Shape Of Power Spectrum Research Articles

Reconstructing the nature of the first cosmic sources from the anisotropic 21-cm signal.

The redshifted 21-cm background is expected to be a powerful probe of the early Universe, carrying both cosmological and astrophysical information from a wide range of redshifts. In particular, the power spectrum of fluctuations in the 21-cm brightness temperature is anisotropic due to the line-of-sight velocity gradient, which in principle allows for a simple extraction of this information in the limit of linear fluctuations. However, recent numerical studies suggest that the 21-cm signal is actually rather complex, and its analysis likely depends on detailed model fitting. We present the first realistic simulation of the anisotropic 21-cm power spectrum over a wide period of early cosmic history. We show that on observable scales, the anisotropy is large and thus measurable at most redshifts, and its form tracks the evolution of 21-cm fluctuations as they are produced early on by Lyman-α radiation from stars, then switch to x-ray radiation from early heating sources, and finally to ionizing radiation from stars. In particular, we predict a redshift window during cosmic heating (at z∼15), when the anisotropy is small, during which the shape of the 21-cm power spectrum on large scales is determined directly by the average radial distribution of the flux from x-ray sources. This makes possible a model-independent reconstruction of the x-ray spectrum of the earliest sources of cosmic heating.

CORONAL FOURIER POWER SPECTRA: IMPLICATIONS FOR CORONAL SEISMOLOGY AND CORONAL HEATING

The dynamics of regions of the solar corona are investigated using Atmospheric Imaging Assembly (AIA) 171\AA\ and 193\AA\ data. The coronal emission from the quiet Sun, coronal loop footprints, coronal moss, and from above a sunspot is studied. It is shown that the mean Fourier power spectra in these regions can be described by a power law at lower frequencies that tails to flat spectrum at higher frequencies, plus a Gaussian-shaped contribution that varies depending on the region studied. This Fourier spectral shape is in contrast to the commonly-held assumption that coronal time-series are well described by the sum of a long time-scale background trend plus Gaussian-distributed noise, with some specific locations also showing an oscillatory signal. The implications of this discovery to the field of coronal seismology and the automated detections of oscillations are discussed. The power law contribution to the shape of the Fourier power spectrum is interpreted as being due to the summation of a distribution of exponentially decaying emission events along the line of sight. This is consistent with the idea that the solar atmosphere is heated everywhere by small energy deposition events.

Primordial power spectrum from Planck

Using modified Richardson-Lucy algorithm we reconstruct the primordial power spectrum (PPS) from Planck Cosmic Microwave Background (CMB) temperature anisotropy data. In our analysis we use different combinations of angular power spectra from Planck to reconstruct the shape of the primordial power spectrum and locate possible features. Performing an extensive error analysis we found the dip near ℓ ∼ 750–850 represents the most prominent feature in the data. Feature near ℓ ∼ 1800–2000 is detectable with high confidence only in 217 GHz spectrum and is apparently consequence of a small systematic as described in the revised Planck 2013 papers. Fixing the background cosmological parameters and the foreground nuisance parameters to their best fit baseline values, we report that the best fit power law primordial power spectrum is consistent with the reconstructed form of the PPS at 2σ C.L. of the estimated errors (apart from the local features mentioned above). As a consistency test, we found the reconstructed primordial power spectrum from Planck temperature data can also substantially improve the fit to WMAP-9 angular power spectrum data (with respect to power-law form of the PPS) allowing an overall amplitude shift of ∼ 2.5%. In this context low-ℓ and 100 GHz spectrum from Planck which have proper overlap in the multipole range with WMAP data found to be completely consistent with WMAP-9 (allowing amplitude shift). As another important result of our analysis we do report the evidence of gravitational lensing through the reconstruction analysis. Finally we present two smooth form of the PPS containing only the important features. These smooth forms of PPS can provide significant improvements in fitting the data (with respect to the power law PPS) and can be helpful to give hints for inflationary model building.

