arXiv subjects

H. C. Spruit

Publications and source records attributed to H. C. Spruit.

At least 19 recordsLinked to original sources

arXiv2018

The formation of (very) slowly rotating stars

The slow rotation of some young stars and the extreme rotation periods of some Ap stars have so far defied explanation. The absence of sufficiently efficient braking mechanisms for newly formed stars points to the star formation process itself as the origin. I find that a mode of star formation exists by which a protostar can form without accreting angular momentum. It depends on the survival of a magnetic connection between the accreting matter and the birth cloud. The conditions for this process to operate are analyzed, and illustrated with a generic (scale-free) model. Depending on the initial rotation rate of the accreting matter, either a Keplerian disk forms, or the gas ends up rotating with the rotation period of the cloud, even if it is at a large distance. The boundary in parameter space between these two outcomes is sharp.

astro-ph.SR↗

arXiv2018

Disruption of a planet spiralling into its host star

The processes leading deformation and destruction of planets spiraling into the convective envelope of their host stars are described. The planet is compressed by the ram pressure, and deformed into a flattened shape for which a quantitative model is developed. Compression increases the planet's density contrast with the envelope and its gravitational binding energy. This increases the survivability especially of gas planets. An estimate is given for the depth of disruption by ram pressure, and for the subsequent fragmentation of the remnants. We show how the debris of rocky or iron planets, instead of mixing through the convection zone, sinks below the base of the convection zone. The time scale of the entire sequence of events is of the order of a few orbital times of the planet. If spiral-in of (partly) icy, rocky or iron planets has happened to the pre-main sequence Sun, it could account for the higher opacity below the base of the convection zone as inferred from helioseismology.

astro-ph.EP↗

arXiv2017

Magnetic fields in non-convective regions of stars

We review the current state of knowledge of magnetic fields inside stars, concentrating on recent developments concerning magnetic fields in stably stratified (zones of) stars, leaving out convective dynamo theories and observations of convective envelopes. We include the observational properties of A, B and O-type main-sequence stars, which have radiative envelopes, and the fossil field model which is normally invoked to explain the strong fields sometimes seen in these stars. Observations seem to show that Ap-type stable fields are excluded in stars with convective envelopes. Most stars contain both radiative and convective zones, and there are potentially important effects arising from the interaction of magnetic fields at the boundaries between them. Related to this, we discuss whether the Sun could harbour a magnetic field in its core. Recent developments regarding the various convective and radiative layers near the surfaces of early-type stars and their observational effects are examined. We look at possible dynamo mechanisms that run on differential rotation rather than convection. Finally we turn to neutron stars with a discussion of the possible origins for their magnetic fields.

astro-ph.SR↗

arXiv2016

Instability of mass transfer in a planet-star system

We show that the angular momentum exchange mechanism governing the evolution of mass transferring binary stars does not apply to Roche-lobe filling planets, because most of the angular momentum of the mass transferring stream is absorbed by the host star. Apart from a correction for the difference in specific angular momentum of the stream and the centre of mass of the planet, the orbit does not expand much on Roche-lobe overflow. We explore the conditions for dynamically unstable Roche-lobe overflow as a function of planet mass and mass and radius (age) of host star and equation of state of planet. For a Sun-like host, gas giant planets in a range of mass and entropy can undergo dynamical mass transfer. Examples of the evolution of the mass transfer process are given. Dynamic mass transfer of rocky planets depend somewhat sensitively on equation of state used. Silicate planets in the range $1 M_{\oplus} <M_{\mathrm{p}} < 10 M_{\oplus} $ typically go through a phase of dynamical mass transfer before settling to slow overflow when their mass drops to less than $1 M_{\oplus}$.

