Costo Estimado

In order to create realistic maps of the tSZ and kSZ signals produced by the cos- mic large-scale structure, we use a similar approach for tessellating the backwards light-cone as described in Carbone et al. (2008a); Zavala et al. (2009). The method is based on the replication of the original simulation box along the line of sight, where at each redshift the simulation output closest to this time is used. In order to avoid that the same structures are repeated along a given line-of-sight, we ran- domly translate and rotate the simulation box within concentric shells of comoving thickness equal to the simulation box size. Within each of these shells, the same randomization process is applied to a full, coherent tilting of the shell. Unlike in simpler stacking techniques used in the past, this approach has the advantage that

the reconstructed light cone has no discontinuities in the transverse direction. It is therefore ideal to construct maps that are larger than the box size itself, and in particular, it can be used to construct all-sky maps, if desired.

Figure 3.5 gives a sketch of the map-making procedure. The concentric shells represent regions covered by a single simulation output, and within each shell, a different choice for the randomization process is used. We produced dumps spaced

by a comoving 100h−1_{Mpc in light travel time for the ΛCDM cosmology, which}

is also the thickness of our box, so that each shell is covered approximately by one simulation dump (exactly one for our ΛCDM cosmology). However, the map- making code can also deal with an arbitrary spacing of the output times of a given simulation, and will automatically select an optimum use of them for reconstructing the backwards light-cone.

For the projection itself we work in comoving coordinates and take advantage of the periodic boundary conditions of our simulation. For each pixel, we sum up contributions of all the particles that overlap it within their SPH smoothing length. In practice, we first produce partial maps that correspond to those parts of the backwards light-cone that are covered by a particular snapshot dump. The full light-cone is then obtained by adding all partial maps together. In principle, our method can produce arbitrarily large maps, including full sky ones, if desired, but here we focus on smaller maps in order to more easily reach very high angular resolution. In particular, we create maps of two different sizes, one set is 3 square degrees on a side, the other has a field of 12 square degrees on a side. In both

cases we consider 40962pixels, corresponding to a resolution of _∼2.64 and_∼10.55

arcsec, respectively, and we integrate over the redshift range 0 < z < 9.6. As

we will discuss in more detail in Section 3.4, this range is enough to account for essentially all of the tSZ signal, and especially also for the kSZ effect that is believed to have a non-negligible contribution even forz >6. In order to assess the statistical robustness of our results and the influence of cosmic variance we have created 16 different light-cone realizations with different random number seeds, eight for each resolution.

In order to compute the y and b parameters along each light ray, we need to

convert the line-of-sight integral in Equations (3.1) and (3.4) into a discretized ex- pression for the individual SPH particles. Calculating the SZ effect requires knowl- edge of the number density, temperature, and velocity of the electron distribution. In the non-relativistic limit relevant for the thermal SZ effect, we first compute for each particle the product of pressure and specific volume of the gas:

p= (γ₋1)(1₋Y_p)muµx_e, (3.22)

whereγis the ratio of specific heats,Yp= 0.24 is the primordial4He mass fraction,

m the particle mass, u the internal energy per unit mass, µ the mean molecular

SPH smoothing kernel, W(x)_∝      1₋6x2+ 6x3, 06x <0.5 , 2(1₋x)3_{, 0.5< x61 ,} 0, x >1,

that is used in the simulation code for the computation of hydrodynamical forces for distributing these quantities over the pixels of our maps. In equation (3.23),

x _≡ ∆θ/αi, where ∆θ represents the angular distance between the pixel centre

and the projected particle position, and αi is the angle subtended by the particle

smoothing length. We make sure that the sum of the projected smoothing kernels

w is normalized to unity for the pixels actually covered by a particle. Then, the

contribution to the thermal SZ effect due to the particleαis given by

yijL2pix = σT m_ec2 X α pαwα,ij , (3.23)

whereLpix is the physical size of the pixel at the particle’s distance.

We use a similar procedure for constructing the maps of the Dopplerb-parameter.

The only difference is that in this case the quantity that needs to be distributed over the angular grid is

bijL2pix= σT c X α vr,αne,αwα,ij , (3.24)

wherev_r,α is the radial component of the peculiar velocity of the particle α.

As a final remark, in the non-radiative simulations we study here, we do not track

the ionization fraction xe explicitly. Instead, we fixed it to 1.158 for temperatures

T >104 _{Kelvin. In other words, we adopt this temperature as a delimiter between}

cold and completely neutral gas, and fully ionized hot gas. For our simple non- radiative simulations it is necessary to assume that the gas is neutral at very high redshift, otherwise the finite box size of our simulation would lead to a very strong kSZ signal on large angular scales, arising from gas motions described by the largest modes in the simulation box.