Initial Mass Distribution Research Articles

A Modified Initial Mass Function of the First Stars with Explodability Theory under Different Enrichment Scenarios

The most metal-poor stars record the earliest metal enrichment triggered by Population III stars. By comparing observed abundance patterns with theoretical yields of metal-free stars, physical properties of their first star progenitors can be inferred, including zero-age main-sequence mass and explosion energy. In this work, the initial mass distribution of the first stars is obtained from the largest analysis to date of 406 very metal-poor stars with the newest LAMOST/Subaru high-resolution spectroscopic observations. However, the mass distribution fails to be consistent with the Salpeter initial mass function, which is also reported by previous studies. Here, we modify the standard power-law function with explodability theory. The mass distribution of Population III stars could be well explained by ensuring that the initial metal enrichment originates from successful supernova explosions. Based on the modified power-law function, we suggest an extremely top-heavy or nearly flat initial mass function with a large exponent for the explosion energy. This indicates that supernova explodability should be considered in the earliest metal enrichment process in the Universe.

Reconstruction of Fermi and eROSITA Bubbles from Magnetized Jet Eruption with Simulations

The Fermi bubbles and the eROSITA bubbles around the Milky Way Galaxy are speculated to be the aftermaths of past jet eruptions from a supermassive black hole in the galactic center. In this work, a 2.5D axisymmetric relativistic magnetohydrodynamic (RMHD) model is applied to simulate a jet eruption from our galactic center and to reconstruct the observed Fermi bubbles and eROSITA bubbles. High-energy non-thermal electrons are excited around forward shock and discontinuity transition regions in the simulated plasma distributions. The γ-ray and X-ray emissions from these electrons manifest patterns on the skymap that match the observed Fermi bubbles and eROSITA bubbles, respectively, in shape, size and radiation intensity. The influence of the background magnetic field, initial mass distribution in the Galaxy, and the jet parameters on the plasma distributions and hence these bubbles is analyzed. Subtle effects on the evolution of plasma distributions attributed to the adoption of a galactic disk model versus a spiral-arm model are also studied.

Exploring Low-mass Black Holes through Tidal Disruption Events in the Early Universe: Perspectives in the Era of the JWST, Roman Space Telescope, and LSST Surveys

The James Webb Space Telescope (JWST) has recently uncovered the presence of low-luminosity active galactic nuclei (AGNs) at z = 4–11. Spectroscopic observations have provided estimates of the nuclear black hole (BH) masses for these sources, extending the low-mass boundary down to M • ∼ 106–7 M ⊙. Despite this breakthrough, the observed lowest mass of BHs is still ≳1–2 orders of magnitude heavier than the predicted mass range of their seed population, thereby leaving the initial mass distribution of massive BHs poorly constrained. In this paper, we focus on UV-to-optical (in the rest frame) flares of stellar tidal disruption events (TDEs) embedded in low-luminosity AGNs as a tool for exploring low-mass BH populations with ≲104–6 M ⊙. We provide an estimate of the TDE rate over z = 4–11, associated with the properties of JWST-detected AGN host galaxies, and we find that deep and wide survey programs with JWST and the Roman Space Telescope (RST) can detect and identify TDEs up to z ≃ 4–7. The predicted detection numbers of TDEs at z > 4 in 1 yr are NTDE∼2–10(0.2–2) for the JADES-Medium (and COSMOS-Web) survey with JWST and NTDE∼2–10(8–50) for the deep (and wide) tiers of the High Latitude Time Domain Survey with RST. We further discuss survey strategies for hunting for transient high-redshift TDEs in wide-field surveys with RST, as well as a joint observation campaign with the Vera C. Rubin Observatory for enhancing the detection number. The high-redshift TDE search will give us a unique opportunity to probe the mass distribution of early BH populations.

Constrain the Dark-matter Distribution of Ultra-diffuse Galaxies with Globular-cluster Mass Segregation: A Case Study with NGC5846-UDG1

