If you use the software, please consider citing astroML. See if you can get the blue line to match the red line, which is based on the measurements from the WMAP cl_bb.d BB power spectrum (3 columns): l, vector, tensor pk_lin.d linear CDM P(k) (2 columns): k/h Mpc^{-1}, 4piP(k) NOTE: Output for TT,TE,EE and BB is (T_cmb)^2 l(l+1)Cl/2pi. Power spectra are \([L(L+1)]^2C_L^{\phi\phi}/2\pi\) and corresponding deflection cross-correlations. For the moment a and H are rather perversely only available via get_time_evolution(), n_eta x len(vars) 2D numpy array of outputs or dict of 1D arrays, Get the evolution of background variables a function of conformal time. WMAP power spectrum analysis with HealPy; Links. Get CMB power spectra, as requested by the ‘spectra’ argument. power spectra. . lensing potential and cross: L TT EE BB TE PP PT PE. インフレーション宇宙を検証するCMB偏光観測小型科学衛星 LiteBIRD 2012/3/21 日本天文学会2012年春季年会 於龍谷大学(深草キャンパス) 羽澄昌史(KEK) 1 宇宙年齢 10-38秒?38 万年 1 億年 137 億年 イ ン フ レ ー シ ョ ン 再 結 power spectra using a new set of initial power spectrum parameters with otherwise the same cosmology. points in z. . Calculate \(\sigma_R\) values, the RMS linear matter fluctuation in spheres of radius R in linear theory. Note that P is the lensing deflection, lensing windows Wx give convergence. Note that numerical errors are slightly different to get_sigma8 for R=8 Mpc/h. 2. XPol - A power spectrum estimator based on cross-correlation between maps. CMB frequency spectrum Ending Inflation Component separation and the Planck maps CMB power spectra, likelihood, and cosmological parameters CMB lensing copy_of_erc18b2_f4._scaled.png Figure1_scaled.png erc18b2_f4 \(\frac{r}{1+z_2}\text{sin}_K\left(\frac{\chi(z_2) - \chi(z_1)}{r}\right)\), model.CAMBparams.set_custom_scalar_sources(), Matter power spectrum and matter transfer function variables, results.CAMBdata.get_matter_transfer_data(), Code for Anisotropies in the Microwave Background (CAMB), angular diameter distances, matching rank of z, rs/DV, H, DA, F_AP for each requested redshift (as 2D array), rho, w arrays at redshifts 1/a-1 [or scalars if a is scalar], dictionary of derived parameter values, indexed by name (‘kd’, ‘age’, etc..), array of f*sigma_8 values, in order of increasing time (decreasing redshift), numpy array CL[0:, 0:,0:lmax+1], where 0.. index T, E, lensing potential, source window functions, array of computed L, array of computed q, transfer functions T(L,q), Transfer_nonu = 8 (total matter excluding neutrinos), Transfer_tot_de = 9 (total including dark energy perturbations), Transfer_Newt_vel_cdm = 11 (Newtonian CDM velocity), Transfer_Newt_vel_baryon = 12 (Newtonian baryon velocity), Transfer_vel_baryon_cdm = 13 (relative baryon-cdm velocity). For com-parison we show in the Use hubble_parameter instead if you want in [km/s/Mpc] units. All values match to the same precision as our best measurement data. The power spectrum of the cosmic microwave background radiation temperature anisotropy in terms of the angular scale (or multipole moment). An object for storing calculational data, parameters and transfer functions. Must have called calc_background(), calc_background_no_thermo() or calculated transfer functions Observations at high-l For general models \(f\sigma_8\) is defined as in the Planck 2015 parameter paper in terms of CMB polarization band-power plotting tool - an IDL tool and dataset for making summary plots of CMB polarization bandpowers. Get dark energy density in units of the dark energy density today, and w=P/rho. Does not include CMB spectra. Figure 13 The CMB polarization power spectrum (EE or BB) for a network of cosmic string wakes. . ABSTRACT We compute the integrated Sachs–Wolfe type contribution to the CMB polar-ization power spectrum from cosmic string wakes. The hemispherical CMB power asymmetry, large at low l < 100, implies that the power spectrum from inflation must be modified. Must have already calculated power spectra. Tristram xQML - Quadratic Maximum Likelihood estimator for CMB cross-correlation power … We combine this power spectrum with the power spectra from the seven-year Wilkinson (WMAP ducing a CMB map to a power spectrum and its uncer-tainties. value of k_hunit (default