astro-ph.EP↗

arXiv2016

Essential Magnetohydrodynamics for Astrophysics

This text is intended as an introduction to magnetohydrodynamics in astrophysics, emphasizing a fast path to the elements essential for physical understanding. It assumes experience with concepts from fluid mechanics: the fluid equation of motion and the Lagrangian and Eulerian descriptions of fluid flow. In addition, the basics of vector calculus and elementary special relativity are needed. Not much knowledge of electromagnetic theory is required. In fact, since MHD is much closer in spirit to fluid mechanics than to electromagnetism, an important part of the learning curve is to overcome intuitions based on the vacuum electrodynamics of one's high school days. The first chapter (only 39 pp) is meant as a practical introduction including exercises. This is the `essential' part. The exercises are important as illustrations of the points made in the text (especially the less intuitive ones). Almost all are mathematically unchallenging. The supplement in chapter 2 contains further explanations, more specialized topics and connections to the occasional topic somewhat outside MHD. The emphasis is on physical understanding by the visualization of MHD processes, as opposed to more formal approaches.

astro-ph.IM↗

arXiv2015

The growth of helium burning cores

Helium burning in the convective cores of horizontal branch and `red clump' stars appears to involve a process of `ingestion' of unburnt helium into the core, the physics of which has not been identified yet. I show here that a limiting factor controlling the growth is the buoyancy of helium entering the denser C+O core. It yields a growth rate which scales directly with the convective luminosity of the core, and agrees with constraints on core size from current asteroseismology.

astro-ph.SR↗

arXiv2015

Convective settling in main sequence stars: Li and Be depletion

The process of convective settling is based on the assumption that a small fraction of the low-entropy downflows sink from the photosphere down to the bottom of the star's envelope convection zone retaining a substantial entropy contrast. We have previously shown that this process could explain the slow Li depletion observed in the Sun. We construct a parametric model of convective settling to investigate the dependence of Li and Be depletion on stellar mass and age. Our model is generally in good agreement with the Li abundances measured in open clusters and solar twins, although it seems to underestimate the Li depletion in the first ~1 Gyr. The model is also compatible with the Be abundances measured in a sample of field stars.

astro-ph.SR↗

arXiv2015

Small-scale dynamos on the solar surface: dependence on magnetic Prandtl number

The question of possible small-scale dynamo action in the surface layers of the Sun is revisited with realistic 3D MHD simulations. As in other MHD problems, dynamo action is found to be a sensitive function of the magnetic Prandtl number ${\rm P_{\rm m} }=ν/η$; it disappears below a critical value ${\rm P_{\rm c}}$ which is a function of the numerical resolution. At a grid spacing of 3.5 km, ${\rm P_{\rm c}}$ based on the hyperdiffusivities implemented in the code (STAGGER) is $\approx 1$, increasing with increasing grid spacing. As in other settings, it remains uncertain whether small scale dynamo action is present in the astrophysical limit where ${\rm P_{\rm m} }<<1$ and magnetic Reynolds number ${\rm R_m}\gg 1$. The question is discussed in the context of the strong effect that external stray fields are observed to have in generating and maintaining dynamo action in other numerical and laboratory systems, and in connection with the type-II hypertransient behavior of dynamo action observed in the absence of such external fields.

astro-ph.SR↗

arXiv2015

Overshooting by differential heating

On the long nuclear time scale of stellar main-sequence evolution, even weak mixing processes can become relevant for redistributing chemical species in a star. We investigate a process of "differential heating," which occurs when a temperature fluctuation propagates by radiative diffusion from the boundary of a convection zone into the adjacent radiative zone. The resulting perturbation of the hydrostatic equilibrium causes a flow that extends some distance from the convection zone. We study a simplified differential-heating problem with a static temperature fluctuation imposed on a solid boundary. The astrophysically relevant limit of a high Reynolds number and a low Péclet number (high thermal diffusivity) turns out to be interestingly non-intuitive. We derive a set of scaling relations for the stationary differential heating flow. A numerical method adapted to a high dynamic range in flow amplitude needed to detect weak flows is presented. Our two-dimensional simulations show that the flow reaches a stationary state and confirm the analytic scaling relations. These imply that the flow speed drops abruptly to a negligible value at a finite height above the source of heating. We approximate the mixing rate due to the differential heating flow in a star by a height-dependent diffusion coefficient and show that this mixing extends about $4\%$ of the pressure scale height above the convective core of a $10\,M_\odot$ zero-age main sequence star.

