Comportamiento estacional del contenido de polen en el aire durante

While for the previous section we considered only a SKA-Low experiment for EoR observations, the telescope aimed to observe the post-EoR frequencies (νc ∼ 450MHz) treated in this work is SKA-Mid. A quick overview on SKA-Mid

has been given on Section 1.1.2. As already stated SKA-Mid can observe in single-dish (autocorrelation) mode or in interferometer mode.

6.4.1

Single-Dish Mode Thermal Noise

If we consider a single dish effective area A_eff, the noise RMS per pixel for a Gaussian process is

σN =

2kBTsys

AeffpNpol∆ν tp

, (6.39)

where Tsysis the system temperature, thermal sky noise and/or receiver noise,

Npol takes into account the possibility of having more than one uncorralated

polarization channels,∆ν is the bandwidth centered around a given observa- tional frequency, and tp is the time per pointing. Following an analogous ar-

gumentation to the one developed in Appendix E, we can write the expression for the noise angular power spectrum

C_lN_,∆ν = " λ₂ (z) AeffΩs(ν) #2 _T2 sys(ν) Npol∆ν to Sarea Nb , (6.40)

where we used tp = to/Np = toΩs/Sarea, since for a given survey area Sarea, Np

pointings are needed given a total observation time to. The instantaneous

FoV of the telescope is hence increased using focal plane arrays with multiple phased feeds (PAF). Sarea ≥ NbΩs, since nothing is gained from observing same

parts of the sky. As seen in Appendix E.1, below a certain critical frequency the beams will overlap for PAFs (in order to achieve uniformity on the noise across sky maps), so

Ωs(ν)= Ωs(νc)

( (νc/ν)2 for ν ≤ νc

1 for ν > νc

(6.41) So, the pixel size corresponds to the instantaneous FoV with FWHM

Ωs ≈ π 8 1.3 λ Ddish !2 [sr] ≈ FoV (6.42)

or smaller. The effective area of one dish is

Aeff = πD2dish/4, (6.43)

where the antenna efficiency  ∼ 0.7 − 0.8. So the factor in round brackets in Eq. 6.40 is of order ∼ 1/2_{. So, we can write}

C_lN_,∆ν ≈ T 2 sys(ν) 2_N pol∆ν to Sarea Nb ( (νc/ν)2 for ν ≤ νc 1 for ν > νc , (6.44)

(Bull, 2015; Santos et al., 2015). So the power spectrum is insensitive to the way we pack the feeds for mosaicking, since this is connected to the pixel resolution that is canceled out in this final expression.

If more than one dish is considered, the total power spectrum is modified with a further factor 1/Ndish, since the signal can be added incoherently.

6.4.2

Interferometer Mode Thermal Noise

The interferometer thermal noise model is analogous to what we have de- veloped for SKA-Low in Section 5.6, with the main difference that SKA-Mid is not an aperture array, so the collecting area is not frequency dependent. The station elements are hence substituted by Ndishdishes of diameter Ddish, which

cover a primary beam Ωs ≈ FoV and are distributed in visibility space with

density function n(U, ν).

Thus, including the possibility of having multiple beams Nbwith PAFs and

multiple pointings of the sky Np = Sarea/[NbΩs(ν)], the thermal noise power

spectrum is C_lN_,∆ν = "λ2_(z) Aeff #2 _T2 sys(ν) Npol∆ν toNbn[U = l/(2π), ν] Sarea Ωs(ν) , (6.45)

(?) (compare with Eq. (5.21)). Note that the time per pointing is increased at lowest frequencies (for a fixed to) and the full beam is Nbtimes the single pixel

feedΩs.

6.4.3

SKA1 and SKA2-Mid Specifications

The original SKA-Mid design (Dewdney, 2013) considers 2 bands for SKA1- Mid, the first, B1, covering a frequency range ν= 350−1050 MHz (z ∼ 3.06−0.35), while the second, B2, a frequency range of ν= 950−1760 (z ∼ 0.5−(0)). The band B1 has dishes of 15 m diameter each with effective area of 133 m2_{, while B2}

dishes have an effective area of 150 m2_{. The primary beam of B1 and B2 SKA1-}

Mid bands is 1.78 deg2and 0.48 deg2 respectively and the critical frequency is placed at half of the frequency range, so 700 MHz (z ∼ 1) and 1 GHz (z ∼ 0.42) respectively. The instrumental noise due to the receiver is Trcv = 23 K for B1

and Trcv = 15.5 K for B2 dishes and there are Npol = 2 polarization channels for

each band.

The recent rebaselining reduced the number of MID receiver elements of the 30%, reducing the number of dishes from Ndish = 190 to Ndish = 130 in both

bands.

We plan to mainly use SKA1-Mid B1 in interferometer mode, using a band- width of ∆ν = 40 MHz (∆z ∼ 0.345) centered at z = 2.5, a total survey area of 25000deg2 and a total observation time of 4000 hrs. Note that with respect to the EoR redshits case, we can use a larger bandwidth, since the convergence power spectrum variation within this redshift range is small. At z= 8 we had to use a much thinner bandwidth. Nb = Np = 1 is going to be preliminarly used.

With this approximation Eq. (6.45) becomes C_lN_,∆ν= "λ2_(z) Aeff #2 _T2 sys(ν) 2∆ν ton(l, ν) (6.46) (Pourtsidou et al., 2015). The observation frequency at z= 2.5 is ν = 405.83 MHz (corresponding to λ = 0.74 m), and the sky noise temperature is Tsky ≈ 30.55K,

and so it has comparable magnitude with the receiver noise for B1 band.

The fiducial dish distribution function for SKA1-Mid is pictured in Figure 6.2.

102 103 104 105 10−5 10−4 10−3 10−2 10−1 102 103 104 105 L 10−5 10−4 10−3 10−2 10−1 n(L, ν ) z=2.5 z=0.85

Figure 6.2: The array distribution in visibility space computed at z = 2.5 (red) compared to the fiducial one at z= 0.85 (blue).

As can be seen lmin= 300, corresponding to

√

Ωs= 1.2°. Following Eq. (6.42)

we deduce that this n(U, ν) is computed at a fiducial redshift of z ≈ 0.85, corre- sponding to a fiducial frequency of νf = 768 MHz. From lmax ≈ 105, we deduce

that the baseline length at this redshift is of ≈ 6500 m. With these data we com- puted, using Eq. (E.9), the baseline array density at z = 2.5 plotted on Figure 6.2, with a FoVΩs ' 4.36deg

2

, lmin ' 172, and lmax' 52735.

Again the effect of rebaselining can be modeled on the n(U, ν), since it is proportional to the square of the number of dishes. This means that the noise Eq. 6.46 is increased by a factor (190/130)2_{∼ 2.14.}

The thermal noise is shown in Figure 6.3, for both sky and receiver noise at z= 2.5.

6.5

The 21 cm Power Spectrum Model at Post-EoR Red-