arXiv subjects

Szabolcs Mészáros

Publications and source records attributed to Szabolcs Mészáros.

At least 19 recordsLinked to original sources

arXiv2026

SDSS-IV MaStar: Determination of Stellar Parameters Using Bayesian Averaging

We present the stellar parameters for 59,266 high-quality spectra of 24,130 unique stars from the MaNGA Stellar Library (MaStar) in the Sloan Digital Sky Survey (SDSS) Data Release 17 (DR17). The median signal-to noise ratio per pixel of the spectra is 96. We derive four stellar parameters, effective temperature (Teff), surface gravity (log g), metallicity ([M/H]), and {$α$}-enhancement ratio ($\rm [α/M]$), by comparing the data with BOSZ (ATLAS-9 based) and MARCS theoretical atmospheric models. We adopt a Bayesian method and use color and absolute magnitude derived from Gaia to select a subset of theoretical models for each star. We then perform full-spectrum fitting to estimate the likelihood of each model in the subset and then compute their likelihood-weighted mean parameters as the final parameters. We set stellar-parameter quality flags to facilitate the use of the derived stellar parameters. The MaStar stellar parameters derived herein span an effective temperature range of $\rm 2,600 \leq T_{eff} \leq 29,861 K$, a surface gravity range of $0 \leq \log g \leq 5.5$, a metallicity range of $-4.9 \leq \rm[M/H] \leq 1.0$, and an {$α$}-abundance range of $\rm -0.98 \leq [α/M] \leq 1.0$. We compare these parameters with those from APOGEE and Gaia for stars in common, finding general consistency within the uncertainties. However, some artifacts and systematic differences are present, and we discuss their potential causes. These new stellar parameters are available through the MaStar SDSS-IV DR17 value-added catalog (https://www.sdss4.org/dr17/mastar/mastar-stellar-parameters/).

astro-ph.SR↗

arXiv2026

Payne4GAIN: NLTE Corrections for Red Giants in Milky Way Mapper using H-Band Neural Network Emulators

The majority of spectroscopic surveys assume local thermodynamic equilibrium (LTE) during the modeling of stellar spectra. This assumption begins to break down for luminous stars, like the red giants targeted by SDSS-V's Milky Way Mapper Survey in its Galactic Genesis program. In this work, we present non-LTE (NLTE) abundances for 360,000 red giant stars in Milky Way Mapper DR19, from infrared APOGEE spectra. We generate NLTE spectra using precomputed departure coefficient grids for Na, Mg, Si, Al, Ca, Ti, Mn, and Ni. To fit APOGEE spectra at scale, we train neural network emulators (NNEs) to synthesize LTE and NLTE H-band spectra. After verifying that the NNEs are accurate, we fit the APOGEE spectra with ASPCAP results that fall within the same parameter range as the training data. We find strong NLTE effects on the order of 0.1\,dex for Al, Mn, and Ti, and smaller effects for Si and Ni. We provide a catalog of the results of our LTE and NLTE fits, as well as NLTE-corrected ASPCAP abundances using a polynomial fit correction.

astro-ph.SR↗

arXiv2026

Radial velocity and atmospheric parameter calculations for the GaiaNIR spectrograph

Context. The upcoming GaiaNIR mission is currently planning to add a near-infrared spectrograph to its payload in order to enhance its scientific return, particularly for mapping the dust-obscured regions of the Milky Way. Aims. This study aims to identify the optimal wavelength region between 800 and 2300 nm for the proposed GaiaNIR spectrograph to maximize the precision of radial velocities and atmospheric parameters. Methods. To find its spectral range, we generated 10000 synthetic spectra from the BOSZ library across a wide range of stellar parameters, with resolutions varying from 5000 to 20000. By cross-correlating these mock observations with ideal templates, we assessed the statistical scatter of velocity residuals to isolate six candidate windows for further atmospheric parameter testing. Results. Our analysis finds that the 1926 - 1968 nm window at R = 16100 - 20100 in the K-band is the preferred strategic choice, because it has the potential to reach radial velocity precision for the brightest FGKM stars of about 160 - 260 m/s depending on resolution, while providing precision of the atmospheric parameters close to Gaia's Radial Velocity Spectrometer. We also identified a second region between 1158 and 1202 nm (R = 9300 - 11600), that has slightly lower radial velocity precision, but at a wider temperature range than the K-band. Both regions make it possible to derive abundances of ten species at these resolutions: O, Na, Mg, Si, Ca, Ti, V, Cr, Mn, Ni in the K-band, and Mg, Si, K, Ca, Ti, V, Cr, Mn, Co, Ni between 1158 - 1202 nm. Conclusions. The K-band delivers sufficiently precise measurements for the mission's primary cool star targets while taking advantage of significantly lower interstellar extinction, enabling the mapping of the dust-obscured regions of the Milky Way.

