ACCRETION DISK MODEL OF SHORT-TIMESCALE INTERMITTENT ACTIVITY IN YOUNG RADIO SOURCES

The duty cycle of active galactic nuclei (AGNs) is still a subject of debate. Different mechanisms are likely to operate. On long timescales, up to 10⁸ yr, the merger activity is broadly considered as the cause of an enhanced accretion flow and the main provider of material for the black hole growth. However, at later stages, AGNs are also likely to pass through subsequent stages of higher and lower activity. Intermittent behavior of this type is likely to be caused by minor mergers or instabilities in the accretion flow.

There are several observational arguments for this intermittent behavior. For example, morphology of X-ray clusters studied with Chandra  X-ray Observatory and XMM-Newton indicate a past intermittent AGN activity of the central dominant galaxy that is responsible for heating of the central cluster regions. X-ray images show cavities and ripples that give the timescales of repetitive outbursts and provide a measure of their power (e.g., Ruszkowski et al. 2004; McNamara & Nulsen 2007; Sanders & Fabian 2008). Such AGN intermittency seems to be closely related to the feedback process operating in galaxy clusters.

Radio galaxies that are not associated with clusters, also provide signatures of the intermittent activity. First, in many cases studies of radio structure directly showed evidence of two or more of active periods (e.g., Burns et al. 1983; Bridle et al. 1989; Clarke et al. 1992; Schoenmakers et al. 2000a, 2000b; Marecki et al. 2003; Jamrozy et al. 2007; Giovannini et al. 2007). In some sources, the new radio structure is highly inclined to the old one (e.g., Cheung 2007), thus indicating an independent accretion/black hole merger episode resulting in renewing activity of the central engine accompanied by the re-orientation of the jet axis (e.g., Merritt & Ekers 2002; Gopal-Krishna et al. 2003; Blundell 2008; Lal et al. 2008). Some sources of this type are very compact, only a few kpc in size (Marecki et al. 2006). In other sources, both structures (old and new) are aligned (e.g., Saripalli et al. 1996; Schoenmakers et al. 2000a, 2000b; Konar et al. 2006; Marecki et al. 2006), which is consistent with the development of perturbations in the accretion rate within the existing accretion disks and subsequent intermittent radio activity along the same (unchanged) direction of the outflow (Siemiginowska et al. 1996; Siemiginowska & Elvis 1997; Hatziminaoglou et al. 2001; Janiuk et al. 2004). An extreme example of such an activity is a triple–double source in which three periods of activity led to the aligned features (B0925+420; Brocksopp et al. 2007).

Second, the population studies show the existence of far too many compact ("young") sources in comparison with the number of galaxies with extended old radio structures (O'Dea & Baum 1997; Snellen et al. 2000) although the full discussion is complex due to various limitations of the available samples (Tinti & De Zotti 2006). If the total activity period lasts 10⁸ yr, the number of sources with the ages below 10³ yr should be roughly 10⁵ times lower than the number of sources older than 10³ yr, which is not the case. One possible explanation is that the jet gets frustrated, and the source is in fact old, although it is small in size (van Breugel et al. 1984; Readhead et al. 1996). However, the important argument against this interpretation is the lack of the required amount of the thermal matter to quench the jet expansion within host galaxies of gigahertz-peaked spectrum (GPS) sources (Siemiginowska et al. 2005, and references therein). A single short-lasting episode of activity can explain the observed ages (Readhead et al. 1996) but there is no natural explanation of such a timescale. Therefore, a possible explanation is that the activity is intermittent and the source is reborn every few thousand years, without displaying any strong evidence of the previous activity phase, as discussed by several authors (e.g., Reynolds & Begelman 1997; Kaiser et al. 2000; Kunert-Bajraszewska et al. 2005, 2006; Jamrozy et al. 2007; Giroletti 2008). Detection of several candidates for dying compact sources supports this view (e.g., Giroletti et al. 2005; Kunert-Bajraszewska et al. 2006; Parma et al. 2007).

