An Irregular Galaxy is a galaxy that doesn't fit into the other forms of galaxy, they being lenticular galaxy, Spherical and Elliptical. Our galaxy is a Spherical Galaxy for the record so scientists currently believe. These galaxies do not have any shape or definition.
These galaxies are normally small and have a lot of star formation going on inside it. Due to the high number of star-formation, the galaxy can look a little brighter than what otherwise be possible. Caltech.
As they have a high star formation, they can be classed as a Starburst Galaxy as well as being an irregular galaxy. A number of them are satellite galaxies, galaxies that orbit other galaxies like the Large Magellanic Cloud ref:Study
An Irregular Galaxy could have been formed by a collision or "fly-past" by another galaxy. Irregular galaxies can be found mainly but not exclusively in groups of galaxies where interaction between galaxies is common in the group. SDSS
The Tadpole Galaxy in the constellation of Draco in the Northern Hemisphere is more a spherical galaxy than an irregular galaxy. The main bulk of the galaxy is spherical but it has a tail. The tail is the result of a collision between that another galaxy causing the weaker galaxy to be pasted across space.
Irregular galaxies can be split into two main groups, types I and II.
A Type I Irregular Galaxy are similar to normal spherical galaxies with bulges and spiral arms. The centres of these, the Supermassive Black Hole centres may not actually be at the centre but off-centre so to speak. These galaxies tend to be on their own, not in groups. The NGC 55 galaxy in Sculptor is a typical Type I irregular.
Another way in whichy I have alluded to earlier is the interaction between galaxies. When a galaxy interacts with another, it can create shockwaves that can cause the shape to be irregular but also starburst. This is the system mentioned above. Leicester
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