strong-field electromagnetic tests of general relativistic ...luthier/vincent/pdf/apc2012.pdf ·...

Context Rossby non-Kerr

Strong-field electromagnetic tests of generalrelativistic effects

Frédéric VINCENT1

1Nicolaus Copernicus Astronomical Center, Warsaw

1/38 Frédéric VINCENT GR strong-field tests


1 A new era of observations

2 Rossby wave instability for high frequency QPOs

3 Ray-tracing simulations in non-Kerr spacetime

4 Conclusion



GRAVITY (2014)EHT (2015)

LOFT (2020)

A new era of strong-field GR observations

GRAVITY : probe the Galactic center quasi-periodicoscillations (QPOs)EHT : image the silhouette of a black holeLOFT : probe X-ray binaries QPOs



GC flare light curve (Hamaus+09)

Fréquence

DSP

GRS1915+105 power spectrum (Remillard+06)

First strong-field probe : QPOs

Observations :light curve / power spectrum / rms / astrometry...



Synchrotron

Magneticfield

BH

Rotating HotSpot

Hot spot model for GC flaresRossby wave instability model

(Credit : P. Varniere)

Epicyclic resonance model (Török 05)

First strong-field probe : QPOsModel :Hot spot, MHD instability, epicyclic resonance, jets...



First strong-field probe : QPOs

Probably no model is able of reproducing ALL observedconstraintsEven reproducing a few is not easy...Goal : discriminate some models by showing they cannotaccount for some observables

My interestGRAVITY, LOFT : sharp precision in infrared astrometry /X-ray timingGoal : develop observable exclusive predictions foralternative QPO models



Geometrically thin disk, GYOTO simulation

Second strong-field probe : SilhouetteBH silhouette = due to photons orbiting close to the event horizon onthe observer’s sky.

Silhouette apparent angular size depends on BH spin.



Second strong-field probe : Silhouette

Perfect ‘astrophysics-unpolluted’ probe of strong-field GRWill be different for different metrics (Kerr, or non-Kerr)

My interestEHT : sharp angular resolution at Sgr A* and M87Goal : develop silhouette computations for alternativemetrics

My main toolStrong-field⇒ ray-tracing (http://gyoto.obspm.fr/)

→ Vincent, Paumard, Gourgoulhon, Perrin, Class. Quantum Grav. 28, 225011 (2011)


http://gyoto.obspm.fr/


Outline of this talkQPOs :→ first ray-traced observation simulations in the context ofRossby wave instability QPO modelSilhouette :→ first ray-traced observation simulations in non-Kerrspacetime






4 Conclusion



0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.000

0.005

0.010

0.015

0.020

0.025

0.030

rr0

Κ

1.2 1.4 1.6 1.8 2.00

1

2

3

4

5

rr0

L

Rossby wave instabilityTriggered where the inverse vortensityL = ΣΩ/2κ2 × p/Σγ shows an extremum→ extremum of Σ (density bump)→ extremum of κ (epicyclic frequency bump)



Meheut+10

Credit : P. Varniere

Rossby wave instabilityVortices develop at the extremum location rextDensity waves extend on both sides of rextr > rext ⇒ wave faster than gas rotationr < rext ⇒ wave slower than gas rotation→ Spiral wave



Credit : P. VarniereVincent+12

Rossby wave instabilityNumber of vortices = number of spiral arms = modenumber mThe dominant mode evolves from m >≈ 1 to m = 1Different modes can coexist



Rossby Wave Instability model of QPOsTagger&Varniere 2006 proposed RWI to account for HFQPOs in microquasarsAccretion disk around BH are very unstable to RWIparticularly if B 6= 0, β ≈ 1Coexistence of modes is a natural explanation for 2 :3resonanceAnother instability, close to RWI, the Accretion EjectionInstability, can account for LF QPOsThe two instabilities can coexist (thus explaining bothtypes of QPOs)

Need for RWI observation simulations !