The properties of globular clusters (GCs) contain valuable information of their host galaxies and dark-matter halos. In the remarkable example of ultra-diffuse galaxy, NGC5846-UDG1, the GC population exhibits strong radial mass segregation, indicative of dynamical-friction-driven orbital decay, which opens the possibility of using imaging data alone to constrain the dark-matter content of the galaxy. To explore this possibility, we develop a semianalytical model of GC evolution, which starts from the initial mass, structural, and spatial distributions of the GC progenitors, and follows the effects of dynamical friction, tidal evolution, and two-body relaxation. Using Markov Chain Monte Carlo, we forward-model the GCs in a UDG1-like potential to match the observed GC statistics, and to constrain the profile of the host halo and the origin of the GCs. We find that, with the assumptions of zero mass segregation when the star clusters were born, UDG1 is relatively dark-matter-poor compared to what is expected from stellar-to-halo–mass relations, and its halo concentration is lower than the cosmological average, irrespective of having a cuspy or a cored profile. Its GC population has an initial spatial distribution more extended than the smooth stellar distribution. We discuss the results in the context of scaling laws of galaxy–halo connections, and warn against naively using the GC-abundance–halo–mass relation to infer the halo mass of ultra-diffuse galaxies. Our model is generally applicable to GC-rich dwarf galaxies, and is publicly available.

Influence of Rheological and Morphological Characteristics of Polyhydroxybutyrate on Its Meltblown Process Behavior.

Polyhydroxybutyrate (PHB) is a promising biopolymer. However, processing PHB in pure form in thermoplastic processes is limited due to its rapid degradation, very low initial crystallization rate, strong post-crystallization, and its low final stretchability. In this article, we screened commercial PHBs for morphological characteristics, rheological properties, and "performance" in the meltblown process in order to reveal process-relevant properties and overcome the shortcoming of PHB in thermoplastic processes for fiber formation. An evaluation of degradation (extruded (meltblown) material vs. granules) was performed via rheological and SEC analysis. The study revealed large differences in the minimum melt temperature (175 up to 200 °C) and the grade-dependent limitation of accessible throughput on a 500 mm plant. The average fiber diameter could be lowered from around 10 μm to 2.4 μm in median, which are the finest reported values in the literature so far. It was found that the determination of the necessary process temperature can be predicted well from the complex shear viscosity. Different to expectations, it became apparent that a broader initial molar mass distribution (>8) is suitable to overcome the state-of-the art limitations of PHAs in order to stabilize fiber formation, increase the productivity, and obtain better resistance towards thermal degradation in process. Accordingly, longer polymer chain fractions could be more affected by degradation than medium and short polymer chains in the distribution. Further, a low initial narrow distributed molar mass resulted in too brittle fabrics.

Predicting pesticide residues in pod fruits with a modified peel-like uptake model: A green pea demonstration

Peas are among the most popular leguminous plants, consumed by both humans and animals in large quantities. Pesticides are widely used globally to increase pea yield, and as a result, pesticide residues can be taken up by pea plants and bioaccumulate in their fruits, including peas and pods. However, there is a lack of modeling approaches available to predict residue concentrations in peas. To address this issue, a pod fruit model (specifically designed for neutral organic compounds) was proposed to simulate the bioaccumulation process of pesticide residues in pea plants, which was developed by modifying a peel-like uptake model. The simulation results, based on green pea as the modeling demonstration, reveal that moderately-lipophilic pesticides (i.e., log KOW around 3) have higher simulated concentrations in peas at harvest compared to hydrophilic (i.e., log KOW less than 0) or highly-lipophilic (i.e., log KOW over 5) pesticides, which is due to the enhanced uptake process of moderately-lipophilic compounds in the pod-pea system, such as their ability to penetrate the pod cuticle and be transported via phloem sap. The sensitivity test and variability analysis conducted in this study revealed that the degradation kinetics, including metabolism, hydrolysis, and photolysis, had a significant impact on moderately-lipophilic pesticides due to their high simulated concentrations in the pea plant. This can result in substantial loss of residue mass via degradation. The validation of the model demonstrated that the simulation results, specifically residue concentrations in the fruit, were consistent with the harvested data. However, some inconsistency was observed immediately after pesticide application, which could be attributed to plant growth dynamics and initial surface mass distributions. The proposed pod fruit model provides new insights into the bioaccumulation process of pesticide residues in pea plants and enables high-throughput simulations of residue concentrations at harvest. To enhance the performance of the pod fruit model, future research should consider plant growth dynamics, plant uptake of ionizable compounds, and initial mass distribution functions.