astro-ph.IM↗

arXiv2026

Variations in the Milky Way's Stellar Mass Function at [Fe/H] < -1

We present the first determination of the Galactic stellar mass function (MF) for low-mass stars (0.2-0.5 M_sun) at metallicities [Fe/H] < -1. A sample of ~53,000 stars was selected as metal-poor on the basis of both their halo-like orbits and their spectroscopic [Fe/H] from Gaia DR3 BP/RP (XP) spectra. These metallicity estimates for low-mass stars were enabled by calibrating Gaia XP spectra with stellar parameters from SDSS-V. For -1.5 < [Fe/H] < -1, we find that the MF below 0.5 M_sun exhibits a "bottom-heavy" power-law slope of alpha ~ -1.6. We tentatively find that at even lower metallicities, the MF becomes very bottom-light, with a near-flat power-law slope of alpha ~ 0 that implies a severe deficit of low-mass stars. This metallicity-dependent variation is insensitive to the adopted stellar evolution model. These results show that the Galactic low-mass MF is not universal, with variations in the metal-poor regime. A further calibration of XP metallicities in the regime of M < 0.5 M_sun and [Fe/H] < -1.5 will be essential to verify these tentative low-metallicity trends.

astro-ph.GA↗

arXiv2025

The Gothard Observatory Synthetic Stellar Photometry Database

Context. In order to determine stellar luminosities and radii, it is necessary to know the total bolometric fluxes emitted by the stars, or equivalently the bolometric corrections (BCs) as accurately as possible. Aims. The aim of this paper is to present and describe a new database of synthetic stellar magnitudes and bolometric corrections for 752 filters from 78 ground- and space-based instruments calculated using the most recent version of the BOSZ synthetic stellar spectral library. Methods. From the entire grid of the BOSZ theoretical spectra, our synthetic magnitudes in the Vega magnitude system were determined using the corresponding routines of the Python package species. Results. The database spans effective temperatures from 2800 to 16000~K, log g from $-0.5$ to 5.5, metallicities from $-2.5$ to 0.75, [$α$/M] from $-0.25$ to 0.5, [C/M] from $-0.75$ to 0.5, and reddening up to $A_V$ = 3.1 mag. Using high-resolution (R = 50000) synthetic spectra allowed us to precisely track the effect of abundances on the bolometric corrections and luminosity of stars. Conclusions. By applying the new bolometric corrections (BCs) to 192\,000 APOGEE stars we calculated luminosities, and also demonstrated that neglecting carbon can introduce up to $\pm$0.2\% errors in luminosity. The new Gothard Observatory Synthetic Stellar Photometry Database may enable more accurate fundamental parameter determinations for large stellar samples using a vast amount of past, present, and upcoming surveys, such as Gaia, LSST, and the Roman Space Telescope.

astro-ph.SR↗

arXiv2025

Stellar Parameters of BOSS M dwarfs in SDSS-V DR19

We utilized the Stellar LAbel Machine (SLAM), a data-driven model based on Support Vector Regression, to derive stellar parameters ([Fe/H], $T_{\rm eff}$, and $\log{g}$) for SDSS-V M dwarfs using low-resolution optical spectra (R$\sim$2000) obtained with the BOSS spectrographs. These parameters are calibrated using LAMOST F, G or K dwarf companions ([Fe/H]), and APOGEE Net ($T_{\rm eff}$ and $\log{g}$), respectively. Comparisons of SLAM predicted [Fe/H] values between two components of M+M dwarfs wide binaries show no bias but with a scatter of 0.11 dex. Further comparisons with two other works, which also calibrated the [Fe/H] of M dwarfs by using the F/G/K companions, reveal biases of -0.06$\pm$0.16 dex and 0.02$\pm$0.14 dex, respectively. The SLAM-derived effective temperatures agree well with the temperature which is calibrated by using interferometric angular diameters (bias: -27$\pm$92 K) and those of the LAMOST (bias: -34$\pm$65 K), but are systematically lower than those from an empirical relationship between the color index and $T_{\rm eff}$ by 146$\pm$45 K. The SLAM surface gravity aligns well with those of LAMOST (bias: -0.01$\pm$0.07 dex) and those derived from the stellar mass and radius (bias: -0.04$\pm$0.09 dex). Finally, we investigated a bias in [Fe/H] between SLAM and APOGEE ASPCAP. It depends on ASPCAP's [Fe/H] and $T_{\rm eff}$, we provide an equation to correct the ASPCAP metallicities.

