Towards a gravitational-wave catalogue of Proca-star mergers
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Towards a gravitational-wave catalogue of Proca-star mergers
Juan Calderón Bustillo*
Nicolás Sanchis-Gual, Samson Leong, Koustav Chandra, Alejandro Torres-Forné, Toni Font, Avi Vajpeyi,
Rory Smith, Carlos Herdeiro, Eugen Radu & Isaac Wong
XI Iberian Gravitational-Wave Meeting, June 2021 Phys.Rev.Lett 126.081101 & Phys.Rev.Lett 126.201101 (2021) *juan.calderon.bustillo@gmail.com
Typical LIGO-Virgo observation Inspiral
Typical LIGO-Virgo observation Inspiral Merger
Typical LIGO-Virgo observation Inspiral Merger Ringdown Safe tu assume a “vanilla” quasi-circular inspiral process
Typical LIGO-Virgo observation
Inspiral Merger Ringdown
Eccentricity 90% level upper bounds
Romero-Shaw+ (2019)
Safe tu assume a “vanilla” quasi-circular inspiral process
GW190521 May 21st 2019 LIGO-Virgo (LVC) 2020
What produced GW190521?
LVC 2020
• Barely any (visible) pre-merger emission
Merger Ringdown Final BH
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
What produced GW190521?
LVC 2020
• Barely any (visible) pre-merger emission
¿¿¿??? Merger Ringdown Final BH
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
What produced GW190521?
• Barely any pre-merger emission
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
No
IMBH
remnant
LVC 2020
Waveform Model NRSur7dq4 (Varma+ ’19)
What produced GW190521?
PISN
• Barely any pre-merger emission Gap
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
• Mild precession signatureWhat produced GW190521?
• Barely any pre-merger emission
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
• Mild precession signature
Extremely detailed study: Estellés et. al. 2021
P (precession|qBBH) 10 : 1What produced GW190521?
• Barely any pre-merger emission
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
• Mild precession signature
Extremely detailed study: Estellés et. al. 2021
P (precession|qBBH) 10 : 1What produced GW190521?
• Barely any pre-merger emission
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
• Mild precession signature
Extremely detailed study: Estellés et. al. 2021
• But: Precession can mimic eccentricity! (JCB + 2021)
JCB+ 2021What produced GW190521?
• Barely any pre-merger emission
• Remnant: intermediate-mass black hole.
S1 S2
• If BBH: primary black hole in the
pair instability supernova gap. M1 M2
• Mild precession signature
Extremely detailed study: Estellés et. al. 2021
• But: Precession can mimic eccentricity! (JCB + 2021)
JCB+ 2021What produced GW190521?
• Barely any pre-merger emission
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
• Alternative interpretations
• Small eccentricity (Romero-Shaw+)
• High Eccentricity (Gayahtri+)
• Head-on merger (JCB+)
Romero-Shaw+ (2020)
• Boson-star merger (this talk)What produced GW190521?
• Barely any pre-merger emission
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
• Alternative interpretations
• Small eccentricity (Romero-Shaw+)
• High Eccentricity (Gayahtri+)
• Head-on merger (JCB+)
• Boson-star merger (this talk)What produced GW190521?
• Barely any pre-merger emission
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
• Alternative interpretations
• Small eccentricity (Romero-Shaw+)
• High Eccentricity (Gayahtri+)
• Head-on merger (JCB+)
• Boson-star merger (this talk) Gamba+ (Today)
See also: Gamba et al (dynamical capture, on arxiv today)What produced GW190521?
• Barely any pre-merger emission
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
• Alternative interpretations
• Small eccentricity (Romero-Shaw+)
• High Eccentricity (Gayahtri+)
• Head-on merger (JCB+)
• Boson-star merger (this talk)What produced GW190521?
• Barely any pre-merger emission
• Remnant: intermediate-mass black hole.
• If BBH: primary black hole in the
pair instability supernova gap.
• Alternative interpretations
• Small eccentricity (Romero-Shaw+)
• High Eccentricity (Gayahtri+)
• Head-on merger (JCB+)
Lack of pre-merger
signal
• Boson-star merger (this talk)What produced GW190521?
