Precise measures of growth rate from RSD in the void-galaxy correlation

Transcription

1 Precise measures of growth rate from RSD in the void-galaxy correlation Seshadri Nadathur Moriond Cosmology, La Thuile

2 Based on work with Paul Carter and Will Percival SN & Percival, arxiv: SN, Carter & Percival, due soon

3 Motivation Improving modelling of void-galaxy RSD Problems with measuring void-galaxy RSD Solutions

4 Motivation - Voids might be great tools for Alcock-Paczynski measurement with Stage-IV survey data Potentially outperform BAO with Euclid? Lavaux & Wandelt 2012 wa But RSD is degenerate with AP distortions, need precise RSD modelling! w 0 - Environment-dependence of growth rate! f = dlnd dlna density-dependent screening in modified gravity models

5 A note All simulation results shown in this talk are from custom-made mock void and galaxy catalogues from the Big MultiDark simulation The mock galaxies match CMASS galaxies, z = 0.52 Void-finding uses ZOBOV algorithm though results are quite general

6 The void-galaxy correlation function vg (r) : cross-correlation between void and galaxy positions (equivalent to the galaxy density profile around a void) Real space Redshift space

7 A linear model Assumption #1: number of void-galaxy pairs conserved (1 + s (s)) d 3 s =(1+ r (r)) d 3 r Assumption #2: RSD due to galaxy motions only s = r + v ˆX ah ˆX Assumption #3: Linear dynamics, governed by void alone v(r) = 1 3 fah (r)r v rˆr ; (r) 3 r 3 Z r 0 (y)y 2 dy

8 A linear model Assumption #1 + Assumption #2 + Assumption #3 gives 1+ s (s) =(1+ r (r)) apple 1 f 3 (r) fµ 2 ( (r) (r)) 1 Expand to linear order in,

9 Linear model, take 1 s (r, µ) = r (r)+ f 3 (r) + fµ 2 [ (r) (r)] Cai, Taylor, Peacock, Padilla 2016 (see also Hamaus et al. 2017) Pro: simple, nice quadrupole-to-monopole estimator for f Con: doesn t work well in void centres

10 Linear model, take 1 s (r, µ) = r (r)+ f 3 (r) + fµ 2 [ (r) (r)] Cai, Taylor, Peacock, Padilla 2016 (see also Hamaus et al. 2017) (simulation) data

11 Linear model, take 1 s (r, µ) = r (r)+ f 3 (r) + fµ 2 [ (r) (r)] Cai, Taylor, Peacock, Padilla 2016 (see also Hamaus et al. 2017) model

12 Linear model, take 1 s (r, µ) = r (r)+ f 3 (r) + fµ 2 [ (r) (r)] Cai, Taylor, Peacock, Padilla 2016 (see also Hamaus et al. 2017) residuals (data model)

13 Improved linear model s (s, µ) = r (r)+ f 3 (r)(1+ r (r)) + fµ 2 [ (r) (r)] (1 + r (r)) SN & Percival 2017

14 Improved linear model s (s, µ) = r (r)+ f 3 (r)(1 + r (r)) +fµ 2 [ (r) (r)] (1 + r (r)) Key features: SN & Percival 2017, are linear order inside voids!

15 Improved linear model s (s, µ) = r (r)+ f 3 (r)(1 + r (r)) +fµ 2 [ (r) (r)] (1 + r (r)) Key features: SN & Percival 2017, are linear order inside voids!

16 Improved linear model s (s, s µ) = r (r)+ r f 3 (r)(1 + r (r)) +fµ 2 [ (r) (r)] (1 + r (r)) Key features: SN & Percival 2017, are linear order inside voids! Coordinate shift important at linear order! (r) = (s)+ 0 (s) f 3 s (s)µ2 +...

17 Improved linear model s (s, s µ) = r (r)+ r f 3 (r)(1 + r (r)) +fµ 2 [ (r) (r)] (1 + r (r)) Key features: SN & Percival 2017, are linear order inside voids! Coordinate shift important at linear order! (r) = (s)+ 0 (s) f 3 s (s)µ Linear galaxy bias does not hold, (r) 6= b (r)

18 Improved linear model s (s, s µ) = r (r)+ r f 3 (r)(1 + r (r)) +fµ 2 [ (r) (r)] (1 + r (r)) Key features: SN & Percival 2017, are linear order inside voids! Coordinate shift important at linear order! (r) = (s)+ 0 (s) f 3 s (s)µ Linear galaxy bias does not hold, (r) 6= b (r)

