Absolute spectrophotometry in M31 and M32

For a number of places in the bulge of M31 and for two places in M32 photometric scans from 3300 A to 10,600 A have been obtained with the multichannel spectrometer on the 5-meter Hale telescope. The scans show that in both objects the color temperature (particularly shortwards of 5000 A) decreases towards the center and that the strength of the CN bands increases towards the center in both objects in agreement with earlier observations. The new data can all be interpreted in terms of an increase of heavy element abundance towards the center in both objects by a factor probably less than 2 and by an excess of heavy elements in M31 compared to M32 by a factor probably greater than 2, in qualitative agreement with earlier conclusions

Dynamics of the Fisher Information Metric

We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional $J[g^{\mu\nu}(\theta^i)]$, where $g^{\mu\nu}(\theta^i)$ is the Fisher metric. We postulate that this functional of the dynamical variable $g^{\mu\nu}(\theta^i)$ is stationary with respect to small variations of these variables. Our approach enables a dynamical approach to Fisher information metric. It allows to impose symmetries on a statistical system in a systematic way. This work is mainly motivated by the entropy approach to nonmonotonic reasoning.Comment: 11 page

Does gravity prefer the Poincare dodecahedral space?

The missing fluctuations problem in cosmic microwave background observations is naturally explained by well-proportioned small universe models. Among the well-proportioned models, the Poincare dodecahedral space is empirically favoured. Does gravity favour this space? The residual gravity effect is the residual acceleration induced by weak limit gravity from multiple topological images of a massive object on a nearby negligible mass test object. At the present epoch, the residual gravity effect is about a million times weaker in three of the well-proportioned spaces than in ill-proportioned spaces. However, in the Poincare space, the effect is 10,000 times weaker still, i.e. the Poincare space is about 10^{10} times "better balanced" than ill-proportioned spaces. Both observations and weak limit dynamics select the Poincare space to be special.Comment: 6 pages, Honorable Mention in 2009 Gravity Research Foundation essay competitio

The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps

Several studies have proposed that the shape of the Universe may be a Poincare dodecahedral space (PDS) rather than an infinite, simply connected, flat space. Both models assume a close to flat FLRW metric of about 30% matter density. We study two predictions of the PDS model. (i) For the correct model, the spatial two-point cross-correlation function, \ximc, of temperature fluctuations in the covering space, where the two points in any pair are on different copies of the surface of last scattering (SLS), should be of a similar order of magnitude to the auto-correlation function, \xisc, on a single copy of the SLS. (ii) The optimal orientation and identified circle radius for a "generalised" PDS model of arbitrary twist $\phi$, found by maximising \ximc relative to \xisc in the WMAP maps, should yield $\phi \in \{\pm 36\deg\}$. We optimise the cross-correlation at scales < 4.0 h^-1 Gpc using a Markov chain Monte Carlo (MCMC) method over orientation, circle size and $\phi$. Both predictions were satisfied: (i) an optimal "generalised" PDS solution was found, with a strong cross-correlation between points which would be distant and only weakly correlated according to the simply connected hypothesis, for two different foreground-reduced versions of the WMAP 3-year all-sky map, both with and without the kp2 Galaxy mask: the face centres are $(l,b)_{i=1,6}\approx (184d, 62d), (305d, 44d), (46d, 49d), (117d, 20d), (176d, -4d), (240d, 13d) to within ~2d, and their antipodes; (ii) this solution has twist \phi= (+39 \pm 2.5)d, in agreement with the PDS model. The chance of this occurring in the simply connected model, assuming a uniform distribution$\phi \in [0,2\pi]$, is about 6-9%.Comment: 20 pages, 22 figures, accepted in Astronomy & Astrophysics, software available at http://adjani.astro.umk.pl/GPLdownload/dodec/ and MCMCs at http://adjani.astro.umk.pl/GPLdownload/MCM

Necessary and sufficient condition for hydrostatic equilibrium in general relativity

We present explicit examples to show that the `compatibility criterion' is capable of providing a {\em necessary} and {\em sufficient} condition for any regular configuration to be compatible with the state of hydrostatic equilibrium. This conclusion is drawn on the basis of the finding that the $M-R$ relation gives the necessary and sufficient condition for dynamical stability of equilibrium configurations only when the compatibility criterion for these configurations is appropriately satisfied. In this regard, we construct an appropriate sequence composed of core-envelope models on the basis of compatibility criterion, such that each member of this sequence satisfies the extreme case of causality condition $v = c = 1$ at the centre. The maximum stable value of $u \simeq 0.3389$ (which occurs for the model corresponding to the maximum value of mass in the mass-radius relation) and the corresponding central value of the local adiabatic index, $(\Gamma_1)_0 \simeq 2.5911$, of this model are found fully consistent with those of the corresponding {\em absolute} values, $u_{\rm max} \leq 0.3406$, and $(\Gamma_1)_0 \leq 2.5946$, which impose strong constraints on these parameters of such models. In addition to this example, we also study dynamical stability of pure adiabatic polytropic configurations on the basis of variational method for the choice of the `trial function', $\xi =re^{\nu/4}$, as well as the mass-central density relation, since the compatibility criterion is appropriately satisfied for these models. The results of this example provide additional proof in favour of the statement regarding compatibility criterion mentioned above.Comment: 31 pages (double-spaced) revtex style, 1 figure in `ps' forma

