arXiv subjects

Evan H. Anders

Publications and source records attributed to Evan H. Anders.

28 records · Page 2Linked to original sources

arXiv2022

Stellar convective penetration: parameterized theory and dynamical simulations

Most stars host convection zones in which heat is transported directly by fluid motion, but the behavior of convective boundaries is not well understood. Here we present 3D numerical simulations which exhibit penetration zones: regions where the entire luminosity \emph{could} be carried by radiation, but where the temperature gradient is approximately adiabatic and convection is present. To parameterize this effect, we define the "penetration parameter" $\mathcal{P}$ which compares how far the radiative gradient deviates from the adiabatic gradient on either side of the Schwarzschild convective boundary. Following Roxburgh (1989) and Zahn (1991), we construct an energy-based theoretical model in which $\mathcal{P}$ controls the extent of penetration. We test this theory using 3D numerical simulations which employ a simplified Boussinesq model of stellar convection. The convection is driven by internal heating and we use a height-dependent radiative conductivity; this allows us to separately specify $\mathcal{P}$ and the stiffness $\mathcal{S}$ of the radiative-convective boundary. We find significant convective penetration in all simulations. Our simple theory describes the simulations well. Penetration zones can take thousands of overturn times to develop, so long simulations or accelerated evolutionary techniques are required. In stars, we expect $\mathcal{P} \approx 1$ and in this regime our results suggest that convection zones may extend beyond the Schwarzschild boundary by up to $\sim$20-30% of a mixing length. We present a MESA stellar model of the Sun which employs our parameterization of convective penetration as a proof of concept. We discuss prospects for extending these results to more realistic stellar contexts.

astro-ph.SR↗

arXiv2022

Schwarzschild and Ledoux are equivalent on evolutionary timescales

Stellar evolution models calculate convective boundaries using either the Schwarzschild or Ledoux criterion, but confusion remains regarding which criterion to use. Here we present a 3D hydrodynamical simulation of a convection zone and adjacent radiative zone, including both thermal and compositional buoyancy forces. As expected, regions which are unstable according to the Ledoux criterion are convective. Initially, the radiative zone adjacent to the convection zone is Schwarzschild-unstable but Ledoux-stable due to a composition gradient. Over many convective overturn timescales the convection zone grows via entrainment. The convection zone saturates at the size originally predicted by the Schwarzschild criterion, although in this final state the Schwarzschild and Ledoux criteria agree. Therefore, the Schwarzschild criterion should be used to determine the size of stellar convection zones, except possibly during short-lived evolutionary stages in which entrainment persists.

astro-ph.SR↗

arXiv2022

A Transparent Window into Early-Type Stellar Variability

Subsurface convection zones are ubiquitous in early-type stars. Driven by narrow opacity peaks, these thin convective regions transport little heat but play an important role in setting the magnetic properties and surface variability of stars. Here we demonstrate that these convection zones are \emph{not} present in as wide a range of stars as previously believed. In particular, there are regions which 1D stellar evolution models report to be convectively unstable but which fall below the critical Rayleigh number for onset of convection. For sub-solar metallicity this opens up a \emph{stability window} in which there are no subsurface convection zones. For LMC metallicity this surface stability region extends roughly between $8M_\odot$ and $16M_\odot$, increasing to $8M_\odot$ -- $35M_\odot$ for SMC metallicity. Such windows are then an excellent target for probing the relative influence of subsurface convection and other sources of photometric variability in massive stars.

astro-ph.SR↗

arXiv2021

Surface Manifestation of Stochastically Excited Internal Gravity Waves

Recent photometric observations of massive stars show ubiquitous low-frequency "red-noise" variability, which has been interpreted as internal gravity waves (IGWs). Simulations of IGWs generated by convection show smooth surface wave spectra, qualitatively matching the observed red-noise. On the other hand, theoretical calculations by Shiode et al (2013) and Lecoanet et al (2019) predict IGWs should manifest at the surface as regularly-spaced peaks associated with standing g-modes. In this work, we compare these theoretical approaches to simplified 2D numerical simulations. The simulations show g-mode peaks at their surface, and are in good agreement with Lecoanet et al (2019). The amplitude estimates of Shiode et al (2013) did not take into account the finite width of the g-mode peaks; after correcting for this finite width, we find good agreement with simulations. However, simulations need to be run for hundreds of convection turnover times for the peaks to become visible; this is a long time to run a simulation, but a short time in the life of a star. The final spectrum can be predicted by calculating the wave energy flux spectrum in much shorter simulations, and then either applying the theory of Shiode et al (2013) or Lecoanet et al (2019).

astro-ph.SR↗

arXiv2021

A Refined Model of Convectively-Driven Flicker in Kepler Light Curves

Light curves produced by the Kepler mission demonstrate stochastic brightness fluctuations (or "flicker") of stellar origin which contribute to the noise floor, limiting the sensitivity of exoplanet detection and characterization methods. In stars with surface convection, the primary driver of these variations on short (sub-eight-hour) timescales is believed to be convective granulation. In this work, we improve existing models of this granular flicker amplitude, or $F_8$, by including the effect of the Kepler bandpass on measured flicker, by incorporating metallicity in determining convective Mach numbers, and by using scaling relations from a wider set of numerical simulations. To motivate and validate these changes, we use a recent database of convective flicker measurements in Kepler stars, which allows us to more fully detail the remaining model--prediction error. Our model improvements reduce the typical misprediction of flicker amplitude from a factor of 2.5 to 2. We rule out rotation period and strong magnetic activity as possible explanations for the remaining model error, and we show that binary companions may affect convective flicker. We also introduce an "envelope" model which predicts a range of flicker amplitudes for any one star to account for some of the spread in numerical simulations, and we find that this range covers 78% of observed stars. We note that the solar granular flicker amplitude is lower than most Sun-like stars. This improved model of convective flicker amplitude can better characterize this source of noise in exoplanet studies as well as better inform models and simulations of stellar granulation.

