Search%20for%20Large%20Extra%20Dimensions%20with%20Kaluza%20Klein%20Gravitons%20via%20Observations%20of%20Neutron%20Stars%20with%20Fermi-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 by
  Arkani-Hamed, Dimopoulos, and Dvali (1998, Phys.
  Lett. B 436 263272).
• 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 n4 dimensions, MP,n4 would be brought
  closer to the electroweak scale.
• They considered compactified dimensions of the
  same size R in this model.

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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 lt 5)
• In this model, neutron stars will shine in 100
  MeV
• g-rays.

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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)

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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)

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Validation Data Points and Fit Curves for a
Generic Simulated High Latitude Source

• Modeled a source accounting for decay, with n
  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, 7.7510-7
  cm-2 s-1
• Upper limit value agrees with integral flux
  (conservatively).

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Criteria for Selecting a Sample of Pulsars

• Galactic b gt 10?
• Avoid large galactic diffuse background near
  galactic plane
• Bsurf lt 1010 G above this, photon pair
  production occurs (into ee-)
• Approximately, EgBsurf lt 4.01012 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.

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Fermi Data Analysis

• 9 months of Fermi-LAT data beginning from Aug
  2008
• Event selection
• diffuse class g-rays
• instrument theta lt 66?
• zenith angle lt 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.

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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

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Data on Sample of Pulsars
Parameter PSR J0711-6830 PSR J1629-6902
RA (?) 107.97 247.29
Dec (?) -68.51 -69.05
l (?) 279.53 320.37
b (?) -23.28 -13.93
Age (yr) 5.81109 9.51109
Period/P0 (ms) 5.49 6.00
Period-dot/P1 1.510-20 1.010-20
Distance (kpc) 1.04 1.36
Bsurf (G) 2.9108 2.48108

• 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)

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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
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Extra Dimensions Size Calculation

• According to Hannestad Raffelt, the following
  equation applies

• Dimensionless constants depending on n

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Results for a Sample of Pulsars
PRELIMINARY Table of values (left 2 columns),
using fitted flux.
n PSR J1629-6902 R m PSRJ0711-6830 R m R (HR, 2003) m
2 3.5E-6 1.6E-6 5.1E-8
3 1.9E-9 2.4E-10 1.1E-10
4 4.5E-11 3.0E-11 5.5E-12
5 4.9E-12 3.6E-12 9.1E-13
6 1.1E-12 8.7E-13 2.8E-13
7 4.0E-13 3.2E-13 1.2E-13

• For their limit, HannestadRaffelt 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 gt 100 MeV.

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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 (gt1 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)

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BACKUP SLIDES
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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 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).

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Extra Dimensions, Gravitational Force, and
Gausss Law
Relation between extra dimensions size R, 4-dim.
Planck mass, and n4 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 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.

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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 (n3) was
  specified for PSR.
• GALPROP galactic diffuse (collaboration standard)
  and isotropic diffuse models were accounted for
  in background.

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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