Accurate estimators of power spectra in N-body simulations

A method to rapidly estimate the Fourier power spectrum of a point distribution is presented. This method relies on a Taylor expansion of the trigonometric functions. It yields the Fourier modes from a number of fast Fourier transforms (FFTs), which is controlled by the order N of the expansion and by the dimension D of the system. In three dimensions, for the practical value   N = 3  , the number of FFTs required is 20.
We apply the method to the measurement of the power spectrum of a periodic point distribution that is a local Poisson realization of an underlying stationary field. We derive an explicit analytic expression for the spectrum, which allows us to quantify – and correct for – the biases induced by discreteness and by the truncation of the Taylor expansion, and to bound the unknown effects of aliasing of the power spectrum. We show that these aliasing effects decrease rapidly with the order N . For   N = 3  , they are expected to be, respectively, smaller than  ∼10⁻⁴  and 0.02 at half the Nyquist frequency and at the Nyquist frequency of the grid used to perform the FFTs. The only remaining significant source of errors is reduced to the unavoidable cosmic/sample variance due to the finite size of the sample.
The analytical calculations are successfully checked against a cosmological N -body experiment. We also consider the initial conditions of this simulation, which correspond to a perturbed grid. This allows us to test a case where the local Poisson assumption is incorrect. Even in that extreme situation, the third-order Fourier–Taylor estimator behaves well, with aliasing effects restrained to at most the per cent level at half the Nyquist frequency.
We also show how to reach arbitrarily large dynamic range in Fourier space (i.e. high wavenumber), while keeping statistical errors in control, by appropriately 'folding' the particle distribution.     

Discovery of a Color-selected Quasar at z = 5.50

I show how the existing observational data on Local Group dwarf galaxies can be used to estimate the average star formation law during the first 3 Gyr of the history of the universe. I find that the observational data are consistent with the orthodox Schmidt law with a star formation efficiency of about 4% if the star formation is continuous (during the first 3 Gyr). The efficiency is proportionally higher if most of the gas in the dwarfs was consumed (and never replenished) in a short time interval well before the universe turned 3 Gyr.     

Granta MIST

The magnetosphere, ionosphere and solar–terrestrial physics community gathered at Selwyn College, University of Cambridge, for three days between Tuesday 5 April and Thursday 7 April 2005. Neil Arnold and Andrew Lyons report.     

Infrared constraints on the dark mass concentration observed in the cluster Abell 1942

We present a deep H -band image of the region in the vicinity of the cluster Abell 1942 containing the puzzling dark matter concentration detected in an optical weak lensing study by Erben et al. We demonstrate that our limiting magnitude, H =22 , would be sufficient to detect clusters of appropriate mass out to redshifts comparable with the mean redshift of the background sources. Despite this, our infrared image reveals no obvious overdensity of sources at the location of the lensing mass peak, nor an excess of sources in the I − H versus H colour–magnitude diagram. We use this to constrain further the luminosity and mass-to-light ratio of the putative dark clump as a function of its redshift. We find that for spatially flat cosmologies, background lensing clusters with reasonable mass-to-light ratios lying in the redshift range 0< z <1 are strongly excluded, leaving open the possibility that the mass concentration is a new type of truly dark object.     

Sedimentology, stratigraphy and landscape evolution of a Holocene coastal dune system, Lodbjerg, NW Jutland, Denmark

The stratigraphy and landscape evolution of the Lodbjerg coastal dune system record the interplay of environmental and cultural changes since the Late Neolithic. The modern dunefield forms part of a 40 km long belt of dunes and aeolian sand‐plains that stretches along the west coast of Thy, NW Jutland. The dunefield, which is now stabilized, forms the upper part of a 15–30 m thick aeolian succession. The aeolian deposits drape a glacial landscape or Middle Holocene lake sediments. The aeolian deposits were studied in coastal cliff exposures and their large‐scale stratigraphy was examined by ground‐penetrating radar mapping. The contact between the aeolian and underlying sediments is a well‐developed peaty palaeosol, the top of which yields dates between 2300 BC and 600 BC . Four main aeolian units are distinguished, but there is some lateral stratigraphic variation in relation to underlying topography. The three lower aeolian units are separated by peaty palaeosols and primarily developed as 1–4 m thick sand‐plain deposits; these are interpreted as trailing edge deposits of parabolic dunes that moved inland episodically. Local occurrence of large‐scale cross‐stratification may record the head section of a migrating parabolic dune. The upper unit is dominated by large‐scale cross‐stratification of various types and records cliff‐top dune deposition. The nature of the aeolian succession indicates that the aeolian landscape was characterized by alternating phases of activity and stabilization. Most sand transported inland was apparently preserved. Combined evidence from luminescence dating of aeolian sand and radiocarbon dating of palaeosols indicates that phases of aeolian sand movement were initiated at about 2200 BC , 700 BC and AD 1100. Episodes of inland sand movement were apparently initiated during marked climate shifts towards cooler, wetter and more stormy conditions; these episodes are thought to record increased coastal erosion and strong‐wind reworking of beach and foredune sediments. The intensity, duration and areal importance of these sand‐drift events increased with time, probably reflecting the increasing anthropogenic pressure on the landscape. The formation of the cliff‐top dunes after AD 1800 records the modern retreat of the coastal cliffs.     

Use of low frequencies for sub-basalt imaging

Many prospective passive ocean margins are covered by large areas of basalts. These basalts are often extremely heterogeneous and scatter the seismic energy of the conventional seismic reflection system so that it becomes difficult to obtain information on deeper reflectors. Since high frequencies are scattered more than low frequencies, we argue that the acquisition system for sub-basalt targets should be modified to emphasize the low frequencies, using much larger airguns, and towing the source and receivers at about 20 m depth. In the summer of 2001 we obtained seismic reflection data over basalt in the northeast Atlantic using a system modified to enhance the low-frequency energy. These new data show deep reflections that are not visible on lines shot in the same places with a conventional system.