Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “MULTIPOLES”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

IS THE COSMIC MICROWAVE BACKGROUND ASYMMETRY DUE TO THE KINEMATIC DIPOLE?

Parity violation found in the cosmic microwave background (CMB) radiation is a crucial clue for the non-standard cosmological model or the possible contamination of various foreground residuals and/or calibration of the CMB data sets. In this paper, we study the directional properties of the CMB parity asymmetry by excluding the m = 0 modes in the definition of parity parameters. We find that the preferred directions of the parity parameters coincide with the CMB kinematic dipole, which implies that the CMB parity asymmetry may be connected with the possible contamination of the residual dipole component. We also find that such tendency is not only localized at l = 2, 3, but in the extended multipole ranges up to l {approx} 22.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

ON THE RELATIVISTIC PRECESSION AND OSCILLATION FREQUENCIES OF TEST PARTICLES AROUND RAPIDLY ROTATING COMPACT STARS

Whether or not analytic exact vacuum (electrovacuum) solutions of the Einstein (Einstein-Maxwell) field equations can accurately describe the exterior space-time of compact stars still remains an interesting open question in relativistic astrophysics. As an attempt to establish their level of accuracy, the radii of the innermost stable circular orbits (ISCOs) of test particles given by analytic exterior space-time geometries have been compared with those given by numerical solutions for neutron stars (NSs) obeying a realistic equation of state (EOS). It has been so shown that the six-parametric solution of Pachon et al. (PRS) more accurately describes the NS ISCO radii than other analytic models do. We propose here an additional test of accuracy for analytic exterior geometries based on the comparison of orbital frequencies of neutral test particles. We compute the Keplerian, frame-dragging, and precession and oscillation frequencies of the radial and vertical motions of neutral test particles for the Kerr and PRS geometries and then compare them with the numerical values obtained by Morsink and Stella for realistic NSs. We identify the role of high-order multipole moments such as the mass quadrupole and current octupole in the determination of the orbital frequencies, especially in the rapid rotation regime. The results of this work are relevant to cast a separatrix between black hole and NS signatures and to probe the nuclear-matter EOS and NS parameters from the quasi-periodic oscillations observed in low-mass X-ray binaries.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

AN ACCRETION MODEL FOR THE ANOMALOUS X-RAY PULSAR 4U 0142+61

We propose that the quiescent emission of anomalous X-ray pulsars/soft gamma-ray repeaters (AXPs/SGRs) is powered by accretion from a fallback disk, requiring magnetic dipole fields in the range 10{sup 12}-10{sup 13} G, and that the luminous hard tails of their X-ray spectra are produced by bulk-motion Comptonization in the radiative shock near the bottom of the accretion column. This radiation escapes as a fan beam, which is partly absorbed by the polar cap photosphere, heating it up to relatively high temperatures. The scattered component and the thermal emission from the polar cap form a polar beam. We test our model on the well-studied AXP 4U 0142+61, whose energy-dependent pulse profiles show double peaks, which we ascribe to the fan and polar beams. The temperature of the photosphere (kT {approx} 0.4 keV) is explained by the heating effect. The scattered part forms a hard component in the polar beam. We suggest that the observed high temperatures of the polar caps of AXPs/SGRs, compared with other young neutron stars, are due to the heating by the fan beam. Using beaming functions for the fan beam and the polar beam and taking gravitational bending into account, we fit the energy-dependent pulse profiles and obtain the inclination angle and the angle between the spin axis and the magnetic dipole axis, as well as the height of the radiative shock above the stellar surface. We do not explain the high-luminosity bursts, which may be produced by the classical magnetar mechanism operating in super-strong multipole fields.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

CONCENTRIC MACLAURIN SPHEROID MODELS OF ROTATING LIQUID PLANETS

I present exact expressions for the interior gravitational potential V of a system of N concentric constant-density (Maclaurin) spheroids. I demonstrate an iteration procedure to find a self-consistent solution for the shapes of the interfaces between spheroids, and for the interior gravitational potential. The external free-space potential, expressed as a multipole expansion, emerges as part of the self-consistent solution. The procedure is both simpler and more precise than perturbation methods. One can choose the distribution and mass densities of the concentric spheroids so as to reproduce a prescribed barotrope to a specified accuracy. I demonstrate the method's efficacy by comparing its results with several published test cases.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

