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
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).
19 GeV
 Planck scale, MP,4 ~ 10
 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.
M
2
P,4
R M
n
n+2
P,n+4
2
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.
3
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:
Below: normalized
SEDs for a few h
modes (n = 2, 3, 4)
E Ec 

dN
 N0
dE
1  exp  E Ec 
n2


N0: prefactor, (cm-2 s-1 MeV-1)
Ec: parent core supernova
temperature ~ 30 MeV.
1 ≤ n ≤ 7 (integer)
4
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:
3

tage 
E Ec 

dN
E
 
 N0
exp 
f


9
 6 10 yr  50 MeV  
dE
1  exp  E Ec 


n2





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)
5
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, 7.75×10-7 cm-2 s-1
•Upper limit value agrees with
integral flux (conservatively).
6
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.
7
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.
8
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
9
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)
5.81×109
9.51×109
Period/P0
(ms)
5.49
6.00
Perioddot/P1
1.5×10-20
1.0×10-20
Distance
(kpc)
1.04
1.36
Bsurf (G)
2.9×108
2.48×108
•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)
10
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
11
Extra Dimensions’ Size Calculation
According to Hannestad & Raffelt, the following equation
applies:
2 1
 ( E  100 MeV) cm s    n ( RT ) I n
*
0
n
2
*0  8.11023 cm 2s 1  d kpc
1/ n
}
  1 
R(m)   *

 0 n I n 
Ec  30 MeV
c
Ec
•Dimensionless constants
depending on n
12
Results for a Sample of Pulsars
PRELIMINARY Table of values (left 2 columns), using fitted flux.
n
PSR
J1629-6902
R [m]
PSR
J0711-6830
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,
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.
13
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 FermiLAT:





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)
14
BACKUP SLIDES
15
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).
16
Extra Dimensions, Gravitational Force,
Relation between
and Gauss’s Law
extra dimensions
size R, 4-dim.
Planck mass, and
n+4 dim. Planck
mass:
2
n+2
M P,4
 Rn M P,n+4
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.
17
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 timeindependent 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.
18
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:
 ( E  100 MeV) cm 2s 1  *0 n ( RT ) n I n
2
*0  8.11023 cm 2s 1  d kpc
1/ n
  1  1
R(MeV )   *

 0 n I n  T
conversion to length scale: c  197.326 MeV  fm  1
d kpc  0.26 (PSR J0953+0755)
1
T  30 MeV
19