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

…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

Extra Spatial Dimensions

Spatial Dimensions z …nothing all that mysterious y x x

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

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

“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”

…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 < 10-17 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

How would extra dimensions explain why gravity is weak? …

Terrestrial Searches for Extra Dimensions LHC TeV scale L ~ 10-18 m Eot-Wash “Cavendish Experiment” Adelberger et al. UW: Upper limit on L of 44 mm

Astrophysical Test

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

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

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

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”

The “Binary Pulsar” PSR B1913+16 Weisberg and Taylor 2005 ap sin i = 2.3417725(8) s e = 0.6171338(4) P = 0.322997448930 days (7.75 hours) Mpulsar = 1.4414 +/- 0.0002 M* Mcompanion = 1.3867 +/- 0.0002 M* dP/dt = (-0.076 +/- 0.00003) ms/y dP/dt = (1.0013 +/- 0.0021) dP/dtGR …unlikely to improve Limited by galactic acceleration term Will lose the pulsar beam in ~ 10 years (geodetic precession)

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

For mass loss both increase

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!

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

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 1913+16). 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 1913+16 precision, can set a limit on L < 0.056 microns. 800 times better than the current limit L < 44 microns.

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?

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

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

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

Arecibo Observatory

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

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

The Assembled Ingredients For mass loss both increase

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

Precision on orbital period determination for PSR B1913+16 +/- 0.00003 ms y-1 0.40 ms y-1 / 0.00003 ms y-1 = 13000 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

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

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

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

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

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 1913+16). 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).

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!

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

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 ~ 0.1-10 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.

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 10-18 to 10-20 m.

LWA-1

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 B1913+16) 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