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Externally Triggered GW Searches and Tests of Alternate Gravity Models
Emre Kahya
FSU, Jena
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Search Strategy Using External Triggers:
Look for gravitational wave signals associated with different
astrophysical observations and extract information based on it.
Possible Sources:
• Gamma-ray bursts (GRBs) -- NS-NS (BH) mergers
• Soft gamma-ray repeaters (SGRs)
• Optical transients (Supernovae)
• Neutrino triggers
• …
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● Correlation in time: Search within an astrophysically motivated trigger time window● Correlation in direction: Search only the relevant portion of the sky or
veto candidates not consistent with expected Δt● Correlation in frequency: Frequency-band specific analysis of data set ● Source Properties: Host galaxy, distance...
Confident detection of GWs. Better background rejection => Higher sensitivity to GW signals. More information about the source/engine. Measurements made possible through coincident detection.
Information from External Observations
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Short-duration GRBs (less than ~2 s)• coalescing compact binaries
e.g. neutron star—black hole merger• SGR flares
Long-duration GRBs => Supernovae
Gamma-ray bursts (GRBs)
Soft Gamma Repeaters (SGRs) Possibly highly magnetized neutron stars
● emit short duration X- and gamma-ray bursts at irregular intervals
● occasional giant flares (e.g. SGR1806-20, Dec 27, 2004) up to 15% of GRBs can be accounted for SGR flares
● might be accompanied by catastrophic non-radial motion in stellar matter => Galactic SGRs may produce Gws
● several hundred SGRs were observed during S5
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Other SourcesLow Mass X-ray Binaries
Low mass star + compact object (neutron star or a black hole) GW production => by r -modes inside the neutron star are driven by accretion
Disruption of neutron star's crust should excite oscillatory modes => might lead to emission of bursts of GWs
Pulsar Glitches
NeutrinosSeveral astrophysical phenomena => both GWs and neutrinos
Core-collapse supernovae, binary mergers ...
Negligible absorption => travel cosmological distances
No deflection by magnetic fields => tracing back feasible
Weakly interacting => can escape from dense object
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Testing Alternate GR Models with GW ObservationStrong Field Tests
Weak Field Tests Relativistic but only small corrections to Newtonian
Not many tests exist in this regime => negligible effects...
LISA and other space observatories
Inspiral of stellar compact objects into massive BH
=> extreme-mass-ratio inspirals (EMRIs)
GW s emitted by cosmological binaries
Chern-Simons mod gr, Brans-Dicke, Massive Graviton theories
DGP, Einstein-Aether Theories,
All tests => assuming coincidence in galactic distances => looking at the data within a narrow time window around the EM trigger
What about dark matter? So what about it?
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Why do we need Dark Matter ?
• The missing mass problem Zwicky (1933)
• The rotation curves of spiral galaxies Rubin, Ford, Thonnard 1970’s
• Weak lensing to probe DM in galactic clusters 1990’s
Rotation Curves
∴ Classical theory doesn’t work !
• Bullet Cluster, WMAP power spectrum etc… 2000’s
Tully−Fisher reln: V 4 = const ~ L ~ M
⇒ V 2 = const ~ G M
Newtonian ⇒ GM mr 2 = mV 2
r⇒ V 2 = GM
r
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where a => core radius
Possible Solutions
I. Dark Matter
Isothermal Halo:
• plausible candidates: axions, wimps, sterile neutrinos…
• none yet observed for 20 years !
r = 0
1 ra
2
M = V ⇒M~r when r≫a
V 2 = GMr
⇒ constant
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II. Modified Gravity Models
• MOND, Milgrom (1983) designed to explain rot. curves
• Question : Can we make a compare the two ?
• can’t explain gravitational lensing and many other cosmological events, other problems…
• without having a (complete) relativistic formulation, no real comparison
• Question : What can we do about it ?
F = m aa0 a where x ={x x≪11 otherwise
F = m a2
a0⇒ m
a0
V 4
r 2 = GMmr2
∴ V 4 = aoGM where a0 ~ 10−10 m s2
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No-Go Theorem *
* Soussa, Woodard (2003) astro-ph/0307358
Assumptions:
• the theory of gravitation is generally covariant.• gravitation force is carried by the metric, and the source is usual
• MOND force is realized in weak field perturbation theory.• the theory of gravitation is absolutely stable.• E&M couples conformally to gravity
• • MOND significant only for small a, derv. of the metric.
