Robustness of Regularity for the 33D Convective Brinkman-Forchheimer Equations

We prove a robustness of regularity result for the $3$D convective Brinkman-Forchheimer equations \partial_tu -\mu\Delta u + (u \cdot \nabla)u + \nabla p + \alpha u + \beta\abs{u}^{r - 1}u = f, for the range of the absorption exponent $r \in [1, 3]$ (for $r > 3$ there exist global-in-time regular solutions), i.e. we show that strong solutions of these equations remain strong under small enough changes of the initial condition and forcing function. We provide a smallness condition which is similar to the robustness conditions given for the $3$D incompressible Navier-Stokes equations by Chernyshenko et al. (2007) and Dashti & Robinson (2008).Comment: 22 page

Accelerated post-AGB evolution, initial-final mass relations, and the star-formation history of the Galactic bulge

We study the star-formation history of the Galactic bulge, as derived from the age distribution of the central stars of planetary nebulae that belong to this stellar population. The high resolution imaging and spectroscopic observations of 31 compact planetary nebulae are used to derive their central star masses. The Bloecker tracks with the cluster IFMR result in ages, which are unexpectedly young. We find that the Bloecker post-AGB tracks need to be accelerated by a factor of three to fit the local white dwarf masses. This acceleration extends the age distribution. We adjust the IFMR as a free parameter to map the central star ages on the full age range of bulge stellar populations. This fit requires a steeper IFMR than the cluster relation. We find a star-formation rate in the Galactic bulge, which is approximately constant between 3 and 10 Gyr ago. The result indicates that planetary nebulae are mainly associated with the younger and more metal-rich bulge populations. The constant rate of star-formation between 3 and 10 Gyr agrees with suggestions that the metal-rich component of the bulge is formed during an extended process, such as a bar interaction.Comment: accepted for publication in A&

Energy equality for the 3D critical convective Brinkman-Forchheimer equations

In this paper we give a simple proof of the existence of global-in-time smooth solutions for the convective Brinkman-Forchheimer equations (also called in the literature the tamed Navier-Stokes equations) $$\partial_tu -\mu\Delta u + (u \cdot \nabla)u + \nabla p + \alpha u + \beta|u|^{r - 1}u = 0$$ on a $3$D periodic domain, for values of the absorption exponent $r$ larger than $3$. Furthermore, we prove that global, regular solutions exist also for the critical value of exponent $r = 3$, provided that the coefficients satisfy the relation $4\mu\beta \geq 1$. Additionally, we show that in the critical case every weak solution verifies the energy equality and hence is continuous into the phase space $L^2$. As an application of this result we prove the existence of a strong global attractor, using the theory of evolutionary systems developed by Cheskidov.Comment: 17 page

Three-body force from kinematical effects in the three-nucleon system

A Galilean-noninvariant correction to ordinary one-boson-exchange potentials is derived. It gives rise to a three-body force in the three-nucleon system. Its importance for the properties of the three-nucleon bound state is tested and found to be small. This result justifies the common practice which neglects the dependence of the one-boson-exchange potentials on the total momentum of the interacting pair in many-nucleon systems

Disk evaporation in a planetary nebula

We study the Galactic bulge planetary nebula M 2-29 (for which a 3-year eclipse event of the central star has been attributed to a dust disk) using HST imaging and VLT spectroscopy, both long-slit and integral field. The central cavity of M 2-29 is filled with a decreasing, slow wind. An inner high density core is detected, with radius less than 250 AU, interpreted as a rotating gas/dust disk with a bipolar disk wind. The evaporating disk is argued to be the source of the slow wind. The central star is a source of a very fast wind (1000 km/s). An outer, partial ring is seen in the equatorial plane, expanding at 12 km/s. The azimuthal asymmetry is attributed to mass-loss modulation by an eccentric binary. M 2-29 presents a crucial point in disk evolution, where ionization causes the gas to be lost, leaving a low-mass dust disk behind.Comment: 11 pages, accepted for publication in "Astronomy and Astrophysics

The very fast evolution of Sakurai's object

V4334 Sgr (a.k.a. Sakurai's object) is the central star of an old planetary nebula that underwent a very late thermal pulse a few years before its discovery in 1996. We have been monitoring the evolution of the optical emission line spectrum since 2001. The goal is to improve the evolutionary models by constraining them with the temporal evolution of the central star temperature. In addition the high resolution spectral observations obtained by X-shooter and ALMA show the temporal evolution of the different morphological components.Comment: 2 pages, 2 figures to appear in the Proceedings of the IAU Symp. 323: "Planetary nebulae: Multi-wavelength probes of stellar and galactic evolution". Eds. X.-W. Liu, L. Stanghellini and A. Karaka