THE CENTERS OF EARLY-TYPE GALAXIES WITH HST .4. CENTRAL PARAMETER RELATIONS

We analyze Hubble Space Telescope surface-brightness profiles of 61 el liptical galaxies and spiral bulges (hereafter ''hot'' galaxies). The profiles are parameterized by break radius r(b) and break surface brig htness I-b. These are combined with central velocity dispersions, tota l luminosities, rotation velocities, and isophote shapes to explore co rrelations among central and global properties. Luminous hot galaxies (M-V< -22) have cuspy cores with steep outer power-law profiles that b reak at r approximate to r(b) to shallow inner profiles I proportional to r(-gamma) with gamma less than or equal to 0.3. Break radii and co re luminosities for these objects are approximately proportional to ef fective radii and total luminosities. Scaling relations are presented for several core parameters as a function of total luminosity. Cores f ollow a fundamental plane that parallels the global fundamental plane for hot galaxies but is 30% thicker. Some of this extra thickness may be due to the effect of massive black holes (BHs) on central velocity dispersions. Faint hot galaxies (M-V> -20.5) show steep, largely featu reless power-law profiles that lack cores. Measured values of r(b) and I-b for these galaxies are limits only. At a limiting radius of 10 pc , the centers of power-law galaxies are up to 1000 times denser in mas s and luminosity than the cores of large galaxies. At intermediate mag nitudes (-22<M-V< -20.5), core and power-law galaxies coexist, and the re is a range in rb at a given luminosity of at least two orders of ma gnitude. Here, central properties correlate strongly with global rotat ion and shape: core galaxies tend to be boxy and slowly rotating, wher eas power-law galaxies tend to be disky and rapidly rotating. A search for inner disks was conducted to test a claim in the literature, base d on a smaller sample, that power laws originate from edge-on stellar disks. We find only limited evidence for such disks and believe that t he difference between core and power-law profiles reflects a real diff erence in the spatial distribution of the luminous spheroidal componen t of the galaxy. The dense power-law centers of disky, rotating galaxi es are consistent with their formation in gas-rich mergers. The parall el proposition, that cores are the by-products of gas-free stellar mer gers, is less compelling for at least two reasons: (1) dissipationless hierarchical clustering does not appear to produce core profiles like those seen; (2) core galaxies accrete small, dense, gas-free galaxies at a rate sufficient to fill in their low-density cores if the satell ites survived and sank to the center (whether the satellites survive i s still an open question). An alternative model for core formation inv olves the orbital decay of massive BHs that are accreted in mergers: t he decaying BHs may heat and eject stars from the center, eroding a po wer law if any exists and scouring out a core. An average BH mass per spheroid of 0.002 times the stellar mass yields cores in fair agreemen t with observed cores and is consistent with the energetics of AGNs an d the kinematic detection of BHs in nearby galaxies. An unresolved iss ue is why power-law galaxies also do not have cores if this process op erates in all hot galaxies. (C) 1997 American Astronomical Society.