1. John Simonetti Physics Department, Virginia Tech
A Precision Test for an Extra Spatial Dimension Using BH-NS Binary Systems
John Simonetti
Physics Department, Virginia Tech
Physics, VT
Djordje Minic
Vipin Vijayan
ECE, VT
Umair Surani
Physics, LIU
Mike Kavic

2. …the Plan… Motivation Extra spatial dimensions “in a nutshell”
Astrophysical Test Extra dimension of size ~1 micron in the RS2 braneworld scenario  enhanced evaporation of a black hole  observable evolution of a BH-NS binary system

3. Extra Spatial Dimensions

4. Spatial Dimensions z
…nothing all that mysterious y x x

5. Why consider extra dimensions?
*** String Theory ***
6 or 7 extra spatial dimensions
Why don’t we observe them??
Very small
Large, even infinite (but “warped”)
Weird???
Experiment/Observations

6. Very small --- “Compactified”
“garden hose” x x
r = r + L
(Kaluza, Klein
1920s)
How small? x r

7. “Natural” compactification size: Planck Length
Planck energy scale is ~1016 times larger than
the energy scale of particle physics:
the electroweak scale ~ 103 GeV ~ 1 TeV.
Gravity is very much weaker than the other forces
“Hierarchy Problem”

8. …but extra dimensions could be larger than the Planck length
Particle physics experiments
Not even close to the Planck scale
Probe standard model matter, forces
Require L < m, in models where standard
model matter/forces move in the extra dim.
But larger extra dimensions possible, even useful !
Arkani-Hamed, Dimopoulos, and Dvali (1998)
If only gravity propagates in the extra dimensions
L ~ mm possible, without violating known limits !!
And, could explain why gravity is relatively so weak

9. How would extra dimensions explain why gravity is weak?…

10. Terrestrial Searches for Extra Dimensions
LHC
TeV scale
L ~ m
Eot-Wash “Cavendish Experiment”
Adelberger et al. UW:
Upper limit on L of 44 mm

11. Astrophysical Test

12. Evaporation of a Black Hole by “standard” Hawking Radiation
The power radiated by a blackbody is

13. Infinitely large “warped” extra dimension
Branes
(consistency of string theory)
Bulk
Braneworlds
Randall-Sundrum 2 (1999) x y
bulk
brane
infinite 4th spatial dimension
Our brane --- flat, positive cosmological constant (tension),
standard model particles/forces confined to the brane
The bulk AdS: vacuum, negative cosmological constant, gravity only,
“warped” (redshift scaling factor confines gravitons near our brane)
No stable BH solutions on the brane, due to enhanced Hawking radiation modes

14. Emparan, Fabbri, Kaloper (2002)
Emparan, García-Bellido, Kaloper (2003)
Enhanced black hole evaporation rate in RS 2 braneworld,
due to a greatly enhanced number of emission modes
(gravitons propagating into the bulk, i.e., “Kaluza-Klein” gravitons)
(L is the length scale of warp)
Lifetimes for stellar-mass black holes
< age of the universe

15. But X-ray binary systems are messy A Cleaner system:
Look for effects in
X-Ray Binary Systems?
Psaltis (2007)
Johannsen (2008)
But X-ray binary systems are messy
A Cleaner system:
Two compact objects (point masses)
…and one is a “pulsar”

16. The “Binary Pulsar” PSR B1913+16
Weisberg and Taylor 2005
ap sin i = (8) s
e = (4)
P = days (7.75 hours)
Mpulsar = / M*
Mcompanion = / M*
dP/dt = ( / ) ms/y
dP/dt = ( / ) dP/dtGR
…unlikely to improve
Limited by galactic acceleration term
Will lose the pulsar beam in
~ 10 years (geodetic precession)

17. Evolution of a BH-NS Binary in an RS 2 braneworld ?
Black hole is losing mass…
Intuitively:
Decreasing gravitational binding Angular momentum conserved
Increasing orbital radius
Increasing orbital period

18. For mass loss both
increase

19. For the“Binary Pulsar ballpark”
P = 7.75 hours
BH mass = 3 solar masses
NS mass = 1.4 solar masses
solar radii
dP/dt is 13,000 times larger than the precision on P for the Binary Pulsar!

20. Gravitational radiation: inspiral.
BH mass loss:
outspiral.
Gravitational radiation:
inspiral.
…Competition  a critical orbital period separating the two effects
If P > Pcritical outspiral
If P < Pcritical inspiral

21. Prospects No currently known BH-NS binaries
NS-NS binaries were a surprise
SN: if the system loses half its mass, it becomes unbound.
But a handful are known (including the PSR ).
Pfahl, Podsiadlowski, Rappaport (2005)
Expect fewer than ~10 BH-NS binaries in our Galaxy.
But the argument hinges partly on coalescence due to gravitational
radiation (in under 108 years).
For BH-NS in the “Pulsar Binary Ballpark”
For PSR precision, can set a limit on L < microns.
800 times better than the current limit L < 44 microns.

