small changes to text
@@ -491,7 +491,7 @@ The \citet{Tinker2010} model parameterizes the halo mass function and the halo b
f(\nu) &=& \alpha[1+(\beta\nu)^{-2\phi}]\nu^{2\eta}e(-\gamma\nu^2/2).
\end{eqnarray}
-Again, while high {\em numerical} accuracy has been verified, there is a remaining uncertainty. \citet{Tinker2010} found a $\sim6\%$ scatter when determining the halo bias due to differences in simulations alone. In addition, this parameterization does not include a careful exploration of any impact due to changes in the dark energy equation of state. As with the halo mass function, studies will be required to reach accuracy at the percent level for any cosmological predictions. \elisa{I think we need some further references here of scale-dependen bias, assembly bias, etc.}
+Again, while high {\em numerical} accuracy has been verified, there is a remaining uncertainty to the {\em physical accuracy}. \citet{Tinker2010} found a $\sim6\%$ scatter when determining the halo bias due to differences in simulations alone. In addition, this parameterization does not include a careful exploration of any impact due to changes in the dark energy equation of state. As with the halo mass function, studies will be required to reach accuracy at the percent level for any cosmological predictions. \elisa{I think we need some further references here of scale-dependen bias, assembly bias, etc.}
We note that many observables are tuned to utilizing a linear halo bias (e.g. scale independent). While the current functionality of \ccl is to return the \citet{Tinker2010} model for halo bias, it is entirely possible to generate simpler models of halo bias and pass this into further functions. \elisa{I think this is a bit confusing: from this I understand that \ccl can predict $b(k)$ but cannot pass anything but linear bias to the angular power spectra.}
@@ -706,7 +706,7 @@ Also note that for $\sigma(M)$, it is important to set the desired precision lev
Derivatives are calculated utilizing a spline that is built off of the previously described $\sigma(M)$ spline. As such, these splines cover the range from $10^6$ to $10^{17} M_\odot$. For each value of $\log(M)$ in our spline evaluation, we calculate the value of $\sigma(M)$ half a step in either direction. We use the difference compared to the mass spacing to calculate an approximate derivative, which is then used in the spline interpolation. This has been tested to meet our necessary precision for the halo mass function within the mass range explored by \citet{Tinker2010}. We note that there the accuracy is reduced at the edges of these splines and exploring extreme mass ranges may require changes in the parameters to initialize these splines.
-In order to accomodate a wide range of values of the overdensity parameter $\Delta$, we have generated a spline interpolation between best fit values as defined by \citet{Tinker2008} and \citet{Tinker2010}. This covers a dynamic range from $\Delta=200$ to $3200$. Within this range, we interpolate in the space of the fit parameter and $\log\Delta$ using the Akima interpolation built from piecewise third order polynomials. We have chosen this rather than the fitting formulas utilized in \citet{Tinker2010} in order to assure high precision match to the Tinker halo mass function when choosing a value of $\Delta$ directly from the paper.
+In order to accomodate a wide range of values of the overdensity parameter $\Delta$, we have generated a spline interpolation between best fit values as defined by \citet{Tinker2008} and \citet{Tinker2010}. This covers a dynamic range from $\Delta=200$ to $3200$, with respect to the mean density. Within this range, we interpolate in the space of the fit parameter and $\log\Delta$ using the Akima interpolation built from piecewise third order polynomials. We have chosen this rather than the fitting formulas utilized in \citet{Tinker2010} in order to assure high precision match to the Tinker halo mass function when choosing a value of $\Delta$ directly from the paper.
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