True gives k/h). Observational Cosmology Lectures 2+5 (K. Basu): CMB theory and experiments Check the WMAP website 9. e.g. power spectrum is a missing pressure (relative to theory) in lower mass clusters. numpy array CL[0:lmax+1,0:4], where 0..3 indexes TT, EE, BB, TE. • First direct images of CMB polarization • New limits on inflation from the tilting of the power 5 In a flat universe q=k, in a closed universe q is quantized. background cosmology or the transfer function settings. \(\nabla T\nabla T\) where the first six are as defined in appendix C nd array, A_{qti}, size(q) x size(times) x len(vars), or 2d array if q is scalar, Get \(\sigma_8\) values at Params.PK_redshifts (must previously have calculated power spectra), Get \(\sigma_8\) value today (must previously have calculated power spectra). . æ4bÌýÏ7F?€¶SÜA¡ïz¾F^Rlº éFœ&e*\Ã^wk —/9BÊCŒ%м_aº@4T_ç ¬èe*Õ4ÄÀÑ2ꐠ38kAFô¤2ÂÉqi. Here we present the power spectrum over the multipole range 650 << 3000, where it is dominated by primary CMB anisotropy. numpy array CL[0:lmax+1,0:4], where 0..3 indexes TT, EE, BB, TE. and PK[i,j] is the value at z[i], k[j]/h or k[j]. The blue line is the CMB power spectrum for "your" universe. Get unlensed scalar CMB power spectra. (2010) r = (gravitational waves)2 / (gravitational potential)2. dictionary of power spectrum arrays, index as TxT, TxE, PxW1, W1xW2, custom_name_1xT… etc. of Food and Nutri. Box 644, 48080 Bilbao, Spain cPhysics Department, FCFM, Universidad de Chile Blanco … Position of peaks mainly sensitive to curvature; Shapes fixed by the physical density of matter and baryons; Missing or "dark energy" plays a small roll in the position of peaksAs advertised, the position of that first peak in the power spectrum of the anisotropies, and indeed all of the peaks, depend sensitively on the spatial curvature of the universe. 1 INTRODUCTION Topological defects are decidedly underrepresented in physics. . Get (non-comoving) angular diameter distance to redshift z. for accurate back integration with correlations.corr2cl(). (arXiv:1101.2234). The CMB has a thermal black body spectrum at a temperature of 2.725 48 ± 0.000 57 K. The spectral radiance dE ν /dν peaks at 160.23 GHz, in the microwave range of frequencies, corresponding to a photon energy of about 6.626 ⋅ 10 −4 eV. Get luminosity distance from to redshift z. Grey. numpy array CL[0:lmax+1,0:3], where 0..2 indexes PP, PT, PE. CMB power spectrum alone has several more or less exact degeneracies in parameter space (see, e.g., Efstathiou & Bond 1999), which can only be reduced substantially or 57 Figure 15 Power spectrum for a single dominant cosmic string wake. Must have already calculated power spectra. Scaling relations, gas pressure, and entropy of low-mass clusters and groups have been studied in the literature.41 Leauthaud et al. Get all unlensed auto and cross power spectra, including any custom source functions set All power spectra are Note that lmax used to calculate results may need to be substantially larger than the lmax Calculates \(P_{xy}(k/h)\), where x, y are one of model.Transfer_cdm, model.Transfer_xx etc. Observational Cosmology K. Basu: CMB theory and experiments Power at small angular scales 21 The signal is actually Cl ! Scalar or array. No expansionary period is needed. Get comoving radial distance from us to redshift z in Mpc. CMB Power Spectrum Formula in the Background-Field Method Shoichi Ichinose ichinose@u-shizuoka-ken.ac.jp Laboratory of Physics, SFNS, University of Shizuoka Aug. 7, 2012 The 3rd UTQuest workshop ExDiP 2012 ”Superstring Cosmophysics” , Tokachi-Makubetsu Granvrio Hotel, Hokkaidou, Japan Shoichi Ichinose (Univ. of Physics, ... (95% cl) at l ~15000 Planck Non-Gaussianity bound: WMAP5 Planck Large angle power asymmetry: A = 0.072 (Average over l < l max = 64) Hirata 0907.0703 Erickcek et al 0907.0705 => Need scale-dependent asymmetry . if xvals not given: corrs, xvals, weights; if xvals specified, just corrs. For the lens_potential the power spectrum returned is that of the deflection. Must have already calculated power spectra. Furthermore, after showing that the method works, we apply it to the temperature power spectrum from the WMAP seven-year … There is a degeneracy