arXiv subjects

H. -G. Ludwig

Publications and source records attributed to H. -G. Ludwig.

At least 19 recordsLinked to original sources

arXiv2026

Modeling brightness temperature of sunspots using ALMA single-dish observations

We model sunspot brightness temperature in the wavelength range 0.3-10mm using the Atacama Large Millimeter/submillimeter Array (ALMA) single-dish measurements together with other instruments. Our modeling idea starts from an existing model, the 1D semi-empirical Avrett-Tian-Landi-Curdt-Wülser (ATLCW) model for sunspots. The original model is then modified in density and temperature with a constant factor over all heights. A least-square fit in both density and temperature to the observed values yields an improved model for sunspot brightness temperature. Observations show that sunspots are darker than QS at wavelengths below 2 mm and brighter beyond, while fitting of the ATLCW sunspot model imply that sunspots should be darker than QS over the entireALMArange. The best-fitted sunspot brightness temperature profiles resulted in 3.6-4.0 times lower sunspot density compared to the original sunspot ATLCW model, or 1.4-1.8 times higher density compared to QS. The temperature came out around 1.2 times higher than the original ATLCW predictions for sunspots, or 1.2 times lower than QS temperature. Even with improved density and temperature parameters, the remaining discrepancy between the bestfitted models and observations indicated that additional improvements are needed in the ATLCW model and modeling assumptions.

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arXiv2025

Unveiling the nature of HE 0107-5240

The vast majority of the most iron-poor stars in the Galaxy exhibit a strong carbon enhancement, with C/H ratios only about two orders of magnitude below solar. This unusual chemical composition likely reflects the properties of the gas cloud from which these stars formed, having been enriched by one, or at most a few, supernovae. A remarkable member of this stellar class, HE 0107-5240 with [Fe/H]=-5.56, has been identified as part of a binary system. To constrain its orbital parameters, radial velocity monitoring has been carried out using the ESPRESSO spectrograph. Radial velocities were derived using cross-correlation with a template, taking advantage of the strong G-band feature. Combining all observations yielded a high signal-to-noise spectrum, which has been used to refine our understanding of the stellar chemical composition. Additionally, a co-added UVES spectrum in the blue was used to complement the wavelength coverage of ESPRESSO. Observations of HE 0107-5240 over a span of more than four years have yielded a revised orbital period of about 29 years. Updated elemental abundances have been determined for Sc, Cr, Co, and, tentatively, Al, along with a new upper limit for Be. The iron abundance has been derived from ionised Fe lines. Significant upper limits have been established for Li, Si, and Sr. The star is confirmed to be a long-period binary. Iron abundances derived from neutral and ionised lines are consistent with local thermodynamical equilibrium (LTE) assumption, casting doubt on published deviation from LTE corrections for Fe for this star. The heavy elements Sr and Ba remain undetected, confirming the classification of HE 0107-5240 as a carbon enhanced metal-poor and non enhanced in heavy elements (CEMP-no) star and supporting the absence of an n-capture element plateau at the lowest metallicities.

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arXiv2025

Modeling brightness temperature of prominences on the solar disk using ALMA single-dish observations

Prominences (PRs) are among the most common solar phenomena, yet their full physical picture, particularly their chromospheric mm emission, remains incomplete. The new Atacama Large Millimeter/submillimeter Array (ALMA) presents an opportunity to study PRs at mm and sub-mm wavelengths through a combination of measurements and theoretical modeling. We utilize ALMA single-dish measurements alongside data from other radio instruments to model the PR brightness temperature through adaptation and modification the 1D semi-empirical Avrett-Tian-Landi-Curdt-Wülser (ATLCW) quiet-Sun (QS) model. The calculated and measured PR brightness temperatures were found to be lower than the measured QS value and predictions from the unperturbed ATLCW QS model across the ALMA wavelength range, consistent with PRs appearing in absorption. The PR density was found to be 60 - 163 times higher and temperature 155 - 163 times lower than the QS level, aligning with previous measurements. A key finding emerged with the non-hydrostatic equilibrium assumption, yielding a more physically consistent PR brightness temperature. This suggests that PR stability is most likely maintained by its magnetic field obeying magnetostatic conditions rather than by pure hydrostatic equilibrium, supporting recent studies. Additionally, our results confirm that thermal bremsstrahlung is the dominant radiation mechanism for PRs at mm and sub-mm wavelengths.

