Genesis and evolution of dust in galaxies in the early Universe II. Rapid dust evolution in quasars at z ≳ 6

Aims. We intend to assess the most plausible scenarios for generating large amounts of dust in high-z quasars (QSOs) on the basis of observationally derived physical properties of QSOs at z greater than or similar to 6. Methods. We use a chemical evolution model to compute the temporal progression of quantities such as the amount of dust and gas, stellar masses, star formation rates (SFRs) and the metallicity for various combinations of the initial mass function (IMF), the mass of the galaxy, dust production efficiencies, and the degree of dust destruction in the ISM. We investigate the influence of the SFR on the evolution of these quantities, and determine the earliest epochs at which agreement with observations can be achieved. We apply the obtained results to individual QSOs at z greater than or similar to 6. Results. We find that large quantities of dust can be generated rapidly as early as 30 Myr after the onset of the starburst when the SFR of the starburst is greater than or similar to 10(3) M-circle dot yr(-1). The amount of dust and several other physical quantities of individual QSOs at z greater than or similar to 6 are satisfactorily reproduced by models at epochs 30, 70, 100, and 170 Myr for galaxies with initial gas masses of 1-3 x 10(11) M-circle dot. The best agreement with observations is obtained with top-heavy IMFs. A sizable dust contribution from supernovae (SNe) is however required, while at these epochs dust production by asymptotic giant branch (AGB) stars is negligible. Moderate dust destruction in the ISM can be accommodated.