[Cosmo-torun] 16.00 Fri 27 March - Agnieszka Szaniewska - synchrotron radiation - dark matter annihilations

[Agnieszka Szaniewska]

   Hi everyone,

On Sat, 21 Mar 2009, Boud Roukema wrote:

> hi cosmo-torun
>
>   Next talk: Agnieszka will talk about something (maybe a journal
>   article?)  next week 16.00 Fri 27.03.2009.

   I will talk about synchrotron radiation as a result of DM annihilations.

   You can read about it eg. here:
   http://xxx.lanl.gov/abs/hep-ph/0406083

   Pozdr,
   Agnieszka


>
>
> In this message, i'll try to clarify what got confused about Table 2
> of Copi et al. 0808.3767. Partly this was my fault for not
> understanding what they did carefully enough. As it turns out, what
> they did is simpler than what i thought, but the results are
> consistent with what i summarised.
>
> In short, the statistical isotropy in independent spherical
> harmonics assumption is at least violated for 2 \le l \le 5
> if we take the "best estimates" based on those assumptions;
> and if we use the best-fit infinite flat model instead of
> the "best estimates" directly, then we require l=2,3 to violate
> the same assumptions and extremely low C_2, C_3 values.
>
> Either from the observations "directly" or from the best-fit
> model, the statistical isotropy in independent spherical
> harmonics assumption is invalidated for either 4 or 2 l values
> respectively.
>
> Details of how Copi et al. get to these conclusions:
>
>
> On Thu, 19 Mar 2009, Boud Roukema wrote:
>
>> Witam cosmo-torun
>>
>> On Wed, 18 Mar 2009, Boud Roukema wrote:
>>
>>> hi cosmo-torun,
>>>
>>> It's my turn to give a talk this Friday @16.00.
>>
>> i'll present and stimulate a discussion about:
>>
>> (1) the missing fluctuations problem - Copi et al.
>> http://arXiv.org/abs/0808.3767  - new paper!
>
> http://arXiv.org/abs/0808.3767v1  - let's look at v1, in case later
> there is v2 and someone reads this email on the mailman archive.
>
> Table 2  page 8.
>
> The infinite, flat, gaussian-fluctuations-in-spherical-harmonics model
> says that the different l's are statistically independent. People often put
> error bars on the different C_l's and show a plot of the angular
> power spectrum with infinite-flat model vs observations + error bars, and
> then it looks like only the quadrupole is significantly in disagreement
> with the model.
>
> A key point of Copi et al. is that this interpretation is correct
> *only if* the statistical assumptions are correct. If the statistical
> assumptions are wrong, then the error bars cannot be interpreted as
> being independent from one another. Since the most common
> presentations of this data assume statistical independence and
> gaussianity in the spherical harmonics to extrapolate from high
> galactic latitudes to the "galactic plane" (e.g. KQ75 mask), these
> presentations are based on wrong assumptions.  So what can be done to
> get a valid statistical statement?
>
> One answer is in Table 2 (bits in Table 1) and the accompanying
> discussion. Here's a simplified explanation.
>
> Let us *assume* that statistical isotropy and independence of C_l's
> are correct assumptions.  (*)
>
> (1) Consider the line labelled "WMAP". Let us suppose that the "best"
> estimates of the C_l's are correct. Using assumptions (*), we have
> Eq.(3) and Eq.(6) of Copi et al., i.e. we can analytically calculate
> S using these C_l's.  For example, this gives  S = 8833 muK^4  in the
> 2nd last line of Table 1.  Comparing this to 1152 muK^4 says that
> these C_l's have a lot of "power" in the galactic plane, which is
> the most suspicious part of the data set.   But maybe just a few C_l's
> are "biased" by the galactic plane, and could be "removed" ?
>
>
> (2) Now, since we consider the galactic plane area to most likely to
> have systematic error, we decide to violate (*) for the lowest l's,
> and we find out how many C_l's can be chosen in a correlated ("tuned",
> "dependent") way in order for the full set  of C_l's (tuned + untuned)
> to give an S that is consistent with the S for the high galactic
> latitudes (1152 muK^4).
>
> Naively, it might seem that we can set C_2 = 0, C_3 = 0, ..., C_i = 0
> as "tuned" values, and then calculate S using the C_{i+1}, ..., C_8
> untuned (same as the same "best" estimates), and we should get a lower
> S. However, Copi et al decide to allow even more "tuning", since it
> might happen that negative or positive "tuned" low C_l's are better
> than zero values for "cancelling" the high C_l's in order to get low
> S. [The P_l(cos theta)'s include negative values.] So they allow arbitrary
> violation of statistical isotropy/gaussianity in just a few C_l's,
> in order to try to "save" the statistical isotropy model.  Then it is
> possible to argue that just a few C_l's are extreme events, and the other
> C_l's are OK.
>
> (3) Let's start with the first column, still in the row "WMAP" of Table 2.
> So the first number is 8290 muK^4.  This means that allowing arbitrary
> values for C_2, either zero or negative or positive, it is *not* possible
> to get S anywhere near  1152 muK^4.
>
> (4) Next column, row "WMAP", we have 2530 muK^4. This means that for
> some "tuned" values (NOT given in the table) of C_2 and C_3, we can
> get S calculated from C_2, ..., C_8, ... C_infinity (value of
> "infinity" is probably not stated in the paper?) to be 2530 muK^4, but
> not any lower.  This is still more than twice the high galactic
> latitude value of 1152.
>
> (5) Continue to columns C_4, C_5. It is only after we have "tuned" all
> of C_2, C_3, C_4, and C_5 *arbitrarily* in order to minimise S, that
