Probing Dark Energy with Baryon Acoustic Oscillations from Future Large Galaxy Redshift Surveys

Size: px
Start display at page:

Download "Probing Dark Energy with Baryon Acoustic Oscillations from Future Large Galaxy Redshift Surveys"

Transcription

1 Probing Dark Energy with Baryon Acoustic Oscillations from Future Large Galaxy Redshift Surveys Hee-Jong Seo (Steward Observatory) Daniel J. Eisenstein (Steward Observatory) Martin White, Edwin Sirko, David Spergel CITA. Jan p.1/42

2 Dark energy Observational implications SNIa redshift magnitude relation (Perlmutter et al. 1998, Riess et al. 1998) - Open? - Flat & an energy responsible for the acceleration? CMBR implies nearly Flat Universe. Matter estimated 1 4 of critical density. 3/4 of total energy, Negative pressure, Smooth and inert, Very little is known. Q: What is energy density versus redshift over time? measuring growth rate in structure formation - weak lensing surveys measuring expansion rate - SNIa surveys, the BAO from galaxy redshift surveys CITA. Jan p.2/42

3 Outline Physics of acoustic oscillations Physics of the standard ruler test Error forecasts on D A and H for future surveys Degradations of the baryonic signature due to nonlinear effects Quantification of the degradation Fitting formula Reconstruction Baryonic signature in future galaxy redshift surveys can provide measurements of D A and H to excellent precision. CITA. Jan p.3/42

4 Baryon acoustic oscillations (BAO) Primordial overdensity peak of dark matter, gas, photons at origin. CITA. Jan p.4/42

5 Baryon acoustic oscillations (BAO) Overpresured peak a spherical sound wave at c s c/ 3 CITA. Jan p.4/42

6 Baryon acoustic oscillations (BAO) Overpresured peak a spherical sound wave at c s c/ 3 CITA. Jan p.4/42

7 Baryon acoustic oscillations (BAO) Overpresured peak a spherical sound wave at c s c/ 3 CITA. Jan p.4/42

8 Baryon acoustic oscillations (BAO) At recombination (at z 1000), Optically thick optically thin Baryons decouple from photons in the CMB. Sound speed of gas decreases. The traveling wave stalls. CITA. Jan p.4/42

9 Baryon acoustic oscillations (BAO) A spherical peak at the distance that the wave has travelled before the recombination This is called the sound horizon scale at recombination (150 Mpc). CITA. Jan p.4/42

10 Baryon acoustic oscillations (BAO) WMAP3 from Hinshaw et al The sound horizon scale can be measured from the CMB itself. CITA. Jan p.4/42

11 Baryon acoustic oscillations (BAO) We expect to see the same features in the matter distribution and recently observed in large galaxy redshift surveys (e.g., Eisenstein et al. 2005; Cole et al. 2005). CITA. Jan p.4/42

12 A Standard Ruler Test to derive D A & H D A & H as geometric traces of the expansion history r = c z H CITA. Jan p.5/42

13 A Standard Ruler Test to derive D A & H D A & H as geometric traces of the expansion history r = (1 + z)d A θ D A = z cdz H(z) CITA. Jan p.5/42

14 A Standard Ruler Test to derive D A & H D A & H as geometric traces of the expansion history Knowing r D A and H separately measured STANDARD RULER TEST CITA. Jan p.5/42

15 Dark Energy to cosmological distances We characterize dark energy by the equation of state w X (z) = p X z ρx Parametrization : e.g., w X (z) = w 0 + w 1 z or w X (z) = w 0 + w a z/(1 + z) (For ΛCDM, w 0 = 1, w 1 = 0) Integrate Energy density of dark energy as a function of time Hubble parameter Integrate Angular diameter distance Going from D A to w 1 : 3 derivatives Going from H to w 1 : 2 derivatives CITA. Jan p.6/42

16 D A & H from galaxy redshift surveys Observables : ρ(z, θ) or δ(z, θ) two-point correlation function ( δδ ) or power spectrum map (z, θ) to (r H, r /D A ) or (k /H, k D A ) the acoustic peak Silk dampling The physical scale of the BAO (i.e., r or k) is well constrained by future CMB data detecting the BAO in the galaxy redshift surveys measures H and D A. CITA. Jan p.7/42

17 Why baryon oscillations? If matter power spectrum is a simple power law, CITA. Jan p.8/42

18 Why baryon oscillations? If matter power spectrum is a simple power law, CITA. Jan p.8/42

19 Why baryon oscillations? If matter power spectrum is a simple power law, CITA. Jan p.8/42

20 Why baryonic oscillations? With a distinct signature, CITA. Jan p.9/42

21 Why baryonic oscillations? With a distinct signature, CITA. Jan p.9/42

22 Why baryonic oscillations? With a distinct signature, CITA. Jan p.9/42

23 Why baryonic oscillations? With a distinct signature, CITA. Jan p.9/42

24 Section summary Future CMB data will measure the characteristic scale of the BAO to excellent precision. Then, using the baryon oscillations in galaxy redshift surveys as a standard ruler, we can measure cosmological distances that geometrically trace the expansion history of the Universe, which in turn depends on dark energy properties. CITA. Jan p.10/42

25 How good are the constraints? Assume Gaussian random density field. Propagate observational errors on power spectrum to errors on D A and H. Measure errors on D A and H σ P (z = 3) CITA. Jan p.11/42

26 How good are the constraints? Assume Gaussian random density field. Propagate observational errors on power spectrum to errors on D A and H. Measure errors on D A and H σ P (z = 3) 5% in D A or H CITA. Jan p.11/42

27 How good are the constraints? When the density field follows Gaussian ramdom distribution, the statistical error on the observed power spectrum at k is σ P P = P + 1 n P When the power spectrum is averaged over a wavenumber bin, the error decreases by the square root of the number of the independent modes within the bin, N modes. When averaged over k and µ, ( σ P P = np Nmodes np where N modes = 2πV survey k 2 k µ/(2(2π) 3 ) σ P decreases as V survey or n increases ) CITA. Jan p.12/42

28 Astrophysical complications In reality, the later-time density field is non-gaussian. And this degrades the baryonic signature on small scales. Nonlinear structure growth Also there are additional effect that may degrade the baryonic signature. Redshift distortions Galaxy bias * Results from N-body Simulations CITA. Jan p.13/42

29 Nonlinear structure growth Primordial perturbation Structure formation Galaxies Small halos Groups,Clusters, Super clusters Large halos With structure growth z = 0.3 z = 1 z = 3 z = 49 CITA. Jan p.14/42

30 Nonlinear structure growth Primordial perturbation Structure formation Galaxies Small halos Groups,Clusters, Super clusters Large halos Erases features on nonlinear scales (σ R 1) Nonlinear scale advances to smaller k (Larger scale) as structures grow hierarchically. We ignored k smaller than k max with conservative choice of k max (σ R 0.5) (Seo & Eisenstein 2003). In reality, remnant nonlinearity may not be simple. CITA. Jan p.14/42

