Towards A unified model of Xray variability in Xray binaries and AGN

1
(Towards) A unified model of X-ray variability in
X-ray binaries and AGN

• Phil Uttley (NASA-GSFC)
• with
• Ian McHardy (Southampton),
• Simon Vaughan (Leicester)

2
Introduction

• What is the origin of the aperiodic variability
  in accreting compact objects? We shall look at
• Clues from power spectra
• Clues from the rms-flux relation and flux
  distributions
• QPOs
• Spectral-timing properties
• Will refer to Cyg X-1 data extensively throughout!

3
Aperiodic X-ray variability
In 1972 Terrell showed that the X-ray variability
of Cyg X-1 on s time-scales was consistent with
an aperiodic process, by comparing with a simple
shot-noise model
4
Rapid X-ray variability in accreting black hole
systems
The aperiodic red-noise nature of AGN
short-term variability was recognised in late
1980s (Lawrence et al. 1987 McHardy Czerny
1987 and see next talk), along with hints of
similarity with BHXRBs
5
Shot noise models and their interpretation
Shots can be interpreted as flares, but
shot-noise has never been anything other than a
mathematical description of the data. The common
interpretation of X-ray power-law variability as
being due to large-scale magnetic reconnection
flares is not observationally motivated!
6
Quantifying variability the power spectral
density (PSD) of Cyg X-1
High state Low state


7
Comparison of AGN and BHXRB PSDs
(Markowitz Uttley 2005 Uttley McHardy 2005)
8
The low/hard state multiple lorentzians
Cyg X-1 Dec 16 1996
9
Comparison of NS and BH PSDs
(See Sunyaev Revnivtsev 2000)
10
A fluctuating accretion-flow model
(Lyubarskii 1997, see also Churazov et al. 2001)
11
Key feature underlying variability independent
of type of emitting region
The model is also multiplicative, not additive
fractional mdot variations on different
time-scales multiply together...is evidence for
this observed?
12
The rms-flux relation
rms-flux relation of Cygnus X-1 Uttley
McHardy 2001 (UM01)





1 s segments
rms sqrt (1/N) ?i1,N (fluxi - mean)2
13
The rms-flux relation in different BHXRB states
and systems
Cyg X-1 (Uttley McHardy 2001, Gleissner et al.
2004)
PSDs and rms-flux relations of different states
of Cyg X-1 (Gleissner et al 2004)
low/hard
transition
high/soft
14
The rms-flux relation in SAX J1808.4-3658
SAX J1808.4-3658 (Uttley McHardy 2001)
15
What time-scales does the rms-flux relation
operate on in Cyg X-1?
16
A simple mathematical model
Linear rms-flux is mathematically equivalent to
amplitude modulation a non-linear process

• Linear light curves can be generated by a sum of
  sine waves
• L(t) 1 ? Ai sin(?i t ?i)
• But here, we have a product.
• X(t) ? 1Ai sin(?i t ?i)

17
The rms-flux relation phenomenological
implications

• If a large number of independently distributed
  components in the light curve multiply together,
  the resulting distribution of fluxes will be
  lognormal

• This result can explain the extreme variability
  behaviour of some AGN

18
Explains rapid powerful flares in Cyg X-1 (at
least in the low/hard state)
19
The power of simplicity lognormal flux
distributions are hard to make and to keep
lognormal!
20
QPOs as noise components
QPOs are often associated with Keplerian motion,
i.e. completely different to broadband noise,
they should show some sinusoidal structure
To the eye, the observed low-frequency QPOs dont
look very sinusoidal, but could they be sinusoids
that vary randomly in phase/frequency?
21
Are the LF QPOs really sinusoidal?
The QPO-folded profiles are mostly sinusoidal.
Remarkably, all four investigated QPOs are
broadened in frequency by a random walk in
oscillation phase. Morgan, Remillard
Greiner 1997
BUT random walks in phase are equivalent to the
offsets between QPO peaks being randomly
distributed about some average value, and this
the definition of a QPO! i.e. this result can be
trivially explained with any QPO model, not just
sinusoids of varying phase
22
Flux distribution of strong QPOs
In GRS 1915105 hard states (weak disk
emission), low-frequency QPOs can dominate the
variability If QPOs are sinusoidal, but
wandering in phase, the flux distribution should
be that of a sinusoid, i.e. double-peaked
GRS 1915105, July 23 1996
23
Distortion of the QPO flux distribution, evidence
for relativistic effects?
July 23 1996 July 29 1996

• The flux distribution for the 0.7 Hz QPO light
  curve is much more distorted than for 0.5 Hz QPO.
• Are orbital relativistic effects coming into play?

24
GRS 1915105 coupling of noise to the QPO and
the rms-flux relation
25
GRS 1915105 low-frequency QPO rms-flux
relations
26
Evolution of Lorentzians in Cyg X-1
(From Pottschmidt et al. 2003)
27
Cyg X-1 low/hard state spectral-timing behaviour
Ratio of soft/hard PSDs
2-4 keV PSD 8-13 keV PSD
8-13 keV vs 2-4 keV lags
28
The emitting region as a variability filter
(Based on Kotov, Churazov Gilfanov 2001)

• In any type of propagation model, the signal must
  be convolved with the response function of the
  emitting region. This will
• Reduce signal PSD normalisation by the squared
  ratio of emission inside signal origin to that
  outside (assuming only inwards propagation)
• Suppress signal at high frequencies due to travel
  time across region
• Introduce Fourier-frequency dependent time lags
  between bands if different bands have different
  emissivity profiles

29
Modelling the spectral-timing behaviour
Assumptions each Lorentzian corresponds to a
signal at a single radius, R??-3/2 and propagates
in on viscous time-scale, emissivity profiles
have power-law indices -4 and -3 in hard and soft
bands respectively, innermost emitting radius
corresponds to 30 Hz
30
Conclusions

• Several independent arguments imply that
  variability is produced in the accretion flow
  (similarity of BH and NS variability, long
  observed time-scales of variability, rms-flux
  relations in NS and BH)
• The observed lognormal distribution in aperiodic
  variability can strongly constrain models for
  variability, and higher order effects on
  variability such as relativistic boosting
• The quasi-lognormal distributions of the lt1 Hz LF
  QPOs are puzzling, are these just filtered
  noise from the accretion flow too?
• Spectral-timing properties (lags,
  energy-dependence of PSD) could be a useful and
  powerful probe of the X-ray emitting region if
  simple models where signals (e.g. in the
  accretion flow) propagate through the emitting
  region are correct.