Nonlinear reconstruction Yu Yu (SJTU) Tianlai Workshop, 17 Sep 2018 - - PowerPoint PPT Presentation

Nonlinear reconstruction

Yu Yu (SJTU) Tianlai Workshop, 17 Sep 2018

OUTLINE

➤ Motivation ➤ Nonlinear reconstruction ➤ On BAO ➤ On RSD ➤ On velocity field ➤ Conclusion

Nonlinear evolution

Correlation between different k-bins Information saturation

Rimes & Hamilton 2005

BAO reconstruction

linear continuity equation Padmanabhan+ 2012

BAO reconstruction

➤ Sharper peak / weaker damping z=49 z=0.3

• recon. w/ 10 Mpc/h s
• recon. w/ 20 Mpc/h s

Eisenstein+ 2007 Seo+ 2016 damped BAO wiggles = linear wiggle * damping

BAO reconstruction

Padmanabhan+ 2012

heavy smooth to validate the linear continuity equation Linear displacement

OUTLINE

➤ Motivation ➤ Nonlinear reconstruction ➤ On BAO ➤ On RSD ➤ On velocity field ➤ Conclusion

NEW reconstruction method

➤ solve for a curvilinear coordinate, in which the mass per grid

is constant.

NEW reconstruction method

➤ solve for a curvilinear coordinate, in which the mass per grid is

constant.

Algorithm

➤ Moving mesh approach ➤ Originally used in moving mesh simulation (N-body and

hydrodynamic; see Pen 1995 & 1998)

➤ solve for a mesh following the nonlinear density evolution ➤ to keep (approximately) constant mass/energy resolution ➤ In our case, we need solve for a mesh consistent with the

nonlinear density field, perturbatively and iteratively.

➤ POTENTIAL ISOBARIC GAUGE/COORDINATE

➤

Provide us an estimate of the E-mode displacement.

NEW reconstruction method

Displacement

➤ We could reconstruct the E-mode component, ψENL + ψEL

OUTLINE

➤ Motivation ➤ Nonlinear reconstruction ➤ On BAO ➤ On RSD ➤ Other applications ➤ Conclusion

Comparison with linear field

Zhu, YU and Pen (2016) up-limit Cross-correlation coefficient point to point comparison

Acoustic peak recovery

Wang et al. (2017) linear up-limit This method standard nonlinear

Fractional error on the distance measurement

linear limit Eisenstein’s a factor of 1.8 improvement Wang et al. (2017) nonlinear density New recon. a factor of 2.7 improvement

Halo fields

Yu et al. (2017)

Cross- correlation coefficient dark matter nh=2.77×10-2 (h/Mpc)3 nh=2.77×10-3 (h/Mpc)3 nh=2.77×10-4 (h/Mpc)3

Summary for BAO reconstruction

➤ For DM field, the fractional error in BAO measurement is

reduced by a factor of 2.7, close to the linear limit.

➤ For SDSS-like sample, the characteristic scale is improved to

k>0.36 h/Mpc, a factor of 2.29 improvement in scale, or 12 in number of linear modes.

➤ We expect this to substantially improve the BAO accuracy of

dense, low redshift survey, including the SDSS main sample, 6dFGS and 21cm intensity mapping initiatives.

➤ move on SDSS MGS, BOSS LOWZ, CMASS … ➤ forecast for 21cm initiatives (see Xin’s talk)

OUTLINE

➤ Motivation ➤ Nonlinear reconstruction ➤ On BAO ➤ On RSD ➤ On velocity ➤ Conclusion

Reconstruction with RSD

Algorithm works with RSD

Lagrangian

➤ Thus, RSD resides in the reconstructed density field. ➤ Before reconstruction: nonlinear density + nonlinear RSD ➤ After reconstruction: more linear density + more linear RSD?

E-mode B-mode ➤ The E-mode part of shift velocity could be reconstruction (vsEz). ➤ Unwanted byproducts, vsEx, vsEy

Shift velocity

ψ vs ψ vsEz vsEx

Shift velocity

total want don’t want miss

1D Cross-correlation coefficient

➤ 1D cross-correlation coefficient with linear field + linear RSD,

i.e., <δNL (1+fμ2)δL> and <δrecon (1+fμ2)δL>

2D Cross-correlation coefficient

➤ 2D cross-correlation coefficient with linear field + linear RSD,

i.e., <δNL (1+fμ2)δL> and <δrecon (1+fμ2)δL>

Reconstruction with RSD

➤ Usually we use upto k=0.1, since nonlinear RSD is not well

understood.

