Does eSATA require power source?

The original eSATA specification does not provide power. You'll need a USB cable or wall adapter to power the hard drive. The new eSATAp specification utilizes the USB bus to provide power over one cable, but is relatively rare.

The easiest way to be sure if you have an eSATAp device or not is to check the plug. This helpful image from Wikipedia shows the difference:

Here is a eSATAp to SATA+SATA Power so that any standard SATA drive can utilize the power from the eSATAp connection without the need of a USB connection, and only requires the eSATAp connection on the computer end:

They also make cables that convert the standard SATA data/power connections to eSATA for data and USB for power:

However, a far better option IMHO is to buy an external drive enclosure, which is essentially a box you insert your hard drive into with cables provided for USB power and eSATA data. The enclosure will protect your bare drive from damage, and as far as I can tell, aren't that much more expensive than regular cables.

Quoting Wikipedia

Where a PC-hosted port is concerned, eSATA connectors cannot supply power, and would therefore be more cumbersome to use. Note that this problem has been solved by the introduction of eSATAp.

I guess your external interface comes with power adapter?