astro-ph.SR↗

arXiv2025

A Galactic Self-Portrait: Density Structure and Integrated Properties of the Milky Way Disk

The evolution history of the Milky Way disk is imprinted in the ages, positions, and chemical compositions of individual stars. In this study, we derive the intrinsic density distribution of different stellar populations using the final data release of the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. A total of 203,197 red giant branch stars are used to sort the stellar disk ($R \leq 20$ kpc) into sub-populations of metallicity ($Δ$[M/H]$= 0.1$ dex), age ($Δ\log(\frac{\textrm{age}}{\textrm{yr}})= 0.1$), and $α$-element abundances ([$α$/M]). We fit the present-day structural parameters and density distribution of each stellar sub-population after correcting for the survey selection function. The low-$α$ disk is characterized by longer scale lengths and shorter scale heights, and is best fit by a broken exponential radial profile for each population. The high-$α$ disk is characterized by shorter scale lengths and larger scale heights, and is generally well-approximated by a single exponential radial profile. These results are applied to produce new estimates of the integrated properties of the Milky Way from early times to the present day. We measure the total stellar mass of the disk to be $5.27^{+0.2}_{-1.5} \times 10^{10}$ M$_\odot$ and the average mass-weighted scale length is $R_{d} = 2.37 \pm 0.2$ kpc. The Milky Way's present-day color of $(g-r) = 0.72 \pm 0.02$ is consistent with the classification of a red spiral galaxy, although it has only been in the "green valley" region of the galaxy color-mass diagram for the last $\sim 3$ Gyr.

astro-ph.GA↗

arXiv2025

The Open Cluster Chemical Abundances and Mapping Survey: VIII. Galactic Chemical Gradient and Azimuthal Analysis from SDSS/MWM DR19

The Open Cluster Chemical Abundances and Mapping (OCCAM) survey seeks to curate a large, comprehensive, uniform dataset of open clusters and member stars to constrain key Galactic parameters. This eighth entry from the OCCAM survey, based on the newly released SDSS-V/MWM Data Release 19 (DR19), has established a sample of 164 high quality open clusters that are used to constrain the radial and azimuthal gradients of the Milky Way. The DR19 cluster sample [Fe/H] abundances are roughly consistent with measurements from other large-scale spectroscopic surveys. However, the gradients we calculate deviate considerably for some elements. We find an overall linear Galactic radial [Fe/H] gradient of $-0.075 \pm 0.006$ dex kpc$^{-1}$ using the cluster's current Galactocentric Radius ($R_{GC}$) and a gradient of $-0.068 \pm 0.005$ dex kpc$^-1$ with respect to the cluster's guiding center radius. We do not find strong evidence for significant evolution of the differential element gradients ([X/Fe]) investigated here (O, Mg, Si, S, Ca, Ti, Cr, Mn, Fe, Co, Ni, Na, Al, K, Ce, Nd). For the first time using the OCCAM sample we have sufficient numbers of clusters to investigate Galactic azimuthal variations. In this work, we do find evidence of azimuthal variations in the measured radial abundance gradient in the Galactic disk using our open cluster sample.

astro-ph.GA↗

arXiv2025

SDSS-V Milky Way Mapper (MWM): ASPCAP Stellar Parameters and Abundances in SDSS-V Data Release 19

The goal of this paper is to describe the science verification of Milky Way Mapper (MWM) APOGEE Stellar Parameter and Chemical Abundances Pipeline (ASPCAP) data products published in Data Release 19 (DR19) of the fifth phase of the Sloan Digital Sky Survey (SDSS-V). We compare MWM ASPCAP atmospheric parameters T$_{\rm eff}$, log g, 24 abundances of 21 elements (carbon, nitrogen, and oxygen have multiple sources for deriving their abundance values) and their uncertainties determined from Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectrograph spectra with those of the literature and evaluate their accuracy and precision. We also test the zero-point calibration of the v$_{\rm rad}$ derived by the APOGEE Data Reduction Pipeline. This data release contains ASPCAP parameters for 964,989 stars, including all APOGEE-2 targets expanded with new observations of 336,511 stars from the Apache Point Observatory observed until 4 July 2023. Overall, the new T$_{\rm eff}$ values show excellent agreement with the IRFM scale, while the surface gravities exhibit slight systematic offsets compared to asteroseisimic gravities. The estimated precision of T$_{\rm eff}$ is between 50 and 70 K for giants and 70$-$100 K for dwarfs, while surface gravities are measured with a precision of 0.07$-$0.09 dex for giants. We achieve an estimated precision of 0.02$-$0.04 dex for multiple elements, including metallicity, $α$, Mg, and Si, while the precision of at least 10 elements is better than 0.1 dex.

