Pressureless Fluid Research Articles

Dusty disks as safe havens for terrestrial planets: Effect of the back-reaction of solid material on gas

Previous studies have shown that there is considerable variation in the dust-to-gas density ratio in the vicinity of low-mass planets undergoing growth. This can lead to a significant change in the planetary momentum exerted by the gas and solid material. However, due to the low dust-to-gas mass ratio of protoplanetary disks (about one percent), the effect of the solid material on the gas dynamics -- that is, the back-reaction of the solid material -- is often neglected. We aim to study the effect of the back-reaction of solid material on the torques felt by low-mass planets. The effect of the back-reaction of solid material is investigated by comparing non-accreting and accreting models. We performed locally isothermal, global two-dimensional hydrodynamic simulations of planet-disk interactions using the code GFARGO2 . Low-mass planets in the range of $0.1-10 M_⊕$ accrete only solid material. The solid component of the disk was treated as a pressureless fluid. Simulations were compared with taking and not taking into account the back-reaction of the solid material on the gas. The solid component was assumed to have a fixed Stokes number in the range of $0.01-10$. All models assumed a canonical solid-to-gas mass ratio of 0.01. The back-reaction of the solid has been shown to have a significant effect on the total torque exerted on a low-mass planet. In general, the inclusion of the back-reaction results in a greater number of models with positive torque values compared to models that neglect the back-reaction. It is clear, therefore, that the simulation of planetary growth and migration via hydrodynamic modeling requires the inclusion of a solid-gas back-reaction. As a result of the back-reaction and accretion, a Mars-sized planetary embryo will experience positive total torques from the disk containing coupled solid components (mathrm St ≤0.01). Earth-mass planets also experience positive total torques from the disk containing boulder-sized solid components ($2≤ St ≤5$). The accretion of weakly coupled solid material tends to increase the positive torques and decrease the negative torques. Our results suggest that the combined effect of back-reaction and accretion is beneficial to the formation of planetary systems by reducing the likelihood of a young planet being engulfed by the central star.

Dusty substructures induced by planets in ALMA disks: How dust growth and dynamics changes the picture

Abstract Protoplanetary disks exhibit a rich variety of substructure in millimeter continuum emission, often attributed to unseen planets. As these planets carve gaps in the gas, dust particles can accumulate in the resulting pressure bumps, forming bright features in the dust continuum. We investigate the role of dust dynamics in the gap-opening process with 2D radiation hydrodynamics simulations of planet–disk interaction and a two-population dust component modeled as a pressureless fluid. We consider the opacity feedback and backreaction due to drag forces as mm grains accumulate in pressure bumps at different stages of dust growth. We find that dust dynamics can significantly affect the resulting substructure driven by the quasi-thermal-mass planet with Mp/M⋆ = 10−4. Opacity feedback causes nonaxisymmetric features to become more compact in azimuth, whereas the drag-induced backreaction tends to dissolve nonaxisymmetries. For our fiducial model, this results in multiple concentric rings of dust rather than the expected vortices and corotating dust clumps found in models without dust feedback. A higher coagulation fraction disproportionately enhances the effect of dust opacity feedback, favoring the formation of crescents rather than rings. Our results suggest that turbulent diffusion is not always necessary to explain the rarity of observed nonaxisymmetric features, and that incorporating dust dynamics is vital for interpreting the observed substructure in protoplanetary disks. We also describe and test the implementation of the publicly-available dust fluid module in the PLUTO code.

Interacting ultralight dark matter and dark energy and fits to cosmological data in a field theory approach

The description of dark matter as a pressure-less fluid and of dark energy as a cosmological constant, both minimally coupled to gravity, constitutes the basis of the concordanceΛCDM model. However, the concordance model is based on using equations of motion directly for the fluids with constraints placed on their sources, andlacks an underlying Lagrangian. In this work, we propose a Lagrangian model of two spin zero fields describing dark energy and dark matter with an interaction term between the two along with self-interactions. We study the background evolution of the fields as well as their linear perturbations, suggesting an alternative to ΛCDM with dark matter and dark energy being fundamental dynamical fields. The parameters of the model are extracted using a Bayesian inference tool based on multiple cosmological data sets which include those of Planck (with lensing), BAO, Pantheon, SH0ES, and WiggleZ. Using these data, we set constraints on the dark matter mass and the interaction strengths. Furthermore, we find that the model is able to alleviate the Hubble tension for some data sets while also resolving the S 8 tension.