31 Cosmological N-body simulations We ran a total volume of 6.85h 3 Gpc 3 using the Hydra code (Couchman, Thomas, & Pearce 1995) in collisionless P 3 M mode. Ω m = 0.27, Ω X = 0.73, Ω b = 0.046, h = 0.72 and n = σ 8 = 0.9 at z = 0 Volume of h 3 Mpc 3 per box, grids, dark matter particles ( M sun /particle) Initial random density fields at z = 49 Output at z = 3 (4h 3 Gpc 3 ), z = 1 and z = 0.3 (6.85h 3 Gpc 3 ) CITA. Jan p.15/42

32 Nonlinear growth from N-body results z = 49 & z = 3 : 4h 3 Gpc 3 z = 1 & z = 0.3 : 6.85h 3 Gpc 3 Seo & Eisenstein 2005 Baryonic peaks survive on large scales! Mild nonlinearity within k max (σ R 0.5). CITA. Jan p.16/42

33 Nonlinear growth from N-body results Subtract nonlinear growth effect on the broadband power Seo & Eisenstein 2005 CITA. Jan p.17/42

34 Section summary Baryonic peaks on large scales survive well despite mild nonlinearity of gravity. Nonlinear growth gradually erases baryonic peaks, gradually proceeding from small scales to larger scales with time. More peaks survive at high redshift. However, we still lack a quantitative description of the nonlinear effects on the baryonic signature. CITA. Jan p.18/42

35 Modeling nonlinear effects on the BAO Two-point correlation function The characteristic separation of 150 Mpc of pairs is blurred by structure formation. As a result, the baryonic peak is harder to centroid. CITA. Jan p.19/42

36 Modeling nonlinear effects on the BAO Let s consider a pair of objects initially separated by 150 Mpc. CITA. Jan p.19/42

37 Modeling nonlinear effects on the BAO Structure formation moves particles around. By 10 Mpc at z = 0.3. CITA. Jan p.19/42

38 Modeling nonlinear effects on the BAO u 12 u 12 is also the difference between the displacements of individual particles. CITA. Jan p.19/42

39 Distribution of u 12 At z = 0.3 The distributions are close to Gaussian with σ = 8.15h 1 Mpc at z = 0.3. Eisenstein, Seo, & White 2006 CITA. Jan p.20/42

40 The model Gaussian displacement distribution ξ lin (r) No free parameter! z = 0.3 z = 1 Dashed: linear ξ Solid black: from N-body results Red: the model ξ Eisenstein, Seo, & White 2006 CITA. Jan p.21/42

41 The model In Fourier space, the corresponding exponential factor P lin (k) z = 0.3 z = 1 Red: the model P/P lin. Data points: from N-body results. Eisenstein, Seo, & White 2006 CITA. Jan p.21/42

42 Redshift distortions Again, what we observe is galaxy distribution at (z,θ). Without peculiar velocities, (z c, θ) (r H, r /D A ) With peculiar velocities,(z, θ)=(z c +v/c, θ) (r H, r /D A ) On large scales, CITA. Jan p.22/42

43 Redshift distortions CITA. Jan p.22/42

44 Redshift distortions On large scales (linear scales), angle-dependent multiplicative change in power by (1 + βµ 2 ) 2 On small scales, the thermal velocity suppress the power (a.k.a. the finger-of- God effect). Solid lines: real space Dashed line: redshift space CITA. Jan p.23/42

45 Redshift distortions Redshift distortions decrease contrasts and introduce noises within k max CITA. Jan p.23/42

46 Modeling redshift distortions on the BAO CITA. Jan p.24/42

47 Modeling redshift distortions on the BAO The characteristic separation of 150 Mpc (100h 1 Mpc) of pairs is further blurred by large-scale peculiar velocity that distorts the true distance to the galaxies. CITA. Jan p.24/42

48 Modeling redshift distortions on the BAO CITA. Jan p.24/42

49 Modeling redshift distortions on the BAO u 12 u 12,real CITA. Jan p.24/42

50 Distribution of u 12 in redshift space At z = 0.3 The distributions along the lineof-sight are close to Gaussian with σ = 13.6h 1 Mpc at z = 0.3. (across the line-of-sight σ = 8.15h 1 Mpc at z = 0.3. Eisenstein, Seo, & White 2006 CITA. Jan p.25/42

51 The model z = 0.3 z = 1 Eisenstein, Seo, & White 2006 Red: the model P/P lin Data points: from N-body results CITA. Jan p.26/42

52 Redshift evolution of rms displacement Solid line: Σ = (12.4h 1 Mpc)G(z) Dashed line:σ = (12.4h 1 Mpc)G(z)(1 + f), where f Ω 0.6 m Data points: real space - radial direction, redshift space - radial direction line-of-sight direction CITA. Jan p.27/42

53 Section summary We can explain the gradual degradation of the baryonic signature due to nonlinear growth and redshift distortions by: we estimate the amount of differential motions of pairs initially separated by the characteristic scales of the sound horizon at the recombination. We can now quantify the amount of degradation due to various nonlinear effects. Estimating the Lagrangian displacement fields with a reasonable precision does not require a simulation as large as estimating the degradation in the BAO does. CITA. Jan p.28/42

54 Galaxy (halo) bias Lagrangian displacements are dominated by bulk flows and super cluster formation. The motions within halos adds only small portion to Σ, i.e, 10%. Generated power spectrum with simple halo bias model from the N-body results. CITA. Jan p.29/42

55 Bias at z = 0.3 (central + satellite galaxies) Real space Redshift space Red: the model P bias /P lin Data points: from N-body results Eisenstein, Seo, & White 2006 Halo bias adds only small amount of additional nonlinear degradation. CITA. Jan p.30/42

56 How good are the constraints? When the density field follows Gaussian ramdom distribution, the statistical error on the observed power spectrum at k is σ P P = P + 1 n P When the power spectrum is averaged over a wavenumber bin, the error decreases by the square root of the number of the independent modes within the bin, N modes. When averaged over k and µ, ( σ P P = np Nmodes np where N modes = 2πV survey k 2 k µ/(2(2π) 3 ) σ P decreases as V survey or n increases ) CITA. Jan p.31/42

57 Fisher information matrix Error propagation of Gaussian observation error to cosmological parameters p i. χ 2 of observables = k (P model(k) P obs (k)) 2 /2σ 2 P (k). The covariance matrix of parameter p i is derived from Cov 1 ij = F ij = 2 χ 2 p i p j CITA. Jan p.32/42

58 Fisher information matrix F ij kmax k0 V survey P ( k) P ( k) (P ( k) + 1/n) 2 p i p j d k 2(2π) 3 Tegmark (1997), Seo & Eisenstein (2003) CITA. Jan p.33/42

59 Fisher information matrix F ij kmax 0 V survey P ( k) P ( k) (P ( V eff ( k) + 1/n) 2 p i p d k) k j 2(2π) 3 CITA. Jan p.33/42

60 Fisher information matrix F ij kmax 0 V survey P ( k) P ( k) (P ( k) + 1/n ) 2 p i p j d k 2(2π) 3 CITA. Jan p.33/42

61 Fisher information matrix F ij kmax 0 V survey P ( k) P ( k) (P ( k) + 1/n) 2 p i p j d k 2(2π) 3 CITA. Jan p.33/42

62 Fisher information matrix F ij kmax 0 V survey P ( k) P ( k) (P ( k) + 1/n) 2 p i p j d k 2(2π) 3 P ( k) p i when p i = D A or H P (k) k k p i Nonlinear effects damp the BAO contribution to this quantity CITA. Jan p.33/42

