arXiv subjects

F. Ahlborn

Publications and source records attributed to F. Ahlborn.

9 recordsLinked to original sources

arXiv2026

Testing the 3-equation Kuhfuss Convection Model using the Sun

Simplified, one-dimensional models are necessary to model convection in the context of stellar evolution. By including the non-local effects of convection, turbulent convection models describe convection in a more physical way compared to mixing length theory, which is typically used in one-dimensional stellar evolution models. We recently showed that the 1-equation Kuhfuss turbulent convection model is not sufficient to model the solar convective envelope satisfactorily. Using the Sun as a benchmark, we test the physically more complete 3-equation Kuhfuss turbulent convection model. We calculate a solar calibrated model with the 3-equation Kuhfuss turbulent convection model using the one-dimensional stellar evolution code GARSTEC. We compare the predicted interior structure of the model with helioseismic measurements of the Sun. Furthermore, we investigate how the free parameters and the closure relations of the 3-equation model influence the results. We find that, with the 3-equation model, the temperature gradient at the inner boundary of the convective envelope is modelled more realistically compared to the mixing length theory or the 1-equation model. This also improves the agreement for the sound speed profile between the model and the Sun, and reduces the asteroseismic surface effect. However, close to the surface, the 3-equation model results in a layer having an unphysical, negative temperature gradient. This layer is connected to the closure relations used in the 3-equation model. Our results demonstrate the capabilities of turbulent convection models, and can serve as a next step towards an improved and more realistic modelling of convection in stellar evolution codes.

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arXiv2026

The sensitivity and behaviour of the curvature in the \'echelle diagram of red-giant stars

In the convective envelopes of relatively cool stars, oscillations are excited by turbulent convection. In these so-called solar-like oscillators, radial oscillation modes appear at nearly equally spaced frequencies. This spacing is referred to as the `large frequency separation'. Deviations from equally-spaced frequencies are a result of the internal structure of a star being different from a sphere of ideal gas at constant temperature. Hence, these deviations provide information on the internal structure of the star. In this work, we investigate the second-order deviation from uniform spacing, referred to as curvature. We aim to provide homegeneous values for observed red-giant stars, understand differences between the results from observations and predictions from stellar models, and reveal the connection between curvature and stellar structure. We used Kepler data of red-giant stars and computed the curvature for several thousand stars. We compared these to the curvature derived from MESA models. We subsequently investigated the trends and differences between results from observations and models. Finally, we computed sensitivity kernels to identify the stellar region to which the curvature is most sensitive and performed a glitch analysis. We found that the curvature is sensitive to evolutionary phase and mass. The observed values and values from models show discrepancies. The glitch analysis shows that in theory this provides information on the location and strength of the HeI and HI ionisation layers. The curvature provides a probe into the near-surface structure of the star. The deviations between the curvature derived from observations and models call henceforth for improvements in the near-surface layers of stellar models.

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arXiv2025

Impact of near-degeneracy effects on linear rotational inversions for red-giant stars

Accurate estimates of internal red-giant rotation rates are a crucial ingredient for constraining and improving current models of stellar rotation. Asteroseismic rotational inversions are a method to estimate these internal rotation rates. In this work, we focus on the observed differences in the rotationally-induced frequency shifts between prograde and retrograde modes, which were ignored in previous works when estimating internal rotation rates of red giants using inversions. We systematically study the limits of applicability of linear rotational inversions as a function of the evolution on the red-giant branch and the underlying rotation rates. We solve for the oscillation mode frequencies in the presence of rotation in the lowest-order perturbative approach. This enables a description of the differences between prograde and retrograde modes through the coupling of multiple mixed modes. We compute synthetic rotational splittings taking these near-degeneracy effects into account. We use red-giant models with one solar mass, a large frequency separation between 16 and 9 microhertz and core rotation rates between 500 and 1500 nHz covering the regime of observed parameters of Kepler red-giant stars. Finally, we use these synthetic data to quantify the systematic errors of internal rotation rates estimated by means of rotational inversions in the presence of near-degeneracy effects. We show that the systematic errors in the estimated rotation rates introduced by near-degeneracy effects surpass observational uncertainties for more evolved and faster rotating stars. The estimated rotation rates of some of the previously analysed red giants suffer from significant systematic errors that have not been taken into account yet. Notwithstanding, reliable analyses with existing inversion methods are feasible for a number of red giants within the parameter ranges determined here.

