The relation between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime

The connection between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime is studied. Under a scaling hypothesis, we find that the three-point correlation function, $\zeta$, obeys the scaling law $\zeta\propto \xi^{\frac{3m+4w-2\epsilon}{2m+2w}}$ in the nonlinear regime, where $\xi$, $m$, $w$, and $\epsilon$ are the two-point correlation function, the power index of the power spectrum in the nonlinear regime, the number of spatial dimensions, and the power index of the phase correlations, respectively. The new formula reveals the origin of the power index of the three-point correlation function. We also obtain the theoretical condition for which the ``hierarchical form'' $\zeta\propto\xi^2$ is reproduced.Comment: 16 pages, 4 figures. Accepted for publication in APJ. Some sentences and figures are revise

Metallicity dependence of the Hercules stream in Gaia/RAVE data -- explanation by non-closed orbits

The origin of the Hercules stream, the most prominent velocity substructure in the Solar neighbour disc stars, is still under debate. Recent accurate measurements of position, velocity, and metallicity provided by Tycho Gaia Astrometric Solution (TGAS) and RAdial Velocity Experiments (RAVE) have revealed that the Hercules stream is most clearly seen in the metal-rich region ([Fe/H] > 0), while it is not clearly seen in lower metallicity region ([Fe/H] < -0.25). By using a large number of chemo-dynamical 2D test-particle simulations with a rotating bar and/or spiral arms, we find that the observed [Fe/H] dependence of the Hercules stream is a natural consequence of the inside-out formation of the stellar disc and the existence of highly non-closed orbits in the rotating frame of the bar or spiral arms. Our successful models that reproduce the observed properties of the Hercules stream include not only fast-bar-only and fast-bar+spiral models, but also slow-bar+spiral models. This indicates that it is very difficult to estimate the pattern speed of the bar or spiral arms based only on the observations of the Hercules stream in the Solar neighbourhood. As a by-product of our simulations, we make some predictions about the locations across the Galactic plane where we can observe velocity bimodality that is not associated with the Hercules stream. These predictions can be tested by the forthcoming Gaia data, and such a test will improve our understanding of the evolution of the Milky Way stellar disc

Universality in the distribution of caustics in the expanding Universe

We numerically investigate the long--time evolution of density perturbations after the first appearance of caustics in an expanding cosmological model with one--dimensional `single--wave' initial conditions. Focussing on the time--intervals of caustic appearances and the spatial distribution of caustics at subsequent times, we find that the time--intervals of caustic appearances approach a constant, i.e., their time--subsequent ratio converges to 1; it is also found that the spatial distribution of caustics at a given time features some universality rules, e.g., the ratio between the position of the nearest caustic from the center and that of the second nearest caustic from the center approaches a constant. Furthermore we find some rules for the mass distribution for each caustic. Using these universality constants we are in the position to predict the spatial distribution of caustics at an arbitrary time in order to give an estimate for the power spectral index in the fully--developed non--dissipative turbulent (`virialized') regime.Comment: 23 pages, 19 figure

Metallicity dependence of the Hercules stream in Gaia/RAVE data -- explanation by non-closed orbits

The origin of the Hercules stream, the most prominent velocity substructure in the Solar neighbour disc stars, is still under debate. Recent accurate measurements of position, velocity, and metallicity provided by Tycho Gaia Astrometric Solution (TGAS) and RAdial Velocity Experiments (RAVE) have revealed that the Hercules stream is most clearly seen in the metal-rich region ([Fe/H] > 0), while it is not clearly seen in lower metallicity region ([Fe/H] < -0.25). By using a large number of chemo-dynamical 2D test-particle simulations with a rotating bar and/or spiral arms, we find that the observed [Fe/H] dependence of the Hercules stream is a natural consequence of the inside-out formation of the stellar disc and the existence of highly non-closed orbits in the rotating frame of the bar or spiral arms. Our successful models that reproduce the observed properties of the Hercules stream include not only fast-bar-only and fast-bar+spiral models, but also slow-bar+spiral models. This indicates that it is very difficult to estimate the pattern speed of the bar or spiral arms based only on the observations of the Hercules stream in the Solar neighbourhood. As a by-product of our simulations, we make some predictions about the locations across the Galactic plane where we can observe velocity bimodality that is not associated with the Hercules stream. These predictions can be tested by the forthcoming Gaia data, and such a test will improve our understanding of the evolution of the Milky Way stellar disc

