Search for Large Extra Dimensions Search for Large Extra Dimensions with Kaluza Klein Gravitons via with Kaluza Klein Gravitons via

Observations of Neutron Stars with Observations of Neutron Stars with Fermi-LAT Fermi-LAT

Bijan Berenji Bijan Berenji Representing the Fermi-LAT CollaborationRepresenting the Fermi-LAT CollaborationJuly 2009 TeV Particle Astrophysics Conf. July 2009 TeV Particle Astrophysics Conf.

SLAC National Accelerator LaboratorySLAC National Accelerator Laboratory

22

Large Extra DimensionsLarge Extra Dimensions

Goal: to set limits on the size of large extra dimensionsGoal: to set limits on the size of large extra dimensions, , according to the theory proposed byaccording to the theory proposed by Arkani-Hamed, Arkani-Hamed, Dimopoulos, andDimopoulos, and DvaliDvali (1998, (1998, Phys. Lett. BPhys. Lett. B 436436: 263–272).: 263–272).They postulated the existence of large extra dimensions, in They postulated the existence of large extra dimensions, in which only the gravitational force propagates, as an explanation which only the gravitational force propagates, as an explanation for the relative weakness of gravitational to electroweak for the relative weakness of gravitational to electroweak interactions (the hierarchy problem)interactions (the hierarchy problem).. Planck scale, Planck scale, MMP,4P,4 ~ 10 ~ 101919 GeV GeV Electroweak scale, Electroweak scale, MMEW EW ~ 1 TeV~ 1 TeV

Due to extra dimensions, the effective Planck mass in Due to extra dimensions, the effective Planck mass in nn+4 +4 dimensions, dimensions, MMP,n+4P,n+4 would be brought closer to the electroweak would be brought closer to the electroweak scale.scale.They considered compactified dimensions of the same size They considered compactified dimensions of the same size R R in in this model.this model. 2 n+2

P,4 P,n+4nM R M=

33

Large Extra Dimensions with Neutron StarsLarge Extra Dimensions with Neutron StarsKaluza-KleinKaluza-Klein ((KKKK) ) gravitonsgravitons ((hh)) are produced via nucleon- are produced via nucleon-nucleon gravi-bremsstrahlung in supernova cores: nucleon gravi-bremsstrahlung in supernova cores:

NN NN →→ NNh NNh

These These hh particles have masses ~ 100 MeV, and decay into particles have masses ~ 100 MeV, and decay into photons:photons: hh→→Restrictive limits on the size of extra dimensions can be Restrictive limits on the size of extra dimensions can be placed from neutron star placed from neutron star emission originating from trapped emission originating from trapped hh graviton decay.graviton decay.

(see for example: Hannestad and Raffelt, 2003, (see for example: Hannestad and Raffelt, 2003, Phys. Rev. DPhys. Rev. D 67 67 125008) 125008)

more stringent than the limits derived by indirect signals of extra more stringent than the limits derived by indirect signals of extra dimensions at colliders (for n < 5)dimensions at colliders (for n < 5)

In this model, neutron stars will shine in ~100 MeV In this model, neutron stars will shine in ~100 MeV -rays.-rays.

44

The Hannestad-Raffelt ModelThe Hannestad-Raffelt Modelfor Pulsar Gamma Ray Spectrumfor Pulsar Gamma Ray Spectrum

Hannestad and Raffelt derived a Hannestad and Raffelt derived a formula for the gamma-ray spectrum formula for the gamma-ray spectrum of of hh decay (Hannestad and Raffelt, decay (Hannestad and Raffelt, 2003, 2003, Phys. Rev. DPhys. Rev. D 67 67 125008 ) 125008 )The spectra depend on energy and The spectra depend on energy and the integer number of extra spatial the integer number of extra spatial dimensions as:dimensions as:

NN00: prefactor, (cm: prefactor, (cm-2-2 s s-1-1 MeV MeV-1-1) ) EEcc: parent core supernova : parent core supernova temperature ~ 30 MeV.temperature ~ 30 MeV.

1 ≤ n ≤ 7 (integer)1 ≤ n ≤ 7 (integer)

( )( )

2

c0

c1 exp

nE EdN

NdE E E

+

=+

Below: normalized SEDs for a few h modes (n = 2, 3, 4)

55

Correction for Decay Correction for Decay for KK Graviton Spectrum in Vicinityfor KK Graviton Spectrum in Vicinity

Decay correction factor depends as: ~exp(-tDecay correction factor depends as: ~exp(-tageage//22))22 ~ (6e9 yr) ~ (6e9 yr)××(100 MeV)(100 MeV)33//mm33

The spectra depend on energy and the integer number of extra The spectra depend on energy and the integer number of extra spatial dimensions as:spatial dimensions as:

NN00: prefactor, (cm: prefactor, (cm-2-2 s s-1-1 MeV MeV-1-1) ) EEcc: parent core supernova temperature ~ 30 MeV [fixed]: parent core supernova temperature ~ 30 MeV [fixed] ttageage: age of NS/PSR (yr) [fixed]: age of NS/PSR (yr) [fixed] ff: factor accounting for mean mass of trapped gravitons : factor accounting for mean mass of trapped gravitons 1 ≤ n ≤ 7 (integer)1 ≤ n ≤ 7 (integer)

66

Validation: Data Points and Fit Curves for a Validation: Data Points and Fit Curves for a Generic Simulated High Latitude SourceGeneric 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).

