  In this paper we analyze the diffuse X-ray coronae surrounding the elliptical
galaxy NGC5846, combining measurements from two observatories, ROSAT and ASCA.
We map the gas temperature distribution and find a central cool region within
an approximately isothermal gas halo extending to a radius of about 50 kpc, and
evidence for a temperature decrease at larger radii. With a radially falling
temperature profile, the total mass converges to 9.6+/-1.0 10^12 Msun at ~230
kpc radius. Using the spectroscopic measurements, we also derive radial
distributions for the heavy elements silicon and iron and find that the
abundances of both decrease with galaxy radius. The mass ratio of Si to Fe lies
between the theoretical predictions for element production in SN Ia and SN II,
suggesting an important role for SN Ia, as well as SN II, for gas enrichment in
ellipticals. Using the SN Ia yield of Si, we set an upper limit of 0.012 SNU
for the SN Ia rate at radii >50 kpc, which is independent of possible
uncertainties in the iron L-shell modeling. We compare our observations with
the theoretical predictions for the chemical evolution of ellipticals, taken
from Matteucci & Gibson (1995). We conclude that the metal content in stars, if
explained by the star formation duration, requires a significant decline in the
duration of star formation with galaxy radius, ranging from ~1 Gyr at the
center to ~0.01 Gyr at 100 kpc radius. Alternatively, the decline in
metallicity with galaxy radius may be caused by a similar drop with radius in
the efficiency of star formation. Based on the Si and Fe measurements presented
in this paper, we conclude that the latter scenario is preferred, unless a
dependence of the SN Ia rate on stellar metallicity is invoked. (Abridged).
