Outline 1 Motivation / Methodology Peculiar velocities from LF - - PowerPoint PPT Presentation

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Outline 1 Motivation / Methodology Peculiar velocities from LF - - PowerPoint PPT Presentation

May 13, 2023 292 likes •475 views

Motivation / Methodology Application to SDSS DR7 Conclusions Tracing the cosmic velocity field at z 0 . 1 from galaxy luminosities in the SDSS DR7 Martin Feix (with Adi Nusser and Enzo Branchini; arXiv:1405.6710) Department of Physics,

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SLIDE 1

Motivation / Methodology Application to SDSS DR7 Conclusions

Tracing the cosmic velocity field at z ∼ 0.1 from galaxy luminosities in the SDSS DR7

Martin Feix

(with Adi Nusser and Enzo Branchini; arXiv:1405.6710)

Department of Physics, Technion, Haifa Frontiers of Fundamental Physics XIV, Marseille July 15th 2014

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SLIDE 2

Motivation / Methodology Application to SDSS DR7 Conclusions

Outline

1 Motivation / Methodology

Peculiar velocities from LF variations Estimating power spectra

2 Application to SDSS DR7 3 Conclusions

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SLIDE 3

Motivation / Methodology Application to SDSS DR7 Conclusions

The large-scale peculiar velocity field

A cosmological probe

  • No bias issues:

→ Galaxies are honest tracers

  • Common approaches:

→ Velocity catalogs → SNe, kSZ effect → Systematics?

  • Need for novel approaches
  • Go beyond current limitations and

simple BF estimation

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SLIDE 4

Motivation / Methodology Application to SDSS DR7 Conclusions

Peculiar velocities from LF variations

Basic concept

  • Peculiar motion introduces systematic variations in the observed luminosity

distribution of galaxies (Nusser et al. 2011; Tammann et al. 1979) M = Mobs + 5 log10 DL(zobs) DL(z)

  • To first order in linear theory (c = 1):

zobs − z 1 + zobs = V(t, r) − Φ(t, r) − ISW ≈ V(t, r)

  • Maximize probability of observing galaxies given their magnitudes and redshifts:

log Ptot =

i

log Pi(Mi|zi, Vi) = φ(Mi) bi

ai φ(M)dM

  • Method independent of galaxy bias and traditional distance indicators
  • However: meaningful results require large number statistics

→ large galaxy (spectroscopic or photometric) redshift surveys

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SLIDE 5

Motivation / Methodology Application to SDSS DR7 Conclusions

Peculiar velocities from LF variations

Velocity model and large-scale power estimation

  • Our approach: sample velocity field in redshift bins: V(t, r) → ˜

V(ˆ r)

  • Expand binned velocity field in SHs:

˜ V(ˆ r) =

l,m

almYlm(ˆ r)

  • For large galaxy numbers, likelihood function is well approximated by a Gaussian

(simplifies computation enormously): log Ptot(d|x) ≈ −1 2(x − x0)T Σ−1(x − x0) + const, where xT =

  • {q j}, {alm}
  • Marginalize over LF parameters {q j} and construct posterior for Cl =
  • |alm|2

by applying Bayes’ theorem: P ({Cl}) ∝

  • P (d|{alm}) P ({alm}|{Cl}) dalm
  • Assume {alm} as normally distributed
  • For a ΛCDM model prior, Cl = Cl ({ck}):

Cl = 2 π

  • dkk2PΦ(k)
  • drW(r)

l jl r − k jl+1

  • 2
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SLIDE 6

Motivation / Methodology Application to SDSS DR7 Conclusions

Outline

1 Motivation / Methodology 2 Application to SDSS DR7

“Bulk flows” Estimating Cl’s Cosmological constraints

3 Conclusions

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SLIDE 7

Motivation / Methodology Application to SDSS DR7 Conclusions

SDSS Data Release 7 Galaxy Catalog

NYU Value-Added Galaxy Catalog (Blanton et al. 2005)

  • Use r-band magnitudes (Petrosian)
  • 14.5 < mr < 17.6
  • −22.5 < Mobs < −17.0
  • Consider two velocity bins:

0.02 < z1 < 0.07 < z2 < 0.22

  • N1 ∼ 1.5 × 105, N2 ∼ 3.5 × 105
  • Adopt pre-Planck cosmological parameters

(Calabrese et al. 2013)

  • Realistic mocks for testing

→ SDSS footprint → photometric offsets between stripes → overall tilt over the sky

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SLIDE 8

Motivation / Methodology Application to SDSS DR7 Conclusions

LF estimators

“Non-parametric” spline-estimator of φ(M)

0.4 0.2 0.1r-band α⋆ = −1.10±0.03 M⋆ −5log10 h = −20.52±0.04 Q0 = 1.60±0.11

  • 18
  • 19
  • 17

0.001 0.01 0.1 1

  • 20
  • 19
  • 18
  • 17

φ [(Mpc/h)−3] Mr −5log10h

  • 23
  • 22
  • 21
  • Normalization unimportant for our analysis
  • Two-parameter Schechter function does

quite well

  • To reduce errors, adopt more flexible form

for φ(M)

