ddd/bachelor-prep-paper
1
Fork 0
Code Activity

Update on Overleaf.

Browse source
This commit is contained in:
juso.koc 2025-03-13 15:16:33 +00:00 committed by node
parent b4e3927aae
commit 13317e5d6c
1 changed files with 2 additions and 2 deletions

4
main.tex
View file

@ -335,9 +335,9 @@ To test the assumption of statistical isotropy, we examine the mean of $a_{\ell
\[
S_i = \sum_{j} W_{ij} M_j
\]
where $W$ is a decorrelation matrix derived from the covariance structure. If significant anomalies appear in the mean values of $a_{\ell m}$, this suggests deviations from isotropy that may indicate new physics or systematic effects in the data.
where $W$ is a decorrelation matrix derived from the covariance structure. If significant anomalies appear in the mean values of $a_{\ell m}$, this suggests deviations from isotropy that may indicate the need for new theories.
For plotting, we used the results of different frequency channels used in the CMB analysis, originating from the WMAP (Wilkinson Microwave Anisotropy Probe) data. This corresponds to the following frequency band categories: Q-band $(~40 GHz)$, V-band $(~60 GHz)$ and W-band $(~90 GHz)$ \cite{Jarosik_2011}. Each band has slightly different noise levels and sensitivity to galactic foregrounds.
For plotting, we used the results of different frequency channels used in the CMB analysis, originating from the WMAP (Wilkinson Microwave Anisotropy Probe) data. This corresponds to the following frequency band categories: Q-band $(\~40 GHz)$, V-band $(~60 GHz)$ and W-band $(~90 GHz)$ \cite{Jarosik_2011}. Each band has slightly different noise levels and sensitivity to galactic foregrounds.
Taking these data, we plot the comparison between expected noise levels and observed anomalies in the mean multipole moments. Let the x-axis represent the multipole moment $\ell$, which corresponds to angular scales, with lower values representing large-scale features and higher values representing smaller-scale fluctuations. The y-axis represents the test statistic $S_i$, which quantifies deviations from statistical isotropy, or in other words the temperature fluctuations from the expected results for an isotropical space.