The $16.49 Apple (AAPL) rose Thursday was only its sixth largest one-day dollar gain, according to AAPLInvestors, and in percentage terms, 3.46% doesn’t even make the top 10.

But when the world’s most valuable company rallies a few points, its market capitalization gets a whole lot bigger. According to the Bespoke Investment Group, Apple’s one-day gain Thursday — $15.4 billion — was larger than the market cap of half the companies in the S&P 500.

Why Thursday? There are no definitive answers but plenty of theories. Among them:

• The second-hand report in the Wall Street Journal‘s AllThingsD blog that Apple will introduce a new iPad the first week in March
• Rumors that the company will announce its first dividend since 1995 at its Feb. 23 stockholders meeting
• The positive remarks of Saudi billionaire Prince Alwaleed bin Talal made about Apple on Charlie Rose Tuesday night, which may have been taken as a green light by what one investor called “deep sovereign pockets in the Middle East”
• Speculation (unfounded, as near as we can tell) that Warren Buffet has been buying into the company
• The impact of Apple’s blow-out Q1 2012 earnings finally sinking in among the broader investment community

One footnote: Richard Bloch points out on Seeking Alpha that most of the action Thursday was in the derivatives market, not the stock itself. Volume on the NASDAQ was high, but not record-setting. The options volume, however, was off the charts. See above.