Mass Models of Dwarf Spheroidal Galaxies with Variable Stellar
  Anisotropy. I. Jeans Analysis
  Using a flexible galactic model with variable stellar velocity anisotropy, I
apply the classical Jeans mass modeling approach to the five dwarf spheroidal
galaxies with the largest homogeneous datasets of stellar line-of-sight
velocities (between 330 and 2500 stars per galaxy) -- Carina, Fornax, Leo~I,
Sculptor, and Sextans. I carry out an exhaustive model parameter search,
assigning absolute probabilities to each parameter combination. My main finding
is that there is a well defined radius (unique for each galaxy) where the Jeans
analysis constraints on the enclosed mass are tightest, and are much better
than the constraints at previously suggested radii (e.g. 300~pc). For Carina,
Fornax, Leo~I, Sculptor, and Sextans the enclosed DM mass is $0.94 \pm 0.20$
(at 410~pc), $7.1 \pm 0.9$ (at 925~pc), $1.75 \pm 0.20$ (at 390~pc), $2.59 \pm
0.42$ (at 435~pc), and $2.3 \pm 0.9$ (at 1035~pc), respectively (two-sigma
uncertainties; in $10^7$~M$_\odot$ units). Local DM density has the tightest
constraints at smaller (and also unique for each galaxy) radii. The largest
central DM density constraint is for Sculptor: $\rho_0\gtrsim
0.09$~$M_\odot$~pc$^{-3}$ (at two-sigma level). I show that the DM density
logarithmic slope is totally unconstrained by the Jeans analysis at all the
radii probed by the data (and not just at the center, as was demonstrated
before). Stellar velocity anisotropy has only very weak constraints. In
particular, pure central tangential anisotropy is ruled out at better than two
sigma level for three dwarfs, and the data are consistent with the global
stellar velocity isotropy for all the five galaxies.
