The lifetime of a comet

There are many physical mechanisms that can limit the dynamical lifetime of a comet (or in other words the period of time the comet is active). In fact, the typical dynamical lifetime of a comet is about 1/2 million years. After this period, the comet is no longer active, and becomes a dead comet. This characteristic of comets introduces a new problem: if comets cannot survive as long as the Solar System's has been alive, how can we still see comets around us?

Why do comets have a limited lifetime?

First of all, comets, as they travel through their path, leave behind them a large amount of debris, loosing mass at rates that cannot be sustained for very long (click here to know more about comets' tails). In addition to this, a large comet nucleus could shatter, for whatever reason, as seen on comet Shoemaker-Levy 9, producing a stream of fragments in its way. The debris left behind can range in size form a few microns to a few thousands of meters and spread in the path of the original motion, generating the fascinating phenomena of meteors when they interfere with the atmosphere.
In addition, comets are under the gravitational control of the planets and there is a chance that they will be either ejected from the solar system, injected to the Sun, or absorbed by an impact with one of the planets (as in the case of Shoemaker-Levy).

The impact of comet Shoemaker-Levy 9 on planet Jupiter (NASA)

What are dead comets?
But what exactly is a dead comet? Once a comet has outgassed all the available volatile, its coma and tail will disappear and the remaining inert nucleus will take on the appearance of a low albedo asteroid. After 500 times or so a comet passes near the Sun, most of its ice and gas is lost, leaving a rocky object.
Today, there is an increasing evidence that there might be a significant population of dead comets occupying Halley Type orbits. In fact, many asteroids have orbits that can't be distinguished from the orbits of some comets, as the graph below shows. Furthermore, scientists think that perhaps half of the near-Earth asteroids may be "dead" comets.

The similar orbits of 9 comets and 8 asteroids (image : Andrea Carusi)

The comets' reservoirs: birth of a comet
The comets we can now observe have a dynamical lifetime much shorter than the life of the solar system and therefore, they cannot have been always present as today in the Solar System. There are two possibilities to explain this mystery.
The first possible explanation is that comets are relatively young objects that are created and then dumped in the inner solar system where they become active and are discovered. But at the present time, no place in the solar system where comets could be formed has been discovered.
So, a second more reasonable explanation is needed. The most accredited theory of comets' formation affirms that comets were born with the rest of the solar system and have been stored since formation in a cold place where the nuclear ices could be stable. The two deep-freeze locations now under discussion are the Oort Cloud and the Kuiper Belt.