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The empirical upper limit to Red Supergiant (RSG) luminosity, known as the Humphreys-Davidson (HD) limit, has been commonly explained as being caused by the stripping of stellar envelopes by metallicity-dependent, line-driven winds. As such, the theoretical expectation is that the HD limit should be higher at lower metallicity, where weaker mass-loss rates mean that higher initial masses are required for an envelope to be stripped. In this work, we test this prediction by measuring the luminosity function of RSGs in M31 and comparing to those in the LMC and SMC. We find that $\[\log ({L_{{\rm{m}}ax}}/{L_ \odot }) = 5.53 \pm 0.03\]$ in M31 (Z ≳ Z⊙), consistent with the limit found for both the LMC (Z ∼ 0.5 Z⊙) and SMC (Z ∼ 0.25 Z⊙), while the RSG luminosity distributions in these 3 galaxies are consistent to within 1σ. We therefore find no evidence for a metallicity dependence on both the HD limit and the RSG luminosity function, and conclude that line-driven winds on the main sequence are not the cause of the HD limit. [ABSTRACT FROM AUTHOR]

Since massive stars form preferentially as members of close binary systems, we use dense grids of detailed binary evolution models to explore how binary evolution shapes the main-sequence morphology of young star clusters. We propose that binary mergers might be the origin of the blue main sequence stars in young star clusters. Our results imply that stars may either form by accretion, or through a binary merger, and that both paths lead to distinctly different spins, magnetic fields, and stellar mass distributions. [ABSTRACT FROM AUTHOR]

Differential equations are a fundamental and versatile mathematical tool that finds widespread application across diverse academic disciplines, from physics and biology to economics and engineering. The primary objectives of this report are to demonstrate the application of differential equations in stellar evolution, construct a mathematical model to demonstrate nuclear reactions in a star, and illustrate energy transport within a star. Triangulation was used to prepare this report, with literature studies being the primary method. This study includes several documents and field data analyzed using qualitative research. Through research and observations, two hypothetical case studies illustrate the indispensable application of differential equations in modeling energy transport and nuclear reactions within stars through which the value of luminosity was calculated in a particular star due to both radiative energy transport and convective energy transport while in another star, the helium abundance in the core was estimated to approach a value of 1.195*1077. These differential equations are not only limited to the growth of a lead but also have broader applications that are essential for understanding the chemical composition of the universe and its prolonged evolution. The report also underscores the enduring importance of differential equations in advancing our understanding of the cosmos and their vital role in space exploration and technological innovations.

We present Color Magnitude Diagrams (CMDs) created by using our database of 43,340 synthetic CMFGEN spectra. For each calculated spectra we measure the absolute flux by Johnson and Gaia photometry filters and build synthetic CMDs. [ABSTRACT FROM AUTHOR]

We have applied the method of star counts with Wolf diagrams to determine the interstellar extinction in five Galactic cirri in Sloan Digital Sky Survey (SDSS) Stripe 82. For this purpose, we have used the photometry of stars in the GALEX NUV filter and the photometry of red dwarfs in five SDSS bands and four SkyMapper Southern Sky Survey DR2 bands. We have identified the cirri as sky regions with an enhanced infrared emission from the Schlegel+1998 map. The extinction in them has been calculated relative to the nearby comparison regions with a reduced emission. The results for different filters agree well, giving the range of distances and the extinction law for each cirrus. The distances in the range 140–415 pc found are consistent with the 3D reddening maps. In the range between the and filters the extinctions found are consistent with the estimates from Schlegel+1998 for the Cardelli+1989 extinction law with . However, the extinctions found for all of the filters are best described not by the Cardelli+1989 extinction law with some , but by the inverse proportionality of the extinction and wavelength with its own coefficient for each cirrus. In one of the cirri our results suggest a very slight decrease in extinction with wavelength, i.e., a large contribution of gray extinction. In the remaining cirri a manifestation of gray extinction is not ruled out either. This is consistent with the previous measurements of the extinction law far from the Galactic midplane. [ABSTRACT FROM AUTHOR]

Astronomical imaging of a star cluster is one of the paramount ways to learn about stellar evolution, stellar dynamics. A large telescope is not generally accessible to all observers. In that context, small telescope observations with a proper denoising scheme can be an excellent alternative. This paper proposes a technique to denoise star cluster data using an undecimated wavelet transform, with a modified thresholding process. Our work aims to prove the effectiveness of such a wavelet-based technique on real-time data. We present drastically noise-infested observational data of the NGC 2301 star cluster, captured over five nights from Fr. Eugene Lafont Observatory, Kolkata. We observe that for highly noise-polluted data, the conventional methods of dark frame subtraction and flat frame division are inadequate to produce the desired quality of images due to functioning exclusively in the spatial domain. Thus, we take the wavelet-based multiresolution approach to ameliorate those raw images. We also introduce a modified thresholding function to modulate the image at different resolution levels. A standard star detecting software Daophot II quantifies the increment in the number of detected stars from raw images to the images processed by our proposed method as: for red filter 397–903, for green filter 663–945, for blue filter 362–896. On the contrary, Daophot II can’t detect any star in the highly noise-polluted images processed by the conventional methods. Therefore, we hope our proposed processing methodology will motivate others to initiate small telescope observations from any site restrained by its geographical location. [ABSTRACT FROM AUTHOR]

