arXiv subjects

S. Hekker

Publications and source records attributed to S. Hekker.

At least 19 recordsLinked to original sources

arXiv2026

The role of specific entropy in the onset of the luminosity bump

During their evolution, stars follow a distinct path in luminosity--temperature space. Low-mass stars that have exhausted hydrogen in their core follow the so-called red-giant branch which is predominantly in the direction of increasing luminosity and decreasing surface temperature. The luminosity bump is a temporary decrease in luminosity against this otherwise increasing trend. The bump is present in both observations and stellar evolution models. However, with canonical physics included in the models, the bump in computed evolutionary tracks appears at higher luminosities than the observed bump. To understand why the bump appears later in the models than in observations, the physics of the bump needs to be unravelled. The end point of the bump is well-understood; however, the onset of the bump is still an enigma. Here, we report on the physical origin of the onset of the luminosity bump. We show that the difference in specific entropy at the mean molecular weight discontinuity decreases due to the discontinuity moving in. This decrease is attributed to the decrease in the ratio of the temperature to the pressure at smaller radii. Upon reaching a critical value the specific entropy difference at the mean molecular weight discontinuity is reduced sufficiently to reduce the specific entropy in the convective envelope. The latter is a key signature of the bump. Hence the evolution of the specific entropy at the mean molecular weight discontinuity provides a viable description for the onset of the bump.

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arXiv2026

Facing the phase: Gravity-mode offset and buoyancy glitches in red--giant branch stars

With the increasing precision of asteroseismic observations, it becomes possible to reliably measure oscillation properties of an increasing number of stars. Interpreting these measurements requires a good theoretical understanding of their link to fundamental stellar properties. In this study, we focus on the phase offset in gravity(g)-mode frequencies, which is imprinted in the asymptotic eigenfrequency pattern of mixed dipole modes observed in red--giant branch stars. We aim to unravel its physical origin and thus enable an informed interpretation of observations. Using stellar models, we empirically test the contribution of the g-mode offset $\varepsilon_\mathrm{g}$ (which is related to the wave reflection at cavity boundaries and commonly considered to be the dominant phase term) and glitches to the total observable phase. We find that, additionally to $\varepsilon_\mathrm{g}$, buoyancy glitches play an important role in the correct interpretation of the g--mode frequency phase. We further find that glitches in the evanescent zone also contribute to the phase, and we present a formalism to quantify this contribution. Finally, we propose a modification to the widely used formula for $\varepsilon_\mathrm{g}$. The g--mode frequency phase carries more information than previously considered. It has large analytic potential to study not only the reflection properties of the buoyancy cavity, but also the properties of glitches in the Brunt-V\"ais\"al\"a frequency.

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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

Weak or strong: coupling of mixed oscillation modes on the red-giant branch

Context. The high precision of recent asteroseismic observations of red-giant stars has revealed the presence of mixed dipole modes in their oscillation spectra. These modes allow for a look inside the stars. Among the parameters used to characterize mixed modes is the coupling strength q, which is sensitive to the stellar structure in the evanescent zone near the bottom of the convective envelope. Aims. The aim of this work is to probe the validity of the weak and strong coupling approximations, commonly used to calculate q, during stellar evolution along the red-giant branch (RGB). Methods. To test the approximations empirically, we calculate q-values in both, the weak and strong limit for stellar models on the RGB and compare them to the coupling derived from the mixed mode frequency pattern obtained from numerical solutions to the oscillation equations. Results. We find good agreement with the strong coupling approximation on the early RGB, when the evanescent zone lies in the radiative layer right above the hydrogen-burning shell; and with the weak coupling approximation once the evanescent zone is situated in the convective envelope. This is consistent with earlier studies. Additionally, we find that it is viable to use the weak coupling approximation as an estimate for q in the intermediate regime, in the mass range considered in this work (1.00 Msun <= M <= 2.00 Msun). Conclusions. The width of the evanescent zone serves as a good measure for which approximation to use. The serendipitous alignment of the weak coupling approximation with the observable q in the regime where neither approximation is expected to be valid simplifies the asymptotic calculation of mixed mode properties.

