Theoretical Scaling Relations Research Articles

A Close Pair of Orbiters Embedded in a Gaseous Disk: The Repulsive Effect

We develop a theoretical framework and use 2D hydrodynamical simulations to study the repulsive effect between two close orbiters embedded in an accretion disk. We consider orbiters on fixed Keplerian orbits with masses low enough to open shallow gaps. The simulations indicate that the repulsion is larger for more massive orbiters and decreases with the orbital separation and the disk’s viscosity. We use two different assumptions to derive theoretical scaling relations for the repulsion. A first scenario assumes that each orbiter absorbs the angular momentum deposited in its horseshoe region by the companion’s wake. A second scenario assumes that the corotation torques of the orbiters are modified because the companion changes the underlying radial gradient of the disk surface density. We find a substantial difference between the predictions of these two scenarios. The first one fails to reproduce the scaling of the repulsion with the disk viscosity and generally overestimates the strength of the repulsion. The second scenario, however, gives results that are broadly consistent with those obtained in the simulations.

Galactic Magnetic Fields. I. Theoretical Model and Scaling Relations

Galactic dynamo models have generally relied on input parameters that are very challenging to constrain. We address this problem by developing a model that uses observable quantities as input: the galaxy rotation curve, the surface densities of the gas, stars and star formation rate, and the gas temperature. The model can be used to estimate parameters of the random and mean components of the magnetic field, as well as the gas scale height, root-mean-square velocity and the correlation length and time of the interstellar turbulence, in terms of the observables. We use our model to derive theoretical scaling relations for the quantities of interest, finding reasonable agreement with empirical scaling relations inferred from observation. We assess the dependence of the results on different assumptions about turbulence driving, finding that agreement with observations is improved by explicitly modeling the expansion and energetics of supernova remnants. The model is flexible enough to include alternative prescriptions for the physical processes involved, and we provide links to two open-source python programs that implement it.

Detection of p-mode Oscillations in HD 35833 with NEID and TESS

We report the results of observations of p-mode oscillations in the G0 subgiant star HD 35833 in both radial velocities and photometry with NEID and TESS, respectively. We achieve separate, robust detections of the oscillation signal with both instruments (radial velocity amplitude A RV = 1.11 ± 0.09 m s−1, photometric amplitude A phot = 6.42 ± 0.60 ppm, frequency of maximum power μHz, and mode spacing Δν = 36.65 ± 0.96 μHz) as well as a nondetection in a TESS sector concurrent with the NEID observations. These data shed light on our ability to mitigate the correlated noise impact of oscillations with radial velocities alone and on the robustness of commonly used asteroseismic scaling relations. The NEID data are used to validate models for the attenuation of oscillation signals for exposure times , and we compare our results to predictions from theoretical scaling relations and find that the observed amplitudes are weaker than expected by >4σ, hinting at gaps in the underlying physical models.

Filtration Rates and Scaling in Demosponges

Demosponges are modular filter-feeding organisms that are made up of aquiferous units or modules with one osculum per module. Such modules may grow to reach a maximal size. Various demosponge species show a high degree of morphological complexity, which makes it difficult to classify and scale them regarding filtration rate versus sponge size. In this regard, we distinguish between: (i) small single-osculum sponges consisting of one aquiferous module, which includes very small explants and larger explants; (ii) multi-oscula sponges consisting of many modules, each with a separate osculum leading to the ambient; and (iii) large single-osculum sponges composed of many aquiferous modules, each with an exhalant opening (true osculum) leading into a common large spongocoel (atrium), which opens to the ambient via a static pseudo-osculum. We found the theoretical scaling relation between the filtration rate (F) versus volume (V) for (i) a single-osculum demosponge to be F = a3V2/3, and hence the volume-specific filtration rate to scale as F/V ≈ V−1/3. This relation is partly supported by experimental data for explants of Halichondria panicea, showing F/V = 2.66V−0.41. However, for multi-oscula sponges, many of their modules may have reached their maximal size and hence their maximal filtration rate, which would imply the scaling F/V ≈ constant. A similar scaling would be expected for large pseudo-osculum sponges, provided their volume was taken to be the structural tissue volume that holds the pumping units, and not the total volume that includes the large atrium volume of water. This may explain the hitherto confusing picture that has emerged from the power-law correlation (F/V = aVb) of many various types of demosponges that show a range of negative b-exponents. The observed sharp decline in the volume-specific filtration rate of demosponges from their very small to larger sizes is discussed.

