The angular homogeneity scale of the Universe - Centre for ...
The angular homogeneity scale of the Universe - Centre for ...
The angular homogeneity scale of the Universe - Centre for ...
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<strong>The</strong> fractal dimension<br />
• To study <strong>the</strong> transition to <strong>homogeneity</strong><br />
fractality <strong>of</strong> <strong>the</strong> galaxy<br />
distribution<br />
• Fractal dimension is also useful to quantify clustering<br />
• How do we specify this<br />
C 2 (r) = 1 N<br />
NX<br />
nP (n; r, N) / r 3<br />
Correlation integral<br />
• Departures from D 2 = 3 due to:<br />
- Clustering<br />
- Shot noise<br />
n=0<br />
D 2 (r) ⌘ d log C 2(r)<br />
d log r<br />
! 3<br />
Volume<br />
As <strong>homogeneity</strong><br />
is approached<br />
J. S. Bagla, J. Yadav and T. R. Seshadri, 2007, MNRAS, 390:829<br />
Alicia Bueno Belloso <strong>The</strong> <strong>angular</strong> <strong>homogeneity</strong> <strong>scale</strong> <strong>of</strong> <strong>the</strong> <strong>Universe</strong> 2 nd September 2013
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