Fast Timing Variability in X-Ray Binaries : Motivations, Methods, & Diagnosis

FAST TIMING VARIABILITY IN X-RAY BINARIES : MOTIVATIONS, METHODS, & DIAGNOSIS

J. Rodriguez, CEA Saclay - Astrophysics division ACCRETION(-EJECTION) AN UBIQUITOUS PHENOMENON Star formation…… fate of the most Centres of massive stars galaxies

Stars disrupted by …And XRBs black hole MICROQUASARS = LABS OF EXTREME PHYSICS

Fundamental physics: -Strong gravity -Black Holes Astronomy -Plasma physics -Population -Dense matter Astrophysics -Strong B ﬁeld (NS) -Star evolution -Link with Galactic evolution -Accretion -Geometry of media -Acceleration -Feedback on ISM -Radiation -Matter-radiation -Fast variability MOTIVATIONS & SPECTRAL METHODS

=>Close objects / Galactic (~8 kpc)

2 dm 35 =>Bright L = ⌘c L = 10 erg/s acc dt acc

L T = ( acc )0.25 0.2 keV =>Strong X-ray emitters b 2 4⇥ROC

Soft Spectrum Hard Spectrum

)

-1

-2 EF(E) (keVcm EF(E)

Énergie (keV)

McConnell+ ’02 BASIC VIEW: EMITTING MEDIA

Thermal emission black body: soft X- rays ~1keV /

Optical (External) disc/companion: IR -

Visible

Jet emission: radio to

Hard X-ray (10-200 keV): « Corona » γ-ray emission 0.2-10 MeV: Origin? BASIC VIEW: EMITTING MEDIA

Thermal emission black body: soft X- rays ~1keV /

Optical (External) disc/companion: IR -

Visible STATICJet emission: radio to VIEW!!!!

Hard X-ray (10-200 keV): « Corona » γ-ray emission 0.2-10 MeV: Origin? THE X-RAY SKY: VIOLENT & VARIABLE

Sco X-1 GRS 1915+105 Cygnus

Norma Credit: Zhan Yan (SHAO)

RXTE/ASM: 16 years all sky monitoring of the X-ray sky THE X-RAY SKY: VIOLENT & VARIABLE

Sco X-1 GRS 1915+105 Cygnus

Norma Credit: Zhan Yan (SHAO)

RXTE/ASM: 16 years all sky monitoring of the X-ray sky X-RAY VARIABILITY: EXPECTED

r3 dyn,Kepler dyn,Kepler 2 ms(1 M , 100 km) GMOC

1 hr Porb 100 j

Spin of neutron stars : 1 ms . P . 1hr

Variability can be expected just because of natural periods in systems

EP Dra IGRJ16393-4643

Ramsay+ ‘04 Bodaghee+ ‘06 NOT ALWAYS THAT SIMPLE

V404 Cygni: • ~10 sol M black hole • 6.2 d orbital period • Dormant for 30 years

(Extreme) Variability obvious Origin? No evident recurrent pattern How can it be probed ? No links with ‘natural’ periods NOT ALWAYS THAT SIMPLE

V404 Cygni: • ~10 sol M black hole • 6.2 d orbital period • Dormant for 30 years

(Extreme) Variability obvious Origin? No evident recurrent pattern How can it be probed ? No links with ‘natural’ periods MULTI-WAVELENGTH VARIABILITY Days to years Seconds to hours

Radio (15 GHz) Flux (mJy) Flux

X-ray (1-5 keV)

(cts/s) Mirabel+’98 R.+ ‘08 X-ray (5-12 keV) Count rate Count

Time (Modified Julian Day) X-rays (accretion, disc) lead variability =>Jet in response to accretion inst. => Lags give constraints on : =>Jet matter from inner ﬂow =>Causal relationship =>Jet energised by inner ﬂow/BH =>Geometries =>Distances (see G. Ponti’s talk) Physical mechanism yet to be discovered UNDERSTANDING OF THE LONG TERM EVOLUTION

Tex t TO GO FURTHER SUB-SECOND VARIABILITY

Soft spectrum (disc) Hard spectrum (‘corona’)

Variability clear in some cases Periodic ﬂuctuations? Relation with spectral state? Origin and link with disc/jet?