astro-ph.SR↗

arXiv2014

Brightness of the Sun's small scale magnetic field: proximity effects

The net effect of the small scale magnetic field on the Sun's (bolometric) brightness is studied with realistic 3D MHD simulations. The direct effect of brightening within the magnetic field itself is consistent with measurements in high-resolution observations. The high 'photometric accuracy' of the simulations, however, reveal compensating brightness effects that are hard to detect observationally. The influence of magnetic concentrations on the surrounding nonmagnetic convective flows (a 'proximity effect') reduces the brightness by an amount exceeding the brightening by the magnetic concentrations themselves. The net photospheric effect of the small scale field (~ -0.34% at a mean flux density of 50 G) is thus negative. We conclude that the main contribution to the observed positive correlation between the magnetic field and total solar irradiance must be magnetic dissipation in layers around the temperature minimum and above (not included in the simulations). This agrees with existing inferences from observations.

astro-ph.SR↗

arXiv2013

Overshooting by convective settling

We study a process of slow mixing in stars with convective envelopes, which is driven by the settling of cool downward plumes below the base of the convection zone. If a small fraction (of order $10^{-7}$) of the material cooled at the surface retains a significant entropy deficit while descending in plumes, it can reach the depth where lithium burning takes place. The model calculates the thermal response and mixing below the convection zone due to the settling process, assuming that the plumes arrive at the base of the convection zone with a broad range of entropy contrasts. We obtain a good fit to the observed lithium depletion in the Sun by assuming that the settling mass flux is distributed with respect to the entropy contrast as a power law with a slope around -2. We find convective settling to have a negligible influence on the stratification below the convection zone, although mixing induced by it could modify the gradient of helium concentration.

astro-ph.SR↗

arXiv2013

Semiconvection: theory

A model is developed for the transport of heat and solute in a system of double-diffusive layers under astrophysical conditions (viscosity and solute diffusivity low compared with the thermal diffusivity). The process of formation of the layers is not part of the model but, as observed in geophysical and laboratory settings, is assumed to be fast compared to the life time of the semiconvective zone. The thickness of the layers is \tbf{a} free parameter of the model. When the energy flux of the star is specified, the effective semiconvective diffusivities are only weakly dependent on this parameter. An estimate is given of the evolution of layer thickness with time in a semiconvective zone. The model predicts that the density ratio has a maximum for which a stationary layered state can exist, $R_ρ\la \mr{Le}^{-1/2}$. Comparison of the model predictions with a grid of numerical simulations is presented in a companion paper.

astro-ph.SR↗

arXiv2013

The large scale magnetic fields of thin accretion disks

Large scale magnetic field threading an accretion disk is a key ingredient in the jet formation model. The most attractive scenario for the origin of such a large scale field is the advection of the field by the gas in the accretion disk from the interstellar medium or a companion star. However, it is realized that outward diffusion of the accreted field is fast compared to the inward accretion velocity in a geometrically thin accretion disk if the value of the Prandtl number Pm is around unity. In this work, we revisit this problem considering the angular momentum of the disk is removed predominantly by the magnetically driven outflows. The radial velocity of the disk is significantly increased due to the presence of the outflows. Using a simplified model for the vertical disk structure, we find that even moderately weak fields can cause sufficient angular momentum loss via a magnetic wind to balance outward diffusion. There are two equilibrium points, one at low field strengths corresponding to a plasma-beta at the midplane of order several hundred, and one for strong accreted fields, beta~1. We surmise that the first is relevant for the accretion of weak, possibly external, fields through the outer parts of the disk, while the latter one could explain the tendency, observed in full 3D numerical simulations, of strong flux bundles at the centers of disk to stay confined in spite of strong MRI turbulence surrounding them.

astro-ph.HE↗

arXiv2012

The relative significance of the H-index

Use of the Hirsch-index ($h$) as measure of an author's visibility in the scientific literature has become popular as an alternative to a gross measure like total citations (c). I show that, at least in astrophysics, $h$ correlates tightly with overall citations. The mean relation is $h=0.5(\sqrt c+1)$. Outliers are few and not too far from the mean, especially if `normalized' ADS citations are used for $c$ and $h$. Whatever the theoretical reasoning behind it, the Hirsch index in practice does not appear to measure something significantly new.

