# I How is the first multipole calculated from the Plank Study?

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1. Dec 25, 2016

### Jules Winnfield

Reading through the Plank 2013 Results we can see that the angular scale is $0.0104147$ or $0.60^\circ$. However, the Power Spectrum chart clearly shows the first multipole at $220$ $l$. Using the relation $$\theta = \frac {180^\circ}{l},$$I calculate the first multipole to peak at $302$ $l$. Would someone please show the steps of how you go from $0.0104147$ to $220$ $l$?

2. Dec 30, 2016

### Greg Bernhardt

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Dec 31, 2016

### Jules Winnfield

Rewording the question a little: In the Plank 2013 results, there is a chart on the third page that shows the location of the acoustic peaks in the Power Spectrum.

As I understand it, these peaks correspond to the correlation of temperatures at a given angle. The first peak corresponds to the angle (projected onto the sky from our perspective) of the distance that a sound wave could travel from the beginning of time to the last scattering. According to the above chart, that occurred at a multipole moment of 220. Using the formula in the original post, that corresponds to an angle of $0.8181^\circ$. Could someone please explain the relation between this angle and the 'angular scale' of $0.59^\circ$ quoted in the same Plank study?

4. Dec 31, 2016

### Staff: Mentor

Be careful with the graph. It does not show the power, it shows the power multiplied by l(l+1). The calculation of the angular scale might measure the peak of something else, i. e. with a different l-dependent prefactor.