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In the early Universe, while galaxies were still forming, black holes as massive as a billion solar masses powered quasars. Supermassive black holes are found at the centers of most galaxies today, where their masses are related to the velocity dispersions of stars in their host galaxies and hence to the mass of the central bulge of the galaxy. This suggests a link between the growth of the black holes and the host galaxies, which has indeed been assumed for a number of years. But the origin of the observed relation between black hole mass and stellar velocity dispersion, and its connection with the evolution of galaxies have remained unclear. Here we report simulations that simultaneously follow star formation and the growth of black holes during galaxy-galaxy collisions. We find that in addition to generating a burst of star formation, a merger leads to strong inflows that feed gas to the supermassive black hole and thereby power the quasar. The energy released by the quasar expels enough gas to quench both star formation and further black hole growth. This determines the lifetime of the quasar phase (approaching 100 million years) and explains the relationship between the black hole mass and the stellar velocity dispersion.

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Geographic constraints systematically limit the horizontal expansion of urban areas but promote denser, taller urban development worldwide, according to an analysis that uses urban and climate data, geographic and growth urban metrics, and a statistical approach

We present calculations of the early stages of the formation of Jupiter via core nucleated accretion and gas capture. The core begins as a seed body of about 350 kilometers in radius and orbits in a swarm of planetesimals whose initial radii range from 15 meters to 50 kilometers. The evolution of the swarm accounts for growth and fragmentation, viscous and gravitational stirring, and for drag-assisted migration and velocity damping. During this evolution, less than 9% of the mass is in planetesimals smaller than 1 kilometer in radius; < ~25% is in planetesimals with radii between 1 and 10 kilometers; and < ~7% is in bodies with radii larger than 100 kilometers. Gas capture by the core substantially enhances the size-dependent cross-section of the planet for accretion of planetesimals. The calculation of dust opacity in the planet's envelope accounts for coagulation and sedimentation of dust particles released as planetesimals are ablated. The calculation is carried out at an orbital semi-major axis of 5.2 AU and the initial solids' surface density is 10 g/cm^2 at that distance. The results give a core mass of nearly 7.3 Earth masses (Mearth) and an envelope mass of approximately 0.15 Mearth after about 4e5 years, at which point the envelope growth rate surpasses that of the core. The same calculation without the envelope yields a core of only about 4.4 Mearth.

[Abridged] We model the growth of Jupiter via core nucleated accretion, applying constraints from hydrodynamical processes that result from the disk-planet interaction. We compute the planet's internal structure using a Henyey-type stellar evolution code. The planet's interactions with the protoplanetary disk are calculated using 3-D hydrodynamic simulations. Previous models of Jupiter's growth have taken the radius of the planet to be approximately one Hill sphere radius, Rhill. However, 3-D hydrodynamic simulations show that only gas within 0.25Rhill remains bound to the planet, with the more distant gas eventually participating in the shear flow of the protoplanetary disk. Therefore in our new simulations, the planet's outer boundary is placed at the location where gas has the thermal energy to reach the portion of the flow not bound to the planet. We find that the smaller radius increases the time required for planetary growth by ~5%. Thermal pressure limits the rate at which a planet less than a few dozen times as massive as Earth can accumulate gas from the protoplanetary disk, whereas hydrodynamics regulates the growth rate for more massive planets. Within a moderately viscous disk, the accretion rate peaks when the planet's mass is about equal to the mass of Saturn. In a less viscous disk hydrodynamical limits to accretion are smaller, and the accretion rate peaks at lower mass. To account for disk dissipation, we perform some of our simulations of Jupiter's growth within a disk whose surface gas density decreases on a timescale of 3Myr. According to our simulations, proto-Jupiter's distended and thermally-supported envelope was too small to capture the planet's current retinue of irregular satellites as advocated by Pollack et al. (1979).

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