SASI ACTIVITY IN THREE-DIMENSIONAL NEUTRINO-HYDRODYNAMICS SIMULATIONS OF SUPERNOVA CORES

The relevance of the standing accretion shock instability (SASI) compared to neutrino-driven convection in three-dimensional (3D) supernova-core environments is still highly controversial. Studying a 27 M{sub Sun} progenitor, we demonstrate, for the first time, that violent SASI activity can develop in 3D simulations with detailed neutrino transport despite the presence of convection. This result was obtained with the PROMETHEUS-VERTEX code with the same sophisticated neutrino treatment so far used only in one-dimensional and two-dimensional (2D) models. While buoyant plumes initially determine the nonradial mass motions in the postshock layer, bipolar shock sloshing with growing amplitude sets in during a phase of shock retraction and turns into a violent spiral mode whose growth is only quenched when the infall of the Si/SiO interface leads to strong shock expansion in response to a dramatic decrease of the mass accretion rate. In the phase of large-amplitude SASI sloshing and spiral motions, the postshock layer exhibits nonradial deformation dominated by the lowest-order spherical harmonics (l = 1, m = 0, {+-}1) in distinct contrast to the higher multipole structures associated with neutrino-driven convection. We find that the SASI amplitudes, shock asymmetry, and nonradial kinetic energy in three dimensions can exceed those of the corresponding 2D case during extended periods of the evolution. We also perform parameterized 3D simulations of a 25 M{sub Sun} progenitor, using a simplified, gray neutrino transport scheme, an axis-free Yin-Yang grid, and different amplitudes of random seed perturbations. They confirm the importance of the SASI for another progenitor, its independence of the choice of spherical grid, and its preferred growth for fast accretion flows connected to small shock radii and compact proto-neutron stars as previously found in 2D setups.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

TESTING THE NO-HAIR THEOREM WITH OBSERVATIONS IN THE ELECTROMAGNETIC SPECTRUM. IV. RELATIVISTICALLY BROADENED IRON LINES

According to the no-hair theorem, astrophysical black holes are fully characterized by their masses and spins and are described by the Kerr metric. This theorem can be tested observationally by measuring (at least) three different multipole moments of the spacetimes of black holes. In this paper, we calculate the profiles of fluorescent iron lines emitted from the accretion flows around black hole candidates within a framework that allows us to perform the calculation as a function of its mass and spin as well as of a free parameter that measures potential deviations from the Kerr metric. We show that such deviations lead to line profiles that are significantly altered and may exhibit a modified flux ratio of the two peaks in their characteristic double-peaked shape. We also show that the disk inclination can be measured independently of the spin and the deviation parameter at low to intermediate inclination angles, as in the case of Kerr black holes. We estimate the precision that near-future X-ray missions such as Astro-H and ATHENA+ are required to achieve in order to resolve deviations from the Kerr metric in iron line profiles and show that constraints on such deviations will be strongest for rapidly spinning black holes. More generally, we show that measuring the line profile with a precision of {approx}5% at disk inclinations of 30 Degree-Sign or 60 Degree-Sign constrains the deviation parameter to order unity for values of the spin a {approx}> 0.5M.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

COSMIC MICROWAVE BACKGROUND LIKELIHOOD APPROXIMATION FOR BANDED PROBABILITY DISTRIBUTIONS

We investigate sets of random variables that can be arranged sequentially such that a given variable only depends conditionally on its immediate predecessor. For such sets, we show that the full joint probability distribution may be expressed exclusively in terms of uni- and bivariate marginals. Under the assumption that the cosmic microwave background (CMB) power spectrum likelihood only exhibits correlations within a banded multipole range, Δl{sub C}, we apply this expression to two outstanding problems in CMB likelihood analysis. First, we derive a statistically well-defined hybrid likelihood estimator, merging two independent (e.g., low- and high-l) likelihoods into a single expression that properly accounts for correlations between the two. Applying this expression to the Wilkinson Microwave Anisotropy Probe (WMAP) likelihood, we verify that the effect of correlations on cosmological parameters in the transition region is negligible in terms of cosmological parameters for WMAP; the largest relative shift seen for any parameter is 0.06σ. However, because this may not hold for other experimental setups (e.g., for different instrumental noise properties or analysis masks), but must rather be verified on a case-by-case basis, we recommend our new hybridization scheme for future experiments for statistical self-consistency reasons. Second, we use the same expression to improve the convergence rate of the Blackwell-Rao likelihood estimator, reducing the required number of Monte Carlo samples by several orders of magnitude, and thereby extend it to high-l applications.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

