Hiding its age: the case for a younger bulge

The determination of the age of the bulge has led to two contradictory results. On the one side, the color-magnitude diagrams in different bulge fields seem to indicate a uniformly old ($>$10 Gyr) population. On the other side, individual ages derived from dwarfs observed through microlensing events seem to indicate a large spread, from $\sim$ 2 to $\sim$ 13 Gyr. Because the bulge is now recognised as being mainly a boxy peanut-shaped bar, it is suggested that disk stars are one of its main constituents, and therefore also stars with ages significantly younger than 10 Gyr. Other arguments as well point to the fact that the bulge cannot be exclusively old, and in particular cannot be a burst population, as it is usually expected if the bulge was the fossil remnant of a merger phase in the early Galaxy. In the present study, we show that given the range of metallicities observed in the bulge, a uniformly old population would be reflected into a significant spread in color at the turn-off which is not observed. Inversely, we demonstrate that the correlation between age and metallicity expected to hold for the inner disk would conspire to form a color-magnitude diagram with a remarkably small spread in color, thus mimicking the color-magnitude diagram of a uniformly old population. If stars younger than 10 Gyr are part of the bulge, as must be the case if the bulge has been mainly formed through dynamical instabilities in the disk, then a very small spread at the turn-off is expected, as seen in the observations.Comment: 11 pages, 11 figures. Accepted for publication in A&

Discretisation for odd quadratic twists

The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random matrix theory prediction. The situation for odd quadratic twists is much more mysterious, as the height of a point enters the picture, which does not necessarily take integral values (as does the order of the Shafarevich-Tate group). We discuss a couple of models and present data on this question.Comment: To appear in the Proceedings of the INI Workshop on Random Matrix Theory and Elliptic Curve

Random Matrix Theory and the Fourier Coefficients of Half-Integral Weight Forms

Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of conjectures concerning the value-distribution of the Fourier coefficients of half-integral weight modular forms related to these L-functions. Our conjectures may be viewed as being analogous to the Sato-Tate conjecture for integral weight modular forms. Numerical evidence is presented in support of them.Comment: 28 pages, 8 figure

Signatures of radial migration in barred galaxies: Azimuthal variations in the metallicity distribution of old stars

By means of N-body simulations, we show that radial migration in galaxy disks, induced by bar and spiral arms, leads to significant azimuthal variations in the metallicity distribution of old stars at a given distance from the galaxy center. Metals do not show an axisymmetric distribution during phases of strong migration. Azimuthal variations are visible during the whole phase of strong bar phase, and tend to disappear as the effect of radial migration diminishes, together with a reduction in the bar strength. These results suggest that the presence of inhomogeneities in the metallicity distribution of old stars in a galaxy disk can be a probe of ongoing strong migration. Such signatures may be detected in the Milky Way by Gaia (and complementary spectroscopic data), as well as in external galaxies, by IFU surveys like CALIFA and ATLAS3D. Mixing - defined as the tendency toward a homogeneous, azimuthally symmetric, stellar distribution in the disk - and migration turns out to be two distinct processes, the effects of mixing starting to be visible when strong migration is over.Comment: 8 pages, 10 figures, accepted for publication on Astronomy and Astrophysic

Autocorrelation of Random Matrix Polynomials

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than large-matrix asymptotic approximations. They also mirror exactly autocorrelation formulae conjectured to hold for L-functions in a companion paper. This then provides further evidence in support of the connection between Random Matrix Theory and the theory of L-functions

The stellar metallicity gradients in galaxy discs in a cosmological scenario

Indexación: Web of ScienceContext. The stellar metallicity gradients of disc galaxies provide information on disc assembly, star formation processes, and chemical evolution. They also might store information on dynamical processes that could affect the distribution of chemical elements in the gas phase and the stellar components. Understanding their joint effects within a hierarchical clustering scenario is of paramount importance. Aims. We studied the stellar metallicity gradients of simulated discs in a cosmological simulation. We explored the dependence of the stellar metallicity gradients on stellar age and on the size and mass of the stellar discs. Methods. We used a catalogue of galaxies with disc components selected from a cosmological hydrodynamical simulation performed including a physically motivated supernova feedback and chemical evolution. Disc components were defined based on angular momentum and binding energy criteria. The metallicity profiles were estimated for stars with different ages. We confront our numerical findings with results from the Calar Alto Legacy Integral Field Area (CALIFA) Survey. Results. The simulated stellar discs are found to have metallicity profiles with slopes in global agreement with observations. Low stellar mass galaxies tend to have a larger variety of metallicity slopes. When normalized by the half-mass radius, the stellar metallicity gradients do not show any dependence and the dispersion increases significantly, regardless of the galaxy mass. Galaxies with stellar masses of around 10(10) M-circle dot show steeper negative metallicity gradients. The stellar metallicity gradients correlate with the half-mass radius. However, the correlation signal is not present when they are normalized by the half-mass radius. Stellar discs with positive age gradients are detected to have negative and positive metallicity gradients, depending on the relative importance of recent star formation activity in the central regions. Conclusions. Our results suggest that inside-out formation is the main process responsible for the metallicity and age profiles. The large dispersions in the metallicity gradients as a function of stellar mass could be ascribed to the effects of dynamical processes such as mergers, interactions and/or migration as well as those regulating the conversion of gas into stars. The fingerprints of the inside-out formation seem better preserved by the stellar metallicity gradients as a function of the half-mass radius.http://www.aanda.org/articles/aa/abs/2016/08/aa28188-16/aa28188-16.htm

