A Simple Model for Solar Isorotational Contours

The solar convective zone, or SCZ, is nearly adiabatic and marginally convectively unstable. But the SCZ is also in a state of differential rotation, and its dynamical stability properties are those of a weakly magnetized gas. This renders it far more prone to rapidly growing rotational baroclinic instabilities than a hydrodynamical system would be. These instabilities should be treated on the same footing as convective instabilites. If isentropic and isorotational surfaces coincide in the SCZ, the gas is marginally (un)stable to {\em both} convective and rotational disturbances. This is a plausible resolution for the instabilities associated with these more general rotating convective systems. This motivates an analysis of the thermal wind equation in which isentropes and isorotational surfaces are identical. The characteristics of this partial differential equation correspond to isorotation contours, and their form may be deduced even without precise knowledge of how the entropy and rotation are functionally related. Although the exact solution of the global SCZ problem in principle requires this knowledge, even the simplest models produce striking results in broad agreement with helioseismology data. This includes horizontal (i.e. quasi-spherical) isorotational contours at the poles, axial contours at the equator, and approximately radial contours at midlatitudes. The theory does not apply directly to the tachocline, where a simple thermal wind balance is not expected to be valid. The work presented here is subject to tests of self-consistency, among them the prediction that there should be good agreement between isentropes and isorotational contours in sufficiently well-resolved large scale numerical MHD simulations.Comment: Final version: 21 pages, 4 figures, to appear in MNRAS; thorough revision, typos and minor errors corrected, expanded development and reordering of the material. Conclusions unchanged from origina

The stability of stratified, rotating systems and the generation of vorticity in the Sun

We examine the linear behavior of three-dimensional Lagrangian displacements in a stratified, shearing background. The isentropic and iso-rotation surfaces of the equilibrium flow are assumed to be axisymmetric, but otherwise fully two-dimensional. Three-dimensional magnetic fields are included in the perturbation equations; however the equilibrium is assumed to be well-described by purely hydrodynamic forces. The model, in principle very general, is used to study the behavior of fluid displacements in an environment resembling the solar convection zone. Some very suggestive results emerge. All but high-latitude displacements align themselves with the observed surfaces of constant angular velocity. The tendency for the angular velocity to remain constant with depth in the bulk of the convective zone, together with other critical features of the rotation profile, emerge from little more than a visual inspection of the governing equation. In the absence of a background axial angular velocity gradient, displacements exhibit no poleward bias, suggesting that solar convection "plays-off" of prexisting shear rather than creates it. We argue that baroclinic vorticity of precisely the right order is generated at the radiative/convective zone boundary due to centrifugal distortion of equipotential surfaces that is not precisely followed by isothermal surfaces. If so, many features of the Sun's internal rotation become more clear, including: i) the general appearance of the tachocline; ii) the extension of differential rotation well into the radiative zone; iii) the abrupt change of morphology of convective zone isorotation surfaces; and iv) the inability of current numerical simulations to reproduce the solar rotation profile without imposed entropy boundary conditions.Comment: 30 pages, 2 figures. Accepted for publication in MNRA

The effect of the tachocline on differential rotation in the Sun

In this paper, we present a model for the effects of the tachocline on the differential rotation in the solar convection zone. The mathematical technique relies on the assumption that entropy is nearly constant ("well-mixed") in isorotation surfaces both outside and within the tachocline. The resulting solutions exhibit nontrivial features that strikingly resemble the true tachocline isorotation contours in unexpected detail. This strengthens the mathematical premises of the theory. The observed rotation pattern in the tachocline shows strong quadrupolar structure, an important feature that is explicitly used in constructing our solutions. The tachocline is treated locally as an interior boundary layer of small but finite thickness, and an explicit global solution is then constructed. A dynamical link can thus be established between the internal jump in the angular velocity at the tachocline and the spread of angular velocities observed near the solar surface. In general, our results suggest that the bulk of the solar convection zone is in thermal wind balance, and that simple quadrupolar stresses, local in radius, mediate the tachocline transition from differential rotation to uniform rotation in the radiative interior.Comment: 20 Pages, 4 figures, to appear in MNRA