A measurement of the cosmic microwave background damping tail from the 2500-square-degree SPT-SZ survey

We present a measurement of the cosmic microwave background (CMB) temperature power spectrum using data from the recently completed South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) survey. This measurement is made from observations of 2540 deg{sup 2} of sky with arcminute resolution at 150 GHz, and improves upon previous measurements using the SPT by tripling the sky area. We report CMB temperature anisotropy power over the multipole range 650 < ℓ < 3000. We fit the SPT bandpowers, combined with the 7 yr Wilkinson Microwave Anisotropy Probe (WMAP7) data, with a six-parameter ΛCDM cosmological model and find that the two datasets are consistent and well fit by the model. Adding SPT measurements significantly improves ΛCDM parameter constraints; in particular, the constraint on θ {sub s} tightens by a factor of 2.7. The impact of gravitational lensing is detected at 8.1σ, the most significant detection to date. This sensitivity of the SPT+WMAP7 data to lensing by large-scale structure at low redshifts allows us to constrain the mean curvature of the observable universe with CMB data alone to be Ω{sub k}=−0.003{sub −0.018}{sup +0.014}. Using the SPT+WMAP7 data, we measure the spectral index of scalar fluctuations to be n{sub s} = 0.9623 ± 0.0097 in the ΛCDM model, a 3.9σ preference for a scale-dependent spectrum with n{sub s} < 1. The SPT measurement of the CMB damping tail helps break the degeneracy that exists between the tensor-to-scalar ratio r and n{sub s} in large-scale CMB measurements, leading to an upper limit of r < 0.18 (95% C.L.) in the ΛCDM+r model. Adding low-redshift measurements of the Hubble constant (H {sub 0}) and the baryon acoustic oscillation (BAO) feature to the SPT+WMAP7 data leads to further improvements. The combination of SPT+WMAP7+H {sub 0}+BAO constrains n{sub s} = 0.9538 ± 0.0081 in the ΛCDM model, a 5.7σ detection of n{sub s} < 1, and places an upper limit of r < 0.11 (95% C.L.) in the ΛCDM+r model. These new constraints on n{sub s} and r have significant implications for our understanding of inflation, which we discuss in the context of selected single-field inflation models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

North-south asymmetric solar cycle evolution: Signatures in the photosphere and consequences in the corona

The heliospheric current sheet is the continuum of the coronal magnetic equator that divides the heliospheric magnetic field into two sectors (polarities). Several recent studies have shown that the heliospheric current sheet is southward shifted during approximately 3 years in the solar declining phase (the so-called bashful ballerina phenomenon). In this article we study the hemispherical asymmetry in the photospheric and coronal magnetic fields using Wilcox Solar Observatory measurements of the photospheric magnetic field since 1976 as well as the potential field source surface model. Multipole analysis of the photospheric magnetic field shows that during the late declining phase of solar cycles since the 1970s, the 'bashful ballerina phenomenon' is a consequence of the g{sub 2}{sup 0} quadrupole term, signed oppositely to the dipole moment. Surges of new flux transport magnetic field from low latitudes to the poles, thus leading to a systematically varying contribution to the g{sub 2}{sup 0}-term from different latitudes. In the case of a north-south asymmetric flux production, this is seen as a quadrupole contribution traveling toward higher latitudes. When the quadrupole term is largest, the main contribution comes from the polar latitudes. At least during the four recent solar cycles, the g{sub 2}{sup 0}-term arises because the magnitude of the southern polar field is larger than the magnitude found in the north in the declining phase of the cycle. In the heliosphere this hemispheric asymmetry of the coronal fields is seen as a southward shift of the heliospheric current sheet by about 2°.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A measurement of the secondary-CMB and millimeter-wave-foreground bispectrum using 800 deg{sup 2} of south pole telescope data

