Uncertainty in Theoretical Atmospheric Antiproton Flux at Balloon Altitude Partha Joarder Center for Astroparticle Physics and Space Science (CAPSS), Bose Institute, Kolkata Collaborators: Arunava Bhadra, Biplab Bijay High Energy and Cosmic Ray Research Centre (HECRRC), North Bengal University (NBU), Siliguri Sanjay K. Ghosh, Sibaji Raha Centre for Astroparticle Physics and Space Science (CAPSS), Bose Institute, Kolkata

Uncertainty in Theoretical Atmospheric Antiproton Flux at Balloon Altitude 1. Introduction Atmospheric pbar flux estimated by various microscopic ( theory driven) hadronic interaction models through CORSIKA (Heck et al. 1998) simulations. Attempt to quantify the uncertainty due to interaction models. Why antiprotons?  Galactic pbar flux informs regarding the propagation of CR in the Galaxy.  Potential tool to probe into the possible DM sources in the Galaxy.

Theoretical estimates favor pure interstellar origin of pbar. Important to quantify the uncertainty in such estimates. PAMELA measurements of galactic pbar (60 MeV < K.E < 190 GeV; Adriani et al. 2009, 2010)

 Production mechanism of pbar is possibly similar in earth’s atmosphere and in the Galaxy.  Objective is to quantify the uncertainties in predicted pbar flux at atmospheric depth (10.7 gm/sq.cm) comparable to the depth traversed by CRs in the Galaxy (5-10 gm/sq.cm; Gaisser 1991).  Direct comparison with BESS-2001 Balloon observations at Ft. Sumner (0.2 GeV < K.E < 3.4 GeV; Yamato et al. 2006) corresponds to mean vertical geomagnetic rigidity cutoff at Ft. Sumner (4.2 GV) Measured pbars are mostly of atmospheric origin

2. Simulation Procedure 2.1 Hadronic interaction models Steeply falling energy spectra of primary CRs. Simulations of BESS-2001 pbar spectra require Low energy ( ~50 MeV/n – 80 GeV/n; Default setting in CORSIKA ) Hadronic Interaction models in CORSIKA : 1. UrQMD 1.3 (Bleicher et al. 1999) 2. FLUKA b (Ferrari et al. 2005; Battistoni et al. 2007) DPMJET-III (Roesler, Engel and Ranft 2001). Accelerator and collider-based experiments, RHIC experiment. Being used in LHC experiment too.

UrQMD 1.3 and FLUKA b each in combination with the High Energy ( > 80 GeV/n ) Hadronic Interaction model QGSJET01c. Extension of atmospheric pbar spectra beyond BESS-2001 upper cutoff up to 100 GeV Requires High Energy Interaction Models. We choose : 1. QGSJET 01c (Kalmykov, Ostapchenko and Pavlov 1997) 2. VENUS 4.2 (Werner 1993) 3. NEXUS 3.97 (Pierog et al. 2003) 4. EPOS 1.6 (Werner, Liu and Pierog 2006) each in combination with FLUKA model. NEXUS and EPOS have most consistent implementation of conservation laws.

2.2 Input Primary Spectra  Second major uncertainty in the simulations (Wentz et al. 2003).  We reproduced precisely determined BESS-98 (Sanuki et al. 2000) primary proton and alpha fluxes that used the same detector as in BESS-2001 observations.  Effect of Solar Modulation handled in terms of a time dependent solar modulation potential (Usoskin et al. 2005). ~6-7% deviation in primary alpha spectra at ~1 GeV/n. Additional error caused to atmospheric particle flux is small (Wentz et al. 2003)

Fluxes of primary heavier nuclei Wiebel-Sooth et al. (1998). Contribute < 5% to the atmospheric pbar flux. Residual galactic antiprotons Input spectra from a fit with PAMELA data (Adriani et al. 2009, 2010). Integral flux is about 1/10000 of integral primary proton flux at Ft. Sumner. 2.3 Geomagnetic Rigidity Cutoff Cutoff calculations by back-trajectory tracing technique (Shea and Smart 1967) Depending on location and primary particle direction: 1. Umbra: Sharp cutoff below a minimum rigidity value. 2. Penumbra: Complex series of allowed and forbidden bands in particle rigidity range. Effective transmission coefficient calculated.

Mean Geomagnetic Rigidity cutoff as function of direction at Ft. Sumner (Bhadra et al. 2012, Elsevier Pre-print) Cutoff calculations used to modify primary spectra from CORSIKA. Satisfactory for secondary proton spectra at mountain altitude (Bhadra et al. 2009) and muon fluxes at balloon altitude (Bhadra et al. 2011)

2.4 Atmospheric Models US Standard Atmospheric Model ( Linsley, Pvt. Commun. ) in Planer Approximation (theta < 70 deg in CORSIKA) satisfactory for BESS-1999 proton flux (Bhadra et al. 2009) and BESS muon fluxes (Djemil, Atallah and Capdevielle 2007, Bhadra et al. 2011) 2.5 Other Settings BESS-1998 Power Spectra extended to 1 PeV/n. K.E of Primary particles chosen randomly between minimum geomagnetic cutoff and 1PeV/n million events generated to reduce statistical error.

3. Results Simulated pbar flux at multiple observation levels with corresponding BESS-observations.

 UrQMD – derived fluxes are consistent with observations at mountain altitude and at sea-level.  FLUKA - generated pbar fluxes are consistently higher than UrQMD flux and BESS-observations, particularly at low energies.  Discrepancy between FLUKA results and measured fluxes decreases at increasing atmospheric depth.  Strongly enhanced antiproton production in FLUKA.  Almost 80% model dependent uncertainty at low ( ~ 300 MeV ) energy at balloon altitude. Implications for PAMELA experiment extend energy range of pbars up to 100 GeV.

High energy interaction models start influencing the results.

Quantification of uncertainties Ratios of mean fluxes from various models plotted with FLUKA + NEXUS – derived mean fluxes as the reference.

Model dependent uncertainty varies with energy : o 80% uncertainty at ~ 300 MeV due to differences between FLUKA and UrQMD. o 60% uncertainty at ~ 100 GeV due to differences between High Energy Interaction Models. Systematic deviations : o QGSJET01 predicted pbar flux tends to be lower than other predictions. o EPOS 1.6 derived pbar flux tends to be higher than other predictions. EPOS is known to produce more baryons/anti-baryons than other models.

4. Conclusions o PAMELA observations of excess positron but no excess antiproton over the standard interstellar production models lead to strong constraints on DM models (Boezio et al. 2009).

o Standard interstellar pbar spectra are calculated by galactic propagation codes with either empirical (eg. Moskalenko et al. 2002) or microscopic (eg. Simon, Molner and Roesler 1998) interaction models. o Calculations of atmospheric pbar flux at balloon altitude find much larger uncertainty (60-80%) due to model dependence than the ones (20-40%) quoted in the interstellar pbar calculations. o Such large uncertainty possibly makes some room for DM models. o Further study of galactic antiproton flux by exploiting various microscopic models seems to be necessary in the context of PAMELA results.

Acknowledgements The support from the Department of Science and Technology (Govt. of India) under the IRHPA Scheme is gratefully acknowledged.

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