Effects Of Small-scale Structure Research Articles

Cosmology on all scales: A two-parameter perturbation expansion

We propose and construct a two-parameter perturbative expansion around a Friedmann-Lema\^{i}tre-Robertson-Walker geometry that can be used to model high-order gravitational effects in the presence of non-linear structure. This framework reduces to the weak-field and slow-motion post-Newtonian treatment of gravity in the appropriate limits, but also includes the low-amplitude large-scale fluctuations that are important for cosmological modelling. We derive a set of field equations that can be applied to the late Universe, where non-linear structure exists on supercluster scales, and perform a detailed investigation of the associated gauge problem. This allows us to identify a consistent set of perturbed quantities in both the gravitational and matter sectors, and to construct a set of gauge-invariant quantities that correspond to each of them. The field equations, written in terms of these quantities, take on a relatively simple form, and allow the effects of small-scale structure on the large-scale properties of the Universe to be clearly identified. We find that inhomogeneous structures source the global expansion, that there exist new field equations at new orders, and that there is vector gravitational potential that is a hundred times larger than one might naively expect from cosmological perturbation theory. Finally, we expect our formalism to be of use for calculating relativistic effects in upcoming ultra-large-scale surveys, as the form of the gravitational coupling between small and large scales depends on the non-linearity of Einstein's equations, and occurs at what is normally thought of as first order in cosmological perturbations.

The Integral Field View of the Orion Nebula

This paper reviews the major advances achieved in the Orion Nebula through the use of integral field spectroscopy (IFS). Since the early work of Vasconcelos and collaborators in 2005, this technique has facilitated the investigation of global properties of the nebula and its morphology, providing new clues to better constrain its 3D structure. IFS has led to the discovery of shock-heated zones at the leading working surfaces of prominent Herbig-Haro objects as well as the first attempt to determine the chemical composition of Orion protoplanetary disks, also known asproplyds. The analysis of these morphologies using IFS has given us new insights into the abundance discrepancy problem, a long-standing and unresolved issue that casts doubt on the reliability of current methods used for the determination of metallicities in the universe from the analysis of H II regions. Results imply that high-density clumps and high-velocity flows may play an active role in the production of such discrepancies. Future investigations based on the large-scale IFS mosaic of Orion will be very valuable for exploring how the integrated effect of small-scale structures may have impact at larger scales in the framework of star-forming regions.

Warm dark matter primordial spectra and the onset of structure formation at redshiftz

Analytic formulas reproducing the warm dark matter (WDM) primordial spectra are obtained for WDM particles decoupling in and out of thermal equilibrium which provide the initial data for WDM non-linear structure formation. We compute and analyze the corresponding WDM overdensities and compare them to the CDM case. We consider the ratio of the WDM to CDM primordial spectrum and the WDM to CDM overdensities: they turn to be self-similar functions of k/k_{1/2} and R/R_{1/2} respectively, k_{1/2} and R_{1/2} being the wavenumber and length where the WDM spectrum and overdensity are 1/2 of the respective CDM magnitudes. Both k_{1/2} and R_{1/2} show scaling as powers of the WDM particle mass m while the self-similar functions are independent of m. The WDM primordial spectrum sharply decreases around k_{1/2} with respect to the CDM spectrum, while the WDM overdensity slowly decreases around R_{1/2}. The nonlinear regions where WDM structure formation takes place are shown and compared to those in CDM: the WDM non-linear structures start to form later than in CDM, and as a general trend, decreasing the DM particle mass delays the onset of the non-linear regime. The non-linear regime starts earlier for smaller objects than for larger ones; smaller objects can form earlier both in WDM and CDM. We compute and analyze the differential mass function dN/dM for WDM at redshift z in the Press-Schechter approach. The WDM suppression effect of small scale structure increases with the redshift z. Our results for dN/dM are useful to be contrasted with observations, in particular for 4 < z < 12. We perfom all these studies for the most popular WDM particle physics models. Contrasting them to observations should point out the precise value of the WDM particle mass in the keV scale, and help to single out the best WDM particle physics model (Abridged).

Effects of small-scale structure on the progress and duration of reionization

The propagation of cosmological ionization fronts during the reionization of the universe is strongly influenced by small-scale (∼ kpc) gas inhomogeneities caused by struc- ture formation. In this paper we study this important effect by performing detailed radiative- hydrodynamic simulations of photoevaporation of cosmological minihalos (MHs) and incorpo- rating the results into a semi-analytical model of reionization, which also includes the effect of mean intergalactic medium (IGM) clumping and the nonlinear clustering of minihalos. We find that small-scale structures have a significant effect on the process of reionization, slowing it down and extending it in time. This can help in understanding the recent observations by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite, which point to an early and extended reionization epoch.