Differential rotation in fully convective stars

Under the assumption of thermal wind balance and effective entropy mixing in constant rotation surfaces, the isorotational contours of the solar convective zone may be reproduced with great fidelity. Even at this early stage of development, this helioseismology fit may be used to put a lower bound on the midlatitude {\em radial} solar entropy gradient, which in good accord with standard mixing length theory. In this paper, we generalize this solar calculation to fully convective stars (and potentially planets), retaining the assumptions of thermal wind balance and effective entropy mixing in isorotational surfaces. It is found that each isorotation contour is of the form $R^2 = A+B\Phi(r)$, where $R$ is the radius from the rotation axis, $\Phi(r)$ is the (assumed spherical) gravitational potential, and $A$ and $B$ are constant along the contour. This result is applied to simple models of fully convective stars. Both solar-like surface rotation profiles (angular velocity decreasing toward the poles) as well as "antisolar" profiles (angular velocity increasing toward the poles) are modeled; the latter bear some suggestive resemblance to numerical simulations. We also perform exploratory studies of zonal surface flows similar to those seen in Jupiter and Saturn. In addition to providing a practical framework for understanding the results of large scale numerical simulations, our findings may also prove useful in dynamical calculations for which a simple but viable model for the background rotation profile in a convecting fluid is needed. Finally, our work bears directly on an important goal of the CoRoT program: to elucidate the internal structure of rotating, convecting stars.Comment: 21 pages, 20 figures. Accepted for publication in MNRA

Gravity modes as a way to distinguish between hydrogen- and helium-burning red giant stars

Red giants are evolved stars that have exhausted the supply of hydrogen in their cores and instead burn hydrogen in a surrounding shell. Once a red giant is sufficiently evolved, the helium in the core also undergoes fusion. Outstanding issues in our understanding of red giants include uncertainties in the amount of mass lost at the surface before helium ignition and the amount of internal mixing from rotation and other processes. Progress is hampered by our inability to distinguish between red giants burning helium in the core and those still only burning hydrogen in a shell. Asteroseismology offers a way forward, being a powerful tool for probing the internal structures of stars using their natural oscillation frequencies. Here we report observations of gravity-mode period spacings in red giants that permit a distinction between evolutionary stages to be made. We use high-precision photometry obtained with the Kepler spacecraft over more than a year to measure oscillations in several hundred red giants. We find many stars whose dipole modes show sequences with approximately regular period spacings. These stars fall into two clear groups, allowing us to distinguish unambiguously between hydrogen-shell-burning stars (period spacing mostly about 50 seconds) and those that are also burning helium (period spacing about 100 to 300 seconds).Comment: to appear as a Letter to Natur

The Milky Way's circular velocity curve between 4 and 14 kpc from APOGEE data

We measure the Milky Way's rotation curve over the Galactocentric range 4 kpc <~ R <~ 14 kpc from the first year of data from the Apache Point Observatory Galactic Evolution Experiment (APOGEE). We model the line-of-sight velocities of 3,365 stars in fourteen fields with b = 0 deg between 30 deg < l < 210 deg out to distances of 10 kpc using an axisymmetric kinematical model that includes a correction for the asymmetric drift of the warm tracer population (\sigma_R ~ 35 km/s). We determine the local value of the circular velocity to be V_c(R_0) = 218 +/- 6 km/s and find that the rotation curve is approximately flat with a local derivative between -3.0 km/s/kpc and 0.4 km/s/kpc. We also measure the Sun's position and velocity in the Galactocentric rest frame, finding the distance to the Galactic center to be 8 kpc < R_0 < 9 kpc, radial velocity V_{R,sun} = -10 +/- 1 km/s, and rotational velocity V_{\phi,sun} = 242^{+10}_{-3} km/s, in good agreement with local measurements of the Sun's radial velocity and with the observed proper motion of Sgr A*. We investigate various systematic uncertainties and find that these are limited to offsets at the percent level, ~2 km/s in V_c. Marginalizing over all the systematics that we consider, we find that V_c(R_0) 99% confidence. We find an offset between the Sun's rotational velocity and the local circular velocity of 26 +/- 3 km/s, which is larger than the locally-measured solar motion of 12 km/s. This larger offset reconciles our value for V_c with recent claims that V_c >~ 240 km/s. Combining our results with other data, we find that the Milky Way's dark-halo mass within the virial radius is ~8x10^{11} M_sun.Comment: submitted to Ap