  • Model φ(M) as a spline with sampling

points {φj(M)} for M j < M < M j+1

  • Advantage: smoothness, nice analytic

properties for integrals / derivatives)

  • Parameterize luminosity evolution:

e(z) = Q0(z − z0) + O

  • z2
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SLIDE 9

Motivation / Methodology Application to SDSS DR7 Conclusions

“Bulk flow” estimates for SDSS DR7

Mocks versus data

K = 19±194 K = 5±169 10 20 30 40 50 60 70

  • 600
  • 400
  • 200

200 400

Number of mocks

600

K [km/s]

Estimates for the “dipole”

  • Mask allows only measurement of

combined multipoles

  • First z-bin:

vx = −175 (−227, −151) ± 126 km/s vy = −278 (−326, −277) ± 111 km/s vz = −147 (−239, −102) ± 70 km/s

  • Second z-bin:

vx = −340 (−367, −423) ± 90 km/s vy = −409 (−439, −492) ± 81 km/s vz = −45 (−25, −150) ± 69 km/s

  • “Kashlinsky-direction”

v1 ≈ 120 ± 115 km/s v2 ≈ 355 ± 80 km/s

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SLIDE 10

Motivation / Methodology Application to SDSS DR7 Conclusions

Constraints on the power spectrum

Influence of a photometric tilt (random mock, lmax = 2)

0.02 < z < 0.07 0.07 < z < 0.22 0.02 < z < 0.07 0.07 < z < 0.22 200 300

˜ C1 [km/s]

40 80 100 200 300 160

˜ C2 [km/s] ˜ C1 [km/s]

100 120

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SLIDE 11

Motivation / Methodology Application to SDSS DR7 Conclusions

Constraints on the power spectrum

Results for SDSS data (lmax = 2, 3)

lmax = 2 50 100 150 200 100 200 300 400 500

˜ C2 [km/s] ˜ C1 [km/s]

lmax = 3 ˜ C1 vs. ˜ C3 ˜ C2 vs. ˜ C3 ˜ C1 vs. ˜ C2 50 100 150 200 250 50 150 200 250 300

˜ Ci [km/s] ˜ Cj [km/s]

100

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SLIDE 12

Motivation / Methodology Application to SDSS DR7 Conclusions

Constraints on σ8

Results from mock analysis (lmax = 5)

σ8 = 0.93±0.40 σ8 = 0.85±0.40 σ8 = 1.32±0.38 σ8 = 0.86±0.34 low-z bin only both bins 10 15 20 25 30 0.5 1 1.5 2

Number of mocks

35 5 0.5

σ8 σ8

1 1.5 2

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SLIDE 13

Motivation / Methodology Application to SDSS DR7 Conclusions

Constraints on σ8

Results from SDSS data analysis (lmax = 5)

σ8 = 1.61±0.38 σ8 = 1.52±0.37 σ8 = 1.55±0.40 σ8 = 1.08±0.53 σ8 = 1.01±0.45 σ8 = 1.06±0.51 both bins low-z bin only 0.5 1 1.5 2 1 2 3 4 5 0.5 1 1.5 2

∆χ2 σ8 σ8

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SLIDE 14

Motivation / Methodology Application to SDSS DR7 Conclusions

Constraints on σ8

Results from SDSS data analysis (lmax = 5)

σ8 = 1.61±0.38 σ8 = 1.52±0.37 σ8 = 1.55±0.40 σ8 = 1.08±0.53 σ8 = 1.01±0.45 σ8 = 1.06±0.51 both bins low-z bin only 0.5 1 1.5 2 1 2 3 4 5 0.5 1 1.5 2

∆χ2 σ8 σ8

σ8 ≈ 1.1 ± 0.4 σ8 ≈ 1.0 ± 0.5

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SLIDE 15

Motivation / Methodology Application to SDSS DR7 Conclusions

Alternative way to estimate the growth rate

Constraints on β in the local Universe from 2MRS (Branchini et al. 2012)

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Motivation / Methodology Application to SDSS DR7 Conclusions

Outline

1 Motivation / Methodology 2 Application to SDSS DR7 3 Conclusions

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Motivation / Methodology Application to SDSS DR7 Conclusions

Conclusions

  • ML estimators extracting the large-scale velocity field through variations in the
  • bserved LF of galaxies offer a powerful and complementary alternative to currently

used methods

  • Especially at high redshifts, such approaches (appropriately modified) may provide

the only way of collecting any meaningful information

  • SDSS data are fully consistent with the standard ΛCDM cosmology
  • Low-z results robust, high-z results in agreement with known 1% photometric tilt
  • Findings are compatible with results from the Planck collaboration (upper BF limit

≈ 250 km/s at a 95% confidence limit)

  • Method may be useful for checking / detecting systematics in photometric calibration
  • Currently tackled: environmental dependence of the LF, estimation of β through

modeling of density field, new datasets