astro-ph.SR↗

arXiv2020

Convective dynamics with mixed temperature boundary conditions: why thermal relaxation matters and how to accelerate it

Astrophysical simulations of convection frequently impose different thermal boundary conditions at the top and the bottom of the domain in an effort to more accurately model natural systems. In this work, we study Rayleigh-Benard convection (RBC) under the Boussinesq approximation. We examine simulations with mixed temperature boundary conditions in which the flux is fixed at the bottom boundary and the temperature is fixed at the top ("FT"). We aim to understand how FT boundaries change the nature of the convective solution compared to the traditional choice of thermal boundaries, in which the temperature is fixed at the top and bottom of the domain ("TT"). We demonstrate that the timescale of thermal relaxation for FT simulations is dependent upon the initial conditions. "Classic" initial conditions which employ a hydrostatically -- and thermally -- balanced linear temperature profile exhibit a long thermal relaxation. This long relaxation is not seen in FT simulations which use a TT simulation's nonlinear state as initial conditions ("TT-to-FT"). In the thermally relaxed, statistically stationary state, the mean behavior of an FT simulation corresponds to an equivalent simulation with TT boundaries, and time- and volume-averaged flow statistics like the Nusselt number and the Peclet number are indistinguishable between FT and TT simulations. FT boundaries are fundamentally asymmetric, and we examine the asymmetries that these boundaries produce in the flow. We find that the fixed-flux boundary produces more extreme temperature events than the fixed-temperature boundary. However, these near-boundary asymmetries do not measurably break the symmetry in the convective interior. We briefly explore rotating RBC to demonstrate that our findings with respect to thermal relaxation carry over to this more complex case, and to show the power of TT-to-FT initial conditions.

physics.flu-dyn↗

arXiv2019

Entropy Rain: Dilution and Compression of Thermals in Stratified Domains

Large-scale convective flows called giant cells were once thought to transport the Sun's luminosity in the solar convection zone, but recent observations have called their existence into question. In place of large-scale flows, some authors have suggested the solar luminosity may instead be transported by small droplets of rapidly falling, low entropy fluid. This "entropy rain" could propagate as dense vortex rings, analogous to rising buoyant thermals in the Earth's atmosphere. In this work, we develop an analytical theory describing the evolution of dense, negatively buoyant thermals. We verify the theory with 2D cylindrical and 3D cartesian simulations of laminar, axisymmetric thermals in highly stratified atmospheres. Our results show that dense thermals fall in two categories: a stalling regime in which the droplets slow down and expand, and a falling regime in which the droplets accelerate and shrink as they propagate downwards. We estimate that solar downflows are in the falling regime and maintain their entropy perturbation against diffusion until they reach the base of the convection zone. This suggests that entropy rain may be an effective nonlocal mechanism for transporting the solar luminosity.

astro-ph.SR↗

arXiv2019

Predicting the Rossby number in convective experiments

The Rossby number is a crucial parameter describing the degree of rotational constraint on the convective dynamics in stars and planets. However, it is not an input to computational models of convection but must be measured ex post facto. Here, we report the discovery of a new quantity, the Predictive Rossby number, which is both tightly correlated with the Rossby number and specified in terms of common inputs to numerical models. The Predictive Rossby number can be specified independent of Rayleigh number, allowing suites of numerical solutions to separate the degree of rotational constraint from the strength of the driving of convection. We examine the scaling of convective transport in terms of the Nusselt number and the degree of turbulence in terms of the Reynolds number of the flow, and we find scaling laws nearly identical to those in nonrotational convection at low Rossby number when the Predictive Rossby number is held constant. Finally, we describe the boundary layers as a function of increasing turbulence at constant Rossby number.

astro-ph.SR↗

arXiv2018

Accelerated evolution of convective simulations

High Peclet number, turbulent convection is a classic system with a large timescale separation between flow speeds and the thermal relaxation time. In this paper, we present a method of fast-forwarding through the long thermal relaxation of convective simulations, and we test the validity of this method. This accelerated evolution (AE) method involves measuring the dynamics of convection early in a simulation and using its characteristics to adjust the mean thermodynamic profile within the domain towards its evolved state. We study Rayleigh-Bénard convection as a test case for AE. Evolved flow properties of AE solutions are measured to be within a few percent of solutions which are reached through standard evolution (SE) over a full thermal timescale. At the highest values of the Rayleigh number at which we compare SE and AE, we find that AE solutions require roughly an order of magnitude fewer computing hours to evolve than SE solutions.

physics.flu-dyn↗

arXiv2017

Convective heat transport in stratified atmospheres at low and high Mach number

We study fully compressible convection in the context of plane-parallel, polytropically stratified atmospheres. We perform a suite of 2D and 3D simulations in which we vary the initial superadiabaticity ($ε$) and the Rayleigh number (Ra) while fixing the initial density stratification, aspect ratio, and Prandtl number. The evolved heat transport, quantified by the Nusselt number (Nu), follows scaling relationships similar to those found in the well-studied, incompressible Rayleigh-Bénard problem. This scaling holds up in both 2D and 3D and is not appreciably affected by the magnitude of $ε$.

physics.flu-dyn↗