Use of synchronization and adaptive control in parameter estimation from a time series

A technique is introduced for estimating unknown parameters when time series of only one variable from a multivariate nonlinear dynamical system is given. The technique employs a combination of two different control methods, a linear feedback for synchronizing system variables and an adaptive control. The technique is shown to work even when the unknown parameter appears in the evolution equations of the variables other than the one for which the time series is given. The technique not only esablishes that explicit detailed information about all system variables and parameters is contained in a scalar time series, but also gives a way to exract it out under suitable conditions. Illustrations are presented and effect of noise is studied.Comment: Revised for simultaneous estimation of many parameters. 24 pages of RevTex, 12 figures in postscript files. To appear in PR(E

Measurement of non-axisymmetry in centres of advanced mergers of galaxies

We measure the non-axisymmetry in the luminosity distribution in the inner few kpc of the remnants of advanced mergers of galaxies with a view to understand the relaxation in the central regions. For this, we analyze the images from the 2MASS archival data for a selected sample of 12 merging galaxies, which show signs of interaction but have a single nucleus. The central regions are fitted by elliptical isophotes whose centres are allowed to vary to get the best fit. The centres of isophotes show a striking sloshing pattern with a spatial variation of up to 20-30 % within the central 1 kpc. This indicates mass asymmetry and a dynamically unrelaxed behaviour. Next, we Fourier-analyze the galaxy images while keeping the centre constant and measure the deviation from axisymmetry in terms of the fractional Fourier amplitudes (A_1, A_2 etc) as a function of radius. All mergers show a high value of lopsidedness (upto A_1 ~ 0.2) in the central 5 kpc. The m=2 asymmetry is even stronger, with values of A_2 upto ~ 0.3, and in three cases these are shown to represent bars. The corresponding values denoting non-axisymmetry in inner regions of a control sample of eight non-merger galaxies are found to be several times smaller. Surprisingly, this central asymmetry is seen even in mergers where the outer regions have relaxed into a smooth elliptical-like r^{1/4} profile or a spiral-like exponential profile. Thus the central asymmetry is long-lived, estimated to be ~ 1 Gyr, and hence lasts for over 100 local dynamical timescales. These central asymmetries are expected to play a key role in the future dynamical evolution of the central region of a merger, and can help in feeding a central AGN.Comment: 14 pages, 3 figures, accepted for publication in MNRA

Lopsidedness and Sloshing in Centres of Advanced Mergers of Galaxies

We measure the non-axisymmetry in the luminosity distribution in the central few kpc of a sample of advanced mergers of galaxies, by analyzing their 2MASS images. All mergers show a high central asymmetry: the centres of isophotes show a striking sloshing pattern with a spatial variation of upto 30 % within the central 1 kpc; and the Fourier amplitude for lopsidedness (m=1) shows high values upto 0.2 within the central 5 kpc. The central asymmetry is estimated to be long-lived, lasting for ~ a few Gyr or ~ 100 local dynamical timescales. This will significantly affect the dynamical evolution of this region, by helping fuel the central active galactic nucleus, and also by causing the secular growth of the bulge driven by lopsidedness.Comment: 2 pages, 1 figure; to appear in the Proceedings of the IAU Symposium 245, "Formation and Evolution of Galaxy Bulges", held at Oxford, U.K., July 2007, Eds. M. Bureau, E. Athanassoula, B. Barbu

The Formation of Spheroids in Early-Type Spirals: Clues From Their Globular Clusters

We use deep Hubble Space Telescope images taken with the Advanced Camera for Surveys (ACS) in the F475W and F814W filters to investigate the globular cluster systems in four edge-on Sa spiral galaxies covering a factor of 4 in luminosity. The specific frequencies of the blue globular clusters in the galaxies in our sample fall in the range 0.34 -- 0.84, similar to typical values found for later-type spirals. The number of red globular clusters associated with the bulges generally increases with the bulge luminosity, similar to what is observed for elliptical galaxies, although the specific frequency of bulge clusters is a factor of 2-3 lower for the lowest luminosity bulges than for the higher luminosity bulges. We present a new empirical relation between the fraction of red globular clusters and total bulge luminosity based on the elliptical galaxies studied by ACSVCS (ACS Virgo Cluster Survey), and discuss how this diagram can be used to assess the importance that dissipative processes played in building spiral bulges. Our results suggest a picture where dissipative processes, which are expected during gas-rich major mergers, were more important for building luminous bulges of Sa galaxies, whereas secular evolution may have played a larger role in building lower-luminosity bulges in spirals.Comment: accepted for publication in Ap

