Non-relativistic stellar structure in higher-curvature gravity: systematic construction of solutions to the modified Lane-Emden equations

We study the structure of static spherical stars made up of a non-relativistic polytropic fluid in linearized higher-curvature theories of gravity (HCG). We first formulate the modified Lane-Emden (LE) equation for the stellar profile function in a gauge-invariant manner, finding it boils down to a sixth order differential equation in the generic case of HCG, while it reduces to a fourth order equation in two special cases, reflecting the number of additional massive gravitons arising in each theory. Moreover, the existence of massive gravitons renders the nature of the boundary-value problem unlike the standard LE: some of the boundary conditions can no longer be formulated in terms of physical conditions at the stellar center alone, but some demands at the stellar surface necessarily come into play. We present a practical scheme for constructing solutions to such a problem and demonstrate how it works in the cases of the polytropic index n = 0 and 1, where analytical solutions to the modified LE equations exist. As physical outcomes, we clarify how the stellar radius, mass, and Yukawa charges depend on the theory parameters and how these observables are mutually related. Reasonable upper bounds on the Weyl-squared correction are obtained.Comment: 27 pages, 17 figure

Atmospheres of Hot Super-Earths

Hot super-Earths likely possess minimal atmospheres established through vapor saturation equilibrium with the ground. We solve the hydrodynamics of these tenuous atmospheres at the surface of Corot-7b, Kepler 10b and 55 Cnc-e, including idealized treatments of magnetic drag and ohmic dissipation. We find that atmospheric pressures remain close to their local saturation values in all cases. Despite the emergence of strongly supersonic winds which carry sublimating mass away from the substellar point, the atmospheres do not extend much beyond the day-night terminators. Ground temperatures, which determine the planetary thermal (infrared) signature, are largely unaffected by exchanges with the atmosphere and thus follow the effective irradiation pattern. Atmospheric temperatures, however, which control cloud condensation and thus albedo properties, can deviate substantially from the irradiation pattern. Magnetic drag and ohmic dissipation can also strongly impact the atmospheric behavior, depending on atmospheric composition and the planetary magnetic field strength. We conclude that hot super-Earths could exhibit interesting signatures in reflection (and possibly in emission) which would trace a combination of their ground, atmospheric and magnetic properties.Comment: 14 pages, 4 figures, 1 table, accepted for publication in ApJ

Thermal evolution and lifetime of intrinsic magnetic fields of Super Earths in habitable zones

We have numerically studied the thermal evolution of various-mass terrestrial planets in habitable zones, focusing on duration of dynamo activity to generate their intrinsic magnetic fields, which may be one of key factors in habitability on the planets. In particular, we are concerned with super-Earths, observations of which are rapidly developing. We calculated evolution of temperature distributions in planetary interior, using Vinet equations of state, Arrhenius-type formula for mantle viscosity, and the astrophysical mixing length theory for convective heat transfer modified for mantle convection. After calibrating the model with terrestrial planets in the Solar system, we apply it for 0.1--$10M_{\oplus}$ rocky planets with surface temperature of 300~\mbox{K} (in habitable zones) and the Earth-like compositions. With the criterion for heat flux at the CMB (core-mantle boundary), the lifetime of the magnetic fields is evaluated from the calculated thermal evolution. We found that the lifetime slowly increases with the planetary mass ($M_p$) independent of initial temperature gap at the core-mantle boundary ($\Delta T_{\rm CMB}$) but beyond a critical value $M_{c,p}$ ($\sim O(1)M_{\oplus}$) it abruptly declines by the mantle viscosity enhancement due to the pressure effect. We derived $M_{c,p}$ as a function of $\Delta T_{\rm CMB}$ and a rheological parameter (activation volume, $V^*$). Thus, the magnetic field lifetime of super-Earths with $M_p > M_{p,c}$ sensitively depends on $\Delta T_{\rm CMB}$, which reflects planetary accretion, and $V^*$, which has uncertainty at very high pressure. More advanced high-pressure experiments and first-principle simulation as well as planetary accretion simulation are needed to discuss habitability of super-Earths.Comment: 19pages, 15 figures, accepted for publication in Ap

Quinolizidines. XXVIII. Racemic and chiral syntheses of ochromianine, an indoloquinolizidine alkaloid from Neisosperma miana