Exponential gravity with logarithmic corrections in the presence of axion dark matter

An exponential modified gravity with additional logarithmic corrections is considered with the presence of an axion-like scalar field in the role of dark matter. Axion fields are thought to become important at late-times when the axion-like scalar field oscillates around its vacuum expectation value, mimicking dark matter behaviour. The model is compared with the usual pressureless fluid description of dark matter. Both models are tested with observational data including some of the latest sources, providing similar fits in comparison with the ΛCDM model. Despite results are not statistically relevant to rule out any model, the number of free parameters still favours ΛCDM model, as shown by computing the goodness of the fits.

No-go theorem for static spherically symmetric configurations composed of two charged pressureless fluid species

We present a no-go theorem for spherically symmetric configurations of two charged fluid species in equilibrium. The fluid species are assumed to be dusts, that is, perfect fluids without pressure, and the equilibrium can be attained for a single dust from the balance of electrostatic repulsion and gravitational attraction. We show that this is impossible for two dust species unless both of them are indistinguishable in terms of their electric charge density to matter density ratio. The result is obtained in the main three theories of mechanics, that is, in Newtonian Mechanics, in Special Relativity and in General Relativity. In particular, as charged dust solutions have been used to study the possibility of black hole mimickers, this result shows that such mimickers can not be constructed unless the underlying charged particle has the correct charge to mass ratio.

Simultaneously probing the sound speed and equation of state of the early Universe with pulsar timing arrays

Recently, several major pulsar timing array (PTA) collaborations have assembled strong evidence for the existence of a gravitational-wave background at frequencies around the nanohertz regime. Assuming that the PTA signal is attributed to scalar-induced gravitational waves, we jointly employ the PTA data from the NANOGrav 15-year data set, PPTA DR3, and EPTA DR2 to probe the conditions of the early Universe. Specifically, we explore the equation of state parameter (w), the reheating temperature (T rh), and the sound speed (cs ), finding w = 0.59+0.36 -0.40 (median + 90% credible interval), and T rh ≲ 0.2 GeV at the 95% credible interval for a lognormal power spectrum of the curvature perturbation. Furthermore, we compute Bayes factors to compare different models against the power-law spectrum model, effectively excluding the pressure-less fluid domination model. Our study underscores the significance of scalar-induced gravitational waves as a powerful tool to explore the nature of the early Universe.

Relative entropy inequality for capillary fluids with density dependent viscosity and applications

We derive a relative entropy inequality for capillary compressible fluids with density dependent viscosity. Applications in the context of weak–strong uniqueness analysis, pressureless fluids and high-Mach number flows are presented.

Dark matter vorticity and velocity dispersion from truncated Dyson-Schwinger equations

Large-scale structure formation is studied in a kinetic theory approach, extending the standard perfect pressureless fluid description for dark matter by including the velocity dispersion tensor as a dynamical degree of freedom. The evolution of power spectra for density, velocity and velocity dispersion degrees of freedom is investigated in a non-perturbative approximation scheme based on the Dyson-Schwinger equations. In particular, the generation of vorticity and velocity dispersion is studied and predictions for the corresponding power spectra are made, which qualitatively agree well with results obtained from N-body simulations. It is found that velocity dispersion grows strongly due to non-linear effects and at late times its mean value seems to be largely independent of the initial conditions. By taking this into account, a rather realistic picture of non-linear large-scale structure formation can be obtained, albeit the numerical treatment remains challenging, especially for very cold dark matter models.

The Riemann problem for pressureless compressible fluid system with time- and space-dependent external force

We concern with Riemann problem for an one-dimensional pressureless compressible fluid system with time- and space-dependent external force. Under the concept of α-solution to this model, we obtain the α-solutions to the Riemann problem and the criteria of appearance of each α-solution. It is observed that the expressions of these α-solutions do not depend on α. Besides, the vacuum solution arises although the initial values do not involve vacuum. Furthermore, the delta wave solution emerges for certain initial values, in which internal energy variable and density variable contain the Dirac measure. Finally, our technique can be applied to study the other singular solutions to systems of conservation laws with a source term.

