I am hoping that NASA or some military units have been carefully photographing the asteroid during its close encounter with the Earth. The tidal forces due to the gradient of the gravitational field of the Earth should have disrupted the big rock to some degree unless it is entirely composed of a solid chunk of material. It has been in orbit around the sun for many billions of years so it has undergone uncountable collisions with smaller bodies which have ejected materials with each hit.
It seems logical to assume that a small portion of the material ejected in this manner would not have sufficient velocity to escape the gravitational pull of the main body. This dust and other small pebbles should eventually find their way back to the big rock and rest upon its surface. Unless there is a cleaning operation due to solar wind or some other mechanism I would think that the main body of the asteroid would be knee deep in debris. A close encounter to a large mass such as Earth would tend to extract some of this material away from the asteroid and leave a form of dust trail somewhat similar to what happened with the recent Jupiter comet encounter. One near encounter took a single body and converted it into a long string of individual bodies which lead to the final fascinating demonstration. Of course Jupiter is a lot bigger than the Earth, but the process should be the same although in a far smaller model. Has anyone seen any published pictures or papers that support my expectations? Dave