Simulated 2D disk imageBeaming : approaching side strongly enhancedHigh order imagesDifferent emission times for different photons



−0.45

0.45timpact

i=5°

TISCO

TISCO −0.45

0.45TISCO

TISCO

timpact

i=85°

observer

Simulated 2D disk image

Different emission times for different photonsEffect depending on inclinationLensing of photons by BH→ concentrate ‘behind’ the BHConsequence : more time slices of data needed at higherinclinationHowever : beaming moderates this effect



0 5 10

0.9

1.0

1.1

t / tISCO

Norm

aliz

ed flu

x

0 5 100

2

4

6

8

t / tISCO

Dis

pers

ion (%

)

2keV

85°

45°

5°

Simulated 2D light curvesRadiative process = blackbodyRWI able of modulating flux at a few percent levelModulation increasing with inclination (beaming)



0 5 10

0.9

1.0

1.1

t / tISCO

Norm

aliz

ed flu

x

Simulated 2D light curves : mode analysisTime sampling allows to see mode evolutionThis is a prediction of the model, to compare withobservations



0 5 10 15

0.9

1.0

1.1

t / tISCO

Nor

mal

ized

flux

t / tISCO

Nor

mal

ized

flux

t / tISCO

Nor

mal

ized

flux

0 5 10 15 0

2

4

6

8

t / tISCO

Dis

pers

ion (

%)

t / tISCO

Dis

pers

ion (

%)

t / tISCO

Dis

pers

ion (

%)

Simulated 3D light curves

RWI exists at 3D : Meheut et al. (2010)Radiative process = bremsstrahlungRWI still able of modulating flux at a few percent level



0 5 10 15

0.9

1.0

1.1

t / tISCO

Nor

mal

ized

flux

t / tISCO

Nor

mal

ized

flux

t / tISCO

Nor

mal

ized

flux

Simulated 3D light curves : mode analysis

Coarser time sampling, but mode evolution still visible



Section conclusionRWI able to modulate the ray-traced light curve at 2D and3DMode evolution is visible on the light curveUse this signature to test the model with LOFT ?

→ Vincent, Meheut, Varniere, Paumard, 2012, submitted to A&A,accepted providing minor modifs.



Perspectives : oscillating torus model

0 1 2

1.00

1.02

1.04

Number of periods (2*π/ωθ)

Vertical deformation

Nor

mal

ized

flux

Mazur+12 (in prep.)

In progress : the oscillating torus model

Epicyclic oscillations of a slender torus

Light curves under construction...

→ collab. with G. Mazur, M. Abramowicz (at CAMK)To be compared with RWI predictions

Can LOFT discriminate ?


MovieOscilTorusVertical.mpgMedia File (video/mpeg)


Perspectives : GC flares

Synchrotron

Magneticfield

BH

Rotating HotSpot

−40 −20 0

−20

0

20

x (µas)

y (µ

as)

Vincent+11

In progress : astrometric signatures of flare models

Done : astrometric signature of hot spot model as observed byGRAVITY

In progress : astrometric signature for RWI, jet models

→ collab. with P. Varniere, F. Casse, T. Paumard, G. Perrin(at APC + LESIA)

Can GRAVITY discriminate ?






4 Conclusion



74 5 3+1 decomposition of Einstein equation

5.2 Coordinates adapted to the foliation

5.2.1 Definition

The system (5.17)+(5.20)+(5.21) is a system of tensorial equations. In order to trans-form it into a system of partial differential equations (PDE), one must introduce co-ordinates on the spacetime manifold M , which we have not done yet. Coordinatesadapted to the foliation (Σt)t∈R are set in the following way. On each hypersurfaceΣt one introduces some coordinate system (xi) = (x1,x2,x3). If this coordinate sys-tem varies smoothly between neighbouring hypersurfaces, then (xα) = (t,x1,x2,x3)constitutes a well-behaved coordinate system on M . We shall call (xi) = (x1,x2,x3)the spatial coordinates.

Let us denote by (∂∂∂ α) = (∂∂∂ t ,∂∂∂ i) the natural basis of Tp(M ) associated with thecoordinates (xα), i.e. the set of vectors

∂∂∂ t :=∂∂ t

(5.23)

∂∂∂ i :=∂

∂xi, i ∈ {1,2,3}. (5.24)

Notice that the vector ∂∂∂ t is tangent to the lines of constant spatial coordinates, i.e.the curves of M defined by (x1 = K1,x2 = K2,x3 = K3), where K1, K2 and K3 arethree constants (cf. Fig. 5.1). We shall call ∂∂∂ t the time vector.

Remark 5.5. ∂∂∂ t is not necessarily a timelike vector. This will be discussed furtherbelow [Eqs. (5.32)-(5.34)].

Fig. 5.1 Coordinates (xi) on the hypersurfaces Σt : each line xi = const cuts across the foliation(Σt)t∈R and defines the time vector ∂∂∂ t and the shift vector βββ of the spacetime coordinate system(xα ) = (t,xi).