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arXiv2025

Testing gravity with wide binaries -- 3D velocities and distances of wide binaries from Gaia and HARPS

Wide Binaries (WBs) are interesting systems to test Newton-Einstein gravity in low potentials. The basic concept is to verify whether the difference in velocity between the WB components is compatible with what is expected from the Newton law. Previous attempts, based solely on Gaia proper motion differences scaled to transverse velocity differences using mean parallax distances, do not provide conclusive results. Here we add to the Gaia transverse velocities precise measurements of the third velocity component, the radial velocity (RV), in order to identify multiple stars, and to improve the reliability of the test by using velocity differences and positions in three dimensions. We use the HARPS spectra to determine accurate RV difference between the WB components, correcting the observed velocities for gravitational redshift and convective shift. We exploit the Gaia distance distributions to determine the projected and intrinsic separations s and r and the 3-dimensional velocity differences of the binaries. Of the 44 pairs observed with HARPS, 27% show sign of multiplicity or are not suitable for the test, and 32 bona-fide WBs survive our selection. Their projected separation s is up to 14 kAU, or 0.06 parsec. We determine distances, eccentricities and position angles to reproduce the velocity differences according to Newton's law, finding reasonable solutions for all WBs but one, and with some systems possibly too near pericenter and/or at too high inclination. Our (limited) number of WBs does not show obvious trends with separation or acceleration and is consistent with Newtonian dynamics. We are collecting a larger sample of this kind to robustly assess these results.

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arXiv2024

SDSS J102915.14+172927.9: Revisiting the chemical pattern

Context: The small- to intermediate-mass ($M <0.8 M_\odot$), most metal-poor stars that formed in the infancy of the Universe are still shining today in the sky. They are very rare, but their discovery and investigation brings new knowledge on the formation of the first stellar generations. Aims: SDSS J102915.14+172927.9 is one of the most metal-poor star known to date. Since no carbon can be detected in its spectrum, a careful upper limit is important, both to classify this star and to distinguish it from the carbon-enhanced stars that represent the majority at these metallicities. Methods: We undertook a new observational campaign to acquire high-resolution UVES spectra. The new spectra were combined with archival spectra in order to increase the signal-to-noise ratio. From the combined spectrum, we derived abundances for seven elements (Mg, Si, Ca, Ti, Fe, Ni, and a tentative Li) and five significant upper limits (C, Na, Al, Sr, and Ba). Results: The star has a carbon abundance A(C) <4.68 and therefore is not enhanced in carbon, at variance with the majority of the stars at this Fe regime, which typically show A(C)> 6.0. A feature compatible with the Li doublet at 670.7 nm is tentatively detected. Conclusions: The upper limit on carbon implies $Z<1.915 \times 10^{-6}$, more than 20 times lower than the most iron-poor star known. Therefore, the gas cloud out of which the star was formed did not cool via atomic lines but probably through dust. Fragmentation of the primordial cloud is another possibility for the formation of a star with a metallicity this low.

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arXiv2024

A regularisation technique to precisely infer limb darkening using transit measurements: can we estimate stellar surface magnetic fields?

The high-precision measurements of exoplanet transit light curves that are now available contain information about the planet properties, their orbital parameters, and stellar limb darkening (LD). Recent 3D magneto-hydrodynamical (MHD) simulations of stellar atmospheres have shown that LD depends on the photospheric magnetic field, and hence its precise determination can be used to estimate the field strength. Among existing LD laws, the uses of the simplest ones may lead to biased inferences, whereas the uses of complex laws typically lead to a large degeneracy among the LD parameters. We have developed a novel approach in which we use a complex LD model but with second derivative regularisation during the fitting process. Regularisation controls the complexity of the model appropriately and reduces the degeneracy among LD parameters, thus resulting in precise inferences. The tests on simulated data suggest that our inferences are not only precise but also accurate. This technique is used to re-analyse 43 transit light curves measured by the NASA Kepler and TESS missions. Comparisons of our LD inferences with the corresponding literature values show good agreement, while the precisions of our measurements are better by up to a factor of 2. We find that 1D non-magnetic model atmospheres fail to reproduce the observations while 3D MHD simulations are qualitatively consistent. The LD measurements, together with MHD simulations, confirm that Kepler-17, WASP-18, and KELT-24 have relatively high magnetic fields ($>200$ G). This study paves the way for estimating the stellar surface magnetic field using the LD measurements.

