1. Semi-Numerical Simulations of
HII Bubble Growth During
Reionization
August 14, 2008
Patrick Ho, SULI Program
Mentor: Marcelo Alvarez, SLAC KIPAC

2. Reionization
Recombination (z ~ 1100)
Key phase transition in cosmological history: HI becomes HII.
First star formation leads to HII “bubble growth” and eventually complete reionization.
“First light” and beginning of reionization. (z < 14)
Reionization completes (z > 6)

3. Motivation for Studying Reionization
Small-scale density fluctuations.
Structure formation and early stars.
Segue from relative homogeneity and primordial perturbations in CMB spectrum to modern-day complexity.

4. Motivation for Reionization Simulations
Observational results:
Ly- measurements:
Gunn-Peterson trough: Very small amount of HI absorbs completely.
CMB Polarization:
Fan et. al. 2000
Fan, Carilli, and Keating 2006
Simulation can probe details regarding reionization history in between observational constraints.
Also investigate models and fit to constraints.

5. Simulating Reionization
Brute force: N-body and radiative transfer simulations.
Computationally taxing.
Semi-analytical method (Zahn, et. al. 2006).
Calculate one set of values over domain: when does each position become ionizing?
Much more efficient. dt dt dt N3 N3 N3 N3

6. Semi-Numerical Method
Ionization efficiency simplification:
Ionization condition (using Extended Press-Schechter theory for collapse fraction):
Extract from above; find earliest (maximum) redshift of reionization.

7. Semi-Numerical Method
Simplified chart for algorithm:
Input: density distribution derived
from random Gaussian field.
Read in values.
Calculate values at each point
and thus at each point for a
range of smoothing scales.
Look up values for each point
and find earliest value. Output as
time of reionization for that point.

8. Our Simulation
Ultimate aim is efficiency for testing parameter space of model.
Radiative transfer simulations prohibitively slow, must use semi-numerical method.
Our simulation: tree code, calculates smoothed overdensity in real space.
Vs. FFT k-space smoothing, optimal for use with Graphics Processing Unit (GPU).
On a single CPU, code runs ~10-15 minutes.
In other simulations, GPU has provided x increase in speed.

9. Results: Cross correlation
Comparison of our tree code to existing FFT code.
Cross correlation coefficient, measure of similarity between sets of data.
Where power spectrum:

10. Results: Cross Correlation cont’d
Very well correlated, insensitive to ionization efficiency, smoothing scale resolution.

11. Results: Cross Correlation cont’d
Illustration of effect of parameters: minimum scale Rmin has a profound effect on correlation on small scales.

12. Results: Cross Correlation cont’d
Comparison of FFT-based (left) and real-space (right) simulations, from z = 16.0 to z = 8.3.

13. Results: HII Bubble Evolution
z = 28.9
z = 21.6
z = 18.8
z = 16.9
z = 14.5
z = 12.3
HII region formation under conditions:

14. Results: HII Bubble Evolution

15. Conclusions and Future work
Simulation successfully produces results corresponding very closely to output of previous simulations.
Simulation optimized sufficiently to run relatively efficiently.
Sampling of parameter space so far shows little effect on accuracy from ionization efficiency or resolution in smoothing scales; but large effect from minimum scale Rmin.
(Near) Future work:
Continue sampling parameter space for efficiency and accuracy.
Compile code for GPU.
Increase from 1283 to 2563, 5123, even sized domains.
Sample parameter space for investigating reionization physics.

16. Acknowledgements
Thanks to Marcelo Alvarez for his mentorship; Matt Turk for his help.
Thanks to Steve Rock, Farah Rahbar, and Susan Schultz for their stewardship of the SULI program.
Thanks to the DOE Office of Science and SLAC for sponsoring the program.

17. Happy (21st!) Birthday Ted