PRISM: Recovery of the primordial spectrum fromPlanckdata

The primordial power spectrum describes the initial perturbations that seeded the large-scale structure we observe today. It provides an indirect probe of inflation or other structure-formation mechanisms. In this letter, we recover the primordial power spectrum from the Planck PR1 dataset, using our recently published algorithm PRISM. PRISM is a sparsity-based inversion method, that aims at recovering features in the primordial power spectrum from the empirical power spectrum of the cosmic microwave background (CMB). This ill-posed inverse problem is regularised using a sparsity prior on features in the primordial power spectrum in a wavelet dictionary. Although this non-parametric method does not assume a strong prior on the shape of the primordial power spectrum, it is able to recover both its general shape and localised features. As a results, this approach presents a reliable way of detecting deviations from the currently favoured scale-invariant spectrum. We applied PRISM to 100 simulated Planck data to investigate its performance on Planck-like data. We also tested the algorithm's ability to recover a small localised feature at $k \sim 0.125$ Mpc$^{-1}$, which caused a large dip at $\ell \sim 1800$ in the angular power spectrum. We then applied PRISM to the Planck PR1 power spectrum to recover the primordial power spectrum. We find no significant departures from the fiducial Planck PR1 near scale-invariant primordial power spectrum with $A_s=2.215\times10^{-9}$ and $n_s = 0.9624$.

Dependence of the cosmic microwave background lensing power spectrum on the matter density

The anisotropies in the cosmic microwave background (CMB) provide our best laboratory for testing models of the formation and evolution of large-scale structure. The rich features in the cosmic microwave background anisotropy spectrum, in combination with highly precise observations and theoretical predictions, also allow us to simultaneously constrain a number of cosmological parameters. As observations have progressed, measurements at smaller angular scales have provided increasing leverage. These smaller angular scales provide sensitive measures of the matter density through the effect of gravitational lensing. In this work we provide an analytic explanation of the manner in which the lensing of CMB anisotropies depends on the matter density, finding that the dominant effect comes from the shape of the matter power spectrum set by the decay of small-scale potentials between horizon crossing and matter-radiation equality.

A joint analysis of Planck and BICEP2 B modes including dust polarization uncertainty

We analyze BICEP2 and Planck data using a model that includes CMB lensing, gravity waves, and polarized dust. Recently published Planck dust polarization maps have highlighted the difficulty of estimating the amount of dust polarization in low intensity regions, suggesting that the polarization fractions have considerable uncertainties and may be significantly higher than previous predictions. In this paper, we start by assuming nothing about the dust polarization except for the power spectrum shape, which we take to be ClBB,dust ∝ l-2.42. The resulting joint BICEP2+Planck analysis favors solutions without gravity waves, and the upper limit on the tensor-to-scalar ratio is r<0.11, a slight improvement relative to the Planck analysis alone which gives r<0.13 (95% c.l.). The estimated amplitude of the dust polarization power spectrum agrees with expectations for this field based on both HI column density and Planck polarization measurements at 353 GHz in the BICEP2 field. Including the latter constraint on the dust spectrum amplitude in our analysis improves the limit further to r < 0.09, placing strong constraints on theories of inflation (e.g., models with r>0.14 are excluded with 99.5% confidence). We address the cross-correlation analysis of BICEP2 at 150 GHz with BICEP1 at 100 GHz as a test of foreground contamination. We find that the null hypothesis of dust and lensing with 0r= gives Δ χ2 < 2 relative to the hypothesis of no dust, so the frequency analysis does not strongly favor either model over the other. We also discuss how more accurate dust polarization maps may improve our constraints. If the dust polarization is measured perfectly, the limit can reach r < 0.05 (or the corresponding detection significance if the observed dust signal plus the expected lensing signal is below the BICEP2 observations), but this degrades quickly to almost no improvement if the dust calibration error is 20% or larger or if the dust maps are not processed through the BICEP2 pipeline, inducing sampling variance noise.

MEASURING GALAXY CLUSTERING AND THE EVOLUTION OF [C II] MEAN INTENSITY WITH FAR-IR LINE INTENSITY MAPPING DURING 0.5 &lt;z&lt; 1.5

Infrared fine-structure emission lines from trace metals are powerful diagnostics of the interstellar medium in galaxies. We explore the possibility of studying the redshifted far-IR fine-structure line emission using the three-dimensional (3D) power spectra obtained with an imaging spectrometer. The intensity mapping approach measures the spatio-spectral fluctuations due to line emission from all galaxies, including those below the individual detection threshold. The technique provides 3D measurements of galaxy clustering and moments of the galaxy luminosity function. Furthermore, the linear portion of the power spectrum can be used to measure the total line emission intensity including all sources through cosmic time with redshift information naturally encoded. Total line emission, when compared to the total star formation activity and/or other line intensities, reveals evolution of the interstellar conditions of galaxies in aggregate. As a case study, we consider measurement of [C ii] autocorrelation in the 0.5 < z < 1.5 epoch, where interloper lines are minimized, using far-IR/submillimeter balloon-borne and future space-borne instruments with moderate and high sensitivity, respectively. In this context, we compare the intensity mapping approach to blind galaxy surveys based on individual detections. We find that intensity mapping is nearly always the best way to obtain the total line emission because blind, wide-field galaxy surveys lack sufficient depth and deep pencil beams do not observe enough galaxies in the requisite luminosity and redshift bins. Also, intensity mapping is often the most efficient way to measure the power spectrum shape, depending on the details of the luminosity function and the telescope aperture.

