Ayodeji ibitoye

SUMMARY FOR POSTER
Ayodeji Ibitoye

SLIDE 1
Today in Cosmology (the study of how the universe begin and how it grows with time), cross-correlation of cosmic fields is an important avenue to probe the large-scale structure of the Universe. In this poster I describe the cross-correlation work between the Planck (Compton-y) map, and the projected galaxy density field assuming a specially falt ΛCDM model. Cosmology is set to Planck 2018.

The spherical projection of the Compton y-map and projected density field are both shown at the bottom.

The Compton y-parameter map encloses the process by which hot gas in clusters transfers energy to the CMB photons left over from Big Bang. This process/effect is called the Thermal Sunyaev-Zeldovich effect (tSZ). It is quite useful in Cosmology because it is independent of redshift (a unit of distance).

On the other hand, the projected galaxy density field map encloses the distribution of galaxy clusters in the Infrared-sky up to redshift ~0.8. We reconstruct this map using Data from the Wide-field Infrared Survey Explorer (WISE; a space based telescope).


SLIDE 2

Figure on the top-left is what happens inside a cluster (a group of many galaxies) when the hot dense ionized electrons in it collide with Cosmic Microwave Background (the photons left behind after the big-bang).

When this happen, the result is what you see on the top-right. The CMB photons is boosted and thus the shifts in frequency.

Why are we interested in this project?
The mass of cluster measured is often underestimated and the attempt to reconcil that underestimation, the parameter called: hydrostatic mass-bias has been constrain by many other correlation project. Here we study the beauty of doing this with the cross-correlation between tSZ-data and WISE-data.

To the bottom left is the equation one would use to calculate the angular power spectrum of any two observable. And in our own case X will later be replaced with “y” while Y will be replaced with “g”.

To the bottom-right are the two space telescope that measures the data. The Planck satellite measures tSZ effect while WISE measures galaxies, stars & dust. However, for this project we made some magnitude cut to extract out galaxies.

SLIDE 3

The first figure in the first column shows us how the galaxies probed by WISE are statistically distributed in redshift. We fit this with a polynomial.

The table under it corroborate paragraph 3 under Slide 2.

The second column is interesting as it shows us the bestfit from our theoretical calculation to the data for the auto (using the same observable-y*y & g*g), and cross (with the two observable- y * g) spectra.


In the second column, I show the power spectrum measured from map. In each case; the black dot are the mean of the spectrum and the error bars are the standard deviation of the covariance matrix in each case.

The first panel in the 2nd column shows the measured yy-auto spectrum . The orange curve is the spectrum of the foreground components. The baby-blue curve is the model of the tSZ effect. The Navy-blue curve is nthe sum of the tSZ and foreground component fitted to data.


The second panel in the second column shows how well we have been able to model the auto-power spectrum measured using the WISE data by our calculation. When we fit the theory to the data we have the Navy-blue curve (theory)

The WISE-data was subtracted from short-noise hence the label. The shot-noise is something that arises any time you discretise your data by splitting them into a set of bins or pixels.

The last panel shows the bestfit from our theory to the cross-correlation data. Interestingly, we consider the impact of the cosmic infrared background in this. And why did we do that?, because the CIB becomes relevant at about redshift z~1. And since WISE probe galaxies up to z~0.8, we decided to see how this impact our result.


SLIDE 4

Here we see something interesting. Figure to the right is the cross-correlation matrix. A calculation that tells us how well the signal from the data correlated within multipoles (the multipole space is another way to look at angle on the sky. High multipole relates to small angle and vice-versa). Going by the colour bar, you will see that gg,yy/gg,gy/yy,gy are very very close to zero to tell us our analysis is not contaminated from spurious values.

And the figure to the left here, shows the posterior distribution constrain reached on all the parameters we considered.

Now, the contours are green and purple. The purple-contours are gotten from fitting our theory to the covariance from the diagonal on the right plot. And the green-contours are the constrain reached when we decide to use all the covariance from the correlation on the right plot.

And ultimately, we see that they agree.

Conclusively, cross correlating these two cosmic fields gives a 15.6 sigma detection level. And also a value for mass-bias parameter within the range suggested by Planck for the bias-parameter.