1. Search for Large Extra Dimensions with Kaluza Klein Gravitons via Observations of Neutron Stars with Fermi-LAT Bijan Berenji Representing the Fermi-LAT Collaboration July 2009 TeV Particle Astrophysics Conf. SLAC National Accelerator Laboratory

2. 2 Large Extra Dimensions Goal: to set limits on the size of large extra dimensions, according to the theory proposed by Arkani-Hamed, Dimopoulos, and Dvali (1998, Phys. Lett. B 436: 263–272). They postulated the existence of large extra dimensions, in which only the gravitational force propagates, as an explanation for the relative weakness of gravitational to electroweak interactions (the hierarchy problem). Planck scale, M P,4 ~ 10 19 GeV Planck scale, M P,4 ~ 10 19 GeV Electroweak scale, M EW ~ 1 TeV Electroweak scale, M EW ~ 1 TeV Due to extra dimensions, the effective Planck mass in n +4 dimensions, M P,n+4 would be brought closer to the electroweak scale. They considered compactified dimensions of the same size R in this model. `

3. 3 Large Extra Dimensions with Neutron Stars Kaluza-Klein (KK) gravitons (h) are produced via nucleon-nucleon gravi-bremsstrahlung in supernova cores: NN → NNh  These h particles have masses ~ 100 MeV, and decay into photons: h →  Restrictive limits on the size of extra dimensions can be placed from neutron star  emission originating from trapped h graviton decay. (see for example: Hannestad and Raffelt, 2003, Phys. Rev. D 67 125008) (see for example: Hannestad and Raffelt, 2003, Phys. Rev. D 67 125008) more stringent than the limits derived by indirect signals of extra dimensions at colliders (for n < 5) more stringent than the limits derived by indirect signals of extra dimensions at colliders (for n < 5) In this model, neutron stars will shine in ~100 MeV  -rays.

4. 4 The Hannestad-Raffelt Model for Pulsar Gamma Ray Spectrum Hannestad and Raffelt derived a formula for the gamma-ray spectrum of h decay (Hannestad and Raffelt, 2003, Phys. Rev. D 67 125008 ) The spectra depend on energy and the integer number of extra spatial dimensions as: N 0 : prefactor, (cm -2 s -1 MeV -1 ) E c : parent core supernova temperature ~ 30 MeV. N 0 : prefactor, (cm -2 s -1 MeV -1 ) E c : parent core supernova temperature ~ 30 MeV. 1 ≤ n ≤ 7 (integer) 1 ≤ n ≤ 7 (integer) Below: normalized SEDs for a few h modes (n = 2, 3, 4)

5. 5 Correction for Decay for KK Graviton Spectrum in Vicinity Decay correction factor depends as: ~exp(-t age /  2  )  2  ~ (6e9 yr)×(100 MeV) 3 / m 3 The spectra depend on energy and the integer number of extra spatial dimensions as: N 0 : prefactor, (cm -2 s -1 MeV -1 ) N 0 : prefactor, (cm -2 s -1 MeV -1 ) E c : parent core supernova temperature ~ 30 MeV [fixed] E c : parent core supernova temperature ~ 30 MeV [fixed] t age : age of NS/PSR (yr) [fixed] t age : age of NS/PSR (yr) [fixed] f : factor accounting for mean mass of trapped gravitons f : factor accounting for mean mass of trapped gravitons 1 ≤ n ≤ 7 (integer) 1 ≤ n ≤ 7 (integer)

6. 6 Validation: Data Points and Fit Curves for a Generic Simulated High Latitude Source Modeled a source accounting for decay, with n = 3, E c = 30 MeV Modeled background with galactic diffuse (GALPROP) and isotropic extragalactic diffuse (index 2.1), with a point source. Input point source integral flux above 100 MeV : 7.29 ×10 -7 cm -2 s -1 Output fitted flux above 100 MeV: (7.28 ± 0.60)×10 -7 cm -2 s -1 Model-dependent upper limit: 90% CL, 7.75×10 -7 cm -2 s -1 Upper limit value agrees with integral flux (conservatively).

7. 7 Criteria for Selecting a Sample of Pulsars Galactic b > 10  Avoid large galactic diffuse background near galactic plane Avoid large galactic diffuse background near galactic plane B surf < 10 10 G: above this, photon pair production occurs (into e + e - ) Approximately, E  B surf < 4.0·10 12 G MeV to avoid pair production (Sturrock, 1971) Approximately, E  B surf < 4.0·10 12 G MeV to avoid pair production (Sturrock, 1971) Neutron stars not so old that h have mostly decayed Not in binary system Complicates analysis, such as in pulsar accretion Complicates analysis, such as in pulsar accretion Not in globular clusters. Not LAT identified pulsars (pulsating in gamma rays) LAT identified sources are greater than 3.5  away Avoid signal confusion, due to Fermi-LAT PSF. Avoid signal confusion, due to Fermi-LAT PSF. These criteria taken together curtail the number of potential sources for analysis.

8. 8 Fermi Data Analysis ~ 9 months of Fermi-LAT data beginning from Aug 2008 Event selection: diffuse class  rays diffuse class  rays instrument theta < 66  instrument theta < 66  zenith angle < 105  zenith angle < 105  fit data between 100 MeV and 400 MeV fit data between 100 MeV and 400 MeV Include galactic background diffuse convolved with instrument PSF, as well as isotropic diffuse. Background subtract nearby sources in Fermi-LAT 9 month catalog Use of most recent approved collaboration-released instrument response functions (IRF) for Fermi-LAT for exposure and PSF calculations.