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arXiv2025

Implications of a turbulent convection model for classical Cepheids

The appearance of blue loops in the evolutionary tracks of intermediate-mass core He-burning stars is essential for explaining the observed characteristics of Cepheids. The blue loops for lower mass Cepheids cannot always be reproduced when only classical, local mixing length theory (MLT) is used. Additionally, classical models result in a mass discrepancy compared to pulsational and dynamical mass determinations. Both problems can be resolved through an ad-hoc extension of the MLT for convection. We use the non-local Kuhfuss turbulent convection model (TCM) which can explain overshooting directly from the solution of the TCM equations. The primary objective of this study is to test the predictions of the Kuhfuss TCM when applied to intermediate-mass core He-burning stars and validate the model predictions against observations of Cepheids. We used the state-of-the-art 1D stellar evolution code GARSTEC with the implementation of the Kuhfuss TCM and computed evolutionary tracks for intermediate-mass core He-burning stars. We compare these tracks with those computed with MLT including and excluding ad-hoc overshooting and with observations of five Cepheids in detached binary systems obtained from the literature. The stellar evolution tracks generated using the Kuhfuss TCM and MLT with ad-hoc overshooting exhibit similar appearances. Overshoot mixing from the convective boundaries and the occurrence of the Cepheid blue-loop have been achieved naturally as solutions to the Kuhfuss TCM equations. Furthermore, these models successfully reproduce observed stellar parameters including mass, luminosity, radius, and effective temperature. In conclusion, our TCM approach reproduces Cepheid blue loops and agrees with observations similarly well as MLT models with overshooting, however, without fine-tuning the model parameters or ad-hoc assumptions.

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arXiv2024

The robustness of inferred envelope and core rotation rates of red-giant stars from asteroseismology

Rotation is an important, yet poorly-modelled phenomenon of stellar structure and evolution. Accurate estimates of internal rotation rates are therefore valuable for constraining stellar evolution models. We aim to assess the accuracy of asteroseismic estimates of internal rotation rates and how these depend on the fundamental stellar parameters. We apply the recently-developed method called extended-MOLA inversions to infer localised estimates of internal rotation rates of synthetic observations of red giants. We search for suitable reference stellar models following a grid-based approach, and assess the robustness of the resulting inferences to the choice of reference model. We find that matching the mixed mode pattern between the observation and the reference model is an important criterion to select suitable reference models. We propose to i) select a set of reference models based on the correlation between the observed rotational splittings and the mode-trapping parameter ii) compute rotation rates for all these models iii) use the mean value obtained across the whole set as the estimate of the internal rotation rates. We find that the effect of a near surface perturbation in the synthetic observations on the rotation rates estimated based on the correlation between the observed rotational splittings and the mode-trapping parameter is negligible. We conclude that when using an ensemble of reference models, constructed based on matching the mixed mode pattern, the input rotation rates can be recovered across a range of fundamental stellar parameters like mass, mixing-length parameter and composition. Further, red-giant rotation rates determined in this way are also independent of a near surface perturbation of stellar structure.

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arXiv2024

Testing a non-local 1-equation turbulent convection model: A solar model

Turbulent convection models treat stellar convection more physically than standard mixing-length theory by including non-local effects. We recently successfully applied the Kuhfuss version to convective cores in main sequence stars. Its usefulness for convective envelopes remains to be tested. The solar convective envelope constitutes a viable test bed for investigating the usefulness of the 1-equation Kuhfuss turbulent convection model. We used the one-dimensional stellar evolution code GARSTEC to calculate a standard solar model with the 1-equation Kuhfuss turbulent convection model, and compared it to helioseismic measurements and a solar model using standard mixing-length theory. Additionally, we investigated the influence of the additional free parameters of the convection model on the solar structure. The 1-equation Kuhfuss model reproduces the sound-speed profile and the lower boundary of the convective region less well than the mixing-length model, because the inherent non-local effects overestimate the amount of convective penetration below the Schwarzschild boundary. We trace this back to the coupling of the temperature gradient to the convective flux in the 1-equation version of the Kuhfuss theory. The temperature stratification of the solar convective envelope is not well modelled by the 1-equation Kuhfuss turbulent convection model, and the more complex 3-equation version is needed to improve the modelling of convection in the envelopes of 1D stellar evolution models.