Morphological Classification of the Convective Regimes in Rotating Stars

Abstract We present a set of numerical simulations that model the convection zones of solar-like stars. With this suite of numerical experiments, we explore how the nature of the convective structures transitions through a series of morphological regimes as the reduced Rayleigh number increases. Convection first manifests as a belt of rotationally aligned, convective, Taylor columns that circumscribes the equator. As the supercriticality increases, the poles begin to convect, initially in a cellular form, but eventually a plumy form emerges. Finally, at extremely high values of the Rayleigh number, a weakly rotating regime is achieved with antisolar differential rotation, i.e., the equator rotates more slowly than the poles. For all of these regimes, we provide theoretical and empirical scaling relations that summarize how global quantities—such as the bulk Rossby number and Reynolds number—scale with the Rayleigh and Ekman numbers. We demonstrate that a Rossby number based on the properties of the thermal boundary layer that clings to the outer surface of the convection zone works particularly well to predict the transition to antisolar differential rotation.

The X-Ray Emission Effectiveness of Plasma Mirrors: Reexamining Power-Law Scaling for Relativistic High-Order Harmonic Generation

Ultrashort pulsed lasers provide uniquely detailed access to the ultrafast dynamics of physical, chemical, and biological systems, but only a handful of wavelengths are directly produced by solid-state lasers, necessitating efficient high-power frequency conversion. Relativistic plasma mirrors generate broadband power-law spectra, that may span the gap between petawatt-class infrared laser facilities and x-ray free-electron lasers; despite substantial theoretical work the ultimate efficiency of this relativistic high-order-harmonic generation remains unclear. We show that the coherent radiation emitted by plasma mirrors follows a power-law distribution of energy over frequency with an exponent that, even in the ultrarelativistic limit, strongly depends on the ratio of laser intensity to plasma density and exceeds the frequently quoted value of −8/3 over a wide range of parameters. The coherent synchrotron emission model, when adequately corrected for the finite width of emitting electron bunches, is not just valid for p-polarized light and thin foil targets, but generally describes relativistic harmonic generation, including at normal incidence and with finite-gradient plasmas. Our numerical results support the ω−4/3 scaling of the synchrotron emission model as a limiting efficiency of the process under most conditions. The highest frequencies that can be generated with this scaling are usually restricted by the width of the emitting electron bunch rather than the Lorentz factor of the fastest electrons. The theoretical scaling relations developed here suggest, for example, that with a 20-PW 800-nm driving laser, 1 TW/harmonic can be produced for 1-keV photons.

Two’s a crowd? Characterising the effect of photometric contamination on the extraction of the global asteroseismic parameter νmax in red-giant binaries

Context. Theoretical scaling relations for solar-like oscillators and red giants are widely used to estimate fundamental stellar parameters. The accuracy and precision of these relations have often been questioned in the literature, with studies often utilising binarity for model-independent validation. However, it has not been tested if the photometric effects of binarity introduce a systematic effect on the extraction of the seismic properties of the pulsating component(s). Aims. In this paper, we present an estimation of the impact of a contaminating photometric signal with a distinct background profile on the global asteroseismic parameter νmax through the analysis of synthetic red-giant binary light curves. Methods. We generated the pulsational and granulation parameters for single red giants with different masses, radii and effective temperatures from theoretical scaling relations and use them to simulate single red-giant light curves with the characteristics of Kepler long-cadence photometric data. These are subsequently blended together according to their light ratio to generate binary red-giant light curves of various configurations. We then performed a differential analysis to characterise the systematic effects of binarity on the extraction of νmax. Results. We quantify our methodological uncertainties through the analysis of single red-giant light curves, both in the presence and absence of granulation. This is used as a reference for our subsequent differential binary analysis, where we find that the νmax extraction for red-giant power spectra featuring overlapping power excesses is unreliable if unconstrained priors are used. Outside of this scenario, we obtain results that are nearly identical to single-star case. Conclusions. We conclude that (i) the photometric effects of binarity on the extraction of νmax are largely negligible as long as the power excesses of the individual components do not overlap, and that (ii) there is minimal advantage to using more than two super-Lorentzian components to model the granulation signal of a binary red-giant.