An accretion disk scenario is a likely explanation of the intermittent behavior on timescales much shorter than 10⁸ yr. Studies of accretion disks in other accreting objects show that cold accretion disks are subject to two types of instabilities: ionization instability, operating on longer timescales and responsible for dwarf nova and X-ray nova phenomenon (Osaki 1974; Meyer & Meyer-Hofmeister 1981; Smak 1982; see Lasota 2001 for a review), and radiation pressure instability, operating on shorter timescales and responsible for regular outbursts in GRS 1915+105 (Nayakshin et al. 2000; Janiuk et al. 2000, 2002; Merloni & Nayakshin 2006; see also Fender & Belloni 2004, and Done et al. 2004 for general reviews on this source). The ionization instability in the context of AGN was studied by a number of authors (Lin & Shields 1986; Clarke 1988; Mineshige & Shields 1990; Siemiginowska et al. 1996; Siemiginowska & Elvis 1997; Hatziminaoglou et al. 2001; Janiuk et al. 2004). The derived separations between outbursts were on order of 10⁶ yr for a 10⁸ M_☉ black hole, while the outburst duration was an order of magnitude shorter.

In this paper, we concentrate on the shorter timescale, radiation-pressure-driven instability operating above the threshold accretion rate $\dot{m}=0.025$ (in the Eddington units), and we test whether this mechanism is likely to be responsible for very short average ages of Compact Symmetric Objects (CSOs), a subgroup of GPSs. In Section 2, we present our sample of GPS sources. In Section 3, we present our model of the time evolution of the accretion disk under the radiation pressure instability, and in Section 4 we show the resulting intermittent activity patterns for a range of black hole mass, accretion rates, and viscosity coefficients. In Section 5, we discuss our results. Throughout this paper, we use the cosmological parameters based on the Wilkinson Microwave Anisotropy Probe (WMAP) measurements (Spergel et al. 2003): H₀=71 km s⁻¹ Mpc⁻¹, Ω_M = 0.27, and Ω_vac = 0.73.

GPS radio sources are compact and selected based on the convex shape of the radio spectrum that peaks at GHz frequencies (for a review see O'Dea 1998). They have a compact radio morphology with the radio emission contained within <1 kpc (O'Dea 1998) of the host galaxy center. Their radio morphologies on miliarcsec scales resemble the ones observed in large (≫10 kpc) radio galaxies with lobes, terminal hot spots and, in some cases, clear core-jet structures. Because of this similarity and the observed high radio power the GPS sources are thought to be the precursors of large radio galaxies observed at the early stage of their expansion (Fanti et al. 1995; O'Dea & Baum 1997; O'Dea 1998). However, as noted above, the number of these sources is too high to support a uniform self-consistent expansion from a compact to a large megaparsec scale radio source. In order to explain the observed overabundance of the compact sources, Reynolds & Begelman (1997) suggested an intermittent activity of radio-loud active galaxies, with the characteristic activity timescales of 10⁴–10⁵ yr based on the observed statistics (O'Dea & Baum 1997).

CSO comprise a subgroup of GPS sources that was introduced as a separate class over 10 yr ago (Wilkinson et al. 1994) on the basis of their "classical double" but extremely compact (lessthan500 pc) radio morphology. The small size of the radio structures was usually interpreted as an indication of the age below 10⁴ yr (Readhead et al. 1996; Owsianik & Conway 1998; Owsianik et al. 1998; Taylor et al. 2000; for an alternative suggestion of a frustrated jet see Carvalho 1994, 1998). The strong observational support for the source's young age comes from Very Long Baseline Interferometry (VLBI) monitoring observations and measured hot-spots propagation velocities ∼0.1–0.2c indicating the kinematic ages of ∼10³ yrs (Conway 2002; Polatidis & Conway 2003). It should be noted that there is no debate on the intrinsic compactness of CSOs, as opposed to many GPS objects displaying a clear core-jet morphology, since the latter ones may appear rather small due to the projection effects.