63 Fisher information matrix F ij 0 kmax V survey P ( k) P ( k) (P ( k) + 1/n) 2 p i p j d k 2(2π) 3 with linear P ( k) in P ( k) p i. In Seo & Eisenstein 2003, we excluded nonlinear regime by a conservative choice of k max ( σ R 0.5). CITA. Jan p.33/42

64 Fisher information matrix F ij kmax 0 V survey P ( k) P ( k) (P ( k) + 1/n) 2 p i p j d k 2(2π) 3 We can now include nonlinear effect in P ( k) in P ( k) p i. CITA. Jan p.33/42

65 Fisher information matrix F ij exp 0 V survey P (k, µ) P (k, µ) (P (k, µ) + 1/n) 2 p i p j [ ] k 2 Σ 2 k 2 µ 2 (Σ 2 Σ2 ) d k 2(2π) 3 where P (k, µ) in the derivatives is a linear power spectrum. In Seo & Eisenstein 2007, we implemented the Fisher matrix with the Lagrangian Displacement field. Nonlinear growth, redshift distortions, and bias effect on the BAO is simply parameterized by Σ and Σ. CITA. Jan p.33/42

66 Fisher information matrix CMB data (Planck Temperature and Polarization) + redshift surveys (V survey, number density, Σ) Cosmological parameters p i : 6 parameters (Ω m h 2, Ω b h 2, τ, n s, T/S, As) & D A tocmb & [D A, H, Unknown growth functions, β, P shot ] at each redshift Ignore distance information from growth rate and suppress distance information from the shape of the power spectrum. Subtract any non-baryonic distance information: F ij F ij where F is a Fisher matrix with no baryon. Now the remaining Fisher matrix contains mainly distance information from the BAO. F 1 ij, p i, p j ; Ω m h 2, D A s, H s CITA. Jan p.34/42

67 A physically motivated 1 and 2-D fitting formula Once we isolate the distance information from the BAO only, the process is basically the problem of centroiding a peak in the presence of noise. Assuming the peak in correlation function is a delta function damped by the Silk damping effect and Nonlinear damping, P b (k) sin ks o ks o exp ( (kσ s ) 1.4 ) exp ( k 2 Σ 2 nl/2). F ln so = V survey 0 1 (P (k) + n 1 ) 2 [ Pb (k) ln s o ] 2 4πk 2 dk 2(2π) 3. Leading term of P b(k) ln s o constant cos ks o exp ( (kσ s ) 1.4 ) exp ( k 2 Σ 2 nl/2) We approximate cos 2 ks o inside the integral as 1 2. CITA. Jan p.35/42

68 A physically motivated 1 and 2-D fitting formula F ij = V survey A dµ f i (µ)f j (µ) dk k2 exp [ 2(kΣ s ) 1.4] ( ) 2 exp P (k) 1 P np 0.2 R(µ) where f 1 (µ) = µ 2 1 and f 2 (µ) = µ 2 [ ] k 2 (1 µ 2 )Σ 2 k 2 µ 2 Σ 2 From Seo & Eisenstein 2007 C-prgram available in eisenste/acousticpeak/bao_forecast.html CITA. Jan p.35/42

69 Photometric redshift survey How does the redshift error affect the result? Deep wide-field multicolor imaging surveys will offer photometric redshifts over a wide field σ z (or Σ z ) increases σ DA and especially σ H increase Power spectra over a range of D A overlap Features are smeared 4% in (1+z) seems safe Modes with k σ r 1 strongly suppressed (P (k, µ) exp ( k 2 µ 2 Σ 2 z)) σ DA increases and we lose information on H. CITA. Jan p.36/42

70 Photometric redshift survey P (k, µ) exp ( k 2 µ 2 Σ 2 z) not only decreases a signal but also decreases a noise. F ij = V survey A dµ f i (µ)f j (µ) dk k2 exp [ 2(kΣ s ) 1.4] ( ) 2 exp P (k) 1 P np 0.2 R(µ) [ ] k 2 (1 µ 2 )Σ 2 k 2 µ 2 Σ 2 With 3% error in (1 + z), one gets 4% in D A for 0.6 < z < 1.0 for every 1000 deg 2. CITA. Jan p.36/42

71 Distance errors from N-body results Applied Lagrangian displacement distributions to a construct a model P m (k) that is used to fit the N-body data Jacknknife subsampling of the data χ 2 analysis measures a mean and a distance error Distance errors Fisher matrix calculations and χ 2 analysis using the N-body results agree to excellent precision (< 13%). From N-body results at z = 0.3 σ distance = 0.6% for 6.85h 3 Gpc 3 σ distance = 1.57% for 1h 3 Gpc 3 From the Fisher matrix, σ distance = 1.50% for 1h 3 Gpc 3 CITA. Jan p.37/42

72 Fractional errors of D A and H 3π steradian of skys with z = 0.1. Black: the cosmic variance limit Blue: full nonlinear degradation with a reasonable shot noise. Red: after reconstruction with a reasonable shot noise. CITA. Jan p.38/42

73 Reconstruction Recover the erased portion of baryonic acoustic oscillations by undoing the Lagrangian displacement (Eisenstein, Seo, Sirko, & Spergel 2006). Overdensity Overdensity CITA. Jan p.39/42

74 Reconstruction The Lagrangian displacement ( q) is estimated from the nonlinear density fields by applying the linear continuity equation to the nonlinear density fields (δ = divergence of q) Overdensity Overdensity CITA. Jan p.39/42

75 Reconstruction The Lagrangian displacement ( q) is estimated from the nonlinear density fields by applying the linear continuity equation to the nonlinear density fields (δ = divergence of q) CITA. Jan p.39/42

76 Future surveys CITA. Jan p.40/42

77 Future surveys w X = w 0 + w a z/(1 + z) CITA. Jan p.41/42

78 Summary We can measure the cosmological distance scale using the baryonic signature in galaxy redshift surveys as a standard ruler. Baryonic oscillations on large scales survive well while nonlinear growth and redshift distortions obscure the features. Galaxy (halo) bias adds only small additional degradation. Using Lagranginan displacement distributions, we can quantify the nonlinear effects on the baryonic signature in galaxy redshift surveys. By reversing the Lagrangian displacement distributions, we can reconstruct a portion of the baryonic signature degraded by the various nonlinearities We improved error forecasts by implementing the Fisher matrix calculation with the Lagrangian displacement distributions. We provide a physical motivated fitting formula for the covariance matrix of D A and H. CITA. Jan p.42/42

arxiv:0805.0117v2 [astro-ph] 7 Aug 2008

arxiv:0805.0117v2 [astro-ph] 7 Aug 2008 Accepted for publication in the Astrophysical Journal Preprint typeset using L A TEX style emulateapj v. 2/4/05 NON-LINEAR STRUCTURE FORMATION AND THE ACOUSTIC SCALE Hee-Jong Seo,2, Ethan R. Siegel 2,

More information

Dark Energy, Modified Gravity and The Accelerating Universe

Dark Energy, Modified Gravity and The Accelerating Universe Dark Energy, Modified Gravity and The Accelerating Universe Dragan Huterer Kavli Institute for Cosmological Physics University of Chicago Makeup of universe today Dark Matter (suspected since 1930s established

