arXiv:astro-ph/0403326v2 18 Mar 2004 Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 2 February 2008 (MN L a T E X style file v2.2) Black hole mass estimation from X-ray variability measurements in AGN M. Nikolajuk 1 , I.E. Papadakis 2 and B. Czerny 1 1 N. Copernicus Astronomical Centre, Bartycka 18, 00-716 Warsaw, Poland 2 Physics Department, University of Crete, 71 003, Heraklion, Crete, Greece 2 February 2008 ABSTRACT We propose a new method of estimation of the black hole masses in AGN based on the normalized excess variance, σ 2 nxs . We derive a relation between σ 2 nxs , the length of the observation, T , the light curve bin size, Δt, and the black hole mass, assuming that (i) the power spectrum above the high frequency break, ν bf , has a slope of -2, (ii) the high frequency break scales with black hole mass, (iii) the power spectrum amplitude (in frequency × power space) is universal and (iv) σ 2 nxs is calculated from observations of length T< 1/ν bf . Values of black hole masses in AGN obtained with this method are consistent with estimates based on other techniques such as reverberation mapping or the M BH -stellar velocity dispersion relation. The method is formally equivalent to methods based on power spectrum scaling with mass but the use of σ 2 nxs has the big advantage of being applicable to relatively low quality data. Key words: galaxies: active – galaxies: Seyfert – X-rays: galaxies 1 INTRODUCTION The X-ray emission of active galactic nuclei (AGN) displays variations over a wide range of time scales. The first con- vincing demonstration of this phenomenon came with the EXOSAT ‘long looks’ (Lawrence et al. 1987; McHardy & Cz- erny 1987). The data showed no characteristic time-scales, and the power spectral density function (PSD) showed a ‘red-noise’ shape. At the same time, it was also noticed that more luminous sources show slower variations. Various methods have been used in the past in order to determine the X-ray variability amplitude of AGN: determination of the ‘two-folding’ time-scale (i.e. the time-scale for the emit- ted flux to change by a factor of two), calculation of the PSD amplitude at a given frequency, and estimation of the so called ‘normalized excess variance’ (σ 2 nxs , i.e. the variance of a light curve normalized by its mean squared after correct- ing for the experimental noise). In all cases, these quantities appear to anti-correlate with the source luminosity (Barr & Mushotzky 1986; Lawrence & Papadakis 1993; Green, McHardy & Lehto 1993; Nandra et al. 1997; Turner et al. 1999; Leighly 1999; Markowitz & Edelson 2001). One pos- sible explanation for the observed anti-correlation between the X-ray variability amplitude and X-ray luminosity, LX, is that more luminous AGN have larger black hole masses (MBH) as well. In this case, as MBH increases, so does the size of the X-ray source, and a change of the source lumi- nosity by a constant fraction takes relatively longer; equiv- alently, variability amplitude measured at a fixed timescale should decrease with mass. The significant progress in the measurement of the black hole (BH) mass in the centers of nearby galaxies has made it possible to actually directly test the dependence of the X-ray variability amplitude on MBH in AGN. The data show that σ 2 nxs measured at a cer- tain timescale is indeed anti-correlated with MBH (Lu & Yu 2001; Bian & Zao 2003; Papadakis 2004). If there is an intrinsic correlation between X-ray vari- ability and MBH, then X-ray variability measurements could be used in order to measure the central black hole mass in these objects. This possibility has already been stud- ied in the past. Hayashida et al. (1998) and Czerny et al. (2001) have used the PSD normalized by the square of the mean flux as a measure of the X-ray variability of a source. By calculating the ratio of the frequencies at which the PSD×frequency has a certain value in AGN and Cyg X- 1, they were able to estimate the MBH in AGN. Recently, long, well-sampled RXTE light curves have been used in or- der to accurately estimate the X-ray PSD of AGN. One of the main results from these studies has been the unambigu- ous detection of a characteristic ‘break frequency’, ν bf , at which the power spectrum changes its slope from a value of −2 to −1 above and below ν bf , respectively (Uttley et al. 2002; Markowitz et al. 2003). This break frequency is anal- ogous to the high frequency break in galactic sources and should not be confused with the low frequency break, where the spectrum changes slope from −1 above to 0 below. This high frequency break appears to correlate well with MBH, in the sense that 1/ν bf ∝ MBH (Markowitz et al. 2003). Thus