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arXiv2024

Calculated brightness temperatures of solar structures compared with ALMA and Metsähovi measurements

The Atacama Large Millimeter/submillimeter Array (ALMA) allows for solar observations in the wavelength range of 0.3$-$10 mm, giving us a new view of the chromosphere. The measured brightness temperature at various frequencies can be fitted with theoretical models of density and temperature versus height. We use the available ALMA and Metsähovi measurements of selected solar structures (quiet sun (QS), active regions (AR) devoid of sunspots, and coronal holes (CH)). The measured QS brightness temperature in the ALMA wavelength range agrees well with the predictions of the semiempirical Avrett$-$Tian$-$Landi$-$Curdt$-$Wülser (ATLCW) model, better than previous models such as the Avrett$-$Loeser (AL) or Fontenla$-$Avrett$-$Loeser model (FAL). We scaled the ATLCW model in density and temperature to fit the observations of the other structures. For ARs, the fitted models require 9%$-$13% higher electron densities and 9%$-$10% higher electron temperatures, consistent with expectations. The CH fitted models require electron densities 2%$-$40% lower than the QS level, while the predicted electron temperatures, although somewhat lower, do not deviate significantly from the QS model. Despite the limitations of the one-dimensional ATLCW model, we confirm that this model and its appropriate adaptations are sufficient for describing the basic physical properties of the solar structures.

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arXiv2024

The Gaia RVS benchmark stars II. A sample of stars selected for their Gaia high radial velocity

The Gaia satellite has already provided the astronomical community with three data releases, and the Radial Velocity Spectrometer (RVS) on board Gaia has provided the radial velocity for 33 million stars. When deriving the radial velocity from the RVS spectra, several stars are measured to have large values. To verify the credibility of these measurements, we selected some bright stars with the modulus of radial velocity in excess of 500\ to be observed with SOPHIE at OHP and UVES at VLT. This paper is devoted to investigating the chemical composition of the stars observed with UVES. We derived atmospheric parameters using Gaia photometry and parallaxes, and we performed a chemical analysis using the code. We find that the sample consists of metal-poor stars, although none have extremely low metallicities. The abundance patterns match what has been found in other samples of metal-poor stars selected irrespective of their radial velocities. We highlight the presence of three stars with low Cu and Zn abundances that are likely descendants of pair-instability supernovae. Two stars are apparently younger than 1\,Ga, and their masses exceed twice the turn-off mass of metal-poor populations. This makes it unlikely that they are blue stragglers because it would imply they formed from triple or multiple systems. We suggest instead that they are young metal-poor stars accreted from a dwarf galaxy. Finally, we find that the star RVS721 is associated with the Gjoll stream, which itself is associated with the Globular Cluster NGC\,3201.

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arXiv2024

Entropy-calibrated stellar modeling: Testing and improving the use of prescriptions for entropy of adiabatic convection

The modeling of convection is a long standing problem in stellar physics. Up-to-now, all ad hoc models rely on a free parameter alpha (among others) which has no real physical justification and is therefore poorly constrained. However, a link exists between this free parameter and the entropy of the stellar adiabat. Prescriptions, derived from 3D stellar atmospheric models, are available that provide entropy as a function of stellar atmospheric parameters (effective temperature, surface gravity, chemical composition). This can provide constraints on alpha through the development of entropy-calibrated models. Several questions arise as these models are increasingly used. Which prescription should be used? How do uncertainties impact entropy-calibrated models? We aim to study the three existing prescriptions and determine which one should be used, and how. We implemented the entropy-calibration method into the stellar evolution code Cesam2k20 and performed comparisons with the Sun and the alpha Cen system. In addition, we used data from the CIFIST grid of 3D atmosphere models to evaluate the accuracy of the prescriptions. Of the three entropy prescriptions available, we determine which one best reproduces the entropies of the 3D models. We also demonstrate that the entropy obtained from this prescription should be corrected for the evolving chemical composition and for an entropy offset different between various EoS tables, following a precise procedure, otherwise classical parameters obtained from the models will be strongly biased. Finally, we also provide table with entropy of the adiabat of the CIFIST grid, as well as fits of these entropies. We performed a precise examination of entropy-calibrated modelling, and gave recommendations on which adiabatic entropy prescription to use, how to correct it and to implement the method into a stellar evolution code.