Running with BICEP2: implications for small-scale problems in CDM

The BICEP2 results, when interpreted as a gravitational wave signal and combined with other CMB data, suggest a roll-off in power towards small scales in the primordial matter power spectrum. Among the simplest possibilities is a running of the spectral index. Here we show that the preferred level of running alleviates small-scale issues within the $\Lambda$CDM model, more so even than viable WDM models. We use cosmological zoom-in simulations of a Milky Way-size halo along with full-box simulations to compare predictions among four separate cosmologies: a BICEP2-inspired running index model ($\alpha_s$ = -0.024), two fixed-tilt $\Lambda$CDM models motivated by Planck, and a 2.6 keV thermal WDM model. We find that the running BICEP2 model reduces the central densities of large dwarf-size halos ($V_\mathrm{max}$ ~ 30 - 80 km s$^{-1}$) and alleviates the too-big-to-fail problem significantly compared to our adopted Planck and WDM cases. Further, the BICEP2 model suppresses the count of small subhalos by ~50% relative to Planck models, and yields a significantly lower "boost" factor for dark matter annihilation signals. Our findings highlight the need to understand the shape of the primordial power spectrum in order to correctly interpret small-scale data.

γ-ray anisotropies from dark matter in the Milky Way: the role of the radial distribution

The annihilation of dark matter particles in the halo of galaxies may end up into gamma rays, which travel almost unperturbed till to their detection at Earth. This annihilation signal can exhibit an anisotropic behavior quantified by the angular power spectrum, whose properties strongly depend on the dark matter distribution and its clumpiness. We use high resolution pure dark matter N-body simulations to quantify the contribution of different components (main halo and satellites) to the global signal as a function of the analytical profile adopted to describe the numerical results. We find that the smooth main halo dominates the angular power spectrum of the gamma-ray signal up to quite large multipoles, where the sub-haloes anisotropy signal starts to emerge, but the transition multipole strongly depends on the assumed radial profile. The extrapolation down to radii not resolved by current numerical simulations can affect both the normalization and the shape of the gamma-ray angular power spectrum. For the sub-haloes described by an asymptotically cored dark matter distribution, the angular power spectrum shows an overall smaller normalization and a flattening at high multipoles. Our results show the criticality of the dark matter density profile shape in gamma-ray anisotropy searches, and evaluate quantitatively the intrinsic errors occurring when extrapolating the dark matter radial profiles down to spatial scales not yet explored by numerical simulations.

PRISM: Sparse recovery of the primordial power spectrum

The primordial power spectrum describes the initial perturbations in the Universe which eventually grew into the large-scale structure we observe today, and thereby provides an indirect probe of inflation or other structure-formation mechanisms. Here, we introduce a new method to estimate this spectrum from the empirical power spectrum of cosmic microwave background (CMB) maps. A sparsity-based linear inversion method, coined \textbf{PRISM}, is presented. This technique leverages a sparsity prior on features in the primordial power spectrum in a wavelet basis to regularise the inverse problem. This non-parametric approach does not assume a strong prior on the shape of the primordial power spectrum, yet is able to correctly reconstruct its global shape as well as localised features. These advantages make this method robust for detecting deviations from the currently favoured scale-invariant spectrum. We investigate the strength of this method on a set of WMAP 9-year simulated data for three types of primordial power spectra: a nearly scale-invariant spectrum, a spectrum with a small running of the spectral index, and a spectrum with a localised feature. This technique proves to easily detect deviations from a pure scale-invariant power spectrum and is suitable for distinguishing between simple models of the inflation. We process the WMAP 9-year data and find no significant departure from a nearly scale-invariant power spectrum with the spectral index $n_s = 0.972$. A high resolution primordial power spectrum can be reconstructed with this technique, where any strong local deviations or small global deviations from a pure scale-invariant spectrum can easily be detected.