More information

Galaxy Survey data analysis using SDSS-III as an example

Galaxy Survey data analysis using SDSS-III as an example Galaxy Survey data analysis using SDSS-III as an example Will Percival (University of Portsmouth) showing work by the BOSS galaxy clustering working group" Cosmology from Spectroscopic Galaxy Surveys"

More information

Gravity Testing and Interpreting Cosmological Measurement

Gravity Testing and Interpreting Cosmological Measurement Cosmological Scale Tests of Gravity Edmund Bertschinger MIT Department of Physics and Kavli Institute for Astrophysics and Space Research January 2011 References Caldwell & Kamionkowski 0903.0866 Silvestri

More information

Malcolm S. Longair. Galaxy Formation. With 141 Figures and 12 Tables. Springer

Malcolm S. Longair. Galaxy Formation. With 141 Figures and 12 Tables. Springer Malcolm S. Longair Galaxy Formation With 141 Figures and 12 Tables Springer Contents Part I Preliminaries 1. Introduction, History and Outline 3 1.1 Prehistory 3 1.2 The Theory of the Expanding Universe

More information

OUTLINE The Hubble parameter After these lectures, you should be able to: Define the Hubble parameter H Sketch a(t) for k>0, k=0, k<0 assuming Λ=0 Def

OUTLINE The Hubble parameter After these lectures, you should be able to: Define the Hubble parameter H Sketch a(t) for k>0, k=0, k<0 assuming Λ=0 Def Observational cosmology: The Friedman equations 2 Filipe B. Abdalla Kathleen Lonsdale Building G.22 http://zuserver2.star.ucl.ac.uk/~hiranya/phas3136/phas3136 OUTLINE The Hubble parameter After these lectures,

More information

Neutrino properties from Cosmology

Neutrino properties from Cosmology Neutrino properties from Cosmology Anže Slosar, BNL Neutrino16, July 16 1 / 30 plan for the talk Pedagogical introduction to the role neutrinos play in Cosmology aimed at a non-cosmo community Neutrinos

More information

The Search for Dark Matter, Einstein s Cosmology and MOND. David B. Cline

The Search for Dark Matter, Einstein s Cosmology and MOND. David B. Cline The Search for Dark Matter, Einstein s Cosmology and MOND David B. Cline Astrophysics Division, Department of Physics & Astronomy University of California, Los Angeles, CA 90095 USA dcline@physics.ucla.edu

More information

Mapping structure of the Universe. the very large scale. INAF IASF Milano

Mapping structure of the Universe. the very large scale. INAF IASF Milano Mapping the large scale structure of the Universe the very large scale structure Marco Scodeggio INAF IASF Milano The large scale structure (100Mpc) Zero order approximation: the Universe is homegeneous

More information

Baryon Acoustic Oscillations: A standard ruler method for determining the expansion rate of the Universe. Martin White UC Berkeley/LBNL

Baryon Acoustic Oscillations: A standard ruler method for determining the expansion rate of the Universe. Martin White UC Berkeley/LBNL Baryon Acoustic Oscillations: A standard ruler method for determining the expansion rate of the Universe. Martin White UC Berkeley/LBNL Outline Dark energy and standard rulers. Cosmic sound: baryon acoustic

More information

Detailed Mass Map of CL 0024+1654 from Strong Lensing

Detailed Mass Map of CL 0024+1654 from Strong Lensing Detailed Mass Map of CL 0024+1654 from Strong Lensing Tyson, Kochanski, & Dell Antonio (1998) HST WFPC2 image of CL0024+1654 slides based on presentation by Yue Zhao Rutgers Physics 690 February 21, 2008

More information

Cosmological and Solar System Tests of. f (R) Cosmic Acceleration

Cosmological and Solar System Tests of. f (R) Cosmic Acceleration Cosmological and Solar System Tests of f (R) Cosmic Acceleration Wayne Hu Origins Institute, May 2007 Why Study f(r)? Cosmic acceleration, like the cosmological constant, can either be viewed as arising

More information

Photo-z Requirements for Self-Calibration of Cluster Dark Energy Studies

Photo-z Requirements for Self-Calibration of Cluster Dark Energy Studies Photo-z Requirements for Self-Calibration of Cluster Dark Energy Studies Marcos Lima Department of Physics Kavli Institute for Cosmological Physics University of Chicago DES Collaboration Meeting Barcelona

More information

Self Calibration of Cluster Counts: Observable-Mass Distribution. Wayne Hu Kona, March 2005

Self Calibration of Cluster Counts: Observable-Mass Distribution. Wayne Hu Kona, March 2005 Self Calibration of Cluster Counts: Observable-Mass Distribution Wayne Hu Kona, March 2005 Self Calibration of Cluster Counts: Observable-Mass Distribution Wayne Hu Kona, August 2004 Scattered Forecasts

More information

Institut für Kern- und Teilchenphysik Neutrinos & Cosmology

Institut für Kern- und Teilchenphysik Neutrinos & Cosmology Neutrinos & Cosmology 1 Cosmology: WHY??? From laboratory experiment limits can be set ONLY in neutrino mass difference No information if neutrino masses are degenerated From kinematic experiment limits

More information

Big Bang Cosmology. Big Bang vs. Steady State

Big Bang Cosmology. Big Bang vs. Steady State Big Bang vs. Steady State Big Bang Cosmology Perfect cosmological principle: universe is unchanging in space and time => Steady-State universe - Bondi, Hoyle, Gold. True? No! Hubble s Law => expansion

More information

arxiv:1302.1640v2 [astro-ph.co] 11 Apr 2013

arxiv:1302.1640v2 [astro-ph.co] 11 Apr 2013 Draft version April, 03 Preprint typeset using L A TEX style emulateapj v. 5// MASS-DEPENDENT BARYON ACOUSTIC OSCILLATION SIGNAL AND HALO BIAS Qiao Wang and Hu Zhan Key Laboratory of Optical Astronomy,

More information

World of Particles Big Bang Thomas Gajdosik. Big Bang (model)

World of Particles Big Bang Thomas Gajdosik. Big Bang (model) Big Bang (model) What can be seen / measured? basically only light (and a few particles: e ±, p, p, ν x ) in different wave lengths: microwave to γ-rays in different intensities (measured in magnitudes)

More information

Gravity is everywhere: Two new tests of gravity. Luca Amendola University of Heidelberg

Gravity is everywhere: Two new tests of gravity. Luca Amendola University of Heidelberg Gravity is everywhere: Two new tests of gravity Luca Amendola University of Heidelberg Gravity in polarization maps and in supernovae Gravity in polarization maps and in supernovae Why testing gravity?

