Of the five points raised by Wright, three are already addressed in our paper(s), one is a typo, and one is a technicality that does not affect our measurements. We provide a detailed response below. Our measurements and their interpretation are not affected by Ned Wright’s concerns.

Wright writes
· An error of a factor of sqrt(4π/3) in the relation between C1 and the velocity, so the quoted effect should be divided by 2.05. Of course Kashlinsky et al. (2008) may have used a non-standard definition of C1 as well, but their papers are never clear on this point.

We correct:

The first sentence of the second paragraph of Sec. 1 in our ApJLetter states

Near the top of p. 4 of the technical paper it says, likewise:

Hence there is no error “of sqrt(4π/3)”; we simply use a different normalization. Our papers are very clear about this issue.

Wright writes
· Inconsistent treatment of the WMAP beam function. In the ApJ Letter the beam response function is not used, while in the methods paper the model angular power spectrum is multiplied by the beam response function. Both of these treatments are wrong. The correct window function is the square of the beam response function.

We reply:

Wright is referring to a square missing in equation 2 of the technical paper. We thank Ned Wright for alerting to this typographic error in our technical supplement paper. It will be corrected in the proofs stage. Our analysis throughout both papers uses the correct definition.

Wright writes
· The Wiener filter formula used is peculiar. Normally one would use

filter = noise/(cmb+noise),

but Kashlinsky uses

filter = (total-cmb)/total.

If total = cmb+noise these are equivalent, but actually the observed

total = cmb +/- cosmic variance + noise

and there are large cosmic variance fluctuations in the low order multipoles, so Kashlinsky's filter gives a map with large amplitude structure on large angular scales which can interact with the non-uniform catalog of clusters of galaxies to give a false dipole.

Motivation for this filter is explained in the technical details paper. Numerical analysis shows that there is no “large amplitude structure on large angular scales which can interact with the non-uniform catalog of clusters of galaxies to give a false dipole”.

NOTES added Nov 2010: 1) Subsequent studies by our group have shown that the amplitude of the measured dipole correlates strongly with the cluster X-ray luminosity cut. Subsamples of brighter clusters lead to larger dipoles as expected from the KSZ effect. The pronounced, approximately linear correlation between the amplitudes of the dipole and the monopole in the central cluster regions argues strongly against the dipole being caused by unknown systematics that are not related to the SZ effect.  Here are links to the Astrophysical Journal Letters article showing this (http://adsabs.harvard.edu/abs/2010ApJ...712L..81K) and to its preprint version (http://arxiv.org/abs/0910.4958). 2) Detailed peer-reviewed studies done by our group show that the filter we employ removes primary CMB down to the fundamental limit of cosmic variance while preserving the KSZ terms from cluster motions. This has appeared in the Astrophysical Journal (http://adsabs.harvard.edu/abs/2010ApJ...719...77A) available also from preprint archive (http://arxiv.org/abs/0910.4958). The article presents the formalism for evaluating uncertainties of the filtering maps (equations 3,4) and Figure 1 shows that the filter indeed removes primary CMB down to cosmic variance as necessary in such studies.

Wright writes
· The functions G(ν) and H(ν) given by Kashlinsky et al. are for Rayleigh-Jeans brightness temperatures, while WMAP gives Planck brightness temperatures. Thus H(ν) should be exactly one, and G(ν) should be just [x coth(x/2)-4].

We reply:

Agreed. This point is technically correct and was pointed out to us by Carlos Hernandez-Monteagudo (MPI) in private correspondence. Correcting this leads to very minor modifications in the SED over the three WMAP frequencies studied in our papers. It, of course, does not influence our dipole measurement at all. We will correct this minor point in the proofs stage.


Wright writes
· The sizes of the X-ray emitting clusters are determined in a way that depends on the noise in the observation. Thus there will be a systematic shift when better X-ray data is obtained instead of just a reduction in the uncertainty.

We correct:

Sec. 3 of our technical paper states explicitly (top of p. 10):

No systematic shift is present. Our final clusters are effectively 30 arcmin wide in radius. Repeating computations with the constant 30 arcmin radius gives essentially identical results.

Note: Interestingly, the results from a recent study done by Watkins, Feldman and Hudson (arXiv:0809.4041) "Consistently Large Cosmic Flows on Scales of 100h^-1Mpc: a Challenge for the Standard LCDM Cosmology" , which appeared after our papers have been posted, are in excellent agreement with our results, albeit done on smaller scales and obtained with different methods