Hi Will,

Thanks for your interest in our paper.

Taking all the sources in a 10 degree radius around the found dipole and anti-dipole, the mean value of the mean observation MJD (i.e. the mean of the MJD values for all individual observations that went into each catalog source) is 57,230 for the pole and 57,229 for the anti-pole, each with a standard error (stdv/sqrtN) of 1 day. So the data at the pole (where we see the strongest excess) and the anti-pole (where we see the strongest decrement) are *consistent* with having the same mean observation epoch, 2015 July 27. The corresponding temperature of the instrument was about 74.5 K:

So, it is unlikely that the found dipole is induced by a temperature difference. Hope that assuages your concern.

Nathan Secrest – on behalf of the authors

PS: Subir comments: Will, since you emphasise our “very small” ~10^-3 signal, are you not also concerned about satellite measurements of the *much smaller* fluctuations in the CMB? Planck was of course at L2 rather than on a Sun-synchronous polar orbit like WISE – but the HFI sub-K bolometric detectors suffered serious damage by cosmic rays (arXiv:1403.6592, arXiv:1404.1305). There was indeed “a lot of modelling” done to “to work this out in detail” (arXiv:1303.5071). Our signal may not be precision cosmology but we believe it is accurate cosmology!

]]>I can think of three: firstly there’s the obvious ~ 7 percent January-June difference in solar heating.

Secondly, WISE uses a “sun-synchronous” polar orbit which is inclined ~ 98 deg from the equator and precesses once per year so the orbit pole points near the Sun. The telescope looks “up” away from the earth scanning great circles. There is a possible “6am/6pm” effect, i.e. going down Arctic to Antarctic is at 6am local time , going up is 6pm local time (or vice versa), so the Earth is order 10K warmer on the 6pm side and there’s 15 percent more Earth heating.

Third: the radio transmitter probably turns on at specific locations w.r.t. Earth over the ground-station, creating heat.

All these partially average out over the scan-pattern, but they may not cancel precisely.

While it would take a lot of modelling to work this out in any detail, in principle any of these could leak into a tiny residual of the size observed. ]]>

Although the only evidence for a notion of statistical homogeneity occurs on scales > 100/h Mpc, the FLRW assumption is usually applied below this scale. That is implicit in treating the dipole only with special relativity. In GR differential expansion on scales < 100/h Mpc will not always be reducible to FLRW plus a boost. See arXiv:1512.07364 [JCAP 06 (2016) 035].

A purely kinematic dipole relative to an isotropic CMB has a specific expansion in powers of

While the Planck team published a paper arXiv:1303.5087 [A&A 571 (2014) A27] claiming to verify the kinematic nature of the transformation to the CMB frame (through special relativistic aberration and modulation) the conclusion works only for small angles only. If one looks at large angles then the putative boost direction moves across the sky to point in the direction of the “modulation dipole anomaly”. While this in itself is not a proof of our hypothesis, it is consistent with it.

I have looked into the question of whether we could test alternative models directly on CMB data, and had discussions with Francois Bouchet (a Planck PI) a few years ago. Unfortunately the empirical modeling of the galaxy foreground appears to intimately tied in with the dipole subtraction which makes this highly nontrivial.

We were led to study these issues firstly on account of the observation that the spherically averaged Hubble expansion on > 5): arXiv:1201.5371 [Phys Rev D 88 (2013) 083529]. If one does arbitrary boosts to try to find a frame in which the expansion is most uniform then given a lack of peculiar velocity data in the Zone of Avoidance, one cannot distinguish the local group frame from frames related by a boost in the plane of the galaxy. All such frames could be the “most uniform frame”: arXiv:1503.04192 [MNRAS 457 (2016) 3285; 463 (2016) 3113].

Kraljic and Sarkar (arXiv:1607.07377 [JCAP 10 (2016) 016]) subsequently showed that our results on the spherically averaged Hubble expansion could also be reproduced with FLRW + Newtonian N-body with a sufficiently large bulk flow. One then gets into the problem of how unusual are such large bulk flows, and different observations not agreeing. The latest result with quasars is a very strong signal that something is amiss in the standard approach.

Thus we consider it promising to continue with a hypothesis which is consistent with known physics, and our best theory of gravity, even if it is not popular. ]]>