Geometric and dynamic distortions in anisotropic galaxy clustering

We examine the signature of dynamic (redshift-space) distortions and geometric distortions (including the Alcock-Paczynski effect) in the context of the galaxy power spectrum measured in upcoming galaxy redshift surveys. Information comes from both the baryon acoustic oscillation (BAO) feature and the broadband power spectrum shape. Accurate modeling is required to extract this information without systematically biasing the result. We consider an analytic model for the power spectrum of dark matter halos in redshift space, based on the distribution function expansion, and compare with halo clustering measured in N-body simulations. We forecast that the distribution function model is sufficiently accurate to allow the inclusion of broadband information on scales down to k ∼ 0.2h Mpc−1, with somewhat better accuracy for higher bias halos. Compared with a BAO-only analysis with reconstruction, including broadband shape information can improve unbiased constraints on distance measures H(z) and DA(z) by ∼ 30% and 20%, respectively, for a galaxy sample similar to the DESI luminous red galaxies. The gains in precision are larger in the absence of BAO reconstruction. Furthermore, including broadband shape information allows the measurement of structure growth, through redshift-space distortions. For the same galaxy sample, the distribution function model is able to constrain fσ8 to ∼ 2%, when simultaneously fitting for H(z) and DA(z). We discuss techniques to optimize the analysis of the power spectrum, including removing modes near the line-of-sight that are particularly challenging to model, and whether these approaches can improve parameter constraints. We find that such techniques are unlikely to significantly improve constraints on geometry, although they may allow higher precision measurements of redshift-space distortions.

What can the spatial distribution of galaxy clusters tell about their scaling relations?

We aim to quantify the capability of the inhomogeneous distribution of galaxy clusters, represented by the two-point statistics in Fourier space, to retrieve information on the underlying scaling relations. We make a case study using the mass X-ray luminosity scaling relation for galaxy clusters and study its impact on the clustering pattern of these objects. We define the luminosity-weighted power spectrum and introduce the luminosity power spectrum as direct assessment of the clustering of the property of interest, in our case, the cluster X-ray luminosity. Using a suite of halo catalogs extracted from N-body simulations and realistic estimates of the mass X-ray luminosity relation, we measured these statistics with their corresponding covariance matrices. By carrying out a Fisher matrix analysis, we quantified the content of information (by means of a figure-of merit) encoded in the amplitude, shape, and full shape of our probes for two-point statistics. The full shape of the luminosity power spectrum, when analyzed up to scales of k~0.2 h/Mpc, yields a figure of merit which is two orders of magnitude above the figure obtained from the unweighted power spectrum, and only one order of magnitude below the value encoded in X-ray luminosity function estimated from the same sample. This is a significant improvement over the analysis developed with the standard (i.e., unweighted) clustering probes. The measurements of the clustering of galaxy clusters and its explicit dependence on the cluster intrinsic properties can contribute to improving the degree of knowledge regarding the underlying links between cluster observables and the cluster masses (Abridged).

Cosmological constraints from the large-scale weak lensing of SDSS MaxBCG clusters

We derive constraints on the matter density \Om and the amplitude of matter clustering \sig8 from measurements of large scale weak lensing (projected separation R=5-30\hmpc) by clusters in the Sloan Digital Sky Survey MaxBCG catalog. The weak lensing signal is proportional to the product of \Om and the cluster-mass correlation function \xicm. With the relation between optical richness and cluster mass constrained by the observed cluster number counts, the predicted lensing signal increases with increasing \Om or \sig8, with mild additional dependence on the assumed scatter between richness and mass. The dependence of the signal on scale and richness partly breaks the degeneracies among these parameters. We incorporate external priors on the richness-mass scatter from comparisons to X-ray data and on the shape of the matter power spectrum from galaxy clustering, and we test our adopted model for \xicm against N-body simulations. Using a Bayesian approach with minimal restrictive priors, we find \sig8(\Om/0.325)^{0.501}=0.828 +/- 0.049, with marginalized constraints of \Om=0.325_{-0.067}^{+0.086} and \sig8=0.828_{-0.097}^{+0.111}, consistent with constraints from other MaxBCG studies that use weak lensing measurements on small scales (R<=2\hmpc). The (\Om,\sig8) constraint is consistent with and orthogonal to the one inferred from WMAP CMB data, reflecting agreement with the structure growth predicted by GR for an LCDM cosmological model. A joint constraint assuming LCDM yields \Om=0.298 +/- 0.020 and \sig8=0.831 +/- 0.020. Our cosmological parameter errors are dominated by the statistical uncertainties of the large scale weak lensing measurements, which should shrink sharply with current and future imaging surveys.

