambiguous. A further complication is that "TDE signatures" have not been uniformly observed to similar sensitivities or even targeted across all candidates. This chapter reviews those events that are unusual relative to other TDEs, including the possibility of TDEs in pre-existing AGN, and summarises those characteristics thought to best distinguish TDEs from continuously accreting AGN, strongly flaring AGN, SNe, and Gamma-Ray Bursts (GRBs), as well as other potential impostors like stellar collisions, "micro-TDEs," and circumbinary accretion flows. We conclude that multiple observables should be used to classify any one event as a TDE. We also consider the TDE candidate population as a whole, which, for certain host galaxy or SMBH characteristics, is distinguishable statistically from non-TDEs, suggesting that at least some TDE candidates do in fact arise from SMBH-disrupted stars., 57 pages, 17 figures. Accepted for publication in Springer Space Science Reviews. Chapter in ISSI review "The Tidal Disruption of Stars by Massive Black Holes" vol. 79. Corrected several typos from previous submission

Understanding how giant planets form requires observational input from directly imaged protoplanets. We used VLT/NACO and VLT/SPHERE to search for companions in the transition disc of 2MASS J19005804-3645048 (hereafter CrA-9), an accreting M0.75 dwarf with an estimated age of 1-2 Myr. We found a faint point source at $\sim$0.7'' separation from CrA-9 ($\sim$108 au projected separation). Our 3-epoch astrometry rejects a fixed background star with a $5\sigma$ significance. The near-IR absolute magnitudes of the object point towards a planetary-mass companion. However, our analysis of the 1.0-3.8$\mu$m spectrum extracted for the companion suggests it is a young M5.5 dwarf, based on both the 1.13-$\mu$m Na index and comparison with templates of the Montreal Spectral Library. The observed spectrum is best reproduced with high effective temperature ($3057^{+119}_{-36}$K) BT-DUSTY and BT-SETTL models, but the corresponding photometric radius required to match the measured flux is only $0.60^{+0.01}_{-0.04}$ Jovian radius. We discuss possible explanations to reconcile our measurements, including an M-dwarf companion obscured by an edge-on circum-secondary disc or the shock-heated part of the photosphere of an accreting protoplanet. Follow-up observations covering a larger wavelength range and/or at finer spectral resolution are required to discriminate these two scenarios., Comment: 24 pages, 14 figures, 4 tables, to be published in MNRAS

IRAS~04158+2805 has long been thought to be a very low mass T-Tauri star (VLMS) surrounded by a nearly edge-on, extremely large disc. Recent observations revealed that this source hosts a binary surrounded by an extended circumbinary disc with a central dust cavity. In this paper, we combine ALMA multi-wavelength observations of continuum and $^{12}$CO line emission, with H$\alpha$ imaging and Keck astrometric measures of the binary to develop a coherent dynamical model of this system. The system features an azimuthal asymmetry detected at the western edge of the cavity in Band~7 observations and a wiggling outflow. Dust emission in ALMA Band 4 from the proximity of the individual stars suggests the presence of marginally resolved circumstellar discs. We estimate the binary orbital parameters from the measured arc of the orbit from Keck and ALMA astrometry. We further constrain these estimates using considerations from binary-disc interaction theory. We finally perform three SPH gas + dust simulations based on the theoretical constraints; we post-process the hydrodynamic output using radiative transfer Monte Carlo methods and directly compare the models with observations. Our results suggest that a highly eccentric $e\sim 0.5\textrm{--}0.7$ equal mass binary, with a semi-major axis of $\sim 55$ au, and small/moderate orbital plane vs. circumbinary disc inclination $\theta\lesssim 30^\circ$ provides a good match with observations. A dust mass of $\sim 1.5\times 10^{-4} {\rm M_\odot}$ best reproduces the flux in Band 7 continuum observations. Synthetic CO line emission maps qualitatively capture both the emission from the central region and the non-Keplerian nature of the gas motion in the binary proximity., Comment: 19 pages, 14 figures, 1 table, accepted for publication in MNRAS