between r and n s as shown in the left panel of Fig. The shape and amplitude of these vectors give an intuitive feel for the physics of the CMB, the View Profile View Forum Posts Order of Kilopi Join Date May 2003 Posts 6,180. input parameters. that can be called with PK.P(z,kh) or PK(z,log(kh)) to get log matter power values. Hemispherical CMB power asymmetry: observation vs. models John McDonald, Dept. tSZ cluster counts and power spectrum combined with CMB Laura Salvati in collaboration with Nabila Aghanim and Marian Douspis Constraints on cosmological parameters from galaxy clusters: ByoPiC The Baryon Picture of the Results are dimensionless, and not scaled by custom_scaled_ell_fac. Calculates transfer functions and power spectra. Convert conformal time array to redshift array. If NonLinear is set, the result is non-linear. Odegard Much like we can take the spectrum of an electronic signal by integrating it with Fourier functions, we can integrate the CMB with spherical harmonics to produce the angular power spectrum… In chapter 5, we will show that the angular power spectrum is given by Cl = 47r / d3k P (k)D2(k). Get \(f\sigma_8\) growth values (must previously have calculated power spectra). Get \(\theta_{\rm MC}\), an approximation of the ratio of the sound horizon to the angular diameter The final plot contains what is commonly called "the angular power spectrum of the CMB." For the lens_potential the power spectrum returned is that of the deflection. Convert comoving radial distance array to redshift array. CMB偏光と重力レンズ効果 • 典型的なdeflection angle: a few arcmin • ~2度スケールにわたってコヒーレント 観測されるCMB偏光 ~: 元々のCMB偏光 deflection angle (重力レンズ効果) ~分角の分解能を持った望遠鏡による 数度スケールの The Planck best-fit CMB temperature power spectrum, shown in figure below, covers the wide range of multipoles [math] \ell [/math] = 2-2479. Get the mode evolution as a function of conformal time for some k values. Videos. The second term of the integral involves D (k), the CMB transfer function. Get BAO values for redshifts set in Params.z_outputs, Get the evolution of background variables a function of redshift. The CMB Power Spectrum is traditionally interpreted using well-known principles of light with respect to a model of events identified as Lambda CDM. Get comoving sound horizon as function of redshift in Megaparsecs, the integral of the sound speed Lensed power spectra must be already calculated. Probing Inflation (2-point Function) • Joint constraint on the primordial tilt, n s, and the tensor-to-scalar ratio, r. • Not so different from the 5-year limit. Planck Power Spectrum 21/03/2013 5978 views 18 likes 288796 ID Like Download JPG [504.62 kB] Thank you for liking You have already liked this page, you can only like it once! CMB Polarization Power Spectra tro-Temperature Anisotropy 6 Current Required inflation potential r = T/S (tensor to scalar ratio、重力波の相対的な大きさ) 質量分布による時空 のゆがみの効果 ピークはl~100 (重力波の V1/4 r power spectrum as function of z and k/h (or k). For a description of outputs for different var1, var2 see Matter power spectrum and matter transfer function variables. Must have already calculated power spectra. Try changing amounts of each ingredient and property. Exactly which quantities are already calculated depends on which of these functions you use and the JPG [504.62 kB] Thank you for liking. Scipy 2012 (15 minute talk) Scipy 2013 (20 minute talk) Citing. 2009. Get BAO parameters at given redshifts, using parameters in params, array of rs/DV, H, DA, F_AP for each redshift as 2D array, Get density relative to critical density of variables var. Revision df2de32b. • Only three months of data. call this if you want to get derived parameters and call background functions, Calculate the background evolution without calculating thermal or ionization history. Get lensed gradient scalar CMB power spectra in flat sky approximation (the default). Inflaton Superhorizon inflaton modulation can modulate the CMB power spectrum => … Generally applicable exact methods for finding the an-gular power spectrum, Cl, that maximize the likelihood have operation counts proportional to N3 where N is the 3 We also show how such a parameterization allows to retrieve the Cl spectra from the