Halo Distribution Research Articles

Lensing magnification: implications for counts of submillimetre galaxies and SZ clusters

We study lensing magnification of source galaxies by intervening galaxy groups and clusters using a halo model. Halos are modeled with truncated NFW profiles with ellipticity added to their lensing potential and propagated to observable lensing statistics. We present the formalism to calculate observable effects due to a distribution of halos of different masses at different redshifts along the l ine of sight. We calculate the effects of magnification on the number counts of high-redshift galaxies. Using BLAST survey data for submillimeter galaxies (SMGs), we find that magnification affects the steep, high flux par t of the counts by about 60%. The effect becomes much stronger if the intrinsic distribution is signi ficantly steeper than observed. We also consider the effect of this high-redshift galaxy population on contaminating the Sunyaev-Zel'dovich (SZ) signal of massive clusters using the halo model approach. We find that for the majority of clusters expected to be detected with ongoing SZ surveys, there is significant contamination from the Poisson noise due to background SMGs. This contr ibution can be comparable to the SZ increment for typical clusters and can also contaminate the SZ decrement of low mass clusters. Thus SZ observations, especially for the increment part of the SZ spectrum, need to include careful modeling of this irreducible contamination for mass estimation. Lensing further enhances the contamination, especially close to the cores of massive clusters and for very disturbed clusters with large magnification cross-section.

KPG 390: A pair of trailing spirals.

AbstractIn this study we present scanning Fabry-Perot Hα observations of the isolated interacting galaxy pair NGC 5278/79. We derived velocity fields, various kinematic parameters and rotation curves for both galaxies. These kinematical results together with the fact that dust lanes have been detected in both galaxies, as well as the analysis of surface brightness profiles along the minor axis, allowed us to determine univocally that both components of the interacting pair are trailing spirals. We have also estimated the mass of NGC 5278 fitting its rotation curve with a disk-halo component. We have tested three different types of halo (pseudo-isothermal, Hernquist and Navarro Frenk White) and we have obtained that the rotation curve can be fitted either with a pseudo-isothermal, an Hernquist halo or a Navarro Frenk White halo component, although in the first case the amount of dark matter required is about ten times smaller than for the other two halo distributions.

DISSECTING GALAXY FORMATION. II. COMPARING SUBSTRUCTURE IN PURE DARK MATTER AND BARYONIC MODELS

We compare the substructure evolution in pure dark matter (DM) halos with those in the presence of baryons, hereafter PDM and BDM models, respectively. The prime halos have been analyzed in the previous work. Models have been evolved from identical initial conditions which have been constructed by means of the constrained realization method. The BDM model includes star formation and feedback from stellar evolution onto the gas. A comprehensive catalog of subhalo populations has been compiled and individual and statistical properties of subhalos analyzed, including their orbital differences. We find that subhalo population mass functions in PDM and BDM are consistent with a single power law, Mαsbh, for each of the models in the mass range of ∼2 × 108 M☉–2 × 1011 M☉. However, we detect a nonnegligible shift between these functions, the time-averaged α ∼ −0.86 for the PDM and −0.98 for the BDM models. Overall, α appears to be a nearly constant in time, with variations of ±15%. Second, we find that the radial mass distribution of subhalo populations can be approximated by a power law, with a steepening that occurs at the radius of a maximal circular velocity, Rvmax, in the prime halos. Here we find that γsbh ∼ −1.5 for the PDM and −1 for the BDM models, when averaged over time inside Rvmax. The slope is steeper outside this region and approaches −3. We detect little spatial bias (less than 10%) between the subhalo populations and the DM distribution of the main halos. Also, the subhalo population exhibits much less triaxiality in the presence of baryons, in tandem with the shape of the prime halo. Finally, we find that, counter-intuitively, the BDM population is depleted at a faster rate than the PDM one within the central 30 kpc of the prime halo. The reason for this is that although the baryons provide a substantial glue to the subhalos, the main halo exhibits the same trend. This assures a more efficient tidal disruption of the BDM subhalo population. However, this effect can be reversed for a more efficient feedback from stellar evolution and the central supermassive black holes, which will expel baryons from the center and decrease the central concentration of the prime halo. We compare our results with via Lactea and Aquarius simulations and other published results.