The JWST Galactic Center Survey -- A White Paper

The inner hundred parsecs of the Milky Way hosts the nearest supermassive black hole, largest reservoir of dense gas, greatest stellar density, hundreds of massive main and post main sequence stars, and the highest volume density of supernovae in the Galaxy. As the nearest environment in which it is possible to simultaneously observe many of the extreme processes shaping the Universe, it is one of the most well-studied regions in astrophysics. Due to its proximity, we can study the center of our Galaxy on scales down to a few hundred AU, a hundred times better than in similar Local Group galaxies and thousands of times better than in the nearest active galaxies. The Galactic Center (GC) is therefore of outstanding astrophysical interest. However, in spite of intense observational work over the past decades, there are still fundamental things unknown about the GC. JWST has the unique capability to provide us with the necessary, game-changing data. In this White Paper, we advocate for a JWST NIRCam survey that aims at solving central questions, that we have identified as a community: i) the 3D structure and kinematics of gas and stars; ii) ancient star formation and its relation with the overall history of the Milky Way, as well as recent star formation and its implications for the overall energetics of our galaxy's nucleus; and iii) the (non-)universality of star formation and the stellar initial mass function. We advocate for a large-area, multi-epoch, multi-wavelength NIRCam survey of the inner 100\,pc of the Galaxy in the form of a Treasury GO JWST Large Program that is open to the community. We describe how this survey will derive the physical and kinematic properties of ~10,000,000 stars, how this will solve the key unknowns and provide a valuable resource for the community with long-lasting legacy value.Comment: This White Paper will be updated when required (e.g. new authors joining, editing of content). Most recent update: 24 Oct 202

JASMINE: Near-infrared astrometry and time-series photometry science

The Japan Astrometry Satellite Mission for INfrared Exploration (JASMINE) is a planned M-class science space mission by the Institute of Space and Astronautical Science, the Japan Aerospace Exploration Agency. JASMINE has two main science goals. One is Galactic archaeology with a Galactic Center survey, which aims to reveal the Milky Way’s central core structure and formation history from Gaia-level (∼25 ${\mu}$as) astrometry in the near-infrared (NIR) Hw band (1.0–1.6 ${\mu}$m). The other is an exoplanet survey, which aims to discover transiting Earth-like exoplanets in the habitable zone from NIR time-series photometry of M dwarfs when the Galactic Center is not accessible. We introduce the mission, review many science objectives, and present the instrument concept. JASMINE will be the first dedicated NIR astrometry space mission and provide precise astrometric information on the stars in the Galactic Center, taking advantage of the significantly lower extinction in the NIR. The precise astrometry is obtained by taking many short-exposure images. Hence, the JASMINE Galactic Center survey data will be valuable for studies of exoplanet transits, asteroseismology, variable stars, and microlensing studies, including discovery of (intermediate-mass) black holes. We highlight a swath of such potential science, and also describe synergies with other missions

An approximation algorithm for the pickup and delivery vehicle routing problem on trees

This paper presents an approximation algorithm for a vehicle routing problem on a tree-shaped network with a single depot where there are two types of demands, pickup demand and delivery demand. Customers are located on nodes of the tree, and each customer has a positive demand of pickup and/or delivery. Demands of customers are served by a fleet of identical vehicles with unit capacity. Each vehicle can serve pickup and delivery demands. It is assumed that the demand of a customer is splittable, i.e., it can be served by more than one vehicle. The problem we are concerned with in this paper asks to find a set of tours of the vehicles with minimum total lengths. In each tour, a vehicle begins at the depot with certain amount of goods for delivery, visits a subset of the customers in order to deliver and pick up goods and returns to the depot. At any time during the tour, a vehicle must always satisfy the capacity constraint, i.e., at any time the sum of goods to be delivered and that of goods that have been picked up is not allowed to exceed the vehicle capacity. We propose a 2-approximation algorithm for the problem