Oort cloud (exo)planets

ABSTRACT Dynamical instabilities among giant planets are thought to be nearly ubiquitous and culminate in the ejection of one or more planets into interstellar space. Here, we perform N-body simulations of dynamical instabilities while accounting for torques from the galactic tidal field. We find that a fraction of planets that would otherwise have been ejected are instead trapped on very wide orbits analogous to those of Oort cloud comets. The fraction of ejected planets that are trapped ranges from 1 to 10 per cent, depending on the initial planetary mass distribution. The local galactic density has a modest effect on the trapping efficiency and the orbital radii of trapped planets. The majority of Oort cloud planets survive for Gyr time-scales. Taking into account the demographics of exoplanets, we estimate that one in every 200–3000 stars could host an Oort cloud planet. This value is likely an overestimate, as we do not account for instabilities that take place at early enough times to be affected by their host stars’ birth cluster or planet stripping from passing stars. If the Solar system’s dynamical instability happened after birth cluster dissolution, there is a ∼7 per cent chance that an ice giant was captured in the Sun’s Oort cloud.

Multiple Populations in Low-mass Globular Clusters: Eridanus

Multiple populations (MPs), characterized by variations in light elemental abundances, have been found in stellar clusters in the Milky Way, Magellanic Clouds, as well as several other dwarf galaxies. Based on a large number of observations, mass has been suggested to be a key parameter affecting the presence and appearance of MPs in stellar clusters. To further investigate the existence of MPs in low-mass clusters and explore the mass threshold for the formation of MPs, we carried out a project studying the composition of the stellar population in several low-mass Galactic globular clusters. Here we present our study on the cluster Eridanus. With blue-UV low-resolution spectra obtained with the OSIRIS/Multi-object spectrograph on the Gran Telescopio Canarias, we computed the spectral indices of CH and CN for a sample of giant stars and derived their carbon and nitrogen abundances using model spectra. A significant dispersion in the initial surface abundance of nitrogen was found in the sample, indicating the existence of MPs in Eridanus. Inspecting the age–initial mass distribution of in situ clusters with MPs, we find a slight trend that initial mass increases with increasing age, and the lowest initial masses of ∼ 4.98 and 5.26 are found at the young and old end, respectively, which might provide a rough reference for the mass threshold for clusters to form MPs. However, more observations of clusters with low initial masses are still necessary before any firm conclusion can be drawn.

Water emission tracing active star formation from the Milky Way to high-z galaxies

Context. The question of how most stars in the Universe form remains open. While star formation predominantly takes place in young massive clusters, the current framework focuses on isolated star formation. This poses a problem when trying to constrain the initial stellar mass and the core mass functions, both in the local and distant Universe. Aims. One way to access the bulk of protostellar activity within star-forming clusters is to trace signposts of active star formation with emission from molecular outflows. These outflows are bright (e.g., in water emission), which is observable throughout cosmological times, providing a direct observational link between nearby and distant galaxies. We propose to utilize the in-depth knowledge of local star formation as seen with molecular tracers, such as water, to explore the nature of star formation in the Universe. Methods. We present a large-scale statistical galactic model of emission from galactic active star-forming regions. Our model is built on observations of well-resolved nearby clusters. By simulating emission from molecular outflows, which is known to scale with mass, we create a proxy that can be used to predict the emission from clustered star formation on galactic scales. In particular, the para-H2O 202 − 111 line is well suited for this purpose as it is one of the brightest transitions observed toward Galactic star-forming regions and is now routinely observed toward distant galaxies. Results. We evaluated the impact of the most important global star formation parameters (i.e., initial stellar mass function, molecular cloud mass distribution, star formation efficiency, and free-fall time efficiency) on simulation results. We observe that for emission from the para-H2O 202 − 111 line, the initial mass function and molecular cloud mass distribution have a negligible impact on the emission, both locally and globally, whereas the opposite holds for star formation efficiency and free-fall time efficiency. Moreover, this water transition proves to be a low-contrast tracer of star formation, with ∫Iν ∝ Menv. Conclusions. The fine-tuning of the model and adaptation to morphologies of distant galaxies should result in realistic predictions of observed molecular emission and make the galaxy-in-a-box model a tool for analyzing and better understanding star formation throughout cosmological times.

Growth after the streaming instability: The radial distance dependence of the planetary growth

