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We consider an internally heated fluid between parallel plates with fixed thermal fluxes. For a large class of heat sources that vary in the direction of gravity, we prove that $\langle\delta T \rangle_h \geq \sigma R^{-1/3} - \mu$, where $\langle\delta T \rangle_h$ is the average temperature difference between the bottom and top plates, $R$ is a `flux' Rayleigh number and the constants $\sigma,\mu >0$ depend on the geometric properties of the internal heating. This result implies that mean downward conduction (for which $\langle\delta T \rangle_h< 0$) is impossible for a range of Rayleigh numbers smaller than a critical value $R_0$. The bound demonstrates that $R_0$ depends on the heating distribution and can be made arbitrarily large by concentrating the heating near the bottom plate. However, for any given fixed heating profile of the class we consider, the corresponding value of $R_0$ is always finite. This points to a fundamental difference between internally heated convection and its limiting case of Rayleigh-B\'enard convection with fixed flux boundary conditions, for which $\langle\delta T \rangle_h$ is known to be positive for all $R$., Comment: 13 pages, 4 figures

Some hydrogen-rich core-collapse supernovae (type IIP SNe) exhibit evidence for a sustained energy source powering their light curves, resulting in a brighter and/or longer-lasting hydrogen-recombination plateau phase. We present a semi-analytic SNIIP light curve model that accounts for the effects of an arbitrary internal heating source, considering as special cases $^{56}$Ni/$^{56}$Co decay, a central engine (millisecond magnetar or accreting compact object), and shock interaction with a dense circumstellar disk. While a sustained internal power source can boost the plateau luminosity commensurate with the magnitude of the power, the duration of the recombination plateau can typically be increased by at most a factor $\sim 2-3$ compared to the zero-heating case. For a given ejecta mass and initial kinetic energy, the longest plateau duration is achieved for a constant heating rate at the highest magnitude that does not appreciably accelerate the ejecta. This finding has implications for the minimum ejecta mass required to explain particularly long-lasting supernovae such as iPTF14hls, and for confidently identifying rare explosions of the most-massive hydrogen-rich (e.g. population III) stars. We present a number of analytic estimates which elucidate the key features of the detailed model., Comment: 28 pages, 15 figures, 1 table, accepted for publication in ApJ

The cooling of neutron stars (hereafter NS) has the potential to reveal important features of superdense matter. Their surface temperatures are known for a fair sample of NS with ages $\leq 10^{6} \, {\it{yr}}$, and with a few exceptions, can be accommodated by standard cooling mechanisms (neutrino+photon emission without internal heating). However, for the older objects it is necessary to consider some internal heating to explain surface temperatures higher than expected. We revisit in this paper the kinetic heating by fermionic dark matter, rotochemical heating and magnetic field decay. We found that NS slightly older than $\sim 10^{6} \, {\it{yr}}$ can be explained by them, but the older ``black widow'' systems are much hotter than the values predicted by these three mechanisms, pointing towards a yet unknown heating factor for old NS., Comment: Accepted for publication in IJMPD, 25 pages, 10 figures, 3 tables

The role of electron captures by nuclei in the shallow heating of magnetars is further investigated using both nuclear measurements and the theoretical atomic mass table HFB-27. Starting from the composition of the outer crust in full equilibrium, we have calculated the onset of electron captures and the heat released due to the slow decay of the magnetic field. Numerical results are found to be similar to those previously obtained with the HFB-24 atomic mass model and are consistent with neutron-star cooling data., Comment: 6 pages, 1 figure. Contribution to the proceedings of the XLIV Brazilian Workshop on Nuclear Physics

