Variability of the Flux Densities of Radio Sources on Timescales Shorter than a Month A.G. Gorshkov 1, V.K.Konnikova 1 M. Mingaliev Sternberg Astronomical Institute 2 - Special Astrophysical Observatory

Introduction As a result of more than 40 years of studies of variability, it has become clear that the overwhelming majority of discrete radio sources with flat spectra are variable on timescales from tens of years to tens of minutes. There is virtually no doubt that long-term variability is a consequence of non-stationary processes in AGN. The most adequate explanation of the observed character of the variability is given by shock models (see, e.g., A.P. Marscher and W. K. Gear, ApJ., 1985; H. D. Aller et al., ApJ., 1985)

Introduction It is most likely that flux variability on daily and IDV timescales has an external cause, and is due scintillation on the turbulent interstellar medium (see, e.g., B. J. Rickett et al., A&A. Suppl. Ser., 1995). In the case of intrinsic variability, the implied brightness temperatures are much higher than the Compton limit of K, and reach up to K. This requires Doppler ( δ ) and Lorentz ( γ ) factors of several dozen.

Introduction Of course a small number of sources could have such Doppler and Lorentz factors. The main criterion enabling us to choose between intrinsic and external origins of IDV, particularly at centimeter wavelengths, is the form of the spectrum. If the spectrum is rising, the cause of the IDV is intrinsic; otherwise, other criteria are required to distinguish between the alternatives.

Introduction Variations on diurnal timescales are small: as a rule, the variability index is a few per cent (J. H. Simoneti et al., ApJ., 1985). However, they are detected in virtually all sources with flat spectra. The variations have an average timescale of about four days and, on average, a flat spectrum in the range 13–1.35 cm (A. G. Gorshkov et al., ApJ., 1985 Aph. Space Sci., 2001).

Introduction Intraday flux variations are also found in most sources with flat spectra and frequently have even greater amplitude of variability than variations on timescales longer than a day. The detection of flux density variations by up to a factor of three on timescales shorter than an hour in the source J was reported in ( Dennet-Thorpe and A. G. de Bruyn, AJ., 2000) The existence of IDV inevitably implies the presence in radio sources with flat spectra of structures with angular sizes not exceeding a milliarcsecond.

Samples and Observations 1.S  200 mJy at 3.9 GHz (Zelenchuk Survey)  RA = 00 h  24 h, Declination = +04˚  06˚, |b| > 15˚;  N = 138 objects (70 – steep spectra; 68 – flat spectra);  56 objects (82%) are identified: 42 – QSO, 6 – BLOs and 5 – Galaxies. 2.S  200 mJy at 4.85 GHz (MGB Survey)  RA = 00 h  24 h, Declination = +10˚  12.5˚, |b| > 15˚  N = 153 objects (70 – steep spectra; 83 – flat spectra)  72 objects (87%) are identified: 52 – QSO, 7 – BLOs and 11 – Galaxies. 3.Observations were done with the RATAN-600 at 6 frequencies: 0.97, 2.3, 3.9 (4.85 since 2004), 7.7, 11.1, and 21.7 GHz. 4.Since 1998 we observed daily all sources with flat spectra in several sets by duration of days.

Data reduction and analysis The search for and study of temporal scale of variability of sources with significant variability was done in several stages: 1. At first we filtered out measured flux densities distorted by various sources of interference (weather conditions or man-made) using the Fisher test. Further we used only flux densities selected by the F test for a given set of measurements; 2. Then a long-term variability with timescales longer than the duration of the observations have been removed (various types of trends, which were approximated by second degree polynomials and subtracted from the raw data).

Data reduction and analysis For the rough estimation the variability timescale a structure function was used: τ- temporal lag. Above the level of the instrumental noise, the SF grows as a power law until it reaches the saturation level. The intersection of its power-law part with the saturation level yields the timescale τ sf. We also calculated autocorrelation functions: time delay corresponding to the first ACF minimum corresponds to the time delay where the SF reaches its maximum: SF(τ) = 2(ACF(0) − ACF(τ)). The ACF enable us to determine the variability timescale more accurately as well as the character of the variability.

Analysis of the ACFs shows that the variability can be clearly divided into four groups corresponding to different types of variability. Examples of each group are shown in the left panel. The solid curves are the ACF estimates used to derive the timescales indicated in the figures.

