In this Section, the discovery of extreme (amplitude variability with a factor larger than 10) and rapid (time scales of hours) X-ray variability in the two NLS1s IRAS 13224-3809 and PHL 1092 as well as their physical implications is described. The combination of extreme, rapid and persistent amplitude variability was discovered in 1996 within the first monitoring campaign on a narrow-line Seyfert 1 galaxy. Rapid and extreme X-ray variability in a second object, the X-ray luminous narrowline quasar PHL 1092, was discovered one year later, in 1997. Although extreme amplitude X- ray variability had already been reported in a few active galaxies, RE J 1237+264 , E1615+061 , WPVS 007 , their time scales of variability are of the order of years.
126.96.36.199 IRAS 13224-3809, The Most Extremely Variable Seyfert Galaxy
The NLS1 IRAS 13224-3809 was observed over a time scale of 30 days, between January 11, 1996 (0:33:42 UT) and February 9, 1996 (13:23:28 UT), using the ROSAT HRI detector, the total observing time being 111,313 seconds. The number of source photons is 5602. The mean count rate is 0.05 photons per second. A careful analysis of the arrival times of the source photons shows a strong deviation from the mean count rate. This extreme X-ray variability is shown in Fig. 22.4. The minimum count rate is observed at day 5.0408 (in units of the Julian date) with (4.7 ± 2.5) • 10-3 counts s-1. The maximum count rate, observed at day 17.9861, is (0.287 ± 0.019) 10-1 counts s-1. The resulting maximum amplitude variability is therefore a factor of 61. The most extreme amplitude variability on a short time scale is detected between day 16.0160 and 17.9861. The count rate increases from (5.0 ± 1.9) • 10-3 counts s-1 to (0.287 ±0.019) counts s-1. This corresponds to amplitude variability by a factor of about 57 within only two days. The resulting luminosity (the conversion between flux and luminosity was done using the relations given by  for a value of Hubble constant of 50, a value of q0 of 0.5) for one HRI count per second is 2.9 • 1045 erg s-1. Assuming isotropic emission from IRAS 13224-3809, the resulting increase in luminosity from 1.5 • 1043 erg s-1 to 8.3 • 1044 erg s-1 within about 2 days, and the corresponding change in luminosity of AL ~ 8.2 • 1044 erg s-1 is remarkable. Relativistic flux amplification in the inner accretion disc due to hot spots orbiting the central black hole provides a physical explanation. In this model, the extreme flux variations are only detected in the observers frame .
Discovery of extreme and rapid X-ray vcriability in the ncrrow-line Seyfert 1 galaxy IRAS 13224-3809
ROSAT observation TL January - 9. February 1996
Julian date [2450093.523 days]
Fig. 22.4 ROSAT HRI light curve of IRAS 13224-3809, obtained during a 30 day monitoring campaign between January 11,1996 (0:33:42 UT) and February 9,1996 (13:23:28 UT). The x-axis gives the Julian date minus 2450093.523 days. The dashed line shows the background count rate as a function of time. At least 5 giant amplitude variations are clearly visible. IRAS 13224-3809 shows the most extreme persistent X-ray variability so far measured from active galactic nuclei
188.8.131.52 Discovery of Extreme and Rapid X-ray Variability in the Narrow-line Quasar PHL 1092
Figure 22.5 shows the X-ray light curve of PHL 1092. Strong X-ray variability is detected throughout the observation. For the most extreme combination of amplitude variability with time, at day 8.6, we obtain a change in luminosity of AL = (5.0 ± 1.1) 1045 erg s-1 within a time interval of At = 3580 seconds. The observed variability per time of AL • At = 1.40 • 1042 erg s-2 is presently the largest value measured in a radio-quiet galaxy. This value exceeds the efficiency limit for accretion onto a Kerr black hole , and supports the model of relativistic flux boosting for the rapid and extreme variability detected in PHL 1092.
184.108.40.206 Physical Models for Rapid and Extreme X-ray Variability
In this Section, physical models for the recently discovered rapid and extreme X-ray variability are discussed. The most probable explanation is given by the effect of strong relativistic flux amplification in the inner accretion disc [24,48]. The rapid and extreme variation, as well as the low values of absorption by neutral hydrogen along the line of sight, suggest that the innermost parts of the accretion disc in IRAS
Julian date [2450645.120 days]
Fig. 22.5 ROSAT HRI light curve of PHL 1092, obtained within an 18-day observation between July 16, 1997 (02:47:15 UT) and August 2, 1997 (13:53:58 UT). The x-axis gives the Julian date minus 2450645.120 days). The dashed line gives the background count rate as function of time. The maximum factor of the amplitude variability is 13.9. PHL 1092 shows the most extreme change of luminosity per time interval so far found in an active galaxy
13224-3809 must be directly visible. At such distances to the central black hole, the X-ray emitting regions move with relativistic velocities and, as a consequence strong intensity variations occur due to the relativistic Doppler effect. The relativistic Doppler effect  gives a relation between the observed frequency v and the frequency v in the system of the moving particles:
The relativistic Doppler effect can result in strong apparent flux variations, if the emission region is not steady or inhomogeneous. For the system of the rotating accretion disc, this means that the X-ray emitting regions moving towards the observer are increased in their intensity in the observers frame. In the case where the temperature distribution on the accretion disc is not homogeneous, which may be caused by X-ray hot spots on the accretion disc, strong intensity variations occur in the observers frame. In the following, the resulting intensity variation in the observers frame is derived for a single hot spot orbiting the black hole. The flux value at the frequency v of the emission of a hot spot orbiting the black hole is called fy in the following. The flux value measured by the observer at the frequency v is fv. From Lorentz-transformation theory , it follows that the ratio of the flux to the third power of the frequency is invariant for Lorentz-transformations:
Assuming a simple power-law model for the energy distribution1 fv ~ v a and ly ~ v it follows that the flux ratios integrated over a limited frequency interval (v1, v2) are given by:
The ratio of the observed flux f to the emitted flux f' is, besides the Doppler factor, a strong function of the slope of the spectral energy distribution a. Especially for narrow-line Seyfert 1 galaxies, with their extremely steep X-ray spectra, high values of the ratio f are expected.
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