astro-ph.SR↗

arXiv2025

Reconstructing the Milky Way chemical map with Galactic Chemical Evolution tool OMEGA+ from SDSS-MWM

We obtain two-infall galactic chemical evolution (GCE) models simulating the chemical evolution of the Milky Way as constrained by a golden sample of $394,000$ stellar abundances of the Milky Way Mapper survey from the 19th data release of SDSS-V. The separation between the chemical thin and thick disks is defined using [Mg/M]. We use the chemical evolution environment $\texttt{OMEGA+}$, combined with Levenberg-Marquardt and bootstrapping. We simulate the entire Galactic disk and six galactocentric regions for a more detailed analysis of the formation of the inner, middle, and outer Galaxy. We investigate the evolution of $α$, odd-Z, and iron-peak elements: 15 species altogether. The chemical thin and thick disks are separated by Mg observations, which the other $α$-elements show similar trends with, while odd-Z species demonstrate different patterns as functions of metallicity. In the inward Galactic disk regions the locus of the low-Mg sequence is gradually shifted toward higher metallicity, while the high-Mg phase is less populated. The best-fit GCE models show a well-defined peak in the rate of the infalling matter as a function of the Galactic age, confirming a merger event about $10$ Gyr ago. We show that the timescale of gas accretion, the time of the second infall as well as the ratio between the surface mass densities associated to the second infall and the formation event vary with the distance from the Galactic center. The disk is assembled within a timescale of $(0.32\pm0.02)~$Gyr during a primary formation phase, then a $(0.55\pm0.06)~$Gyr-timescale, increasing accretion rate was followed by a relaxation that lasted $(2.86\pm0.70)~$Gyr, with a second peak of the infall rate at $(4.13\pm0.19)~$Gyr. Our best Galaxy evolution models are consistent with an inside-out formation scenario of the Milky Way disk, in agreement with recent chemo-dynamical simulations.

astro-ph.GA↗

arXiv2024

The updated BOSZ synthetic stellar spectral library

Context. The modeling of stellar spectra of flux standards observed by the Hubble and James Webb space telescopes requires a large synthetic spectral library that covers a wide atmospheric parameter range. Aims. The aim of this paper is to present and describe the calculation methods behind the updated version of the BOSZ synthetic spectral database, which was originally designed to fit the CALSPEC flux standards. These new local thermodynamic equilibrium (LTE) models incorporate both MARCS and ATLAS9 model atmospheres, updated continuous opacities, and 23 new molecular line lists. Methods. The new grid was calculated with Synspec using the LTE approximation and covers metallicities [M/H] from -2.5 to 0.75 dex, [alpha/M] from -0.25 to 0.5 dex, and [C/M] from -0.75 to 0.5 dex, providing spectra for 336 unique compositions. Calculations for stars between 2800 and 8000 K use MARCS model atmospheres, and ATLAS9 is used between 7500 and 16,000 K. Results. The new BOSZ grid includes 628,620 synthetic spectra from 50 nm to 32 microns with models for 495 Teff - log g parameter pairs per composition and per microturbulent velocity. Each spectrum has eight different resolutions spanning a range from R = 500 to 50,000 as well as the original resolution of the synthesis. The microturbulent velocities are 0, 1, 2, and 4 km/s. Conclusions. The new BOSZ grid extends the temperature range to cooler temperatures compared to the original grid because the updated molecular line lists make modeling possible for cooler stars. A publicly available and consistently calculated database of model spectra is important for many astrophysical analyses, for example spectroscopic surveys and the determination of stellar elemental compositions.

astro-ph.SR↗

arXiv2023

Revealing the Chemical Structure of the Magellanic Clouds with APOGEE. III. Abundance Gradients of the Small Magellanic Cloud

