<p>Yes, the Milky Way black hole is about a factor of ten (or possibly a factor of a few, see edit) less massive than we might expect, but there is a broad scatter in the correlations meaning that it is not <em>exceptionally</em> small.</p>
<p><strong>Details</strong></p>
<p>There is no tight correlation between the total mass of a spiral galaxy and the mass of its central black hole.</p>
<p>The correlation that is well-established is that between the velocity dispersion of stars <em>in the bulge</em> of a galaxy and the mass of its central black hole. The bulge is the pseudo-spherical region in the middle of a spiral galaxy or the bulk of an elliptical galaxy.</p>
<p>There is a slightly more scattered correlation between the stellar mass in the bulge and and the central black hole mass.</p>
<p>Since the bulge contains relatively little dark matter compared with baryonic matter, the fraction of the total mass of the galaxy that is dark plays little role in these correlations.</p>
<p>A bulge mass vs black hole mass correlation, specifically for spiral galaxies, is shown below (from <a href="https://iopscience.iop.org/article/10.3847/1538-4357/aaf3b8" rel="nofollow noreferrer">Davis et al. (2019)</a> ). The bulge mass of the Milky Way is about 20 billion solar masses (<span class="math-container">$2\times 10^{10}M_\odot$</span>, <a href="https://www.aanda.org/articles/aa/abs/2016/03/aa27500-15/aa27500-15.html" rel="nofollow noreferrer">Valenti et al. 2016</a>) and the central black hole is about 5000 times less massive at 4.3 million solar masses (<span class="math-container">$4.3 \times 10^6 M_\odot$</span>). You can see that Milky Way, with log bulge (spheroid) mass of 10.3 and log black hole mass of 6.6 is below the trend by about a factor of ten, but is not unprecedented. i.e. The general scatter in this relationship is about <span class="math-container">$\pm$</span> a factor of ten.</p>
<p><a href="https://i.sstatic.net/Eb55JNZP.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Eb55JNZP.jpg" alt="Bulge mass vs black hole mass correlation" /></a></p>
<p>The black hole in M31 is much more massive at around <span class="math-container">$1.4\times 10^8 M_\odot$</span> (<a href="https://ui.adsabs.harvard.edu/abs/2005ApJ...631..280B/abstract" rel="nofollow noreferrer">Bender et al. 2005</a>) and the bulge mass is a bit more massive - <span class="math-container">$3.3\times 10^{10}M_\odot$</span> (<a href="https://academic.oup.com/mnras/article/466/4/4279/2726589" rel="nofollow noreferrer">Blana Diaz et al. 2016</a>). Looking at the diagram again, we see that the point (10.5, 8.15) is more or less right on the average trend.</p>
<p><strong>Edit:</strong> Peter Erwin points out that the values I have cited for the bulge/spheroid mass are a factor 2 or so too big for the Milky Way and M31, or at least estimated in a way that is a factor of 2 too big to be directly compared with the Davis et al. plot I have shown. If so, then then the headline answer changes to: Yes, it is less massive than you might expect by a factor of a few, rather than a factor of ten and thus well within the observed scatter.</p>

