Searching for Large Extra Dimensions with Neutron Stars and Fermi-LAT

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. ` Large Extra Dimensions • Goal: to set limits on the size of large extra dimensions, according to the theory proposed byArkani-Hamed, Dimopoulos, andDvali (1998, Phys. Lett. B436: 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, MP,4 ~ 1019 GeV • Electroweak scale, MEW ~ 1 TeV • Due to extra dimensions, the effective Planck mass in n+4 dimensions, MP,n+4 would be brought closer to the electroweak scale. • They considered compactified dimensions of the same size R in this model.

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→gg • Restrictive limits on the size of extra dimensions can be placed from neutron star gemission originating from trapped h graviton decay. • (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) • In this model, neutron stars will shine in ~100 MeV g-rays.

4. The Hannestad-Raffelt Modelfor Pulsar Gamma Ray Spectrum Below: normalized SEDs for a few h modes (n = 2, 3, 4) • 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: • N0: prefactor, (cm-2 s-1 MeV-1) Ec: parent core supernova temperature ~ 30 MeV. • 1 ≤ n ≤ 7 (integer)

5. Correction for Decay for KK Graviton Spectrum in Vicinity • Decay correction factor depends as: ~exp(-tage/t2g) • t2g ~ (6e9 yr)×(100 MeV)3/m3 • The spectra depend on energy and the integer number of extra spatial dimensions as: • N0: prefactor, (cm-2 s-1 MeV-1) • Ec: parent core supernova temperature ~ 30 MeV [fixed] • tage: age of NS/PSR (yr) [fixed] • f: factor accounting for mean mass of trapped gravitons • 1 ≤ n ≤ 7 (integer)

6. Validation: Data Points and Fit Curves for a Generic Simulated High Latitude Source • Modeled a source accounting for decay, withn = 3 , Ec = 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)×10-7cm-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. Criteria for Selecting a Sample of Pulsars • Galactic b > 10 • Avoid large galactic diffuse background near galactic plane • Bsurf< 1010 G: above this, photon pair production occurs (into e+e-) • Approximately, EgBsurf< 4.0·1012 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 • 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. • These criteria taken together curtail the number of potential sources for analysis.

8. Fermi Data Analysis • ~ 9 months of Fermi-LAT data beginning from Aug 2008 • Event selection: • diffuse class g-rays • instrument theta < 66 • zenith angle < 105 • 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. Pulsars for Analysis • PSR J0711-6830 • 1 nearby Fermi-LAT source 3.7  away • PSR J1629-6902 • 3 nearby Fermi-LAT sources • closest 5.1 away

10. Data on Sample of Pulsars • Both are isolated millisecond pulsars (magnetic field constraint makes this likely). • Parameters from ATNF Pulsar Catalog (http://www.atnf.csiro.au/research/pulsar/psrcat/) • Manchester, R.N., Hobbs, G.B., Teoh, A, & Hobbs, M. The Astronomical Journal, 129, 1993-2006 (2005)

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 J0711-6830 PSR J1629-6902 PRELIMINARY PRELIMINARY

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

13. Results for a Sample of Pulsars 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-2s-1, for Eg > 100 MeV.

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). • Extend energy range down to 50 MeV (pending) • Increase sample of pulsars with listed criteria to obtain better limits. • Statistically combine limits from different sources. • Look for pulsars closer to Earth to obtain the most restrictive limits (limit scales as d2/n)

15. BACKUP SLIDES

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)spectrumdue to the KK graviton (Hall & Smith, Hannestad & Raffelt) • Neutron star g-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. • 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. Extra Dimensions, Gravitational Force, and Gauss’s Law Relation between extra dimensions size R, 4-dim. Planck mass, and n+4 dim. Planck mass: • In three (infinite) dimensions Gauss's law states that the force associated with such a field falls off as 1/r2 because the lines of force are spread over an area that is proportional to r2. In general, Gauss's law predicts that a force that falls off as 1/rn-1, where nis 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.

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. 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: