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I would love to know! I can find lots about the mass-velocity dispersion relation. There's a mass-luminosity relation (but not really tight). I hope you can include references, as I'm spending hours looking for this and not finding answers. thanks

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There's a fairly tight $M_\text{BH}-M_\text{bulge}$ relation but not one for total masses of galaxies. The "bulge" refers to the central, bright, spherical component of stars in spiral galaxies. It's usually the yellowish bit in images, unlike the bluer spiral arms.

In the case of elliptical galaxies, the "bulge" is actually in effect the whole galaxy. So in this case there is a relation between the total galactic mass and BH mass but only because it's an extension of the more general relationship.

For references, most of the major papers on the subject are cited in the Wiki article on the $M-\sigma$ relation. I know those are mostly $M-\sigma$ relations but most make some mention of the $M_\text{BH}-M_\text{bulge}$. Also, have a look at the papers that refer to those major hitters. Follow the ADS links, hit "Refereed citations" and maybe sort those by citation for major more recent papers.

I'm not a galaxy specialist so I stand to be correct by an expert.

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Thanks! I was thinking of connecting the SMBH mass to Luminosity and then making note that there is also a bit of correlation between galaxy mass and luminosity . . . but I'm really hard pressed to find any scientific writing about it. – Gigi Giles Mar 30 '12 at 17:32
Above are two references showing the bulge is typically 500 to 1000 times as massive as the black hole. So for bulge dominated galaxies this is a reasonable approximation. On the other hand, some disk dominated galaxies and dwarf galaxies (a minority) may not even have a black hole.

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Apparently, there is a relationship between the Black Hole's mass and the galaxy's mass. And it's $M_{BlackHole}\times 3\times10^{6}=M_{galaxy}$

It's just a mere aproximation, but it works for almost all galaxies.

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Thanks, do you have a reference for that, or a name? – Gigi Giles Mar 30 '12 at 17:26
@GigiGiles Nope. – Garmen1778 Apr 23 '12 at 20:14
For our own galaxy the factor seems to be 8 x 10^5. So in the ballpark, within an order of magnitude. – Halfdan Faber Dec 5 '15 at 21:07

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