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.