CC BY-SA 4.0
2024-09-15T14:48:47.410Z
"`Since the bulge contains relatively little dark matter compared with baryonic matter`"  Is dark matter not over-clustering in the center generally true, or just happens to be true with the Milkyway?
Jamin Grey
CC BY-SA 4.0
2024-09-15T15:16:47.913Z
@JaminGrey In pretty much all galaxies (MW included), the baryonic matter is more concentrated than the dark matter. (Some lower-mass galaxies may still be dominated by dark matter, though.)
Peter Erwin
CC BY-SA 4.0
2024-09-15T15:29:43.523Z
Note that the bulge masses used by Davis et al in those plots are $9.1 \times 10^{9} M_{\odot}$ for the MW and $1.3 \times 10^{10}M_{\odot}$ for M31, not the larger values you are using. Since they are deliberately trying to exclude the contribution of bars to their "bulge" mass estimates (I think they fail for the MW, so *their* value is probably an overstimate!), you should not be using those large values (dominated in both cases by bars) for comparison.
Peter Erwin
CC BY-SA 4.0
2024-09-15T15:34:13.977Z
Admittedly, trying to figure out the "bulge mass" for the Milky Way is really tricky. But if you mean "pseudo-spherical region in the middle of a spiral galaxy or the bulk of an elliptical galaxy", then $2 \times 10^{10} \M_{\odot}$ is almost certainly a huge overestimate.
Peter Erwin
CC BY-SA 4.0
2024-09-15T16:12:21.213Z
@JaminGrey baryonic matter is much more centrally concentrated than dark matter, so baryonic matter dominates within the radius of the bulge of a spiral galaxy.
ProfRob
CC BY-SA 4.0
2024-09-17T04:21:08.667Z
This is a great answer, with additional thanks to Peter Erwin.  I'll wait until tomorrow to  accept as is recommended.  Thank you very much.
JohnHunt
CC BY-SA 4.0
2024-09-15T08:06:05.850Z
2024-09-15T16:37:03.473Z
2024-09-15T16:37:03.473Z
ProfRob
<p>M31* has a mass almost ten times that of Sagittarius A*, despite the Milky Way having greater mass, as measured by escape velocity, than Andromeda.  I have seen numbers for several other spiral galaxies' central SMBHs and many, if not all, seem to have a higher SMBH-mass to galactic-mass ratio than does the Sagittarius A* and the Milky Way system.</p>
<p>I have considered if the Milky Way's significantly higher mass of Dark Matter might play a role.  I have also considered observation bias as I do not have a comprehensive list of ratios, giving me a smaller sample size than I would prefer.  So, my question is; is Sagittarius A* smaller than we would predict and, if so, do we have theories as to why?</p>

CC BY-SA 4.0
2024-09-15T02:00:55.180Z
It may be difficult to get a solid answer to this question. We don't yet have a precise model of the role of the central SMBH in galaxy formation. We don't even know how SMBHs managed to get so large so early in the evolution of the universe.
PM 2Ring
CC BY-SA 4.0
2024-09-15T06:48:38.273Z
See https://physics.stackexchange.com/questions/26246/is-there-a-correlation-between-the-mass-of-a-supermassive-black-hole-and-the-mas
ProfRob
CC BY-SA 4.0
2024-09-15T14:48:06.643Z
Note that "M31*" is not the name of M31's supermassive black hole. (It doesn't really have a name.) "Sagitarrius A*" is the name of a *radio source*, which has been identified as the accretion disk around the Milky Way's supermassive black hole.
Peter Erwin
CC BY-SA 4.0
2024-09-16T14:53:09.290Z
@PeterErwin If it doesn't have a name, that means the OP gets to name it (if nobody beats them to it). Little known IAU rule.
Ray
<mass><smbh><andromeda><sagittarius>
Is Sagittarius A* smaller than we might expect given the mass of the Milky Way?
JohnHunt
# Is Sagittarius A* smaller than we might expect given the mass of the Milky Way?

(Asked by: username_0 on 2024-09-15)

M31\* has a mass almost ten times that of Sagittarius A\*, despite the Milky Way having greater mass, as measured by escape velocity, than Andromeda. I have seen numbers for several other spiral galaxies' central SMBHs and many, if not all, seem to have a higher SMBH-mass to galactic-mass ratio than does the Sagittarius A\* and the Milky Way system.

I have considered if the Milky Way's significantly higher mass of Dark Matter might play a role. I have also considered observation bias as I do not have a comprehensive list of ratios, giving me a smaller sample size than I would prefer. So, my question is; is Sagittarius A\* smaller than we would predict and, if so, do we have theories as to why?

**Tags:** mass, smbh, andromeda, sagittarius
> **Comments:**
> **username_1**: It may be difficult to get a solid answer to this question. We don't yet have a precise model of the role of the central SMBH in galaxy formation. We don't even know how SMBHs managed to get so large so early in the evolution of the universe.  
> **username_2**: See https://physics.stackexchange.com/questions/26246/is-there-a-correlation-between-the-mass-of-a-supermassive-black-hole-and-the-mas  
> **username_3**: Note that "M31*" is not the name of M31's supermassive black hole. (It doesn't really have a name.) "Sagitarrius A*" is the name of a *radio source*, which has been identified as the accretion disk around the Milky Way's supermassive black hole.  
> **username_4**: @PeterErwin If it doesn't have a name, that means the OP gets to name it (if nobody beats them to it). Little known IAU rule.  