Evidence for Massive Neutrinos from Cosmic Microwave Background and Lensing Observations

We discuss whether massive neutrinos (either active or sterile) can reconcile some of the tensions within cosmological data that have been brought into focus by the recently released Planck data. We point out that a discrepancy is present when comparing the primary CMB and lensing measurements both from the CMB and galaxy lensing data using CFHTLenS, similar to that which arises when comparing CMB measurements and SZ cluster counts. A consistent picture emerges and including a prior for the cluster constraints and BAOs we find that for an active neutrino model with three degenerate neutrinos, ∑m(ν)=(0.320±0.081) eV, whereas for a sterile neutrino, in addition to 3 neutrinos with a standard hierarchy and ∑m(ν)=0.06 eV, m(ν,sterile)(eff)=(0.450±0.124) eV and ΔN(eff)=0.45±0.23. In both cases there is a significant detection of modification to the neutrino sector from the standard model and in the case of the sterile neutrino it is possible to reconcile the BAO and local H0 measurements. However, a caveat to our result is some internal tension between the CMB and lensing and cluster observations, and the masses are in excess of those estimated from the shape of the matter power spectrum from galaxy surveys.

Adaptive Iterative Dose Reduction 3D Versus Filtered Back Projection in CT: Evaluation of Image Quality

The purpose of this study was to evaluate image quality with filtered back projection (FBP) and adaptive iterative dose reduction 3D (AIDR 3D). Phantom acquisitions were performed at six dose levels to assess spatial resolution, noise, and low-contrast detectability (LCD). Spatial resolution was assessed with the modulation transfer function at high and low contrast levels. Noise power spectrum and SD of attenuation were assessed. LCD was calculated with a mathematic model observer applied to phantom CT images. The subjective image quality of clinical CT scans was assessed by five radiologists. Compared with FBP, AIDR 3D resulted in substantial noise reduction at all frequencies with a similar shape of the noise power spectrum. Spatial resolution was similar for AIDR 3D and FBP. LCD improved with AIDR 3D, which was associated with a potential average dose reduction of 36% (range, 9-86%). The observer study showed that overall image quality improved and artifacts decreased with AIDR 3D. AIDR 3D performs better than FBP with regard to noise and LCD, resulting in better image quality, and performs similarly with respect to spatial resolution. The evaluation of image quality of clinical CT scans was consistent with the objective assessment of image quality with a phantom. The amount of dose reduction should be investigated for each clinical indication in studies with larger numbers of patients.

Using the topology of large-scale structure in the WiggleZ Dark Energy Survey as a cosmological standard ruler

We present new and accurate measurements of the cosmic distance–redshift relation, spanning 0.2 < z < 1, using the topology of large-scale structure as a cosmological standard ruler. Our results derive from an analysis of the Minkowski functionals of the density field traced by the WiggleZ Dark Energy Survey. The Minkowski functionals are a set of statistics which completely describe the topological nature of each isodensity surface within the field, as a function of the density value. Given the shape of the underlying matter power spectrum, measured by fluctuations in the cosmic microwave background radiation, the expected amplitudes of the Minkowski functionals are specified as an excursion set of a Gaussian random field, with minimal non-Gaussian corrections for the smoothing scales ≥10 h−1 Mpc considered in this analysis. The measured amplitudes then determine the cosmic distance DV(z), which we obtain with 3–7 per cent accuracies in six independent redshift slices, with the standard ruler originating in the known curvature of the model power spectrum at the smoothing scale. We introduce a new method for correcting the topological statistics for the sparse-sampling of the density field by the galaxy tracers, and validate our overall methodology using mock catalogues from N-body simulations. Our distance measurements are consistent with standard models which describe the cosmic expansion history, and with previous analyses of baryon acoustic oscillations (BAOs) detected by the WiggleZ Survey, with the topological results yielding a higher distance precision by a factor of 2. However, the full redshift-space power-spectrum shape is required to recover the topological distances, in contrast to the preferred length scale imprinted by BAOs, which is determined by simpler physics.