THE INTERACTING GALAXY PAIR KPG 390: H{alpha} KINEMATICS

In this work, we present scanning Fabry-Perot (FP) H{alpha} observations of the isolated interacting galaxy pair NGC 5278/79 obtained with the PUMA FP interferometer. We derived velocity fields and rotation curves for both galaxies. For NGC 5278 we also obtained the residual velocity map to investigate the non-circular motions, and estimated its mass by fitting the rotation curve with disk+halo components. We test three different types of halos (pseudo-isothermal, Hernquist, and Navarro-Frenk-White) and obtain satisfactory fits to the rotation curve for all profiles. The amount of dark matter required by the pseudo-isothermal profile is about 10 times smaller than that for the other two halo distributions. Finally, our kinematical results together with the analysis of dust lane distribution and of surface brightness profiles along the minor axis allowed us to determine univocally that both components of the interacting pair are trailing spirals.

One simulation to fit them all - changing the background parameters of a cosmologicalN-body simulation

We demonstrate that the output of a cosmological N-body simulation can, to remarkable accuracy, be scaled to represent the growth of large-scale structure in a cosmology with parameters similar to but different from those originally assumed. Our algorithm involves three steps: a reassignment of length, mass and velocity units, a relabelling of the time axis, and a rescaling of the amplitudes of individual large-scale fluctuation modes. We test it using two matched pairs of simulations. Within each pair, one simulation assumes parameters consistent with analyses of the first-year WMAP data. The other has lower matter and baryon densities and a 15% lower fluctuation amplitude, consistent with analyses of the three-year WMAP data. The pairs differ by a factor of a thousand in mass resolution, enabling performance tests on both linear and nonlinear scales. Our scaling reproduces the mass power spectra of the target cosmology to better than 0.5% on large scales (k < 0.1 h/Mpc) both in real and in redshift space. In particular, the BAO features of the original cosmology are removed and are correctly replaced by those of the target cosmology. Errors are still below 3% for k < 1 h/Mpc. Power spectra of the dark halo distribution are even more precisely reproduced, with errors below 1% on all scales tested. A halo-by-halo comparison shows that centre-of-mass positions and velocities are reproduced to better than 90 kpc/h and 5%, respectively. Halo masses, concentrations and spins are also reproduced at about the 10% level, although with small biases. Halo assembly histories are accurately reproduced, leading to central galaxy magnitudes with errors of about 0.25 magnitudes and a bias of about 0.13 magnitudes for a representative semi-analytic model.

Structure formation from non-Gaussian initial conditions: Multivariate biasing, statistics, and comparison withN-body simulations

We study structure formation in the presence of primordial non-Gaussianity of the local type with parameters ${f}_{\mathrm{NL}}$ and ${g}_{\mathrm{NL}}$. We show that the distribution of dark-matter halos is naturally described by a multivariate bias scheme where the halo overdensity depends not only on the underlying matter density fluctuation $\ensuremath{\delta}$ but also on the Gaussian part of the primordial gravitational potential $\ensuremath{\varphi}$. This corresponds to a non-local bias scheme in terms of $\ensuremath{\delta}$ only. We derive the coefficients of the bias expansion as a function of the halo mass by applying the peak-background split to common parametrizations for the halo mass function in the non-Gaussian scenario. We then compute the halo power spectrum and halo-matter cross spectrum in the framework of Eulerian perturbation theory up to third order. Comparing our results against $N$-body simulations, we find that our model accurately describes the numerical data for wave numbers $k\ensuremath{\le}0.1--0.3h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ depending on redshift and halo mass. In our multivariate approach, perturbations in the halo counts trace $\ensuremath{\varphi}$ on large scales, and this explains why the halo and matter power spectra show different asymptotic trends for $k\ensuremath{\rightarrow}0$. This strongly scale-dependent bias originates from terms at leading order in our expansion. This is different from what happens using the standard univariate local bias where the scale-dependent terms come from badly behaved higher-order corrections. On the other hand, our biasing scheme reduces to the usual local bias on smaller scales, where $|\ensuremath{\varphi}|$ is typically much smaller than the density perturbations. We finally discuss the halo bispectrum in the context of multivariate biasing and show that, due to its strong scale and shape dependence, it is a powerful tool for the detection of primordial non-Gaussianity from future galaxy surveys.