Head-on
final spins
Lack of orbital angular momentum
Cosmic Censorship aBH < 1 Final Spin is too lowWhat produced GW190521?
• Barely any pre-merger emission
• Remnant: intermediate-mass black
hole.
• If BBH: primary black hole in the
pair instability supernova gap.
• Alternative interpretations
• Small eccentricity (Romero-Shaw+)
• High Eccentricity (Gayahtri+)
• Head-on merger (JCB+) Credit: Nicolás Sanchis-Gual, Rocío García-Souto
• Boson-star merger (this talk) ?Boson stars, Proca stars and ultralight bosons
Self-gravitating Bose Einstein condensates of ultralight bosons
Compact objects with no event horizon (black hole mimickers)
• Can have spins larger than 1!!!
• Can produce highly spinning remnant black holes!
Two “new physics” parameters
• Oscillation frequency of the field: !
Determines the “compactness” of the star
• Boson mass: µ
Determines the maximum mass of the star
(before collapsing to a black hole)
• Dark-Matter candiatesBoson stars, Proca stars and ultralight bosons
Self-gravitating Bose Einstein condensates of ultralight bosons
Compact objects with no event horizon (black hole mimickers)
• Can have spins larger than 1!!!
• Can produce highly spinning remnant black holes!
Two “new physics” parameters
• Oscillation frequency of the field: !
Determines the “compactness” of the star
• Boson mass: µ
Determines the maximum mass of the star
(before collapsing to a black hole)
• Dark-Matter candiatesBoson stars, Proca stars and ultralight bosons
Self-gravitating Bose Einstein condensates of ultralight bosons
Compact objects with no event horizon (black hole mimickers)
• Can have spins larger than 1!!!
• Can produce highly spinning remnant black holes!
Two “new physics” parameters
• Oscillation frequency of the field: !
Determines the “compactness” of the star
• Boson mass: µ
Determines the maximum mass of the star
(before collapsing to a black hole)
• Dark-Matter candiatesBoson stars, Proca stars and ultralight bosons
Self-gravitating Bose Einstein condensates of ultralight bosons
Compact objects with no event horizon (black hole mimickers)
• Can have spins larger than 1!!!
• Can produce highly spinning remnant black holes!
Two “new physics” parameters
• Oscillation frequency of the field: !
Determines the “compactness” of the star
• Boson mass: µ
Determines the maximum mass of the star
(before collapsing to a black hole)
• Dark-Matter candiatesBoson stars, Proca stars and ultralight bosons
Self-gravitating Bose Einstein condensates of ultralight bosons
Compact objects with no event horizon (black hole mimickers)
• Can have spins larger than 1!!!
• Can produce highly spinning remnant black holes!
Two “new physics” parameters
• Oscillation frequency of the field: !/µV
Determines the “compactness” of the star
• Boson mass: µV
Determines the maximum mass of the star
(before collapsing to a black hole)
• Dark-Matter candiatesBoson stars, Proca stars and ultralight bosons
Self-gravitating Bose Einstein condensates of ultralight bosons
Compact objects with no event horizon (black hole mimickers)
• Can have spins larger than 1!!!
• Can produce highly spinning remnant black holes!
Two “new physics” parameters
• Oscillation frequency of the field: !/µV
Determines the “compactness” of the star
• Boson mass: µV
Determines the maximum mass of the star
(before collapsing to a black hole)
• Dark-Matter candiatesBoson stars, Proca stars and ultralight bosons
Self-gravitating Bose Einstein condensates of ultralight bosons
Compact objects with no event horizon (black hole mimickers)
• Can have spins larger than 1!!!
• Can produce highly spinning remnant black holes!