We determine radial- and age-abundance gradients of the Small Magellanic Cloud (SMC) using spectra of 2,062 red giant branch (RGB) field stars observed by SDSS-IV / APOGEE-2S. With coverage out to $\sim$9 kpc in the SMC, these data taken with the high resolution ($R \sim 22,500$) APOGEE $H$-band spectrograph afford the opportunity to measure extensive radial gradients for as many as 24 abundance ratios. The SMC is found to have an overall metallicity gradient of $-$0.0546 $\pm$ 0.0043 dex/kpc. Ages are calculated for every star to explore the evolution of the different abundance gradients. As a function of age, many of the gradients show a feature 3.66--5.58 Gyr ago, which is especially prominent in the [X/H] gradients. Initially many gradients flatten until about $\sim$5.58 Gyr ago, but then steepen in more recent times. We previously detected similar evolutionary patterns in the Large Magellanic Cloud (LMC) which are attributed to a recent interaction between the LMC and SMC. It is inferred that the feature in the SMC gradients was caused by the same interaction. The age-[X/Fe] trends, which track average [X/Fe] over time, are flat, demonstrating a slow enrichment history for the SMC. When comparing the SMC gradients to the LMC and MW, normalized to disk scale length ($R_\text{d}$), the [X/Fe] and [X/Mg] gradients are similar, but there is a dichotomy between the dwarfs and the Milky Way (MW) for the [X/H] gradients. The median MW [X/H] gradient around $-$0.125 dex/$R_\text{d}$ whilst the Clouds have gradients of about $-$0.075 dex/$R_\text{d}$.

astro-ph.GA↗

arXiv2023

The APOGEE Value Added Catalogue of Galactic globular cluster stars

We introduce the SDSS/APOGEE Value Added Catalogue of Galactic Globular Cluster (GC) Stars. The catalogue is the result of a critical search of the APOGEE data release 17 (DR17) catalogue for candidate members of all known Galactic GCs. Candidate members are assigned to various GCs on the basis of position on the sky, proper motion, and radial velocity. The catalogue contains a total of 7,737 entries for 6,422 unique stars associated with 72 Galactic GCs. Full APOGEE DR17 information is provided, including radial velocities and abundances for up to 20 elements. Membership probabilities estimated on the basis of precision radial velocities are made available. Comparisons with chemical compositions derived by the GALAH survey, as well as optical values from the literature, show good agreement. This catalogue represents a significant increase in the public database of GC star chemical compositions and kinematics, providing a massive homogeneous data set that will enable a variety of studies. The catalogue in fits format is available for public download from the SDSS-IV DR17 value added catalogue website.

astro-ph.GA↗

arXiv2023

To Grow Old and Peculiar: A Survey of Anomalous Variable Stars in M80 and Age Determination using K2 and Gaia

The globular cluster Messier 80 was monitored by the Kepler space telescope for 80 days during the K2 mission. Continuous, high-precision photometry of such an old, compact cluster allows us to study its variable star population in unprecedented detail. We extract light curves for 27 variable stars using differential-image photometry. A search for new variables in the images led to the discovery of two new variable stars: an RR Lyrae and a variable red giant star, respectively. Analysis of the RR Lyrae population reveals multiple RRc stars with additional modes and/or peculiar modulation cycles. We newly classify star V28 as a spotted extreme horizontal branch variable. Despite their faintness, we clearly detect the three SX Phe stars but we did not find new pulsation modes beyond the known ones in them. Spectra taken with the VLT and Magellan Clay telescopes, as well as absolute color-magnitude diagrams of the cluster based on Gaia and Pan-STARRS observations confirm the classification of the peculiar modulated variables as bona-fide RRc stars. We propose that they highlight a subgroup of overtone stars that may have been overlooked before. We fit MESA isochrones to the CMDs to estimate the age and metallicity of the cluster. We confirm that M80 is old and metal-poor, but show that isochrone fitting to old populations comes with numerous uncertainties.

