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
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
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
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) D L ( z obs ) M = M obs + 5 log 10 D L ( z ) • To first order in linear theory ( c = 1 ): z obs − z = V ( t , r ) − Φ ( t , r ) − ISW ≈ V ( t , r ) 1 + z obs • Maximize probability of observing galaxies given their magnitudes and redshifts: φ ( M i ) log P tot = � log P i ( M i | z i , V i ) = � b i i a i 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
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: ˜ r ) = � V (ˆ a lm Y lm (ˆ r ) l , m • For large galaxy numbers, likelihood function is well approximated by a Gaussian (simplifies computation enormously): log P tot ( d | x ) ≈ − 1 2( x − x 0 ) T Σ − 1 ( x − x 0 ) + const , where x T = � � { q j } , { a lm } • Marginalize over LF parameters { q j } and construct posterior for C l = � | a lm | 2 � by applying Bayes’ theorem: � P ( { C l } ) ∝ P ( d |{ a lm } ) P ( { a lm }|{ C l } ) da lm • Assume { a lm } as normally distributed • For a Λ CDM model prior, C l = C l ( { c k } ) : � l j l 2 � �� C l = 2 � � � � dkk 2 P Φ ( k ) � drW ( r ) r − k j l + 1 � � � π � � � �
Motivation / Methodology Application to SDSS DR7 Conclusions Outline 1 Motivation / Methodology 2 Application to SDSS DR7 “Bulk flows” Estimating C l ’s Cosmological constraints 3 Conclusions
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 < m r < 17 . 6 • − 22 . 5 < M obs < − 17 . 0 • Consider two velocity bins: 0 . 02 < z 1 < 0 . 07 < z 2 < 0 . 22 • N 1 ∼ 1 . 5 × 10 5 , N 2 ∼ 3 . 5 × 10 5 • Adopt pre-Planck cosmological parameters (Calabrese et al. 2013) • Realistic mocks for testing → SDSS footprint → photometric offsets between stripes → overall tilt over the sky
Motivation / Methodology Application to SDSS DR7 Conclusions LF estimators “Non-parametric” spline-estimator of φ ( M ) • Normalization unimportant for our analysis 1 • Two-parameter Schechter function does 0 . 1 r -band quite well 0.1 • To reduce errors, adopt more flexible form for φ ( M ) φ [ ( Mpc / h ) − 3 ] 0.4 • Model φ ( M ) as a spline with sampling points { φ j ( M ) } for M j < M < M j + 1 0.01 0.2 • Advantage: smoothness, nice analytic -19 -18 -17 properties for integrals / derivatives) Q 0 = 1 . 60 ± 0 . 11 0.001 • Parameterize luminosity evolution: M ⋆ − 5log 10 h = − 20 . 52 ± 0 . 04 α ⋆ = − 1 . 10 ± 0 . 03 � z 2 � e ( z ) = Q 0 ( z − z 0 ) + O -23 -22 -21 -20 -19 -18 -17 M r − 5log 10 h
Motivation / Methodology Application to SDSS DR7 Conclusions “Bulk flow” estimates for SDSS DR7 Mocks versus data Estimates for the “dipole” • Mask allows only measurement of 70 � K = 5 ± 169 combined multipoles � K = 19 ± 194 60 • First z -bin: v x = − 175 ( − 227 , − 151) ± 126 km/s 50 Number of mocks v y = − 278 ( − 326 , − 277) ± 111 km/s v z = − 147 ( − 239 , − 102) ± 70 km/s 40 • Second z -bin: 30 v x = − 340 ( − 367 , − 423) ± 90 km/s v y = − 409 ( − 439 , − 492) ± 81 km/s 20 v z = − 45 ( − 25 , − 150) ± 69 km/s • “Kashlinsky-direction” 10 v 1 ≈ 120 ± 115 km/s 0 v 2 ≈ 355 ± 80 km/s -600 -400 -200 0 200 400 600 � K [km/s]
Motivation / Methodology Application to SDSS DR7 Conclusions Constraints on the power spectrum Influence of a photometric tilt (random mock, l max = 2 ) 0 . 02 < z < 0 . 07 0 . 02 < z < 0 . 07 160 0 . 07 < z < 0 . 22 0 . 07 < z < 0 . 22 120 C 2 [km/s] ˜ 80 40 0 0 100 200 300 0 100 200 300 ˜ ˜ C 1 [km/s] C 1 [km/s]
Motivation / Methodology Application to SDSS DR7 Conclusions Constraints on the power spectrum Results for SDSS data ( l max = 2 , 3 ) 250 C 1 vs. ˜ ˜ l max = 3 C 2 C 1 vs. ˜ ˜ C 3 l max = 2 200 C 2 vs. ˜ ˜ C 3 200 150 C j [km/s] 150 C 2 [km/s] ˜ 100 ˜ 100 50 50 0 0 0 50 100 150 200 250 300 0 100 200 300 400 500 ˜ C i [km/s] ˜ C 1 [km/s]
Motivation / Methodology Application to SDSS DR7 Conclusions Constraints on σ 8 Results from mock analysis ( l max = 5 ) σ 8 = 1 . 32 ± 0 . 38 σ 8 = 0 . 93 ± 0 . 40 35 both bins low- z bin only σ 8 = 0 . 86 ± 0 . 34 σ 8 = 0 . 85 ± 0 . 40 30 25 Number of mocks 20 15 10 5 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 σ 8 σ 8
Motivation / Methodology Application to SDSS DR7 Conclusions Constraints on σ 8 Results from SDSS data analysis ( l max = 5 ) 5 σ 8 = 1 . 61 ± 0 . 38 σ 8 = 1 . 08 ± 0 . 53 σ 8 = 1 . 52 ± 0 . 37 σ 8 = 1 . 01 ± 0 . 45 4 σ 8 = 1 . 55 ± 0 . 40 σ 8 = 1 . 06 ± 0 . 51 3 ∆χ 2 2 1 both bins low- z bin only 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 σ 8 σ 8
Motivation / Methodology Application to SDSS DR7 Conclusions Constraints on σ 8 Results from SDSS data analysis ( l max = 5 ) 5 σ 8 = 1 . 61 ± 0 . 38 σ 8 = 1 . 08 ± 0 . 53 σ 8 = 1 . 52 ± 0 . 37 σ 8 = 1 . 01 ± 0 . 45 4 σ 8 = 1 . 55 ± 0 . 40 σ 8 = 1 . 06 ± 0 . 51 3 σ 8 ≈ 1 . 1 ± 0 . 4 σ 8 ≈ 1 . 0 ± 0 . 5 ∆χ 2 2 1 both bins low- z bin only 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 σ 8 σ 8
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)
Motivation / Methodology Application to SDSS DR7 Conclusions Outline 1 Motivation / Methodology 2 Application to SDSS DR7 3 Conclusions
Motivation / Methodology Application to SDSS DR7 Conclusions Conclusions • ML estimators extracting the large-scale velocity field through variations in the observed 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 Λ CDM 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
Recommend
More recommend