• • General covariance can choose flat metric a single point
• • Weak field limit small gradient expand around
• E = 8Gc2 T
T
E is not necessarilyG , caninvolve higher derivatives ,nonlocal functional of g
• Generally covariant⇒ g E ;= 0
• g= h
∴T−F reln ⇒ V ∞2 a0G M h should scale likeGM
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Static, spherically symmetric geometries
• Geodesic motion along a circle
geodesic equations:
• A factors out !
ds2=−B r dt2Ar dr 2r2d2
= ctr=R=
2
= 0
= t , = gives tautologies = ⇒ = const
= r ⇒ r ttr c t 2
r 2 = 0
⇒ B'2A
c2 t2 = rA
2
∴ ddt 2
= B'2r c2
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The first three assumptions have led us:
• Question: Which components?
• • All components ?
unstable
Some components, but which (should obey gen. coord. inv.)?
Thm: A sym. 2nd rank tensor field contains two distinguished subsets:
i) divergence ii) trace
• can’t be div. zero to all orders
• Answer: The trace
• the theory of gravitation is absolutely stable.
g E ;= 0
H ~ h3
Since T ~ M at least one comp. E [h]~ h2
∴
∴
T = − 2−g
S g
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Result:
• But that’s bad news!
• E&M couples conformally to gravity
• traceless metric field equations conformal invariance
Linearized field equations are traceless
Conclusion:No-Go theorem: If all the assumptions are correct MOND can’t give enough lensing.
• photons are unaware of MOND
Question: Which assumption is incorrect ?
T−F relation imposes gE[h ]~ O h2
∴
L = −14F F g
g−g g ⇒ 2 g
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Question: Which assumption is incorrect ?
• Answer: 1st one Multiple metric formulations (e.g. TeVeS)
TeVeS Bekenstein (2004)
• gravitational waves and matter follow different metrics :
• post Newtonian parameters √
• structure formation √
• non-relativistic MOND limit √
TeVeS is just one example of the class of models that we are considering !
Dark Matter Emulators: All the alternate gravity models which give both the gravitational lensing and the rotation curves right to agree with DM+GR without dark matter.
= e−2gA A e2 A A
g and
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Static, spherically symmetric geometries
• Geodesic motion along a circle
geodesic equations:
• A factors out !
ds2=−B r dt2Ar dr 2r2d2
= ctr=R=
2
= 0
= t , = gives tautologies = ⇒ = const
= r ⇒ r ttr c t 2
r 2 = 0
⇒ B'2A
c2 t2 = rA
2
∴ ddt 2
= B'2r c2
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How to mimic DM?
Grr∝T rr = 0 for DM fixes Ar ; G tt=8Gc2 fixes Br as well
ds2= −[1− 2GMc2r
2V∞
2
c2 ln rr S]c2dt2 1 2GM
c2 r
2V∞2
c2 dr 2 r 2d2
ds2= −c2dt 2d x⋅d x 2GMc2r
c2dt2dr 2 2V∞2
c2 ln rr Sc2 dt2 dr 2
= −c2dt2d x⋅d x ' c2 dt2dr 2 ln rr Sc2 dt2 dr2
= dxdx ' gdx
dx gdxdx
where ≡2V∞
c2 , ' ≡2GMc2 r
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198778
S N at days∆ = −
Time Lag Calculation
Geodesic Equations:
Conclusion:
Neutrinos from 1987A should arrive 78 days later than the gravitational waves and one can calculate the time lag for a source in MW galaxy analytically for isothermal halo model.
For isothermal halo model:
t = xc [1
2ln
r L
r S − −2 tan−1−2
] ≡
x L⋅x x2 ≡
r L2
x 2 and
r S = 8.0 kpc , r L = 50.9 kpc , x = 51.4 kpc⇒ = −0.9775 , = 0.9793
= 0
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• Calculations were done using isothermal halo model, NFW and Moore99 and the effect of choosing different halo models was investigated.
Conclusion: Gravitational Waves should have arrived 2 years earlier than the optical pulse and 2 months for 1987A and five days for Sco-X1.
Time Lag Calculations (SN1987A, GRB 070201, Sco-X1)
• The time lags can only be calculated numerically for NFW and Moore profiles unlike simple isothermal halo model.
• One would naturally expect the neutrinos/photons to arrive later than the gravitational waves.
• SN’s: Potential sources of gravitational waves• GRB 070201: short hard gamma-ray burst mergers of two neutron stars or a neutron star and a black hole.• Sco-X1 (2.8 kpc) one of the brightest Low Mass X-ray Binaries (LMXBs).
