A comparison of active region temperatures and emission measures observed in soft X-rays and microwaves and implications for coronal heating

We have determined active region temperatures and emission measures using both broad-band soft X-ray images from the Yohkoh satellite and spatially and spectrally resolved microwave data from the Owens Valley Radio Observatory (OVRO). This work differs from previous work in that the microwave temperatures and emission measures are directly measured from the microwave spectrum, and are not model-dependent. The soft X-ray temperatures and emission measures are ≈2.5 times greater than the corresponding microwave values, on average. Detailed error analysis indicates that the temperature differences are real, but that the emission measure differences may not be. We have simulated Yohkoh and OVRO observations of idealized plane-parallel and nested-loop coronal models. The plane-parallel model reproduces the observed temperature differences if the coronal temperature decreases exponentially with height from a maximum value of ≈4 × 10⁶ K at the base to an asymptotic value of ≈ 10⁶ K. The nested-loop model, which assumes quasi-static loop equilibrium, also reproduces the observed temperature differences and indicates that the volumetric coronal heating rate varies inversely with loop length to a power greater than 2. Both models predict microwave emission measures that are larger than observed. We suggest that a more complex model is required to explain the observed emission measures and that more than one coronal heating mechanism may be operative in solar active regions. We present derivations of the temperature and emission measure uncertainties that result from random and systematic errors in the Yohkoh observations. The expression for the random error emission measure uncertainty is different from that used previously and is especially important for observations of nonflaring plasmas.