We present a measurement of the angular bispectrum of the millimeter-wave sky in observing bands centered at roughly 95, 150, and 220 GHz, on angular scales of 1' ≲ θ ≲ 10' (multipole number 1000 ≲ l ≲ 10,000). At these frequencies and angular scales, the main contributions to the bispectrum are expected to be the thermal Sunyaev-Zel'dovich (tSZ) effect and emission from extragalactic sources, predominantly dusty, star-forming galaxies (DSFGs) and active galactic nuclei. We measure the bispectrum in 800 deg{sup 2} of three-band South Pole Telescope data, and we use a multi-frequency fitting procedure to separate the bispectrum of the tSZ effect from the extragalactic source contribution. We simultaneously detect the bispectrum of the tSZ effect at >10σ, the unclustered component of the extragalactic source bispectrum at >5σ in each frequency band, and the bispectrum due to the clustering of DSFGs—i.e., the clustered cosmic infrared background (CIB) bispectrum—at >5σ. This is the first reported detection of the clustered CIB bispectrum. We use the measured tSZ bispectrum amplitude, compared to model predictions, to constrain the normalization of the matter power spectrum to be σ{sub 8} = 0.787 ± 0.031 and to predict the amplitude of the tSZ power spectrum at l = 3000. This prediction improves our ability to separate the thermal and kinematic contributions to the total SZ power spectrum. The addition of bispectrum data improves our constraint on the tSZ power spectrum amplitude by a factor of two compared to power spectrum measurements alone and demonstrates a preference for a nonzero kinematic SZ (kSZ) power spectrum, with a derived constraint on the kSZ amplitude at l = 3000 of A {sub kSZ} = 2.9 ± 1.6 μK{sup 2}, or A {sub kSZ} = 2.6 ± 1.8 μK{sup 2} if the default A {sub kSZ} > 0 prior is removed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

CMB lensing power spectrum biases from galaxies and clusters using high-angular resolution temperature maps

The lensing power spectrum from cosmic microwave background (CMB) temperature maps will be measured with unprecedented precision with upcoming experiments, including upgrades to the Atacama Cosmology Telescope and the South Pole Telescope. Achieving significant improvements in cosmological parameter constraints, such as percent level errors on σ{sub 8} and an uncertainty on the total neutrino mass of ∼50 meV, requires percent level measurements of the CMB lensing power. This necessitates tight control of systematic biases. We study several types of biases to the temperature-based lensing reconstruction signal from foreground sources such as radio and infrared galaxies and the thermal Sunyaev-Zel'dovich effect from galaxy clusters. These foregrounds bias the CMB lensing signal due to their non-Gaussian nature. Using simulations as well as some analytical models we find that these sources can substantially impact the measured signal if left untreated. However, these biases can be brought to the percent level if one masks galaxies with fluxes at 150 GHz above 1 mJy and galaxy clusters with masses above M {sub vir} = 10{sup 14} M {sub ☉}. To achieve such percent level bias, we find that only modes up to a maximum multipole of l {sub max} ∼ 2500 should be included in the lensing reconstruction. We also discuss ways to minimize additional bias induced by such aggressive foreground masking by, for example, exploring a two-step masking and in-painting algorithm.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

New constraints on cosmic polarization rotation from B-mode polarization in the cosmic microwave background

SPTpol, POLARBEAR, and BICEP2 have recently measured the cosmic microwave background (CMB) B-mode polarization in various sky regions of several tens of square degrees and obtained BB power spectra in the multipole range 20-3000, detecting the components due to gravitational lensing and to inflationary gravitational waves. We analyze jointly the results of these three experiments and propose modifications to their analyses of the spectra to include in the model, in addition to the gravitational lensing and the inflationary gravitational wave components, and also the effects induced by the cosmic polarization rotation (CPR), if it exists within current upper limits. Although in principle our analysis would also lead to new constraints on CPR, in practice these can only be given on its fluctuations (δα{sup 2}), since constraints on its mean angle are inhibited by the derotation which is applied by current CMB polarization experiments, in order to cope with the insufficient calibration of the polarization angle. The combined data fits from all three experiments (with 29% CPR-SPTpol correlation, depending on the theoretical model) gives the constraint (δα{sup 2}){sup 1/2} < 27.3 mrad (1.°56), with r = 0.194 ± 0.033. These results show that the present data are consistent with no CPR detection and the constraint on CPR fluctuation is about 1.°5. This method of constraining the CPR is new, is complementary to previous tests, which use the radio and optical/UV polarization of radio galaxies and the CMB E-mode polarization, and adds a new constraint for the sky areas observed by SPTpol, POLARBEAR, and BICEP2.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Expansion techniques for collisionless stellar dynamical simulations