Tunable Toughness of Model Fibers With Bio-Inspired Progressive Uncoiling Via Sacrificial Bonds and Hidden Length

Nature has a proven track record of advanced materials with outstanding mechanical properties, which has been the focus of recent research. A well-known trade-off between ultimate strength and toughness is one of the main challenges in materials design. Progress has been made by mimicking tough biological fibers by applying the concepts of (1) sacrificial bond and (2) hidden length, providing a so-called “safety-belt” for biological materials. Prior studies indicate a relatively common behavior across scales, from nano- to macro-, suggesting the potential of a generalized theoretical mechanistic framework. Here, we undertake molecular dynamics (MD) based simulation to investigate the mechanical properties of model nanoscale fibers. We explore representative models of serial looped or coiled fibers with different parameters—specifically number of loops, loop radii, cross-link strength, and fiber stiffness—to objectively compare strength, extensibility, and fiber toughness gain. Observing consistent saw-tooth like behavior, and adapting worm-like chain (WLC) mechanics (i.e., pseudo-entropic elasticity), a theoretical scaling relation which can describe the fiber toughness gain as a function of the structural factors is developed and validated by simulation. The theoretical model fits well with the simulation results, indicating that engineering the mechanical response based on controlled structure is possible. The work lays the foundation for the design of uniaxial metamaterials with tunable and predictable tensile behavior and superior toughness.

Mocca-survey Database I: Galactic globular clusters harbouring a black hole subsystem

There have been increasing theoretical speculations and observational indications that certain globular clusters (GCs) could contain a sizeable population of stellar mass black holes (BHs). In this paper, we shortlist at least 29 Galactic GCs that could be hosting a subsystem of BHs (BHS). In a companion paper, we analysed results from a wide array of GC models (simulated with the MOCCA code for cluster simulations) that retained few tens to several hundreds of BHs at 12 Gyr and showed that the properties of the BHS in those GCs correlate with the GC's observable properties. Building on those results, we use available observational properties of 140 Galactic GCs to identify 29 GCs that could potentially be harbouring up to a few hundreds of BHs. Utilizing observational properties and theoretical scaling relations, we estimate the density, size and mass of the BHS in these GCs. We also calculate the total number of BHs and the fraction of BHs contained in a binary system for our shortlisted Galactic GCs. Additionally, we mention other Galactic GCs that could also contain significant number of single BHs or BHs in binary systems.

Electron holes in the outer radiation belt: Characteristics and their role in electron energization

AbstractVan Allen Probes have detected electron holes (EHs) around injection fronts in the outer radiation belt. Presumably generated near equator, EHs propagate to higher latitudes potentially resulting in energization of electrons trapped within EHs. This process has been recently shown to provide electrons with energies up to several tens of keV and requires EH propagation up to rather high latitudes. We have analyzed more than 100 EHs observed around a particular injection to determine their kinetic structure and potential energy sources supporting the energization of trapped electrons. EHs propagate with velocities from 1000 to 20,000 km/s (a few times larger than the thermal velocity of the coldest background electron population). The parallel scale of observed EHs is from 0.3 to 3 km that is of the order of hundred Debye lengths. The perpendicular to parallel scale ratio is larger than one in a qualitative agreement with the theoretical scaling relation. The amplitudes of EH electrostatic potentials are generally below 100 V. We determine the properties of the electron population trapped within EHs by making use of the Bernstein‐Green‐Kruskal analysis and via analysis of EH magnetic field signatures. The density of the trapped electron population is on average 20% of the background electron density. The perpendicular temperature of the trapped population is on average 300 eV and is larger for faster EHs. We show that energy losses of untrapped electrons scattered by EHs in the inhomogeneous background magnetic field may balance the energization of trapped electrons.