Recent multi-wavelength ALMA observations of the protoplanetary disk orbiting around Elias 2-27 revealed a two armed spiral structure. The observed morphology together with the young age of the star and the disk-to-star mass ratio estimated from dust continuum emission make this system a perfect laboratory to investigate the role of self-gravity in the early phases of star formation. This is particularly interesting if we consider that gravitational instabilities could be a fundamental first step for the formation of planetesimals and planets. In this Letter, we model the rotation curve obtained by CO data of Elias 2-27 with a theoretical rotation curve including both the disk self-gravity and the star contribution to the gravitational potential. We compare this model with a purely Keplerian one and with a simple power-law function. We find that (especially for the $^{13}$CO isotopologue) the rotation curve is better described by considering not only the star, but also the disk self-gravity. We are thus able to obtain for the first time a dynamical estimate of the disk mass of $0.08\pm0.04\,M_{\odot}$ and the star mass of $0.46\pm0.03\,M_{\odot}$ (in the more general case), the latter being comparable with previous estimates. From these values, we derive that the disk is 17$\%$ of the star mass, meaning that it could be prone to gravitational instabilities. This result would strongly support the hypothesis that the two spiral arms are generated by gravitational instabilities., Comment: 14 pages, 9 figures, 2 tables, accepted for publication on ApJL

GrailQuest(Gamma Ray Astronomy International Laboratory for QUantum Exploration of Space-Time) is a mission concept based on a constellation (hundreds/thousands) of nano/micro/small-satellites in low (or near) Earth orbits. Each satellite hosts a non-collimated array of scintillator crystals coupled with Silicon Drift Detectors with broad energy band coverage (keV-MeV range) and excellent temporal resolution (≤ 100 nanoseconds) each with effective area$\sim 100 \text {cm}^{2}$∼100cm2. This simple and robust design allows for mass-production of the satellites of the fleet. This revolutionary approach implies a huge reduction of costs, flexibility in the segmented launching strategy, and an incremental long-term plan to increase the number of detectors and their performance; this will result in a living observatory for next-generation, space-based astronomical facilities.GrailQuestis conceived as an all-sky monitor for fast localisation of high signal-to-noise ratio transients in the X-/gamma-ray band, e.g. the elusive electromagnetic counterparts of gravitational wave events. Robust temporal triangulation techniques will allow unprecedented localisation capabilities, in the keV-MeV band, of a few arcseconds or below, depending on the temporal structure of the transient event. The ambitious ultimate goal of this mission is to perform the first experiment, in quantum gravity, to directly probe space-time structure down to the minuscule Planck scale, by constraining or measuring a first-order dispersion relation for lightin vacuo. This is obtained by detecting delays between photons of different energies in the prompt emission of Gamma-Ray Bursts.

It is likely that young protostellar disks undergo a self-gravitating phase. Such systems are characterized by the presence of a spiral pattern that can be either in a quasi-steady state or in a nonlinear unstable condition. This spiral wave affects both the gas dynamics and kinematics, resulting in deviations from the Keplerian rotation. Recently, a lot of attention has been devoted to kinematic studies of planet-forming environments, and we are now able to measure even small perturbations of velocity field ($\lesssim 1 \%$ of the Keplerian speed) thanks to high spatial and spectral resolution observations of protostellar disks. In this work, we investigate the kinematic signatures of gravitational instability: we perform an analytical study of the linear response of a self-gravitating disk to a spiral-like perturbation, focusing our attention on the velocity field perturbations. We show that unstable disks have clear kinematic imprints into the gas component across the entire disk extent, due to the GI spiral wave perturbation, resulting in deviations from Keplerian rotation. The shape of these signatures depends on several parameters, but they are significantly affected by the cooling factor: by detecting these features, we can put constraints on protoplanetary disk cooling., Comment: Accepted for publication in APJL, 13 pages, 4 figures

Accretion onto black holes is an efficient mechanism in converting the gas mass-energy into energetic outputs as radiation, wind and jet. Tidal disruption events, in which stars are tidally torn apart and then accreted onto supermassive black holes, offer unique opportunities of studying the accretion physics as well as the wind and jet launching physics across different accretion regimes. In this review, we systematically describe and discuss the models that have been developed to study the accretion flows and jets in tidal disruption events. A good knowledge of these physics is not only needed for understanding the emissions of the observed events, but also crucial for probing the general relativistic space-time around black holes and the demographics of supermassive black holes via tidal disruption events., Comment: Accepted for publication in Springer Space Science Reviews. Chapter in ISSI review, "The Tidal Disruption of Stars by Massive Black Holes," vol. 79

