On the linear fractional self-attracting diffusion

In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2<H<1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its convergence and the corresponding weighted local time. For 2-dimensional process, as a related problem, we show that the renormalized self-intersection local time exists in L^2 if $\frac12<H<\frac3{4}$.Comment: 14 Pages. To appear in Journal of Theoretical Probabilit

The K2 Galactic Archaeology Program Data Release 2: Asteroseismic Results from Campaigns 4, 6, and 7

Studies of Galactic structure and evolution have benefited enormously from Gaia kinematic information, though additional, intrinsic stellar parameters like age are required to best constrain Galactic models. Asteroseismology is the most precise method of providing such information for field star populations en masse, but existing samples for the most part have been limited to a few narrow fields of view by the CoRoT and Kepler missions. In an effort to provide well-characterized stellar parameters across a wide range in Galactic position, we present the second data release of red giant asteroseismic parameters for the K2 Galactic Archaeology Program (GAP). We provide V_{max} and Delta_{v} based on six independent pipeline analyses; first-ascent red giant branch (RGB) and red clump (RC) evolutionary state classifications from machine learning; and ready-to-use radius and mass coefficients, K_{R} and K_{M}, which, when appropriately multiplied by a solar-scaled effective temperature factor, yield physical stellar radii and masses. In total, we report 4395 radius and mass coefficients, with typical uncertainties of 3.3% (stat.) ± 1% (syst.) for K_{R} and 7.7% (stat.) ± 2% (syst.) for κM among RGB stars, and 5.0% (stat.) ± 1% (syst.) for K_{R} nd 10.5% (stat.) ± 2% (syst.) for κM among RC stars. We verify that the sample is nearly complete—except for a dearth of stars with V_{max} \leqslant 10-20 mHz-by comparing to Galactic models and visual inspection. Our asteroseismic radii agree with radii derived from Gaia Data Release 2 parallaxes to within 2.2% ± 0.3% for RGB stars and 2.0% ± 0.6% for RC stars

Confirming chemical clocks: asteroseismic age dissection of the Milky Way disk(s)

Investigations of the origin and evolution of the Milky Way disk have long relied on chemical and kinematic identification of its components to reconstruct our Galactic past. Difficulties in determining precise stellar ages have restricted most studies to small samples, normally confined to the solar neighbourhood. Here we break this impasse with the help of asteroseismic inference and perform a chronology of the evolution of the disk throughout the age of the Galaxy. We chemically dissect the Milky Way disk population using a sample of red giant stars spanning out to 2~kpc in the solar annulus observed by the {\it Kepler} satellite, with the added dimension of asteroseismic ages. Our results reveal a clear difference in age between the low- and high-$\alpha$ populations, which also show distinct velocity dispersions in the $V$ and $W$ components. We find no tight correlation between age and metallicity nor [$\alpha$/Fe] for the high-$\alpha$ disk stars. Our results indicate that this component formed over a period of more than 2~Gyr with a wide range of [M/H] and [$\alpha$/Fe] independent of time. Our findings show that the kinematic properties of young $\alpha$-rich stars are consistent with the rest of the high-$\alpha$ population and different from the low-$\alpha$ stars of similar age, rendering support to their origin being old stars that went through a mass transfer or stellar merger event, making them appear younger, instead of migration of truly young stars formed close to the Galactic bar

Confirming chemical clocks: asteroseismic age dissection of the Milky Way disc(s)

Investigations of the origin and evolution of the Milky Way disc have long relied on chemical and kinematic identifications of its components to reconstruct our Galactic past. Difficulties in determining precise stellar ages have restricted most studies to small samples, normally confined to the solar neighbourhood. Here, we break this impasse with the help of asteroseismic inference and perform a chronology of the evolution of the disc throughout the age of the Galaxy. We chemically dissect the Milky Way disc population using a sample of red giant stars spanning out to 2 kpc in the solar annulus observed by the Kepler satellite, with the added dimension of asteroseismic ages. Our results reveal a clear difference in age between the low- and high-α populations, which also show distinct velocity dispersions in the V and W components. We find no tight correlation between age and metallicity nor [α/Fe] for the high-α disc stars. Our results indicate that this component formed over a period of more than 2 Gyr with a wide range of [M/H] and [α/Fe] independent of time. Our findings show that the kinematic properties of young α-rich stars are consistent with the rest of the high-α population and different from the low-α stars of similar age, rendering support to their origin being old stars that went through a mass transfer or stellar merger event, making them appear younger, instead of migration of truly young stars formed close to the Galactic bar

