Make sure that KingPotential = -GM/r outside of the tidal radius by i…

…ncluding offset and solving the relevant ODE more accurately (also making sure that the King mass is consistent)

galpy/df/kingdf.py

@@ -138,7 +138,7 @@ def solve(self, npt=1001):
             ],
             [0.0, rbreak],
             [self.W0, 0.0],
-            method="LSODA",
+            method="DOP853",
             t_eval=r[: npt // 2],
         )
         W[: npt // 2] = sol.y[0]
@@ -155,7 +155,7 @@ def solve(self, npt=1001):
             ],
             [sol.y[0, -1], 0.0],
             [rbreak, sol.y[1, -1]],
-            method="LSODA",
+            method="DOP853",
             t_eval=W[npt // 2 - 1 :],
         )
         r[npt // 2 - 1 :] = sol.y[0]
@@ -171,18 +171,7 @@ def solve(self, npt=1001):
         # Interpolate solution
         self._W_from_r = interpolate.InterpolatedUnivariateSpline(self._r, self._W, k=3)
         # Compute the cumulative mass and store the total mass
-        mass_shells = numpy.array(
-            [
-                integrate.quad(lambda r: _FOURPI * r**2 * self.dens(r), rlo, rhi)[0]
-                for rlo, rhi in zip(r[:-1], r[1:])
-            ]
-        )
-        self._cumul_mass = numpy.hstack(
-            (
-                integrate.quad(lambda r: _FOURPI * r**2 * self.dens(r), 0.0, r[0])[0],
-                numpy.cumsum(mass_shells),
-            )
-        )
+        self._cumul_mass = -self._dWdr * self._r**2.0
         self.mass = self._cumul_mass[-1]
         return None
 

galpy/potential/KingPotential.py

@@ -68,7 +68,7 @@ def __init__(self, W0=2.0, M=3.0, rt=1.5, npt=1001, _sfkdf=None, ro=None, vo=Non
             / radius_scale**2.0
             * numpy.interp(r / radius_scale, sfkdf._r, sfkdf._dWdr),
             rgrid=sfkdf._r * radius_scale,
-            Phi0=-W0 * mass_scale / radius_scale,
+            Phi0=-W0 * mass_scale / radius_scale - M / rt,
             ro=ro,
             vo=vo,
         )

tests/test_potential.py

@@ -7734,6 +7734,19 @@ def test_InterpSnapshotRZPotential_pickling():
     return None
 
 
+# Test that the King potential goes as -GM/r at r > rt
+def test_king_potential_beyond_tidal():
+    mass = 3.0
+    kp = potential.KingPotential(W0=6.0, rt=2.0, M=mass)
+    r = numpy.linspace(2.1, 10.0, 1001)
+    # Accuracy is limited because of the numerical solution of the King ODE and
+    # the fact that interpSphericalPotential doesn't directly use the solved W potential
+    assert numpy.all(
+        numpy.fabs(kp(r, 0.0) / mass * r + 1.0) < 1e-3
+    ), "King potential does not go as GM/r at r > rt"
+    return None
+
+
 # Test that trying to plot a potential with xy=True and effective=True raises a RuntimeError
 def test_plotting_xy_effective_error():
     # First a single potential