Evolutionary Models of Super-Earths and Mini-Neptunes Incorporating Cooling and Mass Loss

We construct models of the structural evolution of super-Earth- and mini-Neptune-type exoplanets with hydrogen-helium envelopes, incorporating radiative cooling and XUV-driven mass loss. We conduct a parameter study of these models, focusing on initial mass, radius, and envelope mass fractions, as well as orbital distance, metallicity, and the specific prescription for mass loss. From these calculations, we investigate how the observed masses and radii of exoplanets today relate to the distribution of their initial conditions. Orbital distance and initial envelope mass fraction are the most important factors determining planetary evolution, particular radius evolution. Initial mass also becomes important below a "turnoff mass," which varies with orbital distance, with mass-radius curves being approximately flat for higher masses. Initial radius is the least important parameter we study, with very little difference between the hot start and cold start limits after an age of 100 Myr. Model sets with no mass loss fail to produce results consistent with observations, but a plausible range of mass loss scenarios is allowed. In addition, we present scenarios for the formation of the Kepler-11 planets. Our best fit to observations Kepler-11b and Kepler-11c involves formation beyond the snow line, after which they moved inward, circularized, and underwent a reduced degree mass loss.Comment: 17 pages, 18 figures, 1 table, Accepted to Ap

The supermembrane revisited

The M2-brane is studied from the perspective of superembeddings. We review the derivation of the M2-brane dynamics and the supergravity constraints from the standard superembedding constraint and we discuss explicitly the induced d=3, N=8 superconformal geometry on the worldvolume. We show that the gauged supermembrane, for a target space with a U(1) isometry, is the standard D2-brane in a type IIA supergravity background. In particular, the D2-brane action, complete with the Dirac-Born-Infeld term, arises from the gauged Wess-Zumino worldvolume 4-form via the brane action principle. The discussion is extended to the massive D2-brane considered as a gauged supermembrane in a massive D=11 superspace background. Type IIA supergeometry is derived using Kaluza-Klein techniques in superspace.Comment: Latex, 46 pages, clarifying remarks and references adde

Mass-Radius Relations and Core-Envelope Decompositions of Super-Earths and Sub-Neptunes

Many exoplanets have been discovered with radii of 1-4 Earth radii, between that of Earth and Neptune. A number of these are known to have densities consistent with solid compositions, while others are "sub-Neptunes" likely to have significant hydrogen-helium envelopes. Future surveys will no doubt significantly expand these populations. In order to understand how the measured masses and radii of such planets can inform their structures and compositions, we construct models both for solid layered planets and for planets with solid cores and gaseous envelopes, exploring a range of core masses, hydrogen-helium envelope masses, and associated envelope entropies. For planets in the super-Earth/sub-Neptune regime for which both radius and mass are measured, we estimate how each is partitioned into a solid core and gaseous envelope, associating a specific core mass and envelope mass with a given exoplanet. We perform this decomposition for both "Earth-like" rock-iron cores and pure ice cores, and find that the necessary gaseous envelope masses for this important sub-class of exoplanets must range very widely from zero to many Earth masses, even for a given core mass. This result bears importantly on exoplanet formation and envelope evaporation processes.Comment: 26 pages, 21 figures, 16 tables, accepted to Ap

The Schwinger SU(3) construction - I: Multiplicity problem and relation to induced representations

The Schwinger oscillator operator representation of SU(3) is analysed with particular reference to the problem of multiplicity of irreducible representations. It is shown that with the use of an $Sp(2,R)$ unitary representation commuting with the SU(3) representation, the infinity of occurrences of each SU(3) irreducible representation can be handled in complete detail. A natural `generating representation' for SU(3), containing each irreducible representation exactly once, is identified within a subspace of the Schwinger construction; and this is shown to be equivalent to an induced representation of SU(3).Comment: Latex, 25 page

Harmonic Analysis on GLnGL_n over Finite Fields

There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio trace(\pi(g)) / dim(\pi), for an irreducible representation \pi of G and an element g of G. It turns out [Gurevich-Howe15, Gurevich-Howe17] that for classical groups G over finite fields there are several (compatible) invariants of representations that provide strong information on the character ratios. We call these invariants collectively rank. Rank suggests a new way to organize the representations of classical groups over finite and local fields - a way in which the building blocks are the "smallest" representations. This is in contrast to Harish-Chandra's philosophy of cusp forms that is the main organizational principle since the 60s, and in it the building blocks are the cuspidal representations which are, in some sense, the "LARGEST". The philosophy of cusp forms is well adapted to establishing the Plancherel formula for reductive groups over local fields, and led to Lusztig's classification of the irreducible representations of such groups over finite fields. However, analysis of character ratios might benefit from a different approach. In this note we discuss further the notion of tensor rank for GL_n over a finite field F_q and demonstrate how to get information on representations of a given tensor rank using tools coming from the recently studied eta correspondence, as well as the well known philosophy of cusp forms, mentioned just above. A significant discovery so far is that although the dimensions of the irreducible representations of a given tensor rank vary by quite a lot (they can differ by large powers of q), for certain group elements of interest the character ratios of these irreps are nearly equal to each other