Cosmic string cusps with small-scale structure: Their forms and gravitational waveforms

We present a method for the introduction of small-scale structure into strings constructed from products of rotation matrices. We use this method to illustrate a range of possibilities for the shape of cusps that depends on the properties of the small-scale structure. We further argue that the presence of structure at cusps under most circumstances leads to the formation of loops at the size of the smallest scales. On the other hand we show that the gravitational waveform of a cusp remains generally unchanged; the primary effect of small-scale structure is to smooth out the sharp waveform emitted in the direction of cusp motion.

Tomographic imaging of the lowermost mantle with differential times of refracted and diffracted core phases (PKP, Pdiff)

The mapping of variations in P wave speed in the deep mantle is restricted by the uneven sampling of P waves, in particular beneath the Southern Hemisphere. To enhance data coverage, we augmented the ∼1.6 million summary rays of P, pP, and pwP that we used in previous studies with differential travel times of diffracted and refracted core phases. For the core‐refracted differential travel time residuals (PKPAB‐PKPDF and PKPAB‐PKPBC) we used 1383 cross‐correlated digital waveforms as well as ∼27,000 routinely processed bulletin data. We used the waveform data to define quality criteria for the selection and reduction of the bulletin PKP data. For PKPDF‐Pdiff we only considered 543 records derived from waveform cross correlation. No PcP data were used in this study. We used optical ray theory to calculate the ray paths associated with the P, pP, pwP, and PKP data, which are measured at 1 Hz. However, to account for the large Fresnel zones of the low‐frequency (∼50 mHz) PKPDF‐Pdiff data we estimated the three‐dimensional shape of the Fréchet sensitivity kernels from kernels calculated by normal mode summation. The use of these kernels allows us to properly distribute the sensitivity for a given seismic phase over a large mantle volume while allowing the high‐frequency data to constrain small‐scale structure. The differential times are relatively insensitive to source mislocation and to structure in the shallow mantle beneath source and receivers, and they have previously been interpreted exclusively in terms of lateral structure directly above the core mantle boundary (CMB). However, images thus obtained can be contaminated by effects of small scale structure elsewhere in the mantle. Here, we do not make a priori assumptions about the mantle source of anomalous time differentials. From test inversions we conclude that (both upper and lower) mantle structures that are poorly resolved by P data can be mapped into the core along PKP paths but that the effect of outer core structures, if any, on the mantle model is small. Compared to the inversion of the P, pP, and pwP alone, the inclusion of the PKPAB‐PKPDF and PKPAB‐PKPBC and PKPDF‐Pdiff data improves the resolution of structure beneath 2200 km depth. In particular, the joint inversion puts better constraints on the long‐wavelength variations in the very deep mantle and yields an increase in the amplitude of velocity perturbations near the CMB that is in agreement with but still smaller than inferences from shear wave studies. Resolution tests indicate that in some regions the enhanced definition of structure is significant, but in most regions the improvements are subtle and structure remains poorly resolved in large regions of the mantle.

Geology, geometry and effective flow

The effects of small-scale structure are frequently ignored in reservoir simulation, although they may have a significant effect on hydrocarbon recovery. Many sandstones exhibit lamination, and in such rock structures, permeability may vary by an order of magnitude over distances of a centimetre or less. Frequently, laminations are inclined with respect to the pressure gradient, which gives rise to cross-flow within the unit. In this case a tensor may be used to represent the effective permeability of the bed. In this paper the effect of small-scale geological structure on single-phase flow is investigated using a model of a cross-bedded unit to determine which factors have the greatest effect on cross-flow. In addition, a range of other types of bedding are considered, including models with stochastic variation. We have found that, in general, the geometry of the sedimentary structure has a significant effect on flow. The cross-flow is greater (and therefore tensors are more likely to be necessary) when the angle of the laminae is large relative to the pressure gradient (up to 45 degrees ), when the permeability contrast between laminae is large, or when the structure is asymmetric.

Effect of small-scale structure on the dynamics of cosmic strings.

The effective equation of state for a string with short-wavelength perturbations is shown to be $\ensuremath{\mu}T={\ensuremath{\mu}}_{0}^{2}$, where $\ensuremath{\mu}$ and $T$ are the mass density and tension in the rest frame of the string and ${\ensuremath{\mu}}_{0}$ is the unperturbed string tension. The dynamics of wiggly strings in flat spacetime is discussed. The conclusions are in agreement with the results obtained by Carter using different methods.

Reconnection in two dimensions: Localization of vorticity and current near magnetic X‐points

Simulations of reconnection utilizing spectral methods show that the “reconnection zone” exhibits internal structure in the form of a current filament and a “quadrupole” of kinetic vorticity. A qualitative model of the dynamical role of these local structures is presented. It is suggested that the effect of small scale structures near the X‐point is to increase the rate of reconnection.