The empirical upper limit to Red Supergiant (RSG) luminosity, known as the Humphreys-Davidson (HD) limit, has been commonly explained as being caused by the stripping of stellar envelopes by metallicity-dependent, line-driven winds. As such, the theoretical expectation is that the HD limit should be higher at lower metallicity, where weaker mass-loss rates mean that higher initial masses are required for an envelope to be stripped. In this work, we test this prediction by measuring the luminosity function of RSGs in M31 and comparing to those in the LMC and SMC. We find that $\[\log ({L_{{\rm{m}}ax}}/{L_ \odot }) = 5.53 \pm 0.03\]$ in M31 (Z ≳ Z⊙), consistent with the limit found for both the LMC (Z ∼ 0.5 Z⊙) and SMC (Z ∼ 0.25 Z⊙), while the RSG luminosity distributions in these 3 galaxies are consistent to within 1σ. We therefore find no evidence for a metallicity dependence on both the HD limit and the RSG luminosity function, and conclude that line-driven winds on the main sequence are not the cause of the HD limit. [ABSTRACT FROM AUTHOR]

Since massive stars form preferentially as members of close binary systems, we use dense grids of detailed binary evolution models to explore how binary evolution shapes the main-sequence morphology of young star clusters. We propose that binary mergers might be the origin of the blue main sequence stars in young star clusters. Our results imply that stars may either form by accretion, or through a binary merger, and that both paths lead to distinctly different spins, magnetic fields, and stellar mass distributions. [ABSTRACT FROM AUTHOR]

Since identifying the gap in the H-R Diagram (HRD) marking the transition between partially and fully-convective interiors, a unique type of slowly pulsating M dwarf has been proposed. These unstable M dwarfs provide new laboratories in which to understand how changing interior structures can produce potentially observable activity at the surface. In this work, we report the results of the largest high-resolution spectroscopic H α emission survey to date spanning this transition region, including 480 M dwarfs observed using the CHIRON spectrograph at CTIO/SMARTS 1.5 m. We find that M dwarfs with H α in emission are almost entirely found 0–0.5 mag above the top edge of the gap in the HRD, whereas effectively no stars in and below the gap show emission. Thus, the top edge of the gap marks a relatively sharp activity transition, and there is no anomalous H α activity for stars in the gap. We also identify a new region at 10.3 < M _G < 10.8 on the main sequence where fewer M dwarfs exhibit H α emission compared to M dwarfs above and below this magnitude range. Careful evaluation of the results in the literature indicates that (1) rotation and H α activity distributions on the main-sequence are closely related, and (2) fewer stars in this absolute magnitude range rotate in less than ∼13 days than populations surrounding this region. This result suggests that the most massive fully-convective stars lose their angular momentum faster than both partially convective stars and less massive fully-convective stars.

Our statistical analysis (based on Kolmogorov–Smirnov tests) of the mass and radius distributions of planets hosted by stars of different classes reveals their significant differences, depending on the class of host stars. These differences can be explained by (1) the long-term dynamical evolution of planetary systems, (2) the long-term physical evolution of host stars, and (3) the initial differences in the structure of systems. Kolmogorov–Smirnov tests show at a high significance level that during the transition of a star from the main sequence to the red giant branch its planetary system disintegrates, at least partially. We provide estimates of the dynamical disintegration timescale for various architectures of planetary systems. From a comparison of the estimates of the physical and dynamical evolution timescales we have concluded that the disintegration of the inner regions of planetary systems is mainly physical (absorption by the stellar atmosphere) rather than dynamical (breakup within the N-body problem) in nature. As regards the outer parts of planetary systems, their disintegration can be both purely dynamical (intrinsic disintegration, close encounters with neighboring stars) and mixed physical–dynamical (i.e., the physical destruction of the system's inner component can trigger a dynamical breakup of the outer part) in nature. [ABSTRACT FROM AUTHOR]

We present Color Magnitude Diagrams (CMDs) created by using our database of 43,340 synthetic CMFGEN spectra. For each calculated spectra we measure the absolute flux by Johnson and Gaia photometry filters and build synthetic CMDs. [ABSTRACT FROM AUTHOR]