> we can get the integral for C_2, ... C_infinity (which assumes (*)
> statistical isotropy) to give something as low as 1152 muK^4.  In
> other words, we need a very special relationship between C_2, C_3, C_4
> and C_5 in order for these plus the higher l observational C_l
> estimates to give a value of S \le 1152 \muK^4.
>
> Informally, we could say that this shows an "amplitude alignment"
> between all these four multipoles and the galactic plane, not just the
> quadrupole and the octopole with each other. This is not an alignment
> in orientation, it's a tuning of the amplitudes C_l, so "amplitude
> alignment" is probably a bad way to say this, but let's use this just
> for this discussion, where "amplitude alignment" is temporarily
> defined to mean the procedure done to get Table 2.
>
> Is it cosmologically reasonable to claim that the different C_l's are
> statistically independent from one another but that C_2, C_3, C_4, and
> C_5 are all "amplitude aligned" with each other and the Galactic
> Plane?
>
>
> (6) Now let's go to the line "Theory". This says that if we use the
> "best-fit" infinite flat model and then forget the fact that the
> actual measurements should be closer to the truth than the model,
> we do not have to do as much "tuning". It is enough to tune just
> C_2 and C_3, i.e. we get 922 muK^4 if we can choose some arbitrary
> values of C_2 and C_3 and then use C_4, ... C_infinity from the
> best-fit model (forgetting the measured values).
>
> So, we could say that we only need to "amplitude align" the quadrupole
> and octopole in order to get S \le 1152 muK^4, if we accept the
> best-fit infinite flat model and then forget about the measured
> values. However, i think what is meant in paragraph 3, page 7,
> 2nd column, is that the two C_l's which give this minimisation of S are
> 6 C_2/2\pi = 149 muK^2 and 12 C_3/2\pi = 473 muK^2.  (i don't
> see any other reasonable interpretation of the sentence - i think it's just a
> typo between "Table 2" and "Table 1".)
>
> So, in order to "amplitude align" the quadrupole and octopole in order
> to get S \le 1152 muK^4 using the best-fit infinite flat model, the
> l(l+1)C_l/(2\pi) 's we get are 149 and 473 muK^2, as the true values.
> For l \ge 4 we have independence of C_l's and gaussian distributions,
> but for l=2,3, we have a special selection with these two values.
> These are very low values, see e.g. the last line of Table 1 - they
> should be about 1207 and 1114  muK^2 according to the infinite flat
> model with independent gaussian distributions in the spherical
> harmonics, not 149 and 473 muK^2.  (Look at these on a typical C_l
> plot, e.g. Figs 3,4 Caillerie et al. arXiv:astro-ph/0705.0217.)
>
>
> So now let's get back to the question of statistical isotropy and
> statistically independent l's. Either for the observational estimates
> or the best-fit infinite flat model "estimates", we need to choose
> special values of the C_l's in order to get  S  \le 1152 muK^4.
>
> This means that representing the WMAP sky map in terms of statistically
> independent C_l's gives a representation of the data inconsistent with
> statistical isotropy - i.e. the galactic plane should not be special.
>
> One key point in Copi et al's conclusion is that they recommend that
> any attempted physical or statistical error or other explanation of
> the "low l" problems in the WMAP data should better concentrate on
> explaining the nearly zero two-point correlation function for theta >
> 60 degrees, rather than trying to explain the large length
> scale/angular scale problems in terms of low l spherical harmonics,
> since use of the low l spherical harmonics requires assumptions which
> are inconsistent with the properties of the observational data.
>
>
> A few things which may help if you are going to re-read this and
> the relevant bits of the paper in order to get things clear in
> your mind:
>
> * Table 2 does *not* show the tuned (correlated) C_l's which give
> the minimal S values. The table *only* shows the S values. One comment
> in the text (see above) gives what seem to be two C_l values in one
> case. Probably the table would have been clearer if C_l values had
> been listed too. In principle, it should not be difficult to calculate
> them.
>
> * The sum in Eq.(3) and the integral in Eq.(6) are taken over theta,
> *not* over 4 pi steradians. So it is invalid to say that the S values
> for the full sky and the cut sky calculated using Eqs (3) and (6)
> from the full sky and cut sky C_l values should be different unless
> statistical isotropy is violated.
>
> * If we consider the galactic plane region to have a serious
> systematic error (for the obvious reason), then we do not have a
> violation of statistical isotropy, and we don't have a
> quadrupole-octopole-ecliptic-plane alignment problem ("not readily
> testable"), but we do have C_theta which is unusually close to zero
> given the infinite flat statistically isotropic gaussian,
> k^1 spatial power spectrum model as a whole.  In other words,
> rather than a violation of statistical isotropy, we have
> "The New Isotropy Problem" - the COBE and WMAP skies are *too*
> isotropic on scales greater than one present-day matter-horizon
> radius, i.e. 60 degrees in angular scale.
>
> pozdr
> boud
>
>
>
>>
>> +
>> (2) the hot pixel correction for WMAP data - Aurich et al.
>> http://arXiv.org/abs/0903.3133 - thanks to Bartek for
>> pointing me to this :)
>>
>>
>> pozdr
>> boud
>>
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>
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