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## 1 answers

### Answer by username_2 on 2024-09-15. Score: 9 | Accepted answer

Yes, the Milky Way black hole is about a factor of ten (or possibly a factor of a few, see edit) less massive than we might expect, but there is a broad scatter in the correlations meaning that it is not *exceptionally* small.

**Details**

There is no tight correlation between the total mass of a spiral galaxy and the mass of its central black hole.

The correlation that is well-established is that between the velocity dispersion of stars *in the bulge* of a galaxy and the mass of its central black hole. The bulge is the pseudo-spherical region in the middle of a spiral galaxy or the bulk of an elliptical galaxy.

There is a slightly more scattered correlation between the stellar mass in the bulge and and the central black hole mass.

Since the bulge contains relatively little dark matter compared with baryonic matter, the fraction of the total mass of the galaxy that is dark plays little role in these correlations.

A bulge mass vs black hole mass correlation, specifically for spiral galaxies, is shown below (from [Davis et al. (2019)](https://iopscience.iop.org/article/10.3847/1538-4357/aaf3b8) ). The bulge mass of the Milky Way is about 20 billion solar masses ($2\times 10^{10}M\_\odot$, [Valenti et al. 2016](https://www.aanda.org/articles/aa/abs/2016/03/aa27500-15/aa27500-15.html)) and the central black hole is about 5000 times less massive at 4.3 million solar masses ($4.3 \times 10^6 M\_\odot$). You can see that Milky Way, with log bulge (spheroid) mass of 10.3 and log black hole mass of 6.6 is below the trend by about a factor of ten, but is not unprecedented. i.e. The general scatter in this relationship is about $\pm$ a factor of ten.

[![Bulge mass vs black hole mass correlation](https://i.sstatic.net/Eb55JNZP.jpg)](https://i.sstatic.net/Eb55JNZP.jpg)

The black hole in M31 is much more massive at around $1.4\times 10^8 M\_\odot$ ([Bender et al. 2005](https://ui.adsabs.harvard.edu/abs/2005ApJ...631..280B/abstract)) and the bulge mass is a bit more massive - $3.3\times 10^{10}M\_\odot$ ([Blana Diaz et al. 2016](https://academic.oup.com/mnras/article/466/4/4279/2726589)). Looking at the diagram again, we see that the point (10.5, 8.15) is more or less right on the average trend.

**Edit:** Peter Erwin points out that the values I have cited for the bulge/spheroid mass are a factor 2 or so too big for the Milky Way and M31, or at least estimated in a way that is a factor of 2 too big to be directly compared with the Davis et al. plot I have shown. If so, then then the headline answer changes to: Yes, it is less massive than you might expect by a factor of a few, rather than a factor of ten and thus well within the observed scatter.

> **Comments:**
> **username_5**: "`Since the bulge contains relatively little dark matter compared with baryonic matter`"  Is dark matter not over-clustering in the center generally true, or just happens to be true with the Milkyway?  
> **username_3**: @JaminGrey In pretty much all galaxies (MW included), the baryonic matter is more concentrated than the dark matter. (Some lower-mass galaxies may still be dominated by dark matter, though.)  
> **username_3**: Note that the bulge masses used by Davis et al in those plots are $9.1 \times 10^{9} M_{\odot}$ for the MW and $1.3 \times 10^{10}M_{\odot}$ for M31, not the larger values you are using. Since they are deliberately trying to exclude the contribution of bars to their "bulge" mass estimates (I think they fail for the MW, so *their* value is probably an overstimate!), you should not be using those large values (dominated in both cases by bars) for comparison.  
> **username_3**: Admittedly, trying to figure out the "bulge mass" for the Milky Way is really tricky. But if you mean "pseudo-spherical region in the middle of a spiral galaxy or the bulk of an elliptical galaxy", then $2 \times 10^{10} \M_{\odot}$ is almost certainly a huge overestimate.  
> **username_2**: @JaminGrey baryonic matter is much more centrally concentrated than dark matter, so baryonic matter dominates within the radius of the bulge of a spiral galaxy.  
> **username_0**: This is a great answer, with additional thanks to Peter Erwin.  I'll wait until tomorrow to  accept as is recommended.  Thank you very much.  

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