By comparing two age indicators of high-mass white dwarfs (WDs) derived from Gaia data, two discoveries have been made recently: one is the existence of a cooling anomaly that produces the Q branch structure on the Hertzsprung–Russell diagram, and the other is the existence of high-mass WDs as double-WD merger products. The former poses a challenge for WD cooling models, and the latter has implications on binary evolution and type-Ia supernovae. [ABSTRACT FROM AUTHOR]

Evolution of post-AGB stars is extremely fast. They cross the HR diagram vertically on a timescale of hundreds to some ten thousands of years to reach maximum temperature in their lifetime. This is reflected in an increasing excitation of planetary nebulae on a timescale of years and decades. Since evolutionary timescale of post-AGB stars is very sensitive to their mass, observed changes can be used to determine model dependent central star masses. If an additional parameter is determined (e.g. luminosity or dynamic age), the observed evolution of planetary nebulae can be utilized for observational verification of theoretical models. [ABSTRACT FROM AUTHOR]

We compare the spatial stellar color variations with our three-dimensional analytical model of the spatial dust distribution to refine the properties of the dust layer in Galactic solar neighborhoods. We use a complete sample of 93 992 clump giants with a small admixture of branch giants from the Gaia DR2 catalogue in a spatial cylinder with a radius of 700 pc around the Sun extending to |Z| = 1800 pc along the Galactic Z axis. Accurate parallaxes and photometry of these stars in the Gaia DR2 GRP and WISE W3 bands have allowed the spatial GRP - W3 color variations to be used to calculate the model parameters and two characteristics of the sample, the mode of the dereddened color (GRP - W3)0 of the giant clump and the linear change of this mode with coordinate |Z|. As a result, an improved version of the three-dimensional model first proposed by Gontcharov (2009b) has been obtained. As in the previous version, the model suggests two dust layers, along the Galactic equator and in the Gould Belt, that intersect near the Sun at an angle of 18° ± 2°. In contrast to the previous version of the model with a midplane of the Gould Belt dust layer in the form of a circle with the center at the Sun, in the new version this midplane is an ellipse decentered relative to the Sun. A scale height of 170 ± 40 pc has been found for both dust layers. A rather large reddening E(GRP - W3) = 0.16 ± 0.02 through half of the Galactic dust layer above or below the Sun has been found for giants far from the Galactic plane (|Z| > 600 pc). This can be explained by a possible difference between the extinction law far from the Galactic plane and the commonly adopted law by Cardelli et al. (1989) with RV = 3.1. The modes of the absolute magnitude MW3 = -1.70 ± 0.02 and the dereddened color (GRP - W3)0 = (1.43 ± 0.01) - (0.020 ± 0.007)|Z|, where Z is expressed in kpc, have been calculated for the giant clump near the Sun. These estimates are consistent with the estimates from the theoretical PARSEC and MIST isochrones for a sample dominated by giants with an age of 2 Gyr and metallicity [Fe/H] = -0.1 in agreement with the TRILEGAL stellar population model. The dispersions of the quantities under consideration have allowed the natural small-scale density fluctuations of the dust medium relative to the mean reddening calculated from the model to be characterized. These fluctuations make a major contribution to the uncertainty in the reddening. Because of them, the reddening of a specific star can differ from the model reddening by a random value that decreases from 80 to <20% of the model reddening when passing from low latitudes far from the Sun to the remaining space. [ABSTRACT FROM AUTHOR]

Parallaxes with an accuracy better than 10% and proper motions from the Gaia DR1 TGAS catalogue, radial velocities from the Pulkovo Compilation of Radial Velocities (PCRV), accurate Tycho-2 photometry, theoretical PARSEC, MIST, YaPSI, BaSTI isochrones, and the most accurate reddening and interstellar extinction estimates have been used to analyze the kinematics of 9543 thin-disk B-F stars as a function of their dereddened color. The stars under consideration are located on the Hertzsprung-Russell diagram relative to the isochrones with an accuracy of a few hundredths of a magnitude, i.e., at the level of uncertainty in the parallax, photometry, reddening, extinction, and the isochrones themselves. This has allowed us to choose the most plausible reddening and extinction estimates and to conclude that the reddening and extinction were significantly underestimated in some kinematic studies of other authors. Owing to the higher accuracy of TGAS parallaxes than that of Hipparcos ones, the median accuracy of the velocity components U, V, W in this study has improved to 1.7 km s−1, although outside the range −0.1m < (BT − VT)0 < 0.5m the kinematic characteristics are noticeably biased due to the incompleteness of the sample. We have confirmed the variations in the mean velocity of stars relative to the Sun and the stellar velocity dispersion as a function of their dereddened color known from the Hipparcos data. Given the age estimates for the stars under consideration from the TRILEGAL model and the Geneva-Copenhagen survey, these variations may be considered as variations as a function of the stellar age. A comparison of our results with the results of other studies of the stellar kinematics near the Sun has shown that selection and reddening underestimation explain almost completely the discrepancies between the results. The dispersions and mean velocities from the results of reliable studies fit into a ±2 km s−1 corridor, while the ratios σV/σU and σW/σU fit into ±0.05. Based on all reliable studies in the range −0.1m < (BT − VT)0 < 0.5m, i.e., for an age from 0.23 to 2.4 Gyr, we have found: W⊙ = 7.15 km s−1, σU=16.0e1.29(BT−VT)ο, σV=10.9e1.11(BT−VT)ο, σW=6.8e1.46(BT−VT)ο, the stellar velocity dispersions in km s−1 are proportional to the age in Gyr raised to the power βU = 0.33, βV = 0.285, and βW = 0.37. [ABSTRACT FROM AUTHOR]