We compiled a sample of the GPS/CSO sources from the data available in the literature. In this sample, 10 sources with a measured age are from Polatidis & Conway (2003) and 14 sources come from the studies of the COINS sample by Gugliucci et al. (2005, 2007). The kinematic ages of these sources were determined on the basis of the measured hot-spot separation speed. 47 sources are taken from a much larger sample of GPS sources (including larger size, 1–10 kpc Compact Steep Spectrum (CSS)) that were studied by Murgia et al. (1999). Determination of their ages is based on the synchrotron cooling time that gives a rather high upper limit. These sources had a significant dispersion of the physical dimensions and derived ages. Note that Murgia et al. (1999) distinguished two classes of sources: the radio spectrum dominated by lobes (class "a") or jets and hot spots (class "b"). The sources within the class "a" have the morphology similar to the CSO sources and exhibit a correlation between the source age and the radio linear size. Three individual sources were taken from other publications (Orienti et al. 2007; Tschager et al. 2000).

The whole sample consists of 72 objects with a measured age, and the details are provided in Table 1. The majority of the age values are between 200 yr and 10⁴ yr, with three sources with the spectral ages considerably longer than 10⁵ yr. We plot the age distribution in Figure 1. The distribution looks strikingly bimodal but this may well be an artifact of the sample composition. Some age values (usually the shorter ones) are based on the kinematic determination and thus represent a lower limit to the source age, while the other age values (usually the longer ones) come from the synchrotron aging method and give an upper limit to the true age of the source (note that effects of radio source expansion, or deviation from the equipartition may result in the true age of a source to be shorter than its synchrotron age estimated for the fixed radiative cooling rate). A larger sample of sources with the ages determined with a single method is necessary to test if any bimodality is really present in the age distribution. On the other hand, we can be reasonably convinced that the ages of the sources in our sample capture the typical age values well.

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We estimated the monochromatic radio luminosities (νL_ν at 5 GHz) for all the sources in our sample (see Table 1) using the measured 5 GHz flux density available in the NASA/IPAC Extragalactic Database (NED)⁵ database. Figure 2 shows the radio luminosity distribution within the sample. These luminosities can be used to infer the bolometric luminosities of the underlying accretion disks. Note first that, assuming the ratio L_syn/L_5  GHz of the order of 1 and no relativistic beaming (Wilkinson et al. 1994), almost all the collected objects turn out to be characterized by relatively large intrinsic synchrotron powers in a range L_syn ∼ 10⁴³–10⁴⁶ erg s⁻¹. This, with the 10% radiative efficiency found/claimed in the evolutionary models for young radio sources (De Young 1993; Stawarz et al. 2008), implies the jet kinetic luminosities in the range L_j ∼ 10⁴⁴–10⁴⁷ erg s⁻¹, as required if GPS sources are indeed precursors of the extended FR I and FR II radio galaxies. Therefore, the estimated jet powers set lower limits on the accretion rates in the considered objects which, with the standard 10% radiative efficiency of the disk, would correspond to the accretion luminosities L_acc > L_5  GHz.

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On the other hand, if the observed radio flux is beamed, the intrinsic synchrotron power of the analyzed sources may be smaller than quoted above. However, relativistic beaming is not expected to play any role in the case of CSO objects (believed to be highly inclined), as well as GPS sources with radio fluxes dominated by lobes (class "a"). Only if the contribution of the inner jets (and possibly hot spots) to the observed radio emission is significant, could the assumed isotropy of the radio flux be questioned. And indeed the median 5 GHz luminosity of class "b" sources in our sample, 3 × 10⁴⁴ erg s⁻¹, is 1 order of magnitude larger than for the corresponding median for rest of the analyzed objects (see Table 1). Such a difference is also apparent in Figure 2, where in addition to the whole sample, radio luminosity distribution is plotted for the two different classes separately. Having said that, majority of the objects included in our sample are of the CSO type or class "a," and thus our averaged estimates presented in this section should be robust.