Clipping the cosmos. II. Cosmological information from nonlinear scales

We present a method for suppressing contributions from higher-order terms in perturbation theory, greatly increasing the amount of information that may be extracted from the matter power spectrum. In an evolved cosmological density field the highest density regions are responsible for the bulk of the nonlinear power. By suitably down-weighting these problematic regions we find that the one- and two-loop terms are typically reduced in amplitude by $\ensuremath{\sim}70%$ and $\ensuremath{\sim}95%$, respectively, relative to the linear power spectrum. This greatly facilitates modeling the shape of the galaxy power spectrum, potentially increasing the number of useful Fourier modes by more than 2 orders of magnitude. We provide a demonstration of how this technique allows the galaxy bias and the amplitude of linear matter perturbations ${\ensuremath{\sigma}}_{8}$ to be determined from the power spectrum on conventionally nonlinear scales, $0.1&lt;k&lt;0.7\text{ }h{\mathrm{Mpc}}^{\ensuremath{-}1}$.

A place for time: the spatiotemporal structure of neural dynamics during natural audition

We use functional magnetic resonance imaging (fMRI) to analyze neural responses to natural auditory stimuli. We characterize the fMRI time series through the shape of the voxel power spectrum and find that the timescales of neural dynamics vary along a spatial gradient, with faster dynamics in early auditory cortex and slower dynamics in higher order brain regions. The timescale gradient is observed through the unsupervised clustering of the power spectra of individual brains, both in the presence and absence of a stimulus, and is enhanced in the stimulus-locked component that is shared across listeners. Moreover, intrinsically faster dynamics occur in areas that respond preferentially to momentary stimulus features, while the intrinsically slower dynamics occur in areas that integrate stimulus information over longer timescales. These observations connect the timescales of intrinsic neural dynamics to the timescales of information processing, suggesting a temporal organizing principle for neural computation across the cerebral cortex.

EISCAT and ESRAD radars observations of polar mesosphere winter echoes during solar proton events on 11–12 November 2004

Abstract. Polar mesosphere winter echoes (PMWE) were detected by two radars, ESRAD at 52 MHz located near Kiruna, Sweden, and EISCAT at 224 MHz located near Tromsø, Norway, during the strong solar proton event on 11–12 November 2004. PMWE maximum volume reflectivity was estimated to be 3 × 10−15 m−1 for ESRAD and 2 × 10−18 m−1 for EISCAT. It was found that the shape of the echo power spectrum is close to Gaussian inside the PMWE layers, and outside of them it is close to Lorentzian, as for the standard ion line of incoherent scatter (IS). The EISCAT PMWE spectral width is about 5–7 m s−1 at 64–67 km and 7–10 m s−1 at 68–70 km. At the lower altitudes the PMWE spectral widths are close to those for the IS ion line derived from the EISCAT data outside the layers. At the higher altitudes the PMWE spectra are broader by 2–4 m s−1 than those for the ion line. The ESRAD PMWE spectral widths at 67–72 km altitude are 3–5 m s−1, that is, 2–4 m s−1 larger than ion line spectral widths modelled for the ESRAD radar. The PMWE spectral widths for both EISCAT and ESRAD showed no dependence on the echo strength. It was found that all these facts cannot be explained by turbulent origin of the echoes. We suggested that evanescent perturbations in the electron gas generated by the incident infrasound waves may explain the observed PMWE spectral widths. However, a complete theory of radar scatter from this kind of disturbance needs to be developed before a full conclusion can be made.

LOFAR insights into the epoch of reionization from the cross-power spectrum of 21 cm emission and galaxies

Using a combination of N-body simulations, semi-analytic models and radiative transfer calculations, we have estimated the theoretical cross power spectrum between galaxies and the 21cm emission from neutral hydrogen during the epoch of reionization. In accordance with previous studies, we find that the 21cm emission is initially correlated with halos on large scales (> 30 Mpc), anti-correlated on intermediate (~ 5 Mpc), and uncorrelated on small (< 3 Mpc) scales. This picture quickly changes as reionization proceeds and the two fields become anti-correlated on large scales. The normalization of the cross power spectrum can be used to set constraints on the average neutral fraction in the intergalactic medium and its shape can be a tool to study the topology of reionization. When we apply a drop-out technique to select galaxies and add to the 21cm signal the noise expected from the LOFAR telescope, we find that while the normalization of the cross power spectrum remains a useful tool for probing reionization, its shape becomes too noisy to be informative. On the other hand, for a Lyalpha Emitter (LAE) survey both the normalization and the shape of the cross power spectrum are suitable probes of reionization. A closer look at a specific planned LAE observing program using Subaru Hyper-Suprime Cam reveals concerns about the strength of the 21cm signal at the planned redshifts. If the ionized fraction at z ~ 7 is lower that the one estimated here, then using the cross power spectrum may be a useful exercise given that at higher redshifts and neutral fractions it is able to distinguish between two toy models with different topologies.