Does semen exiting without touching the penis, merely by seeing something that arouses lust (such as a girl or pornographic images), necessitate ghusl and invalidate prayer?

A Muslim must lower his gaze. If an accidental glance occurs, there is no sin upon him due to the lack of intention and the difficulty of avoiding it, for the Prophet, peace and blessings be upon him, said: "Do not follow up a glance with another, for the first is yours but the last is not." Thus, sin falls upon the one who intentionally looks or prolongs the gaze. What is discharged upon seeing forbidden sights is either maniy (seminal fluid) or madhiy (pre-seminal fluid). Prayer is not valid except by purifying oneself from both. The ruling depends on what exits, not on touching the male organ, and each requires a different purification.