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tokens: T 0 versus X-ray luminosity from equation ( 21 ) compared to data (Johnstone et al. 2015 ). The solid and dashed curves, respectively, correspond to the equilibrium temperatures for solar minimum and maximum, T x, ⊙1 = 0.97 × 10 6 K and T x, ⊙2 = 2.57 × 10 6 K (Johnstone et al. 2015 ). The plot shows that equation ( 21 ) is consistent with the data. Although the total wind power escaping from the scale height of the corona is given by , the total wind power escaping from the star is at least . Assuming constant , mean molecular mass m p /2, and thus c s = 2 k b T / m p and c V = 3 k b / m p (Hearn 1975 ), the relation between the total wind power and the coronal wind flux is where . Fig. 1(b) shows this total integrated wind power (blue) along with (green), and (orange) with all three quantities normalized to the same constant . We see that in regime II. Note also that when the equilibrium p 0 is plugged back into the expressions for F x and F W , the ratio of scales with . Therefore, although we focus on m * = r * = 1, for the temperature range of interest we would predict for a range of late-type stars, largely independent of mass since for the relevant stellar models (Kippenhahn, Weigert Weiss 2012 ). Figs 1(c) and (d) are similar to Figs 1(a) and (b) but apply when the last exponent in equation ( 16 ) is reduced by a factor of 2, highlighting the sensitivity of the temperature dependence. Here the power-law fit more accurately matches regime II than the exponential of equation ( 22 ). With the physics included in our present model, we do not identify a huge drop in mass-loss rate at high as suggested by two data points in Wood et al. ( 2014 ). More data are needed to confirm this is a statistically significant effect. There does not seem to be evidence of a corresponding change of magnetic configuration (Vidotto et al. 2016 ), so that would not provide an explanation if the effect were real. Suzuki et al. ( 2013 ) suggested that a decrease in mass loss for young active stars might arise because the increase in coronal density could lead to runaway cooling that drains the thermal energy that would otherwise accelerate the wind. This model does not employ coronal equilibrium arguments that we have used herein to determine our coronal properties. We leave further consideration of this for future work. 4.2 X-ray luminosity as function of magnetic field strength Having established that in regime II, we now connect both of these quantities to the source of magnetic energy. Blackman Thomas ( 2015 ) estimated from the dynamo-produced magnetic energy rising up through the convection zone. To accommodate our present result that 1/2 of source magnetic energy goes into , the relevant expression becomes where B ∼ B φ and Θ/4π is the solid angle fraction through which the field rises (proportional to, if not equal to of the previous section), and we have used the expression for u b below equation ( 12 ). Using equation ( 13 ) in equation ( 24 )