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arXiv2025

Asteroseismic predictions for a massive main-sequence merger product

The products of stellar mergers between two massive main-sequence (MS) stars appear as seemingly normal MS stars after a phase of thermal relaxation, if not for certain peculiarities. Since these peculiarities are not limited to the merger product's surface, we use asteroseismology to predict how the differences in the internal structure of a merger product and a genuine single star manifest via properties of non-radial stellar pulsations. We mapped the result of a 3D MHD stellar merger simulation between a 9 and an 8 solar-mass MS star to 1D and evolved it through the MS. We compare the predicted pressure (p) and gravity (g) modes for the merger product model with those predicted for a corresponding genuine single-star model. The p-mode frequencies are consistently lower for the merger product than for the genuine single star, and the differences between them are more than a thousand times larger than the current best observational uncertainties for measured mode frequencies of this kind. Even though g-mode period spacing differences vary in value and sign throughout the MS, they, too, are larger than the current best observational uncertainties for such long-period modes. This, combined with additional variability in the merger product's period spacing patterns, shows the potential of identifying merger products in future-forward modelling. We also attempt to replicate the merger product's structure using three widely applied 1D merger prescriptions and repeat the asteroseismic analysis. Although none of the 1D prescriptions reproduces the entire merger product's structure, we conclude that the prescription with shock heating shows the highest potential, provided that it can be calibrated on binary-evolution-driven 3D merger simulations. Our work should be expanded to encompass the various possible merger product structures predicted to exist in the Universe. (abridged)

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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

Red giants evolutionary status determination: the complete Kepler catalog

Evolved cool stars have three distinct evolutionary status: shell Hydrogen-burning (RGB), core Helium and shell Hydrogen burning (RC), and double shell burning (AGB). Asteroseismology can distinguish between the RC and the other status, but distinguishing RGB and AGB has been difficult seismically and spectroscopically. The precise boundaries of different status in the HR diagram have also been difficult to establish. In this article, we present a comprehensive catalog of asteroseismic evolutionary status, RGB and RC, for evolved red giants in the Kepler field. We carefully examine boundary cases to define the lower edge of the RC phase in radius and surface gravity. We also test different published asteroseisemic methods claiming to distinguish AGB and RGB stars against a sample where AGB candidates were selected using a spectrocopic identification method. We used six different seismic techniques to distinguish RC and RGB stars, and tested two proposed methods for distinguishing AGB and RGB stars. These status were compared with those inferred from spectroscopy. We present consensus evolutionary status for 18,784 stars out of the 30,337 red giants present in the Kepler data, including 11,516 stars with APOGEE spectra available. The agreement between seismic and spectroscopic classification is excellent for distinguishing RC stars, agreeing at the 94% level. Most disagreements can be traced to uncertainties in spectroscopic parameters, but some are caused by blends with background stars. We find a sharp lower boundary in surface gravity at log(g) = 2.99+/-0.01 for the RC and discuss the implications. We demonstrate that asteroseismic tools for distinguishing AGB and RGB stars are consistent with spectroscopic evolutionary status at near the RC but that the agreement between the different methods decreases rapidly as the star evolves.

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arXiv2023

Seismic and spectroscopic analysis of 9 bright red giants observed by Kepler

Photometric time series gathered by space telescopes such as CoRoT and Kepler allow to detect solar-like oscillations in red-giant stars and to measure their global seismic constraints, which can be used to infer global stellar properties (e.g. masses, radii, evolutionary states). Combining such precise constraints with photospheric abundances provides a means of testing mixing processes that occur inside red-giant stars. In this work, we conduct a detailed spectroscopic and seismic analysis of nine nearby (d < 200 pc) red-giant stars observed by Kepler. Both seismic constraints and grid-based modelling approaches are used to determine precise fundamental parameters for those evolved stars. We compare distances and radii derived from Gaia Data Release 3 parallaxes with those inferred by a combination of seismic, spectroscopic and photometric constraints. We find no deviations within errorsbars, however the small sample size and the associated uncertainties are a limiting factor for such comparison. We use the period spacing of mixed modes to distinguish between ascending red-giants and red-clump stars. Based on the evolutionary status, we apply corrections to the values of $Δν$ for some stars, resulting in a slight improvement to the agreement between seismic and photometric distances. Finally, we couple constraints on detailed chemical abundances with the inferred masses, radii and evolutionary states. Our results corroborate previous studies that show that observed abundances of lithium and carbon isotopic ratio are in contrast with predictions from standard models, giving robust evidence for the occurrence of additional mixing during the red-giant phase.

