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Register a new userConstraining Dynamical Dark Energy Models through the Abundance of High-Redshift Supermassive Black Holes
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Alessandra Lamastra
Publication date
2011
fields
Physics
and research's language is
English
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We compute the number density of massive Black Holes (BHs) at the centre of galaxies at z=6 in different Dynamical Dark Energy (DDE) cosmologies, and compare it with existing observational lower limits, to derive constraints on the evolution of the Dark Energy equation of state parameter w. Our approach only assumes the canonical scenario for structure formation from the collapse of overdense regions of the Dark Matter dominated primordial density field on progressively larger scales; the Black Hole accretion and merging rate have been maximized in the computation so as to obtain robust constraints on w and on its look-back time derivative w_a. Our results provide independent constraints complementary to those obtained by combining Supernovae, Cosmic Microwave Background and Baryonic Acoustic Oscillations; while the latter concern combinations of w_0 and w_a leaving the time evolution of the state parameter w_a highly unconstrained, the BH abundance mainly provide upper limits on w_a, only weakly depending on w_0. Combined with the existing constraints, our results significantly restrict the allowed region in DDE parameter space, ruling out DDE models not providing cosmic time and fast growth factor large enough to allow for the building up of the observed abundance of BHs; in particular, models with -1.2 leq w_0 leq -1 and positive redshift evolution w_a > 0.8 - completely consistent with previous constraints - are strongly disfavoured by our independent constraints from BH abundance. Such range of parameters corresponds to Quintom DDE models, with w crossing -1 starting from larger values.
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The population of supermassive black holes (SMBHs) is composed by quiescent SMBHs, such as those seen in local galaxies including the Milky Ways, and active ones, resulting in quasars and active galactic nuclei (AGN). Outside our neighbourhood, all the information we have on SMBHs is derived from quasars and AGN, giving us a partial view. We study the evolution of the SMBH population, total and active, by the continuity equation, backwards in time from z=0 to z=4. Type-1 and type-2 AGN are differentiated in the model on the basis of the Eddington ratio distribution, chosen on the basis of observational estimates. The duty cycle is obtained by matching the luminosity function of quasars, and the average radiative efficiency is the only free parameter in the model. For higher radiative efficiencies (>~0.07) a large fraction of the SMBH population, most of them quiescent, must already be in place by z=4. For lower radiative efficiencies (~0.05), the duty cycle increases with the redshift and the SMBH population evolves dramatically since z=4. The mass function of active SMBHs does not depend on the choice of the radiative efficiency or of the local SMBH mass function, but it is mainly determined by the quasar luminosity function, once the Eddington ratio distribution is fixed. Only a direct measurement of the total BHMF at redshifts z>~2 could break these degeneracies giving important constraints on the average radiative efficiency. Focusing on type-1 AGN, for which observational estimates of the mass function and Eddington ratio distribution exist at various redshift, models with lower radiative efficiencies reproduce better the high-mass end of the mass function at high-z, but they tend to over-predict it at low-z, and vice-versa for models with higher radiative efficiencies.
We compare the maximal abundance of massive systems predicted in different dynamical dark energy (DDE) models at high redshifts z = 4-7 with the measured abundance of the most massive galaxies observed to be already in place at such redshifts. The aim is to derive constraints for the evolution of the dark energy equation of state parameter w which are complementary to existing probes. We adopt the standard parametrization for the DDE evolution in terms of the local value w_0 and of the look-back time derivative w_a of the equation of state. We derive constraints on combinations (w_0, w_a) in the different DDE models by using three different, independent probes: (i) the observed stellar mass function of massive objects at z = 6 derived from the CANDELS survey; (ii) the estimated volume density of massive halos derived from the observation of massive, star-forming galaxies detected in the submillimeter range at z = 4; (iii) The rareness of he most massive system (estimated gas mass exceeding 3 10^11 M_sun) observed to be in place at z = 7, a far-infrared-luminous object recently detected in the South Pole Telescope (SPT) survey. Finally, we show that the combination of our results from the three above probes excludes a sizable fraction of the DDE parameter space w_a > -3/4 - (w_0 + 3/2) presently allowed (or even favored) by existing probes.
The energy and momentum deposited by the radiation from accretion onto the supermassive black holes (BHs) that reside at the centres of virtually all galaxies can halt or even reverse gas inflow, providing a natural mechanism for supermassive BHs to regulate their growth and to couple their properties to those of their host galaxies. However, it remains unclear whether this self-regulation occurs on the scale at which the BH is gravitationally dominant, on that of the stellar bulge, the galaxy, or that of the entire dark matter halo. To answer this question, we use self-consistent simulations of the co-evolution of the BH and galaxy populations that reproduce the observed correlations between the masses of the BHs and the properties of their host galaxies. We first confirm unambiguously that the BHs regulate their growth: the amount of energy that the BHs inject into their surroundings remains unchanged when the fraction of the accreted rest mass energy that is injected, is varied by four orders of magnitude. The BHs simply adjust their masses so as to inject the same amount of energy. We then use simulations with artificially reduced star formation rates to demonstrate explicitly that BH mass is not set by the stellar mass. Instead, we find that it is determined by the mass of the dark matter halo with a secondary dependence on the halo concentration, of the form that would be expected if the halo binding energy were the fundamental property that controls the mass of the BH. We predict that the logarithmic slope of the relation between dark matter halo mass and black hole mass is 1.55+/-0.05 and that the scatter around the mean relation in part reflects the scatter in the halo concentration-mass relation.
We exploit the recent, wide samples of far-infrared (FIR) selected galaxies followed-up in X rays and of X-ray/optically selected active galactic nuclei (AGNs) followed-up in the FIR band, along with the classic data on AGN and stellar luminosity functions at high redshift z>1.5, to probe different stages in the coevolution of supermassive black holes (BHs) and host galaxies. The results of our analysis indicate the following scenario: (i) the star formation in the host galaxy proceeds within a heavily dust-enshrouded medium at an almost constant rate over a timescale ~0.5-1 Gyr, and then abruptly declines due to quasar feedback; over the same timescale, (ii) part of the interstellar medium loses angular momentum, reaches the circum-nuclear regions at a rate proportional to the star formation and is temporarily stored into a massive reservoir/proto-torus wherefrom it can be promptly accreted; (iii) the BH grows by accretion in a self-regulated regime with radiative power that can slightly exceed the Eddington limit L/L_Edd< 4, particularly at the highest redshifts; (iv) for massive BHs the ensuing energy feedback at its maximum exceeds the stellar one and removes the interstellar gas, thus stopping the star formation and the fueling of the reservoir; (v) afterwards, if the latter has retained enough gas, a phase of supply-limited accretion follows exponentially declining with a timescale of about 2 e-folding times. We show that the ratio of the FIR luminosity of the host galaxy to the bolometric luminosity of the AGN maps the various stages of the above sequence. Finally, we discuss how the detailed properties and the specific evolution of the reservoir can be investigated via coordinated, high-resolution observations of starforming, strongly-lensed galaxies in the (sub-)mm band with ALMA and in the X-ray band with Chandra and the next generation X-ray instruments.
For a general dark-energy equation of state, we estimate the maximum possible radius of massive structures that are not destabilized by the acceleration of the cosmological expansion. A comparison with known stable structures constrains the equation of state. The robustness of the constraint can be enhanced through the accumulation of additional astrophysical data and a better understanding of the dynamics of bound cosmic structures.
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