By performing magnetohydrodynamical ( MHD ) simulations , we investigate the mass loss of intermediate- and low-mass stars from main sequence ( MS ) to red giant branch ( RGB ) phases .
Alfvén waves , which are excited by the surface convections travel outwardly and dissipate by nonlinear processes to accelerate and heat the stellar winds .
We dynamically treat these processes in open magnetic field regions from the photospheres to \simeq 25 stellar radii .
When the stars evolve to slightly blueward positions of the dividing line ( Linsky & Haisch ) , the steady hot corona with temperature , T \approx 10 ^ { 6 } K , suddenly disappears .
Instead , many hot ( \sim 10 ^ { 6 } K ) and warm ( \gtrsim 10 ^ { 5 } K ) bubbles are formed in cool ( T \lesssim 2 \times 10 ^ { 4 } K ) chromospheric winds because of thermal instability ; the red giant wind is not a steady stream but structured outflow .
As a result , the mass loss rates , \dot { M } , largely vary in time by 3-4 orders or magnitude in the RGB stars .
Supported by magnetic pressure , the density of hot bubbles can be kept low to reduce the radiative cooling and to maintain the high temperature long time .
Even in the stars redward of the dividing line , hot bubbles intermittently exist , and they can be sources of ultraviolet/soft X-ray emissions from hybrid stars .
Nearly static regions are formed above the photospheres of the RGB stars , and the stellar winds are effectively accelerated from several stellar radii .
Then , the wind velocity is much smaller than the surface escape speed , because it is regulated by the slower escape speed at that location .
We finally derive an equation that determines \dot { M } from the energetics of the simulated wave-driven winds in a forward manner .
The relation explains \dot { M } from MS to RGB , and it can play a complementary role to the Reimers ’ formula , which is mainly for more luminous gaints .