[Paper Review] Hydrodynamical simulations of convection-related stellar micro-variability

Fredrik Svensson, H.‐G. Ludwig|arXiv (Cornell University)|Sep 29, 2004

Solar and Space Plasma Dynamics7 citations

TL;DR

This study uses 3D CO 5 BOLD hydrodynamical simulations to model convection-related photometric and photocentric variability across the Hertzsprung-Russell diagram, finding a systematic increase in variability with decreasing surface gravity. The key result is that while granulation noise in the Sun and Procyon differs by a factor of ≈3 in amplitude, only nearby giants are significantly affected by photocentric variability at GAIA mission precision levels.

ABSTRACT

We used a series of COBOLD hydrodynamical model atmospheres covering stellar objects from white dwarfs to red giants to derive theoretical estimates of the photometric and photocentric stellar variability in wavelength-integrated light across the Hertzsprung-Russell diagram. We validated our models against solar measurements from the SOHO/VIRGO instrument. Within our set of models we find a systematic increase of the photometric as well as photocentric variability - which turn out to be closely connected - with decreasing surface gravity. The estimated absolute levels of the photocentric variability do not affect astrometric observations on a precision level expected to be achieved by the GAIA mission - with the exception of close-by giants. The case of supergiants remains to be investigated. In view of the ongoing debate about the photometric non-detection of p-modes in Procyon by the Canadian MOST satellite we remark that we obtain a factor of ca. 3 in amplitude between the granular background noise in the Sun and Procyon. This statement refers to a particular representation of temporal power spectra as discussed in Sect. 5.

Motivation & Objective

• To model convection-related micro-variability in stellar atmospheres across diverse stellar types.
• To quantify photometric and photocentric variability as a function of surface gravity, effective temperature, and metallicity.
• To assess the impact of granulation noise on high-precision photometric and astrometric missions like GAIA and Kepler.
• To validate model predictions against Soho/Virgo solar observations.
• To investigate the relative contribution of granulation versus magnetic activity in stellar variability.

Proposed method

• Employed 3D radiation-hydrodynamics simulations using the CO 5 BOLD code to generate local-box model atmospheres.
• Simulated emergent intensity and temporal evolution of granulation patterns across a range of stellar parameters.
• Extrapolated local simulation patches to disk-integrated observables via statistical tiling of the stellar hemisphere.
• Calculated photometric and photocentric variability using time-series data from simulations, accounting for inclination effects.
• Used spectral power density analysis to compare variability amplitudes across models, particularly between the Sun and Procyon.
• Quantified photocentric displacement standard deviation as a function of surface gravity and granular properties.

Experimental results

Research questions

• RQ1 How does convection-related photometric variability vary across the Hertzsprung-Russell diagram?
• RQ2 What is the amplitude of photocentric displacement due to granulation, and how does it scale with surface gravity?
• RQ3 How does metallicity affect the amplitude of brightness fluctuations in stellar granulation?
• RQ4 To what extent does granulation noise limit the precision of astrometric and photometric exoplanet detection missions?
• RQ5 Why is there a discrepancy between theoretical granulation amplitudes and the non-detection of p-modes in Procyon by the MOST satellite?

Key findings

• Photometric and photocentric variability increase systematically with decreasing surface gravity, showing a nearly linear relationship.
• The standard deviation of photocentric displacement reaches 3×10⁻⁴ AU (0.3 mas/D[pc]) for a red giant with log g = 1.0, affecting only nearby giants at GAIA precision levels.
• A factor of ≈3 in amplitude difference is found between the granular background noise in the Sun and Procyon, depending on spectral representation.
• Brightness fluctuations decrease with lower metallicity due to higher densities at τ=1, reducing convective fluctuations.
• The product of relative intensity contrast (δI_rms) and pressure scale height (H_p^surf) correlates strongly with photocentric displacement, indicating a physical link to granular size and contrast.
• Linear extrapolation to supergiants is unreliable due to sphericity effects altering convection patterns compared to Cartesian simulations.