astro-ph.SR↗

arXiv2023

A Tale of Two Disks: Mapping the Milky Way with the Final Data Release of APOGEE

We present new maps of the Milky Way disk showing the distribution of metallicity ([Fe/H]), $α$-element abundances ([Mg/Fe]), and stellar age, using a sample of 66,496 red giant stars from the final data release (DR17) of the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. We measure radial and vertical gradients, quantify the distribution functions for age and metallicity, and explore chemical clock relations across the Milky Way for the low-$α$ disk, high-$α$ disk, and total population independently. The low-$α$ disk exhibits a negative radial metallicity gradient of $-0.06 \pm 0.001$ dex kpc$^{-1}$, which flattens with distance from the midplane. The high-$α$ disk shows a flat radial gradient in metallicity and age across nearly all locations of the disk. The age and metallicity distribution functions shift from negatively skewed in the inner Galaxy to positively skewed at large radius. Significant bimodality in the [Mg/Fe]-[Fe/H] plane and in the [Mg/Fe]-age relation persist across the entire disk. The age estimates have typical uncertainties of $\sim0.15$ in $\log$(age) and may be subject to additional systematic errors, which impose limitations on conclusions drawn from this sample. Nevertheless, these results act as critical constraints on galactic evolution models, constraining which physical processes played a dominant role in the formation of the Milky Way disk. We discuss how radial migration predicts many of the observed trends near the solar neighborhood and in the outer disk, but an additional more dramatic evolution history, such as the multi-infall model or a merger event, is needed to explain the chemical and age bimodality elsewhere in the Galaxy.

astro-ph.GA↗

arXiv2023

The Eighteenth Data Release of the Sloan Digital Sky Surveys: Targeting and First Spectra from SDSS-V

The eighteenth data release of the Sloan Digital Sky Surveys (SDSS) is the first one for SDSS-V, the fifth generation of the survey. SDSS-V comprises three primary scientific programs, or "Mappers": Milky Way Mapper (MWM), Black Hole Mapper (BHM), and Local Volume Mapper (LVM). This data release contains extensive targeting information for the two multi-object spectroscopy programs (MWM and BHM), including input catalogs and selection functions for their numerous scientific objectives. We describe the production of the targeting databases and their calibration- and scientifically-focused components. DR18 also includes ~25,000 new SDSS spectra and supplemental information for X-ray sources identified by eROSITA in its eFEDS field. We present updates to some of the SDSS software pipelines and preview changes anticipated for DR19. We also describe three value-added catalogs (VACs) based on SDSS-IV data that have been published since DR17, and one VAC based on the SDSS-V data in the eFEDS field.

astro-ph.GA↗

arXiv2023

Sub-Jovian desert of exoplanets at its boundaries. Parameter dependence along the main sequence

Context. The lack of sub-Jovian planets on orbits of $P_{\rm orb} < 3$ days is a puzzling aspect of galaxy formation with regard to the distribution of exoplanets whose origins are currently unresolved. Aims. The possible explanations behind the formation of the sub-Jovian or Neptunian desert include several scenarios that can lead to different shapes for the boundary, predicting various dependencies between the position of the boundary and the stellar parameters. Methods. We explored the exoplanet distribution in various 2D and 3D projections, revealing the stellar-dependent substructures in the $P_{\rm orb}-M_{P}$ and the $P_{\rm orb}-R_{P}$ parameter plane. Results. We demonstrate that the upper boundary includes a range of planets, namely, inflated hot Jupiters and normal hot Jupiters, in the two parameter planes, respectively. We confirm the dependence of the boundary on several stellar parameters and, based on a fuzzy clustering analysis, we provide quantitative formulae for the dependencies in groups of smaller and larger planets. The overall period-radius distribution shows chemical substructures as well, with the boundary being dependent on volatiles and alpha-elements, alongside marginal (to none) dependence found for refractory elements. Conclusions. These findings confirm multiple plausible causes for the formation of the desert, particularly preferring those scenarios related to the irradiation-driven loss of the atmospheres of moderately massive planets as the predominant process in shaping planetary distributions.

astro-ph.EP↗

arXiv2022

Generalized solution for the Herman Protocol Conjecture

The Herman Protocol Conjecture states that the expected time $\mathbb{E}(\mathbf{T})$ of Herman's self-stabilizing algorithm in a system consisting of $N$ identical processes organized in a ring holding several tokens is at most $\frac{4}{27}N^{2}$. We prove the conjecture in its standard unbiased and also in a biased form for discrete processes, and extend the result to further variants where the tokens move via certain Lévy processes. Moreover, we derive a bound on the expected value of $\mathbb{E}(α^{\mathbf{T}})$ for all $1\leq α\leq (1-\varepsilon)^{-1}$ with a specific $\varepsilon>0$. Subject to the correctness of an optimization result that can be demonstrated empirically, all these estimations attain their maximum on the initial state with three tokens distributed equidistantly on the ring of $N$ processes. Such a relation is the symptom of the fact that both $\mathbb{E}(\mathbf{T})$ and $\mathbb{E}(α^{\mathbf{T}})$ are weighted sums of the probabilities $\mathbb{P}(\mathbf{T}\geq t)$.

cs.DS↗