Observational rotation curves and density profiles versus the Thomas–Fermi galaxy structure theory

The Thomas-Fermi approach to galaxy structure determines selfconsistently the fermionic warm dark matter (WDM) gravitational potential given the distribution function f(E). This framework is appropriate for macroscopic quantum systems: neutron stars, white dwarfs and WDM galaxies. Compact dwarf galaxies follow from the quantum degenerate regime, while dilute and large galaxies from the classical Boltzmann regime. We find analytic scaling relations for the main galaxy magnitudes as halo radius r_h, mass M_h and phase space density. The observational data for a large variety of galaxies are all well reproduced by these theoretical scaling relations. For the compact dwarfs, our results show small deviations from the scaling due to quantum macroscopic effects. We contrast the theoretical curves for the circular velocities and density profiles with the observational ones. All these results are independent of any WDM particle physics model, they only follow from the gravity interaction of the WDM particles and their fermionic nature. The theory rotation and density curves reproduce very well for r < r_h the observations of 10 different and independent sets of data for galaxy masses from 5x10^9 Msun till 5x10^{11} Msun. Our normalized circular velocity curves turn to be universal functions of r/r_h for all galaxies and reproduce very well the observational curves for r < r_h. Conclusion: the Thomas-Fermi approach correctly describes the galaxy structures (Abridged).

STELLAR GRANULATION AS THE SOURCE OF HIGH-FREQUENCY FLICKER INKEPLERLIGHT CURVES

A large fraction of cool, low-mass stars exhibit brightness fluctuations that arise from a combination of convective granulation, acoustic oscillations, magnetic activity, and stellar rotation. Much of the short-timescale variability takes the form of stochastic noise, whose presence may limit the progress of extrasolar planet detection and characterization. In order to lay the groundwork for extracting useful information from these quasi-random signals, we focus on the origin of the granulation-driven component of the variability. We apply existing theoretical scaling relations to predict the star-integrated variability amplitudes for 508 stars with photometric light curves measured by the Kepler mission. We also derive an empirical correction factor that aims to account for the suppression of convection in F-dwarf stars with magnetic activity and shallow convection zones. So that we can make predictions of specific observational quantities, we performed Monte Carlo simulations of granulation light curves using a Lorentzian power spectrum. These simulations allowed us to reproduce the so-called "flicker floor" (i.e., a lower bound in the relationship between the full light-curve range and power in short-timescale fluctuations) that was found in the Kepler data. The Monte Carlo model also enabled us to convert the modeled fluctuation variance into a flicker amplitude directly comparable with observations. When the magnetic suppression factor described above is applied, the model reproduces the observed correlation between stellar surface gravity and flicker amplitude. Observationally validated models like these provide new and complementary evidence for a possible impact of magnetic activity on the properties of near-surface convection.

Stellar granulation as seen in disk-integrated intensity

A large set of stars observed by CoRoT and Kepler shows clear evidence for the presence of a stellar background, which is interpreted to arise from surface convection, i.e., granulation. These observations show that the characteristic time-scale (tau_eff) and the root-mean-square (rms) brightness fluctuations (sigma) associated with the granulation scale as a function of the peak frequency (nu_max) of the solar-like oscillations. We aim at providing a theoretical background to the observed scaling relations based on a model developed in the companion paper. We computed for each 3D model the theoretical power density spectrum (PDS) associated with the granulation as seen in disk-integrated intensity on the basis of the theoretical model. For each PDS we derived tau_eff and sigma and compared these theoretical values with the theoretical scaling relations derived from the theoretical model and the Kepler measurements. We derive theoretical scaling relations for tau_eff and sigma, which show the same dependence on nu_max as the observed scaling relations. In addition, we show that these quantities also scale as a function of the turbulent Mach number (Ma) estimated at the photosphere. The theoretical scaling relations for tau_eff and sigma match the observations well on a global scale. Our modelling provides additional theoretical support for the observed variations of sigma and tau_eff with nu_m max. It also highlights the important role of Ma in controlling the properties of the stellar granulation. However, the observations made with Kepler on a wide variety of stars cannot confirm the dependence of our scaling relations on Ma. Measurements of the granulation background and detections of solar-like oscillations in a statistically sufficient number of cool dwarf stars will be required for confirming the dependence of the theoretical scaling relations with Ma.