Two “new physics” parameters
• Oscillation frequency of the field: !/µV
Determines the “compactness” of the star
• Boson mass: µV
Determines the maximum mass of the star
(before collapsing to a black hole)
• Dark-Matter candiatesA zoo of boson stars: Proca Stars
Spinning Proca star
Spinning Scalar star
(Unstable)A zoo of boson stars: Proca Stars
Spinning Proca star
Spinning Scalar star
(Unstable)Building a catalogue of Proca-star mergers Credit: Nicolás Sanchis-Gual
Building a catalogue of Proca-star mergers Initial set: Equal-mass, equal field frequency (equal spin) Initial separation = 100M We include (2,0), (2,2), (3,2) modes
Building a catalogue of Proca-star mergers Initial set: Equal-mass, equal field frequency (equal spin) Initial separation = 100M We include (2,0), (2,2), (3,2) modes Secondary set: First frequency fixed, second varies
Building a catalogue of Proca-star mergers Credit: Nicolás Sanchis-Gual
Is GW190521 a Proca-star merger?
Model Selection Fundamentals
⇡(✓)L(✓|d)
p(✓|d) =
Z(✓|d)
L(✓|d) : Likelihood (fit)
⇡(✓) : Prior Assumptions
Z(✓|d) : Evidence for the model
Z
Z(✓|d) = ⇡(✓)L(✓|d)d✓
": Large likelihood
#: Useless parameters (Occam’s Razor)
"#: Choice of priors
P (Model A) ZA
=
P (Model B) ZBIs GW190521 a Proca-star merger?
Model Selection
• Compare Fundamentals
to ~500 simulations, add 33 mode Settings:
⇡(✓)L(✓|d) Frequency range: 11-512Hz
p(✓|d) =
Z(✓|d)
Code: Bilby Ashton+ 18 Romero-Shaw+ 20
L(✓|d) : Likelihood (fit) Sampler: CPNest Veitch+ (Dynesty ongoing)
⇡(✓) : Prior Assumptions Priors:
Z(✓|d) : Evidence for the model Uniform in Total Mass and Mass Ratio
Z
Z(✓|d) = ⇡(✓)L(✓|d)d✓ Standard for the spins, source orientation, sky-location
Uniform in Co-moving volume
": Large likelihood
#: Useless parameters (Occam’s Razor)
"#: Choice of priors
P (Model A) ZA
=
P (Model B) ZBIs GW190521 a Proca-star merger? Published study Initial study
Is GW190521 a Proca-star merger? GW190521 Parameters (Proca-star merger)
Is GW190521 a Proca-star merger? GW190521 Parameters (Proca-star merger)
Is GW190521 a Proca-star merger?
GW190521 Parameters (Proca-star merger)
LVC (BBH)
Circular mergers are louder
272+26
27 M Larger initial mass needed to get same final BHIs GW190521 a Proca-star merger?
GW190521 Parameters (Proca-star merger)
LVC (BBH)
+2600
5300 2400 M pc Much closer than a BBH
Circular mergers are louder
272+26
27 M Larger initial mass needed to get same final BHIs GW190521 a Proca-star merger?
GW190521 Parameters (Proca-star merger)
LVC (BBH)
150+29
17 M Much heavier than the BBH estimation
+2600
5300 2400 M pc Much closer than a BBH
Circular mergers are louder
272+26
27 M Larger initial mass needed to get same final BHIs GW190521 a Proca-star merger?
• CompareInitial
to ~500
study:
simulations,
Model Selection
add 33 mode
Distance prior: Uniform in-comoving volumeIs GW190521 a Proca-star merger?
• CompareInitial
to ~500
study:
simulations,
Model Selection
add 33 mode
Distance prior: Uniform in-comoving volume
P (Proca q=1) (80.9 80.0) P (Proca q6=1)
=e ' 2.5 P (BBH) ' 6.7
P (BBH)
Reasonable, but this favours loud BBH sourcesIs GW190521 a Proca-star merger?
• CompareInitial
to ~500
study:
simulations,
Model Selection
add 33 mode
Distance prior: Uniform in-comoving volume
P (Proca q6=1) P (Proca q=1)
P (BBH) ' 70 P (BBH) ' 30GW190521 Proca-star parameters Head-on black-holes could not provide us with enough final spin
GW190521 Proca-star parameters Head-on Proca stars can
GW190521 Proca-star parameters Lack of power before signal peak: immediate ringdown of final black hole
GW190521 Proca-star parameters Transient hypermassive Proca star: power before signal peak
New Physics
Bosonic field frequency Boson mass
GW190521, q=1 +0.73 13
µV = 8.67 0.82 ⇥ 10 eVUpdated Result
Updated Result
Enlarged waveform family
We add the (3,3) mode See Capano+ 2021
Increased Max LogLikelihood: from 106 to 110
Mildly increased Log Bayes Factor: from 80.9 to 81.46Updated Result GW190521, Updated, Preliminary +0.75 13 µV = 8.70 0.69 ⇥ 10 eV
Can previous events be Proca-star mergers?
