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We present the results of a spectroscopic survey to characterizechromospheric activity, as measured by H$\alpha$ emission, in low-mass membersof the 500-Myr-old open cluster M37. Combining our new measurements ofH$\alpha$ luminosities ($L_{H\alpha}$) with previously cataloged stellarproperties, we identify saturated and unsaturated regimes in the dependence ofthe $L_{H\alpha}$-to-bolometric-luminosity ratio, $L_{H\alpha}/L_{bol}$, on theRossby number $R_o$. All rotators with Ro smaller than 0.03$\pm$0.01 convergeto an activity level of $L_{H\alpha}/L_{bol}$ = (1.27$\pm$0.02) x 10$^{-4}$.This saturation threshold ($R_{o,sat}$ = 0.03$\pm$0.01) is statisticallysmaller than that found in most studies of the rotation-activity relation. Inthe unsaturated regime, slower rotators have lower levels of chromosphericactivity, with $L_{H\alpha}/L_{bol}$($R_o$) following a power-law of index$\beta$ = -0.51$\pm$0.02, slightly shallower than the one found for a combined$\approx$650-Myr-old sample of Hyades and Praesepe stars. By comparing thisunsaturated behavior to that previously found for coronal activity in M37 (asmeasured via the X-ray luminosity, $L_X$), we confirm that chromosphericactivity decays at a much slower rate than coronal activity with increasing$R_o$. While a comparison of $L_{H\alpha}$ and $L_X$ for M37 members withmeasurements of both reveals a nearly 1:1 relation, removing themass-dependencies by comparing instead $L_{H\alpha}/L_{bol}$ and $L_X/L_{bol}$does not provide clear evidence for such a relation. Finally, we find that$R_{o,sat}$ is smaller for our chromospheric than for our coronal indicator ofactivity ($R_{o,sat}$ = 0.03$\pm$0.01 versus 0.09$\pm$0.01). We interpret thisas possible evidence for coronal stripping.

Chromospheric and Coronal Activity in the 500-Myr-old Open Cluster M37: Evidence for Coronal Stripping?