measurement of Fourier rings on the sky (Gamma(m)) or from the angular correlation function (c(theta)) Taking advantage of the smoothness of CMB Cl power spectra, we derive a simple and model-independent parameterization of their measurement. Calculate the background evolution and thermal history. Get lensing deflection angle potential power spectrum, and cross-correlation with T and E. Must have already array is indexed by index+1 gven by: Get transfer function (function of q, for each q in self.q_trans) by name for given redshift index, array of transfer function values for each calculated k, ClTransferData is the base class for storing CMB power transfer functions, as a function of q and \(\ell\). Prepared for submission to JCAP A minimal power-spectrum-based moment expansion for CMB B-mode searches S. Azzoni, 1;2 M. H. Abitbol, D. Alonso, 1A. TEMP_CL: Real*4: K cmb 2: the power spectrum TEMP_CL_ERR: Real*4: K cmb 2: estimate of the uncertainty in the power spectrum Keyword Data Type Value Description LMIN: Integer: 0: First monopole LMAX: Integer: value: Last monopole 2. . The angular power spectrum of the anisotropy of the CMB contains information about the formation of the Universe and its current contents. Returns \(8\pi G a^4 \rho_i\) in Mpc units. . Must have called calc_background(), calc_background_no_thermo() or calculated transfer k/h or k, z, PK, where kz an z are arrays of k/h or k and z respectively, Get physical time from hot big bang to redshift z in Gigayears. . B-mode CMB spectrum estimation pure pseudo cross-spectrum approach J. You have already liked this page, you can only like it once! by params.WantCls, params.WantTransfer). Return \(C_\ell\) trasfer functions as a function of \(\ell\) Get Hubble rate at redshift z, in km/s/Mpc units. Output is lensed total \(\ell(\ell+1)C_\ell/2\pi\) then Results for a set of parameters (given in a CAMBparams instance) are returned by the camb.get_background(), camb.get_transfer_functions() or … Plot your own power spectra (two for each parameter), and sum up the terms! CMB B-mode Polarization Experiments: First Results from POLARBEAR (and BICEP2) Haruki Nishino (Kavli IPMU) @ICRR/IPMU ACP seminar 2014-06-05 First result from ACTpol is out too. This is typically much faster that re-calculating everything, as the transfer functions can be re-used. And yet the best limits on come from the WMAP normalization of the CMB power spectrum used to normalize the power spectrum of galaxies from … dictionary of power spectrum arrays, index as PXP, PxW1, W1xW2, … etc. Get the individual densities as a function of scale factor. To get an instance of this data, call results.CAMBdata.get_matter_transfer_data(). CMB Introduction '96 Intermediate '01 Polarization Intro '01 Cosmic Symphony '04 Polarization Primer '97 Review '02 Power Animations Lensing Power Prehistory … \(\ell(\ell+1)C_\ell/2\pi\) self-owned numpy arrays (0..lmax, 0..3), where 0..3 index up to given redshift. Get tensor CMB power spectra. EXTNAME = 'POW-SPEC' (BINTABLE) Column Name Data Type Units Description TEMP_CL Real*4 K cmb 2 the power spectrum TEMP_CL_ERR Real*4 K cmb 2 estimate of the uncertainty in An introduction to topo-logical defects, cosmic strings, CMB polarization, and spin–s fields is given. • Not statistically significant, but an interesting thing to keep eyes on. We test this method on exact theory Cl as well as on a Wilkinson Microwave Anisotropy Probe (WMAP)-like CMB data set generated from a random realization of a fiducial cosmology, comparing the compression results to those from a full likelihood analysis using CosmoMC. Calculates \(P_{xy}(k)\), where x, y are one of model.Transfer_cdm, model.Transfer_xx etc. Get physical time between two scalar factors in Gigayears. 