A new two-sphere singularity in general relativity

The Florides solution, proposed as an alternative to the interior Schwarzschild solution, represents a static and spherically symmetric geometry with vanishing radial stresses. It is regular at the center, and is matched to an exterior Schwarzschild solution. The specific case of a constant energy density has been interpreted as the field inside an Einstein cluster. In this work, we are interested in analyzing the geometry throughout the permitted range of the radial coordinate without matching it to the Schwarzschild exterior spacetime at some constant radius hypersurface. We find an interesting picture, namely, the solution represents a three-sphere, whose equatorial two-sphere is singular, in the sense that the curvature invariants and the tangential pressure diverge. As far as we know, such singularities have not been discussed before. In the presence of a large negative cosmological constant (anti-de Sitter) the singularity is removed.Comment: 17 pages, 3 figure

Population III star formation in a Lambda CDM universe, I: The effect of formation redshift and environment on protostellar accretion rate

(abridged) We perform 12 extremely high resolution adaptive mesh refinement cosmological hydrodynamic simulations of Population III star formation in a Lambda CDM universe, varying the box size and large-scale structure, to understand systematic effects in the formation of primordial protostellar cores. We find results that are qualitatively similar to those observed previously. We observe that the threshold halo mass for formation of a Population III protostar does not evolve significantly with time in the redshift range studied (33 > z > 19) but exhibits substantial scatter due to different halo assembly histories: Halos which assembled more slowly develop cooling cores at lower mass than those that assemble more rapidly, in agreement with Yoshida et al. (2003). We do, however, observe significant evolution in the accretion rates of Population III protostars with redshift, with objects that form later having higher maximum accretion rates, with a variation of two orders of magnitude (10^-4 - 10^-2 Msolar/year). This can be explained by considering the evolving virial properties of the halos with redshift and the physics of molecular hydrogen formation at low densities. Our result implies that the mass distribution of Population III stars inferred from their accretion rates may be broader than previously thought, and may evolve with redshift. Finally, we observe that our collapsing protostellar cloud cores do not fragment, consistent with previous results, which suggests that Population III stars which form in halos of mass 10^5 - 10^6 Msun always form in isolation.Comment: Accepted by The Astrophysical Journal. Some minor changes. 65 pages, 3 tables, 21 figures (3 color). To appear in January 1, 2007 issu

A constraint on any topological lensing hypothesis in the spherical case: it must be a root of the identity

Three-dimensional catalogues of objects at cosmological distances can potentially yield candidate topologically lensed pairs of sets of objects, which would be a sign of the global topology of the Universe. In the spherical case, a necessary condition, which does not exist for either null or negative curvature, can be used to falsify such hypotheses, without needing to loop through a list of individual spherical 3-manifolds. This condition is that the isometry between the two sets of objects must be a root of the identity isometry in the covering space S^3. This enables numerical falsification of topological lensing hypotheses without needing to assume any particular spherical 3-manifold. By embedding S^3 in R^4, this condition can be expressed as the requirement that M^n = I for an integer n, where M is the matrix representation of the hypothesised lensing isometry and I is the identity. Moreover, this test becomes even simpler with the requirement that the two rotation angles, theta, phi, corresponding to the given isometry, satisfy 2\pi / \theta, 2\pi / \phi \in Z. The calculation of this test involves finding the two eigenplanes of the matrix M. A GNU General Public Licence numerical package, called eigenplane, is made available at http://cosmo.torun.pl/GPLdownload/eigen/ for finding the rotation angles and eigenplanes of an arbitrary isometry M of S^3.Comment: 8 pages, 1 figure, accepted, Astronomy & Astrophysics, v2,v3 minor corrections, numerical caveats, matches accepted versio

How to distinguish a nearly flat Universe from a flat Universe using the orientation independence of a comoving standard ruler

Several recent observations using standard rulers and standard candles now suggest, either individually or in combination, that the Universe is close to flat, i.e. that the curvature radius is about as large as the horizon radius (\sim 10h^{-1}Gpc) or larger. Here, a method of distinguishing an almost flat universe from a precisely flat universe using a single observational data set, without using any microwave background information, is presented. The method (i) assumes that a standard ruler should have no preferred orientation (radial versus tangential) to the observer, and (ii) requires that the (comoving) length of the standard ruler be known independently (e.g. from low redshift estimates). The claimed feature at fixed {\em comoving} length in the power spectrum of density perturbations, detected among quasars, Lyman break galaxies or other high redshift objects, would provide an adequate standard candle to prove that the Universe is curved, if indeed it is curved. For example, a combined intrinsic and measurement uncertainty of 1% in the length of the standard ruler \llss applied at a redshift of $z=3$ would distinguish an hyperbolic $(\Omega_m=0.2,\Omega_\Lambda=0.7)$ or a spherical $(\Omega_m=0.4,\Omega_\Lambda=0.7)$ universe from a flat one to 1-P > 95% confidence.Comment: 7 pages, 3 figures, accepted for Astronomy & Astrophysic

A purely reflective large wide-field telescope

Two versions of a fast, purely reflective Paul-Baker type telescope are discussed, each with an 8.4-m aperture, 3 deg diameter flat field and f/1.25 focal ratio. The first version is based on a common, even asphere type of surface with zero conic constant. The primary and tertiary mirrors are 6th order aspheres, while the secondary mirror is an 8th order asphere (referred to here for brevity, as the 6/8/6 configuration). The D_80 diameter of a star image varies from 0''.18 on the optical axis up to 0''.27 at the edge of the field (9.3-13.5 mcm). The second version of the telescope is based on a polysag surface type which uses a polynomial expansion in the sag z, r^2 = 2R_0z - (1+b)z^2 + a_3 z^3 + a_4 z^4 + ... + a_N z^N, instead of the common form of an aspheric surface. This approach results in somewhat better images, with D_80 ranging from 0''.16 to 0''.23, using a lower-order 3/4/3 combination of powers for the mirror surfaces. An additional example with 3.5-m aperture, 3.5 deg diameter flat field, and f/1.25 focal ratio featuring near-diffraction-limited image quality is also presented.Comment: 14 pages, 6 figures; new examples adde