How does disk gravity really influence type-I migration ?

We report an analytical expression for the locations of Lindblad resonances induced by a perturbing protoplanet, including the effect of disk gravity. Inner, outer and differential torques are found to be enhanced compared to situations where a keplerian velocity field for the dynamics of both the disk and the planet is assumed. Inward migration is strongly accelerated when the disk gravity is only accounted for in the planet orbital motion. The addition of disk self-gravity slows down the planet drift but not enough to stop it.Comment: 4 pages, accepted for publication in A&A Letter

Self-gravity at the scale of the polar cell

We present the exact calculus of the gravitational potential and acceleration along the symmetry axis of a plane, homogeneous, polar cell as a function of mean radius a, radial extension e, and opening angle f. Accurate approximations are derived in the limit of high numerical resolution at the geometrical mean of the inner and outer radii (a key-position in current FFT-based Poisson solvers). Our results are the full extension of the approximate formula given in the textbook of Binney & Tremaine to all resolutions. We also clarify definitely the question about the existence (or not) of self-forces in polar cells. We find that there is always a self-force at radius except if the shape factor a.f/e reaches ~ 3.531, asymptotically. Such cells are therefore well suited to build a polar mesh for high resolution simulations of self-gravitating media in two dimensions. A by-product of this study is a newly discovered indefinite integral involving complete elliptic integral of the first kind over modulus.Comment: 4 pages, 4 figures, A&A accepte

Generation of potential/surface density pairs in flat disks Power law distributions

We report a simple method to generate potential/surface density pairs in flat axially symmetric finite size disks. Potential/surface density pairs consist of a ``homogeneous'' pair (a closed form expression) corresponding to a uniform disk, and a ``residual'' pair. This residual component is converted into an infinite series of integrals over the radial extent of the disk. For a certain class of surface density distributions (like power laws of the radius), this series is fully analytical. The extraction of the homogeneous pair is equivalent to a convergence acceleration technique, in a matematical sense. In the case of power law distributions, the convergence rate of the residual series is shown to be cubic inside the source. As a consequence, very accurate potential values are obtained by low order truncation of the series. At zero order, relative errors on potential values do not exceed a few percent typically, and scale with the order N of truncation as 1/N**3. This method is superior to the classical multipole expansion whose very slow convergence is often critical for most practical applications.Comment: Accepted for publication in Astronomy & Astrophysics 7 pages, 8 figures, F90-code available at http://www.obs.u-bordeaux1.fr/radio/JMHure/intro2applawd.htm

Modelling circumbinary protoplanetary disks I. Fluid simulations of the Kepler-16 and 34 systems

S.L and Z.M.L are supported by the STFC. P.J.C is grateful to NERC Grant NE/K004778/1. S.J.P. is supported by a Royal Society University Research Fellowship

A local prescription for the softening length in self-gravitating gaseous discs

In 2D-simulations of self-gravitating gaseous discs, the potential is often computed in the framework of "softened gravity" initially designed for N-body codes. In this special context, the role of the softening length LAMBDA is twofold: i) to avoid numerical singularities in the integral representation of the potential (i.e., arising when the relative separation vanishes), and ii) to acount for stratification of matter in the direction perpendicular to the disc mid-plane. So far, most studies have considered LAMBDA as a free parameter and various values or formulae have been proposed without much mathematical justification. In this paper, we demonstrate by means of a rigorous calculus that it is possible to define LAMBDA such that the gravitational potential of a flat disc coincides at order zero with that of a geometically thin disc of the same surface density. Our prescription for LAMBDA, valid in the local, axisymmetric limit, has the required properties i) and ii). It is mainly an analytical function of the radius and disc thickness, and is sensitive to the vertical stratification. For mass density profiles considered (namely, profiles expandable over even powers of the altitude), we find that LAMBDA : i) is independant of the numerical mesh, ii) is always a fraction of the local thickness H, iii) goes through a minimum at the singularity (i.e., at null separation), and iv) is such that 0.13 < LAMBDA/H < 0.29 typically (depending on the separation and on density profile). These results should help us to improve the quality of 2D- and 3D-simulations of gaseous discs in several respects (physical realism, accuracy, and computing time).Comment: accepted in A&A, 7 pages, 7 figures, web link for the F90 code and on-line calculations : http://www.obs.u-bordeaux1.fr/radio/JMHure/intro2single.ph

The Bosma effect revisited - I. HI and stellar disc scaling models

The observed proportionality between the centripetal contribution of the dynamically insignificant HI gas in the discs of spiral galaxies and the dominant contribution of DM - the "Bosma effect" - has been repeatedly mentioned in the literature but largely ignored. We have re-examined the evidence for the Bosma effect by fitting Bosma effect models for 17 galaxies in the THINGS data set, either by scaling the contribution of the HI gas alone or by using both the observed stellar disc and HI gas as proxies. The results are compared with two models for exotic cold DM: internally consistent cosmological NFW models with constrained compactness parameters, and URC models using fully unconstrained Burkert density profiles. The Bosma models that use the stellar discs as additional proxies are statistically nearly as good as the URC models and clearly better than the NFW ones. We thus confirm the correlation between the centripetal effects of DM and that of the interstellar medium of spiral galaxies. The edificacy of "maximal disc" models is explained as the natural consequence of "classic" Bosma models which include the stellar disc as a proxy in regions of reduced atomic gas. The standard explanation - that the effect reflects a statistical correlation between the visible and exotic DM - seems highly unlikely, given that the geometric forms and hence centripetal signatures of spherical halo and disc components are so different. A literal interpretation of the Bosma effect as being due to the presence of significant amounts of disc DM requires a median visible baryon to disc DM ratio of about 40%.Comment: Accepted by A&A (Paper I