Lower order terms in the full moment conjecture for the Riemann zeta function

We describe an algorithm for obtaining explicit expressions for lower terms for the conjectured full asymptotics of the moments of the Riemann zeta function, and give two distinct methods for obtaining numerical values of these coefficients. We also provide some numerical evidence in favour of the conjecture.Comment: 37 pages, 4 figure

When the Milky Way turned off the lights: APOGEE provides evidence of star formation quenching in our Galaxy

Quenching, the cessation of star formation, is one of the most significant events in the life cycle of galaxies. We show here the first evidence that the Milky Way experienced a generalised quenching of its star formation at the end of its thick disk formation $\sim$9 Gyr ago. Elemental abundances of stars studied as part of the APOGEE survey reveal indeed that in less than $\sim$2 Gyr the star formation rate in our Galaxy dropped by an order-of-magnitude. Because of the tight correlation between age and alpha abundance, this event reflects in the dearth of stars along the inner disk sequence in the [Fe/H]-[$\alpha$/Fe] plane. Before this phase, which lasted about 1.5 Gyr, the Milky Way was actively forming stars. Afterwards, the star formation resumed at a much lower level to form the thin disk. These events are very well matched by the latest observation of MW-type progenitors at high redshifts. In late type galaxies, quenching is believed to be related to a long and secular exhaustion of gas. In our Galaxy, it occurred on a much shorter time scale, while the chemical continuity before and after the quenching indicates that it was not due to the exhaustion of the gas. While quenching is generally associated with spheroids, our results show that it also occurs in galaxies like the Milky Way, possibly when they are undergoing a morphological transition from thick to thin disks. Given the demographics of late type galaxies in the local universe, in which classical bulges are rare, we suggest further that this may hold true generally in galaxies with mass lower than or approximately $M^*$, where quenching could be directly a consequence of thick disk formation. We emphasize that the quenching phase in the Milky Way could be contemporaneous with, and related to, the formation of the bar. We sketch a scenario on how a strong bar may inhibit star formation.Comment: 17 pages, 8 figures. Published versio

The history of stellar metallicity in a simulated disc galaxy

We explore the chemical distribution of stars in a simulated galaxy. Using simulations of the same initial conditions but with two different feedback schemes (McMaster Unbiased Galaxy Simulations – MUGS – and Making Galaxies in a Cosmological Context – MaGICC), we examine the features of the age–metallicity relation (AMR), and the three-dimensional age– [Fe/H]–[O/Fe] distribution, both for the galaxy as a whole and decomposed into disc, bulge, halo and satellites. The MUGS simulation, which uses traditional supernova feedback, is replete with chemical substructure. This substructure is absent from the MaGICC simulation, which includes early feedback from stellar winds, a modified initial mass function and more efficient feedback. The reduced amount of substructure is due to the almost complete lack of satellites in MaGICC. We identify a significant separation between the bulge and disc AMRs, where the bulge is considerably more metal-rich with a smaller spread in metallicity at any given time than the disc. Our results suggest, however, that identifying the substructure in observations will require exquisite age resolution, of the order of 0.25 Gyr. Certain satellites show exotic features in the AMR, even forming a ‘sawtooth’ shape of increasing metallicity followed by sharp declines which correspond to pericentric passages. This fact, along with the large spread in stellar age at a given metallicity, compromises the use of metallicity as an age indicator, although alpha abundance provides a more robust clock at early times. This may also impact algorithms that are used to reconstruct star formation histories from resolved stellar populations, which frequently assume a monotonically increasing AMR

Boundary conditions associated with the Painlev\'e III' and V evaluations of some random matrix averages

In a previous work a random matrix average for the Laguerre unitary ensemble, generalising the generating function for the probability that an interval $(0,s)$ at the hard edge contains $k$ eigenvalues, was evaluated in terms of a Painlev\'e V transcendent in $\sigma$-form. However the boundary conditions for the corresponding differential equation were not specified for the full parameter space. Here this task is accomplished in general, and the obtained functional form is compared against the most general small $s$ behaviour of the Painlev\'e V equation in $\sigma$-form known from the work of Jimbo. An analogous study is carried out for the the hard edge scaling limit of the random matrix average, which we have previously evaluated in terms of a Painlev\'e \IIId transcendent in $\sigma$-form. An application of the latter result is given to the rapid evaluation of a Hankel determinant appearing in a recent work of Conrey, Rubinstein and Snaith relating to the derivative of the Riemann zeta function