Too massive Proca star: collapse to black hole
10
Mmax 1.34 ⇥ 10 eV
= 1.125 ⇥
M µV
Final Proca star less massive: no collapse, no ringdown
Previous LVC events discarded as head-on Proca star
mergers (with same boson mass)Can previous events be Proca-star mergers?
Too massive Proca star: collapse to black hole
10
Mmax 1.34 ⇥ 10 eV
= 1.125 ⇥
M µV
Final Proca star less massive: no collapse, no ringdown
Previous LVC events discarded as head-on Proca star
mergers (with same boson mass)Can previous events be Proca-star mergers?
Too massive Proca star: collapse to black hole
10
Mmax 1.34 ⇥ 10 eV
= 1.125 ⇥
M µV
Final Proca star less massive: no collapse, no ringdown
Previous LVC events discarded as head-on Proca star
mergers (with same boson mass)
Proca +15
Mmax = 174 14 MOngoing work
PRELIMINAR
Take with a grain of saltS200114f
Second-most significant IMBH trigger reported by LVC
Parameter inconsistency across BBH models
Not ruled out as Proca star merger
LogB ~ 0 (as probable as a BBH)
Boson mass:
200114 +0.69 13 False Alarm Rate ~ 1/17yr
µB = 10.19 0.55 ⇥ 10 eVS200114f: results
Second-most significant IMBH trigger reported by LVC
Parameter inconsistency across BBH models
Not ruled out as Proca star merger
LogB ~ 0 (as probable as a BBH)
Boson mass:
200114 +0.69 13
µB = 10.19 0.55 ⇥ 10 eV
LIGO+Virgo (2021)S200114f: results
Second-most significant IMBH trigger reported by LVC BBH run: IMRPhenomTPHM (Pratten+ 21): MaxLogL = 103
Tried also NRSur7dq4 (Varma+ 20), IMRPhenomXPHM
Parameter inconsistency across BBH models
Not ruled out as Proca star merger
LogB (BBH vs. Proca Star) ~ 0 (as probable as a BBH)
Boson mass: Mtotal (1 + z)[M ] Mass ratio dL [M pc]
200114 +0.69 13 Large individual spin magnitudes Large spin tilts: precession
µB = 10.19 0.55 ⇥ 10 eVS200114f: results
Second-most significant IMBH trigger reported by LVC BBH run: IMRPhenomTPHM (Pratten+ 21): MaxLogL = 103
Tried also NRSur7dq4 (Varma+ 20), IMRPhenomXPHM
Parameter inconsistency across BBH models
Not ruled out as Proca star merger
LogB (BBH vs. Proca Star) ~ 0 (as probable as a BBH)
Boson mass: Mtotal (1 + z)[M ] Mass ratio dL [M pc]
200114 +0.69 13 Large individual spin magnitudes Large spin tilts: precession
µB = 10.19 0.55 ⇥ 10 eV
Proca-star run: MaxLogL = 100
Mtotal (1 + z)[M ] dL [M pc]S200114f: results
Second-most significant IMBH trigger reported by LVC BBH run: IMRPhenomTPHM (Pratten+ 21): MaxLogL = 103
Tried also NRSur7dq4 (Varma+ 20), IMRPhenomXPHM
Parameter inconsistency across BBH models
Not ruled out as Proca star merger
LogB (BBH vs. Proca Star) ~ 0 (as probable as a BBH)
Boson mass: Mtotal (1 + z)[M ] Mass ratio dL [M pc]
200114 +0.69 13 Large individual spin magnitudes Large spin tilts: precession
µB = 10.19 0.55 ⇥ 10 eV
Proca-star run: MaxLogL = 100
We use Newmann-
Penrose scalar as
template
Mtotal (1 + z)[M ] dL [M pc]S200114f: results
Second-most significant IMBH trigger reported by LVC
Parameter inconsistency across BBH models
Not ruled out as Proca star merger
LogB ~ 0 (as probable as a BBH)
Boson mass:
200114 +0.69 13
µB = 10.19 0.55 ⇥ 10 eVGW190521 and S200114: mass consistency with BBH
GW190521 and S200114: boson mass consistency
Conclusions
This talk:
GW190521 has brought us in the realm of ¿what are we observing?