Streaming instability is hypothesized to be triggered at particular protoplanetary disk locations where the volume density of the solid particles is enriched comparable to that of the gas. A ring of planetesimals thus forms when this condition is fulfilled locally. These planetesimals collide with each other and accrete inward drifting pebbles from the outer disk to further increase masses. We investigate the growth of the planetesimals that form in a ring-belt at various disk radii. Their initial mass distributions are calculated based on the formula summarized from the streaming instability simulations. We simulate the subsequent dynamical evolution of the planetesimals with a protoplanetary disk model based either on the minimum mass solar nebula (MMSN) or on the Toomre stability criterion. For the MMSN model, both pebble accretion and planetesimal accretion are efficient at a close-in orbit of 0.3 AU, resulting in the emergence of several super-Earth mass planets after 1 Myr. For comparison, only the most massive planetesimals undergo substantial mass growth when they are born at r = 3 AU, while the planetesimals at r = 30 AU experience little or no growth. On the other hand, in the denser Toomre disk, the most massive forming planets can reach Earth mass at t = 1 Myr and reach a mass between that of Neptune and that of Saturn within 3 Myr at 30 AU and 100 AU. Both the pebble and planetesimal accretion rate decrease with disk radial distance. Nevertheless, planetesimal accretion is less pronounced than pebble accretion at more distant disk regions. Taken together, the planets acquire higher masses when the disk has a higher gas density, a higher pebble flux, and/or a lower Stokes number of pebbles.

Existence, Uniqueness, and Numerical Modeling of Wine Fermentation Based on Integro-Differential Equations

Predictive modeling is the key factor for saving time and resources with respect to manufacturing processes such as fermentation processes arising e.g. in food and chemical manufacturing processes. According to Zhang et al. (2002), the open-loop dynamics of yeast are highly dependent on the initial cell mass distribution. This can be modeled via population balance models describing the single-cell behavior of the yeast cell. There have already been several population balance models for wine fermentation in the literature. However, the new model introduced in this paper is much more detailed than the ones studied previously. This new model for the white wine fermentation process is based on a combination of components previously introduced in literature. It turns it into a system of highly nonlinear weakly hyperbolic partial/ordinary integro-differential equations. This model becomes very challenging from a theoretical and numerical point of view. Existence and uniqueness of solutions to a simplified version of the introduced problem is studied based on semigroup theory. For its numerical solution a numerical methodology based on a finite volume scheme combined with a time implicit scheme is derived. The impact of the initial cell mass distribution on the solution is studied and underlined with numerical results. The detailed model is compared to a simpler model based on ordinary differential equations. The observed differences for different initial distributions and the different models turn out to be smaller than expected. The outcomes of this paper are very interesting and useful for applied mathematicians, winemakers and process engineers.

Dynamic analysis of the wind-wave-current-bridge system considering pile-soil interaction

Coastal bridges are normally confronted with a complex marine environment including wind, wave and current. Present researches rarely take the current action and pile-soil interaction into consideration. It is thus essential to conduct the dynamic analysis of the cable-stayed bridge under wind-wave-current action considering pile-soil interaction. A coupled wind-wave-current-bridge (WWCB) system is proposed in this study to help understand the bridge dynamic performance. In the WWCB system, the bridge model is established through the finite element method, and the pile-soil interaction is considered through the pile-soil solid contact (PSSC) model. The wave-current action is obtained through a numerical wave tank, while the wind is simulated as the stochastic random process and generated with spectrums. The initial geostress, mass and density distribution are also considered in the WWCB system. To illustrate the bridge dynamic characteristics, dynamic responses under different load combinations are presented. Furthermore, the natural frequency and spectral density function comparison between the consolidation model, PSSC model and soil-spring model are provided to investigate the influence of the pile-soil interaction. The results show that different from previous conclusions, the wave-current action plays the dominant role instead of the wind action in some cases when considering the pile-soil interaction. Additionally, the consideration of the pile-soil interaction would decrease the structural stiffness, resulting in lower natural frequencies and wider frequency distribution. Consequently, the influence of the wave-current action and pile-soil interaction should be noted in the practical engineering.

Review of research on lunar dust dynamics

Lunar dust particles are generated by hypervelocity impacts of interplanetary micrometer meteoroids onto the surface of the Moon, which seriously threatens the security of explorations. Studying the lunar dust dynamics helps to understand the origin and migration mechanism of lunar dust, and to provide the theoretical guidelines for the orbital design of lunar space missions. This paper reviews previous research on the lunar dust dynamics, including the interplanetary impactor environment of the Earth–Moon system, the mass production rate, the initial mass, speed and ejecta angle distributions, the related space exploration missions, the dynamical model, and spatial distribution of dust particles originating from the lunar surface in the whole Earth–Moon system.