Dynamic algorithm for parameter estimation and its applications

We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when the time series of a scalar function of the variables of the underlying dynamical system is given. We find that it is possible to obtain synchronization as well as parameter estimation using such a time series. We then consider a general quadratic flow in three dimensions and discuss the applicability of our method of parameter estimation in this case. In practical situations one expects only a finite time series of a system variable to be known. We show that the finite time series can be repeatedly used to estimate unknown parameters with an accuracy that improves and then saturates to a constant value with repeated use of the time series. Finally, we suggest an important application of the parameter estimation method. We propose that the method can be used to confirm the correctness of a trial function modeling an external unknown perturbation to a known system. We show that our method produces exact synchronization with the given time series only when the trial function has a form identical to that of the perturbation

Globular Cluster Populations in Four Early-Type Poststarburst Galaxies

We present a study of the globular cluster systems of four early-type poststarburst galaxies using deep g and I-band images from the ACS camera aboard the Hubble Space Telescope (HST). All the galaxies feature shells distributed around their main bodies and are thus likely merger remnants. The color distribution of the globular clusters in all four galaxies shows a broad peak centered on g-I ~ 1.4, while PGC 6240 and PGC 42871 show a significant number of globular clusters with g-I ~ 1.0. The latter globular clusters are interpreted as being of age ~ 500 Myr and likely having been formed in the merger. The color of the redder peak is consistent with that expected for an old metal-poor population that is very commonly found around normal galaxies. However, all galaxies except PGC 10922 contain several globular clusters that are significantly brighter than the maximum luminosity expected of a single old metal-poor population. To test for multiple-age populations of overlapping g-I color, we model the luminosity functions of the globular clusters as composites of an old metal-poor subpopulation with a range of plausible specific frequencies and an intermediate-age subpopulation of solar metallicity. We find that three of the four sample galaxies show evidence for the presence of an intermediate-age (~ 1 Gyr) globular cluster population, in addition to the old metal-poor GC population seen in normal early-type galaxies. None of the galaxies show a significant population of clusters consistent with an old, metal-rich red cluster population that is typically seen in early-type galaxies.Comment: 41 pages, 13 figures, accepted for publication in AJ. Some figues have been downgraded to reduce their size

Evidence for Three Subpopulations of Globular Clusters in the Early-Type Post-Starburst Shell Galaxy AM 0139-655

We present deep HST ACS images of the post-starburt shell galaxy AM 0139-655. We find evidence for the presence of three distinct globular cluster subpopulations associated with this galaxy: a centrally concentrated young population (~ 0.4 Gyr), an intermediate age population (~ 1 Gyr) and an old, metal-poor population similar to that seen around normal galaxies. The g-I color distribution of the clusters is bimodal with peaks at 0.85 and 1.35. The redder peak at g-I=1.35 is consistent with the predicted color for an old metal-poor population. The clusters associated with the peak at g-I=0.85 are centrally concentrated and interpreted as a younger and more metal-rich population. We suggest that these clusters have an age of ~ 0.4 Gyr and solar metallicity based on a comparison with population synthesis models. The luminosity function of these "blue" clusters is well represented by a power law. Interestingly, the brightest shell associated with the galaxy harbors some of the youngest clusters observed. This seems to indicate that the same merger event was responsible for the formation of both the shells and the young clusters. The red part of the color distribution contains several very bright clusters, which are not expected for an old, metal-poor population. Furthermore, the luminosity function of the "red" GCs cannot be fit well by either a single gaussian or a single power law. A composite (gaussian + power law) fit to the LF of the red clusters yields both a low rms and very plausible properties for an old population plus an intermediate-age population of GCs. Hence, we suggest that the red clusters in AM 0139-655 consist of two distinct GC subpopulations, one being an old, metal-poor population as seen in normal galaxies and one having formed during a recent dissipative galaxy merger.Comment: 35 pages, 12 figures, accepted for publication in A