We map the planetary wake associated with the embedded protoplanet creating the CO kink in the disk of HD~163296. We show that the wake can be traced by a series of correlated perturbations in the peak velocity map. The sign change of the perturbations across the disk major axis confirm that the wake induces predominantly radial motion, as predicted by models of planet-disk interaction. These results provide the first direct confirmation of planet wakes generated by Lindblad resonances. Mapping the wake provides a constraint on the disk aspect ratio, which is required to measure the mass of the planet., Comment: 10 Pages, 6 figures. Accepted in ApJL

New instruments such as the ALMA interferometer and SPHERE on VLT allowed to obtain a large number of high-resolution images of protoplanetary discs. In these images, substructures such as gaps and rings can be clearly resolved and appear to be very common (see eg. Andrews et al. 2018). A natural explanation for the origin of such structures is the dynamical interaction of the gas and dust in the disc with one or more planets embedded in the parental disc (e.g. Lin & Papaloizou 1979, Dipierro et al. 2015, Rosotti et al. 2017, ..). Detections of planets embedded in disks are rare (e.g. Quanz et al. 2013, Keppler et al. 2018) and are mostly related to giant planets at wide orbits. However, the observed structures can be due to the interaction between the disc and low-mass planets. Planet-disc interaction can be studied with a synergy between observational results, current theoretical model and numerical simulations. In particular, theoretical models can find “signatures” to spot the presence of planets in discs, such as dusty or gaseous features due to the presence of circumplanetary discs or accretion streams (Bae et al. 2019, Toci et al. 2020) to be compared with real observations (Isella et al. 2019). I will present an analysis of several 3D SPH numerical simulations devised to analyze planet-disc interaction in presence of two giant planets. I will then compare my results with two observed systems: (1) HD169142 (Fedele et al.2017, Perez et al. 2019), a well studied source with two prominent rings in dust and gas; (2) PDS 70, the first source where protoplanets have been directly observed (Keppler et al. 2018). We initialise the system containing two giant planets in the disc (hereafter planet b and planet c respectively), studying the initial conditions that lead to the formation of a cavity in the gas distribution and rings in the dust. I will present the results about the dynamics of these discs (gap width, ring size and shape, cavity shape) and the properties of the planets (Toci et al., ApJL 2020, Toci et al. 2020, in prep.). My results show that the presence of two giant planets in a 5:1 resonance can be responsible of a long-lived dust ring between them, while at the same time creating a large gas cavity. However, the dust ring is absent when the giant planets end up in a closer resonance (3:1 or 2:1). I will also show how important it is to consider the migration and the accretion of planets for modelling observational results. Indeed, the interaction between the planets and the disc can give signatures both in the dust and gas components, leading to detectable features. In particular, our results suggest that the spur in the observed 1.3 mm continuum images of Perez et al. 2019 can be due to the interaction between the inner giant and the inner dust ring (see Fig. 1 and Fig. 2). If so, the spur should move according to the orbital motion of the planet. This theoretical prediction will be testable in a few years with new ALMA observations. Similarly, in the case of PDS70, the structures observed in Keppler et al. 2018 and Isella et al. 2019 can be explained with an accretion stream from the disc to the planet and the presence of a dusty circumplanetary disc (see Fig. 3 and Fig. 4).

