1. Small-Scale Anisotropy Studies with HiRes Stereo Observations Chad Finley and Stefan Westerhoff Columbia University HiRes Collaboration ICRC 2003 Tsukuba, Japan

2. Angular Resolution HiRes stereo observation has sharp angular resolution In Monte Carlo simulations, 68% of events are reconstructed within 0.7° of their true arrival direction Stereo data set is ideal for small-scale anisotropy study Distribution of opening angles between true and reconstructed arrival directions for HiRes Monte Carlo events.

3. HiRes Stereo Data Set All data from Nov. 1999 through June 2003 Equatorial Coordinates

4. HiRes Stereo Data Set (>10 19 eV) 228 well- reconstructed events above 10 19 eV RMS energy resolution for these events better than 20% Angular resolution better than 0.7º Equatorial Coordinates

5. Autocorrelation Two-Point Correlation Function: Count number of events separated by θ Perform same count on Monte Carlo data sets with same event number and similar exposure. Clustering would show up as excess over fluctuations at small angular scales w(θ) = N(θ) / N MC (θ) - 1 Two-point correlation for HiRes Stereo Events > 10 19 eV RMS fluctuations

6. Autocorrelation Evaluating Significance: A limitation of the correlation function is the necessity of choosing a minimum energy for the data set: –A higher energy threshold may reduce deflections of charged cosmic ray primaries by magnetic fields... –... but it also weakens the statistical power of the data set. No a priori optimal choice for energy threshold or angular separation exists for clustering searches.

7. Autocorrelation Scan Solution: Scan over angular separations and energy thresholds simultaneously Identify the angular separation and energy threshold which maximize the clustering signal Evaluate the significance by performing identical scans over Monte Carlo data sets Scan of HiRes Stereo Events > 10 19 eV

8. Autocorrelation Scan HiRes Results: Strongest clustering signal: N = 97, θ = 1.2° ( E = 1.76×10 19 eV ) n pairs = 4 P min = 1.1% However, there is a statistical penalty for scanning True significance is chance probability for scan of Monte Carlo data to have lower minimum: P chance = 39% No significant clustering signal observed Scan of HiRes Stereo Events > 10 19 eV

9. Comparison with AGASA To compare AGASA and HiRes observations, utilize a simple model to generate clustering in Monte Carlo sets: Generate a simulated AGASA event set from S randomly distributed point sources in the sky. See if clustering signal in this simulated event set matches the AGASA clustering signal Repeat many times for each value of S, and count the number of simulated sets which match the AGASA clustering signal. Distribution of matches to AGASA data for S point sources randomly placed in the sky. (A match is: 6 pairs with angular separation < 2.5° in an event set of 36 events)

10. Prediction for HiRes For each match to AGASA, use the same S point sources to generate a set of events with HiRes exposure. Count the number of pairs with angular separation < 2.5° Current HiRes data set has 20 events in the energy range comparable to AGASA 0 pairs observed in this set: consistent with AGASA clustering signal and isotropy Predicted number of pairs seen by HiRes grows rapidly with the size of the data set Distribution of number of pairs in HiRes simulated sets of 20 and 50 events.

11. BL Lac Correlation Study BL Lac Correlation? AGASA and Yakutsk events above 2×10 19 eV have previously been correlated with positions of 14 gamma-ray loud BL Lac objects. However, the two-point correlation function between these BL Lacs and HiRes events (>2×10 19 eV) shows no correlation (0 pairs out of 77 events) Above: HiRes (black), BL Lacs (red) Below: Two-point cross correlation function

12. Conclusions Autocorrelation for HiRes Stereo data above 10 19 eV: –Significance of the autocorrelation function is ambiguous – depends on energy threshold and angular bin size –Scanning over energy and angular separation identifies the strongest clustering signal – but statistical penalty for the scan must then be determined –The chance probability of the strongest HiRes clustering signal is 39% –No significant small-scale clustering observed Comparison with AGASA model for clustering –AGASA clustering signal is not strong – large fluctuations in the predicted number of clusters for independent data sets –Need statistics comparable to AGASA’s in order to support or refute –HiRes will collect this data over the next two years BL Lac correlation study –No correlation between HiRes events and gamma-ray loud BL Lacs