12122009Paulo Freire,

1
Testing General Relativity Using Binary Pulsars

• Timing the Binary Pulsar PSR J20161947 at
  Arecibo New Constraints on the Strong
  Equivalence Principle.
• ----------------------------
• Paulo Cesar C. Freire
• Cornell University / Arecibo Observatory

2
In this talk

• List previous tests of General Relativity,
• Make a Brief History of the Weak Equivalence
  Principle,
• Present the Strong Equivalence Principle,
• Present the Nordtvedt Effect (which arises if the
  Strong Equivalence Principle is violated), and
  its experimental limits,
• Talk about binary pulsars and the strong field
  tests they enable,
• Discuss the prospects for the timing of the newly
  discovered pulsar PSR J20161947.

3
Testing General Relativity

• The traditional tests of general relativity
  (GR) have been made in the Solar System. They
  include
• Experiment on the equivalence of gravitational
  and inertial mass (Galileo, Newton, Eotvos 1890),
• Advance of the periastron of the orbit of
  Mercury,
• Deflection of light from distant stars near the
  Suns limb (Eddington Dyson, 1919),
• Detection of gravitational redshift (Pound
  Rebka 1960, R. Vessots Gravity Probe A, 1979),
• Detection of the Shapiro delay (Shapiro,
  1968,1971, at Haystack and Arecibo),
• Measurement of frame dragging (Gravity Probe B)

4
The Weak Equivalence Principle

• This is the basis of General Relativity. It is
  required by all metric theories of Gravitation
  (i.e., theories that describe gravity as a
  distortion of space-time alone). It can be seen,
  alternatively, as a prediction of GR and of all
  similar metric theories.
• Universality of free fall was first described
  (and tested?) by Galileo from the leaning tower
  of Pisa, circa 1610. Galileo wanted to prove that
  bodies of different sizes fall with the same
  acceleration.
• Newton introduced the concepts of inertial mass
  and gravitational mass. Intrigued by why should
  these be the same, independently of chemical
  composition, he made a precise test of this
  equality using a pendulum, in 1680.

5
Eotvos, Dicke and Braginsky

• In 1890, in Lake Balaton (Hungary), Baron Roland
  von Eotvos determined that inertial and
  gravitational masses are different for Platinum
  and several other metals by less than 3 x 10-9.
• He did this using a torsion balance. The design,
  with improvements and changes, has been used by
  Dicke et al. (1964) and Braginsky et al. (1971)
  to improve the upper limit of EP violation to
  10-12 approximately.
• There is a proposed space mission (STEP, or
  Scientific Test of the Equivalence Principle)
  than might in principle introduce an upper limit
  of 10-17 to 10-18 to EP violation.

6
The Strong Equivalence Principle (SEP)

• The Strong Equivalence Principle is specific to
  General Relativity,
• Its states that all objects in the Universe fall
  with the same acceleration independently of their
  (gravitational) binding energy,
• Therefore, according to this theory, the Earth
  and the Moon should fall in the gravitational
  field of the Sun at the same rate equally a
  pulsar (with a baryonic mass of 1.6 solar masses,
  and a total mass of 1.4 solar masses) and a white
  dwarf should fall in the gravitational field of
  the Galaxy at the same rate as well.

7
Alternative Theories of Gravitation

• The Brans-Dicke theory includes a scalar
  component that couples only with matter, not the
  metric field. This implies that for objects with
  significant self-gravitational energies, the
  inertial mass is different from the gravitational
  mass, that is, SEP is violated
• Therefore, the Earth and the Moon should fall
  with different accelerations in the Gravitational
  field of the Sun, because the Earth has a larger
  self-gravitational energy than the much lighter
  Moon.

8
The Nordtvedt Effect

• In a neutral atom subjected to a strong electric
  field, the proton and the electron have very
  different ratios for the inertial and electric
  mass (charge) hence they accelerate very
  differently in the external electric field,
• The net result is a polarization of the atom the
  electron cloud points in the direction opposite
  to that of the electric field. The effect is more
  noticeable when the electron is far from the
  nucleus. This effect (first detected
  spectroscopically) is called the Stark effect,
• For a pair of astronomical objects with SEP
  violation, the net result of the difference in
  acceleration is the introduction of an
  eccentricity along the sense of the gravitational
  field.