Consistent with a head-on merger of Proca stars
Second, low significance trigger S200114 (ongoing)
Consistent masses at 90% C.I.
+0.69
µ190521
B = 8.70 +0.75
0.69 ⇥ 10
13
eV µ200114
B = 10.19 0.55 ⇥ 10
13
eVConclusions
This talk:
GW190521 has brought us in the realm of ¿what are we observing?
Consistent with a head-on merger of Proca stars
Second, low significance trigger S200114 (ongoing)
Consistent masses at 90% C.I.
+0.69
µ190521
B = 8.70 +0.75
0.69 ⇥ 10
13
eV µ200114
B = 10.19 0.55 ⇥ 10
13
eV
The future:
Simulations for less eccentric configurations: large room for improvement!!!!
Targeted search for boson-star mergers
Mass consistency across events: population studies. How many ultralight bosons are there, if any?Gravitational-wave data analysis with the Newmann-Penrose scalar
4Using the Newmann-Penrose scalar 4 in GW data analysis
2
d h
Numerical Relativity simulations extract GWs in form of 4 = 2
dt
Obtention of strain requires of double integration plus cleaning procedure
Short numerical simulations may suffer from artefacts
d2 h
4 = 2
dtUsing the Newmann-Penrose
Using the scalar 4 inscalar
Newmann-Penrose GW data
4 in GW analysis
data analysis
2
d h
Numerical Relativity simulations extract GWs in form of 4 = 2
dt
Obtention of strain requires of double integration plus cleaning procedure
Short numerical simulations may suffer from artefacts
d2 h
4 = 2
dtUsing the Newmann-Penrose
Using the scalar 4 inscalar
Newmann-Penrose GW data
4 in GW analysis
data analysis
2
d h
Numerical Relativity simulations extract GWs in form of 4 = 2
dt
Obtention of strain requires of double integration plus cleaning procedure
Short numerical simulations may suffer from artefacts
d2 h
4 = 2
dtUsing the Newmann-Penrose
4 scalar 4 in GW data analysis
Strategy:
Perform second-order differencing of GW strain data
Use as templates 4 directly extracted from NR
simulations
Compute the 4 - PSD as:
( 4)
1 h
S [k] = 4
(6 8 cos(2⇡k/N ) + 2 cos(4⇡k/N ))S [k]
( t)
Run parameter estimation as usualUsing the Newmann-Penrose
4 scalar 4 in GW data analysis
Strategy:
Perform second-order finite differencing of GW strain data
Use as templates 4 directly extracted from NR
simulations
Compute the 4 - PSD as:
( 4)
1 h
S [k] = 4
(6 8 cos(2⇡k/N ) + 2 cos(4⇡k/N ))S [k]
( t)
Run parameter estimation as usualUsing the Newmann-Penrose
4 scalar 4 in GW data analysis
Strategy:
Perform second-order finite differencing of GW strain data
Use as templates 4 directly extracted from NR
simulations
Compute the 4 - PSD as:
( 4)
1 h
S [k] = 4
(6 8 cos(2⇡k/N ) + 2 cos(4⇡k/N ))S [k]
( t)
Run parameter estimation as usualUsing the Newmann-Penrose scalar 4 in GW data analysis
Strategy:
Perform second-order finite differencing of GW strain data
Use as templates 4 directly extracted from NR
simulations
Compute the 4 - PSD as:
( ( 4 )4 ) 11 h h
SS [k]
= (6 8 cos(2⇡k/N ) + 2 cos(4⇡k/N ))S [k]
[k] = ( t)44 (6 8 cos(2⇡k/N ) + 2 cos(4⇡k/N ))S [k] Isaac Wong (CUHK)
