The underlying physical meaning of the νmax νc relation

By K. Belkacem, M. Goupil, M. Dupret, R. Samadi, F. Baudin, A. Noels, B. Mosser. 2011

166 citations recorded by the source corpus.

Asteroseismology of stars that exhibit solar-like oscillations are enjoying a growing interest with the wealth of observational results obtained with the CoRoT and Kepler missions. In this framework, scaling laws between asteroseismic quantities and stellar parameters are becoming essential tools to study a rich variety of stars. However, the physical underlying mechanisms of those scaling laws are still poorly known. Our objective is to provide a theoretical basis for the scaling between the frequency of the maximum in the power spectrum (νmax) of solar-like oscillations and the cut-off frequency (νc). Using the SoHO GOLF observations together with theoretical considerations, we first confirm that the maximum of the height in oscillation power spectrum is determined by the so-called plateau of the damping rates. The physical origin of the plateau can be traced to the destabilizing effect of the Lagrangian perturbation of entropy in the upper-most layers, which becomes important when the modal period and the local thermal relaxation time-scale are comparable. Based on this analysis, we then find a linear relation between νmax and νc, with a coefficient that depends on the ratio of the Mach number of the exciting turbulence to the third power to the mixing-length parameter.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/977ce63beab768174733bbc3dedf756410b2c1cc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. D. Huber
2. Jo Bovy
3. W. Chaplin
4. D. Stello
5. Hans-Walter Rix
6. T. Bedding
7. A. Miglio
8. G. Marcy

In Instrumentation

1. D. Huber
2. D. Stello
3. W. Chaplin
4. T. Bedding
5. Jo Bovy
6. B. Mosser
7. Hans-Walter Rix
8. G. Marcy

Citations in the corpus

• Asteroseismology and Gaia: Testing Scaling Relations Using 2200 Kepler Stars with TGAS Parallaxes (2017, result): “Additionally, uncertainties in modeling the driving and damping of oscillations typically prevent theoretical tests of the nmax scaling relation, though some studies have shown encouraging results (Belkacem et al. 2011).”
• AN ANCIENT EXTRASOLAR SYSTEM WITH FIVE SUB-EARTH-SIZE PLANETS (2015, background): “The frequency of maximum oscillation amplitude scales to very good approximation as g T −1/2 eff (Brown et al. 1991; Kjeldsen & Bedding 1995; Belkacem et al. 2011).”
• Gaia FGK benchmark stars: Effective temperatures and surface gravities (2015, unknown): “It has been shown (e.g. Belkacem et al. 2011) that this parameter is proportional to the surface gravity and inversely proportional to the square root of the effective temperature.”
• Ages and fundamental properties of Kepler exoplanet host stars from asteroseismology (2015, background): “The 〈∆ν〉 relation in equation 11 has direct theoretical foundation while the νmax scaling in equation 12 is mostly an empirical relation (although see Belkacem et al. 2011).”
• THE APOKASC CATALOG: AN ASTEROSEISMIC AND SPECTROSCOPIC JOINT SURVEY OF TARGETS IN THE KEPLER FIELDS (2014, background): “It has been shown to scale to good approximation as gT −1/2 eff (Brown et al. 1991; Kjeldsen & Bedding 1995; Chaplin et al. 2008; Stello et al. 2009b; Belkacem et al. 2011), where g is the surface gravity and Teff is the effective temperature of the star.”
• Thermohaline instability and rotation-induced mixing - III. Grid of stellar models and asymptotic asteroseismic quantities from the pre-main sequence up to the AGB for low- and intermediate-mass stars of various metallicities (2012, background): “Belkacem et al. (2011) proved that the frequency νmax at which the oscillation modes reach their strongest amplitudes is approximatively proportional to the acoustic cut-off frequency, as suspected by Brown et al. (1991) and Kjeldsen & Bedding (1995), such that νmax = νmax, ( M M ) ( R R )−2 ( Teff…”
• Asteroseismology of 16,000 Kepler Red Giants: Global Oscillation Parameters, Masses, and Radii (2018, background): “The νmax calibration is more difficult since it cannot be calculated theoretically so far (Belkacem et al. 2011).”
• The connection between stellar granulation and oscillation as seen by the Kepler mission (2014, methodology): “…is expected to be proportional to the acoustic cutofffrequency (νac ∝ g/√Teff) of the stellar atmosphere (e.g., Brown et al. 1991; Kjeldsen & Bedding 1995; Belkacem et al. 2011). and large systematic differences have been found between different methods (see Mathur et al. 2011, for a comparison).”
• Red giant masses and ages derived from carbon and nitrogen abundances (2015, unknown): “…is related to the acoustic cut-off frequency (Brown et al. 1991), which mainly depends on surface gravity and temperature (Kjeldsen & Bedding 1995; Belkacem et al. 2011), The standard seismic scaling relations, equations (1) and (2), can be combined to derive the mass of a star as (3) We adopt…”
• The Second APOKASC Catalog: The Empirical Approach (2018, background): “The empirical νmax scaling relation has a weaker theoretical basis than the ∆ν scaling relation, although there have been detailed physical studies of its basis (Belkacem et al. 2011).”