Twisting by the pool Generic black-hole-binary waveform models - - PowerPoint PPT Presentation

Twisting by the pool

Generic black-hole-binary waveform models

Mark Hannam work with Cardiff: Patricia Schmidt, Frank Ohme, Michael Pürrer, Geraint Pratten UIB: Alejandro Bohé, Sascha Husa, Leila Haegel

Motivation

The future of gravitational wave astronomy depends on us!

Black-hole-binary parameter space

Nonspinning Spinning, non-precessing Generic

Phenom (2007) EOBNR (2007--) PhenomB (2009) PhenomC (2010) SEOBNR (2010) PhenSpin (2010) SP-EOBNR (2013) PhenomP (2013)

Untangling precession

[Schmidt et al, 2012]:

We can model generic-binary waveforms by “twisting up” a non-precessing model

PhenomC

h(f) = A(f)eiΨ(f)

• Inspiral: TaylorF2.
• Merger-ringdown:
• power series in f, fit to NR data
• final spin from formulas in literature

Do the twist

Twist: (ι(t), α(t), ε(t))

ˆ L ι α ˆ J x y

(˙ ✏ = ˙ ↵ cos ◆)

Precession parameter

• Non-precessing binaries:

inspiral rate modfied by “inspiral spin”, χefg

• Precessing binaries: precession rate

determined by “precession spin”, χp

• χp: average of the dominant term in PN

precession equation

50000 100000 150000 200000 250000 300000 0.60 0.65 0.70 0.75 0.80 0.85 tM⇥ Χp

Single-spin binaries

• If our approximations hold, we can apply

(χefg, χp) to just one black hole

• “Physical Template Family” (PTF) studies:

single-spin models effective across most of parameter space

• New insight: identification of “equivalent”

generic systems

Orbital plane tilt, ι(t)

ˆ L ι α ˆ J x y

cos ι = ˆ J · ˆ L = L + S|| q (L + S||)2 + S2

⊥

L(t) (or L(f)) can be calculated from PN theory ι(t) mostly affects mode amplitudes, not phases...

Precession angle, α(t)

• Strongly affects waveform phase
• For a single-spin model, to leading order:
• We use next-to-next-to leading order in

spin-orbit terms

Ωp = ✓ 2 + 3m1 2m2 ◆ J r3

Stationary phase approximation

• Assume waveform amplitude varies slowly:
• Precession angles also vary slowly
• See also [Lundgren and O’Shaughnessy 2013]

hP

2m(t) = e−im↵ X |m0|=2

eim0✏d2

m0,m(−ι)h2,m0(t)

Ψ(v) = 2πft(v) − φ(v)

Merger and ringdown

• J is approximately fixed
• Use final spin estimates [Barausse, et. al. 2009]
• Use PN angles through merger/ringdown
• Use SPA through merger/ringdown.

Crude approximations:

Testing the model: PN-NR hybrids

L

ι

• 300
• 200
• 100

100 200 300

• 1.0
• 0.5

0.0 0.5 1.0 t @MD g @radD

α

Hybridize waveforms in co- precessing frame

[Schmidt, et al 2012] (q = 1, 2, 3; single & double-spin cases)

Also use NR initial parameters and evolve PN backwards in time

Comparisons

Most extreme comparison: q=3, χp = 0.75, 50 M⊙ Against PhenomC Against PhenomP

To do list

• Implement for general use & testing
• Perform simulations across (q, χefg, χp)
• Calibrate model to simulations
• Verify / improve assumptions
• Improve merger/ringdown model