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Geophysical tests of gravitational physics

with superconducting gravimeters

Sachie ShiomiSpace Geodesy Laboratory,

Department of Civil Engineering,National Chiao Tung University,

Hsinchu, Taiwan

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Contents

• Introduction– Superconducting Gravimeters (SGs)– Examples of applications to gravitational physics– The global network of SGs

• Application 1: Testing the universality of free-fall• Application 2: Searching for dilatonic waves• Summary

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Superconducting gravimeter (SG)• Sensitive and stable at low frequencies

Hsinchu SG, operated by NCTU and CMS

1 m

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Working principle

J. M. Goodkind, Review of Scientific Instruments 70 (1999)

Φ~ 2.5 cm

• Sphere is levitated by magnetic fields induced by currents in the superconducting levitation coils.

• Motion of the sphere is monitored by capacitor plates.~4.2 K

Gravimeter Sensing Unit

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Applications to gravitational physics

Earliest work (1976)• Search for evidence of a preference frame

(Warburton and Goodkind, Astrophysical Journal, 1976.)

More recent works, e.g.• Test of the inverse-square law (Goodkind et al PRD 1993, Baldi et al PRD, 2001)

• Measurement of gravitational constant G(Baldi et al PRD, 2005)

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The GGP network

• The Global Geodynamics Project (GGP) network of superconducting gravimeters (1997~): about 25 operating sites.

• To study geophysical signals in global nature, i.e. oscillation of the inner core, polar motion and wobbles.

D. Crossley, Journal of Geodynamics 38 (2004)

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D. Crossley

Currently operating

Stopped

To be installed

Newly installed

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Applications of the global network to gravitational physics

• We investigate possible applications of the GGP network to study gravitational physics.

• One of such applications is testing the universality of free-fall.

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Testing the universality of free-fall

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Universality of free-fall

• Every material (point mass) in a given external gravitational field falls at the same rate.

http://www.endex.com/gf/buildings/ltpisa/ltpnews/physnews1.htm

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Motivations of testing the universality

• Fundamental principle– It should be tested as precisely as possible.

• New physics?– Theories towards the unification of the four

fundamental forces predict new interactions that violate the principle.

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Proposed new forces (spin-independent)

Composition dependent

Motivated by Bosons (Spin) Mass Charge References (year)

Conservation of baryon charge

Vector bosons (1)

massless B Lee and Yang (1955)

Supersymmetry U-bosons (1) Massive

(very light)

B, Iz Fayet(1986)

String theory Dilatons(0)

Dilatons(0)

Moduli(0)

massive

massless

massive

(millimeter range)

Ordinary matter

B, Iz, E

Ordinary matter

Fujii(1971);Taylor and Veneziano (1988)

Damour and Polyakov(1994)

Dimopoulos and Giudice(1996)

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Modification of Newton’s law

V(r)

Yukawa-potential type

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Current limits

Fischbach and Talmadge, The Search for Non-Newtonian Gravity (Springer-Verlag, 1999)

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The necessity of variety in experimental approaches

• The universality has to be tested for various putative charges, using different kinds of test bodies, at different ranges.

• To confirm experimental results, it should be tested by at least two different experimental methods.

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Outer core

Mantle + Crust

Inner core

Earth

The concept

• If the universality were violated, the inner core would move relative to the rest part of the Earth.

Surface gravity changes

Sun

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Test bodies: inner core and the rest

• Chemical composition

– Density [kg m-3]

• Inner core (iron, nickel): ~ 13000

• The rest (silicon oxides): ~ 5400

• Gravitational binding energy

– Inner core: -3.7 ×10-11

– The rest: -4.2 ×10-10

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Best observation points

• In Spring and Autumnal equinox points: on the equator

• In Summer and Winter solstices: on Tropic of Cancer or Capricorn

N

S

Taiwan

Summer

Sun

Earth

SG

SG

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Equation of motion of the inner core

Gravitational stiffness

Damping effect Violation effect

S. Shiomi, Physical Review D 74, 027101(2006)

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Surface gravity changes

When the damping coefficient (k) is sufficiently small:

Forced oscillation

10-12 ms-2

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Expected sensitivity

Current limits: a few parts in 1013

;nearly four orders of magnitude improvement is necessary.

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Improving the sensitivity (1)• Carrying out coincidence measurements at

two observatories located opposite side of the Earth near the equators.

Hsinchu,Taiwan

Concepcion, Chile

Inner core

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Improving the sensitivity (2)

• Development of the data analysis method to extract weak signals.

e.g. Non-Linear Damped Harmonic Analysis method (S. Rosat et al, J. Geodyn. in press)

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Summary: expected signals

Direction along the Earth-Sun line

Frequency • once per day

• once per year

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Future works

• Improving noise reduction methods– Identification of environmental noise– Data analyses to extract weak signals

• Figuring out the optimum scheme of global observations– e.g. coincidence measurements

• Improvements of the sensitivity of SGs

• Application of elaborate Earth models

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Conclusions

• The universality of free-fall can be tested using a superconducting gravimeter installed near the equator to ~10-9.

• Some improvements can be expected from global observations and applications of advanced data analysis methods.

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Search for composition-dependent

dilatonic waves

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Introduction

• String theory predicts the existence of relic background of the dilaton (a scalar partner of the graviton).

• Ordinary macroscopic test masses have dilatonic charges, which depend on their internal compositions.

• The response of the test masses to dilatonic waves is non geodesic.

M. Gasperini, Phys. Lett. B 470, 67 (1999)

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The concept

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Estimation of upper limits (1)Spectrum of the displacement ( l ) at resonance

Dimensionless energy density for massless dilaton

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Estimation of upper limits (2)

Effective viscosity: 10-3 ~ 1012 Pa s(R.A. Secco, A Handbook of Physical Constants)

S. Shiomi, “Geophysical search for dilatonic waves” (submitted in 2007)

From residual gravity data,an upper limit on the displacement is

1.1 ×10-4 m Hz-1/2 at 7 ×10-5 Hz. (S. Rosat et al, J. of Geodyn. 38

(2004))

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• Nucleosynthesis and measurements of cosmic microwave background:

Ωh2100 ≤ 10-5

• To reach this limit, the effective viscosity

has to be smaller than ~ 2 × 106 Pa s.

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Conclusions

• Dilatonic waves can be searched for using superconducting gravimeters.

• The sensitivity is currently limited by the uncertainty in the Earth model.

• If the effective viscosity were determined

to be smaller than ~ 2 × 106 Pa s, this method would provide an upper limit better than the astrophysical limits.

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Other possible future applications

• Improved tests of the existence of a preference frame and an anisotropy of the gravitational constant.

• Direct detection of gravitational waves using the Earth as the receiver.

• Measurement of G– Tests for a distant dependence, time

dependence and a spatial anisotropy.

• Improved tests of the inverse square law.

J. M. Goodkind, Review of Scientific Instruments 70 (1999)

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Summary

• Superconducting gravimeters have been proved to be stable and sensitive in geophysical studies and also they have been used to study gravitational physics since 1970’s.

• The global network of superconducting gravimeters has been developed to study the Earth’s interior. By using the Earth as the test body, we investigate possible applications of the network to gravitational physics.

• We have discussed the geophysical test of the universality of free-fall and the search for dilatonic waves.

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Thank you.

Any new ideas for possible applications of SGs are welcome.