Does the second caustic ring of dark matter cause the Monoceros Ring of stars?

Caustic rings of dark matter were predicted to exist in the plane of the Galaxy at radii $a_n\simeq 40\mathrm{kpc}/n$ for $n=1,2,3,\dots$. The recently discovered Monoceros Ring of stars is located near the $n=2$ caustic, prompting us to consider a possible connection between these two objects. We identify two processes through which the Monoceros Ring of stars may have formed. One process is the migration of gas to an angular velocity minimum at the caustic leading to enhanced star formation there. The other is the adiabatic deformation of star orbits as the caustic slowly grows in mass and radius. The second process predicts an order 100% enhancement of the density of disk stars at the location of the caustic ring.

Figure 1

(a) Dark matter trajectories forming a caustic ring of dark matter, in $\rho -z$ cross section. (b) The envelope of the trajectories shown in (a). We refer to the shape shown in (b) as the “tricusp.” The figure also indicates what is meant by the radius $a$ of a caustic ring, and by its transverse sizes $p$ and $q$. The star indicates the center of the tricusp, as defined in the text.

Figure 2

(a) The function $I(1,X)$ defined in Eq. (22), with $X\equiv \frac{r-a}{p}$. (b) The function $J(X)$ defined in Eq. (26) for $v=b$, $\zeta =1$, and $H(X)=-\frac{1}{2}\tanh (\frac{X}{5})$. (c) The function $V_c(X)$ defined in Eq. (48), in units of $2f{v}_{\mathrm{rot}}^2$, for $J(X)$ as in (b).

Figure 3

The radii $r^{\prime }(r,a)$ of circular orbits in the presence of a caustic, as a function of the caustic radius $a$. $r$ is the radius of the orbit in the absence of caustic. Each line corresponds to a different value of $r$. Each line has an upward kink at $r^{\prime }=a+p$ and a downward kink at $r^{\prime }=a$. As $a$ increases with $p$ fixed, $r^{\prime }$ first decreases from its initial value $r$ until $r^{\prime }=a+p$. For $a<r^{\prime }<a+p$, i.e. when the orbit is within the tricusp, $r^{\prime }$ increases with $a$ but not as fast as $a$, until $a=r^{\prime }$. As $a$ increases yet further $r^{\prime }(r,a)$ returns to the value $r$ from which it started. Note that the radii of circular orbits pile up at $r=a$. Stars on approximately circular orbits oscillate about $r^{\prime }(r,a)$.