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arXiv2022

Improved asteroseismic inversions for red-giant surface rotation rates

Asteroseismic observations of internal stellar rotation have indicated a substantial lack of angular momentum transport in theoretical models of subgiant and red-giant stars. Accurate core and surface rotation rate measurements are therefore needed to constrain internal transport processes included in the models. We eliminate substantial systematic errors of asteroseismic surface rotation rates found in previous studies. We propose a new objective function for the Optimally Localized Averages method of rotational inversions for red-giant stars, which results in more accurate envelope rotation rate estimates obtained from the same data. We use synthetic observations from stellar models across a range of evolutionary stages and masses to demonstrate the improvement. We find that our new inversion technique allows us to obtain estimates of the surface rotation rate that are independent of the core rotation. For a star at the base of the red-giant branch, we reduce the systematic error from about 20% to a value close to 0, assuming constant envelope rotation. We also show the equivalence between this method and the method of linearised rotational splittings. Our new rotational inversion method substantially reduces the systematic errors of red-giant surface rotation rates. In combination with independent measures of the surface rotation rate, this will allow better constraints to be set on the internal rotation profile. This will be a very important probe to further constrain the internal angular momentum transport along the lower part of the red-giant branch.

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arXiv2022

Stellar evolution models with overshooting based on 3-equation non-local theories I. Physical basis and the computation of the dissipation rate

Context. Mixing by convective overshooting has long been suggested to play an important role for the amount of hydrogen available to nuclear burning in convective cores of stars. The best way to model this effect is still debated. Aims. We suggest an improved model for the computation of the dissipation rate of turbulent kinetic energy which can be used in non-local models of stellar convection and can readily be implemented and self-consistently used in 1D stellar evolution calculations. Methods. We review the physics underlying various models to compute the dissipation rate of turbulent kinetic energy, ε, in local and particularly in non-local models of convection in stellar astrophysics. The different contributions to the dissipation rate and their dependence on local stratification and on non-local transport are analysed and a new method to account for at least some of these physical mechanisms is suggested. Results. We show how the new approach influences predictions of stellar models of intermediate-mass main-sequence stars and how these changes differ from other modifications of the non-local convection model that focus on the ratio of horizontal to vertical (turbulent) kinetic energy. Conclusions. The new model is shown to allow for a physically more complete description of convective overshooting and mixing in massive stars. Dissipation by buoyancy waves is found to be a key ingredient which has to be accounted for in non-local models of turbulent convection.

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arXiv2020

Asteroseismic sensitivity to internal rotation along the red-giant branch

Transport of angular momentum in stellar interiors is currently not well understood. Asteroseismology can provide us with estimates of internal rotation of stars and thereby advances our understanding of angular momentum transport. We can measure core-rotation rates in red-giant stars and we can place upper bounds on surface-rotation rates using measurements of dipole ($l=1$) modes. Here, we aim to determine the theoretical sensitivity of modes of different spherical degree towards the surface rotation. Additionally, we aim to identify modes that can potentially add sensitivity at intermediate radii. We used asteroseismic rotational inversions to probe the internal stellar rotation profiles in red-giant models from the base of the red-giant branch up to the luminosity bump. We used the inversion method of multiplicative optimally localised averages (MOLA) to assess how well internal and surface rotation rates can be recovered from different mode sets and different synthetic rotation profiles. We confirm that dipole mixed modes are sufficient to set constraints on the average core-rotation rates in red giants. However, surface-rotation rates estimated with only dipole mixed modes are contaminated by the core rotation. We show that the sensitivity to the surface rotation decreases from the base of the red-giant branch until it reaches a minimum at 0.6-0.8$L_\text{bump}$ due to a glitch in the buoyancy frequency. Thereafter a narrow range of increased surface sensitivity just below the bump luminosity exists. Quadrupole and octopole modes have more sensitivity in the outer parts of the star. If observed, quadrupole and octopole modes enable us to distinguish between differential and solid body rotation in the convection zone. To obtain accurate estimates of rotation rates at intermediate radii, acoustic oscillation modes with a spherical degree of $l\approx10$ are needed.

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