Modelling circumbinary protoplanetary disks II. Gas disk feedback on planetesimal dynamical and collisional evolution in the circumbinary systems Kepler-16 and 34

Aims. We investigate the feasibility of planetesimal growth in circumbinary protoplanetary disks around the observed systems Kepler- 16 and Kepler-34 under the gravitational influence of a precessing eccentric gas disk. Methods. We embed the results of our previous hydrodynamical simulations of protoplanetary disks around binaries into an N-body code to perform 3D, high-resolution, inter-particle gravity-enabled simulations of planetesimal growth and dynamics that include the gravitational force imparted by the gas. Results. Including the full, precessing asymmetric gas disk generates high eccentricity orbits for planetesimals orbiting at the edge of the circumbinary cavity, where the gas surface density and eccentricity have their largest values. The gas disk is able to efficiently align planetesimal pericenters in some regions leading to phased, non-interacting orbits. Outside of these areas eccentric planetesimal orbits become misaligned and overlap leading to crossing orbits and high relative velocities during planetesimal collisions. This can lead to an increase in the number of erosive collisions that far outweighs the number of collisions that result in growth. Gravitational focusing from the static axisymmetric gas disk is weak and does not significantly alter collision outcomes from the gas free case. Conclusions. Due to asymmetries in the gas disk, planetesimals are strongly perturbed onto highly eccentric orbits. Where planetesimals orbits are not well aligned, orbit crossings lead to an increase in the number of erosive collisions. This makes it difficult for sustained planetesimal accretion to occur at the location of Kepler-16b and Kepler-34b and we therefore rule out in-situ growth. This adds further support to our initial suggestions that most circumbinary planets should form further out in the disk and migrate inwards.Comment: 12 pages and 12 figure

Tests at 2K of the beta 0.35 spoke cryomodule prototype with the MTCA.4-based Low Level RF system prototype for the MYRRHA R&D

Within the framework of the first phase of MYRRHA (Multi-purpose hYbrid Research Reactor for High-tech Applications) project, called MINERVA, IJCLab was in charge of a fully equipped Spoke cryomodule prototype development, tested at 2K. It integrates two superconducting single spoke cavities, the RF power couplers and the Cold Tuning Systems associated. On the control side, a MTCA.4-based Low Level Radio Frequency (LLRF) system prototype and the Software/EPICS developments has been realized by IJCLab and the SCK CEN in collaboration with the company IOxOS Technologies. The final version of the global system and the results of the tests at 2K will show with some perspectives.Comment: Poster pr\'esent\'e au LLRF Workshop 2023 (LLRF2023, arXiv : 2310.03199

Debris disks as signposts of terrestrial planet formation. II Dependence of exoplanet architectures on giant planet and disk properties

We present models for the formation of terrestrial planets, and the collisional evolution of debris disks, in planetary systems that contain multiple unstable gas giants. We previously showed that the dynamics of the giant planets introduces a correlation between the presence of terrestrial planets and debris disks. Here we present new simulations that show that this connection is qualitatively robust to changes in: the mass distribution of the giant planets, the width and mass distribution of the outer planetesimal disk, and the presence of gas in the disk. We discuss how variations in these parameters affect the evolution. Systems with equal-mass giant planets undergo the most violent instabilities, and these destroy both terrestrial planets and the outer planetesimal disks that produce debris disks. In contrast, systems with low-mass giant planets efficiently produce both terrestrial planets and debris disks. A large fraction of systems with low-mass outermost giant planets have stable gaps between these planets that are frequently populated by planetesimals. Planetesimal belts between outer giant planets may affect debris disk SEDs. If Earth-mass seeds are present in outer planetesimal disks, the disks radially spread to colder temperatures. We argue that this may explain the very low frequency of > 1 Gyr-old solar-type stars with observed 24 micron excesses. Among the (limited) set of configurations explored, the best candidates for hosting terrestrial planets at ~1 AU are stars older than 0.1-1 Gyr with bright debris disks at 70 micron but with no currently-known giant planets. These systems combine evidence for rocky building blocks, with giant planet properties least likely to undergo destructive dynamical evolution. We predict an anti-correlation between debris disks and eccentric giant planets, and a positive correlation between debris disks and terrestrial planets.Comment: Astronomy and Astrophysics, in press. Movies from simulations are at http://www.obs.u-bordeaux1.fr/e3arths/raymond/movies_debris.htm

On the corotation torque for low-mass eccentric planets

SMF acknowledges the support of an STFC PhD studentship. The simulations presented in this paper were performed on the QMUL HPC facility purchased under the SRIF initiatives