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Intermediate-Mass Black Holes: Unlike other black holes (stellar-mass black holes can be revealed by x-ray emission or gravitational waves and supermassive black holes can be revealed by the distorted orbits of nearby stars), the ways to find intermediate-mass black holes is always a mystery. However, if we can find it in the future, it will provide insights about supermassive black holes such as M87.
Supermassive Black Holes: Most of the galaxies have a supermassive black hole, and the evolution of galaxies is directly related to the evolution of black holes. Supermassive black holes act as cosmic control mechanisms. A good metaphor is that they are like thermostat in your house, if your house gets too hot, the thermostat will kick on the air-conditioner and if it get too cold, it will kick on the heater, black holes do the same things for galaxies.
Ultramassive Black Holes: They are as wide as the solar system and weigh as much as the stars in the milky way; In 2018, scientists discovered a twenty billion solar mass ultra massive black hole growing faster than any other black hole; eat anything, devour massof our sun every two days; blast too much energy and turbulance to the galaxy that stars no longer form; the bigger the black hole, the faster the galaxy dies. But how do they grow that large? It doesn’t make sense! You can’t just grow them from the slow accretion of gas over time, because there’s just simply not enough gas and time!!
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