9
Or, to make it look really simple
10
(No Transcript)
11
Lunar Laser Ranging Experiment

• If the Earth and the Moon are falling at
  different rates in the gravitational field of the
  Sun (as predicted, among others, by the
  Brans-Dicke theory), then the lunar orbit should
  be polarized in the direction of the Sun,
• The distance to the Moon can be measured to a few
  centimeters by timing the return times of laser
  pulses, reflected by corner cubes left on the
  Moon by Apollo astronauts and a Soviet Luna
  mission,
• No polarization is detected. The results
  (Mueller, 1991) indicate that the difference of
  the inertial and gravitational masses of the
  Earths self- binding energy is smaller than 1.5
  x 10-3. Einstein wins again!

12
(No Transcript)
13
Radio PulsarsClocks where they are needed!

• Pulsars are BAD clocks, but recycled pulsars can
  be EXCELLENT clocks. Nature normally places these
  in very interesting places.
• The Hulse-Taylor binary pulsar (PSR B191316) was
  discovered in 1974, at the Arecibo Observatory.
• This is a double neutron star system (and the
  first pulsar known to be in a binary system!)
• It allowed the first significant test of General
  Relativity outside the Solar System
• Gravitational waves exist!
• Brans-Dicke theory does not pass the test (but)

14
Strong-Field Test of General Relativity

• These are only possible using binary pulsars!
• At present, there are very few viable
  alternatives to GR. Among the such few are the
  bi-tensor bi-scalar theories of gravitation
  (e.g., Esposito-Farese, 1992),
• These produce results similar to GR in the Solar
  System, but they indicate SEP violation for
  objects with very large gravitational
  self-energies,
• A pulsar has a gravitational binding energy of
  -15 of its total mass (depending on the equation
  of state). Therefore, pulsars and white dwarfs
  (with small binding energy) should fall in the
  field of the Galaxy with different accelerations.
  Nordtvedt effect again

15
What tool do we need to test this?

• A pulsar white dwarf system (both are small,
  but have very different binding energies),
• Pulsar (system) needs to be old, for effect to
  take time,
• System needs to be wide. As for an atom,
  polarization is stronger when charges are more
  separated (that is, when the external field is
  more relevant compared to the binding energy),
• Eccentricity needs to be small, so that a good
  limit on SEP violation can be placed.
• Figures of merit
• Pb2/e,
• P.(2 dp/dt)-1 1 Gyr or larger.
• Present limit (from pulsar timing) 1 - mI/mG
  lt 0.004 (Wex 1998).

16
Searching for pulsars is good for youThe
discovery of PSR J20161947

• Pulsar found, together with 5 other boring
  pulsars, in an Intermediate Galactic Latitude 430
  MHz survey made at the Arecibo Observatory
  Navarro, Jenet (Schlumberger), Anderson (Caltech)
  and Freire (Cornell), 2002, in preparation.
• Rotational period 64.935 ms Probably recycled.

17
Timing of PSR J20161947

• It orbits a 0.2 solar mass white dwarf,
• The orbital period is 635 days,
• The eccentricity is 0.00147,
• Preliminary lower limit for age 1.8 Gyr!
• Best system to test the Strong Equivalence
  Principle by a factor of five!
• Presently being timed at Arecibo by P. Freire, to
  confirm age and eccentricity (there is still a
  rotational ambiguity). Expect much improved
  limits on SEP violation in the Strong Field
  regime soon!
• These might invalidate the bi-tensor bi-scalar
  theories of gravitation, and introduce severe
  constraints to any future theory of gravitation.

18
In Summary

• If timing parameters of PSR J20161947 can be
  confirmed, we have discovered what might be, by
  far, the best system to test the Strong
  Equivalence Principle,
• We would then be able to impose upper limits on
  SEP violation five times smaller than present
  values,
• This would eliminate several alternatives to
  General Relativity,
• SEP violation limit would be a fundamental
  constraint on any future gravitational theories.

19

• The National Astronomy and Aeronomy Center is
  operated by Cornell University, under a
  cooperative agreement with the National Science
  Foundation.
• Contact me at pfreire_at_naic.edu, or visit my
  website at
• http//www.naic.edu/pfreire.