We ﬁrst need to quantify, characterize, and understand the rapid variability ? FOURIER ANALYSIS

Fourier transform = decomposition of signal into sine waves

N Signal is discrete/binned 2 1 N 2 1 1 i2⇡! t j 1 i2⇡!j tk L(t)= aje Lk = aje k =0,..,N N N N j= N j= 2 X X 2 With aj is the Fourier coef. of pulsation ωj : represent the correlation of L(t) with modulation with pulsation ωj => aj high <=> signal with strong period at ωj

1 ⌫ = ⌫ = min T

1 N ⌫ = = max 2 t 2T ⇥ IN PRACTICE « POWER SPECTRA »

We use the Leahy normalisation (such that WN power has a level of 2): 2 2 Pj = aj Ntot | | N 1 1 2 Var(L )= a 2 k N | j| j= N ,j=0 X2 6

Variance is the sum of powers :

N/2 1 k Lk Var(Lk)= ( Pj +0.5P N ) N 2 j=1 P X Power density gives power per unit frequency => the integral of the power spectrum is the sum of power: equivalent to measuring the variance of signal GRAPHICALLY OBSERVATIONS

• High frequencies <=> high resolution • Large photon stat. <=> large collecting area • => RXTE ~6600 cm2 (1996-2011) • => Astrosat 8000 cm2 (launched 2015) IN PRACTICE (2)

Sum the N Poisson PDS => Gaussian with mean 2N and σ=2/N

Divide in shorter intervals Calculates the indiv. PDS Average PDS (such that poisson level =2)

Signiﬁcance of feature with HWHM Δν and power r is:

2 2 T S n =0.5 rs ( ) ⇥ r ⌫ S + B T is total duration (mean count rate is N/T) , S is source net signal, B is background WITH APPROPRIATE CHOICE

Low frequency QPO 4 − 10

2 ν in Hz

RMS 5 FWHM (or σ) in Hz − High frequency QPO

) 10 Power in % RMS Some continuum QPO <=> Q=ν/σ>2 ie peaked, signal has certain 6 coherence − 10

Count rate =

White noise level

Leahy

1 10 100 1000 Varnière & R., in prep.

⌫2 Power[⌫1, ⌫2] = PDS(⌫)d⌫ s Z⌫1 VARIABILITY QPOS AND SPECTRAL STATES

Complex broad band shape a few % LF and HF QPOs (~1%)

Weak variability dP ⌫ d⌫ / noQPOs 1 ⇠

« Flat top » broad band shape: P cte ⌫ < ⌫ ⇠ break dP ⌫ d⌫ ⌫ > ⌫break; > 1 / 1 Strong variability⇠ (10-40%) LFQPO (10-20%) Remillard & McClintock ‘06 LFQPOS ORIGINATE FROM DISC…..

Frequency vs Hardness and (soft) Flux Frequency vs Disc Temp.

Muno+ ’01 Frequency vs Disc Radius Muno+ ’01, R.+’04

Mikles+ ’09, R.+’02 ….. OR CORONA/JET?

Frequency vs Corona slope

QPOs have hard spectra

Vignarca+ ‘03 Amplitude (%RMS)

Energy (keV) R+ ‘08

Possible link to mechanism giving rise to ejections CONCLUSIONS

Spectral analysis gives a static picture of physics

Accreting sources are highly variable on very different time scales

Variability is complex, with broad band « noise » and (quasi)periodic pulsations

Fourier analysis permits to dig into the properties of variable accretion ﬂows :

Link of variability with accretion states indicates complex phenomena

Models of accretion/ejection cannot ignore the dynamical properties!

Fast variability has to be considered in the picture