Beyond diffusion: a generalized mean-field theory of turbulent dust transport in protoplanetary discs

ABSTRACT Turbulence in protoplanetary discs, when present, plays a critical role in transporting dust particles embedded in the gaseous disc component. When using a field description of dust dynamics, a diffusion approach is traditionally used to model this turbulent dust transport. However, it has been shown that classical turbulent diffusion models are not fully self-consistent. Several shortcomings exist, including the ambiguous nature of the diffused quantity and the non-conservation of angular momentum. Orbital effects are also neglected without an explicit prescription. In response to these inconsistencies, we present a novel Eulerian turbulent dust transport model for isotropic and homogeneous turbulence on the basis of a mean-field theory. Our model is based on density-weighted averaging applied to the pressureless fluid equations and uses appropriate turbulence closures. Our model yields novel dynamic equations for the turbulent dust mass flux and recovers existing turbulent transport models in special limiting cases, thus providing a more general and self-consistent description of turbulent particle transport. Importantly, our model ensures the conservation of global angular and linear momentum unconditionally and implicitly accounts for the effects of orbital dynamics in protoplanetary discs. Furthermore, our model correctly describes the vertical settling–diffusion equilibrium solutions for both small and large particles. Hence, this work presents a generalized Eulerian turbulent dust transport model, establishing a comprehensive framework for more detailed studies of turbulent dust transport in protoplanetary discs.

Subadditive average distances and quantum promptness

A central property of a classical geometry is that the geodesic distance between two events is additive. When considering quantum fluctuations in the metric or a quantum or statistical superposition of different spacetimes, additivity is generically lost at the level of expectation values. In the presence of a superposition of metrics, distances can be made diffeomorphism invariant by considering the frame of a family of free-falling observers or a pressureless fluid, provided we work at sufficiently low energies. We propose to use the average squared distance between two events as a proxy for understanding the effective quantum (or statistical) geometry and the emergent causal relations among such observers. At each point, the average squared distance defines an average metric tensor. However, due to non-additivity, is not the (squared) geodesic distance associated with it. We show that departures from additivity can be conveniently captured by a bi-local quantity . Violations of additivity build up with the mutual separation between x and y and can correspond to C < 0 (subadditive) or C > 0 (superadditive). We show that average Euclidean distances are always subadditive: they satisfy the triangle inequality but generally fail to saturate it. In Lorentzian signature there is no definite result about the sign of C, most physical examples give C < 0 but there exist counterexamples. The causality induced by subadditive Lorentzian distances is unorthodox but not pathological. Superadditivity violates the transitivity of causal relations. On these bases, we argue that subadditive distances are the expected outcome of dynamical evolution, if relatively generic physical initial conditions are considered.

Reconstruction of [formula omitted]CDM Universe from Noether symmetries in Chameleon gravity

We apply the Noether symmetries to constrain the unknown functions of chameleon gravity in the cosmological scenario of a spatially flat Friedmann–Lemaître–Robertson–Walker space–time with an ideal gas. For this gravitational model the field equations admit a point-like Lagrangian with as unknown functions the scalar field potential and the coupling function which is responsible for the chameleon mechanism. Noether’s first theorem provides us with four sets of closed-form functional forms for which variational symmetries exist. We construct the corresponding conservation laws and we use them in order to determine new analytic solutions in chameleon gravity. From the analysis of the physical properties of the new solution it follows that in the late universe they can reproduce the ΛCDM model without having to assume the presence of a pressureless fluid in the cosmological fluid.

Three-dimensional dust stirring by a giant planet embedded in a protoplanetary disc

ABSTRACT The motion of solid particles embedded in gaseous protoplanetary discs is influenced by turbulent fluctuations. Consequently, the dynamics of moderately to weakly coupled solids can be distinctly different from the dynamics of the gas. Additionally, gravitational perturbations from an embedded planet can further impact the dynamics of solids. In this work, we investigate the combined effects of turbulent fluctuations and planetary dust stirring in a protoplanetary disc on three-dimensional dust morphology and on synthetic ALMA continuum observations. We carry out 3D radiative two-fluid (gas + 1-mm-dust) hydrodynamic simulations in which we explicitly model the gravitational perturbation of a Jupiter-mass planet. We derived a new momentum-conserving turbulent diffusion model that introduces a turbulent pressure to the pressureless dust fluid to capture the turbulent transport of dust. The model implicitly captures the effects of orbital oscillations and reproduces the theoretically predicted vertical settling-diffusion equilibrium. We find a Jupiter-mass planet to produce distinct and large-scale three-dimensional flow structures in the mm-sized dust, which vary strongly in space. We quantify these effects by locally measuring an effective vertical diffusivity (equivalent alpha) and find azimuthally averaged values in a range δeff ∼ 5 × 10−3–2 × 10−2 and local peaks at values of up to δeff ∼ 3 × 10−1. In synthetic ALMA continuum observations of inclined discs, we find effects of turbulent diffusion to be observable, especially at disc edges, and effects of planetary dust stirring in edge-on observations.