➤ RSD is more linear in the reconstructed ANISOTROPIC

density field.

➤ More linear RSD means more robust constrain on modified

gravity

GR F6 F5 F4 0.8 0.4 0.6 0.2 0.8 0.4 0.6 0.2 0.8 0.4 0.6 0.2 0.8 0.4 0.6 0.2 0.8 0.4 0.6 0.2 0.8 0.4 0.6 0.2 0.8 0.4 0.6 0.2 0.8 0.4 0.6 0.2

Multipole moments

➤ l=0, 2, 4 (monopole, quadrupole, hexadecapole)

P2(k)/P0(k) —> β

Multipole moments

P0(k) P2(k) 0.2 0.2 simulated reconstructed

Multipole moments ratio

P2(k)/P0(k)

0.2 0.2 linear FR linear GR simulated reconstructed

Multipole moments ratio ratio

[ P2 ( k ) / P0 ( k ) ]f(R) [ P2 ( k ) / P0 ( k ) ]GR

OUTLINE

➤ Motivation ➤ Nonlinear reconstruction ➤ On BAO ➤ On RSD ➤ On velocity field ➤ Conclusion

Velocity reconstruction

➤ Standard method: linear continuity equation ➤ Our attempts: relation with displacement

v(q) v.s. Ψ(q) v(q) v.s. Ψrecon(q)

Velocity reconstruction

➤ Use the relation (transfer function) to convert the

reconstructed displacement to the reconstructed velocity field.

Velocity reconstruction

Lagrangian Eulerian

Velocity reconstruction

E u l e r i a n L a g r a n g i a n Nonlinear Recon. Standard Recon.

CONCLUSION

Conclusion

➤ Reconstruction is useful in ➤ extracting BAO signal in low-redshift high-density survey ➤ using RSD to differ gravity models ➤ velocity reconstruction ➤ reconstruction of the initial condition ➤ mock generation ➤ Quite new area to explore

Constrained simulations

➤ Good cross-correlation coefficient with initial density (DM). ➤ RAW reconstructed field is nonGaussian (uplimit of 3) ➤ Need de-noise (Wiener filter)

Constrained simulations

• riginal

simulation new simulation

Fast mock generation

➤ DESI, PFS ➤ Synergetic surveys, spectroscopic galaxy survey X weak

lensing, need correct density field and velocity field simultaneously.

➤ LPTs have long-standing problems, unable to produce correct

density field, while PM unable to produce correct velocity.

➤ Improved understanding on the displacement will be helpful.

THANK YOU

Improvement

P(k) = Ps(k) + Pn(k) linear signal term Ps(k) = C(k) Plin(k) noise term Pn(k) = P(k) - Ps(k) look at k* Ps(k*) = Pn(k*) scale both P(k) to PNGP(k) dashed line shot noise 1/nh k*=0.157 h/Mpc k*=0.360 h/Mpc a factor of 2.29 improvement in scale,

• r

12 in number of linear modes Yu et al. (2017)

halo v.s. downgraded DM

Yu et al. (2017)

➤ nm=b2nh ➤ This downgraded DM

sample shares the same effective shot noise as the halo sample

➤ This result tells us that

the main limitation comes from the shot- noise, but the bias.

v.s. Eisenstein’s

Yu et al. (2017)

➤ indeed outperform over

the standard BAO reconstruction method for dense sample (ng>10-3(Mpc/h)-3).

modeling of the power spectrum shape

TFL= <δsr δsL>/<δsr δsr> δsL =TFL * δsr P(δsL)/P(δsL) TFE= <δsr δsE>/<δsr δsr> δsE =TFE * δsr P(δsE)/P(δsE)

by transfer functions

Reconstructed V.S. real displacement

➤ Reconstructed displacement Φ v.s. real displacement Ψ ➤ Downgraded correlation in z-direction

Multipole moments

P4(k) 0.2 0.2 simulated reconstructed

Multipole moments ratio

Reference: 2012MNRAS.425.2128J arXiv:1205.2698

linear prediction for f(R) linear prediction for GR measurement for GR (nonlinear) measurement for f(R) (nonlinear)

P2(k)/P0(k)

linear

Multipole moments ratio ratio

Reference: 2012MNRAS.425.2128J arXiv:1205.2698

linear prediction

[ P2 ( k ) / P0 ( k ) ]f(R) [ P2 ( k ) / P0 ( k ) ]GR

Elucid analog

➤ To fully use the correlation, add Gaussian to fill the power

gap.