THE INTERACTING GALAXY PAIR KPG 390: Hα KINEMATICS

In this work we present scanning Fabry-Perot H$\alpha$ observations of the isolated interacting galaxy pair NGC 5278/79 obtained with the PUMA Fabry-Perot interferometer. We derived velocity fields and rotation curves for both galaxies. For NGC 5278 we also obtained the residual velocity map to investigate the non-circular motions, and estimated its mass by fitting the rotation curve with a disk+halo components. We test three different types of halo (pseudo-isothermal, Hernquist and Navarro Frenk White) and obtain satisfactory fits to the rotation curve for all profiles. The amount of dark matter required by pseudo-isothermal profile is about ten times smaller than, that for the other two halo distributions. Finally, our kinematical results together with the analysis of dust lanes distribution and of surface brightness profiles along the minor axis allowed us to determine univocally that both components of the interacting pair are trailing spirals.

THE HALO MASS FUNCTION CONDITIONED ON DENSITY FROM THE MILLENNIUM SIMULATION: INSIGHTS INTO MISSING BARYONS AND GALAXY MASS FUNCTIONS

The baryon content of high-density regions in the universe is relevant to two critical unanswered questions: the workings of nurture effects on galaxies and the whereabouts of the missing baryons. In this paper, we analyze the distribution of dark matter and semianalytical galaxies in the Millennium Simulation to investigate these problems. Applying the same density field reconstruction schemes as used for the overall matter distribution to the matter locked in halos we study the mass contribution of halos to the total mass budget at various background field densities, i.e., the conditional halo mass function. In this context, we present a simple fitting formula for the cumulative mass function accurate to ~ 5% for halo masses between 10^{10} and 10^{15}Msol/h. We find that in dense environments the halo mass function becomes top heavy and present corresponding fitting formulae for different redshifts. We demonstrate that the major fraction of matter in high-density fields is associated with galaxy groups. Since current X-ray surveys are able to nearly recover the universal baryon fraction within groups, our results indicate that the major part of the so-far undetected warm-hot intergalactic medium resides in low-density regions at low temperatures. Similarly, we show that the differences in galaxy mass functions with environment seen in observed and simulated data stem predominantly from differences in the mass distribution of halos. In particular, the hump in the galaxy mass function is associated with the central group galaxies, and the bimodality observed in the galaxy mass function is therefore interpreted as that of central galaxies versus satellites.

New stochastic approach to cumulative weak lensing

We study the weak gravitational lensing effects caused by a stochastic distribution of dark matter halos. We develop a simple approach to calculate the magnification probability distribution function which allows us to easily compute the magnitude bias and dispersion for an arbitrary data sample and a given universe model. As an application we consider the effects of single-mass large-scale cosmic inhomogeneities to the SNe magnitude-redshift relation, and conclude that such structures could bias the PDF enough to affect the extraction of cosmological parameters from the limited size of present-day SNe data samples. We also release turboGL, a simple and very fast (<= 1s) Mathematica code based on the method here presented.

The statistics of voids as a tool to constrain cosmological parameters: σ8 and Γ

We present a general analytical formalism to calculate accurately several statistics related to underdense regions in the Universe. The statistics are computed for dark matter halo and galaxy distributions both in real space and redshift space at any redshift. Using this formalism, we found that void statistics for galaxy distributions can be obtained, to a very good approximation, assuming galaxies to have the same clustering properties as halos above a certain mass. We deducted a relationship between this mass and that of halos with the same accumulated number density as the galaxies. We also found that the dependence of void statistics on redshift is small. For instance, the number of voids larger than 13 Mpc/h (defined to not contain galaxies brighter than M_r=-20.4 +5logh change less than 20% between z=1 and z=0. However, the dependence of void statistics on sigma_8 and Omega_m h is considerably larger, making them appropriate to develop tests to measure these parameters. We have shown how to efficiently construct several of these tests and discussed in detail the treatment of several observational effects. The formalism presented here along with the observed statistics extracted from current and future large galaxy redshift surveys will provide an independent measurement of the relevant cosmological parameters. Combining these measurements with those found using other methods will contribute to reduce their uncertainties.