22. Summary Extra spatial dimensions Experimental/Observational evidence?
are not ruled out by any physics we know
are a major ingredient in current quantum gravity theories
Experimental/Observational evidence?
Terrestrial searches may turn up evidence
Astrophysical searches are also possible
Explosion of PBH
BH-NS binary
Other?

23. Stellar-Mass Black Hole Evaporation
Searching for an extra dimension
just below the current limits probed by
Cavendish-type experiments
L ~ 44 mm
Enhanced BH evaporation
Effects in X-ray binaries?
BH-NS binaries…a result opposite to that produced by gravitational radiation

24. M = 1.4 solar masses R = 10 km Antony Hewish Jocelyn Bell
Nobel Prize 1974
M = 1.4 solar masses
R = 10 km

25. The “Binary Pulsar” PSR B1913+16
1993 Nobel Prize
Russell Hulse
Joseph Taylor

26. Arecibo Observatory

27. Binary systems with isotropic mass loss
Hadjidemetriou (1963, 1967)
Binary systems with isotropic mass loss

28. So we average over one orbit, using
In our case
So we average over one orbit, using
K III

29. The
Assembled
Ingredients
For mass loss both
increase

30. A“Binary Pulsar ballpark”
P = 7.75 hours
BH mass = 3 M* NS mass = 1.4 M*

31. Precision on orbital period determination for PSR B1913+16
+/ ms y ms y-1 / ms y-1 = sigma Accepting 3 sigma results for a BH-NS binary system in the “Binary Pulsar ballpark” we could set an upper limit on L to L ~ 0.2 microns

32. The orbital period increases… But, what about the competing effect due energy loss by gravitational radiation?

34. For comparison, for gravitational radiation alone:
Peters & Matthews
(1968)

35. For comparison, for gravitational radiation alone:
Peters & Matthews
(1968)

36. for
P < Pcritical : gravitational radiation dominates
P > Pcritical : enhanced mass loss dominates

37. Are there any BH-NS binaries?
None known at the moment
NS-NS binaries were a surprise
SN: if the system loses half its mass, it becomes unbound.
But a handful are known (including the PSR ).
Pfahl, Podsiadlowski, Rappaport (2005)
Expect fewer than ~10 BH-NS binaries in our Galaxy.
But the argument hinges partly on coalescence due to gravitational
radiation (in under 108 years).

38. Summary Extra spatial dimensions Experimental/Observational evidence?
are not ruled out by any physics we know
are a major ingredient in current quantum gravity theories
Experimental/Observational evidence?
Terrestrial searches may turn up evidence soon
Astrophysical searches are also possible
Explosion of PBH
BH-NS binary
At least, it’s fun to think about this stuff!

39. Black-string to black hole phase transition
…radio pulse production
Fireball expands to Rc
expelling interstellar B, and
total energy proportional to
Rc3B2 g2
EM pulse of length
cRc/v – Rc ~ Rc / g2
EM pulse of duration
Dt ~ Rc / cg2
…composed of frequencies
< 1 / Dt
For our situation (g ~ 105):
Rc ~ a solar radius
1 / Dt ~ 3 GHz

40. EM pulse can be produced if RS reaches L when kT ~ 0.1-10 TeV
Black-string to black hole phase transition
…radio pulse production
EM pulse can be produced
if RS reaches L when
kT ~ TeV
At too low T (low energy particles)
Energy goes into sweeping up,
accelerating interstellar particles.
At too high T (high energy particles)
Not enough particles to produce
necessary current on surface of
fireball to expell interstellar
magnetic field.

43. Eight-meter-wavelength Transient Array (ETA1, ETA2)
ETA can detect such pulses out to ~ 300 pc.
Such a detection would signify the existence of an extra
spatial dimension of size to m.

44. LWA-1

45. BH-NS Binary System …in a Randall-Sundrum 2 braneworld
Enhanced BH mass loss
Solar mass BH can evaporate in < age of universe!
for length scale of extra dimension ~ 0.2 microns
Binary components outspiral
For system in the “Binary Pulsar ballpark” (PSR B )
P = 7.75 hours
MBH = 3 solar masses
MNS = 1.4 solar masses
Semi-major axis increases 16 m/year
P increases 0.4 ms/year
13,000 times larger than precision on P for Binary Pulsar!
Can set an upper limit on L of ~ 0.2 microns