Viscous time lags between starburst and AGN activity

Abstract There is strong observational evidence indicating a time lag of order of some 100 Myr between the onset of starburst and AGN activity in galaxies. Dynamical time lags have been invoked to explain this. We extend this approach by introducing a viscous time lag the gas additionally needs to flow through the AGN's accretion disc before it reaches the central black hole. Our calculations reproduce the observed time lags and are in accordance with the observed correlation between black hole mass and stellar velocity dispersion. galaxies: active, galaxies: formation, galaxies: interactions, galaxies: nuclei, quasars: general, galaxies: starburst 1 INTRODUCTION Motivated by, for instance, observed correlations between the mass of an AGN's central black hole and the host galaxy's velocity dispersion (e.g. Gebhardt et al. 2000) and between black hole mass and bulge mass (e.g. Kormendy & Richstone 1995), there is an ongoing debate whether, and if so, how starbursts and AGN are connected to each other. Di Matteo, Springel & Hernquist (2005), for instance, explain such correlations as due to a thermal AGN feedback that heats the gas of the galaxy and thus prevents further star formation and AGN activity: more massive galaxies have a deeper gravitational potential well, thus the black hole has to gain more mass before its luminosity is capable of expelling the gas from the galaxy and quenching star formation and AGN activity. This then leads to the velocity dispersion and the bulge mass, respectively, to be related to the black hole mass. In these simulations starburst and AGN activity occur simultaneously, but recent observations show that AGN activity may be delayed with regard to star formation activity by time-scales of 50–250 Myr (e.g. Davies et al. 2007; Schawinski et al. 2009; Wild, Heckman & Charlot 2010). Hopkins (2012) argues that such a time lag can occur for purely dynamical reasons. His high spatial resolution simulations of galaxy mergers show first an inward motion of gas towards the dynamical centre giving rise to (a burst of) star formation. In these models, the gas flowing further inwards can do so only by losing angular momentum by gravitational instabilities. This, in turn, gives rise to a time lag between star formation and AGN activity. We extend this idea by modelling the loss of angular momentum and the ensuing inflow in the framework of an accretion disc scenario. Thus the time lag between starburst and AGN activity consists of a dynamical lag given by the time span the gas needs to reach the accretion disc and a subsequent viscous lag given by the time span the gas needs to flow through the accretion disc until it reaches the black hole. In Section 2 we explain our numerical methods and the setup of the merger event that is, in this scenario, responsible for the inflow of gas to the newly forming galactic centre. In Section 3 we present and discuss the general picture that results from our calculations. As our model depends on a number of parameters, we perform a parameter study in Section 4 to show the robustness of our results against parameter changes. In Section 5 we summarize our findings. 2 NUMERICAL METHODS We simulate galaxy collisions using the TreeSPH code gadget-2 (Springel 2005). Radiative cooling of an optically thin primordial gas in ionization equilibrium is taken into account following Katz, Weinberg & Hernquist (1996). Additionally we include star formation, AGN evolution and AGN feedback as described in the following subsections. 2.1 Star formation Following Scannapieco et al. (2005) a gas particle is considered for star formation if its density ρ exceeds a critical density ρcrit and it is in a converging flow (div v < 0). Then a star particle is created with a probability \begin{equation} p = \frac{m}{m_{{\ast }}} \left[ 1 - \exp \left( - \frac{c_{{\rm eff}} \Delta t}{t_{{\rm g}}} \right)\right] \end{equation} (1) (see Springel & Hernquist 2003) where m is the gas particle's mass, m* = m0/Ng the mass of the star to be formed, m0 the initial gas particle mass, Ng the number of stars that can be formed from one gas particle, ceff the star forming efficiency, Δt the respective time step of the code and |$t_{{\rm g}}=\sqrt{3 {\rm \pi } / 32\,G \rho }$| the free-fall time of the gas particle. If m < 1.5 × m*, condition (1) is dropped and the gas particle is directly converted into a star particle. Gas particles can only reduce their mass due to star formation. In our simulations star particles are collisionless particles and interact with other particles only via gravitational forces. For the star forming efficiency we use a value of ceff = 0.1 following Katz (1992). The parameter Ng determines the numerical resolution of the star formation rate (SFR), like Scannapieco et al. (2005) we use a value of Ng = 2. We furthermore set ρcrit = 4.5 × 108 M⊙ kpc−3. With these parameters the simulation of an isolated galaxy characterized by the parameters given in Table 1 gives an average SFR of 0.26 M⊙ yr−1. This value fits well with the SFR that is expected in such a galaxy: according to Kennicutt (1998) the SFR of an isolated galaxy can be estimated as \begin{equation} \dot{M}_{{\rm SFR}} = 0.017 \frac{M_{{\rm gas}}}{\tau _{{\rm dyn}}} \end{equation} (2) with the total gas mass Mgas and the dynamical time-scale at the half gas-mass radius τdyn. According to this equation an isolated galaxy characterized by the parameters given in Table 1 has a SFR of 0.3 M⊙ yr−1. Table 1. Parameters of our reference model, a galaxy with these parameters has a scale radius of 3.8 kpc. Virial velocityv200160 km s−1Mass fraction of the discmd0.041Mass fraction of the bulgemb0.0137Mass fraction of the gasfg0.3Scale height of the discafd0.2Scale radius of the bulgeafb0.1Halo concentrationchalo15Spin parameter of the haloλ0.05Angular momentum fraction of the discjd0.041 Virial velocityv200160 km s−1Mass fraction of the discmd0.041Mass fraction of the bulgemb0.0137Mass fraction of the gasfg0.3Scale height of the discafd0.2Scale radius of the bulgeafb0.1Halo concentrationchalo15Spin parameter of the haloλ0.05Angular momentum fraction of the discjd0.041 aIn fractions of the disc's scale radius. Open in new tab Table 1. Parameters of our reference model, a galaxy with these parameters has a scale radius of 3.8 kpc. Virial velocityv200160 km s−1Mass fraction of the discmd0.041Mass fraction of the bulgemb0.0137Mass fraction of the gasfg0.3Scale height of the discafd0.2Scale radius of the bulgeafb0.1Halo concentrationchalo15Spin parameter of the haloλ0.05Angular momentum fraction of the discjd0.041 Virial velocityv200160 km s−1Mass fraction of the discmd0.041Mass fraction of the bulgemb0.0137Mass fraction of the gasfg0.3Scale height of the discafd0.2Scale radius of the bulgeafb0.1Halo concentrationchalo15Spin parameter of the haloλ0.05Angular momentum fraction of the discjd0.041 aIn fractions of the disc's s (...truncated)