Insights A Poor Man's CMB Primer. Part 2: Bumps on a Blackbody - Comments

[bapowell]

bapowell submitted a new PF Insights post

A Poor Man's CMB Primer. Part 3: Bumps on a Blackbody

Continue reading the Original PF Insights Post.

 

[Greg Bernhardt]

Pleasure having this Insight series!

 

[Chronos]

Brian you did a wonderful job explaining the reasoning behind predictions then comparing them to observational data. A very commendable effort to render theory understandable to laymen while minimizing collateral damage to peripheral brain cells.

 

[eltodesukane]

"...the velocity of the Earth relative to the CMB can be found..."
so could we say that velocity is not relative, in the sense that there is a fundamental reference frame compared to which we may define the absolute velocity of any observer?

 

[bapowell]

"...the velocity of the Earth relative to the CMB can be found..."
so could we say that velocity is not relative, in the sense that there is a fundamental reference frame compared to which we may define the absolute velocity of any observer?

No! The velocity of the Earth is determined relative to the rest frame of the CMB. The rest frame of the CMB is the frame of reference in which it appears isotropic: it is a frame that is comoving with the universe and so in a very real sense is at rest with respect to the universe. This indeed makes it special, but it is still just any other frame (the physics is the same in this frame as any other we might choose)

 

[bapowell]

For those interested, I have made significant revisions to this post, in particular, I have added a discussion of the temperature power spectrum (new material begins below Figure 11). I was intending to defer these details to the next note, but as I sat down to write that one, it became apparent that they really belong here.

 

[Jorrie]

Thanks Brian; for first time I have a "good feeling" on the secrets lurking in the CMB. ;)

 

[Drakkith]

The error bars correspond to an obnoxious 400 standard deviations, σ. Why 400σ? Because the more well-mannered 3, 4, or 5σ errors are too small to be seen against the thickness of the line making up the theoretical blackbody curve. File this under “superb and insanely exquisite experimental confirmation of deep and profound theoretical result.” It’s truly impressive.

Buahaha!

 

[Beat Toedtli]

Hi,
In Part 3 you write,
ΔT/T0|dipole=3.353±0.024mK [6]
which seems to get the units wrong (ΔT/T0 is dimensionless?). Is it
ΔT|dipole=3.353±0.024mK [6]
?
thanks for this superb post!

Reference https://www.physicsforums.com/insights/poor-mans-cmb-primer-part-2-bumps-blackbody/

 

[bapowell]

Yes, that is correct. Thanks for the correction!

 

[GeorgeDishman]

The minor tick marks on the bottom scale of Fig.14 look weird (the top scale appears fine and I think the bottom should match it).

 

[bapowell]

The minor tick marks on the bottom scale of Fig.14 look weird (the top scale appears fine and I think the bottom should match it).

Thanks for the comment. The axes are measuring different things that are inversely related; hence the difference in minor tick marks.

 

[GeorgeDishman]

I'm assuming it's supposed to be a simple log scale, hence the distance between consecutive ticks should decrease as the values increase. The distance from 30 to 20 is much less that that from 10 to 20, but after that it increases, the distance from "90" to "100" is much larger than from "20" to "30". At a guess, the "20" looks right but the spacing of "30" to "90" seems mirror-imaged. I've marked up an image and included a roughly similar log scale from an Excel graph to illustrate what I mean. I may be mistaken but it just looks odd unless the ticks are not multiples of 10. I've also added a reversed scale if that's what was meant.

p.s. A reversed scale would mean the bottom minor tick marks are 11.11, 12.50, 14.29, 16.67, etc. but I didn't think that $l$ could have fractional values.

 

[GeorgeDishman]

p.p.s [too late to edit the previous] The equation above the graph says ϑ_ℓ=π/ℓ radians but the graph starts at (I think) ℓ=2 and ϑ_ℓ=90 so seems to be in degrees which is fine but if the top ticks are then meant to be 80, 70, 60 degrees etc., I think they might be the wrong way round too.

 

[bapowell]

OK, I see now. Yes, the axes are messed up. I'll go back and check what might have happened: I was having difficulty getting the two separate x-axes to look right...apparently I didn't succeed after all.

 

[GeorgeDishman]

I tried to replicate your graph in Excel but I can't find a simple source of the data, Planck publishes it in FITS format and I don't have any easy way to read that on a basic PC without installing software and writing scripts. Anyway, assuming you use degrees and the highest ell is 2508 (based on the FITS description), I think the scales should look something like this for ℓ from 2 up to 3000 and ϑ_ℓ=180/ℓ from 90 down to 0.06 degrees: