Binding energy of a galaxy? I'm a novice in physics and new to the forms, so please forgive me if this is a dumb question or if this is in the wrong section to be posted, but how would one find the gravitational binding energy of our galaxy? I know their is a formula for a uniform sphere $U= 3GM^2/5r$, however I assume for a galaxy the method would be extremely different if its even possible to give an accurate figure.
So I ask this, what would be the necessary energy needed to break the binding energy of the galaxy with a well placed rapid release of energy (explosion), I know physics would say this hypothetical event is a big no no, but what would it be if this were a possibility?
 A: The first-order estimate of the gravitational binding energy of a galaxy can be obtained by approximating it as an uniform sphere using 
$$U=3GM^2/(5r).$$ 
Let's consider a large elliptical galaxy such as M87 as a concrete example. M87 hosts the supermassive black hole that was imaged with the Event Horizon Telescope. Within a distance of 32 kpc from the center, M87 contains a mass of $2 \times 10^{12} M_\odot$ where $M_\odot$ is a solar mass. Plugging in these two numbers in the equation for $U$ above, we get a binding energy of about $10^{61}$ erg (using CGS units as common in astrophysics).
It is not possible to dump all this energy at once throughout the galaxy and destroy it—gravitationally unbind it. However, if there is a physical process that over time transfers this amount of energy throughout the galaxy, it could considerably affect its properties, and partly destroy it.
Astrophysicists think that the supermassive black holes located at the centers of galaxies dump large amounts of energy in their surroundings while they are growing (being fed with gas). This energy is transferred from the black hole to the galaxy through gas outflows and radiation. 
A supermassive black hole dumps an estimated energy of $$E=0.1 M_{\rm BH} c^2 = 2 \times 10^{61} \left( \frac{M}{10^8 M_\odot} \right) \ {\rm erg}$$ while it is growing into the galaxy (I will not get into the details of how I estimated this, it is a rough estimate). This energy is not released all at once, but takes tens of millions of years to be generated. Tens of millions of years is not a long time compared to the lifetime of a galaxy. 
The conclusion is that the energy released by the central black hole during a galaxy's evolution is comparable to its gravitational binding energy. Therefore, supermassive black holes can potentially change the global properties of galaxies with their energy release. This effect has a name in astrophysics—AGN feedback (AGN stands for active galactic nuclei)—and is a current area of research.