More information

Astronomy & Physics Resources for Middle & High School Teachers

Astronomy & Physics Resources for Middle & High School Teachers Astronomy & Physics Resources for Middle & High School Teachers Gillian Wilson http://www.faculty.ucr.edu/~gillianw/k12 A cosmologist is.... an astronomer who studies the formation and evolution of the

More information

WIMP dark matter and the isotropic radio signal Roberto A. Lineros R. Instituto de Física Corpuscular - CSIC/U. Valencia @Roberto_Lineros Outline Introduction Cosmic ray propagation Synchrotron emission

More information

Structure formation in modified gravity models

Structure formation in modified gravity models Structure formation in modified gravity models Kazuya Koyama Institute of Cosmology and Gravitation University of Portsmouth Dark energy v modified gravity Is cosmology probing the breakdown of general

More information

Topic 3. Evidence for the Big Bang

Topic 3. Evidence for the Big Bang Topic 3 Primordial nucleosynthesis Evidence for the Big Bang! Back in the 1920s it was generally thought that the Universe was infinite! However a number of experimental observations started to question

More information

Extreme Value Modeling for Detection and Attribution of Climate Extremes

Extreme Value Modeling for Detection and Attribution of Climate Extremes Extreme Value Modeling for Detection and Attribution of Climate Extremes Jun Yan, Yujing Jiang Joint work with Zhuo Wang, Xuebin Zhang Department of Statistics, University of Connecticut February 2, 2016

More information

DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION

DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION 1 DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION Daniel S. Orton email: dsorton1@gmail.com Abstract: There are many longstanding

More information

Specific Intensity. I ν =

Specific Intensity. I ν = Specific Intensity Initial question: A number of active galactic nuclei display jets, that is, long, nearly linear, structures that can extend for hundreds of kiloparsecs. Many have two oppositely-directed

More information

Dealing with large datasets

Dealing with large datasets Dealing with large datasets (by throwing away most of the data) Alan Heavens Institute for Astronomy, University of Edinburgh with Ben Panter, Rob Tweedie, Mark Bastin, Will Hossack, Keith McKellar, Trevor

More information

Astro 102 Test 5 Review Spring 2016. See Old Test 4 #16-23, Test 5 #1-3, Old Final #1-14

Astro 102 Test 5 Review Spring 2016. See Old Test 4 #16-23, Test 5 #1-3, Old Final #1-14 Astro 102 Test 5 Review Spring 2016 See Old Test 4 #16-23, Test 5 #1-3, Old Final #1-14 Sec 14.5 Expanding Universe Know: Doppler shift, redshift, Hubble s Law, cosmic distance ladder, standard candles,

More information

Nuclear Physics Lab I: Geiger-Müller Counter and Nuclear Counting Statistics

Nuclear Physics Lab I: Geiger-Müller Counter and Nuclear Counting Statistics Nuclear Physics Lab I: Geiger-Müller Counter and Nuclear Counting Statistics PART I Geiger Tube: Optimal Operating Voltage and Resolving Time Objective: To become acquainted with the operation and characteristics

More information

Searching for Cosmic Strings in New Observational Windows

Searching for Cosmic Strings in New Observational Windows 1 / 62 in Searching for s in New Observational Windows Robert Brandenberger McGill University, Montreal, Canada; and Institute for Theoretical Studies, ETH Zuerich, Switzerland KITPC, Sept. 25 2015 2 /

More information

Cosmic Structure Formation and Dynamics: Cosmological N-body Simulations of Galaxy Formation and Magnetohydrodynamic Simulations of Solar Atmosphere

Cosmic Structure Formation and Dynamics: Cosmological N-body Simulations of Galaxy Formation and Magnetohydrodynamic Simulations of Solar Atmosphere Chapter 3 Epoch Making Simulation Cosmic Structure Formation and Dynamics: Cosmological N-body Simulations of Galaxy Formation and Magnetohydrodynamic Simulations of Solar Atmosphere Project Representative

More information

Physical Self-Calibration of X-ray and SZ Surveys

Physical Self-Calibration of X-ray and SZ Surveys Physical Self-Calibration of X-ray and SZ Surveys Greg L. Bryan, Zoltan Haiman (Columbia University) and Joshua D. Younger (CfA) 1. Cluster Surveys and Self-Calibration Clusters of galaxies form at the

More information

165 points. Name Date Period. Column B a. Cepheid variables b. luminosity c. RR Lyrae variables d. Sagittarius e. variable stars

165 points. Name Date Period. Column B a. Cepheid variables b. luminosity c. RR Lyrae variables d. Sagittarius e. variable stars Name Date Period 30 GALAXIES AND THE UNIVERSE SECTION 30.1 The Milky Way Galaxy In your textbook, read about discovering the Milky Way. (20 points) For each item in Column A, write the letter of the matching

More information

Modified Gravity and the CMB

Modified Gravity and the CMB Modified Gravity and the CMB Philippe Brax, IphT Saclay, France arxiv:1109.5862 PhB, A.C. Davis Work in progress PhB, ACD, B. Li Minneapolis October 2011 PLANCK will give us very precise information on

More information

Data Provided: A formula sheet and table of physical constants is attached to this paper. DARK MATTER AND THE UNIVERSE

Data Provided: A formula sheet and table of physical constants is attached to this paper. DARK MATTER AND THE UNIVERSE Data Provided: A formula sheet and table of physical constants is attached to this paper. DEPARTMENT OF PHYSICS AND ASTRONOMY Autumn Semester (2014-2015) DARK MATTER AND THE UNIVERSE 2 HOURS Answer question

More information

Elliptical Galaxies. Houjun Mo. April 19, 2004. Basic properties of elliptical galaxies. Formation of elliptical galaxies

Elliptical Galaxies. Houjun Mo. April 19, 2004. Basic properties of elliptical galaxies. Formation of elliptical galaxies Elliptical Galaxies Houjun Mo April 19, 2004 Basic properties of elliptical galaxies Formation of elliptical galaxies Photometric Properties Isophotes of elliptical galaxies are usually fitted by ellipses:

More information

Evolution of gravity-dark energy coupled expanding universe

Evolution of gravity-dark energy coupled expanding universe arxiv:1303.6568v1 [astro-ph.co] 26 Mar 2013 Evolution of gravity-dark energy coupled expanding universe Ti-Pei Li 1,2 and Mei Wu 2 1. Department of Physics & Center for Astrophysics, Tsinghua University,

More information

Searching for Cosmic Strings in New Obervational Windows

Searching for Cosmic Strings in New Obervational Windows 1 / 42 Searching for s in New Obervational Windows Robert Brandenberger McGill University Sept. 28, 2010 2 / 42 Outline 1 2 3 4 s in 5 3 / 42 Plan 1 2 3 4 s in 5 s T. Kibble, J. Phys. A 9, 1387 (1976);

More information

arxiv:astro-ph/0101553v1 31 Jan 2001

arxiv:astro-ph/0101553v1 31 Jan 2001 Evidence for Large Stellar Disks in Elliptical Galaxies. Andreas Burkert and Thorsten Naab Max-Planck-Institut für Astronomie, D-69242 Heidelberg, Germany arxiv:astro-ph/0101553v1 31 Jan 2001 Abstract.