Based on the Gaia DR1 TGAS parallaxes and photometry from the Tycho-2, Gaia, 2MASS, andWISE catalogues, we have produced a sample of ~100 000 clump red giants within ~800 pc of the Sun. The systematic variations of the mode of their absolute magnitude as a function of the distance, magnitude, and other parameters have been analyzed. We show that these variations reach 0.7 mag and cannot be explained by variations in the interstellar extinction or intrinsic properties of stars and by selection. The only explanation seems to be a systematic error of the Gaia DR1 TGAS parallax dependent on the square of the observed distance in kpc: 0.18 R mas. Allowance for this error reduces significantly the systematic dependences of the absolute magnitude mode on all parameters. This error reaches 0.1 mas within 800 pc of the Sun and allows an upper limit for the accuracy of the TGAS parallaxes to be estimated as 0.2 mas. A careful allowance for such errors is needed to use clump red giants as 'standard candles.' This eliminates all discrepancies between the theoretical and empirical estimates of the characteristics of these stars and allows us to obtain the first estimates of the modes of their absolute magnitudes from the Gaia parallaxes: mode( M ) = −1.49 ± 0.04, mode( M ) = −1.63 ± 0.03, mode( M ) = −1.67 ± 0.05 mode( M ) = −1.67 ± 0.05, mode( M ) = −1.66 ± 0.02, mode( M ) = −1.73 ± 0.03, as well as the corresponding estimates of their de-reddened colors. [ABSTRACT FROM AUTHOR]

Taking advantage of the Gaia DR1, we combined TGAS parallaxes with the Tycho-2 and APASS photometry to calculate the star formation history (SFH) of the solar neighbourhood within 250 pc using the colour-magnitude diagram fitting technique. Our dynamically-evolved SFH is in excellent agreement with that calculated from the Hipparcos catalogue within 80 pc of the Sun, showing an enhanced star formation rate (SFR) in the past ~4 Gyr. We then correct the SFR for the disc thickening with age to obtain a SFR that is representative of the whole solar cylinder, and show that even with an extreme correction our results are not consistent with an exponentially decreasing SFR as found by recent studies. Finally, we discuss how this technique can be applied out to ~5 kpc thanks to the next Gaia data releases, which will allow us to quantify the SFH of the thin disc, thick disc and halo in situ. [ABSTRACT FROM AUTHOR]

We took advantage of the Gaia DR1 to combine TGAS parallaxes with Tycho-2 and APASS photometry to calculate the star formation history (SFH) of the solar neighbourhood within 250 pc using the colour-magnitude diagram fitting technique. We present the determination of the completeness within this volume, and compare the resulting SFH with that calculated from the Hipparcos catalogue within 80 pc of the Sun. We also show how this technique will be applied out to ~5 kpc thanks to the next Gaia data releases, which will allow us to quantify the SFH of the thin disc, thick disc and halo in situ, rather than extrapolating based on the stars from these components that are today in the solar neighbourhood. [ABSTRACT FROM PUBLISHER]

The recent discovery of a gravitational wave from the merging of two black holes of about 30 solar masses each challenges our incomplete understanding of massive stars and their evolution. Critical ingredients comprise mass-loss, rotation, magnetic fields, internal mixing, and mass transfer in close binary systems. The imperfect knowledge of these factors implies large uncertainties for models of stellar populations and their feedback. In this contribution we summarize our empirical studies of Wolf-Rayet populations at different metallicities by means of modern non-LTE stellar atmosphere models, and confront these results with the predictions of stellar evolution models. At the metallicity of our Galaxy, stellar winds are probably too strong to leave remnant masses as high as ∼30M⊙, but given the still poor agreement between evolutionary tracks and observation even this conclusion is debatable. At the low metallicity of the Small Magellanic Cloud, all WN stars which are (at least now) single are consistent with evolving quasi-homogeneously. O and B-type stars, in contrast, seem to comply with standard evolutionary models without strong internal mixing. Close binaries which avoided early merging could evolve quasi-homogeneously and lead to close compact remnants of relatively high masses that merge within a Hubble time. [ABSTRACT FROM AUTHOR]