Recent high resolution and high fidelity observations of protoplanetary discs are showing us peculiar substructures such as spirals, gaps, rings and horseshoes. In particular recent surveys have shown that the majority of these discs are characterised by rings and gaps. What can we learn from these features? Are these discs hiding planets? I will present the results we have obtained in order to model one specific disc orbiting around DS Tau, an M-type star, in the Taurus star-forming region located at a distance of 159 pc. This disc is showing a wide gap (∼30 au) in the continuum at 1.3 mm (Long et al. 2018) and at 2.9 mm (Long et al. 2020) (left panels of Fig. 1). We performed 3D-hydrodynamical (PHANTOM, Price et al. 2018) and radiative transfer (MCFOST, Pinte et al. 2006, 2009) simulations in order to reproduce the observed gap shape at 1.3 mm. In this modeling, we assumed that the observed gap is carved by a planet between one and five Jupiter masses. We fit the shape of the radial intensity profile along the disc major axis varying the planet mass, the dust disc mass, and the evolution time of the system. In the central panels of Fig. 1 we show the synthetic images, that have been computed for our best fit model (performed on the 1.3 mm case) parameters: Mp=3.5 MJup, Mdust=9.6*10-5 Msun and t=145 orbits. The right panels compare radial cuts of the flux intensity profile along the disc major axis obtained from the synthetic image at 1.3 and 2.9 mm (top and bottom center panel of Fig. 1) with the ALMA data (top and bottom left panel). The left (blue) and right (red) side of the radial cut correspond to the left and right side of the disc major axis. Dot markers represent the data, while the models are in dashed lines. We also computed the CO-isotopologues channel maps for the best model fitting the dust continuum (see Fig. 2 for an example), in order to study the expected signature of the planet in the gas kinematics. We found that the planet mass fitting the ALMA image is 3.5 Mjup and that this planet would be able to produce a kink detectable by ALMA with a reasonable beam size and velocity resolution. Figure 1. First row: ALMA observation (left panel) and continuum mock image (center panel) of the DS Tau disc at 1.3 mm. The synthetic image has been computed for our best fit model Mp=3.5 MJup and Mdust=9.6*10-5 Msun). The Gaussian beam we take to convolve the full resolution image has been chosen to reproduce the observations reported by Long et al. (2018) and Long et al. (2020), respectively 0.14''x0.1'' and 0.13''x0.09''. In the 1.3 mm image we highlight in blue the left side of the major axis and in red the right side. Right panel shows the comparison between the left (blue) - right (red) side of the radial cut along the disc major axis for the data (dot marker) and the modeling (dashed line). Second row: Same as first row but for the 2.9 mm continuum image. Figure 2: Channel maps for C18O isotopologue with a velocity resolution of 0.2 km/s and a beam size of [30,40,50,70] mas (from left to right). The azimuthal position of the planet is φ=225°. We show two velocity channels, Δv=2.7 km/s, where a kink is visible, and the opposite one at Δv=-2.7 km/s.

Observations with the Atacama Large Millimeter/Submillimeter array (ALMA) have dramatically improved our understanding of the site of exoplanet formation: protoplanetary discs. However, many basic properties of these discs are not well-understood. The most fundamental of these is the total disc mass, which sets the mass budget for planet formation. Discs with sufficiently high masses can excite gravitational instability and drive spiral arms that are detectable with ALMA . Although spirals have been detected in ALMA observations of the dust , their association with gravitational instability, and high disc masses, is far from clear. Here we report a prediction for kinematic evidence of gravitational instability. Using hydrodynamics simulations coupled with radiative transfer calculations, we show that a disc undergoing such instability has clear kinematic signatures in molecular line observations across the entire disc azimuth and radius which are independent of viewing angle. If these signatures are detected, it will provide the clearest evidence for the occurrence of gravitational instability in planet-forming discs, and provide a crucial way to measure disc masses., 10 pages, 7 figures, accepted to The Astrophysical Journal

We present new Atacama Large Millimeter/submillimeter Array (ALMA) observations for three protoplanetary disks in Taurus at 2.9\,mm and comparisons with previous 1.3\,mm data both at an angular resolution of $\sim0.''1$ (15\,au for the distance of Taurus). In the single-ring disk DS Tau, double-ring disk GO Tau, and multiple-ring disk DL Tau, the same rings are detected at both wavelengths, with radial locations spanning from 50 to 120\,au. To quantify the dust emission morphology, the observed visibilities are modeled with a parametric prescription for the radial intensity profile. The disk outer radii, taken as 95\% of the total flux encircled in the model intensity profiles, are consistent at both wavelengths for the three disks. Dust evolution models show that dust trapping in local pressure maxima in the outer disk could explain the observed patterns. Dust rings are mostly unresolved. The marginally resolved ring in DS Tau shows a tentatively narrower ring at the longer wavelength, an observational feature expected from efficient dust trapping. The spectral index ($\alpha_{\rm mm}$) increases outward and exhibits local minima that correspond to the peaks of dust rings, indicative of the changes in grain properties across the disks. The low optical depths ($\tau\sim$0.1--0.2 at 2.9\,mm and 0.2--0.4 at 1.3\,mm) in the dust rings suggest that grains in the rings may have grown to millimeter sizes. The ubiquitous dust rings in protoplanetary disks modify the overall dynamics and evolution of dust grains, likely paving the way towards the new generation of planet formation., Comment: accepted for publication in ApJ