More information

FIRST LIGHT IN THE UNIVERSE

FIRST LIGHT IN THE UNIVERSE FIRST LIGHT IN THE UNIVERSE Richard Ellis, Caltech 1. Role of Observations in Cosmology & Galaxy Formation 2. Galaxies & the Hubble Sequence 3. Cosmic Star Formation Histories 4. Stellar Mass Assembly

More information

Solutions to Problems in Goldstein, Classical Mechanics, Second Edition. Chapter 7

Solutions to Problems in Goldstein, Classical Mechanics, Second Edition. Chapter 7 Solutions to Problems in Goldstein, Classical Mechanics, Second Edition Homer Reid April 21, 2002 Chapter 7 Problem 7.2 Obtain the Lorentz transformation in which the velocity is at an infinitesimal angle

More information

A Study on the Comparison of Electricity Forecasting Models: Korea and China

A Study on the Comparison of Electricity Forecasting Models: Korea and China Communications for Statistical Applications and Methods 2015, Vol. 22, No. 6, 675 683 DOI: http://dx.doi.org/10.5351/csam.2015.22.6.675 Print ISSN 2287-7843 / Online ISSN 2383-4757 A Study on the Comparison

More information

New parameterization of cloud optical properties

New parameterization of cloud optical properties New parameterization of cloud optical properties proposed for model ALARO-0 Results of Prague LACE stay 1.8. 1.1005 under scientific supervision of Jean-François Geleyn J. Mašek, 11.1005 Main target of

More information

How to compute Random acceleration, velocity, and displacement values from a breakpoint table.

How to compute Random acceleration, velocity, and displacement values from a breakpoint table. How to compute Random acceleration, velocity, and displacement values from a breakpoint table. A random spectrum is defined as a set of frequency and amplitude breakpoints, like these: 0.050 Acceleration

More information

APPLIED MATHEMATICS ADVANCED LEVEL

APPLIED MATHEMATICS ADVANCED LEVEL APPLIED MATHEMATICS ADVANCED LEVEL INTRODUCTION This syllabus serves to examine candidates knowledge and skills in introductory mathematical and statistical methods, and their applications. For applications

More information

Linear Discrimination. Linear Discrimination. Linear Discrimination. Linearly Separable Systems Pairwise Separation. Steven J Zeil.

Linear Discrimination. Linear Discrimination. Linear Discrimination. Linearly Separable Systems Pairwise Separation. Steven J Zeil. Steven J Zeil Old Dominion Univ. Fall 200 Discriminant-Based Classification Linearly Separable Systems Pairwise Separation 2 Posteriors 3 Logistic Discrimination 2 Discriminant-Based Classification Likelihood-based:

More information

Multiple Optimization Using the JMP Statistical Software Kodak Research Conference May 9, 2005

Multiple Optimization Using the JMP Statistical Software Kodak Research Conference May 9, 2005 Multiple Optimization Using the JMP Statistical Software Kodak Research Conference May 9, 2005 Philip J. Ramsey, Ph.D., Mia L. Stephens, MS, Marie Gaudard, Ph.D. North Haven Group, http://www.northhavengroup.com/

More information

Section 5.0 : Horn Physics. By Martin J. King, 6/29/08 Copyright 2008 by Martin J. King. All Rights Reserved.

Section 5.0 : Horn Physics. By Martin J. King, 6/29/08 Copyright 2008 by Martin J. King. All Rights Reserved. Section 5. : Horn Physics Section 5. : Horn Physics By Martin J. King, 6/29/8 Copyright 28 by Martin J. King. All Rights Reserved. Before discussing the design of a horn loaded loudspeaker system, it is

More information

Sound. References: L.D. Landau & E.M. Lifshitz: Fluid Mechanics, Chapter VIII F. Shu: The Physics of Astrophysics, Vol. 2, Gas Dynamics, Chapter 8

Sound. References: L.D. Landau & E.M. Lifshitz: Fluid Mechanics, Chapter VIII F. Shu: The Physics of Astrophysics, Vol. 2, Gas Dynamics, Chapter 8 References: Sound L.D. Landau & E.M. Lifshitz: Fluid Mechanics, Chapter VIII F. Shu: The Physics of Astrophysics, Vol., Gas Dynamics, Chapter 8 1 Speed of sound The phenomenon of sound waves is one that

More information

Chapter 9 Summary and outlook

Chapter 9 Summary and outlook Chapter 9 Summary and outlook This thesis aimed to address two problems of plasma astrophysics: how are cosmic plasmas isotropized (A 1), and why does the equipartition of the magnetic field energy density

More information

Software challenges in the implementation of large surveys: the case of J-PAS

Software challenges in the implementation of large surveys: the case of J-PAS Software challenges in the implementation of large surveys: the case of J-PAS 1/21 Paulo Penteado - IAG/USP pp.penteado@gmail.com http://www.ppenteado.net/ast/pp_lsst_201204.pdf (K. Taylor) (A. Fernández-Soto)

More information

Estimation and attribution of changes in extreme weather and climate events

Estimation and attribution of changes in extreme weather and climate events IPCC workshop on extreme weather and climate events, 11-13 June 2002, Beijing. Estimation and attribution of changes in extreme weather and climate events Dr. David B. Stephenson Department of Meteorology

More information

A Universe of Galaxies

A Universe of Galaxies A Universe of Galaxies Today s Lecture: Other Galaxies (Chapter 16, pages 366-397) Types of Galaxies Habitats of Galaxies Dark Matter Other Galaxies Originally called spiral nebulae because of their shape.

More information

Cosmological Analysis of South Pole Telescope-detected Galaxy Clusters

Cosmological Analysis of South Pole Telescope-detected Galaxy Clusters Cosmological Analysis of South Pole Telescope-detected Galaxy Clusters March 24th Tijmen de Haan (McGill) - Moriond 2014 Photo credit: Keith Vanderlinde Outline The galaxy cluster sample Calibrating the

More information

Cosmic Surveys and the Composition of the Universe

Cosmic Surveys and the Composition of the Universe 2014 Shaw Lecture Essay in Astronomy Cosmic Surveys and the Composition of the Universe 1. Introduction Shaun Cole 1, Daniel J. Eisenstein 2, John A. Peacock 3 1: Institute for Computational Cosmology,

More information

Origins of the Cosmos Summer 2016. Pre-course assessment

Origins of the Cosmos Summer 2016. Pre-course assessment Origins of the Cosmos Summer 2016 Pre-course assessment In order to grant two graduate credits for the workshop, we do require you to spend some hours before arriving at Penn State. We encourage all of

More information

Gamma-rays from Dark Matter Mini-Spikes in Andromeda Galaxy M31. Mattia Fornasa Dipartimento di Fisica G. Galilei I.N.F.N. Padova

Gamma-rays from Dark Matter Mini-Spikes in Andromeda Galaxy M31. Mattia Fornasa Dipartimento di Fisica G. Galilei I.N.F.N. Padova Gamma-rays from Dark Matter Mini-Spikes in Andromeda Galaxy M31 Mattia Fornasa Dipartimento di Fisica G. Galilei I.N.F.N. Padova based on astro-ph/0703757 by M. Fornasa, M. Taoso and G.Bertone Journal

More information

Frequency-domain and stochastic model for an articulated wave power device

Frequency-domain and stochastic model for an articulated wave power device Frequency-domain stochastic model for an articulated wave power device J. Cândido P.A.P. Justino Department of Renewable Energies, Instituto Nacional de Engenharia, Tecnologia e Inovação Estrada do Paço

More information

Wave-particle and wave-wave interactions in the Solar Wind: simulations and observations

Wave-particle and wave-wave interactions in the Solar Wind: simulations and observations Wave-particle and wave-wave interactions in the Solar Wind: simulations and observations Lorenzo Matteini University of Florence, Italy In collaboration with Petr Hellinger, Simone Landi, and Marco Velli

