How is momentum justified as a common risk factor?
The Jegadeesh and Titman (1993) paper is usually considered Original Source, though I'm sure you could find something earlier that looks similar if you looked hard enough.

I don't think there is a satisfactory explanation. Momentum is not correlated with macroeconomic variables, it does not seem to reflect persistent exposure to other (known) sources of risk, and is driven almost entirely by the 7 to 12 months before stocks are chosen as part of a momentum portfolio. This all makes it extremely difficult to put a solid theoretical model to it that doesn't have a behavioral aspect.

Recently (mid 2009), there was a momentum crash in the market. Daniel and Moskowitz argue that momentum has rare "panics" periods like this, where crashes occur for momentum. So during normal periods investors may be being compensated for this risk. The question becomes "what are these crashes caused by?" The authors make the case that following a period of declining stock values, momentum portfolios will be long a lot of low market beta stocks, and short a lot of high beta stocks. If there is a sudden rebound in the market, momentum strategies will experience a crash. So this is at least suggestive of a direction for more formal modeling, but they ultimately suggest a behavioral interpretation may be necessary as well.

If you have not seen it, Jegadeesh and Titman (2011) review the evidence for momentum in more detail, and explore behavioral explanations for momentum, of which I have little knowledge.