Determining the mechanisms that drive the evolution of protoplanetary disks is a necessary step to understand how planets form. Here we measured the mass accretion rate for young stellar objects at age >5 Myr, a critical test for the current models of disk evolution. We present the analysis of the spectra of 36 targets in the ~5-10 Myr old Upper Scorpius region for which disk masses were measured with ALMA. We find that the mass accretion rates in this sample of old but still survived disks are similarly high as those of the younger (10^-9 Msun/yr while having low disk masses. Furthermore, the median values of the measured mass accretion rates in the disk mass ranges where our sample is complete at a level ~60-80% are compatible in these three regions. At the same time, the spread of mass accretion rates at any given disk mass is still >0.9 dex even at age>5 Myr. These results are in contrast with simple models of viscous evolution, which would predict that the values of the mass accretion rate diminish with time, and a tighter correlation with disk mass at age>5 Myr. Similarly, simple models of internal photoevaporation cannot reproduce the observed mass accretion rates, while external photoevaporation might explain the low disk masses and high accretion rates. A partial possible solution to the discrepancy with the viscous models is that the gas-to-dust ratio of the disks at >5 Myr is significantly different and higher than the canonical 100, as suggested by some dust and gas disk evolution models. The results shown here require the presence of several inter-playing processes, such as detailed dust evolution, external photoevaporation and possibly MHD winds, to explain the secular evolution of protoplanetary disks., Comment: Accepted on Astronomy & Astrophysics. Language edited version

Context. A large portion of stars is found to be part of binary or higher-order multiple systems. The ubiquity of planets found around single stars raises the question of whether and how planets in binary systems form. Protoplanetary disks are the birthplaces of planets, and characterizing them is crucial in order to understand the planet formation process. Aims. Our goal is to characterize the morphology of the GG Tau A disk, one of the largest and most massive circumbinary disks. We also aim to trace evidence for binary-disk interactions. Methods. We obtained observations in polarized scattered light of GG Tau A using the SPHERE/IRDIS instrument in the H-band filter. We analyzed the observed disk morphology and substructures. We ran 2D hydrodynamical models to simulate the evolution of the circumbinary ring over the lifetime of the disk. Results. The disk and also the cavity and the inner region are highly structured, with several shadowed regions, spiral structures, and streamer-like filaments. Some of these are detected here for the first time. The streamer-like filaments appear to connect the outer ring with the northern arc. Their azimuthal spacing suggests that they may be generated through periodic perturbations by the binary, which tear off material from the inner edge of the outer disk once during each orbit. By comparing observations to hydrodynamical simulations, we find that the main features, in particular, the gap size, but also the spiral and streamer filaments, can be qualitatively explained by the gravitational interactions of a binary with a semimajor axis of ~35 au on an orbit coplanar with the circumbinary ring., Astronomy & Astrophysics, 639, ISSN:0004-6361, ISSN:1432-0746