A full account is given of the first racemic and chiral syntheses of 11-methoxydihydrocorynantheol [(-)-1], a candidate structure for the Neisosperma alkaloid ochromianine. Coupling of (±)-trans-6-ethoxy-3-ethyl-2,3,4,5-tetrahydro-4-pyridineacetic acid ethyl ester [(±)-6] with 2-chloro-1-(6-methoxy-1H-indol-3-yl)ethanone (4) in the presence of KBr produced the lactam ketone (±)-7,which was then converted into the lactam (±)-9 through the oxazolium salt (±)-8. Bischler-Napieralski cyclization of (±)-9 followed by catalytic hydrogenation gave the tetracyclic ester (±)-11. On reduction with LiAlH_4,(±)-11 yielded the racemic target (±)-1. A parallel synthetic route starting from (+)-6 and 4 afforded the chiral target (-)-1 via (+)-7,8,(+)-9,and (-)-11. Identity of synthetic (-)-1 with ochromianine unequivocally established the structure and absolute stereochemistry of this alkaloid

Quinolizidines. XXVII. Racemic and chiral syntheses of the Neisosperma and Ochrosia alkaloid ochropposinine

The first total synthesis of ochropposinine (1), a Neisosperma and Ochrosia alkaloid, has been accomplished in the form of a racemic modification by means of an initial coupling of the lactim ether (±)-3 with 5 and succeeding steps proceeding through the intermediates (±)-7,(±)-8,(±)-9,(±)-10,and (±)-11. A parallel synthetic route starting with (+)-3 produced the chiral target molecule (-)-1 via the intermediates (+)-7,(+)-8,(+)-9,10,and (-)-11. As a result, the absolute configuration of ochropposinine has been unequivocally established to be that represented by formula (-)-1

〈資料〉石川県の感化院･少年教護院における低能児の顕在化と特別低能学級開設への過程 : 1908（明治41）年～1935（昭和10）年

本研究では、1908（明治41）年から1935（昭和10）年までの時期を対象に、石川県育成院（以下，育成院）における低能児の顕在化および特別低能学級が開設された過程を明らかにすることを目的とする。育成院では、大正後期に低能児の存在が明確に認識された。その後、昭和期に入ると子どもへの知能測定が行われるようになる。低能児への特別な学級が開設されるのは、1935（昭和10）年頃に特別低能学級が設置されてからであり、全国の先駆的な地域と比べると比較的遅かったと言える。その主な原因として、低能児、あるいは精神薄弱児とみなされた子どもの数が少なかったことが考えられる。特別低能学級の開設は遅かったものの、学科についていけない子どものためには大正期から学力別の学級編成を実施し、彼らの学力に合った教育を行おうとしていた。The purpose of this study is to clarify the process of the exteriorization of feeble-minded children in the reformatory of Ishikawa prefecture during the pre-war period, and also to clarity the process by which these children began to be provided special education. The existence of such children came to light during the latter Taisho era. Children then began to be given intelligence measurements starting in the Showa era. Special education was first offered to the feeble-minded children comparatively late in Ishikawa, with the establishment of "Special Class for the Feeble-minded" in 1935. This is most likely due to the fact that there were few children recognized as feeble-minded. Although it took some time for the children to begin receiving special education, classes were actually split by academic ability during the Taisho era in an attempt to provide education suitable to each level of ability, for the benefit of children who were unable to keep up in class

The influence of thermal evolution in the magnetic protection of terrestrial planets

Magnetic protection of potentially habitable planets plays a central role in determining their actual habitability and/or the chances of detecting atmospheric biosignatures. Here we develop a thermal evolution model of potentially habitable Earth-like planets and super-Earths (SEs). Using up-to-date dynamo-scaling laws, we predict the properties of core dynamo magnetic fields and study the influence of thermal evolution on their properties. The level of magnetic protection of tidally locked and unlocked planets is estimated by combining simplified models of the planetary magnetosphere and a phenomenological description of the stellar wind. Thermal evolution introduces a strong dependence of magnetic protection on planetary mass and rotation rate. Tidally locked terrestrial planets with an Earth-like composition would have early dayside magnetopause distances between 1.5 and 4.0 Rp , larger than previously estimated. Unlocked planets with periods of rotation ~1 day are protected by magnetospheres extending between 3 and 8 Rp . Our results are robust in comparison with variations in planetary bulk composition and uncertainties in other critical model parameters. For illustration purposes, the thermal evolution and magnetic protection of the potentially habitable SEs GL 581d, GJ 667Cc, and HD 40307g were also studied. Assuming an Earth-like composition, we found that the dynamos of these planets are already extinct or close to being shut down. While GL 581d is the best protected, the protection of HD 40307g cannot be reliably estimated. GJ 667Cc, even under optimistic conditions, seems to be severely exposed to the stellar wind, and, under the conditions of our model, has probably suffered massive atmospheric losses