Meanwhile, five GPS/CSO sources studied with the XMM-Newton showed 2–10 keV luminosities comparable to νL_ν measured at 5 GHz (Vink et al. 2006). If the observed X-ray fluxes originate within the accretion flow/disk corona, as advocated by several authors (e.g., Guainazzi et al. 2006, and references therein), the bolometric disk luminosities are then expected to be larger than the observed X-ray ones by at least 1 order of magnitude (Koratkar & Blaes 1999; Elvis et al. 1994). We further note that the GPS/CSS sample of objects studied with Chandra revealed 2–10 keV fluxes by a factor of ∼5 higher (on average) than νL_ν at 5 GHz (Siemiginowska et al. 2008), although the constructed broadband spectral energy distributions also showed a large dispersion.⁶ Thus, the bolometric disk luminosities of GPS sources, including UV part, can easily be as large as ∼100 × L_5  GHz. The caution here is that the observed X-ray fluxes may be dominated by the inverse Compton emission generated within compact lobes rather than by the accretion flow (Stawarz et al. 2008). Assuming an order of magnitude correcting factor of 100, as a safe and conservative guess, implies the bolometric disk luminosities of the studied young radio sources L_acc ∼ 10⁴⁴–10⁴⁷ erg s⁻¹. If this correction term is much higher, some of the sources may slightly exceed the Eddington luminosity, but this may be indeed acceptable for the brightest ones (see, e.g., Collin et al. 2002).

Needless to say, the direct detection of the UV disk radiation in GPS/CSO objects is not possible, since the accretion-related emission at photon energies below 1 keV is known to be significantly obscured. Note in this context that measurements of the H i absorption in radio (Morganti et al. 2007; Pihlström et al. 2003) and the total absorption in X-rays (Guainazzi et al. 2006; Vink et al. 2006; Siemiginowska et al. 2008; Tengstrand et al. 2008) show significant hydrogen column densities (N_H ∼ 10²² cm⁻²) in all the studied GPS sources. In addition, the other independent estimates of the bolometric luminosities on the basis of the ionization power do not seem to work in young radio galaxies, as all the analyzed GPS objects are underluminous in [O iii] line, as if the narrow-line region (NLR) is still in the formation process (Vink et al. 2006), being in addition possibly modified by the interaction with the expanding radio lobes (Labiano 2008).

Only a few sources have the measurements of a black hole mass and we give them in Table 2. The mass estimates are based on properties of emission lines and the correlation established by the reverberation mapping (Vestergaard & Peterson 2006). These few measurements suggest that the black holes in the sources of our sample cover a mass range from M ∼ 10⁸ M_☉ to M ∼ 3 × 10⁹ M_☉, slightly higher than typical masses of radio sources in the Snellen et al. (2003) sample (∼10⁸ M_☉). Also, for a given black hole mass, the younger sources seem to have higher radio luminosities. However, based on this small number of sources we cannot formally assess any trends between the age and the radio luminosity. Unfortunately, without black hole mass measurements for majority of the studied objects, and with only roughly estimated bolometric disk luminosities, we cannot directly calculate the corresponding Eddington ratios. However, if we assume that the representative value of the black hole mass in our sample is the median from Table 2, i.e., M ∼ 3 × 10⁸ M_☉, and take the median monochromatic radio luminosity (for CSOs and class "a" sources only) from Table 1, namely L_5  GHz ∼ 3 × 10⁴³ erg s⁻¹, then with the anticipated correction factor of 100 one obtains the Eddington ratio on the order of $\dot{m} \sim 0.1$.