THE SPIN AND ORIENTATION OF DARK MATTER HALOS WITHIN COSMIC FILAMENTS

Clusters, filaments, sheets and voids are the building blocks of the cosmic web. In this study, we present and compare two distinct algorithms for finding cosmic filaments and sheets, a task which is far less well established than the identification of dark matter halos or voids. One method is based on the smoothed dark matter density field, the other uses the halo distributions directly. We apply both techniques to one high resolution N-body simulation and reconstruct the filamentary/sheet like network of the dark matter density field. We focus on investigating the properties of the dark matter halos inside these structures, in particular on the directions of their spins and the orientation of their shapes with respect to the directions of the filaments and sheets. We find that both the spin and the major axes of filament-halos with masses <= 10^{13} M_sun/h are preferentially aligned with the direction of the filaments. The spins and major axes of halos in sheets tend to lie parallel to the sheets. There is an opposite mass dependence of the alignment strengths for the spin (negative) and major (positive) axes, i.e. with increasing halo mass the major axis tends to be more strongly aligned with the direction of the filament whereas the alignment between halo spin and filament becomes weaker with increasing halo mass. The alignment strengths as a function of distance to the most massive node halo indicate that there is a transit large scale environment impact: from the 2-D collapse phase of the filament to the 3-D collapse phase of the cluster/node halo at small separation. Overall, the two algorithms for filament/sheet identification investigated here agree well with each other. The method based on halos alone can be easily adapted for use with observational data sets.

Dark matter gravitational clustering with a long-range scalar interaction

We explore the possibility of improving the $\ensuremath{\Lambda}\mathrm{CDM}$ model at megaparsec scales by introducing a scalar interaction that increases the mutual gravitational attraction of dark matter particles. Using N-body simulations, we study the spatial distribution of dark matter particles and halos. We measure the effect of modifications in the Newton's gravity on properties of the two-point correlation function, the dark matter power spectrum, the cumulative halo mass function, and density probability distribution functions. The results look promising: the scalar interactions produce desirable features at megaparsec scales without spoiling the $\ensuremath{\Lambda}\mathrm{CDM}$ successes at larger scales.

Hubble expansion and structure formation in time varying vacuum models

We investigate the properties of the FLRW flat cosmological models in which the vacuum energy density evolves with time, $\ensuremath{\Lambda}(t)$. Using different versions of the $\ensuremath{\Lambda}(t)$ model, namely, quantum field vacuum, power series vacuum and power law vacuum, we find that the main cosmological functions such as the scale factor of the Universe, the Hubble expansion rate $H$, and the energy densities are defined analytically. Performing a joint likelihood analysis of the recent supernovae type Ia data, the cosmic microwave background shift parameter and the baryonic acoustic oscillations traced by the Sloan Digital Sky Survey galaxies, we put tight constraints on the main cosmological parameters of the $\ensuremath{\Lambda}(t)$ scenarios. Furthermore, we study the linear matter fluctuation field of the above vacuum models. We find that the patterns of the power series vacuum $\ensuremath{\Lambda}={n}_{1}H+{n}_{2}{H}^{2}$ predict stronger small scale dynamics, which implies a faster growth rate of perturbations with respect to the other two vacuum cases (quantum field and power law), despite the fact that all the cosmological models share the same equation of state parameter. In the case of the quantum field vacuum $\ensuremath{\Lambda}={n}_{0}+{n}_{2}{H}^{2}$, the corresponding matter fluctuation field resembles that of the traditional $\ensuremath{\Lambda}$ cosmology. The power law vacuum ($\ensuremath{\Lambda}\ensuremath{\propto}{a}^{\ensuremath{-}n}$) mimics the classical quintessence cosmology, the best fit being tilted in the phantom phase. In this framework, we compare the observed growth rate of clustering measured from the optical galaxies with those predicted by the current $\ensuremath{\Lambda}(t)$ models. Performing a Kolmogorov-Smirnov statistical test we show that the cosmological models which contain a constant vacuum ($\ensuremath{\Lambda}\mathrm{CDM}$), quantum field vacuum, and power law vacuum provide growth rates that match well with the observed growth rate. However, this is not the case for the power series vacuum models (in particular, the frequently adduced $\ensuremath{\Lambda}\ensuremath{\propto}H$ model) in which clusters form at significantly earlier times ($z\ensuremath{\ge}4$) with respect to all other models ($z\ensuremath{\sim}2$). Finally, we derived the theoretically predicted dark matter halo mass function and the corresponding distribution of cluster-size halos for all the models studied. Their expected redshift distribution indicates that it will be difficult to distinguish the closely resembling models (constant vacuum, quantum field, and power law vacuum), using realistic future x-ray surveys of cluster abundances. However, cluster surveys based on the Sunayev-Zeldovich detection method give some hope to distinguish the closely resembling models at high redshifts.