Amplitudes of solar-like oscillations in red giants: Departures from the quasi-adiabatic approximation

CoRoT and Kepler measurements reveal us that the amplitudes of solar-like oscillations detected in red giant stars scale from stars to stars in a characteristic way. This observed scaling relation is not yet fully understood but constitutes potentially a powerful diagnostic about mode physics. Quasi-adiabatic theoretical scaling relations in terms of mode amplitudes result in systematic and large differences with the measurements performed for red giant stars. The use of a non-adiabatic intensity-velocity relation derived from a non-adiabatic pulsation code significantly reduces the discrepancy with the CoRoT measurements. The origin of the remaining difference is still unknown. Departure from adiabatic eigenfunction is a very likely explanation that is investigated in the present work using a 3D hydrodynamical model of the surface layers of a representative red giant star.

Vegetated mixing layer around a finite‐size patch of submerged plants: Part 2. Turbulence statistics and structures

Dynamics of vegetated mixing layer displays analogy with canonical and shallow mixing layers. Universality of turbulence and minor influence of flexible aquatic plants on the individual turbulent eddies are anticipated as the prerequisites for the analogy. This paper explores theoretically and experimentally some aspects of analogy by examining spatial patterns of turbulence characteristics around a finite‐size patch of submerged flexible vegetation the population density of which was varied between the experimental runs [Sukhodolova and Sukhodolov, 2012]. It introduces analysis of turbulent shear stress, kinetic energy, dissipation rate, and periodicity of organized motions inside the vegetated mixing layer. The theory is compared with the field experiments. The results of the study indicate that the flow structure around the patch with dense population agrees well with the proposed theoretical scaling relations and reveals many aspects of the analogy to hydrodynamic mixing layers. Around the patch with sparse vegetation the flow structure is best represented by a perturbed boundary layer model. These conclusions on the dynamics of the flow are supported by the analysis of scaled turbulence characteristics. The patterns of turbulence profiles are approximated by scaling functions fairly well while the values of scaling parameters differ from the values reported for canonical and shallow mixing layers. This is an important result which agrees with the previous reports of laboratory research with model vegetation and is explained by a combined effect of internal shear and friction at the top of the canopy.

Quantitative Measurements of the Size Scaling of Linear and Circular DNA in Nanofluidic Slitlike Confinement

Quantitative size measurements of single linear and circular DNA molecules in nanofluidic slitlike confinement are reported. A novel experimental method using DNA entropophoresis down a nanofluidic staircase implemented comprehensive variation of slitlike confinement around d ≈ 2p, where d is the slit depth and p is the persistence length, throughout the transition from strong to moderate confinement. A new numerical analysis approximated and corrected systematic imaging errors. Together, these advances enabled the first measurement of an experimental scaling relation between the in-plane radius of gyration, R∥, and d, yielding R∥ ∼ d–1/6 for all DNA samples investigated. This differs from the theoretical scaling relation, Re ∼ d–1/4, for the root-mean-square end-to-end size, Re. The use of different labeling ratios also allowed a new test of the influence of fluorescent labels on DNA persistence length. These results improve understanding of the basic physical behavior of polymers confined to nanofluidic slits and inform the design of nanofluidic technology for practical applications.

Scaling of the strength of the meridional overturning with vertical diffusivity in an idealized global geometry

An important expression of the non-linear character of the ocean’s meridional overturning circulation (MOC) is the scaling of its amplitude with the magnitude of the vertical mixing coefficient (diffusivity) of heat and salt. This paper extends recent work that indicated that the Atlantic and Pacific MOC exhibit different scaling behaviour. An idealized two-basin model configuration is used to study the meridional overturning circulation under restoring boundary conditions. In particular, the effects of wind forcing and the choice of the parametrization of lateral mixing are examined.Without wind, the scaling is similar in the two basins and consistent with theoretical predictions, provided that the diffusivity is small enough. Towards higher diffusivities the scaling of the overturning diverges.With non-zero wind, the sensitivity is strongly determined by the choice of the lateral mixing scheme. In case of traditional horizontal diffusion, the scaling behaviour is asymmetric due to spurious diapycnal mixing.With the Gent-McWilliams parametrization, the scaling is symmetric for the lower range of diffusivities, where results agree partly with theoretical scaling relations. In all cases considered, the pycnocline depth has the same sensitivity to diffusivity in both basins, implying that there is no universally valid relation between overturning strength and pycnocline depth.