Table 2. GPS/CSO Sources with Given Black Hole Masses

Name	log M/M☉	log LEdda (erg s−1)	log SBb (erg s−1 Hz−1)	log LBc (erg s−1)	log Lbold (erg s−1)	$\dot{m}$e	K5  GHzf
0740+38	9.51	47.62	30.76	45.72	46.72	0.12	980
1250+56	8.31	46.42	29.85	44.74	45.74	0.21	470
0134+32	8.74	46.85	30.59	45.48	46.48	0.43	300
0518+16	8.53	46.64	30.88	45.82	46.82	1.49	290
0538+49	9.58	47.69	30.21	45.13	46.13	0.03	41
1458+71	8.98	47.09	30.89	45.84	46.84	0.56	150

Notes. ^aEddington luminosity. ^bB-band (4400 Å) flux from Netzer et al. (1996). ^cB-band (4400 Å) luminosity. ^dBolometric disk luminosity L_bol = 10 × L_B. ^eAccretion rate in the Eddington units. ^fBolometric correction to 5 GHz monochromatic luminosity.

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In addition to such average constraints, for those few sources with the available masses of black holes we can estimate more precisely the bolometric luminosities and the Eddington ratios, assuming the observed fluxes given by Netzer et al. (1996) and the template AGN spectrum given by Elvis et al. (1994). The resulting luminosities and accretion rate values are given in Table 2, and these agree with the rough average estimates given above. Note that, most importantly, the calculated accretion rates exceed the threshold for the radiation pressure instability ($\dot{m}=0.025$) for each analyzed source. The bolometric corrections to 5 GHz flux for those sources are also given in Table 2, and they range from 41 up to 980.

We model the time evolution of an accretion disk under the radiation pressure instability. We adopt the viscosity law using the geometrical mean between the gas and the total pressure for the scaling of the stress, i.e., T_rϕ ∝ α(P_gasP_tot)^1/2. As was shown by Merloni & Nayakshin (2006), such a viscosity law nicely reproduces the effective viscosity resulting from the magnetorotational instability, and describes well the behavior of the Galactic sources. This viscosity law is also favored for the black hole X-ray binaries (Done & Davis 2008).

We are using the time-dependent numerical code developed by ourselves and already presented in a number of works (Janiuk et al. 2002; Janiuk & Czerny 2005; Czerny et al. 2008). The initial conditions are determined by solving the energy balance, F_tot = Q⁺_visc = Q⁻_adv + Q⁻_rad, at every disk radius r. Here, the total energy flux F_tot dissipated within the disk at a radius r is calculated as

$$\begin{equation} F_{\rm tot} = {3 G M \dot{M} \over 8 \pi r^3} f(r), \end{equation} \tag{ 1 }$$

where the boundary condition is $f(r)=1-\sqrt{3\over r}$. The cooling and heating terms in this vertically integrated (over the scale H) energy balance are

$$\begin{equation} Q^{+}_{\rm visc} = \textstyle{3 \over 2}\alpha \Omega H \sqrt{P_{\rm gas}P_{\rm tot},} \end{equation} \tag{ 2 }$$

where α is the viscosity parameter,

$$\begin{equation} Q^{-}_{\rm rad}={ P_{\rm rad} c \over \tau }={ \sigma T^{4} \over \kappa \Sigma } \end{equation} \tag{ 3 }$$

and

$$\begin{equation} Q^{-}_{\rm adv}= {2 r P q_{\rm adv} \over 3 \rho GM} F_{\rm tot,} \end{equation} \tag{ 4 }$$

with q_adv ≈ const ∼ 1.0. The gas and radiation pressure are given by P_gas = k_B/m_pρT and P_rad = 4/3σT⁴, whereτ is the optical depth, Σ = ρH is the gas column density, c, k_B, and σ are physical constants, and we adopt the electron scattering opacity κ = 0.34 cm² g⁻¹. The hydrostatic balance equation gives ${P \over \rho } = \Omega ^{2} H^{2}$, and the Keplerian angular velocity Ω is assumed.