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Eiso ~ 1045 ergs if at M31 distance (more similar to SGR than GRB energy)
GRB 070201 – Sky Location
R.A. = 11.089 deg, Dec = 42.308 deg
DM31≈770 kpc
Possible progenitors for short GRBs:
• NS/NS or NS/BH mergersEmits strong gravitational waves
• SGR May emit GW but weaker
IPN 3-sigma error region [Mazets et al., ApJ 680, 545]
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Exercise matched filtering techniques for inspiral waveform search
No plausible gravitational waves identified
Exclude compact binary progenitor with masses
1 M⊙ < m1< 3 M⊙ and 1 M⊙ < m2 < 40 M⊙ with D < 3.5 Mpc at 90% CL
Exclude any compact binary progenitor in our simulation space
at the distance of M31 at > 99% confidence level
DM31
25%
50%
75%
90%
Abbott, B. et al. (2008), Astrophysical Journal, 681 . pp. 1419-1430
Why did we choose this GRB?
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•Shapiro Delays for GRB 070201 from the Isothermal Profiles of the Milky Way (∆tMW) and Andromeda (∆tM31) at the central value of the angular position and atthe four vertices of the error box. In all cases the distance to the burst was taken to be 780 kpc.
• The time delays for three dark matter profiles.
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• The time delay as a function of radial distance from Earth
• Time lag as a function of the angle of a source located at 400 Mpc.
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Any uncertainty in the calculation?
The time lag depends almost linearly on the total dark matter of the galaxy that we consider.
=> Investigate other simulations for DM profiles of MW and M31
The mass of M31 is much bigger in Klypin et al.
=> huge increase in the time lag (as expected)
What is going on with the DM numerical simulation people?
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Different! Mass estimates of MW and M31
a very long road ahead...
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Observational Prospects for future SN’s
• We have already detected neutrinos from 1987A with Kamiokande-II and Irvine-Michigan-Brookhaven detectors.
• amount of GW from SN oblateness of it from spherical symmetry
Neutrinos
• Super-Kamiokande, Sudbury Neutrino Observatory (SNO+), Kam-LAND and LVD (Italy)
Gravitational Waves
• Current detectors can’t detect sun-like stars
• LIGO should have observed GRB 070201 bh ns or bh bh mergers.
• • Light can also be used instead of neutrinos
• • will get the effect but not the precision.
Other possibilities
• Advanced LIGO certainly will (SN 1987A type explosions)
• Same calculation can be done for SGR 1806-20 (6 to 15 kpc range) was not observed by LIGO or other detectors
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Instrument Timelines
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CONCLUSIONS
• Possible sources: GRBs,, Soft Gamma Repeaters , Neutrinos Low Mass X-Ray Binaries ...
• This gives rise to, even at this stage, a doable test of them
• Huge uncertainty in mass of MW and M31 Numerical simulations estimates. => we need to wait for some time...
• GW Observation => decisive tests for alternate gravity models
• If MOND is correct neutrinos from SN 1987A should arrive 2 months after the gravitational waves and almost 2 years for GRB 070201.
• Externally triggered GW search is a very powerful method for observation
• Modifying GR to do away with dark matter => multiple metric formalisms ( to explain T-F Reln. & Weak lensing)
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• Not fair to compare a non-rel model with DM
• Problems with TeVeS (one of the first proposed formulations)?
- Sure! bullet cluster, third peak in the power spectrum...
but what about the Dark (Matter) side?
(just seen the numerical side...)
• Komatsu et al. (just released the WMAP-7 Year Results arXiv:1001.4538)
"Bullet Cluster: A Challenge to LCDM Cosmology," arXiv:1003.0939:
“It is concluded that the existence of 1E0657-56 (Bullet Cluster) is incompatible with the prediction of a LCDM model”
• Not being able to reveal any coincident GW and EM pulse
=> MOND is right ? Obviously premature to proclaim
But if plausible sources continue to produce null results? Maybe...
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Some Useful References• “Decadal Survey Whitepaper: Coordinated Science in the Gravitational and EM Skies” Bloom et al., arXiv:0902.1527
• “Finding and Using Counterparts of GW Sources”, Phinney et al., arXiv:0903.0098
• “Multimessenger astronomy with the Einstein Telescope”Marka et al., arXiv:1004.1964
• “Reduced time delay for gravitational waves with dark matter emulators” Desai et al., arXiv:0804.3804
• “Constraining the mass of the graviton using coalescing black-hole binaries” Keppel et al., arXiv:1004.0284
• “Parametrized tests of post-Newtonian theory using Advanced LIGO and ET” Mishra et al., arXiv:1005.0304
• “A Useful guide for gravitational wave observers to test modified gravity models” E.O. Kahya, arXiv:1001.0725