Source : Gourgoulhon 2012, 3+1 Formalism in General Relativity, Springer

3+1 formalismGoal : ray-tracing in any numerical metric (not only Kerr !)Numerical relativity speaks 3+1 formalism : foliatingspacetime in 3D hypersurface, parameterized by t



Ray-tracing in non-Kerr spacetimesGYOTO can handle any numerical metricIt should be given in the 3+1 formalismi.e. GYOTO needs lapse, shift, extrinsic curvature at anypointThe metric can be non-stationary, non-axially-symmetric,non-asymptotically-flat, etc...

Why doing this ?

Possibility to handle spacetimes much more diversifiedthan (nearly-)Kerr spacetime, to which all ray-tracing codesare constrained



3+1 geodesic equation4D geodesic equation :

d2Xα

dλ2+ 4Γαµν

dXµ

dλdX ν

dλ= 0 (1)

3+1 equivalent :

dX i

dt= NV i − βi , (2a)

dV i

dt= NV j

[V i(∂j ln N − Kjk V k

)+ 2K i j −

3Γijk Vk]− γ ij∂j N − V j∂jβi . (2b)

→ Vincent, Gourgoulhon, Novak, Class. Quantum Grav. 29, 245005 (2012)



200 400 600 8000.

1.

2.

3.

10−5

t (M)

Err

or

Ke

rr a

na

lytica

l /

nu

me

rica

l

Kerr testIntegration of one geodesic in analytical / numerical KerrThis geodesic goes very close to the BHPlotted : relative error→ nice agreement



0

0.15

Stationary neutron starsMetrics computed by the CoCoNuT codeNeutron stars either non-rotating or rotating at 716 HzEmission : blackbody at 106 K



Collapsing neutron star

Metrics of collapsing non-rotating neutron star computedby CoCoNuTNon-stationary metric, still axially-symetricMetric fields are 3rd-order interpolated in timeGeodesics either hit the star’s surface, or accumulate nearthe event horizonEmission at star’s surface assumed to be still blackbodyGYOTO computes the successive images...



Non-rotating collapsing neutron star

0

0.02



Some non-trivial effectsThe angular size of the image does not vary muchHowever, the radius of the star varies a lot (factor ≈ 2.5)The image appears much bigger than in flat spacetime !Reason : BH lensingPhotons are emitted at different timesThat’s why the horizon appears first at the centerThe radius of the star at emission is different for differentphotons...This effect will become probably very important whenrealistic emission is taken into account



Section conclusionThis is the first example of ray-tracing computation in anon-Kerr spacetimeInterest of stationary NS ray-tracing : compute realisticlight curves, with realistic atmosphere (on-going)→ collab. with M. Bejger, P. Haensel, A. Rozanska, L.Zdunik (at CAMK)Collapsing neutron star case is interesting in terms ofspacetime visualization mainlyCan be used for visualizing other kind of spacetimes



Perspective : Boson starsFeinblum&McKinley (1968) ; Kaup (1968) ;Ruffini&Bonazzola (1969)Boson star = assembly of interacting spin-0 bosonssubject to gravityEquations of this system : Einstein equations +Klein-Gordon equationFor a non-rotating boson star, the solution is matched toSchwarzschild at some r ≡ rBS, with MSch ≡ MBSThe mass MBS can take values from NS typical masses toSMBH masses



Perspective : Boson starsPerspective of EHT : 0.1 angular Schwarzschild radiusprecision at GC...... is it possible to distinguish a Kerr BH from a rotatingboson star by imaging the silhouette ?Near future : ray-tracing computation by GYOTO in anumerically computed boson star spacetime→ collab. with C. Somé, O. Straub, E. Gourgoulhon (atLUTH)






4 Conclusion



ConclusionNew era of observations : access to the vicinity of thehorizon of a BH→ GRAVITY (2014), EHT (2015), LOFT (2020)Needed : accurate observation simulations of strong-fieldphenomena

First probe of strong-field GR : QPOsRWI is able of modulating the flux at a few % levelMode evolution signature in the light curve→ Compare this mode signature to other models→ Use astrometric signature of GC flares



Conclusion

Second probe of strong-field GR : SilhouettePure gravitation signatureGYOTO allows to compute a non-BH silhouetteStrongest alternative to BH : boson stars→ Compare a BH silhouette with a boson star silhouette→ Also at hand : compare a BH silhouette with a non-GRBH silhouette

Thanks for your attention !



Conclusion

Second probe of strong-field GR : SilhouettePure gravitation signatureGYOTO allows to compute a non-BH silhouetteStrongest alternative to BH : boson stars→ Compare a BH silhouette with a boson star silhouette→ Also at hand : compare a BH silhouette with a non-GRBH silhouette

Thanks for your attention !


A new era of observationsRossby wave instability for high frequency QPOsRay-tracing simulations in non-Kerr spacetime

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