The Correlation between Mixing Length and Metallicity on the Giant Branch: Implications for Ages in the Gaia Era

In the updated APOGEE-Kepler catalog, we have asteroseismic and spectroscopic data for over 3000 first ascent red giants. Given the size and accuracy of this sample, these data offer an unprecedented test of the accuracy of stellar models on the post-main-sequence. When we compare these data to theoretical predictions, we find a metallicity dependent temperature offset with a slope of around 100 K per dex in metallicity. We find that this effect is present in all model grids tested, and that theoretical uncertainties in the models, correlated spectroscopic errors, and shifts in the asteroseismic mass scale are insufficient to explain this effect. Stellar models can be brought into agreement with the data if a metallicity-dependent convective mixing length is used, with Delta alpha(ML), YREC similar to 0.2 per dex in metallicity, a trend inconsistent with the predictions of three-dimensional stellar convection simulations. If this effect is not taken into account, isochrone ages for red giants from the Gaia data will be off by as much as a factor of two even at modest deviations from solar metallicity ([Fe/H]- -0.5)

Dynamical heating across the Milky Way disc using APOGEE and Gaia

The kinematics of the Milky Way disc as a function of age are well measured at the solar radius, but have not been studied over a wider range of Galactocentric radii. Here, we measure the kinematics of mono-age, mono-[Fe/H] populations in the low and high [α/Fe] discs between 4 ≲ R ≲ 13 kpc and |z| ≲ 2 kpc using 65 719 stars in common between APOGEE DR14 and Gaia DR2 for which we estimate ages using a Bayesian neural network model trained on asteroseismic ages. We determine the vertical and radial velocity dispersions, finding that the low and high [α/Fe] discs display markedly different age–velocity dispersion relations (AVRs) and shapes σz/σR. The high [α/Fe] disc has roughly flat AVRs and constant σz/σR = 0.64 ± 0.04, whereas the low [α/Fe] disc has large variations in this ratio that positively correlate with the mean orbital radius of the population at fixed age. The high [α/Fe] disc component’s flat AVRs and constant σz/σR clearly indicate an entirely different heating history. Outer disc populations also have flatter radial AVRs than those in the inner disc, likely due to the waning effect of spiral arms. Our detailed measurements of AVRs and σz/σR across the disc indicate that low [α/Fe], inner disc (⁠R≲10kpc⁠) stellar populations are likely dynamically heated by both giant molecular clouds and spiral arms, while the observed trends for outer disc populations require a significant contribution from another heating mechanism such as satellite perturbations. We also find that outer disc populations have slightly positive mean vertical and radial velocities likely because they are part of the warped disc

The quest for the solar g modes

Solar gravity modes (or g modes) -- oscillations of the solar interior for which buoyancy acts as the restoring force -- have the potential to provide unprecedented inference on the structure and dynamics of the solar core, inference that is not possible with the well observed acoustic modes (or p modes). The high amplitude of the g-mode eigenfunctions in the core and the evanesence of the modes in the convection zone make the modes particularly sensitive to the physical and dynamical conditions in the core. Owing to the existence of the convection zone, the g modes have very low amplitudes at photospheric levels, which makes the modes extremely hard to detect. In this paper, we review the current state of play regarding attempts to detect g modes. We review the theory of g modes, including theoretical estimation of the g-mode frequencies, amplitudes and damping rates. Then we go on to discuss the techniques that have been used to try to detect g modes. We review results in the literature, and finish by looking to the future, and the potential advances that can be made -- from both data and data-analysis perspectives -- to give unambiguous detections of individual g modes. The review ends by concluding that, at the time of writing, there is indeed a consensus amongst the authors that there is currently no undisputed detection of solar g modes.Comment: 71 pages, 18 figures, accepted by Astronomy and Astrophysics Revie