Small-Scale Anisotropy Small-Scale Anisotropy Studies with HiRes Studies with HiRes

Stereo ObservationsStereo Observations

Chad Finley

and Stefan Westerhoff

Columbia University

HiRes Collaboration

ICRC 2003 Tsukuba, Japan

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.

HiRes Stereo Data Set

All data from

Nov. 1999

through

June 2003

Equatorial Coordinates

HiRes Stereo Data Set (>1019eV)

• 228 well-reconstructed events above1019 eV

• RMS energy resolution for these events better than 20%

• Angular resolution better than 0.7º Equatorial Coordinates

Autocorrelation

Two-PointCorrelation 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) / NMC(θ) - 1

Two-point correlation for HiRes Stereo Events > 1019 eV

RMS fluctuations

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.

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 > 1019 eV

Autocorrelation ScanHiRes Results:• Strongest clustering signal:

• N = 97 , θ = 1.2° ( E = 1.76×1019 eV )

• npairs = 4• Pmin = 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:• Pchance = 39%

• No significant clustering signal observed Scan of HiRes Stereo Events > 1019 eV

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)

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 has20 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.

BL Lac Correlation StudyBL Lac Correlation?• AGASA and Yakutsk

events above 2×1019 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 (>2×1019 eV) shows no correlation

(0 pairs out of 77 events)

Above: HiRes (black) , BL Lacs (red)Below: Two-point cross correlation function

Conclusions

• Autocorrelation for HiRes Stereo data above 1019 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