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arXiv2023

Implications of time-dependent molecular chemistry in metal-poor dwarf stars

Binary molecules such as CO, OH, CH, CN, and C$_2$ are often used as abundance indicators in stars. These species are usually assumed to be formed in chemical equilibrium. The time-dependent effects of hydrodynamics can affect the formation and dissociation of these species and may lead to deviations from chemical equilibrium. We aim to model departures from chemical equilibrium in dwarf stellar atmospheres by considering time-dependent chemical kinetics alongside hydrodynamics and radiation transfer. We examine the effects of a decreasing metallicity and an altered C/O ratio on the chemistry when compared to the equilibrium state. We used the radiation-(magneto)hydrodynamics code CO5BOLD, and its own chemical solver to solve for the chemistry of 15 species and 83 reactions. The species were treated as passive tracers and were advected by the velocity field. The steady-state chemistry was also computed to isolate the effects of hydrodynamics. In most of the photospheres in the models we present, the mean deviations are smaller than $0.2$ dex, and they generally appear above $\logτ = -2$. The deviations increase with height because the chemical timescales become longer with decreasing density and temperature. A reduced metallicity similarly results in longer chemical timescales and in a reduction in yield that is proportional to the drop in metallicity; a decrease by a factor $100$ in metallicity loosely corresponds to an increase by factor $100$ in chemical timescales. As both CH and OH are formed along reaction pathways to CO, the C/O ratio means that the more abundant element gives faster timescales to the constituent molecular species. Overall, the carbon enhancement phenomenon seen in very metal-poor stars is not a result of an improper treatment of molecular chemistry for stars up to a metallicity as low as [Fe/H] = $-3.0$.

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arXiv2022

Differences in physical properties of coronal bright points and their ALMA counterparts within and outside coronal holes

This study investigates and compares brightness and area of coronal bright points (CBPs) inside and outside of coronal holes (CHs) using the single-dish Band 6 observations by the Atacama Large Millimeter/submillimeter Array (ALMA), combined with extreme-ultraviolet (EUV) 193 $\overset{\circ}{\mathrm{A}}$ filtergrams obtained by the Atmospheric Imaging Assembly (AIA) and magnetograms obtained by the Helioseismic and Magnetic Imager (HMI), both on board Solar Dynamics Observatory (SDO). The CH boundaries were extracted from the SDO/AIA images using the Collection of Analysis Tools for Coronal Holes (CATCH) and CBPs were identified in the SDO/AIA, SDO/HMI, and ALMA data. Measurements of brightness and areas in both ALMA and SDO/AIA images were conducted for CBPs within CHs and quiet Sun regions outside CHs. A statistical analysis of the measured physical properties resulted in a lower average CBP brightness in both ALMA and SDO/AIA data for CBPs within the CHs. Depending on the CBP sample size, the difference in intensity for the SDO/AIA data, and brightness temperature for the ALMA data, between the CBPs inside and outside CHs ranged from between 2$σ$ and 4.5$σ$, showing a statistically significant difference between those two CBP groups. For CBP areas, CBPs within the CH boundaries showed smaller areas on average, with the observed difference between the two CBP groups between 1$σ$ and 2$σ$ for the SDO/AIA data, and up to 3.5$σ$ for the ALMA data, indicating that CBP areas are also significantly different. Given the measured properties, we conclude that the CBPs inside CHs tend to be less bright on average, but also smaller in comparison to those outside of CHs. This conclusion might point to the specific physical conditions and properties of the local CH region around a CBP limiting the maximum achievable intensity (temperature) and size of a CBP.

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arXiv2022

The solar photospheric silicon abundance according to CO5BOLD: Investigating line broadening, magnetic fields, and model effects

In this work, we present a photospheric solar silicon abundance derived using CO5BOLD model atmospheres and the LINFOR3D spectral synthesis code. Previous works have differed in their choice of a spectral line sample and model atmosphere as well as their treatment of observational material, and the solar silicon abundance has undergone a downward revision in recent years. We additionally show the effects of the chosen line sample, broadening due to velocity fields, collisional broadening, model spatial resolution, and magnetic fields. CO5BOLD model atmospheres for the Sun were used in conjunction with the LINFOR3D spectral synthesis code to generate model spectra, which were then fit to observations in the Hamburg solar atlas. We present a sample of 11 carefully selected lines (from an initial choice of 39 lines) in the optical and infrared, made possible with newly determined oscillator strengths for the majority of these lines. Our final sample includes seven optical Si I lines, three infrared Si I lines, and one optical Si II line. We derived a photospheric solar silicon abundance of $\log ε_\mathrm{Si} = 7.57 \pm 0.04$, including a $-0.01$ dex correction from Non-Local Thermodynamic Equilibrium (NLTE) effects. Combining this with meteoritic abundances and previously determined photospheric abundances results in a metal mass fraction Z/X = $0.0220 \pm 0.0020$. We found a tendency of obtaining overly broad synthetic lines. We mitigated the impact of this by devising a de-broadening procedure. The over-broadening of synthetic lines does not substantially affect the abundance determined in the end. It is primarily the line selection that affects the final fitted abundance.

