Update on Neff Forecasts
Dan writing (input from Erminia, Joel and Alex)
I will present updates on the forecasting for Neff and how it will impact the target of σ(Neff) = 0.027. .
Temperature versus Polarization
As shown in the figure below, TE drives the constraints for Neff. Reaching the target is particularly sensitive to TE with l > 2000.
A consequence of this statement is that our Neff is not particularly sensitive to component separation. Specifically, we can use Planck TT for l < 1500 and foregrounds in EE are sufficiently low to recover these constraint. Detailed studies of component separation will be presented in a separate post, but this severs only to motivate why we have ignored it here.
Point Sources and Atmosphere
Point sources act much like an additional source of noise (modulo the correction from the beam). Point sources in TT therefore affect the information we can recover from both TT and TE at high-l. We take the TT point source contribution to be
DTT,ps(l=3000) = 6 ( μK)²
DEE,ps(l=3000) = 0.003× 6 ( μK)²
where we use the few percent polarization fraction of the point sources to estimate DEE,ps(l=3000). In practice, the polarization fraction would have to be order 1 to have any effect on our forecasts.
We will determine that atmospheric noise from the model presented at the SLAC meeting:
NlTT= N0TT(1+ (l /3400)-4.7)
NlEE= N0EE(1+ (l /340)-4.7)
where the factor of 10 reduction in lkneeEE was estimated from the polarization fraction.
The impact of the point sources is more important at low noise, as the point sources at like an irreducible noise source in TT. At higher noise, the atmosphere is more important as it
We can also consider the impact of the atmosphere in polarization by changing the model to
NlEE= N0EE(1+ (l /lknee)α=-4.7, -4)
We noise that the atmosphere has a relatively small impact on Neff, presumably because the information is coming from smaller angular scales. However, this is not a universal property of the cosmological parameters, as we can see from ns.
Summary: Reasonable expectations for point sources and atmosphere have a relatively small impact on our ability to reach the Neff target. 10 percent changes do occur, but this likely lies within the accuracy of the forecasts themselves.
Beam / Pointing Calibration
Our ability to calibrate the power spectra at high-l is important for Neff. A bias in the damping tail of the spectra would look like a bias in Neff. Furthermore, marginalizing over these uncertainties reduces the sensitivity to Neff. We will give a simple model of the beam uncertainty to as
Bl = exp[θ1 arcmin² l(l +1) /(2 log 8) (b_1 + b_2 (l/3000) + b_3 (l /3000)^2 ) ]
where the bi are in units of arcmin² and b1 is the uncertainty in the width of a Gaussian beam. We have added the additional terms to model more complicated beam shapes. This parametrization can be expanded to include many other teams, but with little change. At the level of Fisher matrices, this parameterization is equivalent to many others.
With no external prior, we see that there our constraints weaken significantly. We recover the case without the beam uncertainties when we take the 1σ prior to be less that 0.003 arcmin². The beam uncertainty for these various priors in shown below. Since Neff is driven by l > 2000, we should interpret this as the statement that we need 0.1 percent calibration. This is not a surprising requirement, as cosmic variance is order 0.1 percent on those scales. Therefore, we are requiring that the error in the power spectra from the beam uncertainties are below cosmic variance.