More information

The Crafoord Prize 2005

The Crafoord Prize 2005 I N F O R M A T I O N F O R T H E P U B L I C The Royal Swedish Academy of Sciences has decided to award the Crafoord Prize in Astronomy 2005 to James Gunn, Princeton University, USA, James Peebles, Princeton

More information

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

More information

AS COMPETITION PAPER 2008

AS COMPETITION PAPER 2008 AS COMPETITION PAPER 28 Name School Town & County Total Mark/5 Time Allowed: One hour Attempt as many questions as you can. Write your answers on this question paper. Marks allocated for each question

More information

1 Introduction. 1 There may, of course, in principle, exist other universes, but they are not accessible to our

1 Introduction. 1 There may, of course, in principle, exist other universes, but they are not accessible to our 1 1 Introduction Cosmology is the study of the universe as a whole, its structure, its origin, and its evolution. Cosmology is soundly based on observations, mostly astronomical, and laws of physics. These

More information

Virtual Observatories A New Era for Astronomy. Reinaldo R. de Carvalho DAS-INPE/MCT 2010

Virtual Observatories A New Era for Astronomy. Reinaldo R. de Carvalho DAS-INPE/MCT 2010 Virtual Observatories Virtual Observatories 1%%&'&$#-&6!&9:#,*3),!#,6!6#$C!&,&$D2 *:#%&+-3;& D&);&-$2!!"! "!" &,&$D2 %),-&,-!"#$%&'&#()*! $#%&!(!!! $ '!%&$ $! (% %)'6!6#$C!;#--&$G $! '!!! $#63#-3),G $!

More information

Gravitation modifiée à grande distance & tests dans le système solaire 10 avril 2008

Gravitation modifiée à grande distance & tests dans le système solaire 10 avril 2008 Gravitation modifiée à grande distance et tests dans le système solaire Gilles Esposito-Farèse, GRεCO, IAP et Peter Wolf, LNE-SYRTE 10 avril 2008 Gravitation modifiée à grande distance & tests dans le

More information

Characterizing Digital Cameras with the Photon Transfer Curve

Characterizing Digital Cameras with the Photon Transfer Curve Characterizing Digital Cameras with the Photon Transfer Curve By: David Gardner Summit Imaging (All rights reserved) Introduction Purchasing a camera for high performance imaging applications is frequently

More information

A Preliminary Summary of The VLA Sky Survey

A Preliminary Summary of The VLA Sky Survey A Preliminary Summary of The VLA Sky Survey Eric J. Murphy and Stefi Baum (On behalf of the entire Science Survey Group) 1 Executive Summary After months of critical deliberation, the Survey Science Group

More information

Hubble Diagram S George Djorgovski. Encyclopedia of Astronomy & Astrophysics P. Murdin

Hubble Diagram S George Djorgovski. Encyclopedia of Astronomy & Astrophysics P. Murdin eaa.iop.org DOI: 10.1888/0333750888/2132 Hubble Diagram S George Djorgovski From Encyclopedia of Astronomy & Astrophysics P. Murdin IOP Publishing Ltd 2006 ISBN: 0333750888 Institute of Physics Publishing

More information

Chapter 23 The Beginning of Time

Chapter 23 The Beginning of Time Chapter 23 The Beginning of Time 23.1 The Big Bang Our goals for learning What were conditions like in the early universe? What is the history of the universe according to the Big Bang theory? What were

More information

ABSTRACT. We prove here that Newton s universal gravitation and. momentum conservation laws together reproduce Weinberg s relation.

ABSTRACT. We prove here that Newton s universal gravitation and. momentum conservation laws together reproduce Weinberg s relation. The Speed of Light and the Hubble parameter: The Mass-Boom Effect Antonio Alfonso-Faus E.U.I.T. Aeronáutica Plaza Cardenal Cisneros s/n 8040 Madrid, Spain ABSTRACT. We prove here that Newton s universal

More information

Cosmic Acceleration as an Optical Illusion

Cosmic Acceleration as an Optical Illusion Theoretische Physik TU Wien / Uni Bielefeld April 2016 / Bielefeld based on arxiv:1508.01510, PRD89 (2014) 043506 (arxiv:1310.1028), PRD90 (2014) 063523 (arxiv:1407.6602). Motivation and basics Motivation:

More information

Binary Stars. Kepler s Laws of Orbital Motion

Binary Stars. Kepler s Laws of Orbital Motion Binary Stars Kepler s Laws of Orbital Motion Kepler s Three Laws of orbital motion result from the solution to the equation of motion for bodies moving under the influence of a central 1/r 2 force gravity.

More information

The formation and evolution of massive galaxies: A major theoretical challenge

The formation and evolution of massive galaxies: A major theoretical challenge The formation and evolution of massive galaxies: A major theoretical challenge Thorsten Naab Max-Planck-Institute for Astrophysics L. Oser, M. Hilz, P. Johansson, J. P. Ostriker Tähtitieteilijäpäivät Haikko,

More information

Orbits of the Lennard-Jones Potential

Orbits of the Lennard-Jones Potential Orbits of the Lennard-Jones Potential Prashanth S. Venkataram July 28, 2012 1 Introduction The Lennard-Jones potential describes weak interactions between neutral atoms and molecules. Unlike the potentials

More information

8 Radiative Cooling and Heating

8 Radiative Cooling and Heating 8 Radiative Cooling and Heating Reading: Katz et al. 1996, ApJ Supp, 105, 19, section 3 Thoul & Weinberg, 1995, ApJ, 442, 480 Optional reading: Thoul & Weinberg, 1996, ApJ, 465, 608 Weinberg et al., 1997,

More information

DARK ENERGY, EXTENDED GRAVITY, AND SOLAR SYSTEM CONSTRAINTS BY DANIEL SUNHEDE

DARK ENERGY, EXTENDED GRAVITY, AND SOLAR SYSTEM CONSTRAINTS BY DANIEL SUNHEDE DEPARTMENT OF PHYSICS UNIVERSITY OF JYVÄSKYLÄ RESEARCH REPORT No. 4/2008 DARK ENERGY, EXTENDED GRAVITY, AND SOLAR SYSTEM CONSTRAINTS BY DANIEL SUNHEDE Academic Dissertation for the Degree of Doctor of

More information

arxiv:1207.3646v1 [cs.ce] 16 Jul 2012

arxiv:1207.3646v1 [cs.ce] 16 Jul 2012 jcis@epacis.org OGCOSMO: An auxiliary tool for the study of the Universe within hierarchical scenario of structure formation arxiv:1207.3646v1 [cs.ce] 16 Jul 2012 Eduardo S. Pereira 1, Oswaldo D. Miranda

More information

New Observational Windows to Probe Fundamental Physics

New Observational Windows to Probe Fundamental Physics 1 / 46 String String New Observational Windows to Probe Fundamental Physics Searching for String Signals Robert Brandenberger McGill University May 23, 2012 2 / 46 Outline 1 String String 2 String 3 String

More information

Magnetic Field of a Circular Coil Lab 12

Magnetic Field of a Circular Coil Lab 12 HB 11-26-07 Magnetic Field of a Circular Coil Lab 12 1 Magnetic Field of a Circular Coil Lab 12 Equipment- coil apparatus, BK Precision 2120B oscilloscope, Fluke multimeter, Wavetek FG3C function generator,

More information

Modelling, Extraction and Description of Intrinsic Cues of High Resolution Satellite Images: Independent Component Analysis based approaches

Modelling, Extraction and Description of Intrinsic Cues of High Resolution Satellite Images: Independent Component Analysis based approaches Modelling, Extraction and Description of Intrinsic Cues of High Resolution Satellite Images: Independent Component Analysis based approaches PhD Thesis by Payam Birjandi Director: Prof. Mihai Datcu Problematic

More information

Understanding the Accelerating Universe using the MSE. Gong-Bo Zhao NAOC

Understanding the Accelerating Universe using the MSE. Gong-Bo Zhao NAOC Understanding the Accelerating Universe using the MSE Gong-Bo Zhao NAOC Nobel Prize 2011 a > 0 The expansion of the Universe can accelerate if In GR, to add new repulsive matter, which contributes 70%

More information

AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false?

AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The

More information

Exploring dark energy models with linear perturbations: Fluid vs scalar field. Masaaki Morita (Okinawa Natl. College Tech., Japan)

Exploring dark energy models with linear perturbations: Fluid vs scalar field. Masaaki Morita (Okinawa Natl. College Tech., Japan) Exploring dark energy models with linear perturbations: Fluid vs scalar field Masaaki Morita (Okinawa Natl. College Tech., Japan) September 11, 008 Seminar at IAP, 008 1 Beautiful ocean view from my laboratory

More information

Transcript 22 - Universe

Transcript 22 - Universe Transcript 22 - Universe A few introductory words of explanation about this transcript: This transcript includes the words sent to the narrator for inclusion in the latest version of the associated video.

More information

Detecting and measuring faint point sources with a CCD

Detecting and measuring faint point sources with a CCD Detecting and measuring faint point sources with a CCD Herbert Raab a,b a Astronomical ociety of Linz, ternwarteweg 5, A-400 Linz, Austria b Herbert Raab, chönbergstr. 3/1, A-400 Linz, Austria; herbert.raab@utanet.at

More information

Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of this system is: k m therefore, k

Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of this system is: k m therefore, k Physics 1C Midterm 1 Summer Session II, 2011 Solutions 1. If F = kx, then k m is (a) A (b) ω (c) ω 2 (d) Aω (e) A 2 ω Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of

More information

RANDOM VIBRATION AN OVERVIEW by Barry Controls, Hopkinton, MA

RANDOM VIBRATION AN OVERVIEW by Barry Controls, Hopkinton, MA RANDOM VIBRATION AN OVERVIEW by Barry Controls, Hopkinton, MA ABSTRACT Random vibration is becoming increasingly recognized as the most realistic method of simulating the dynamic environment of military

More information

Lecture - 4 Diode Rectifier Circuits

Lecture - 4 Diode Rectifier Circuits Basic Electronics (Module 1 Semiconductor Diodes) Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Lecture - 4 Diode Rectifier Circuits

More information

On a Flat Expanding Universe

On a Flat Expanding Universe Adv. Studies Theor. Phys., Vol. 7, 2013, no. 4, 191-197 HIKARI Ltd, www.m-hikari.com On a Flat Expanding Universe Bo Lehnert Alfvén Laboratory Royal Institute of Technology, SE-10044 Stockholm, Sweden

More information

PHYSICS FOUNDATIONS SOCIETY THE DYNAMIC UNIVERSE TOWARD A UNIFIED PICTURE OF PHYSICAL REALITY TUOMO SUNTOLA

PHYSICS FOUNDATIONS SOCIETY THE DYNAMIC UNIVERSE TOWARD A UNIFIED PICTURE OF PHYSICAL REALITY TUOMO SUNTOLA PHYSICS FOUNDATIONS SOCIETY THE DYNAMIC UNIVERSE TOWARD A UNIFIED PICTURE OF PHYSICAL REALITY TUOMO SUNTOLA Published by PHYSICS FOUNDATIONS SOCIETY Espoo, Finland www.physicsfoundations.org Printed by

More information

The Technical Archer. Austin Wargo

The Technical Archer. Austin Wargo The Technical Archer Austin Wargo May 14, 2010 Abstract A mathematical model of the interactions between a long bow and an arrow. The model uses the Euler-Lagrange formula, and is based off conservation

More information

Least Squares Estimation

Least Squares Estimation Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN-13: 978-0-470-86080-9 ISBN-10: 0-470-86080-4 Editors Brian S Everitt & David

More information

This paper is also taken for the relevant Examination for the Associateship. For Second Year Physics Students Wednesday, 4th June 2008: 14:00 to 16:00

This paper is also taken for the relevant Examination for the Associateship. For Second Year Physics Students Wednesday, 4th June 2008: 14:00 to 16:00 Imperial College London BSc/MSci EXAMINATION June 2008 This paper is also taken for the relevant Examination for the Associateship SUN, STARS, PLANETS For Second Year Physics Students Wednesday, 4th June

More information

Amptek Application Note XRF-1: XRF Spectra and Spectra Analysis Software By R.Redus, Chief Scientist, Amptek Inc, 2008.

Amptek Application Note XRF-1: XRF Spectra and Spectra Analysis Software By R.Redus, Chief Scientist, Amptek Inc, 2008. Amptek Application Note XRF-1: XRF Spectra and Spectra Analysis Software By R.Redus, Chief Scientist, Amptek Inc, 2008. X-Ray Fluorescence (XRF) is a very simple analytical technique: X-rays excite atoms

More information

CS 591.03 Introduction to Data Mining Instructor: Abdullah Mueen

CS 591.03 Introduction to Data Mining Instructor: Abdullah Mueen CS 591.03 Introduction to Data Mining Instructor: Abdullah Mueen LECTURE 3: DATA TRANSFORMATION AND DIMENSIONALITY REDUCTION Chapter 3: Data Preprocessing Data Preprocessing: An Overview Data Quality Major

More information

Manufacturing Equipment Modeling

Manufacturing Equipment Modeling QUESTION 1 For a linear axis actuated by an electric motor complete the following: a. Derive a differential equation for the linear axis velocity assuming viscous friction acts on the DC motor shaft, leadscrew,

More information

Perfect Fluidity in Cold Atomic Gases?

Perfect Fluidity in Cold Atomic Gases? Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 Elliptic Flow Hydrodynamic expansion converts coordinate space anisotropy to momentum space anisotropy Anisotropy

More information

A high accuracy, small field of view star guider with application to SNAP.

A high accuracy, small field of view star guider with application to SNAP. A high accuracy, small field of view star guider with application to SNAP. Aurélia Secroun and Michael Lampton Space Sciences Laboratory, U.C. Berkeley Michael Levi Lawrence Berkeley National Laboratory,

More information

Frequency response: Resonance, Bandwidth, Q factor

Frequency response: Resonance, Bandwidth, Q factor Frequency response: esonance, Bandwidth, Q factor esonance. Let s continue the exploration of the frequency response of circuits by investigating the series circuit shown on Figure. C + V - Figure The

More information

Measuring Line Edge Roughness: Fluctuations in Uncertainty

Measuring Line Edge Roughness: Fluctuations in Uncertainty Tutor6.doc: Version 5/6/08 T h e L i t h o g r a p h y E x p e r t (August 008) Measuring Line Edge Roughness: Fluctuations in Uncertainty Line edge roughness () is the deviation of a feature edge (as

More information