1. Probing Dark Energy with Black Hole Binaries
Laura Mersini-Houghton
UNC / DAMTP Cambridge U.
Firenze, March 2009

2. Equation of State of Dark Energy W[z]
Too many models, too little data. Knowledge of W[z] seems the most important step for progress at present.
Problem 1: Data Analysis Depends Heavily on Parameterization of W[z], (i.e. assuming Prior Models). Popular one is polynomial: W[z] = W0 + Wa * z +…
Problem 2: Most of our Experiments ‘Contaminated’ by Noise of structure, foreground and background through which signals propagate . Tough since Noise comparable to “Wa”!
Measuring W[z] in a Model-Independent Way is the Highest Priority

3. This New Method Complements Large Scale Efforts on Measuring W[z].
The Main Idea
Black Holes (BH) Accrete Dark Energy. Their Mass Changes Depend on W[z]. (T.Jacobson, Babichev et al.).
Gravitational Waves (GW) of the Binary Depend on the Masses of BH, thus on Dark Energy, W[z].
Energy Losses from the Emission of GW Reduce the Orbital Radius. This effect was discovered as predicted by Hulse-Taylor for CDM universe, (in the absence of Dark Energy).
WHAT’S NEW: GW Emission is different in LCDM! Binary is Modified by Dark Energy. Thus Changes in GW and Orbital Separation carry direct information on Dark Energy W[z].
(For Phantom Energy Orbit is Ripped Apart, Binary Does Not Merge).
BENEFITS: Can Be Observed! Avoids Noise from Large Scale Averaging since BH’s Are Compact Objects and GW propagate Unaffected.
This New Method Complements Large Scale Efforts on Measuring W[z].

4. Black Holes Accrete Dark Energy
Dark Energy Density
Evaporation Lifetime:
Solar Mass Time =10^{32} yrs
BH Mass Before DE Accretion

5. Gravitational Waves Emitted by the Binaries Depend on Dark Energy, W[z]
GW Power emitted by 2 BH’s with mass, m1 and m2 is:
and frequency:
The energy carried away by GW’s induces a loss in the Gravitational Mass ‘M’ of Binary:
BUT BH Mass is:
Equating the Energy Loss of the System to Power carried in GW tells us how the orbital separation ‘R’ changes as a result: PGW = d(M) / dt
Eq.1

6. Binaries in LCDM Background
Let’s take Equal Mass BH’s for simplicity. Then Orbit “R” obtained from Eq.1:
Notice that all the terms in the solution R[t] are due to DE, except the last one which is the well known Hulse-Taylor term: Y2 Y1

7. Time (yrs)
R[t] (m)
W[z]
W[z]
Time (yrs)

8. Can it be observed? Y1 / Y2 = For Supermassive Black Holes (SBH),
m = a Msun and large separation R0 = b Rschwarzchild,
the DE correction terms, Y2, dominates over the standard Hulse-Taylor term, Y1, for 2ba >10^18:
Y1 / Y2 =
Such Binaries Exist!
Two already observed.

9. GALAXY : 2007 VLBA R0 =40 pc, T=10^14 s, a=2 10^8, O =10^(-14) Hz, dR1=(1+w)10^6 m, dR2 = 10^10 m (merge in 1000yrs, 2 orders of magnitude) - Radio GALAXY OJ287: 2008 VLBA R=10 Mpc, T=12yrs, a=10^10, (merging accelerated by 3 orders of magnitude).
Notice that if : W[z] < -1, then Merging does Not occur. Orbits Increase, they are Ripped Apart!