Slides from the talk - CP3-Origins

What about other models?
approach [40]
∆b I = b NG
1 − b G 1 = − ∂ ln RNG (M)
, (6.5)
∂δ c
The scale-dependence of bias can be different
for other models, or not be there at all ...
R NG (M) being the ratio of the non-Gaussian to the Gaussian mass function. Here,
ver, we treat ∆b I as a free parameter and compare it later on with the prediction
ed from the mass functions. We choose q as the second free parameter. All other 1
tities in Eq. (6.4) are we derive from the theory and are kept fixed.
In Fig. 8, we show as an example the effect of local non-Gaussianity on the halo bias
alos of mass 1.2 − 2.4 × 10 14 M ⊙ /h at z = 0. Note that we plot ∆b(k)+0.1. As ∆b I is
tive, this addition of 0.1 is needed to still make use of the logarithmic scale.
The different line types visualize the effect of the different terms in Eq. (6.4). The 0.1
s lines show the best fit to the data (using all modes up to k max =0.1Mpc/h) and
des all terms given above. The short-dashed lines neglects ∆b I appearing inside the
re brackets in Eq. (6.4). The inclusion of this term makes the non-Gaussian bias nonr
in f NL [55], since ∆b I depends on f NL . The dot-dashed line neglects ∆b I completely.
scale-dependent bias shift becomes important on smaller scales (k >0.02), for which
cale-dependent part becomes small.
!b + 0.1
10
1
0.1
1
k
Orthogonal orthogonal NG
Gaussian bias. This has the advantage that by doing this we do not need to include β(k
the modelling of ∆b(k) (seeEq.(2.1) and Eq. (2.4)).
!b + 0.1
0.4
f NL = -1000
1.2x10 14 < M
f NL = -250
halo < 2.4x10 14
3x10 13 < M halo < 6x10
Figure 8. Local non-Gaussian bias of halos with mass 1.2 × 10 14 Mpc/h < 13
M < 2.4 × 10 14 M
at z = 0. The difference of the bias measured from the non-Gaussian simulations and Gau
simulations is depicted 0.2 by the data points (for computation of the errorbars, see App. B). The
lines show the best fit using the model given in Eq. 6.4. The dot-dashed lines show the m
predictions when the scale-independent bias shift, ∆b I , is neglected. The short-dashed lines ne
the term which is non-linear 0 in f NL (see text for details). Thick lines and red symbols correspon
f NL = 250, while thin lines and blue symbols show the results for f NL = 60. Note that we act
show ∆b +0.1 to allow for a logarithmic scale.
!b
10
0.01
0.003 0.01 0.1
-0.2
-0.4
1
k 2
local
Local NG
k [h/Mpc]
f NL = 250
f NL = 60
As the non-Gaussian and the Gaussian simulation share the same realization of
initial Gaussian field, ∆b(k) is almost free of sample variance and, in addition, has sm
shot noise than b NG (k) and b G (k) individually. We estimate the error on ∆b(k) directly f
const.
the distribution of ∆b(k) in each k bin (for details, see App. B).
Following Eq. 2.1, wemodel∆b(k) by equilateral
Wagner & Verde (2010)
Equilateral NG
0.01
0.003 0.01 0.1
k [h/Mpc]
where b G 1
∆b(k) =∆b I + f NL b
G
1 + ∆b I − 1 qδ c F M (k)
D(z) M M (k) , (
-0.6
0.003 0.01 0.1
k [h/Mpc]
is the linear halo bias obtained from the Gaussian simulation on large scales