We present graphics processing unit (GPU) implementations of two fast force calculation methods based on series expansions of the Poisson equation. One method is the self-consistent field (SCF) method, which is a Fourier-like expansion of the density field in some basis set; the other method is the multipole expansion (MEX) method, which is a Taylor-like expansion of the Green's function. MEX, which has been advocated in the past, has not gained as much popularity as SCF. Both are particle-field methods and optimized for collisionless galactic dynamics, but while SCF is a 'pure' expansion, MEX is an expansion in just the angular part; thus, MEX is capable of capturing radial structure easily, while SCF needs a large number of radial terms. We show that despite the expansion bias, these methods are more accurate than direct techniques for the same number of particles. The performance of our GPU code, which we call ETICS, is profiled and compared to a CPU implementation. On the tested GPU hardware, a full force calculation for one million particles took ∼0.1 s (depending on expansion cutoff), making simulations with as many as 10{sup 8} particles fast for a comparatively small number of nodes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A measurement of the cosmic microwave background B-mode polarization power spectrum at sub-degree scales with POLARBEAR

We report a measurement of the B-mode polarization power spectrum in the cosmic microwave background (CMB) using the POLARBEAR experiment in Chile. The faint B-mode polarization signature carries information about the universe's entire history of gravitational structure formation, and the cosmic inflation that may have occurred in the very early universe. Our measurement covers the angular multipole range 500 < ℓ < 2100 and is based on observations of an effective sky area of 25 deg{sup 2} with 3.'5 resolution at 150 GHz. On these angular scales, gravitational lensing of the CMB by intervening structure in the universe is expected to be the dominant source of B-mode polarization. Including both systematic and statistical uncertainties, the hypothesis of no B-mode polarization power from gravitational lensing is rejected at 97.2% confidence. The band powers are consistent with the standard cosmological model. Fitting a single lensing amplitude parameter A{sub BB} to the measured band powers, A{sub BB}=1.12±0.61(stat){sub −0.12}{sup +0.04}(sys)±0.07(multi), where A{sub BB} = 1 is the fiducial WMAP-9 ΛCDM value. In this expression, 'stat' refers to the statistical uncertainty, 'sys' to the systematic uncertainty associated with possible biases from the instrument and astrophysical foregrounds, and 'multi' to the calibration uncertainties that have a multiplicative effect on the measured amplitude A{sub BB}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Tracing magnetic fields by atomic alignment in extended radiation fields

Tracing magnetic field is crucial as magnetic field plays an important role in many astrophysical processes. Earlier studies have demonstrated that ground state alignment (GSA) is an effective way to detect a weak magnetic field (1G≳B≳10{sup −15} G) in a diffuse medium. We explore the atomic alignment in the presence of an extended radiation field for both absorption lines and emission lines. The alignment in the circumstellar medium, binary systems, disks, and the local interstellar medium are considered in order to study the alignment in the radiation field where the pumping source has a clear geometric structure. Furthermore, the multipole expansion method is adopted to study GSA induced in the radiation field with unidentified pumping sources. We study the alignment in the dominant radiation components of the general radiation field: the dipole and quadrupole radiation field. We discuss the approximation of GSA in a general radiation field by summing the contribution from the dipole and quadrupole radiation field. We conclude that GSA is a powerful tool for detecting weak magnetic fields in the diffuse medium in general radiation fields.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

The distribution of galaxies’ gravitational field stemming from their tidal interaction

We calculate the distribution function of astronomical objects’ (like galaxies and/or smooth halos of different kinds) gravitational fields due to their tidal interaction. For that we apply the statistical method of Chandrasekhar, used originally to calculate the famous Holtzmark distribution. We show that in our approach the distribution function is never Gaussian, its form being dictated by the potential of interaction between objects. This calculation permits us to perform a theoretical analysis of the relation between angular momentum and mass (richness) of the galaxy clusters. To do so, we follow the ideas of Catelan and Theuns and Heavens and Peacock. The main difference is that here we reduce the problem to a discrete many-body case, where all physical properties of the system are determined by the interaction potential V(r{sub ij}). The essence of reduction is that we use the multipole (up to quadrupole here) expansion of Newtonian potential so that all hydrodynamic, “extended” characteristics of an object, such as its density mass, are “integrated out,” leaving its “point-like” characteristics, such as mass and quadrupole moment. In that sense we do not distinguish between galaxies and smooth components such as halos. We compare our theoretical results with observational data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