Striatal Pre- and Postsynaptic Profile of Adenosine A2A Receptor Antagonists

Striatal adenosine A2A receptors (A2ARs) are highly expressed in medium spiny neurons (MSNs) of the indirect efferent pathway, where they heteromerize with dopamine D2 receptors (D2Rs). A2ARs are also localized presynaptically in cortico-striatal glutamatergic terminals contacting MSNs of the direct efferent pathway, where they heteromerize with adenosine A1 receptors (A1Rs). It has been hypothesized that postsynaptic A2AR antagonists should be useful in Parkinson's disease, while presynaptic A2AR antagonists could be beneficial in dyskinetic disorders, such as Huntington's disease, obsessive-compulsive disorders and drug addiction. The aim or this work was to determine whether selective A2AR antagonists may be subdivided according to a preferential pre- versus postsynaptic mechanism of action. The potency at blocking the motor output and striatal glutamate release induced by cortical electrical stimulation and the potency at inducing locomotor activation were used as in vivo measures of pre- and postsynaptic activities, respectively. SCH-442416 and KW-6002 showed a significant preferential pre- and postsynaptic profile, respectively, while the other tested compounds (MSX-2, SCH-420814, ZM-241385 and SCH-58261) showed no clear preference. Radioligand-binding experiments were performed in cells expressing A2AR-D2R and A1R-A2AR heteromers to determine possible differences in the affinity of these compounds for different A2AR heteromers. Heteromerization played a key role in the presynaptic profile of SCH-442416, since it bound with much less affinity to A2AR when co-expressed with D2R than with A1R. KW-6002 showed the best relative affinity for A2AR co-expressed with D2R than co-expressed with A1R, which can at least partially explain the postsynaptic profile of this compound. Also, the in vitro pharmacological profile of MSX-2, SCH-420814, ZM-241385 and SCH-58261 was is in accordance with their mixed pre- and postsynaptic profile. On the basis of their preferential pre- versus postsynaptic actions, SCH-442416 and KW-6002 may be used as lead compounds to obtain more effective antidyskinetic and antiparkinsonian compounds, respectively

KEAP1-modifying small molecule reveals muted NRF2 signaling responses in neural stem cells from Huntington's disease patients

The activity of the transcription factor nuclear factor-erythroid 2 p45-derived factor 2 (NRF2) is orchestrated and amplified through enhanced transcription of antioxidant and antiinflammatory target genes. The present study has characterized a triazole-containing inducer of NRF2 and elucidated the mechanism by which this molecule activates NRF2 signaling. In a highly selective manner, the compound covalently modifies a critical stress-sensor cysteine (C151) of the E3 ligase substrate adaptor protein Kelch-like ECH-associated protein 1 (KEAP1), the primary negative regulator of NRF2. We further used this inducer to probe the functional consequences of selective activation of NRF2 signaling in Huntington's disease (HD) mouse and human model systems. Surprisingly, we discovered a muted NRF2 activation response in human HD neural stem cells, which was restored by genetic correction of the disease-causing mutation. In contrast, selective activation of NRF2 signaling potently repressed the release of the proinflammatory cytokine IL-6 in primary mouse HD and WT microglia and astrocytes. Moreover, in primary monocytes from HD patients and healthy subjects, NRF2 induction repressed expression of the proinflammatory cytokines IL-1, IL-6, IL-8, and TNFα. Together, our results demonstrate a multifaceted protective potential of NRF2 signaling in key cell types relevant to HD pathology

Raphaël Levi de Hanovre et la Frühaufklärung juive

Raphael Levi Hannover -Exemplar of Jewish «Fruhaufklärung ». Raphael Levi Hannover (1685-1779) was clerk to «court-Jews » and amenuensis in Leibniz's house from 1700 until the Hatter's death. His Jewishly philosophical and scientific inspiration was Maimonides. He lived long enough to be friends with Moses Mendelssohn. Levi earned his livelihood mostly as a teacher of commercial arithmetic, with which his German books deal, but his chief scholarly concern was calendaric astronomy, with which his Hebrew books deal. In the latter he made adjustments to Copernican astronomy. Levi submitted a scientific plan in person to the Royal Society in London in 1748. A long-lost eschatological essay by him, written in the 1730's, has now been discovered, in which he dates the messianic advent in 1783. Levi's life and work are set in the social economy and culture of the age of Enlightenment.Schwarzschild Steven S. Raphaël Levi de Hanovre et la Frühaufklärung juive. In: Dix-huitième Siècle, n°13, 1981. Juifs et judaïsme. pp. 27-36