How to add an encircling axes around a polar plot?

I'm trying to figure out how to append an axes to my polar projection. The newly added axes is supposed to wrap around the original polar axes like a ring.

For that purpose I tried to use append_axes from a divider created via make_axes_locatable on a polar matplotlib projection ax.

However, there's no option for "outer" or anything that would resemble polar projections with the append_axes arguments. Instead of a ring around the axes, I get a new axes just below the original one (see picture).

Is there any alternative that would allow to create an axes of ring shape around an existing polar axes?

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable

plt.style.use("seaborn-white")
def synthesize(polar=False):
    fig = plt.figure()
    ax = fig.add_subplot(111, polar=polar)
    t = np.linspace(0,2*np.pi)
    r_sin = np.sin(t)
    r_cos = np.cos(t)
    for r in [r_sin, r_cos]:
        ax.scatter(t, r, c=r, s=t*100, edgecolor="white", cmap=plt.cm.magma_r)
        ax.scatter(t, -r, c=r, s=t*100, edgecolor="white", cmap=plt.cm.magma_r)
    ax.set_title("polar={}".format(polar),fontsize=15)
    ax.set_xticklabels([])
    return fig, ax, t

# Rectilinear
fig, ax, t = synthesize(polar=False)
divider = make_axes_locatable(ax)
ax_below = divider.append_axes("bottom", size="32.8%", pad=0.1)
ax_below.scatter(t, np.tan(t), c="black", edgecolor="white")

# Polar
fig, ax, t = synthesize(polar=True)
divider = make_axes_locatable(ax)
ax_below = divider.append_axes("bottom", size="32.8%", pad=0.1)
ax_below.scatter(t, np.tan(t), c="black", edgecolor="white")

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