6 Application to Stellar Flares

It is well known that stellar flares and coronae have many similarities to solar flares and corona (e.g., Haisch, 1989; Güdel, 2002). Not only light curves of stellar flare emissions (in radio, Hα, visible continuum, and X-rays) but also quantitative nature of flares such as time scale, plasma temperature, density, and magnetic field strength are all similar, though the distribution of temperature and total energy of stellar flares is much broader (7 8 T ∼ 10 –10 K, total energy 29 37 10 – 10 erg) than those of solar flares (7 T ∼ 1– 3 × 10 K, total energy 29 32 ∼ 10 – 10 erg).

It is believed that stellar flares are produced by the same mechanism, magnetic reconnection, as solar flares. However, why do some of stellar flares show very high temperature and extremely large total energy? Recent observations of young stars by X-ray satellites ASCA and ROSAT have revealed that young stars such as protostars and T-Tauri stars frequently produce superhot flares with temperature of 108 K (Koyama et al., 1996; Tsuboi et al., 1998; Imanishi et al., 2001, see Feigelson and Montmerle, 1999 for a review). Time variation of X-ray intensity is similar to that of solar flares, while the total energy released by those stellar flares amounts to 1036 – 1037 erg, much larger than those of solar flares. Can these protostellar flares be explained on the basis of magnetic reconnection?

A hint was given in a paper by Feldman et al. (1995). They show that there is a universal correlation between flare temperature (T) and emission measure (EM) not only for solar flares but also for some of stellar flares. Shibata and Yokoyama (1999Jump To The Next Citation Point) extended this universal correlation between T and EM and apply it for solar microflares, T-Tauri star flares, and protostellar flares (see Figure 46View Image). It is remarkable that the correlation holds in a very wide range, 6 8 4 × 10 K < T < 10 K and 1045 cm −3 < EM < 1056 cm −3. Shibata and Yokoyama (1999Jump To The Next Citation Point) then found that this universal correlation can be explained by the simple scaling law (see Figure 46View Image),

48 −3 (-B---)−5( ---n0----)3∕2( --T---)17∕2 EM ≃ 10 cm 50 G 109 cm− 3 107 K , (43 )
which is derived from the following three equations:
2 3 EM = n L , (44 )
2 2nkT = B ∕(8π ), (45 )
7 ( -B---)6∕7( ---n0----)−1∕7(--L---)2∕7 T = 10 K 50 G 109 cm −3 109 K , (46 )
where B is the magnetic field strength and n0 is coronal density, both of which are in a normal state (no occurrence of a flare), L is the length of a flaring loop. Equation (46View Equation) is basically the same as Equation (38View Equation).1

Figure 46View Image shows the observed correlation between the emission measure of solar and stellar flares and their temperatures. It also shows the theoretical relation between the emission measure and temperature given by the Equation (43View Equation) is plotted as solid lines for three cases of B = 15, 50, 150 G in the case of n0 = 109 cm − 3. Figure 46View Image shows that the observed correlation line corresponds to the line of constant magnetic field strength within 30 – 150 G, and indeed the coronal magnetic field strength is estimated to be about 40 – 300 G for solar and stellar flares. Similarly, if we eliminate the magnetic field strength (B) from the Equations (43View Equation) and (46View Equation), we can plot the relation between the emission measure and temperature for constant loop length, which is also shown in Figure 46View Image as dash-dotted lines. We can see that the length of a solar microflaring loop is 108 – 109 cm, and the length of a solar flaring loop is 109 – 1010 cm. These are fully consistent with observations.

View Image

Figure 46: The universal correlation between emission measure and temperature of solar and stellar flares (Shibata and Yokoyama, 1999). The solid lines show the theoretical scaling law EM ∝ B − 5T 17∕2 (Equation (43View Equation)) for B = constant = 15, 50, 150 G, and the dash-dotted lines show EM-T relation for L = constant = 108, 1010, 1012 cm.

It is interesting to see that the length of a stellar flaring loop is 1010 – 1012 cm, much larger than the length of a solar flaring loop. This is consistent with observations that average field strength at the surface of young stars is very strong, which is of order kilo Gauss (e.g., Johns-Krull et al., 1999Jump To The Next Citation Point), indicating that the size of a coronal loop with strong magnetic field (≫ 100 G) is much larger than that in the Sun.

The size of a flaring loop in young stars is estimated to be comparable to or even larger than the solar radius (∼ 7 × 1010 cm). It should be noted here that the range of radius for these young stars is from 1 to 4 solar radii (e.g., Johns-Krull et al., 1999).

Consequently, we found the reason why some of stellar flares, especially young star flares, show very high temperature and extremely large total energy, which is because the size of these flares is much larger than that of solar flares. If the length of a flaring loop is larger, the flare temperature increases in proportion to L2 ∕7 even if the magnetic field is the same, because the conduction cooling (κ0T 7∕2∕L2) become less efficient for a longer loop. The total energy is simply determined by the total magnetic energy contained in the corona in a normal state, ∼ L3B2 ∕(8π), which explains the observations very well, although only a fraction of this energy is available as we mentioned before (Equation (1View Equation)).

Why can such a large coronal loop with strong magnetic field exist? Why is the filling factor of strong magnetic fields large (near unity) in young stars? One possibility is that the protostar is just born, keeping primordial magnetic field whose origin is in interstellar medium. The other possibility is that the strong magnetic field with large filling factor is created by the dynamo action. Since young stars rotate rapidly (more than 30 km s–1 which is much faster than the solar rotation, ∼ 2 km s–1), the dynamo action would be stronger. It is also expected that there is an accretion disk (planet-forming disk) around a young star, so that strong interaction would occur between the central stellar core and the surrounding disk, which may lead to magnetic reconnection. This interacting process has been treated by Hayashi et al. (1996), who performed 2.5-dimensional MHD simulations for the interaction of an accretion disk and stellar magnetosphere (dipole magnetic field). They have shown that vigous magnetic reconnection associated with mass ejection occurs. The reconnection releases a huge amount of magnetic energy up to the order 1036 erg (about 104 times more energetic than solar flares) stored in a sheared loop with a size of 11 L ∼ 10 cm.

  Go to previous page Go up Go to next page