We solve the basic evolutionary equations in one-dimensional and compute the thermal and viscous evolution of the accretion disk:

$$\begin{equation} {\partial \Sigma \over \partial t}={1 \over r}{\partial \over \partial r}\left(3 r^{1/2} {\partial \over \partial r}(r^{1/2} \nu \Sigma)\right) \end{equation} \tag{ 5 }$$

and

$$\begin{eqnarray} {\partial T \over \partial t} + v_{\rm r}{\partial T \over \partial r} &=& {T \over \Sigma }{4-3\beta \over 12-10.5\beta } \left({\partial \Sigma \over \partial t}+ v_{\rm r}{\partial \Sigma \over \partial r}\right) \nonumber\\ &&+\,{T\over P H}{1\over 12-10.5\beta } (Q^{+}-Q^{-}). \end{eqnarray} \tag{ 6 }$$

Here

$$\begin{equation} v_{\rm r} = {3 \over \Sigma r^{1/2}} {\partial \over \partial r} (\nu \Sigma r^{1/2}) \end{equation} \tag{ 7 }$$

is the radial velocity in the disk while $\nu =(2 \sqrt{P_{\rm gas}P_{\rm tot}}\alpha)/(3\rho \Omega)$ is the kinematic viscosity and β is the ratio of the gas pressure to the total pressure, β = P_gas/P.

The code also incorporates the option of a two-phase accretion, with the mass exchange between the disk and a hot corona, which allows us for performing quasi-two-dimensional computations. It can also include the effect of the jet formation in parametric description. However, in the present work, we concentrate only on the evolution of the disk, so the corona and jet are neglected in order to keep the picture as simple as possible. The models are thus parameterized by the black hole mass, M, dimensionless accretion rate, $\dot{m}$, measured in the Eddington units ($\dot{M}_{\rm Edd} = 3.53\,(M/10^8\;M_{\odot })\,M_{\odot }$ yr⁻¹) and the viscosity parameter α.

The time evolution of an accretion disk under the radiation pressure instability is rather fast, in contrast with expectations based on the partial ionization instability. The exemplary light curves representing the evolution of the disk bolometric luminosity for a black hole of mass M = 10⁸ M_☉ are shown in Figure 3. We performed computations for a range of black hole masses likely to be appropriate for GPS sources (M = 10⁷–3 × 10⁹ M_☉). The expected durations of outbursts are shown in Figures 4 and 5 for the value of the viscosity parameter α equal to0.2 and 0.02, correspondingly. The duration of an outburst depends almost linearly on the black hole mass, and strongly varies with the accretion rate. For sources close to the Eddington limit, expected outbursts last 10⁴–10⁵ yr for the smaller value of the viscosity parameter (0.02) and about 10 times shorter for the larger viscosity (0.2). Still shorter outbursts are expected for sub-Eddington rates.

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The overall range of the observed source ages (200–3 × 10⁵ yr) is roughly consistent with the expected outburst duration for the value of viscosity parameter α = 0.02. The larger viscosity parameter (α = 0.2) requires super-Eddington accretion rates to explain the duration of the oldest sources (greaterthan10⁵ yr). Since we do not have the exact black hole mass determinations for the sources in our sample (Table 1) we cannot directly locate them on the the contour maps shown in Figures 4 and 5. However, the lines of a constant time duration of an outburst are almost parallel to the lines of a constant bolometric luminosity for a source with an unknown black hole mass. Therefore, for a given estimate of the source bolometric luminosity we predict almost uniquely the duration of the outburst. If in addition we relate the bolometric luminosity with the 5 GHz monochromatic luminosity through a bolometric correction K_5  GHz, we obtain a relation

$$\begin{eqnarray} \log \left({T_{\rm burst} \over {\rm yr}}\right) \!\!\!\!&\approx&\!\!\!\! 1.25 \, \log \left({\nu L_{\nu } (5\;{\rm GHz}) \over {\rm erg\;s^{-1}}}\right)+\, 0.38 \, \log \left({\alpha \over 0.02}\right)\nonumber\\ &&\!\!\!\!+1.25 \log K_{5\,\,{\rm GHz}}- 53.6. \end{eqnarray} \tag{ 8 }$$

The real age of the source cannot violate this limit, i.e., should be shorter, and on average should correspond to half of the outburst duration with some dispersion around this value.

