A STRINGENT CONSTRAINT ON ALTERNATIVES TO A MASSIVE BLACK-HOLE AT THECENTER OF NGC-4258

There is now dynamical evidence for massive dark objects at the center of several galaxies, but suggestions that these are supermassive blac k holes are based only on indirect astrophysical arguments. As emphasi zed by Kormendy and Richstone, large M/L ratios and gas motions of ord er approximate to 10(3) km s(-1) do not uniquely imply a massive black hole (BH), and it is possible that the central dark objects in these galaxies are massive clusters of stellar remnants, brown dwarfs, low-m ass stars, or halo dark matter. The recent unprecedented measurement o f the rotation curve of maser emission sources at the center of NGC 42 58, and the remarkable discovery that it is Keplerian to high precisio n, provide us with a unique opportunity for testing alternatives to a BH. We use a conservative upper limit on the systematic deviation from a Keplerian rotation curve to constrain the mass distribution at the galaxy center. Based on evaporation and physical collision timescale a rguments, we show that a central cluster is firmly ruled out, unless t he cluster consists of extremely dense objects with mass less than or similar to 0.03 M. (e.g., low-mass BHs or elementary particles). Since both of these dynamically allowed systems are very improbable for oth er astrophysical reasons, we conclude that a central dense cluster at the center of NGC 4258 is very improbable, thus leaving the alternativ e possibility of a massive BH. We also show that the mass of the BH mu st be greater than or similar to 98% of the mass enclosed within the i nner edge of the masering disk (3.6 x 10(7) M.). A substantial contrib ution to that mass from a density cusp in the background mass distribu tion is excluded.