Feb 24th, 2020 - Exploring the Stochasticity of Websky CIB Maps - II: Halo & Galaxy Levels

From LSS Mocks
Jump to navigation Jump to search 
As a follow up of the previous post - https://mocks.cita.utoronto.ca/index.php/Feb_7th,_2020_-_Exploring_the_Stochasticity_of_Websky_CIB_Maps_-_I:_Pixel-Level, I ran the 'halo2fluxmap' code by adding a line in the "makemaps.py" file to induce stochastic effects (by multiplying the fluxes by exp(sigma_lnL*GRD)) at the halo/galaxy-level for 3 different cases: (GRD = Gaussian Random Deviate)

1. variation of [math]\displaystyle{  \sigma_{\ln L} = \sigma_{\ln L_{\text{cen}}} = \sigma_{\ln L_{\text{sat}}}  }[/math] 
2. [math]\displaystyle{  \sigma_{\ln L_{\text{cen}}} = 0.5  }[/math], variation of [math]\displaystyle{  \sigma_{\ln L_{\text{sat}}}  }[/math] 
3. [math]\displaystyle{  \sigma_{\ln L_{\text{sat}}} = 0.5  }[/math], variation of [math]\displaystyle{  \sigma_{\ln L_{\text{cen}}}  }[/math]

Case 1: [math]\displaystyle{ \sigma_{\ln L} = \sigma_{\ln L_{\text{cen}}} = \sigma_{\ln L_{\text{sat}}} }[/math] = (0.3, 0.5, 0.6, 0.7, 0.8) 

[math]\displaystyle{  C_{\ell}  }[/math] (left) and [math]\displaystyle{  b_{\ell\ell\ell}  }[/math] (right)
Cl comp grd 0224.png Bl comp grd 0224.png

 Ratios (Stochastic/Websky): [math]\displaystyle{  C_{\ell}  }[/math], [math]\displaystyle{  b_{\ell\ell\ell}  }[/math], [math]\displaystyle{  b_{\ell\ell\ell}  }[/math] zoomed in
Cl comp grd ratio 0224.png
Bl comp grd ratio 0224.png Bl comp grd ratio zoomed 0224.png

As in the previous post, the stochasiticity-induced maps have higher values of the 2-point and 3-point correlation statistics than the original Websky for all values of [math]\displaystyle{ \sigma_{\ln L} }[/math], and the effects on the bispectra are larger. Compared to stochastic effects induced at the pixel-level, the impact on both the power spectrum and bispectrum is much larger when halo-level stochasticity is induced for equal [math]\displaystyle{ \sigma_{\ln L} }[/math].

For example, at [math]\displaystyle{ \sigma_{\ln L} = 0.5 }[/math], the pixel-level stochasticity causes a 20% increase for [math]\displaystyle{ C_{\ell} }[/math] and a 40% increase for [math]\displaystyle{ b_{\ell\ell\ell} }[/math], while halo-level stochasticity causes a 50% increase for [math]\displaystyle{ C_{\ell} }[/math] and a 150% increase for [math]\displaystyle{ b_{\ell\ell\ell} }[/math] at high [math]\displaystyle{ \ell }[/math].

At high [math]\displaystyle{ \ell }[/math], we see that the ratios (to the original Websky) vary from 1.2 to 3 for [math]\displaystyle{ C_{\ell} }[/math] while they vary from 1.5 to ~13 for [math]\displaystyle{ b_{\ell\ell\ell} }[/math].

Case 2: [math]\displaystyle{ \sigma_{\ln L_{\text{cen}}} = 0.5 }[/math], [math]\displaystyle{ \sigma_{\ln L_{\text{sat}}} }[/math] = (0.2, 0.3, 0.5, 0.7, 0.8) 

[math]\displaystyle{  C_{\ell}  }[/math] (left) and [math]\displaystyle{  b_{\ell\ell\ell}  }[/math] (right)
Cl comp grd difsat 0224.png Bl comp grd difsat 0224.png

 Ratios (Stochastic/Websky): [math]\displaystyle{  C_{\ell}  }[/math], [math]\displaystyle{  C_{\ell}  }[/math] zoomed in, [math]\displaystyle{  b_{\ell\ell\ell}  }[/math], [math]\displaystyle{  b_{\ell\ell\ell}  }[/math] zoomed in
Cl comp grd ratio difsat 0224.png Cl comp grd ratio zoomed difsat 0224.png
Bl comp grd ratio difsat 0224.png Bl comp grd ratio zoomed difsat 0224.png

Here, I have fixed [math]\displaystyle{  \sigma_{\ln L_{\text{cen}}} = 0.5  }[/math] to see the effects on the spectra when [math]\displaystyle{  \sigma_{\ln L_{\text{sat}}}  }[/math] change. At high [math]\displaystyle{  \ell  }[/math], we see that the ratios (to the original Websky) vary from 1.35 to 1.85 for [math]\displaystyle{  C_{\ell}  }[/math] while they vary from 2.3 to ~5 for [math]\displaystyle{  b_{\ell\ell\ell}  }[/math]. 
A takeaway is that inducing stochasticity on only the satellites have a substantial effect, especially on the bispectra.

Case 3: [math]\displaystyle{ \sigma_{\ln L_{\text{sat}}} = 0.5 }[/math], [math]\displaystyle{ \sigma_{\ln L_{\text{cen}}} }[/math] = (0.2, 0.3, 0.5, 0.7, 0.8) 

[math]\displaystyle{  C_{\ell}  }[/math] (left) and [math]\displaystyle{  b_{\ell\ell\ell}  }[/math] (right)
Cl comp grd difcen 0224.png Bl comp grd difcen 0224.png

 Ratios (Stochastic/Websky): [math]\displaystyle{  C_{\ell}  }[/math], [math]\displaystyle{  b_{\ell\ell\ell}  }[/math], [math]\displaystyle{  b_{\ell\ell\ell}  }[/math] zoomed in
Cl comp grd ratio difcen 0224.png 
Bl comp grd ratio difcen 0224.png Bl comp grd ratio zoomed difcen 0224.png

Here, I have fixed [math]\displaystyle{  \sigma_{\ln L_{\text{sat}}} = 0.5  }[/math] to see the effects on the spectra when [math]\displaystyle{  \sigma_{\ln L_{\text{cen}}}  }[/math] change. At high [math]\displaystyle{  \ell  }[/math], we see that the ratios (to the original Websky) vary from 1.2 to 2.7 for [math]\displaystyle{  C_{\ell}  }[/math] while they vary from 1.5 to ~ 10 for [math]\displaystyle{  b_{\ell\ell\ell}  }[/math]. 
The changes in both [math]\displaystyle{  C_{\ell}  }[/math] and math> b_{\ell\ell\ell} </math> are smaller compared to case 1, but they remain quite large. 

Conclusion
It seems to be safe to say that stochasticity induced on both the halo and central/satellite galaxy - levels affect the bispectra considerably more than than the power spectra - an interesting thing to explore would be to fine-tune [math]\displaystyle{  \sigma_{\ln L_{\text{sat}}}  }[/math], [math]\displaystyle{  \sigma_{\ln L_{\text{cen}}}  }[/math], and [math]\displaystyle{  \bar{L}(M_{\text{gal}}, z)  }[/math] to achieve the same power spectra as the Websky maps, but different (higher) bispectra. Even more interesting would be if this can be achieved for different frequency CIB maps.
Retrieved from "https://mocks.cita.utoronto.ca/index.php?title=Feb_24th,_2020_-_Exploring_the_Stochasticity_of_Websky_CIB_Maps_-_II:_Halo_%26_Galaxy_Levels&oldid=2118"