58 10. . This angular power spectrum is a plot of how much the temperature varies from point to point on the sky (the y-axis variable) vs. the angular frequency ell (the x-axis variable). Get all source window function and CMB lensing and cross power spectra. The Q/U Imaging ExperimenT (QUIET) is designed to detect the CMB B-mode polarization induced by primordial gravitational waves created during the inflation era. Get the CMB correlation functions from the power spectra. Must have called calc_background(), calc_background_no_thermo() or calculated transfer functions or Trinitree, it seems like you're trying to raise vague issues without presenting any kind of serious case. If fewer than four redshift points are used the interpolator uses a reduced order spline in z \(B\nabla B\), \(PP_\perp\), \(T\nabla E\), \(TP_\perp\), \((\nabla T)^2\), In chapter 5, we will show that the angular power spectrum is given by Cl = 47r / d3k P (k)D2(k). our power spectrum plots boosts the apparent variance at large l by a factor l2 ! Uses self.Params.Transfer.PK_redshifts as the spline node It is a nearly-uniform and isotropic radiation field, which exhibits a measured perfect black-body spectrum at a temperature of 2.72K. . numpy array CL[0:lmax+1,0:8], where CL[:,i] are \(T\nabla T\), \(E\nabla E\), Note that this function requires the transfers or background to have been calculated with no_thermo=False Over the multipole range [math] \ell [/math] = 2–49, the power spectrum is derived from a component-separation algorithm, Commander, applied to maps in the frequ… \(\Omega_i\) can be simply obtained by taking the ratio of the components to tot. Since the temperature of the CMB is measured to be 2.73K, this makes the fluctuations 1 part in 100,000 as advertised. 56 Figure 14 C l vs l including the contribution from all wakes. Computer resources required. PEAKS AND DIPS IN THE CMB POWER SPECTRUM: EXPERIMENTAL DATA We have to determine the locations and amplitudes of acoustic peaks and dips as well as their uncertainties in the data of the angular power spectrum of CMB temperature fluctuations obtained in BOOMERANG (Netterfield et al. The output k values are not regularly spaced, and not interpolated. (so results at intermediate z may be innaccurate), otherwise it uses bicubic. MQ resolves the same values using only the classical notions described by the Standard Model. To get an instance of this data, call results.CAMBdata.get_cmb_transfer_data(). MatterTransferData is the base class for storing matter power transfer function data for various q values. THE CMB POWER SPECTRUM ABOVE, PRODUCED BY MAXIMA, SHOWS A PRIMARY RESONANCE AND IS CONSISTENT WITH TWO MORE PEAKS; THEIR POSITION AND AMPLITUDE STRONGLY THE TEMPERATURE VARIATIONS IN EARLY UNIVERSE SEEN IN THE BOOMERANG IMAGES ABOVE ARE DUE TO SOUND WAVES IN THE PRIMORDIAL PLASMA. Like. call this if you want to just use angular_diameter_distance() and similar background functions. Details Related. Note that P is the deflection angle, but lensing windows return the kappa power. 21/03/2013 5978 views 18 likes 288796 ID. This primordial radiation field is a prediction from a Big Bang universe - if in its … the velocity-density correlation: \(\sigma^2_{vd}/\sigma_{dd}\) for \(8 h^{-1} {\rm Mpc}\) spheres. Get CMB power spectra, as requested by the ‘spectra’ argument. dictionary of power spectrum arrays, indexed by names of requested spectra. . Alens – (float64) non-physical scaling amplitude for the CMB lensing spectrum power MassiveNuMethod – (integer/string, one of: Nu_int, Nu_trunc, Nu_approx, Nu_best) DoLateRadTruncation – ( boolean ) If true, use smooth approx to radiation perturbations after decoupling on small scales, saving evolution of irrelevant oscillatory multipole equations CMB power spectrum • An extra neutrino ... power spectrum: n s=0.968±0.012 (68%CL) 38 Komatsu et al. Background Field Method and CMB Power Spectrum Shoichi Ichinose Laboratory of Physics, School of Food and Nutritional Sciences, University of Shizuoka Yada 52-1, Shizuoka 422-8526, Japan E-mail: ichinose@u-shizuoka-ken.ac.jp (Received July 15, 2013) A new field theory formulation is presented for the analysis o f the CMB power spectrum distribution in the cosmology. Power spectrum file data structure 1. (Image credit: ESA and the Planck Collaboration.) NOTE: if non-linear lensing is on, the transfer functions have the non-linear correction included when Assuming transfers have been calculated, return a 2D spline interpolation object to evaluate matter By default evaluated at points \(\cos(\theta)\) = xvals that are roots of Legendre polynomials, CMB power spectrum • An extra neutrino (or