Cosmological perturbation theory using generalized Einstein–de Sitter cosmologies

The separable analytical solution in standard perturbation theory for an Einstein--de Sitter (EdS) universe can be generalized to the wider class of such cosmologies (``generalized EdS,'' or gEdS) in which a fraction of the pressureless fluid does not cluster. We derive the corresponding kernels in both Eulerian perturbation theory (EPT) and Lagrangian perturbation theory, generalizing the canonical EdS expressions to a one-parameter family where the parameter can be taken to be the exponent $\ensuremath{\alpha}$ of the growing mode linear amplification $D(a)\ensuremath{\propto}{a}^{\ensuremath{\alpha}}$. For the power spectrum (PS) at one loop in EPT, the contribution additional to standard EdS is given, for each of the ``13'' and ``22'' terms, as a function of two infrared safe integrals. In the second part of the paper we show that the calculation of cosmology-dependent corrections in perturbation theory in standard [e.g., Lambda cold dark matter (LCDM)] models can be simplified, and their magnitude and parameter dependence better understood, by relating them to our analytic results for gEdS models. At second order the time dependent kernels are equivalent to the analytic kernels of the gEdS model with $\ensuremath{\alpha}$ replaced by a single redshift dependent effective growth rate ${\ensuremath{\alpha}}_{2}(z)$. At third order the time evolution can be conveniently parametrized in terms of two additional such effective growth rates. For the PS calculated at one-loop order, the correction to the PS relative to the EdS limit can be expressed in terms of just ${\ensuremath{\alpha}}_{2}(z)$, one additional effective growth rate function, and the four infrared safe integrals of the gEdS limit. This is much simplified compared to expressions in the literature that use six or eight redshift dependent functions and are not explicitly infrared safe. Using the analytic gEdS expression for the PS with $\ensuremath{\alpha}={\ensuremath{\alpha}}_{2}(z)$ gives a good approximation (to $\ensuremath{\sim}25%$) for the exact result.

Effects of turbulent diffusion and back-reaction on the dust distribution around two resonant planets

ABSTRACT In evolved and dusty circumstellar discs, two planets with masses comparable to Jupiter and Saturn that migrate outwards while maintaining an orbital resonance can produce distinctive features in the dust distribution. Dust accumulates at the outer edge of the common gas gap, which behaves as a dust trap, where the local dust concentration is significantly enhanced by the planets’ outward motion. Concurrently, an expanding cavity forms in the dust distribution inside the planets’ orbits, because dust does not filter through the common gaseous gap and grain depletion in the region continues via inward drifting. There is no cavity in the gas distribution because gas can filter through the gap, although ongoing gas accretion on the planets can reduce the gas density in the inner disc. Such behaviour was demonstrated by means of simulations neglecting the effects of dust diffusion due to turbulence and of dust backreaction on the gas. Both effects may alter the formation of the dust peak at the gap outer edge and of the inner dust cavity, by letting grains filter through the dust trap. We performed high-resolution hydrodynamical simulations of the coupled evolution of gas and dust species, the latter treated as pressureless fluids, in the presence of two giant planets. We show that diffusion and backreaction can change some morphological aspects of the dust distribution but do not alter some main features, such as the outer peak and the expanding inner cavity. These findings are confirmed for different parametrizations of gas viscosity.

Stellar instability from parametric resonance

In this paper we examine the stability of stellar configurations in which the interior solution is described by a closed Friedmann-Lemaître-Robertson-Walker (FLRW) geometry sourced with a charged pressureless fluid and radiation. An interacting vacuum component and a conformally coupled massive scalar field are also included. Given a simple factor for the energy transfer between the pressureless fluid and the vacuum component we obtain bounded interior oscillatory solutions. We show that in proper domains of the parameter space the interior dynamics is highly unstable so that the break of the Kolmogorov–Arnold–Moser (KAM) tori leads to a disruptive ejection of mass. For such configurations the interior solution asymptotically matches an exterior Reissner–Nordström–de Sitter spacetime.