In order to obtain a complete census of the stellar and sub-stellar population, down to a few M$_{Jup}$ in the $\sim1$ Myr old Orion Nebula Cluster, we used the infrared channel of the Wide Field Camera 3 of the Hubble Space Telescope with the F139M and F130N filters. These bandpasses correspond to the $1.4 \mu$m H$_2$O absorption feature and an adjacent line-free continuum region. Out of $4,504$ detected sources, $3,352$ (about $75\%$) appear fainter than m$_{130}=14$ (Vega mag) in the F130N filter, a brightness corresponding to the hydrogen-burning limit mass (M$\simeq 0.072 M_\odot$) at $\sim 1$ Myr. Of these, however, only $742$ sources have a negative F130M-139N color index, indicative of the presence of H$_2$O vapor in absorption, and can therefore be classified as bona-fide M and L dwarfs, with effective temperatures T$\lesssim 2850$ K at an assumed $1$ Myr cluster age. On our color-magnitude diagram, this population of sources with H$_2$O absorption appears clearly distinct from the larger background population of highly reddened stars and galaxies with positive F130M-F139N color index, and can be traced down to the sensitivity limit of our survey, m$_{130}\simeq 21.5$, corresponding to a $1$ Myr old $\simeq 3 $M$_{Jup}$, planetary mass object under about 2 magnitudes of visual extinction. Theoretical models of the BT-Settl family predicting substellar isochrones of $1, 2$ and $3$ Myr (down to $\sim 1 $M$_{Jup}$) fail to reproduce the observed H$_2$O color index at M$\lesssim 20 $M$_{Jup}$. We perform a Bayesian analysis to determine extinction, mass and effective temperature of each sub-stellar member of our sample, together with its membership probability., Comment: Accepted for publication in the Astrophysical Journal. The resolution of several figures has been downgraded to comply with the size limit of arXiv submissions

Tidal disruption events involve numerous physical processes (fluid dynamics, magnetohydrodynamics, radiation transport, self-gravity, general relativistic dynamics) in highly nonlinear ways, and, because TDEs are transients by definition, frequently in non-equilibrium states. For these reasons, numerical solution of the relevant equations can be an essential tool for studying these events. In this chapter, we present a summary of the key problems of the field for which simulations offer the greatest promise and identify the capabilities required to make progress on them. We then discuss what has been---and what cannot be---done with existing numerical methods. We close with an overview of what methods now under development may do to expand our ability to understand these events., A chapter in the ISSI review book "The Tidal Disruption of Stars by Massive Black Holes", to be published in Space Science Reviews

Numerical simulations have historically played a major role in understanding the hydrodynamics of the tidal disruption process. Given the complexity of the geometry of the system, the challenges posed by the problem have indeed stimulated much work on the numerical side. Smoothed Particles Hydrodynamics methods, for example, have seen their very first applications in the context of tidal disruption and still play a major role to this day. Likewise, initial attempts at simulating the evolution of the disrupted star with the so-called affine method have been historically very useful. In this Chapter, we provide an overview of the numerical techniques used in the field and of their limitations, and summarize the work that has been done to simulate numerically the tidal disruption process., 34 pages, Accepted chapter for Springer Space Science Reviews book on Tidal Disruption Events

Recent mm-wavelength surveys performed with the Atacama Large Millimeter Array (ALMA) have revealed protoplanetary discs characterized by rings and gaps. A possible explanation for the origin of such rings is the tidal interaction with an unseen planetary companion. The protoplanetary disc around DS Tau shows a wide gap in the ALMA observation at 1.3 mm. We construct a hydrodynamical model for the dust continuum observed by ALMA assuming the observed gap is carved by a planet between one and five Jupiter masses. We fit the shape of the radial intensity profile along the disc major axis varying the planet mass, the dust disc mass, and the evolution time of the system. The best fitting model is obtained for a planet with $M_{\rm p}=3.5\,M_{\rm Jup}$ and a disc with $M_{\rm dust}= 9.6\cdot10^{-5}\,M_{\odot}$. Starting from this result, we also compute the expected signature of the planet in the gas kinematics, as traced by CO emission. We find that such a signature (in the form of a "kink" in the channel maps) could be observed by ALMA with a velocity resolution between $0.2-0.5\,\rm{kms}^{-1}$ and a beam size between 30 and 50 mas., 16 pages, 15 figures, accepted for publication on MNRAS

