On the numerical modelling of astrospheres, including those of luminous blue variable stars, and the modulation of cosmic rays within

Luminous blue variable-type stars are massive O-type stars that show variable outflow parameters. These stars can also undergo eruptions where a large amount of mass is ejected in a very short duration. The astrospheres of these stars are modelled using a magnetohydrodynamic model including the effect of radiative cooling. The variation in outflow parameters is demonstrated to lead to a variation in number density up to the termination shock, after which there is no effect in the post-shocked regions. On the other hand, eruptions increase the size of the astrosphere and cause the termination shock to oscillate between the inner boundary and the astropause. Galactic cosmic ray modulation within these types of astrospheres is also studied using a 1D stochastic differential equation model. It is shown that, even though these astrospheres are considerably larger than the heliosphere, calculated cosmic ray differential intensities remain larger than what is observed in the heliosphere at Earth, implying lower levels of modulation related to larger cosmic ray diffusion coefficients. During eruptive events, modelled cosmic ray intensities fluctuate due to the oscillating termination shock, and varying plasma parameters. It is also shown that such behaviour, can in principle, lead to the acceleration of these particles, but the results of this study, due to the 1D approach taken to solving the Parker transport equation, are argued to represent an upper limit to this phenomenon.

Automated summary

Luminous blue variable-type stars, massive O-type stars, exhibit variable outflow parameters and eruptions. The astrospheres of these stars and the modulation of galactic cosmic rays are studied using a magnetohydrodynamic model and a 1D stochastic differential equation model. The results show that the variation in outflow parameters affects the number density up to the termination shock, and eruptions increase the size of the astrosphere.