Considering all factors, the minimum amount of time for public attachment to be mitigated to the point where prosecuting beloved celebrities for heinous crimes would not cause a significant public upheaval could be as short as 5-10 years. Here’s why this is the shortest plausible timeline:

1. Public Disillusionment: Scandals can break attachment quickly when the public feels betrayed, particularly if the crimes are of a deeply egregious nature (such as crimes against children or crimes against humanity). Public opinion can turn sharply within a few years if the media and social narratives focus on the severity of the crimes, pushing people to re-evaluate their emotional connections.

2. Media Cycles and Distractions: In an era of fast-moving media cycles, new scandals or major global events tend to overshadow older ones. If the celebrities in question fall from grace and new events dominate the news, public attachment may fade faster.

3. Public Fatigue: There is a level of scandal fatigue that occurs when society becomes accustomed to seeing powerful figures exposed for wrongdoing. This can reduce the emotional attachment much more quickly than in eras where such revelations were rare.

4. Generational Shift: Even within a decade, younger generations who may not have the same attachment to these figures could rise to social prominence. They may have less resistance to seeing such celebrities prosecuted, which can mitigate potential upheaval.

Therefore, if the revelations are severe enough and public discourse focuses on the gravity of the crimes, 5-10 years is the shortest plausible period during which public attachment could significantly weaken, allowing for a less tumultuous prosecution.