In Figure 6, we plot the lines corresponding to Equation (8) with α = 0.02 and the anticipated bolometric correction factor 300 (see Section 2). On average, most of the sources are located to the left of the line, as expected if the age of the radio structure directly reflects the age of the central engine. However, there are several outliers. Most of them are relatively old, having their ages determined from the synchrotron method (e.g., 1233+418). This method gives an upper limit to the age, and thus the lifetimes of these, being about ∼10⁵ yr, may be considerably overestimated. However, four sources with kinematically measured age also show considerable departure to the right from the line. The distance from the predicted line is the largest for 0035+227. Its radio spectrum is steep (e.g., Anton et al. 2004). Perhaps the luminosity of the source is already dropping down due to aging and therefore our standard relation between the accretion rate in the model and the observed luminosity does not apply.

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Also, the sources should not be observed in the range where instability does not operate. The exact boundary of the unstable region is complicated and depends on the accretion rate. We can say that the instability operates if $\dot{m} > 0.025$, approximately. None of the sources in our sample with a measured mass violate this limit. As argued in Section 2, we expect that this criterion is also fulfilled on average, at least for the majority of the GPS population.

In Figures 7 and 8, we give the outburst separations for lower and higher values of the viscosity coefficient, respectively. As the figure shows, the separation between the outbursts is a complex nonmonotonic function of the accretion rate. For high-accretion rates, the outburst separation decreases with the accretion rate and increases with the black hole mass. This trend is seen in Figures 7 and 8 as the upper branches of the constant time separation lines. This part of the plot is similar to the plots of the outburst duration (Figures 4 and 5), with the outburst separation being typically by a factor of 10 higher. The typical timescales are then consistent with the ones postulated by Reynolds & Begelman (1997). These timescales give the limits for statistical studies of the galactic activity, and we devote a part of the Discussion to this issue (see Section 5.3).

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However, when the accretion rate approaches the value for which the instability ceases to exist, the trend with the accretion rate is reversed and the time separation goes to infinity. The limiting value of the accretion rate is specific for the given black hole mass. This is seen as the lower branches of the constant separation time lines. The parameter range (accretion rate and black hole mass) where this happens is relatively narrow. At still lower accretion rates, for a given mass, the disk is stable and there are no outbursts. Such a source should evolve in a continuous rather than intermittent way.

We study the possibility that the observed short lifetimes of (some of) GPS sources reflect the intermittent activity of the nucleus caused by the radiation pressure instability in the accretion disk. We model the disk outbursts using T_rϕ ∝ α(P_gasP_tot)^1/2 viscosity law, as previously done by Merloni & Nayakshin (2006) in the context of Galactic sources. This parametric approach seems to be quite successful. For the smaller of the two values of the considered viscosity parameter (α = 0.02), supported by the previous studies of the AGN variability (Siemiginowska & Czerny 1989; Starling et al. 2004), the theoretically obtained outburst durations for a range of black hole masses and accretion rates are comparable to the ages of the radio structures determined for our sample of 72 GPS/CSO objects. Therefore, the radiation pressure instability mechanism offers an interesting possibility for the intermittency of young radio sources, as postulated by Reynolds & Begelman (1997) to explain the apparent overabundance of such. The time separations between outbursts obtained from our model are also comparable to those requested by Reynolds & Begelman. However, our approach leaves several open questions/problems which should be addressed in the future in order to establish the theoretical basis for the intermittent character of jet activity. We discuss these problems below.

5.1. Radiation Pressure Instability

5.2. High- and Low-Luminosity States of Accretion Disk

5.3. Source Evolution between the Outbursts

5.4. Future Applications

We thank Marek Sikora and Brandon Kelly for very helpful discussions. We also thank the anonymous referee for comments. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

This work was supported in part by grant 1P03D00829 of the Polish State Committee for Scientific Research and the Polish Astroparticle Network 621/E-78/BWSN-0068/2008. This research is funded in part by NASA contract NAS8-39073. Partial support for this work was provided by the Chandra grants GO2-3148A, GO5-6113X, and GO8-9125A-R.