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arXiv2022

Interpolation of spectra from 3D model atmospheres

The use of 3D hydrodynamical simulations of stellar surface convection for model atmospheres is computationally expensive. Although these models have been available for quite some time, their use is limited because of the lack of extensive grids of simulations and associated spectra. Our goal is to provide a method to interpolate spectra that can be applied to both 1D and 3D models, and implement it in a code available to the community. This tool will enable the routine use of 3D model atmospheres in the analysis of stellar spectra.} We have developed a code that makes use of radial basis functions to interpolate the spectra included in the CIFIST grid of 84 three-dimensional model atmospheres. Spectral synthesis on the hydrodynamical simulations was previously performed with the code ASS$ε$T. We make a tool for the interpolation of 3D spectra available to the community. The code provides interpolated spectra and interpolation errors for a given wavelength interval, and a combination of effective temperature, surface gravity, and metallicity. In addition, it optionally provides graphical representations of the RMS and mean ratio between 1D and 3D spectra, and maps of the errors in the interpolated spectra across the parameter space.

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arXiv2021

ALMA small-scale features in the quiet Sun and active regions

Aims. The main aim of the present analysis is to decipher (i) the small-scale bright features in solar images of the quiet Sun and active regions obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) and (ii) the ALMA correspondence of various known chromospheric structures visible in the H-alpha images of the Sun. Methods. Small-scale ALMA bright features in the quiet Sun region were analyzed using single-dish ALMA observations (1.21 mm, 248 GHz) and in an active region using interferometric ALMA measurements (3 mm, 100 GHz). With the single-dish observations, a full-disk solar image is produced, while interferometric measurements enable the high-resolution reconstruction of part of the solar disk, including the active region. The selected quiet Sun and active regions are compared with the H-alpha (core and wing sum), EUV, and soft X-ray images and with the magnetograms. Results. In the quiet Sun region, enhanced emission seen in the ALMA is almost always associated with a strong line-of-sight (LOS) magnetic field. Four coronal bright points were identified, while other small-scale ALMA bright features are most likely associated with magnetic network elements and plages. In the active region, in 14 small-scale ALMA bright features randomly selected and compared with other images, we found five good candidates for coronal bright points, two for plages, and five for fibrils. Two unclear cases remain: a fibril or a jet, and a coronal bright point or a plage. A comparison of the H-alpha core image and the 3 mm ALMA image of the analyzed active region showed that the sunspot appears dark in both images (with a local ALMA radiation enhancement in sunspot umbra), the four plage areas are bright in both images and dark small H-alpha filaments are clearly recognized as dark structures of the same shape also in ALMA.

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arXiv2020

Velocity-intensity asymmetry reversal of solar radial p-modes

The development of space-borne missions has significantly improved the quality of the measured spectra of solar-like oscillators. Their $p$-mode line profiles can now be resolved, and the asymmetries inferred for a variety of stars other than the Sun. However, it has been known for a long time that the asymmetries of solar $p$-modes are reversed between the velocity and the intensity spectra. Understanding the origin of this reversal is necessary in order to use asymmetries as a tool for seismic diagnosis. For stars other than the Sun, only the intensity power spectrum is sufficiently resolved to allow for an estimation of mode asymmetries. We recently developed an approach designed to model and predict these asymmetries in the velocity power spectrum of the Sun and to successfully compare them to their observationally derived counterparts. In this paper we expand our model and predict the asymmetries featured in the intensity power spectrum. We find that the shape of the mode line profiles in intensity is largely dependent on how the oscillation-induced variations of the radiative flux are treated, and that modelling it realistically is crucial to understanding asymmetry reversal. Perturbing a solar-calibrated grey atmosphere model, and adopting the quasi-adiabatic framework as a first step, we reproduce the asymmetries observed in the solar intensity spectrum for low-frequency modes. We conclude that, unlike previously thought, it is not necessary to invoke an additional mechanism (e.g. non-adiabatic effects, coherent non-resonant background signal) to explain asymmetry reversal. This additional mechanism is necessary, however, to explain asymmetry reversal for higher-order modes.

