Molly Swanson wrote:Here, Moss, Scott, and Sigurdson build a toy model of this effect, and find that the induced quadrupole signal looks similar the observed signal, but is a factor of ~three smaller in amplitude, so the signal wouldn't be large enough to explain the claimed effect.

I am a little confused regarding the quantitative estimates of

amplitudes of the dipole difference effect. Here I refer to offsets

relative to that chosen by the WMAP team, i.e. relative to what

the WMAP team believe are the midpoints of observing intervals.

(1) Quantitative amplitudes at -25.6 or about -32 ms

The second last paragraph of Section II of Moss et al. states an

amplitude of 6.5 [tex]\mu[/tex] K, presumably meaning [tex]\sqrt{(3/\pi)C_2} = 6.5 \mu[/tex]K.

Section 5.3 of Liu & Li

0907.2731, for the V+W bands, i.e. on

average about -32 ms [half-interval offsets in each case: (25.6+38.4)/2 = 32 ],

gives [tex]\sqrt{(3/\pi)C_2} = \sqrt{37.3} = 6.1[/tex] [tex]\mu[/tex]K vs [tex]\sqrt{108.7} =

10.4[/tex] [tex]\mu[/tex]K from the official WMAP5 map.

WMAP7 Jarosik et al. (Section 4.1.1,

1001.4744) ILC/KQ85

estimate [tex]\sqrt{(3/\pi) C_2} \sim 14 \mu[/tex]K.

It seems to me that 6.5 [tex]\mu[/tex]K for -25.6 ms is consistent with 6.1

[tex]\mu[/tex]K for approx -32 ms, so Liu et al and Moss et al seem to estimate

roughly about the same amplitude. In fact, if C_2 is linear with the offset, then

Moss et al.'s estimate would give [tex]6.5 (32/25.6) = 8.125 \mu[/tex]K at -32 ms.

So Moss et al. estimate an amplitude about 33%

**higher** than that of

Liu & Li

0907.2731.

(2) Estimates for -51.2 ms (Q band half-observation-interval)

Liu et al. 2010 Table 1 estimate 7.23 [tex]\mu[/tex] K for the r.m.s. of the

difference between the two maps in Q, i.e. for -51.2 ms. They do not

state [tex]\sqrt{(3/\pi)C_2}[/tex] for either map directly. If it's linear with

the offset, as the r.m.s. seems to be, then having about [tex]\sqrt{(3/\pi)C_2}=6.1 \mu[/tex]K at -32 ms (from Liu & Li

0907.2731)

would imply having about 9.7 [tex]\mu[/tex]K at -51.2 ms, i.e. about 69%

of the WMAP7/ILC/KQ85 amplitude.

If we take Moss et al's estimate instead, we get [tex]6.5 *(51.2/25.6) = 13 \mu[/tex]K.

That's about 90% of the Jarosik et al. WMAP7/ILC/K85 quadrupole.

(3) Word/colour image description in Moss et al.

Moss et al. in their Fig 1 caption state that a -25.6 ms offset gives

1/3 the amplitude of the WMAP7/ILC (masked or not?) quadrupole. This

implies 19.5[tex]\mu[/tex]K for the WMAP7/ILC quadrupole. That is about 1/3

larger than the WMAP7/ILC/KQ85 estimate of Jarosik et al. (above),

which could be explained by not masking, for example.

The last paragraph of Section II states that Moss et al. find 1/3 the

amplitude of "that claimed in [Liu et al. 2010]". This means that Moss

et al. interpret something in Liu et al. 2010 to mean that Liu et

al. estimate 19.5[tex]\mu[/tex]K for -25.6 ms. I do not see where Liu et

al. state that they estimate 19.5[tex]\mu[/tex]K for -25.6 ms.

In the same paragraph, Moss et al. infer that "if the claimed effect

was real it could not have a large enough amplitude to explain the

WMAP result". i'm not really sure what "explain" means here. It seems

to be a response to Liu et al's rather strong words, e.g. in the Liu

et al. 2010 abstract (v2), saying that the official quadrupole can be

"exactly generated" from the dipole difference effect, and that the

CMB quadrupole "disappears" and is "almost completely artificial and

the real quadrupole of the CMB anisotropy should be near zero". I

agree that Liu et al's words here are too strong compared to what they

have stated quantitatively.

So let's focus on the numbers. Unless I have made some errors above

(which is possible :), it seems to me that Moss et al. get a slightly

higher amplitude than Liu & Li

0907.2731 and get 90% of the WMAP7

amplitude for a -52.1 ms offset. So Moss et al's toy model gives a

(numerically) much

**stronger** result than the authors realised.

Also, they don't seem to refer at all to the fact that the offset is

written in the TOD files - as Liu et al. 2010 say in their footnote

and

on cosmocoffee. The adjective "claimed" is incorrect for the

existence of an offset between the Meta and Science Data Table times:

there is definitely a 25.6 ms offset internally in each file that I

have checked, and this offset is not documented in

the WMAP Explanatory Supplement as of 21 April 2010. What is speculative (or claimed) is

whether or not this had any effect at any of the processing steps by

the WMAP team, and whether or not the true error

was just the offset written in the data files or a multiple of it.

Since the offset is half of a W observing interval,

a true error of a full W observing interval sounds like

a natural error to make. Moss et al. seem to show with

their toy model that the full W interval, -52.1 ms,

would give [tex]\sqrt{(3/\pi)C_2}=13 \mu[/tex]K.