Solar cycle induced variations in GONG p-mode frequencies and splittings

We have analysed the recently available GONG p-mode frequencies and splitting coefficients for a period of three and half years, including the rapidly rising phase of solar cycle 23. The analysis of mean frequency shift with different activity indices shows that the shift is equally correlated with both magnetic and radiative indices. During the onset of the new cycle 23, we notice that the change in $b_4$ splitting coefficient is more prominent than the change in $b_2$. We have estimated the solar rotation rate with varying depth and latitude. In the equatorial region, the rotation first increases with depth and then decreases, while an opposite behaviour is seen in the polar region. We also find a small but significant temporal variation in the rotation rate at high latitudes.Comment: Uses aastex, To appear in Astrophysical Journal, October 10, 2000 issu

Performance of the Birmingham Solar-Oscillations Network (BiSON)

The Birmingham Solar-Oscillations Network (BiSON) has been operating with a full complement of six stations since 1992. Over 20 years later, we look back on the network history. The meta-data from the sites have been analysed to assess performance in terms of site insolation, with a brief look at the challenges that have been encountered over the years. We explain how the international community can gain easy access to the ever-growing dataset produced by the network, and finally look to the future of the network and the potential impact of nearly 25 years of technology miniaturisation.Comment: 31 pages, 19 figures. Accepted by Solar Physics: 2015 October 20. First online: 2015 December 7. Open Acces

BRST quantization of matrix models with constraints and two-dimensional Yang-Mills theory on the cylinder

BRST quantization of the one-dimensional constrained matrix model which describes two-dimensional Yang-Mills theory on the cylinder is performed. Classical and quantum BRST generators and BRST-invariant hamiltonians are constructed. Evolution operator is expressed in terms of BRST path integral. Advantages of the BRST quantization over the reduced phase space approach leading to the theory of $N$ free fermions are discussed.Comment: 8 page

Changes in the sensitivity of solar p-mode frequency shifts to activity over three solar cycles

Low-degree solar p-mode observations from the long-lived Birmingham Solar Oscillations Network (BiSON) stretch back further than any other single helioseismic data set. Results from BiSON have suggested that the response of the mode frequency to solar activity levels may be different in different cycles. In order to check whether such changes can also be seen at higher degrees, we compare the response of medium-degree solar p-modes to activity levels across three solar cycles using data from Big Bear Solar Observatory (BBSO), Global Oscillation Network Group (GONG), Michelson Doppler Imager (MDI) and Helioseismic and Magnetic Imager (HMI), by examining the shifts in the mode frequencies and their sensitivity to solar activity levels. We compare these shifts and sensitivities with those from radial modes from BiSON. We find that the medium-degree data show small but significant systematic differences between the cycles, with solar cycle 24 showing a frequency shift about 10 per cent larger than cycle 23 for the same change in activity as determined by the 10.7 cm radio flux. This may support the idea that there have been changes in the magnetic properties of the shallow subsurface layers of the Sun that have the strongest influence on the frequency shifts.Comment: 6 pages, 3 figures, accepted by MNRAS 3rd July 201

Parametrizing the time-variation of the "surface term" of stellar p-mode frequencies: application to helioseismic data

The solar-cyle variation of acoustic mode frequencies has a frequency dependence related to the inverse mode inertia. The discrepancy between model predictions and measured oscillation frequencies for solar and solar-type stellar acoustic modes includes a significant frequency-dependent term known as the surface term that is also related to the inverse mode inertia. We parametrize both the surface term and the frequency variations for low-degree solar data from Birmingham Solar-Oscillations Network (BiSON) and medium-degree data from the Global Oscillations Network Group (GONG) using the mode inertia together with cubic and inverse frequency terms. We find that for the central frequency of rotationally split multiplets the cubic term dominates both the average surface term and the temporal variation, but for the medium-degree case the inverse term improves the fit to the temporal variation. We also examine the variation of the even-order splitting coefficients for the medium-degree data and find that, as for the central frequency, the latitude-dependent frequency variation, which reflects the changing latitudinal distribution of magnetic activity over the solar cycle, can be described by the combination of a cubic and an inverse function of frequency scaled by inverse mode inertia. The results suggest that this simple parametrization could be used to assess the activity-related frequency variation in solar-like asteroseismic targets.Comment: 13 pages, 11 figures. Accepted by MNRAS 13 October 201