The coma

The comet's coma or head, is the fuzzy haze that surrounds the comet's true nucleus. Together with the tail, the coma is all we actually see of a comet from Earth.

Shape and composition of the coma

The shape of the coma can vary from comet to comet and for the same comet during its apparition, depending on the comet's distance from the Sun and the relative amount of dust and gas production. While for faint comets or bright comets producing little dust, the coma is usually round, comets which are producing significant quantities of dust have fan-shaped or parabolic comae. This is due to the different size of the dust grains released: the larger get left along the comet's orbital path while the smaller can be pushed away from the Sun by light pressure.
The coma has two main constituents: the gas coma and the dust coma. In fact, scientists think that nearly equal masses of dust and gas are ejected by comets.

In this NASA image of comet Hale Bopp, a remarkable emission can be seen from the nucleus

The gas coma
The gas coma consists of molecules liberated from the nucleus by solar heating and relative sublimation. Once they have left the nucleus, these molecules in the coma are exposed to direct solar radiation and can be damaged in various ways: due to the combined action of these reactions, most molecules are broken apart ("dissociated") within a day of their leaving the nucleus.
The most usual among these reactions is photo-dissociation: the molecule (called "parent molecule") absorbs a photon form the Sun's radiation and breaks into two pieces (called "daughter molecules"). These daughter molecules are quite easy to observe because they have strong spectral lines at optical wavelengths (click here to know more about light).
In addition to being photo-dissociated, gas species in comets can also be ionized (they loose one or more electrons). The formed ions are susceptible to a magnetic force due to the solar magnetic field carried by the solar wind. Consequently, the ions are swept almost radially away from the sun, into a long, distinctive tail, called the ion tail.
The outflow speed of the coma combined with the lifetime of molecules, determine the dimension-scale of the coma. In one day, at 1 Km/s, molecules can travel about 50,000 Km and this is the approximate radius of the gas coma.

The dust coma
The dust grains that form the dust coma are dragged from the nucleus by the rush of sublimating gas. The speed these grains will be accelerated to, depends mostly on their size, since smaller grains are lighter and therefore much more accelerated by the gas. The grains can become part of the coma only if they reach a speed greater than the nucleus escape velocity. Grains that are too large to be ejected, fall back to the surface and may become part of a the nucleus mantle. The lighter grains, instead, leave the nucleus and are in free flight around the sun (since the nuclear gravity of the comet is very weak).
Cometary dust grains are found of all sizes. The grains that are most visible to the eye have diameters of about 0.001 mm but even grains of many tens of centimeters can be ejected by the gas flow from a very active, near-sun comet. Many of these grains pass from the tail into the interplanetary medium, giving birth to meteors that blaze across the night.