Extremely metal-poor stars in dwarf galaxies

AbstractWe present Keck/HIRES spectra of six metal-poor stars in two of the ultra-faint dwarf galaxies orbiting the Milky Way, Ursa Major II and Coma Berenices, and a Magellan/MIKE spectrum of a star in the classical dwarf spheroidal galaxy (dSph) Sculptor. Our data include the first high-resolution spectroscopic observations of extremely metal-poor stars ([Fe/H] &lt; −3.0) not belonging to the Milky Way (MW) stellar halo field population. We obtain abundance measurements and upper limits for up to 26 elements between carbon and europium. The stars span a range of −3.8 &lt; [Fe/H] &lt; −2.3, with the ultra-faints having large spreads in Fe. A comparison with MW halo stars of similar metallicity reveals substantial agreement between the abundance patterns of the ultra-faint dwarf galaxies and Sculptor and the MW halo for the light, α and iron-peak elements (C to Zn). This agreement contrasts with the results of earlier studies of more metal-rich stars (−2.5 ≲[Fe/H]≲ −1.0) in more luminous dwarfs, which found significant abundance discrepancies with respect to the MW halo data. The abundances of neutron-capture elements (Sr to Eu) in all three galaxies are extremely low, consistent with the most metal-poor halo stars, but not with the typical halo abundance pattern at [Fe/H]≳ −3.0. Our results are broadly consistent with a galaxy formation model which predicts that massive dwarf galaxies are the source of the metal-rich component ([Fe/H]≳ −2.5) of the MW inner halo, but we propose that dwarf galaxies similar to the dSphs are the primary contributors to the metal-poor end of the metallicity distribution of the MW outer halo.

Baryons and Dark Matter halo distributions in ΛCDM Cosmology

AbstractWe analyse the dark matter (DM) distribution in a ≈1012M⊙ halo extracted from a simulation consistent with the concordance cosmology, where the physics regulating the transformation of gas into stars was allowed to change producing galaxies with different morphologies. Although the DM profiles get more concentrated as baryons are collected at the centre of the haloes compared to a pure dynamical run, the total baryonic mass alone is not enough to fully predict the reaction of the DM profile. Our findings suggest that the response of the DM halo is driven by the history of assembly of baryons into a galaxy. The accretion of satellites could be associated with an expansion of the dark matter profiles, triggered by angular momentum transfer from the incoming satellites. However, we also found that these mechanism have different efficiencies which are set by the history of formation of the structure.

Metallicities and ages of stellar populations at a high Galactic latitude field

We present an analysis of $UBVRI$ data from the Selected Area SA 141. By applying recalibrated methods of measuring ultraviolet excess (UVX), we approximate abundances and absolute magnitudes for 368 stars over 1.3 square degrees out to distances over 10 kpc. With the density distribution constrained from our previous photometric parallax investigations and with sufficient accounting for the metallicity bias in the UVX method, we are able to compare the vertical abundance distribution to those measured in previous studies. We find that the abundance distribution has an underlying uniform component consistent with previous spectroscopic results that posit a monometallic thick disk and halo with abundances of $[Fe/H]$ = $-$0.8 and $-$1.4, respectively. However, there are a number of outlying data points that may indicate contamination by more metal-rich halo streams. The absence of vertical abundance gradients in the Galactic stellar populations and the possible presence of interloping halo streams would be consistent with expectations from merger models of Galaxy formation. We find that our UVX method has limited sensitivity in exploring the metallicity distribution of the distant Galactic halo, owing to the poor constraint on the $UBV$ properties of very metal-poor stars. The derivation of metallicities from broadband $UBV$ photometry remains fundamentally sound for the exploration of the halo but is in need of both improved calibration and superior data.

Reconstructing the cosmic density field with the distribution of dark matter haloes

We develop a new method to reconstruct the cosmic density field from the distribution of dark matter haloes above a certain mass threshold. Our motivation is that well-defined samples of galaxy groups/clusters, which can be used to represent the dark halo population, can now be selected from large redshift surveys of galaxies, and our ultimate goal is to use such data to reconstruct the cosmic density field in the local Universe. Our reconstruction method starts with a sample of dark matter haloes above a given mass threshold. Each volume element in space is assigned to the domain of the nearest halo according to a distance measure that is scaled by the virial radius of the halo. The distribution of the mass in and around dark matter haloes of a given mass is modelled using the cross-correlation function between dark matter haloes and the mass distribution within their domains. We use N-body cosmological simulations to show that the density profiles required in our reconstruction scheme can be determined reliably from large cosmological simulations, and that our method can reconstruct the density field accurately using haloes with masses down to similar to 10(12) h(-1) M(circle dot) (above which samples of galaxy groups can be constructed from current large redshift surveys of galaxies). Working in redshift space, we demonstrate that the redshift distortions due to the peculiar velocities of haloes can be corrected in an iterative way. We also describe some applications of our method.

