Semi-Numerical Simulations of

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 10-100x 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 Correlationcont’d • Very well correlated, insensitive to ionization efficiency, smoothing scale resolution.

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

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

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

14. Results: HII Bubble Evolution

15. Conclusions and Future work • Conclusions: • 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 10243 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