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[1006.3226] Tracing The Sound Horizon Scale With Photometri

Posted: June 29 2010
This paper looks at how to model the baryon acoustic peak in the angular correlation function, and in particular how to compensate for the substantial projection effects which push the peak down to smaller angular scales.

The approach here is to adopt a simple parametric fit, equation (7), involving a power law plus a Gaussian (plus a constant). The key is linking the angular position of the best-fit Gaussian to the expected scale of the acoustic peak, $$\theta_{BAO}$$. After seeing equation (8), I was hoping to find a fitting function for alpha, but I suppose the idea is to interpolate the lines plotted in Figure 3.

The authors claim the fractional shift in the Gaussian's position is unchanged by the background cosmology, which seems like a fairly good approximation. But let’s not forget that this 1% change in $$\theta$$ would typically propagate to a ~4% change in the estimated equation of state $$w$$.

So I’m left with a few questions:

- If we converted the redshift bin width to a fractional change in angular diameter distance, would this help remove the 1% dispersion due to changes in the background cosmology?

- To what extent does the shape of the redshift bin influence Figure 3?

- It would also be nice to see how the uncertainty in $$\theta_{fit}$$ changes as a function of $$z$$ and $$\Delta z$$. For example, for large bin widths the gaussian becomes very hard to identify. Similarly, how much does this error improve if we use fewer degrees of freedom in the parametric fit?

[1006.3226] Tracing The Sound Horizon Scale With Photometri

Posted: July 05 2010
Dear Fergus,

Your questions are very interesting, I will try to clarify them.

1.- We have already studied how the analysis behaves using distances and there is no improvement in the dispersion. On the other hand, we did an effort to use observable quantities for the cosmological analysis, avoiding possible biases, related to a fiducial model. This is why we used the observed angle and the chosen bin width.

2.- This is an important question. We have used in this analysis a Gaussian shape for the photometirc redshift. In the real world, most probably, the redshift will not be Gaussian. The main influence of this fact is that the corresponding true width must be evaluated taking into account the non-gaussianity. However, for future galaxy surveys there are strong requirements in the behaviour of the redshift, and we expect that the deviations from a Gaussian be small.

3.- You are rigth. For redshift bins wide enough, the sensitivity to the Gaussian dissapears. This limit is reached (as an order of magnitude, since this depends on redshift) when the width of the redshift bin is around a factor of 2 wider than the widest bin we have in the analysis.

About the question on the fit, I think you mean using a smaller number of free parameters. This will decrease the error, but we need some criteria to fix the parameters, and these criteria must be cosmology independent, avoiding any bias. We have found that the safest way to do the fit is to keep them free, but if there is any way to fx them it can be an improvement, yes.