A re-interpretation of the Triangulum-Andromeda stellar clouds: a population of halo stars kicked out of the Galactic disk

The Triangulum-Andromeda stellar clouds (TriAnd1 and TriAnd2) are a pair of concentric ring- or shell-like over-densities at large $R$ ($\approx$ 30 kpc) and $Z$ ($\approx$ -10 kpc) in the Galactic halo that are thought to have been formed from the accretion and disruption of a satellite galaxy. This paper critically re-examines this formation scenario by comparing the number ratio of RR Lyrae to M giant stars associated with the TriAnd clouds with other structures in the Galaxy. The current data suggest a stellar population for these over-densities ($f_{\rm RR:MG} < 0.38$ at 95% confidence) quite unlike any of the known satellites of the Milky Way ($f_{\rm RR:MG} \approx 0.5$ for the very largest and $f_{\rm RR:MG} >>1$ for the smaller satellites) and more like the population of stars born in the much deeper potential well inhabited by the Galactic disk ($f_{\rm RR:MG} < 0.01$). N-body simulations of a Milky-Way-like galaxy perturbed by the impact of a dwarf galaxy demonstrate that, in the right circumstances, concentric rings propagating outwards from that Galactic disk can plausibly produce similar over-densities. These results provide dramatic support for the recent proposal by Xu et al. (2015) that, rather than stars accreted from other galaxies, the TriAnd clouds could represent stars kicked-out from our own disk. If so, these would be the first populations of disk stars to be found in the Galactic halo and a clear signature of the importance of this second formation mechanism for stellar halos more generally. Moreover, their existence at the very extremities of the disk places strong constraints on the nature of the interaction that formed them.Comment: 27 pages, 8 figures; published in MNRA

Disk Heating, Galactoseismology, and the Formation of Stellar Halos

Deep photometric surveys of the Milky Way have revealed diffuse structures encircling our Galaxy far beyond the "classical" limits of the stellar disk. This paper reviews results from our own and other observational programs, which together suggest that, despite their extreme positions, the stars in these structures were formed in our Galactic disk. Mounting evidence from recent observations and simulations implies kinematic connections between several of these distinct structures. This suggests the existence of collective disk oscillations that can plausibly be traced all the way to asymmetries seen in the stellar velocity distribution around the Sun. There are multiple interesting implications of these findings: they promise new perspectives on the process of disk heating, they provide direct evidence for a stellar halo formation mechanism in addition to the accretion and disruption of satellite galaxies, and, they motivate searches of current and near-future surveys to trace these oscillations across the Galaxy. Such maps could be used as dynamical diagnostics in the emerging field of "Galactoseismology", which promises to model the history of interactions between the Milky Way and its entourage of satellites, as well examine the density of our dark matter halo. As sensitivity to very low surface brightness features around external galaxies increases, many more examples of such disk oscillations will likely be identified. Statistical samples of such features not only encode detailed information about interaction rates and mergers, but also about long sought-after dark matter halo densities and shapes. Models for the Milky Way's own Galactoseismic history will therefore serve as a critical foundation for studying the weak dynamical interactions of galaxies across the universe.Comment: 20 pages, 5 figures, accepted in for publication in a special edition of the journal "Galaxies", reporting the proceedings of the conference "On the Origin (and Evolution) of Baryonic Galaxy Halos", Puerto Ayora, Ecuador, March 13-17 2017, Eds. Duncan A. Forbes and Ericson D. Lope

Pre-freezing of multifractal exponents in Random Energy Models with logarithmically correlated potential

Boltzmann-Gibbs measures generated by logarithmically correlated random potentials are multifractal. We investigate the abrupt change ("pre-freezing") of multifractality exponents extracted from the averaged moments of the measure - the so-called inverse participation ratios. The pre-freezing can be identified with termination of the disorder-averaged multifractality spectrum. Naive replica limit employed to study a one-dimensional variant of the model is shown to break down at the pre-freezing point. Further insights are possible when employing zero-dimensional and infinite-dimensional versions of the problem. In particular, the latter version allows one to identify the pattern of the replica symmetry breaking responsible for the pre-freezing phenomenon.Comment: This is published version, 11 pages, 1 figur

