Large-Scale Asymmetry of Rotation Curves in Lopsided Spiral Galaxies

Many spiral galaxies show a large-scale asymmetry with a cos\phi dependence in their rotation curves as well as in their morphology, such as M101 and NGC 628. We show that both these features can be explained by the response of a galactic disk to an imposed lopsided halo potential. A perturbation potential of 5 % is deduced for the morphologically lopsided galaxies in the Rix & Zaritsky (1995) sample. This is shown to result in a difference of 10 % or about 20-30 kms^{-1} in the rotation velocity on the two sides of the major axis. Interestingly, the observed isophotal asymmetry in a typical spiral galaxy is not much smaller and it results in a velocity asymmetry of 7 % or about 14-21 kms^{-1} . Hence, we predict that most galaxies show a fairly significant rotational asymmetry. The rotation velocity is shown to be maximum along the elongated isophote - in agreement with the observations along the SW in M101, while it is minimum along the opposite direction. This result leads to the distinctive asymmetric shape of the rotation curve which rises more steeply in one half of the galaxy than the other, as observed by Swaters et al. (1999). This shape is shown to be a robust feature and would result for any centrally concentrated disk. The net disk lopsidedness and hence the asymmetry in the rotation curve is predicted to increase with radius and hence can be best studied using HI gas as the tracer.Comment: 30 pages, accepted for publication in A &

Q criterion for disc stability modified by external tidal field

The standard Q criterion (with Q > 1) describes the local stability of a disc supported by rotation and random motion. Most astrophysical discs, however, are under the influence of an external gravitational field which can affect their stability. A typical example is a galactic disc embedded in a dark matter halo. Here we do a linear perturbation analysis for a disc in an external field, and obtain a generalized dispersion relation and a modified stability criterion. An external field has two effects on the disc dynamics: first, it contributes to the unperturbed rotational field, and second, it adds a tidal field term in the stability parameter. A typical disruptive tidal field results in a higher modified Q value and hence leads to a more stable disc. We apply these results to the Milky Way, and to a low surface brightness galaxy UGC 7321. We find that in each case the stellar disc by itself is barely stable and it is the dark matter halo that stabilizes the disc against local, axisymmetric gravitational instabilities. This result has been largely missed so far because in practice the value for Q for a galactic disc is obtained in a hybrid fashion using the observed rotational field that is set by both the disc and the halo, and hence is higher than for a pure disc.Comment: 7 pages, 3 figures, submitted to MNRA

Reading the Neural Code: What do Spikes Mean for Behavior?

The present study reveals the existence of an intrinsic spatial code within neuronal spikes that predicts behavior. As rats learnt a T-maze procedural task, simultaneous changes in temporal occurrence of spikes and spike directivity are evidenced in “expert” neurons. While the number of spikes between the tone delivery and the beginning of turn phase reduced with learning, the generated spikes between these two events acquired behavioral meaning that is of highest value for action selection. Spike directivity is thus a hidden feature that reveals the semantics of each spike and in the current experiment, predicts the correct turn that the animal would subsequently make to obtain reward. Semantic representation of behavior can then be revealed as modulations in spike directivity during the time. This predictability of observed behavior based on subtle changes in spike directivity represents an important step towards reading and understanding the underlying neural code

An entropy inequality for symmetric random variables

We establish a lower bound on the entropy of weighted sums of (possibly dependent) random variables $(X_1, X_2, \dots, X_n)$ possessing a symmetric joint distribution. Our lower bound is in terms of the joint entropy of $(X_1, X_2, \dots, X_n)$. We show that for $n \geq 3$, the lower bound is tight if and only if $X_i$'s are i.i.d.\ Gaussian random variables. For $n=2$ there are numerous other cases of equality apart from i.i.d.\ Gaussians, which we completely characterize. Going beyond sums, we also present an inequality for certain linear transformations of $(X_1, \dots, X_n)$. Our primary technical contribution lies in the analysis of the equality cases, and our approach relies on the geometry and the symmetry of the problem.Comment: submitted to ISIT 201

Angular momentum transport and evolution of lopsided galaxies

The surface brightness distribution in the majority of stellar galactic discs falls off exponentially. Often what lies beyond such a stellar disc is the neutral hydrogen gas whose distribution also follows a nearly exponential profile at least for a number of nearby disc galaxies. Both the stars and gas are commonly known to host lopsided asymmetry especially in the outer parts of a galaxy. The role of such asymmetry in the dynamical evolution of a galaxy has not been explored so far. Following Lindblad's original idea of kinematic density waves, we show that the outer part of an exponential disc is ideally suitable for hosting lopsided asymmetry. Further, we compute the transport of angular momentum in the combined stars and gas disc embedded in a dark matter halo. We show that in a pure star and gas disc, there is a transition point where the free precession frequency of a lopsided mode, $\Omega -\kappa$, changes from retrograde to prograde and this in turn reverses the direction of angular momentum flow in the disc leading to an unphysical behaviour. We show that this problem is overcome in the presence of a dark matter halo, which sets the angular momentum flow outwards as required for disc evolution, provided the lopsidedness is leading in nature. This, plus the well-known angular momentum transport in the inner parts due to spiral arms, can facilitate an inflow of gas from outside perhaps through the cosmic filaments.Comment: 13 pages, 11 figures, accepted for publication in MNRA

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

The constraining effect of gas and the dark matter halo on the vertical stellar distribution of the Milky Way

We study the vertical stellar distribution of the Milky Way thin disk in detail with particular focus on the outer disk. We treat the galactic disk as a gravitationally coupled, three-component system consisting of stars, atomic hydrogen gas, and molecular hydrogen gas in the gravitational field of the dark matter halo. The self-consistent vertical distribution for stars and gas in such a realistic system is obtained for radii between 4-22 kpc. The inclusion of an additional gravitating component constrains the vertical stellar distribution toward the mid-plane, so that the mid-plane density is higher, the disk thickness is reduced, and the vertical density profile is steeper than in the one-component, isothermal, stars-alone case. We show that the stellar distribution is constrained mainly by the gravitational field of gas and dark matter halo in the inner and the outer Galaxy, respectively. We find that the thickness of the stellar disk (measured as the HWHM of the vertical density distribution) increases with radius, flaring steeply beyond R=17 kpc. The disk thickness is reduced by a factor of 3-4 in the outer Galaxy as a result of the gravitational field of the halo, which may help the disk resist distortion at large radii. The disk would flare even more if the effect of dark matter halo were not taken into account. Thus it is crucially important to include the effect of the dark matter halo when determining the vertical structure and dynamics of a galactic disk in the outer region.Comment: 8 pages,7 figures, Accepted for publication in A &