something else)? distance at recombination. Output for matter power spectrum is 4piP(k). they are calculated, so using this function with a different initial power spectrum will not give quite the 5.2 Changes to cl mod.f90 Once you have the source function, the only remaining task is to integrate this (weighted by the Bessel functions and the power spectrum), to obtain the power spectrum. The new physics must be strongly scale-dependent => Expect shifts of the spectral index and its Get lensed scalar CMB power spectra. CMB Power Spectrum Results from the South Pole Telescope Christian Reichardt ever at the present, the strongest constraints come from the CMB temperature anisotropy. corrs is 2D array corrs[i, ix], where ix=0,1,2,3 are T, Q+U, Q-U and cross, and i indexes xvals. All power spectra are ℓ(ℓ + 1)Cℓ / 2π self-owned numpy arrays (0..lmax, 0..3), where 0..3 index are TT, EE, BB, TE, unless raw_cl is True in which case return just Cℓ. PoS(EPS-HEP2011)073 CMB Power Spectrum Results from the South Pole Telescope Christian Reichardt Figure 2: The SPT power spectrum from K11. This is efficient for arrays. Since the temperature of the CMB is measured to be 2.73K, this makes the fluctuations 1 part in 100,000 as advertised. Mathematically, the power spectrum is actually equal to the square of this quantity times 2π/[ l ( l +1)], where the l 's are there to account for the fact that the sky is two dimensional. array of \(\sigma_R\) values, or 2D array indexed by (redshift, R). And yet the best limits on come from the WMAP normalization of the CMB power spectrum used to normalize the power spectrum of galaxies from the 2dF redshift survey (Bennett et … functions. n_a x len(vars) 2D numpy array or dict of 1D arrays of \(8\pi G a^4 \rho_i\) in Mpc units. CMB-only TT Power Spectrum The plot shows CMB lensed bandpowers from recent ACTPol, Planck, and SPT measurements marginalized over Galactic and extragalactic foreground emission and Sunyaev-Zel'dovich effects. Get unlensed CMB power spectra, including tensors if relevant. CMB Power Spectrum Shoichi Ichinose ichinose@u-shizuoka-ken.ac.jp SFNS, University of Shizuoka KEK-CPWS The 4th UTQuest Workshop: B-mode Cosmology - Intermediate Scale Inflation and Hidden Sector - 2015.02.19-21 Shoichi Ichinose (University of Shizuoka) New Approach to Cosmological Fluctuation and CMB Power Spectrum KEK-CPWS The 4th UTQuest Workshop: B-mode … The auto power spectrum is Ĉℓ = Sℓ + Nℓ with variance ΔĈℓ 2 = 2(Sℓ +Nℓ) 2 / (2ℓ+1) →Noise bias and increased variance • For 2 data-sets with the same signal but … are returned by the camb.get_background(), camb.get_transfer_functions() or camb.get_results() Mathematically, the power spectrum is actually equal to the square of this quantity times 2π/[l(l+1)], where the 3. If return_z_k=True, instead return interpolator, z, k where z, k are the grid used. of 1101.2234. Results for a set of parameters (given in a CAMBparams instance) Get angular diameter distance between two redshifts functions or power spectra. 2007-May-22, 04:54 PM #4. First Results from QUIET: CMB Polarization Power Spectra by Pseudo-Cl Estimator Chinone, Yuji; QUIET Collaboration; Abstract. © Copyright Antony Lewis The red line is the same LCDM model as above, i.e., it is fit to the temperature power spectrum and not to the polarization spectra, showing very good consistency of this model with the polarization data. No new physics is proposed. Get lensed-scalar + tensor CMB power spectra. The output k values are not regularly spaced, and not interpolated. Temperature Power Spectrum Rita Tojeiro March 16, 2006 The Cosmic Microwave Background The Cosmic Microwave Background (CMB) radiation field is an open window to the early Universe. Spatial Curvature Key Concepts. For a description of outputs for different var1, var2 see Matter power spectrum and matter transfer function variables. M. Tristram Archeops Moriond 2004 Exploring the Universe ITALY USA FRANCE LPSC, CRTBT, LAOG (Grenoble) IAS, LAL, (Orsay), SPP-Saclay, IAP, CDF (Paris) CESR, LATT (Toulouse) Univ. Extra Dimension Approach to CMB Power-Spectrum Physics S. Ichinose January 24, 2011 Laboratory of Physics, Sch. The peak at ‘ ˘800 is the third acoustic peak.