A new mechanism for the internal heating of ultra-short-period planets is proposed based on the gravitational perturbation by a non-axisymmetric quadrupole moment of their host stars. Such a quadrupole is due to the magnetic flux tubes in the stellar convection zone, unevenly distributed in longitude and persisting for many stellar rotations as observed in young late-type stars. The rotation period of the host star evolves from its shortest value on the zero-age main sequence to longer periods due to the loss of angular momentum through a magnetized wind. If the stellar rotation period comes close to twice the orbital period of the planet, the quadrupole leads to a spin-orbit resonance that excites oscillations of the star-planet separation. As a consequence, a strong tidal dissipation is produced inside the planet. We illustrate the operation of the mechanism by modeling the evolution of the stellar rotation and of the innermost planetary orbit in the cases of CoRoT-7, Kepler-78, and K2-141 whose present orbital periods range between 0.28 and 0.85 days. If the spin-orbit resonance occurs, the maximum power dissipated inside the planets ranges between $10^{18}$ and $10^{19}$ W, while the total dissipated energy is of the order of $10^{30}-10^{32}$ J over a time interval as short as $(1-4.5) \times 10^{4}$ yr. Such a huge heating over a so short time interval produces a complete melting of the planetary interiors and may shut off their hydromagnetic dynamos. These may initiate a successive phase of intense internal heating owing to unipolar magnetic star-planet interactions and affect the composition and the escape of their atmospheres, producing effects that could be observable during the entire lifetime of the planets [abridged abstract]., Comment: 18 pages, 1 appendix, 9 figures, 3 tables; accepted by Astronomy & Astrophysics

Neutron star models with maximum mass close to $2 \ M_{\odot}$ reach high central densities, which may activate nucleonic and hyperon direct Urca neutrino emission. To alleviate the tension between fast theoretical cooling rates and thermal luminosity observations of moderately magnetized, isolated thermally-emitting stars (with $L_{\gamma} \gtrsim 10^{31}$ erg s$^{-1}$ at $t \gtrsim 10^{5.3}$ yr), some internal heating source is required. The power supplied by the internal heater is estimated for both a phenomenological source in the inner crust and Joule heating due to magnetic field decay, assuming different superfluidity models and compositions of the outer stellar envelope. It is found that a thermal power of $W(t) \approx 10^{34}$ erg s$^{-1}$ allows neutron star models to match observations of moderately magnetized, isolated stars with ages $t \gtrsim 10^{5.3}$ yr. The requisite $W(t)$ can be supplied by Joule heating due to crust-confined initial magnetic configurations with (i) mixed poloidal-toroidal fields, with surface strength $B_{\textrm{dip}} = 10^{13}$ G at the pole of the dipolar poloidal component and $\sim 90$ per cent of the magnetic energy stored in the toroidal component; and (ii) poloidal-only configurations with $B_{\textrm{dip}} = 10^{14}$ G., Comment: 15 pages, 9 figures. Accepted for publication in MNRAS

The mean vertical heat transport $\langle wT \rangle$ in convection between isothermal plates driven by uniform internal heating is investigated by means of rigorous bounds. These are obtained as a function of the Rayleigh number $R$ by constructing feasible solutions to a convex variational problem, derived using a formulation of the classical background method in terms of quadratic auxiliary functions. When the fluid's temperature relative to the boundaries is allowed to be positive or negative, numerical solution of the variational problem shows that best previous bound $\langle wT \rangle \leq 1/2$ can only be improved up to finite $R$. Indeed, we demonstrate analytically that $ \langle wT \rangle \leq 2^{-21/5} R^{1/5}$ and therefore prove that $\langle wT\rangle< 1/2$ for $R < 65\,536$. However, if the minimum principle for temperature is invoked, which asserts that internal temperature is at least as large as the temperature of the isothermal boundaries, then numerically optimised bounds are strictly smaller than $1/2$ until at least $R =3.4\times 10^{5}$. While the computational results suggest that the best bound on $\langle wT\rangle$ approaches $1/2$ asymptotically from below as $R\rightarrow \infty$, we prove that typical analytical constructions cannot be used to prove this conjecture., Comment: 33 pages, 12 figures

Mirror sectors have been proposed to address the problems of dark matter, baryogenesis, and the neutron lifetime anomaly. In this work we study a new, powerful probe of mirror neutrons: neutron star temperatures. When neutrons in the neutron star core convert to mirror neutrons during collisions, the vacancies left behind in the nucleon Fermi seas are refilled by more energetic nucleons, releasing immense amounts of heat in the process. We derive a new constraint on the allowed strength of neutron--mirror-neutron mixing from observations of the coldest (sub-40,000 Kelvin) neutron star, PSR 2144$-$3933. Our limits compete with laboratory searches for neutron--mirror-neutron transitions but apply to a range of mass splittings between the neutron and mirror neutron that is 19 orders of magnitude larger. This heating mechanism, also pertinent to other neutron disappearance channels such as exotic neutron decay, provides a compelling physics target for upcoming ultraviolet, optical and infrared telescopes to study thermal emissions of cold neutron stars., Comment: 4ish pages revtex4 + references, 1 figure; v2 matches PRL