A&A 414, 795-806 (2004)

DOI: 10.1051/0004-6361:20031614

## X-ray time lags from a pivoting power law in black holes

**E. Körding**

^{1}and H. Falcke^{1, 2, 3}^{1}Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany

^{2}
Radio Observatory, ASTRON, Dwingeloo, PO Box 2, 7990 AA
Dwingeloo, The Netherlands
^{3}
Department of Astronomy, University of Nijmegen, PO
Box 9010, 6500 GL Nijmegen, The Netherlands

(Received 11 March 2003 / Accepted 13 October 2003)

** Abstract **

Most black hole candidate X-ray binaries show Fourier time
lags between softer and
harder X-rays. The hard photons seem to arrive up to a few ms after the
soft for a given Fourier frequency of the perturbation.
The energy dependence of the time lags has a roughly logarithmic
behavior.
Up to now most theories fail to explain the observed magnitude and
Fourier frequency dependence of the
lags or fail other statistical tests.
We show that the time lags can arise from a simple pivoting power law model,
which creates the logarithmic dependence on the photon energy at once.
A pivoting power law arises naturally from jet/synchrotron models for the
X-ray emission, but may also be applicable to corona models.
A hint to the coherence features of the light-curves can be obtained from
the power spectral density, which can be decomposed into a few broad
Lorentzians that could arise from a couple of
strongly damped oscillators with low quality factors below one.
Using small variations of the power law index for each Lorentzian separately
the lags can be derived analytically. They show the correct
Fourier frequency dependence of the time lags.
If one assumes variations of the power law
index by
0.2 the model can account for
the observed magnitude of the time lags in Cyg X-1.
The model can also be applied to TeV blazars, where a pivoting power law
and hard lags have been observed directly in some cases.
As a further test we calculated the cross- and auto-correlation functions
for our model, which also show qualitatively the observed behavior.
The auto-correlation function for higher energies has a narrower peak
than at lower energies and the cross-correlation function is
asymmetric but peaks nearly at zero.
The coherence function for the model is in agreement with the observed
data in the Fourier regime, where the model is valid.

**Key words:**X-rays: binaries

**--**accretion, accretion disks

**--**black hole physics

**--**radiation mechanisms: non-thermal

Offprint request: E. Körding, koerding@mpifr-bonn.mpg.de

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**©**

*ESO 2004*