77

Criteria for Selecting a Sample of PulsarsCriteria for Selecting a Sample of PulsarsGalactic Galactic bb > 10 > 10 Avoid large galactic diffuse background near galactic planeAvoid large galactic diffuse background near galactic plane

BBsurfsurf < 10< 101010 G: above this, photon pair production occurs (into G: above this, photon pair production occurs (into ee++ee--) ) Approximately, Approximately, EEBBsurfsurf < 4.0< 4.0··10101212 G MeV to avoid pair G MeV to avoid pair

production production (Sturrock, 1971)(Sturrock, 1971)

Neutron stars not so old that Neutron stars not so old that hh have mostly decayed have mostly decayed Not in binary systemNot in binary system

Complicates analysis, such as in pulsar accretionComplicates analysis, such as in pulsar accretion

Not in globular clusters.Not in globular clusters.

Not LAT identified pulsars (pulsating in gamma rays)Not LAT identified pulsars (pulsating in gamma rays)

LAT identified sources are greater than 3.5LAT identified sources are greater than 3.5 away 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 These criteria taken together curtail the number of potential sources for analysis.sources for analysis.

88

Fermi Data AnalysisFermi Data Analysis~ 9 months of Fermi-LAT data beginning from ~ 9 months of Fermi-LAT data beginning from Aug 2008 Aug 2008 Event selection: Event selection:

diffuse class diffuse class rays rays instrument theta < 66instrument theta < 66 zenith angle < 105zenith angle < 105 fit data between 100 MeV and 400 MeVfit data between 100 MeV and 400 MeV

Include galactic background diffuse convolved with instrument Include galactic background diffuse convolved with instrument PSF, as well as isotropic diffuse.PSF, as well as isotropic diffuse.Background subtract nearby sources in Fermi-LAT 9 month Background subtract nearby sources in Fermi-LAT 9 month catalogcatalogUse of most recent Use of most recent approvedapproved collaboration-released instrument collaboration-released instrument response functions (IRF) for Fermi-LAT for exposure and PSF response functions (IRF) for Fermi-LAT for exposure and PSF calculations.calculations.

99

Pulsars for AnalysisPulsars for Analysis

PSR J0711-6830 PSR J0711-6830 1 nearby Fermi-LAT source 3.7 1 nearby Fermi-LAT source 3.7 away away

PSR J1629-6902PSR J1629-6902 3 nearby Fermi-LAT sources 3 nearby Fermi-LAT sources closest 5.1closest 5.1 away away

1010

Data on Sample of Pulsars Data on Sample of Pulsars ParameterParameter PSR PSR

J0711-6830J0711-6830PSR PSR J1629-6902J1629-6902

RA (RA ()) 107.97107.97 247.29247.29

Dec (Dec ()) -68.51-68.51 -69.05-69.05

l l (()) 279.53279.53 320.37320.37

b b (()) -23.28-23.28 -13.93-13.93

Age (yr)Age (yr) 5.815.81××101099 9.519.51××101099

Period/P0 Period/P0 (ms)(ms)

5.49 5.49 6.006.00

Period-Period-dot/P1dot/P1

1.5×1.5×1010-20-20 1.01.0××1010-20-20

Distance Distance (kpc)(kpc)

1.04 1.04 1.361.36

BBsurf surf (G)(G) 2.9×2.9×101088 2.482.48××101088

•Both are isolated millisecond Both are isolated millisecond pulsars (magnetic field pulsars (magnetic field constraint makes this likely).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)

1111

Upper Limits PlotUpper Limits Plot90% CL upper limits per energy band (red) from 9 months 90% CL upper limits per energy band (red) from 9 months of Fermi-LAT dataof Fermi-LAT datan = 4 model case shown (blue dashed)n = 4 model case shown (blue dashed)

PSR J0711-6830PSR J0711-6830 PSR J1629-6902PSR J1629-6902

PRELIMINARY

PRELIMINARY

PRELIMINARY

PRELIMINARY

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According to Hannestad & Raffelt, the following equation According to Hannestad & Raffelt, the following equation applies:applies:

2 1 *0

* 23 2 1 20

1/

*0

( 100 MeV) cm s ( )

8.1 10 cm s

1(m)

30 MeV

nn n

kpc

n

n n c

c

E RT I

d

cR

I E

E

− −

− − − −

Φ > =Φ Ω

Φ = × ⋅

⎛ ⎞Φ=⎜ ⎟Φ Ω⎝ ⎠

=

h

Extra Dimensions’ Size CalculationExtra Dimensions’ Size Calculation

•Dimensionless constants depending on n

}

1313

Results for a Sample of PulsarsResults for a Sample of Pulsars

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

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 E > 100 MeV.