E1-forbidden transition rates in ions of astrophysical interest

Transition rates in atomic systems may appear to be of little importance in steady-state plasmas that are observed at great distances from Earth. However, some of the transition rates compete with collision rates, and in these cases certain line intensity ratios are affected and can serve as remote indicators of density. In the low-density environments of stellar coronae and planetary nebulae, the transition rates of interest are mostly spin-forbidden E1 decays, higher-multipole order transitions (M1, E2, M2, M3), and hyperfine-induced transitions. On Earth, measurements of the long upper level lifetimes of these atomic systems require the use of ion traps. A fair number of test cases with lifetimes in the range from nanoseconds to many seconds have been treated successfully, and the evolution of calculations along with the experimental progress is notable. Here, a new generation of cold ion traps is expected to extend the atomic lifetime measurements on multiply charged ions into the range of many minutes.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2011

SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP ) OBSERVATIONS: POWER SPECTRA AND WMAP-DERIVED PARAMETERS

The WMAP mission has produced sky maps from seven years of observations at L2. We present the angular power spectra derived from the seven-year maps and discuss the cosmological conclusions that can be inferred from WMAP data alone. With the seven-year data, the temperature (TT) spectrum measurement has a signal-to-noise ratio per multipole that exceeds unity for l < 919; and in band powers of width {Delta}l = 10, the signal-to-noise ratio exceeds unity up to l = 1060. The third acoustic peak in the TT spectrum is now well measured by WMAP. In the context of a flat {Lambda}CDM model, this improvement allows us to place tighter constraints on the matter density from WMAP data alone, {Omega}{sub m} h {sup 2} = 0.1334{sup +0.0056}{sub -0.0055}, and on the epoch of matter-radiation equality, z{sub eq} = 3196{sup +134}{sub -133}. The temperature-polarization (TE) spectrum is detected in the seven-year data with a significance of 20{sigma}, compared to 13{sigma} with the five-year data. We now detect the second dip in the TE spectrum near l {approx} 450 with high confidence. The TB and EB spectra remain consistent with zero, thus demonstrating low systematic errors and foreground residuals in the data. The low-l EE spectrum, a measure of the optical depth due to reionization, is detected at 5.5{sigma} significance when averaged over l = 2-7: l(l + 1)C {sup EE}{sub l}/(2{pi}) = 0.074{sup +0.034}{sub -0.025} {mu}K{sup 2} (68% CL). We now detect the high-l, 24 {<=} l {<=} 800, EE spectrum at over 8{sigma}. The BB spectrum, an important probe of gravitational waves from inflation, remains consistent with zero; when averaged over l = 2-7, l(l + 1)C {sup BB}{sub l}/(2{pi}) < 0.055 {mu}K{sup 2} (95% CL). The upper limit on tensor modes from polarization data alone is a factor of two lower with the seven-year data than it was using the five-year data. The data remain consistent with the simple {Lambda}CDM model: the best-fit TT spectrum has an effective {chi}{sup 2} of 1227 for 1170 degrees of freedom, with a probability to exceed of 9.6%. The allowable volume in the six-dimensional space of {Lambda}CDM parameters has been reduced by a factor of 1.5 relative to the five-year volume, while the {Lambda}CDM model that allows for tensor modes and a running scalar spectral index has a factor of three lower volume when fit to the seven-year data. We test the parameter recovery process for bias and find that the scalar spectral index, n{sub s} , is biased high, but only by 0.09{sigma}, while the remaining parameters are biased by <0.15{sigma}. The improvement in the third peak measurement leads to tighter lower limits from WMAP on the number of relativistic degrees of freedom (e.g., neutrinos) in the early universe: N{sub eff}>2.7(95%CL). Also, using WMAP data alone, the primordial helium mass fraction is found to be Y{sub He} = 0.28{sup +0.14}{sub -0.15}, and with data from higher-resolution cosmic microwave background experiments included, we now establish the existence of pre-stellar helium at >3{sigma}. These new WMAP measurements provide important tests of big bang cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