Extended minimal theories of massive gravity

In this work, we introduce a class of extended Minimal Theories of Massive Gravity (eMTMG), without requiring a priori that the theory should admit the same homogeneous and isotropic cosmological solutions as the de Rham-Gabadadze-Tolley massive gravity. The theory is constructed as to have only two degrees of freedom in the gravity sector. In order to perform this step we first introduce a precursor theory endowed with a general graviton mass term, to which, at the level of the Hamiltonian, we add two extra constraints as to remove the unwanted degrees of freedom, which otherwise would typically lead to ghosts and/or instabilities. On analyzing the number of independent constraints and the properties of tensor mode perturbations, we see that the gravitational waves are the only propagating gravitational degrees of freedom which do acquire a non-trivial mass, as expected. In order to understand how the effective gravitational force works for this theory we then investigate cosmological scalar perturbations in the presence of a pressureless fluid. We then restrict the whole class of models by imposing the following conditions at all times: 1) it is possible to define an effective gravitational constant, $G_{{\rm eff}}$; 2) the value $G_{\text{eff}}/G_{N}$ is always finite but not always equal to unity (as to allow some non-trivial modifications of gravity, besides the massive tensorial modes); and 3) the square of mass of the graviton is always positive. These constraints automatically make also the ISW-effect contributions finite at all times. Finally we focus on a simple subclass of such theories, and show they already can give a rich and interesting phenomenology.

Various phases of irregular energy density in charged spheres

We explore the factors of inhomogeneity in the spherically symmetric distribution of collapsing fluid under the effect of electromagnetic field in f(G) theory. Modified Bianchi identities and two significant equations for the Weyl tensor are formulated to get help in the analysis. Causes of inhomogeneity are analyzed by considering the non-radiating and radiating charged fluid. The non-dissipative type of fluid contains pressureless, isotropic and anisotropic fluid. It is observed that for anisotropic fluid, the inhomogeneity corresponds to the structure scalar. For dissipative dust, the effects of relaxation time in terms of electromagnetic field are brought out.

Dust entrainment in magnetically and thermally driven disk winds

Context.Magnetically and thermally driven disk winds have gained popularity in the light of the current paradigm of low viscosities in protoplanetary disks that nevertheless present large accretion rates even in the presence of inner cavities. The possibility of dust entrainment in these winds may explain recent scattered light observations and constitutes a way of dust transport towards outer regions of the disk.Aims.We aim to study the dust dynamics in these winds and explore the differences between photoevaporation and magnetically driven disk winds in this regard. We quantify maximum entrainable grain sizes, the flow angle, and the general detectability of such dusty winds.Methods.We used the FARGO3D code to perform global, 2.5D axisymmetric, nonideal MHD simulations including ohmic and ambipolar diffusion. Dust was treated as a pressureless fluid. Synthetic observations were created with the radiative transfer code RADMC-3D.Results.We find a significant difference in the dust entrainment efficiency of warm, ionized winds such as photoevaporation and magnetic winds including X-ray and extreme ultraviolet heating compared to cold magnetic winds. The maximum entrainable grain size varies from 3 μm−6 μm for ionized winds to 1 μm for cold magnetic winds. The dust flow angle decreases rapidly with increasing grain size. Dust grains in cold magnetic winds tend to flow along a shallower angle compared to the warm, ionized winds. With increasing distance to the central star, the dust entrainment efficiency decreases. Larger values of the turbulent viscosity increase the maximum grain size radius of possible dust entrainment. Our simulations indicate that diminishing dust content in the outer regions of the wind can be mainly attributed to the dust settling in the disk. The Stokes number along the wind launching front stays constant in the outer region. In the synthetic images, the dusty wind appears as a faint, conical emission region which is brighter for a cold magnetic wind.

Backreaction from inhomogeneous matter fields during large-scale structure formation

We study how inhomogeneities of the cosmological fluid fields backreact on the homogeneous part of energy density and how they modify the Friedmann equations. In general, backreaction requires to go beyond the pressureless ideal fluid approximation, and this can lead to a reduced growth of cosmological large-scale structure. Since observational evidence favors evolution close to the standard growing mode in the linear regime, we focus on two-component fluids in which the nonideal fluid is gravitationally coupled to cold dark matter and in which a standard growing mode persists. This is realized, e.g., for a baryonic fluid coupled to cold dark matter. We calculate the backreaction for this case and for a wide range of other two-fluid models. Here the effect is either suppressed because the nonideal matter properties are numerically too small, or because they lead to a too stringent UV cutoff of the integral over the power spectrum that determines backreaction. We discuss then matter field backreaction from a broader perspective and generalize the formalism such that also far-from-equilibrium scenarios relevant to late cosmological times and nonlinear scales can be addressed in the future.