Making use of the arbitrary shock theory developed by Ulmschneider (1967, 1971) and Ulmschneider and Kalkofen (1978), we have calculated the dissipation rates of upward-travelling slow-mode acoustic shock waves in umbral chromospheres for two umbral chromosphere models, a plateau model by Avrett (1981) and a gradient model by Yun and Beebe (1984). The computed shock dissipation rates are compared with the radiative cooling rate given by Avrett (1981). The results show that the slow-mode acoustic shock waves with a period of about 20 second can heat the low umbral chromospheres travelling with a mechanical energy flux of 2.6 × 10 6 e r g / c m 2 s at a height of 300 ∼ 400 k m above the temperature minimum region.

ABSTRACT
Ⅰ. INTRODUCTION
Ⅱ. MATHEMATICAL FORMULATIONS
Ⅲ. RESULTS AND DISCUSSIONS
Ⅳ. SUMMARY AND CONCLUSIONS
REFERENCES

• LEE MYUNG GYOON(Department of Astronomy, Seoul National University)
• YUN HONG SIK(Department of Astronomy, Seoul National University)