Spiral structure of the galactic disk and its influence on the rotational velocity curve

AbstractMost spiral galaxies have a flat rotational velocity curve, according to the different observational techniques used in several wavelengths domain. In this work, we show that nonlinear terms are able to balance the dispersive effect of the wave, thus reviving the observed rotational curve profiles without the inclusion of any other but baryonic matter concentrated in the bulge and disk. To prove that the considered model is able to restore a flat rotational curve, Milky Way has been chosen as the best‐mapped galaxy, to apply on. Using the gravitational N‐body simulations with up to particles, we test this dynamical model in the case of the Milky Way with two different approaches. Within the direct approach, as an input condition in the simulation runs, we set the spiral surface density distribution which is previously obtained as an explicit solution to nonlinear Schrödinger equation (instead of a widely used exponential disk approximation). In the evolutionary approach, we initialize the runs with different initial mass and rotational velocity distributions, in order to capture the natural formation of spiral arms and to determine their role in the disk evolution. In both cases, we are able to reproduce the stable and nonexpanding disk structures at the simulation end times of years, with no halo inclusion. Although the given model does not take into account the velocity dispersion of stars and finite disk thickness, the results presented here still imply that nonlinear effects can significantly alter the amount of dark matter which is required to keep the galactic disk in a stable configuration.

Monte Carlo simulations of evolving rotational distributions of low-mass stars in young open clusters. Testing the influence of initial conditions

ABSTRACT The rotational evolution of a young stellar population can give informations about the rotation pattern of more evolved clusters. Combined with rotational period values of thousands of young stars and theoretical propositions about the redistribution and loss of stellar angular momentum, it allows us to trace the rotational history of stars according to their mass. We want to investigate how internal and environmental changes on single stars can change the rotational evolution of a young stellar population. We run Monte Carlo simulations of a young cluster composed by solar mass stars of 0.5, 0.8 and 1.0 M⊙ from 1 to 550 Myr taking into account observational and theoretical parameters. In order to compare our results with the observations we run Kolmogorov-Smirnov tests. Our standard model is able to reproduce some clusters younger than h Per and marginally M37, which is 550 Myr old. Varying the disk fraction or the initial period distribution did not improve the results. However, when we run a model with a finer mass grid the Pleiades can be also reproduced. Changing the initial mass distribution to be similar to the empirical ONC mass function also gives good results. Modeling the evolution of a young synthetic cluster from pre-main sequence to early main sequence considering physical mechanisms of extraction and exchange of angular momentum can not be achieved successfully for all clusters for which we have enough rotational data. Clusters of about the same age present different rotational behaviors due perhaps to differences in their initial conditions.

The Nickel Mass Distribution of Stripped-envelope Supernovae: Implications for Additional Power Sources

Abstract We perform a systematic study of the 56Ni mass (M Ni) of 27 stripped-envelope supernovae (SESNe) by modeling their light-curve tails, highlighting that use of “Arnett’s rule” overestimates M Ni for SESNe by a factor of ∼2. Recently, Khatami & Kasen presented a new model relating the peak time (t p) and luminosity (L p) of a radioactively powered supernova to its M Ni that addresses several limitations of Arnett-like models, but depends on a dimensionless parameter, β. Using observed t p, L p, and tail-measured M Ni values for 27 SESNe, we observationally calibrate β for the first time. Despite scatter, we demonstrate that the model of Khatami & Kasen with empirically calibrated β values provides significantly improved measurements of M Ni when only photospheric data are available. However, these observationally constrained β values are systematically lower than those inferred from numerical simulations, primarily because the observed sample has significantly higher (0.2–0.4 dex) L p for a given M Ni. While effects due to composition, mixing, and asymmetry can increase L p none can explain the systematically low β values. However, the discrepancy can be alleviated if ∼7%–50% of L p for the observed sample comes from sources other than radioactive decay. Either shock cooling or magnetar spin-down could provide the requisite luminosity. Finally, we find that even with our improved measurements, the M Ni values of SESNe are still a factor of ∼3 larger than those of hydrogen-rich Type II SNe, indicating that these supernovae are inherently different in terms of the initial mass distributions of their progenitors or their explosion mechanisms.