Binary systems exert a gravitational torque on misaligned discs orbiting them, causing differential precession which may produce disc warping and tearing. While this is well understood for gas-only discs, misaligned cirumbinary discs of gas and dust have not been thoroughly investigated. We perform SPH simulations of misaligned gas and dust discs around binaries to investigate the different evolution of these two components. We choose two different disc aspect ratios: A thin case for which the gas disc always breaks, and a thick one where a smooth warp develops throughout the disc. For each case, we run simulations of five different dust species with different degrees of coupling with the gas component, varying in Stokes number from 0.002 (strongly coupled dust) to 1000 (effectively decoupled dust). We report two new phenomena: First, large dust grains in thick discs pile up at the warp location, forming narrow dust rings, due to a difference in precession between the gas and dust components. These pile ups do not form at gas pressure maxima, and hence are different from conventional dust traps. This effect is most evident for St ~ 10 - 100. Second, thin discs tear and break only in the gas, while dust particles with St > 10 form a dense dust trap due to the steep pressure gradient caused by the break in the gas. We find that dust with St < 0.02 closely follow the gas particles, for both thin and thick discs, with radial drift becoming noticeable only for the largest grains in this range., Accepted for publication in MNRAS, 11 pages, 9 figures

A tidal disruption event (TDE) occurs when a star passes too close to a supermassive black hole and gets torn apart by its gravitational tidal field. After the disruption, the stellar debris form an expanding gaseous stream. The morphology and evolution of this stream is particularly interesting as it ultimately determines the observational properties of the event itself. In this work we perform 3D hydrodynamical simulations of the TDE of a star modelled as a polytropic sphere of index {\gamma} = 5/3, and study the gravitational stability of the resulting gas stream. We provide an analytical solution for the evolution of the stream in the bound, unbound and marginally bound case, that allows us to describe the stream properties and analyse the time-scales of the physical processes involved, applying a formalism developed in star formation context. Our results are that, when fragmentation occurs, it is fueled by the failure of pressure in supporting the gas against its self-gravity. We also show that a stability criterion that includes also the stream gas pressure proves to be far more accurate than one that only considers the black hole tidal forces, giving analytical predictions of the time evolution of the various forces associated to the stream. Our results point out that fragmentation occurs on timescales longer compared with the observational windows of these events and is thus not expected to give rise to significant observational features., Comment: 12 pages,15 figures, accepted for publication in MNRAS

At the final stages of a supermassive black hole coalescence, the emission of gravitational waves will efficiently remove energy and angular momentum from the binary orbit, allowing the separation between the compact objects to shrink. In the scenario where a circumprimary disc is present, a squeezing phase will develop, in which the tidal interaction between the disc and the secondary black hole could push the gas inwards, enhancing the accretion rate on to the primary and producing what is known as an electromagnetic precursor. In this context, using 3D hydrodynamic simulations, we study how an adiabatic circumprimary accretion disc responds to the varying gravitational potential as the secondary falls onto the more massive object. We included a cooling prescription controlled by the parameter \beta = \Omega t_{cool}, which will determine how strong the final accretion rate is: a hotter disc is thicker, and the tidal interaction is suppressed for the gas outside the binary plane. Our main results are that for scenarios where the gas cannot cool fast enough (\beta>30) the disc becomes thick and renders the system invisible, while for \beta, Comment: to be published in MNRAS

Recent ALMA observations of the protoplanetary disc around HD~169142 reveal a peculiar structure made of concentric dusty rings: a main ring at $\sim$20 au, a triple system of rings at $\sim 55-75$ au in millimetric continuum emission and a perturbed gas surface density from the $^{12}$CO,$^{13}$CO and C$^{18}$O$(J=2-1)$ surface brightness profile. In this Letter, we perform three-dimensional numerical simulations and radiative transfer modeling exploring the possibility that two giant planets interacting with the disc and orbiting in resonant locking can be responsible for the origin of the observed dust inner rings structure. We find that in this configuration the dust structure is actually long lived while the gas mass of the disc is accreted onto the star and the giant planets, emptying the inner region. In addition, we also find that the innermost planet is located at the inner edge of the dust ring, and can accrete mass from the disc, generating a signature in the dust ring shape that can be observed in mm ALMA observations., 8 pages, 5 figures, accepted Apj Letters

