Bullet Cluster, ACT 148 GHz
Observing Primordial non-Gaussianity via the Thermal SunyaevZel’dovich Effect
J. Colin Hill1,*, Marilena LoVerde2, David N. Spergel1
1Department
Primordial NG + Halo Mass Function
• Primordial non-Gaussianity (pNG): discriminant between
different models of early-universe physics (e.g., inflation)
- Single field, slow-roll inflation: non-detectable pNG
- Different models: pNG with different shapes, different scale dependence
- Agnostic approach: parametrize and look for generic signatures
Φ(x) = ΦG (x) + fNL (ΦG (x)2 − "Φ2G #) + gNL (ΦG (x)3 − 3"Φ2G #ΦG (x)) + · · ·
Primordial
curvature
2School
of Natural Sciences, Institute for Advanced Study, Princeton, NJ, USA 08540
*Email: jch@astro.princeton.edu
SZ Angular Power Spectrum
• Thermal Sunyaev-Zel’dovich (SZ) effect: change in
brightness of CMB photons due to inverse
Compton scattering off hot electrons
in
intracluster
!
medium (ICM) ∆T = gν y = gν σT
Pe (l)dl
me c2
T
Gaussian
random field
Parameters describing amplitude of pNG
• Current constraints from CMB and halo bias [1,2]
−10 < fNL < 74
5
5
−3.5 × 10 < gNL < 8.2 × 10
- Clusters form when (smoothed) density field crosses a threshold δc
- Positive skewness in density field
more collapsed objects
- Negative skewness in density field
fewer collapsed objects
P (δ)dδ
The number of clusters
provides information about
the tail of the probability
distribution function of the
density field.
δc
Spectral function Compton parameter
SZ effect:
• Angular PS of thermal
!
!
C!tSZ
=
gν2
• Role of pNG:
• Role of pNG in the halo mass function (MF)
SZ 2- and 3-Point
Functions
of Astrophysical Sciences, Princeton University, Princeton, NJ, USA 08544
dV
dz
dz
Pressure profile
• SZ N-point function at zero lag:
tSZ
ξN
(θ
= 0) =
!
dV
dz
dz
!
dn(M, z)
dM
dM
!
∆T (M, z, θ! )N d2 θ!
clust
integral over cluster’s
temp. decrement profile
• SZ PS throws away information,! because SZ is inherently non-Gaussian
5/3
∆T
∝
M
• Note: virial arguments suggest clust
Thus, higher N-point functions should be sensitive to increasingly high powers of M, and
hence increasingly sensitive to pNG (which alters MF most for highest-mass clusters)
Top Panels: SZ 2-pt. vs. fNL (left), gNL (right)
Top Panels: SZ 3-pt. vs. fNL (left), gNL (right)
Bottom Panels: ratio of NG SZ 2-pt. to Gaussian SZ 2-pt. Bottom Panels: ratio of NG SZ 3-pt. to Gaussian SZ 3-pt.
dn(M, z)
|ỹ! (M, z)|2 dM
dM
Mass function
~Fourier transform of
Compton parameter
- Changes the MF, especially at the high-mass end -- these
are the clusters that produce the SZ signal
- SZ PS is sensitive to entire integrated MF over all masses
and redshifts -- not as tricky as measuring individual cluster
masses (and no Eddington bias problem)
• Caveats:
1) Pressure profile remains difficult to pin down precisely
(complicated “gastrophysics”)
2) Uncertainties in MF due to baryonic physics, simulation
transients, and mass definitions (friends-of-friends (FoF) vs.
spherical overdensity (SO)) may be of similar magnitude
• Our approach:
δ
• MF is different than CMB!
- Sensitive to all shapes (loc., eq., ...) and types of pNG (fNL,gNL,...)
- Sensitive to different scales than CMB
Scale-dependent pNG (e.g.,
from DBI inflation), as
shown by the dashed blue
lines, can evade CMB bounds
while remaining large at
cluster scales. Figure from
[3] (CMB bounds are slightly
outdated; plot shows fNLeq).
• How to probe? Directly or indirectly:
- Measure cluster masses and count them up
- Measure power spectrum (PS) sensitive to MF, e.g., the SZ PS
- Gas: Battaglia [4] and Arnaud [5] pressure profiles
- MF: SO Gaussian MF of Tinker [6] for standard case; FoF
NG MF correction of LoVerde & Smith (LVS) [7] (which
multiplies Warren [8] FoF Gaussian MF)
Top Panels: SZ PS for Battaglia profile (left) / Arnaud profile (right) + pNG scenarios
Bottom Panels: ratio of NG SZ PS to Gaussian SZ PS (Warren)
Preliminary Interpretation
• pNG leads to overall amplitude shift of SZ PS (unlike gastrophysics, which
changes shape and amplitude)
• Amplitude shift is ~linear in fNL and gNL (but note higher sensitivity of SZ 3-pt.)
• Amplitude shift is independent of gastrophysics
• Degenerate with change in σ8
- Could investigate pNG by putting strong prior on σ8 from primordial CMB
• Sensitive to pNG on different scales than CMB constraints
• Separability from gastrophysics appears challenging
Outlook
• ACT/SPT already constrain amplitude
of SZ PS to ~20%
• With more frequency channels, Planck
may be able to separate tSZ from other
components and directly measure its PS
• Assuming fixed σ8 and known pressure
profile implies sensitivity to fNL ~ 200
or gNL ~ 2x106 with current data
• May yield interesting constraints!
References
[1] E. Komatsu et al. 2011, ApJS, 192, 18
[2] V. Desjacques & U. Seljak. 2010, PRD, 81,
023006
[3] M. LoVerde et al. 2008, JCAP, 0804, 014
[4] N. Battaglia et al. 2011, arXiv:1109.3711
[5] M. Arnaud et al. 2010, A&A, 517, 92
[6] J. Tinker et al. 2008, ApJ, 688, 709
[7] M. LoVerde & K. Smith. 2011, JCAP, 08, 003
[8] M. Warren et al. 2006, ApJ, 646, 881