A large‐eddy model for cirrus clouds with explicit aerosol and ice microphysics and Lagrangian ice particle tracking

AbstractWe introduce a novel large‐eddy model for cirrus clouds with explicit aerosol and ice microphysics, and validate its central components. A combined Eulerian/Lagrangian approach is used to simulate the formation and evolution of cirrus. While gas and size‐resolved aerosol phases are treated over a fixed Eulerian grid similar to the dynamical and thermodynamical variables, the ice phase is treated by tracking a large number of simulation ice particles. The macroscopic properties of the ice phase are deduced from statistically analysing large samples of simulation ice particle properties. The new model system covers non‐equilibrium growth of liquid supercooled aerosol particles, their homogeneous freezing, heterogeneous ice nucleation in the deposition or immersion mode, growth of ice crystals by deposition of water vapour, sublimation of ice crystals and their gravitational sedimentation, aggregation between ice crystals due to differential sedimentation, the effect of turbulent dispersion on ice particle trajectories, diabatic latent and radiative heating or cooling, and radiative heating or cooling of ice crystals. This suite of explicitly resolved physical processes enables the detailed simulation and analysis of the dynamical–microphysical–radiative feedbacks characteristic of cirrus.We draw special attention to the ice aggregation process which redistributes large ice crystals vertically and changes the ice particle size distributions accordingly. We find that aggregation of ice crystals is the key process to generate precipitation‐sized ice crystals in stratiform cirrus. A process‐oriented algorithm is developed for ice aggregation based on the trajectories and sedimentation velocities of simulation ice particles for use in the dynamically and microphysically complex, multi‐dimensional large‐eddy approach. By virtue of an idealized model set‐up, designed to isolate the effect of aggregation on the cirrus development, we show that aggregation and its effect on the ice crystal size distribution in the model is consistent with a theoretical scaling relation, which was found to be in good agreement within situmeasurements. Copyright © 2010 Royal Meteorological Society

A multiwavelength strong lensing analysis of baryons and dark matter in the dynamically active cluster AC 114

Strong lensing studies can provide detailed mass maps of the inner regions even in dynamically active galaxy clusters. It is shown that proper modelling of the intracluster medium, i.e. the main baryonic component, can play an important role. In fact, the addition of a new contribution accounting for the gas can increase the statistical significance of the lensing model. We propose a parametric method for strong lensing analyses which exploits multi-wavelength observations. The mass model accounts for cluster-sized dark matter halos, galaxies (whose stellar mass can be obtained from optical analyses) and the intracluster medium. The gas distribution is fitted to lensing data exploiting prior knowledge from X-ray observations. This gives an unbiased look at each matter component and allows us to study the dynamical status of a cluster.}The method has been applied to AC 114, an irregular X-ray cluster. We find positive evidence for dynamical activity, with the dark matter distribution shifted and rotated with respect to the gas. On the other hand, the dark matter follows the galaxy density both for shape and orientation, which hints at its collisionless nature. The inner region (< 250kpc) is under-luminous in optical bands whereas the gas fraction (~20+- 5%) slightly exceeds typical values. Evidence from lensing and X-ray suggests that the cluster develops in the plane of the sky and is not affected by the lensing over-concentration bias. Despite the dynamical activity, the matter distribution seems to be in agreement with predictions from N-body simulations. An universal cusped profile provides a good description of either the overall or the dark matter distribution whereas theoretical scaling relations seem to be nicely fitted.

Scaling the Structure Factors of Protein Limit Colloid−Polymer Mixtures

The scaling of the phase boundaries and structure factors of protein limit colloid-polymer mixtures has been investigated through the addition of large nonadsorbing polymer chains to a solution of small microemulsion droplets. The colloid-polymer size ratio has been varied between 10 and 16 by changing the microemulsion droplet size; the phase boundaries were shown previously to observe theoretical scaling relations very well [Langmuir 2009, 25 (7), 3944-3952]. These thermodynamic scaling relations are now shown to also hold extremely well for the individual and cross-term partial structure factors. The structure factors for systems with different size ratios occupying the same point in scaled phase space show extremely good agreement. The properties and stability of these mixtures are governed by the polymer mesh.