astro-ph.IM↗

arXiv2011

A binary merger origin for inflated hot Jupiter planets

We hypothesize that hot Jupiters with inflated sizes represent a separate planet formation channel,the merging of two low-mass stars. We show that the abundance and properties of W UMa stars and low mass detached binaries are consistent with their being possible progenitors. The degree of inflation of the transiting hot Jupiters correlates with their expected spiral-in life time by tidal dissipation, and this could indicate youth if the stellar dissipation parameter Q'* is sufficiently low. Several Jupiter-mass planets can form in the massive compact disk formed in a merger event. Gravitational scattering between them can explain the high incidence of excentric, inclined, and retrograde orbits. If the population of inflated planets is indeed formed by a merger process, their frequency should be much higher around blue stragglers than around T Tauri stars.

astro-ph.SR↗

arXiv2011

The brightness of magnetic field concentrations in the quiet Sun

In addition to the `facular' brightening of active regions, the quiet Sun also contains a small scale magnetic field with associated brightenings in continuum radiation. We measure this contribution of quiet regions to the Sun's brightness from high spatial resolution (0"16-0"32) observations of the Swedish 1-m Solar Telescope (SST) and Hinode satellite. The line-of-sight magnetic field and continuum intensity near \ion{Fe}{i} 6302.5 Å are used to quantify the correlation between field strength and brightness. The data show that magnetic flux density contains a significant amount of intrinsically weak fields that contribute little to brightness. We show that with data of high spatial resolution a calibration of magnetic flux density as a proxy for brightness excess is possible. In the SST data, the magnetic brightening of a quiet region with an average (unsigned) flux density of 10 G is about 0.15%. In the Hinode data, and in SST data reduced to Hinode resolution, the measured brightening is some 40% lower. With appropriate correction for resolution, magnetic flux density can be used as a reliable proxy in regions of small scale mixed polarity. The measured brightness effect is larger than the variation of irradiance over a solar cycle. It is not clear, however, if this quiet Sun contribution actually varies significantly. \keywords{Sun: surface magnetism -- photosphere -- solar-terrestrial relations}

astro-ph.SR↗

arXiv2011

Semiconvection

A grid of numerical simulations of double-diffusive convection is presented for astrophysical conditions. As in laboratory and geophysical cases convection takes place in a layered form. A translation between the astrophysical fluid mechanics and incompressible (Boussinesq) approximation is given, valid for thin layers. Its validity is checked by comparison of the results of fully compressible and Boussinesq simulations of semiconvection. A fitting formula is given for the superadiabatic gradient as a function of this parameter. The superadiabaticity depends on the thickness $d$ of the double diffusive layers, for which no good theory is available, but the effective He-diffusion coefficient is nearly independent of $d$. For a fiducial main sequence model (15 $M_\odot$) the inferred mixing time scale is of the order $10^{10}$ yr.

astro-ph.SR↗

arXiv2010

Striation and convection in penumbral filaments

Observations with the 1-m Swedish Solar Telescope of the flows seen in penumbral filaments are presented. Time sequences of bright filaments show overturning motions strikingly similar to those seen along the walls of small isolated structures in the active regions. The filaments show outward propagating striations with inclination angles suggesting that they are aligned with the local magnetic field. We interpret it as the equivalent of the striations seen in the walls of small isolated magnetic structures. Their origin is then a corrugation of the boundary between an overturning convective flow inside the filament and the magnetic field wrapping around it. The outward propagation is a combination of a pattern motion due to the downflow observed along the sides of bright filaments, and the Evershed flow. The observed short wavelength of the striation argues against the existence of a dynamically significant horizontal field inside the bright filaments. Its intensity contrast is explained by the same physical effect that causes the dark cores of filaments, light bridges and `canals'. In this way striation represents an important clue to the physics of penumbral structure and its relation with other magnetic structures on the solar surface. We put this in perspective with results from the recent 3-D radiative hydrodynamic simulations.

astro-ph.SR↗