19 Improved linear model Much better residuals! old model residuals new model residuals

20 Why does a linear RSD model fit so well? Linear theory for velocities in voids is very good: SN & Percival 2017

21 Why doesn t this RSD model fit perfectly? Dispersion around coherent outflow is large: SN & Percival 2017

22 Adding velocity dispersion to the model Allow for a dispersion in los velocities, v = v rˆr + v ˆX, then: 1+ s (, ) = Z dv P (v )(1 + r (r)) J s r 1 assume Gaussian pdf, can be scale-dependent expand to linear order as before SN & Percival 2017

23 Adding velocity dispersion to the model Allow for a dispersion in los velocities, v = v rˆr + v ˆX, then: 1+ s (, ) = Z dv P (v )(1 + r (r)) J s r 1 Note, not 1+ s (, ) = Z (1 + r (r)) p 2 v (v v r (r)µ) 2 exp 2 2 v dv standard streaming model result does not hold for voids (ask me why later!) SN & Percival 2017

24 Improved linear model with dispersion Even better residuals without dispersion with dispersion

25 Multipole expansion To linear order, only monopole and quadrupole are non-zero monopole quadrupole SN & Percival 2017

26 Multipole expansion To linear order, only monopole and quadrupole are non-zero monopole difference quadrupole Completely linear RSD model works well on all scales SN & Percival 2017

27 Fitting for the growth rate Fitting requires 3 functions as input: r (r) (r) v (r),, either from simulation OR reconstructed from data (must be?) calibrated from simulation Parameter that is fit is f (not f 8!)

28 Fitting for the growth rate Fitting requires 3 functions as input: r (r) (r) v (r),, either from simulation OR reconstructed from data (must be?) calibrated from simulation f =0.78 ± 0.02 (2.7%) using all separation scales f =0.77 ± 0.02 (2.8%) using only scales within mean void scale (f fid =0.761) SN & Percival 2017

29 A major problem e.g. void-finding galaxy field in redshift space A non-linear transformation of a tracer density field after RSD mapping must have RSD itself, and also a velocity bias Seljak 2012, =) Voids found in redshift-space galaxies have RSD themselves Chuang et al 2017 This violates assumption #2 (RSD due to galaxy motions alone)! s = r + v ˆX ah ˆX (Also assumption #1 void numbers not conserved in redshift space) Modelling will be invalid if voids found using redshift-space galaxies

30 A major problem can t be modelled? can t be measured? SN, Carter & Percival, in prep.

31 Solution: reconstruction of real-space galaxy field Eulerian posn. as Lagrangian posn. + displacement, x(q,t)=q + (q,t) Smooth redshift-space galaxy field and solve for displacement: r + f b r ( ˆr )ˆr = g b Remove (linear, Kaiser) RSD component of displacement: RSD = f( ˆr )ˆr Iterate until convergence (2-3 iterations) Obtain pseudo real-space galaxy distribution SN, Carter & Percival, in prep.

32 Reconstruction works can be measured! + can be modelled PRELIMINARY SN, Carter & Percival, in prep.

33 Avoiding circularity Choose parameters f,b Solve for RSD Reconstruct pseudo real-space galaxy field Find voids, measure r If not finished, new parameters Calculate theory for given ; 2 get for fit to data If finished, construct likelihood f Cross-correlate with redshift-space galaxies; measure multipoles SN, Carter & Percival, in prep.

34 Results Keeping bias fixed, Marginalising over bias, f = consistent with fiducial at 1-sigma f = (68% c.l.) consistent with fiducial at 2-sigma (68% c.l.) PRELIMINARY (f fid =0.761) SN, Carter & Percival, in prep.

35 Summary Void-galaxy RSD measurements probe interesting physics, not the same as galaxy correlation A completely linear RSD model is sufficient on all scales! We made major improvements in the modelling The improved model allows precise constraints on growth rate in low density regions Practical issues with measurement are very important, but can be mostly solved using a reconstruction technique Further investigation very much required!

36 spare slides

37 The streaming model 1+ s (, ) = Z dr d 2 e i (r ) Z(if, r) Galaxy autocorrelation Void-galaxy correlation Z(if, r) =he if u z (1 + (x))(1 + (x 0 ))i Z(if, r) =he if u z (1 + r (r))i Average over all space, so h (x)i =0 (and in Gaussian approx., all odd cumulants are zero) Constrained average h r (r)i 6=0 (by definition!) etc. etc.

38 changing void centre doesn t affect conclusions

39 changing void centre doesn t affect conclusions

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