( t)
Run parameter estimation as usualUsing the Newmann-Penrose scalar 4 in GW data analysis
Strategy:
Perform second-order finite differencing of GW strain data
Use as templates 4 directly extracted from NR
simulations
Compute the 4 - PSD as:
( ( 4 )4 ) 11 h h
SS [k]
= (6 8 cos(2⇡k/N ) + 2 cos(4⇡k/N ))S [k]
[k] = ( t)44 (6 8 cos(2⇡k/N ) + 2 cos(4⇡k/N ))S [k] Isaac Wong (CUHK)
( t)
Run parameter estimation as usualUsing the Newmann-Penrose scalar 4 in GW data analysis
Strategy:
Perform second-order finite differencing of GW strain data
Use as templates 4 directly extracted from NR
simulations
Compute the 4 - PSD as:
( ( 4 )4 ) 11 h h
SS [k]
= (6 8 cos(2⇡k/N ) + 2 cos(4⇡k/N ))S [k]
[k] = ( t)44 (6 8 cos(2⇡k/N ) + 2 cos(4⇡k/N ))S [k]
( t)
Run parameter estimation as usualIn which situations can one mistake precession by eccentricity?
“Wrong” Can’t say
Precession anything
JCB, Sanchis-Gual, Torres-Forne and Font: arXiv 2009.01066 (2020), Accepted in Phys. Rev. LettGW190521: Proca-star parameters
• Distance of ~500Mpc (5Gpc for LIGO-Virgo)
• Much lower redshift: much larger source frame mass Msource = Mdet /(1 + z)
• Discard edge-on inclinations
JCB, Sanchis-Gual et. al.,Phys. Rev. Lett. 126, 081101 (2021)GW190521: Proca-star parameters
• Distance of ~500Mpc (5Gpc for LIGO-Virgo)
• Discard edge-on inclinations
• (2,0) mode helps to constrain inclination
JCB, Sanchis-Gual et. al.,Phys. Rev. Lett. 126, 081101 (2021)GW190521: Proca-star parameters
• We can measure the azimuthal angle
• (2,0) mode introduces asymmetries in the GWs
• Star’s trajectories curved by frame-dragging
• Repeat analysis without (2,0) mode
• Evidence of (2:1) for presence of (2,0) mode
• First measurement of frame dragging in GWs
JCB, Sanchis-Gual et. al.,Phys. Rev. Lett. 126, 081101 (2021)Size of the Parameter Space
• Compare to ~500 simulations, add 33 mode
Impact of Occam Penalty
Z
“Averaged” likelihood x Prior
Z(✓|d) = ⇡(✓)L(✓|d)d✓
“Bad” regions of parameter space reduce Z
No support for q > 2Size of the Parameter Space
• Compare to ~500 simulations, add 33 mode
Impact of Occam Penalty
Z
“Averaged” likelihood x Prior
Z(✓|d) = ⇡(✓)L(✓|d)d✓
“Bad” regions of parameter space reduce Z
Precession is a necessary complicationSize of the Parameter Space
• Compare to ~500 simulations, add 33 mode
Impact of Occam Penalty
Z
“Averaged” likelihood x Prior
Z(✓|d) = ⇡(✓)L(✓|d)d✓
“Bad” regions of parameter space reduce Z
Removing q > 2 helps BBHsSize of the Parameter Space
• Compare to ~500 simulations, add 33 mode
Impact of Occam Penalty
Z
“Averaged” likelihood x Prior
Z(✓|d) = ⇡(✓)L(✓|d)d✓
“Bad” regions of parameter space reduce Z
Restricting to q=1 brings BBH closer to ProcaSize of the Parameter Space
• Compare to ~500 simulations, add 33 mode
Impact of Occam Penalty
Z
“Averaged” likelihood x Prior
Z(✓|d) = ⇡(✓)L(✓|d)d✓
“Bad” regions of parameter space reduce Z
Restricting to q=1 brings BBH closer to ProcaYou can also read