We present 3 mm ALMA continuum and line observations at resolutions of 6.5 au and 13 au respectively, toward the Class 0 system IRAS 16293-2422 A. The continuum observations reveal two compact sources towards IRAS 16293-2422 A, coinciding with compact ionized gas emission previously observed at radio wavelengths (A1 and A2), confirming the long-known radio sources as protostellar. The emission towards A2 is resolved and traces a dust disk with a FWHM size of ~12 au, while the emission towards A1 sets a limit to the FWHM size of the dust disk of ~4 au. We also detect spatially resolved molecular kinematic tracers near the protostellar disks. Several lines of the J=5-4 rotational transition of HNCO, NH2CHO and t-HCOOH are detected, with which we derived individual line-of-sight velocities. Using these together with the CS (J=2-1), we fit Keplerian profiles towards the individual compact sources and derive masses of the central protostars. The kinematic analysis indicates that A1 and A2 are a bound binary system. Using this new context for the previous 30 years of VLA observations, we fit orbital parameters to the relative motion between A1 and A2 and find the combined protostellar mass derived from the orbit is consistent with the masses derived from the gas kinematics. Both estimations indicate masses consistently higher (0.5< M1, Comment: Accepted for publication in ApJ. 23 pages, 14 figures, 4 tables

We report the discovery of a low-mass stellar companion around the young Herbig Be star MWC 297. We performed multi-epoch high-contrast imaging in the near infrared (NIR) with the Very Large Telescope (VLT)/Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) instrument. The companion is found at projected separation of 244.7$\pm$13.2 au and a position angle of 176.4$\pm$0.1 deg. The large separation supports formation via gravitational instability. From the spectrum, we estimate a mass of 0.1-0.5 M$_{\odot}$, the range conveying uncertainties in the extinction of the companion and in evolutionary models at young ages. The orbit coincides with a gap in the dust disk inferred from the Spectral Energy Distribution (SED). The young age ($\lesssim$ 1 Myr) and mass ratio with the central star ($\sim 0.01$) makes the companion comparable to PDS 70~b, suggesting a relation between formation scenarios and disk dynamics., Comment: 4 figures

The disc surrounding PDS 70, with two directly imaged embedded giant planets, is an ideal laboratory to study planet-disc interaction. We present three-dimensional smoothed particle hydrodynamics simulations of the system. In our simulations, planets, which are free to migrate and accrete mass, end up in a locked resonant configuration that is dynamically stable. We show that features observed at infrared (scattered light) and millimetre (thermal continuum) wavelengths are naturally explained by the accretion stream onto the outer planet, without requiring a circumplanetary disc around planet c. We post-processed our near-infrared synthetic images in order to account for observational biases known to affect high-contrast images. Our successful reproduction of the observations indicates that planet-disc dynamical interactions alone are sufficient to explain the observations of PDS 70., 15 pages, 11 figures

In this paper we derive the gravitational wave stochastic background from tidal disruption events (TDEs). We focus on both the signal emitted by main sequence stars disrupted by super-massive black holes (SMBHs) in galaxy nuclei, and on that from disruptions of white dwarfs by intermediate mass black holes (IMBHs) located in globular clusters. We show that the characteristic strain $h_{\rm c}$'s dependence on frequency is shaped by the pericenter distribution of events within the tidal radius, and under standard assumptions $h_{\rm c} \propto f^{-1/2}$. This is because the TDE signal is a burst of gravitational waves at the orbital frequency of the closest approach. In addition, we compare the background characteristic strains with the sensitivity curves of the upcoming generation of space-based gravitational wave interferometers: the Laser Interferometer Space Antenna (LISA), TianQin, ALIA, the DECI-hertz inteferometer Gravitational wave Observatory (DECIGO) and the Big Bang Observer (BBO). We find that the background produced by main sequence stars might be just detected by BBO in its lowest frequency coverage, but it is too weak for all the other instruments. On the other hand, the background signal from TDEs with white dwarfs will be within reach of ALIA, and especially of DECIGO and BBO, while it is below the LISA and TianQin sensitive curves. This background signal detection will not only provide evidence for the existence of IMBHs up to redshift $z\sim 3$, but it will also inform us on the number of globular clusters per galaxy and on the occupation fraction of IMBHs in these environments., Comment: Accepted for Publications in MNRAS. 11 pages, 5 figures