Question #43667

A perfectly absorbing spherical dust particle of radius $R$ and initial rest mass $m_0$ is initially at absolute zero ($T = 0\text{ K}$) in deep space. It is illuminated by a unidirectional plane electromagnetic wave (laser) of constant intensity $I$. As the particle absorbs the radiation, it heats up and emits blackbody radiation isotropically in its instantaneous rest frame. Eventually, the particle reaches a thermal steady state at temperature $T_{eq}$. Assume the particle's internal thermal energy is given by $U(T) = \beta T^4$, where $\beta$ is a positive constant, and its velocity remains non-relativistic ($v \ll c$) throughout. Which of the following gives the particle's steady-state rest mass $m_{eq}$ and its instantaneous acceleration $a$ at this steady state? (Here, $c$ is the speed of light and $\sigma$ is the Stefan-Boltzmann constant).