9. 9 Pulsars for Analysis PSR J0711-6830 1 nearby Fermi-LAT source 3.7  away 1 nearby Fermi-LAT source 3.7  away PSR J1629-6902 3 nearby Fermi-LAT sources 3 nearby Fermi-LAT sources closest 5.1  away closest 5.1  away

10. 10 Data on Sample of Pulsars Parameter PSR J0711-6830 PSR J1629-6902 RA (  ) 107.97247.29 Dec (  ) -68.51-69.05 l (  ) 279.53320.37 b (  ) -23.28-13.93 Age (yr) 5.81×10 9 9.51×10 9 Period/P0 (ms) 5.496.00 Period- dot/P1 1.5×10 -20 1.0×10 -20 Distance (kpc) 1.041.36 B surf (G) 2.9×10 8 2.48×10 8 Both are isolated millisecond pulsars (magnetic field constraint makes this likely).Both are isolated millisecond pulsars (magnetic field constraint makes this likely). Parameters from ATNF Pulsar Catalog (http://www.atnf.csiro.au/researc h/pulsar/psrcat/) Manchester, R.N., Hobbs, G.B., Teoh, A, & Hobbs, M. The Astronomical Journal, 129, 1993-2006 (2005)

11. 11 Upper Limits Plot 90% CL upper limits per energy band (red) from 9 months of Fermi-LAT data n = 4 model case shown (blue dashed) PSR J0711-6830PSR J1629-6902 PRELIMINARY PRELIMINARY

12. 12 According to Hannestad & Raffelt, the following equation applies: Extra Dimensions’ Size Calculation Dimensionless constants depending on n }

13. 13 Results for a Sample of Pulsars nPSR J1629-6902 R [m] PSR J0711-6830 R [m] R (HR, 2003*) [m] 23.5E-61.6E-65.1E-8 31.9E-92.4E-101.1E-10 44.5E-113.0E-115.5E-12 54.9E-123.6E-129.1E-13 61.1E-128.7E-132.8E-13 74.0E-133.2E-131.2E-13 PRELIMINARY Table of values (left 2 columns), using fitted flux. *For their limit, Hannestad&Raffelt analyzed 2 neutron stars at distances at least a factor of 10 less than these sources, and assumed an EGRET point source sensitivity of 1E-7 cm -2 s -1, for E  > 100 MeV.

14. 14 Summary Limits on large extra dimensions size can be obtained from neutron star observations in gamma rays using a predicted energy spectrum and flux. Fermi MC simulations provide validation of analysis methods. Planned improvements for upper limits from Fermi- LAT: Analyze over longer observation time (>1 yr). Analyze over longer observation time (>1 yr). Extend energy range down to 50 MeV (pending) Extend energy range down to 50 MeV (pending) Increase sample of pulsars with listed criteria to obtain better limits. Increase sample of pulsars with listed criteria to obtain better limits. Statistically combine limits from different sources. Statistically combine limits from different sources. Look for pulsars closer to Earth to obtain the most restrictive limits (limit scales as d 2/n ) Look for pulsars closer to Earth to obtain the most restrictive limits (limit scales as d 2/n )

15. 15 BACKUP SLIDES

16. 16 Several Ways to set Astrophysical Limits on Extra Dimensions with KK Gravitons Supernova cooling due to graviton emission – an alternative cooling mechanism that would decrease the dominant cooling via neutrino emission (ADD, Savage et al, Hannestad & Raffelt) Distortion of the cosmic diffuse gamma radiation (CDG) spectrum due to the KK graviton (Hall & Smith, Hannestad & Raffelt) Neutron star  -emission from radiative decays of the gravitons trapped during the supernova collapse Neutron star excess heat (Hannestad & Raffelt) KK gravitons impinge on NS, thereby heating it. KK gravitons impinge on NS, thereby heating it. Not an exhaustive list These methods are complementary to collider limits on extra dimensions, because can set more restrictive limits on fewer than 5 extra dimensions (in most models).

17. 17 Extra Dimensions, Gravitational Force, and Gauss’s Law In three (infinite) dimensions Gauss's law states that the force associated with such a field falls off as 1/ r 2 because the lines of force are spread over an area that is proportional to r 2. In general, Gauss's law predicts that a force that falls off as 1/ r n -1, where n is the number of space dimensions. The figure shows the gravitational lines of force produced by a point mass in a space with one infinite dimension (the horizontal green line) and one finite or "curled up" dimension (the green circle). The gravitational force felt by a second point mass a distance r away is proportional to the number of force lines per unit area. When r is less than the size of the curled up dimension, the lines spread uniformly in two dimensions (blue circle), so, according to Gauss's law for n = 2, the gravitational force should vary as 1/ r. But for much larger separations the lines become parallel and the force does not change with distance. Relation between extra dimensions size R, 4-dim. Planck mass, and n+4 dim. Planck mass:

18. 18 Simulation Overview Simulated events with known spectral distribution were generated according to the Fermi collaboration simulation package gtobssim. Fitting these events provide validation of fitting procedure and analysis. Photons were processed according to a specified set of instrument response functions (which parameterize PSF and effective area) By default, gtobssim uses a simplified scanning mode and orbit solution for determining the instrument pointing and livetime history, and it outputs the computed pointing history to a FITS event file. Simulated photon events were generated from a source located at (l,b) = (90 ,45  ) Point sources may be modeled in several different ways. A time- independent spectral function specifying energy and relative counts at discrete point for Hannestad-Raffelt function (n=3) was specified for PSR. GALPROP galactic diffuse (collaboration standard) and isotropic diffuse models were accounted for in background.

19. 19 Extra Dimensions’ Size Calculation Calculation of extra dimensions size: need integral flux from source above 100 MeV (computed above for different n) According to Hannestad & Raffelt, the following equation applies: