Документ взят из кэша поисковой машины. Адрес
оригинального документа
: http://www.adass.org/adass/proceedings/adass96/oknyanskijv.html
Дата изменения: Tue Jun 23 21:16:32 1998 Дата индексирования: Tue Oct 2 03:42:15 2012 Кодировка: Поисковые слова: magnetic north |
Next: Time Series Analysis of Unequally Spaced Data: Intercomparison Between Estimators of the Power Spectrum
Previous: Unified Survey of Fourier Synthesis Methodologies
Up: Algorithms
Table of Contents - Index - PS reprint - PDF reprint
V. L. Oknyanskij
Sternberg Astronomical Institute, Universitetskij Prospekt 13, Moscow, 119899, Russia
Radio-optical variability correlation in Q0957+561 was first reported by Oknyanskij & Beskin (1993, hereafter OB) on the basis of radio observations made in the years 1979 to 1990. OB used an idea to take into account the known gravitational lensing time delay to get combined radio and optical light curves and then to use them for determination of the possible radio-from-optical time delay. It was found this way that radio variations (5MHz) followed optical ones by about 6.4 years with high level of correlation (0.87). Using new radio data (Haarsma et al. 1997), for the interval 1979-1994, we find nearly the same value for the optical-to-radio delay as had been found before. Additionally, we suspect that the time delay value is linearly increasing at about 110 days per year while the portion of reradiated flux in the radio response is decreasing.
We conclude that the variable radio source is ejected from the central part of the QSO compact component.
Time delay determinations in astrophysics are used most often to find time shifts between variations in different spectral bands and/or lines in AGNs, as well as time delays between different images of gravitationally lensed QSOs. In most cases, the task is complicated by uneven spacing of data, so that standard cross-correlation methods become useless. Two different methods are most often used: CCF (Gaskell & Spark 1986) and DCF (Edelson & Krolik 1988), which are based on line interpolation of data sets or binning of correlation coefficients, respectively. We have introduced several simple improvements to CCF (Oknyanskij 1994) and this modernized MCCF combines the best properties of CCF and DCF methods. With MMCF we calculated regression coefficients as functions of time shift. Here, this calculation is generalized for the more complex case where the time delay is a linear function of time, and a portion of the flux density is itself a power-law function of the delay. We apply this method to the optical-to-radio time delay in the gravitationally lensed double quasar Q0957+561. The data sets used here were obtained to determine the gravitational lensing time delay o. Our results are nearly identical for values of o in the interval of 410-550 days. In the discussion below, we take o=425 days.
Our method includes several steps, which are briefly explained below:
We combine these values B´ with the usual B ones, sorting by time. The resulting optical light curve was then smoothed by averaging in 200 day intervals with steps of 30 days. This accounts for the physical argument that radio sources should be bigger than optical ones. The value of 200 days for smoothing was taken as about optimal from the autocorrelation analysis of light curves.
to be added to dates in the optical light curves:
Assuming that a portion of radio flux decreases as a power-law function of time with exponent . We should also correct the optical flux for that fading before computing the cross-correlation function:
Figure: Two-dimensional cross-correlation function (see text).
Original PostScript figure (192kB).
For points (V,) we map the MCCF values (see Figure 1). The best correlation occurs for V100 days/year, and 0.7.
We have calculated the time delay between radio and optical flux variations using a new method. In addition, we have investigated the possibilities that (1) there is a change of the time delay that is a linear function of time, and (2) the radio response has power-law dependence on the time delay value.
Finally, let us stress some additional consequences from our results:
Figure: Radio and optical combined light curves.
(The optical light curve is corrected as described in the text.)
Original PostScript figure (168kB).
In conclusion, we thank Debborah Haarsma for sending us the preprint with the new radio data for Q0957+561 before publication.
Edelson, R. A., & Krolik, J. H. 1988, ApJ, 333, 646
Gaskell, C. M., & Spark, L. S. 1986, ApJ, 305, 175
Haarsma, D. B., Hewitt, J. N., Lehar, J., & Burke, B. F. 1997, ApJ, 479, 102
Oknyanskij, V. L., & Beskin, G. M. 1993, in Gravitational Lenses in the Universe: Proceedings of the 31st Liege International Astrophysical Colloquium, eds. J. Surdej et al. (Liege, Belgium: Universite de Liege, Institut d'Astrophysique), 65
Oknyanskij, V. L. 1994, Ap&SS, 222, 157
Schild, R. E., & Thomson, D. J. 1995, AJ, 109, 1970
Vanderriest, C., et al. 1989, A&A, 215, 1
Next: Time Series Analysis of Unequally Spaced Data: Intercomparison Between Estimators of the Power Spectrum
Previous: Unified Survey of Fourier Synthesis Methodologies
Up: Algorithms
Table of Contents - Index - PS reprint - PDF reprint