Results Periodic processes:  well approximated by one harmonic during all observation sets;  the derived timescale is half the period of this harmonic. Figure shows an example of such type with τ acf = 4.4 days for J The period remains stable during all 103 days of the observations.

Results Cyclic or quasi-periodic processes: The ACF form suggests that the process has a cyclic character, but the cycle period changes appreciably within a series. Figure presents an example of a cyclic process τ acf = 8.7 days for J in This type is more widespread type of weekly variability.

Results The sum of two cyclic processes with different amplitudes and timescales. As a rule, both processes are clearly visible in the SF. Figure presents an example of such process in J in 1999: two processes with τ acf = 5.7 and 24 days.

Results Stochastic processes. These can be isolated or occasional, chaotically arranged pulses; one significant minimum is present in the ACF. In this case fitting is carried out on timescales somewhat exceeding the visual ACF minimum. The value of τ acf gives the timescale of a single pulse or the mean timescale of an ensemble of pulses. Figure presents an example of such process with τ acf = 14 days for J in 2004.

Results 1. Variability on a week time scale is found out at 11 (16%) objects of sample 1 and at 19 (23%) objects of sample All these sources also have a strong long-term variability of flux density. 3. The variability of different types with different timescales can be observed at different frequencies in the same source. These characteristics can also vary at different epochs. Variability may be present in some years and completely absent in others. 4. At four sources ( , , and ) variability is found out in all sets of observations.

Results The weekly variability timescales and modulation indices are listed in the Table:

Results Spectra of a variable components have been derived

Individual sources: J , BLO, z = J has the highest amplitude of weekly variability with m>10%. It was observed in all sets and weekly variability was detected in all years irrespective of the activity phase of the long-term variability. The source has a high amplitude of long-term flux density variability: at 7.7 GHz S min = 64 ±20 mJy (1988) and S max = 1083 ± 9 mJy (1998); S man /S min ≈ 15.

Individual sources: J , BLO, z = Light curves ( ) at 2.3, 4.85, 7.7, 11.1, and 21.7 GHz. The long-term variability has a flare-like character with the flares repeated at an interval of four to six years. Taking into account the flare timescale and red shift one can estimates linear size of 0.22 pc (or 0.04 mas). The brightness temperature in the flare exceeded the Compton limit: T b = 14×10 12 K.

Individual sources

Individual sources: J , QSO, z = Example of a source with two cyclic components. The spectrum of the variable component demonstrates that there may be two sources of variability in this object: the rising part of the spectrum is produced by processes intrinsic to the source, while the falling part has an external origin.

 Number of sources with flat spectra vs Galactic latitude  Modulation index of sources with weekly variability vs Galactic latitude  Timescale of variability vs Galactic latitude

Conclusion  Weekly variability most often meets at BLOs; it is more than half of these objects of the sample have similar variability.  At galaxies weekly variability practically is absent.  Weekly variability is connected with the short-lived details in the jet and can be both flare and cyclic. In one source can exist simultaneously two or more cyclic processes with the different characteristic times.  Characteristic times are from 4 up to 30 days. Mean value is 14 days on all frequencies.  Variability, as a rule, is correlated at the adjacent frequencies. There is no delay of the development of process with a decrease of a frequency.

Conclusion Inmost cases, the available variability parameters are sufficient to distinguish intrinsic and external variability:  The main argument for a particular type of variability is provided by the form of the spectrum and the frequency at which this spectrum is formed.  A falling spectrum at low frequencies unambiguously testifies to an external origin of the variability, while a falling spectrum at high frequencies with the absence of detectable variability at low frequencies most likely suggests intrinsic variability.

Conclusion  But a flat spectrum for the variable component can also result from an external variability; such spectra are just result of an increase in the degree of compactness of the scintillating source with increasing frequency.  A high modulation index at high Galactic latitudes indicates intrinsic weekly variability irrespective of the form of the spectrum.  The variability timescales themselves cannot provide support for either type of variability. A necessary condition for the existence of weekly variability is the presence of strong long-term flare variability in the source.  There is no direct connection between the existence of weekly variability and the phase of the long-term activity.

Thank you for attention! Astronomy Reports, 2010, Vol. 54, No. 10, pp. 908–924.