Rigorous confidence intervals for critical probabilities

We use the method of Balister, Bollobas and Walters to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and ease of verification, rather than obtaining the best possible results. Nevertheless, we obtain intervals of width at most 0.0005 in all cases

Exploring Halo Substructure with Giant Stars. XV. Discovery of a Connection between the Monoceros Ring and the Triangulum-Andromeda Overdensity?

Thanks to modern sky surveys, over twenty stellar streams and overdensity structures have been discovered in the halo of the Milky Way. In this paper, we present an analysis of spectroscopic observations of individual stars from one such structure, "A13", first identified as an overdensity using the M giant catalog from the Two Micron All-Sky Survey. Our spectroscopic observations show that stars identified with A13 have a velocity dispersion of $\lesssim$ 40 $\mathrm{km~s^{-1}}$, implying that it is a genuine coherent structure rather than a chance super-position of random halo stars. From its position on the sky, distance ($\sim$15~kpc heliocentric), and kinematical properties, A13 is likely to be an extension of another low Galactic latitude substructure -- the Galactic Anticenter Stellar Structure (also known as the Monoceros Ring) -- towards smaller Galactic longitude and farther distance. Furthermore, the kinematics of A13 also connect it with another structure in the southern Galactic hemisphere -- the Triangulum-Andromeda overdensity. We discuss these three connected structures within the context of a previously proposed scenario that one or all of these features originate from the disk of the Milky Way.Comment: 12 pages, 9 figures. Accepted for publication in Ap

Boundary conformal field theories and loop models

We propose a systematic method to extract conformal loop models for rational conformal field theories (CFT). Method is based on defining an ADE model for boundary primary operators by using the fusion matrices of these operators as adjacency matrices. These loop models respect the conformal boundary conditions. We discuss the loop models that can be extracted by this method for minimal CFTs and then we will give dilute O(n) loop models on the square lattice as examples for these loop models. We give also some proposals for WZW SU(2) models.Comment: 23 Pages, major changes! title change

Critical curves in conformally invariant statistical systems

We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.Comment: Published versio

Conformal Curves in Potts Model: Numerical Calculation

We calculated numerically the fractal dimension of the boundaries of the Fortuin-Kasteleyn clusters of the $q$-state Potts model for integer and non-integer values of $q$ on the square lattice. In addition we calculated with high accuracy the fractal dimension of the boundary points of the same clusters on the square domain. Our calculation confirms that this curves can be described by SLE$_{\kappa}$.Comment: 11 Pages, 4 figure

Mathematically gifted and talented learners: Theory and practice

This is an Author's Accepted Manuscript of an article published in International Journal of Mathematical Education in Science and Technology, 40(2), 213-228, 2009, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/00207390802566907.There is growing recognition of the special needs of mathematically gifted learners. This article reviews policy developments and current research and theory on giftedness in mathematics. It includes a discussion of the nature of mathematical ability as well as the factors that make up giftedness in mathematics. The article is set in the context of current developments in Mathematics Education and Gifted Education in the UK and their implications for Science and Technology. It argues that early identification and appropriate provision for younger mathematically promising pupils capitalizes on an intellectual resource which could provide future mathematicans as well as specialists in Science or Technology. Drawing on a Vygotskian framework, it is suggested that the mathematically gifted require appropriate cognitive challenges as well as attitudinally and motivationally enhancing experiences. In the second half of this article we report on an initiative in which we worked with teachers to identify mathematically gifted pupils and to provide effective enrichment support for them, in a number of London Local Authorities. A number of significant issues are raised relating to the identification of mathematical talent, enrichment provision for students and teachers’ professional development