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arXiv2023

New red giants in NGC 6791 and NGC 6819 using Kepler superstamps

Context. Stars that are members of stellar clusters are assumed to be formed at the same time and place from material with the same initial chemical composition. These additional constraints on the ensemble of cluster stars make these stars suitable as benchmarks. Aims. We aimed 1) to identify previously unknown red giants in the open clusters NGC 6791 and NGC 6819, 2) to extract their asteroseismic parameters, and 3) to determine their cluster membership. Methods. We followed a dedicated method based on difference imaging to extract the light curves of potential red giants in NGC 6791 and NGC 6819 from Kepler superstamp data. We extracted the asteroseismic parameters of the stars that showed solar-like oscillations. We performed an asteroseismic membership study to identify which of these stars are likely to be cluster members. Results. We found 149 red giant stars within the Kepler superstamps, 93 of which are likely cluster members. We were able to find 29 red giants that are not primary targets of Kepler, and therefore, their light curves had not been released previously. Five of these previously unknown red giants have a cluster membership probability greater than 95%.

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arXiv2023

Low-period spacing core-helium burning giants: `hot subdwarf analogues'?

Global stellar oscillations probe the internal structure of stars. In low- to intermediate-mass red giants, these oscillations provide signatures from both the outer regions of the star as well as from the core. These signatures are imprinted in e.g. the frequency of maximum oscillation power, and in the differences in periods of non-radial oscillations (period spacings), respectively. In core helium burning giants with masses below about 1.7 solar masses, i.e. stars that have gone through a helium flash, the asymptotic period spacings take values of about 220 -350 s at frequency of maximum oscillation power of $\sim$30-50 $μ$Hz. A set of stars with asymptotic period spacings lower than about 200 s at similar frequencies separations has recently been discovered by Elsworth and collaborators. In this work, we present a hypothesis for the formation scenario of these stars. We find that these stars can be the result of a mass-loss event at the end of the red-giant branch phase of stars massive enough to not have a degenerate core, i.e. one of the scenarios to form hot subdwarf stars. Therefore, these stars can be classified as `hot subdwarf analogues'. Interestingly, if mass loss continues gradually during the core helium burning phase, these stars turn hotter and denser, and could, therefore, be hot subdwarf progenitors as they shed more of their envelope.

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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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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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arXiv2020

The Aarhus red giants challenge II. Stellar oscillations in the red giant branch phase

Context. The large quantity of high-quality asteroseismic data that obtained from space-based photometric missions and the accuracy of the resulting frequencies motivate a careful consideration of the accuracy of computed oscillation frequencies of stellar models, when applied as diagnostics of the model properties. Aims. Based on models of red-giant stars that have been independently calculated using different stellar evolution codes, we investigate the extent to which the differences in the model calculation affect the model oscillation frequencies. Methods. For each of the models, which cover four different masses and different evolution stages on the red-giant branch, we computed full sets of low-degree oscillation frequencies using a single pulsation code and, from these frequencies, typical asteroseismic diagnostics. In addition, we carried out preliminary analyses to relate differences in the oscillation properties to the corresponding model differences. Results. In general, the differences in asteroseismic properties between the different models greatly exceed the observational precision of these properties, in particular for the nonradial modes whose mixed acoustic and gravity-wave character makes them sensitive to the structure of the deep stellar interior. In some cases, identifying these differences led to improvements in the final models presented here and in Paper I; here we illustrate particular examples of this. Conclusions. Further improvements in stellar modelling are required in order fully to utilise the observational accuracy to probe intrinsic limitations in the modelling. However, our analysis of the frequency differences and their relation to stellar internal properties provides a striking illustration of the potential of the mixed modes of red-giant stars for the diagnostics of stellar interiors.

