The evidence for this active phase came from a search for the galaxy's missing mass, researchers said.
The centre of the Milky Way galaxy is currently a quiet place where a supermassive black hole slumbers, only occasionally slurping small sips of hydrogen gas.
Measurements show that the Milky Way galaxy weighs about 1-2 trillion times as much as our Sun. About five-sixths of that is in the form of invisible and mysterious dark matter.
However, if you count up all the stars, gas and dust we can see, you only find about 65 billion solar masses.
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The rest of the normal matter - stuff made of neutrons, protons, and electrons - seems to be missing.
"We analysed archival X-ray observations from the XMM-Newton spacecraft and found that the missing mass is in the form of a million-degree gaseous fog permeating our galaxy," said lead author Fabrizio Nicastro, a research associate at the Harvard-Smithsonian Centre for Astrophysics (CfA) in the US.
The astronomers used the amount of absorption to calculate how much normal matter was there, and how it was distributed.
They applied computer models but learned that they couldn't match the observations with a smooth, uniform distribution of gas.
Instead, they found that there is a "bubble" in the centre of our galaxy that extends two-thirds of the way to Earth.
Clearing out that bubble required a tremendous amount of energy. That energy came from the feeding black hole, researchers said.
Six million years later, the shock wave created by that phase of activity has crossed 20,000 light-years of space. Meanwhile, the black hole has run out of nearby food and gone into hibernation.
This timeline is corroborated by the presence of 6-million-year-old stars near the galactic centre. Those stars formed from some of the same material that once flowed toward the black hole.
"The different lines of evidence all tie together very well. This active phase lasted for 4 to 8 million years, which is reasonable for a quasar," said Martin Elvis from CfA.
This might explain where all of the galaxy's missing matter was hiding: it was too hot to be seen.
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