Dependencies of Mantle Shock Heating in Pairwise Accretion

Abstract The final assembly of planets involves mutual collisions of large similar-sized protoplanets (“giant impacts”), setting the stage for modern geologic and atmospheric processes. However, thermodynamic consequences of impacts in diverse (exo)planetary systems/models are poorly understood. Impact velocity in “self-stirred” systems is proportional to the mass of the colliding bodies (v imp ∝ M 1/3), providing a predictable transition to supersonic collisions in roughly Mars-sized bodies. In contrast, nearby larger planets, or migrating gas giants, stir impact velocities, producing supersonic collisions between smaller protoplanets and shifting outcomes to disruption and nonaccretion. Our particle hydrocode simulations suggest that thermodynamic processing can be enhanced in merging collisions more common to calmer dynamical systems due to post-impact processes that scale with the mass of the accreting remnant. Thus, impact heating can involve some contribution from energy scaling, a departure from pure velocity-scaling in cratering scenarios. Consequently, planetary thermal history depends intimately on the initial mass distribution assumptions and dynamical conditions of formation scenarios. In even the gentlest pairwise accretions, sufficiently large bodies feature debris fields dominated by melt and vapor. This likely plays a critical role in the observed diversity of exoplanet systems and certain debris disks. Furthermore, we suggest solar system formation models that involve self-stirred dynamics or only one to a few giant impacts between larger-than-Mars-sized bodies (e.g., “pebble accretion”) are more congruent with the “missing mantle problem” for the main belt, as we demonstrate debris would be predominantly vapor and thus less efficiently retained due to solar radiation pressure effects.

The initial properties of young star clusters in M83

ABSTRACT The initial sizes and masses of massive star clusters provide information about the cluster formation process and also determine how cluster populations are modified and destroyed, which have implications for using clusters as tracers of galaxy assembly. Young massive cluster populations are often assumed to be unchanged since cluster formation; therefore, their distributions of masses and radii are used as the initial values. However, the first few hundred million years of cluster evolution does change both cluster mass and cluster radius, through both internal and external processes. In this paper, we use a large suite of N-body cluster simulations in an appropriate tidal field to determine the best initial mass and initial size distributions of young clusters in the nearby galaxy M83. We find that the initial masses follow a power-law distribution with a slope of −2.7 ± 0.4 , and the half-mass radii follow a lognormal distribution with a mean of 2.57 ± 0.04 pc and a dispersion of 1.59 ± 0.01 pc. The corresponding initial projected half-light radius function has a mean of 2.7 ± 0.3 pc and a dispersion of 1.7 ± 0.2 pc. The evolution of the initial mass and size distribution functions is consistent with mass-loss and expansion due to stellar evolution, independent of the external tidal field and the cluster’s initial density profile. Observed cluster sizes and masses should not be used as the initial values, even when clusters are only a few hundred million years old.

Configuration of the Martian dust rings: shapes, densities, and size distributions from direct integrations of particle trajectories

ABSTRACTIt is expected since the early 1970s that tenuous dust rings are formed by grains ejected from the Martian moons Phobos and Deimos by impacts of hypervelocity interplanetary projectiles. In this paper, we perform direct numerical integrations of a large number of dust particles originating from Phobos and Deimos. In the numerical simulations, the most relevant forces acting on the dust are included: Martian gravity with spherical harmonics up to fifth degree and fifth order, gravitational perturbations from the Sun, Phobos, and Deimos, solar radiation pressure, as well as the Poynting–Robertson drag. In order to obtain the ring configuration, simulation results of various grain sizes ranging from submicrometres to 100 μm are averaged over a specified initial mass distribution of ejecta. We find that for the Phobos ring grains smaller than about 2 μm are dominant; while the Deimos ring is dominated by dust in the size range of about 5–20 μm. The asymmetries, number densities, and geometric optical depths of the rings are quantified from simulations. The results are compared with the upper limits of the optical depth inferred from Hubble observations. We compare to previous work and discuss the uncertainties of the models.

Planet formation and disc mass dependence in a pebble-driven scenario for low-mass stars

ABSTRACT Measured disc masses seem to be too low to form the observed population of planetary systems. In this context, we develop a population synthesis code in the pebble accretion scenario, to analyse the disc mass dependence on planet formation around low-mass stars. We base our model on the analytical sequential model presented by Ormel, Liu, and Schoonenberg and analyse the populations resulting from varying initial disc mass distributions. Starting out with seeds the mass of Ceres formed by streaming instability inside the ice-line, we grow the planets using the pebble accretion process and migrate them inwards using type I migration. The next planets are formed sequentially after the previous planet crosses the ice line. We explore different initial distributions of disc masses to show the dependence of this parameter with the final planetary population. Our results show that compact close-in resonant systems can be pretty common around M dwarfs between 0.09 and 0.2 M⊙ only when the discs considered are more massive than what is being observed by sub-mm disc surveys. The minimum disc mass to form a Mars-like planet is found to be about 2 × 10−3 M⊙. Small variations in the disc mass distribution also manifest in the simulated planet distribution. The paradox of disc masses might be caused by an underestimation of the disc masses in observations, by a rapid depletion of mass in discs by planets growing within 1 million years, or by deficiencies in our current planet formation picture.