1414

SummarySummaryLimits on large extra dimensions size can be obtained Limits on large extra dimensions size can be obtained from neutron star observations in gamma rays using a from neutron star observations in gamma rays using a predicted energy spectrum and flux.predicted energy spectrum and flux.Fermi MC simulations provide validation of analysis Fermi MC simulations provide validation of analysis methods.methods.Planned improvements for upper limits from Fermi-Planned improvements for upper limits from Fermi-LAT: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 Increase sample of pulsars with listed criteria to obtain better

limits. limits. Statistically combine limits from different sources.Statistically combine limits from different sources. Look for pulsars closer to Earth to obtain the most restrictive Look for pulsars closer to Earth to obtain the most restrictive

limits (limit scales as limits (limit scales as dd22/n/n))

1515

BACKUP SLIDESBACKUP SLIDES

1616

Several Ways to set Astrophysical Limits on Several Ways to set Astrophysical Limits on Extra Dimensions with KK GravitonsExtra Dimensions with KK Gravitons

Supernova cooling due to graviton emission – an alternative cooling Supernova cooling due to graviton emission – an alternative cooling mechanismmechanism that would that would decreasedecrease the dominant cooling via the dominant cooling via neutrino neutrino emission (ADD, Savage et al, Hannestad & Raffelt)emission (ADD, Savage et al, Hannestad & Raffelt)Distortion of the cosmic diffuse gamma radiation (CDG)Distortion of the cosmic diffuse gamma radiation (CDG) spectrumspectrum due to the KK graviton (Hall & Smith, Hannestad & Raffelt)due to the KK graviton (Hall & Smith, Hannestad & Raffelt)

Neutron star Neutron star -emission from radiative decays of the -emission from radiative decays of the gravitons trapped during the supernova collapsegravitons trapped during the supernova collapseNeutron star excess heat (Hannestad & Raffelt)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 listNot an exhaustive listThese methods are complementary to collider limits on extra These methods are complementary to collider limits on extra dimensions, because can set more restrictive limits on fewer than 5 dimensions, because can set more restrictive limits on fewer than 5 extra dimensions (in most models).extra dimensions (in most models).

1717

Extra Dimensions, Gravitational Force,Extra Dimensions, Gravitational Force, and Gauss’s Law and Gauss’s Law

In three (infinite) dimensions Gauss's law states that the force associated with such In three (infinite) dimensions Gauss's law states that the force associated with such a field falls off as 1/a field falls off as 1/rr22 because the lines of force are spread over an area that is because the lines of force are spread over an area that is proportional to proportional to rr22. In general, Gauss's law predicts that a force that falls off as 1/. In general, Gauss's law predicts that a force that falls off as 1/rrnn-1-1, , where where nn is the number of space dimensions. is the number of space dimensions. The figure shows the The figure shows the gravitational lines of forcegravitational lines of force produced by a point mass in a produced by a point mass in a space with space with one infinite dimensionone infinite dimension (the horizontal green line)(the horizontal green line) and and one finite or one finite or "curled up" dimension (the green circle)"curled up" dimension (the green circle). . The gravitational force felt by a second point mass a distance The gravitational force felt by a second point mass a distance rr away is proportional away is proportional to the number of force lines per unit area. When to the number of force lines per unit area. When rr is less than the size of the curled is less than the size of the curled up dimension, up dimension, the lines spread uniformly in two dimensions (blue circle)the lines spread uniformly in two dimensions (blue circle),, so, so, according to Gauss's law for according to Gauss's law for nn = 2, the gravitational force should vary as 1/ = 2, the gravitational force should vary as 1/rr. . But for much larger separations the lines become parallel and the force does not But for much larger separations the lines become parallel and the force does not change with distance. change with distance.

2 n+2P,4 P,n+4

nM R M=

Relation between extra dimensions size R, 4-dim. Planck mass, and n+4 dim. Planck mass:

1818

Simulation OverviewSimulation Overview

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

1919

Extra Dimensions’ Size Extra Dimensions’ Size CalculationCalculationCalculation of extra dimensions size: need integral flux from source Calculation of extra dimensions size: need integral flux from source

above 100 MeV (computed above for different n)above 100 MeV (computed above for different n)

According to Hannestad & Raffelt, the following equation applies:According to Hannestad & Raffelt, the following equation applies:

2 1 *0

* 23 2 1 20

1/

1*0

kpc

( 100 MeV) cm s ( )

8.1 10 cm s

1 1(MeV )

conversion to length scale: 197.326 MeV fm 1

0.26 (PSR J0953+0755)

30 MeV

nn n

kpc

n

n n

E RT I

d

RI T

c

d

T

− −

− − − −

−

Φ > =Φ Ω

Φ = × ⋅

⎛ ⎞Φ=⎜ ⎟Φ Ω⎝ ⎠

= ⋅ ≡=

=

h