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arXiv2020

The solar gravitational redshift from HARPS-LFC Moon spectra. A test of the General Theory of Relativity

The General Theory of Relativity predicts the redshift of spectral lines in the solar photosphere, as a consequence of the gravitational potential of the Sun. This effect can be measured from a solar disk-integrated flux spectrum of the Sun's reflected light on solar system bodies. The laser frequency comb (LFC) calibration system attached to the HARPS spectrograph offers the possibility to perform an accurate measurement of the solar gravitational redshift (GRS) by observing the Moon or other solar system bodies. We have analysed the line shift observed in Fe absorption lines from five high-quality HARPS-LFC spectra of the Moon. We select an initial sample of 326 photospheric Fe lines in the spectral range 476-585 nm and measure their line positions and equivalent widths (EWs). Accurate line shifts are derived from the wavelength position of the core of the lines compared with the laboratory wavelengths. We fit the observed spectral Fe lines using CO$^5$BOLD 3D synthetic profiles. Convective motions in the solar photosphere do not affect the line cores of Fe lines stronger than about $\sim 150$ mA. In our sample, only 15 FeI lines have EWs in the range $150 <$ EW(mA) $< 550$, providing a measurement of the solar GRS at $639\pm14$ ${\rm m\;s^{-1}}$, consistent with the expected theoretical value on Earth of $\sim 633.1$ ${\rm m\;s^{-1}}$. A final sample of about 97 weak Fe lines with EW $<180$ mA allows us to derive a mean global line shift of $638\pm6$ ${\rm m\;s^{-1}}$ in agreement with the theoretical solar GRS. These are the most accurate measurements of the solar GRS so far. Ultrastable spectrographs calibrated with the LFC over a larger spectral range, such as HARPS or ESPRESSO, together with a further improvement on the laboratory wavelengths, could provide a more robust measurement of the solar GRS and further tests for the 3D hydrodynamical models.

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arXiv2020

Modelling the asymmetries of the Sun's radial $p$-mode line profiles

In this paper, we aim to develop a predictive model for solar radial $p$-mode line profiles in the velocity spectrum. Unlike the approach favoured by prior studies, this model is not described by free parameters and we do not use fitting procedures to match the observations. Instead, we use an analytical turbulence model coupled with constraints extracted from a 3D hydrodynamic simulation of the solar atmosphere. We then compare the resulting asymmetries with their observationally derived counterpart. We find that stochastic excitation localised beneath the mode upper turning point generates negative asymmetry for $ν< ν_\text{max}$ and positive asymmetry for $ν> ν_\text{max}$. On the other hand, stochastic excitation localised above this limit generates negative asymmetry throughout the $p$-mode spectrum. As a result of the spatial extent of the source of excitation, both cases play a role in the total observed asymmetries. By taking this spatial extent into account and using a realistic description of the spectrum of turbulent kinetic energy, both a qualitative and quantitative agreement can be found with solar observations perfoemed by the GONG network. We also find that the impact of the correlation between acoustic noise and oscillation is negligible for mode asymmetry in the velocity spectrum.

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arXiv2019

Calibration of the mixing length theory for structures of helium-dominated atmosphere white dwarfs

We perform a calibration of the mixing length parameter at the bottom boundary of the convection zone for helium-dominated atmospheres of white dwarfs. This calibration is based on a grid of 3D DB (pure-helium) and DBA (helium-dominated with traces of hydrogen) model atmospheres computed with the CO5BOLD code, and a grid of 1D DB and DBA envelope structures. The 3D models span a parameter space of hydrogen-to-helium abundances between -10.0 and -2.0, surface gravities between 7.5 and 9.0 and effective temperatures between 12000 K and 34000 K. The 1D envelopes cover a similar atmospheric parameter range, but are also calculated with different values of the mixing length parameter, namely ML2/alpha between 0.4 and 1.4. The calibration is performed based on two definitions of the bottom boundary of the convection zone, the Schwarzschild and the zero convective flux boundaries. Thus, our calibration is relevant for applications involving the bulk properties of the convection zone including its total mass, which excludes the spectroscopic technique. Overall, the calibrated ML2/alpha is smaller than what is commonly used in evolutionary models and theoretical determinations of the blue edge of the instability strip for pulsating DB and DBA stars. With calibrated ML2/alpha we are able to deduce more accurate convection zone sizes needed for studies of planetary debris mixing and dredge-up of carbon from the core. We highlight this by calculating examples of metal-rich 3D DBAZ models and finding their convection zone masses. Mixing length calibration represents the first step of in-depth investigations of convective overshoot in white dwarfs with helium-dominated atmospheres.

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