Connection ofXRay Emission with Other Stellar Parameters

Given the observed spread of X-ray luminosity for stars of given spectral type, anat-ural question to ask is which other stellar parameters except those determining the position of a star in the HR diagram determine the X-ray output level. For late-type main-sequence stars the X-ray emission scales with rotation velocity [34]. This relation is believed to trace directly back to the stellar dynamo. On theoretical grounds, the most adequate measure for the dynamo efficiency should be the Rossby number R0, defined as the ratio between the rotation period and the convective turnover time. However, in observational studies R0 often is replaced by the rotation period because the convection time scale is difficult to access observationally.

The current observational situation is summarized in Fig. 10.6, which displays rotation-activity relations for a sample of dwarf stars from the field and various young open clusters (Hyades, Pleiades, a Per, IC 2391, IC 2602). Since stellar rotation is thought to be braked by magnetic winds, the younger stars in clusters rotate much faster than the field stars, and they cover the left part of the diagram.

Stars rotating with periods shorter than about 5 days are in the so-called "saturation limit" of Lx/Lbol ~ 10-3 with no obvious dependence on rotation rate [53]. If one computes for a solar-like star the mean X-ray surface flux corresponding to Lx « 10-3Lbol, one finds Fx = 6.5x 107ergcm-2 s-1, which agrees quite well with the maximally observed surface flux values (cf., Fig. 10.7), if one assumes filling factors at the ~10% level.

For slowly rotating stars (periods longer than «5 days), the observed X-ray luminosity scales inversely with the period, albeit with an unexplained scatter of at least one order of magnitude. Possible explanations for this scatter include long-term variability. Many of the data points used in Fig. 10.6 are derived from snapshot X-ray exposures, and may not be representative for the "mean" X-ray activity. Little information exists on the long-term variability of stellar coronae and, in particular, on the issue if stellar coronal activity cycles exist as observed for the Sun. The solar X-ray emission varies - depending on the X-ray band considered - at least by an order of magnitude during a cycle, while the rotation rate stays clearly constant. Therefore, cycles or other kinds of long-term variability would provide a natural explanation for the observed scatter (Fig. 10.6)

Period (days) log R,

Fig. 10.6 Rotation-activity relation for a sample of ~250 field stars (crosses) and members of young open clusters (squares). Left: X-ray luminosity vs. rotation period; Right: fractional X-ray luminosity vs. Rossby number. Leftward arrows indicate field stars with periods derived from measurements of the rotation velocity vrot sin i, which yields upper limits to the rotation period because of the generally unknown inclination angle. Figs. 3 and 9 from [36]

Period (days) log R,

Fig. 10.6 Rotation-activity relation for a sample of ~250 field stars (crosses) and members of young open clusters (squares). Left: X-ray luminosity vs. rotation period; Right: fractional X-ray luminosity vs. Rossby number. Leftward arrows indicate field stars with periods derived from measurements of the rotation velocity vrot sin i, which yields upper limits to the rotation period because of the generally unknown inclination angle. Figs. 3 and 9 from [36]

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