Carbon monoxide line emission as a CMB foreground: tomography of the star-forming universe with different spectral resolutions

The rotational lines of carbon monoxide and the fine structure lines of CII and of the most abundant metals, emitted during the epoch of enhanced star formation in the universe, are redshifted in the frequency channels where the present-day and future CMB experiments are sensitive. We estimate the contribution to the CMB angular power spectrum by the emission in such lines in merging star-forming galaxies. We used the Lacey-Cole approach to characterize the distribution of the merging halos, together with a parametrization for the star formation rate in each of them. Using observational data from a sample of local, low-redshift, and high-redshift objects, we calibrated the luminosity in each line as a function of the star formation rate. We show that the correlation term arising from CO line emission is a significant source of foreground for CMB in a broad range of frequencies (in particular in the 20-60 GHz band) and for 1000<l<8000, corresponding to angular scales smaller than 10 arcminutes. Moreover, we demonstrate that observing with different spectral resolutions will give the possibility of increasing the amplitude of the signal up to two orders of magnitude in C_l and will help separate the line contribution from practically all other foreground sources and from the primary fluctuations themselves, since these show no significant dependence on the spectral resolution. We propose to perform observations with varying spectral bandwidths as a new tool to construct a tomography of the universe, by probing different redshift slices with varying thickness. (abridged)

The Causes of Halo Shape Changes Induced by Cooling Baryons: Disks versus Substructures

Cold dark matter cosmogony predicts triaxial dark matter halos, whereas observations find quite round halos. This is most likely due to the condensation of baryons leading to rounder halos. We examine the halo phase space distribution basis for such shape changes. Triaxial halos are supported by box orbits, which pass arbitrarily close to the density center. The decrease in triaxiality caused by baryons is thought to be due to the scattering of these orbits. We test this hypothesis with simulations of disks grown inside triaxial halos. After the disks are grown we check whether the phase space structure has changed by evaporating the disks and comparing the initial and final states. While the halos are substantially rounder when the disk is at full mass, their final shape after the disk is evaporated is not much different from the initial. Likewise, the halo becomes (more) radially anisotropic when the disk is grown, but the final anisotropy is consistent with the initial. Only if the baryons are unreasonably compact or massive does the halo change irreversibly. We show that the character of individual orbits is not generally changed by the growing mass. Thus, the central condensation of baryons does not destroy enough box orbits to cause the shape change. Rather, box orbits merely become rounder along with the global potential. However, if angular momentum is transferred to the halo, either via satellites or via bars, a large irreversible change in the halo distribution occurs. The ability of satellites to alter the phase space distribution of the halo is of particular concern to galaxy formation simulations since halo triaxiality can profoundly influence the evolution of disks.

Quantifying the cosmic web - I. The large-scale halo ellipticity-ellipticity and ellipticity-direction correlations

The formation of dark matter halos tends to occur anisotropically along the filaments of the Cosmic Web, which induces both ellipticity-ellipticity (EE) correlations between the shapes of halos, as well as ellipticity-direction (ED) cross-correlations between halo shapes and the directions to neighboring halos. We analyze the halo catalogue and the semi-analytic galaxy catalogue of the recent Millennium Run Simulation to measure the EE and ED correlations numerically at four different redshifts (z=0, 0.5, 1 and 2). For the EE correlations, we find that (i) the major-axis correlation is strongest while the intermediate-axis correlation is weakest; (ii) the signal is significant at distances out to 10 Mpc/h; (iii) the signal decreases as z decreases; (iv) and its behavior depends strongly on the halo mass scale, with larger masses showing stronger correlations at large distances. For the ED correlations, we find that (i) the correlations are much stronger than the EE correlations, and are significant even out to distances of 50 Mpc/h; (ii) the signal also decreases as z decreases; (iii) and it increases with halo mass at all distances. We also provide empirical fitting functions for the EE and ED correlations. The EE correlations are found to scale linearly with the linear density correlation function, xi(r). While the ED cross-correlation is found to scale as xi^{1/2}(r) at large distances beyond 10 Mpc/h. The best-fit values of the fitting parameters for the EE and the ED correlations are all determined through chi^{2}-statistics. Our results may be useful for quantifying the filamentary distribution of dark matter halos over a wide range of scales.