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arXiv2020

Mirror principle and the red-giant bump: the battle of entropy in low-mass stars

The evolution of low-mass stars into red giants is still poorly understood. During this evolution the core of the star contracts and, simultaneously, the envelope expands -- a process known as the `mirror'. Additionally, there is a short phase where the trend for increasing luminosity is reversed. This is known as the red-giant-branch bump. We explore the underlying physical reasons for these two phenomena by considering the specific entropy distribution in the star and its temporal changes. We find that between the luminosity maximum and luminosity minimum of the bump there is no mirror present and the star is fully contracting. The contraction is halted and the star regains its mirror when the hydrogen-burning shell reaches the mean molecular weight discontinuity. This marks the luminosity minimum of the bump.

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arXiv2019

The Aarhus Red Giants Challenge I: Stellar structures in the red giant branch phase

(Abridged). We introduce the Aarhus Red Giants Challenge, a series of detailed comparisons between widely used stellar evolution and oscillation codes aiming at establishing the minimum level of uncertainties in properties of red giants arising solely from numerical implementations. Using 9 state-of-the-art stellar evolution codes, we defined a set of input physics and physical constants for our calculations and calibrated the convective efficiency to a specific point on the main sequence. We produced evolutionary tracks and stellar structure models at fixed radius along the red-giant branch for masses of 1.0 M$_\odot$, 1.5 M$_\odot$, 2.0 M$_\odot$, and 2.5 M$_\odot$, and compared the predicted stellar properties. Once models have been calibrated on the main sequence we find a residual spread in the predicted effective temperatures across all codes of ~20 K at solar radius and ~30-40 K in the RGB regardless of the considered stellar mass. The predicted ages show variations of 2-5% (increasing with stellar mass) which we track down to differences in the numerical implementation of energy generation. The luminosity of the RGB-bump shows a spread of about 10% for the considered codes, which translates into magnitude differences of ~0.1 mag in the optical V-band. We also compare the predicted [C/N] abundance ratio and found a spread of 0.1 dex or more for all considered masses. Our comparisons show that differences at the level of a few percent still remain in evolutionary calculations of red giants branch stars despite the use of the same input physics. These are mostly due to differences in the energy generation routines and interpolation across opacities, and call for further investigations on these matters in the context of using properties of red giants as benchmarks for astrophysical studies.

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arXiv2019

Scaling relations for solar-like oscillations: a review

The scaling relations for solar-like oscillations provide a translation of the features of the stochastic low-degree modes of oscillation in the Sun to predict the features of solar-like oscillations in other stars with convective outer layers. This prediction is based on their stellar mass, radius and effective temperature. Over time, the original scaling relations have been reversed in their use from predicting features of solar-like oscillations to deriving stellar parameters. Updates to the scaling relations as well as their reference values have been proposed to accommodate for the different requirements set by the change in their use. In this review the suggestions for improving the accuracy of the estimates of stellar parameters through the scaling relations for solar-like oscillations are presented together with a discussion of pros and cons of different approaches.

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arXiv2019

Stellar masses from granulation and oscillations of 23 bright red giants observed by BRITE - Constellation

Context: The study of stellar structure and evolution depends crucially on accurate stellar parameters. The photometry from space telescopes has provided superb data that allowed asteroseismic characterisation of thousands of stars. However, typical targets of space telescopes are rather faint and complementary measurements are difficult to obtain. On the other hand, the brightest, otherwise well-studied stars, are lacking seismic characterization. Aims: Our goal is to use the granulation and/or oscillation time scales measured from photometric time series of bright red giants (1.6$\leq$Vmag$\leq$5.3) observed with BRITE to determine stellar surface gravities and masses. Methods: We use probabilistic methods to characterize the granulation and/or oscillation signal in the power density spectra and the autocorrelation function of the BRITE time series. Results: We detect a clear granulation and/or oscillation signal in 23 red giant stars and extract the corresponding time scales from the power density spectra as well as the autocorrelation function of the BRITE time series. To account for the recently discovered non-linearity of the classical seismic scaling relations, we use parameters from a large sample of Kepler stars to re-calibrate the scalings of the high- and low-frequency components of the granulation signal. We develop a method to identify which component is measured if only one granulation component is statistically significant in the data. We then use the new scalings to determine the surface gravity of our sample stars, finding them to be consistent with those determined from the autocorrelation signal of the time series. We further use radius estimates from the literature to determine the stellar masses of our sample stars from the measured surface gravities. We also define a statistical measure for the evolutionary stage of the stars.

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