<p>The gas clouds are much larger than you think: From Fig. 1 of the paper (<a href="https://arxiv.org/abs/1812.10733" rel="nofollow noreferrer">Takakawa 2019</a>), the largest cloud (which they call the "Balloon") is roughly 10 arcsec across. Now they can't actually measure its exact distance, but its projected distance from the Galactic center is only 7 pc, and the authors argue that it's at least 5 kpc away due to absorption from molecular gas which is known at this distance (<a href="http://adsabs.harvard.edu/abs/2006PASJ...58..335S" rel="nofollow noreferrer">Sofue 2006</a>), and since such hot and high density (<span class="math-container">$\sim 10^7\,\mathrm{cm}^{-3}$</span>) molecular gas is abundant in the Galactic center, it is probably located there, i.e. at a distance of <span class="math-container">$R=8\,\mathrm{kpc}$</span>.</p>

<p>The cloud's absolute size is thus
<span class="math-container">$$
D = 10'' \times 8\,\mathrm{kpc} = 80\,000\,\mathrm{AU} \simeq 0.4\,\mathrm{pc}.
$$</span></p>

<p>The mass is measured from dynamics, i.e. they measure the line-of-sight velocities of several clouds. These velocities depend both on the mass of the dynamical center (i.e. whatever object the clouds orbit), and on the total velocity of this object wrt. us. Since they only know the line-of-sight velocities and not the full, 3D motions, they cannot know with certainty the mass, but performing a chi-square fit of 3D models that fit the 2D observations, they determine the best-fit value of the mass to be <span class="math-container">$(3.2\pm0.6)\times10^4 M_\odot$</span>.</p>

<p>Their Fig. 4 shows the model:</p>

<p><a href="https://i.sstatic.net/nUpeP.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/nUpeP.png" alt="model"></a></p>

<p><sup>3D model of the motion of the clouds. The <em>red</em> cloud is the Balloon. Other observed clouds are shown in <em>green</em>, <em>blue</em>, and <em>orange</em> colors. The <em>black</em> dot indicates the position of the black hole. The actual observation is the 2D projection, seen in the bottom plane.</sup></p>

<p>The model of the velocities also gives the actual trajectories of the clouds around the central mass. Because the radius of the Balloon's orbit is <span class="math-container">$\sim0.07\,\mathrm{pc}$</span>, it means that this much mass must be concentrated within a region of maximum that size, and probably significantly smaller. This implies a density of <span class="math-container">$&gt;2\times10^8 M_\odot\,\mathrm{pc}^{-3}$</span>, at least an order of magnitude larger than even the most densely packed globular clusters, and since no luminous counterpart is observed at that location, the authors consider an intermediate-mass black hole as the most promising candidate for the gravitational source.</p>

CC BY-SA 4.0
2019-03-04T09:27:05.593Z
@uhoh I thought so, but that's still roughly 3 zeros to much :) Anyway, I'll remove that line.
pela
CC BY-SA 4.0
2019-03-04T09:38:48.183Z
Thanks, *looks great!* It turns out what I really wanted to but failed to ask was how they know the size of the central mass is smaller than the solar system. The third paragraph in block quote. Should I ask that as a separate question?
uhoh
CC BY-SA 4.0
2019-03-04T09:44:51.020Z
@uhoh I just made an edit where I quoted 0.07 pc (i.e. 15,000 AU) as the max size of the central mass. I see that in the phys.org article they write "much smaller than the Solar System", but I can't really see where they got that from. I suppose it's just their interpretation of "significantly smaller than 0.07 pc".
pela
CC BY-SA 4.0
2019-03-04T09:47:58.220Z
So, to recap: The cloud's orbit around the mass is 0.07 pc, and the whole system is 7 pc (i.e. ~20 lightyears) from the Galactic center.
pela
CC BY-SA 4.0
2019-03-04T10:18:16.650Z
@uhoh I added a bit of detail on how they got the (max) size of the central mass.
pela
CC BY-SA 4.0
2019-03-04T11:53:02.520Z
Okay thanks for all of this! The quote is all over the internet. I have found that [sciencedaily](https://www.sciencedaily.com/releases/2019/02/190228093614.htm) and [iflscience](https://www.iflscience.com/space/intermediatemass-black-hole-discovered-lurking-in-the-core-of-the-milky-way/) link back to the quote on an official NAO page [here](https://www.nao.ac.jp/en/news/science/2019/20190228-nro.html) *Takekawa explains, “Detailed kinematic analyses revealed that an enormous mass, 30,000 times that of the Sun, was concentrated in a region much smaller than our Solar System.”*
uhoh
CC BY-SA 4.0
2019-03-04T12:16:31.960Z
@uhoh Hmm okay, so it's not in the paper, but from an interview with Takekawa. Maybe they get constraints from their model that aren't explicitly written in the paper, e.g. that some of the clouds' trajectories have "recently" been even closer to the center of mass, but I don't see it reported in the paper. But of course, if indeed it _is_ a black hole, then its Schwarzschild radius is ~100,000 km, which is indeed "much smaller than the Solar System".
pela
CC BY-SA 4.0
2019-03-04T12:23:18.680Z
I'm going to go ahead and ask about the origin and veracity of this quote and the science behind its origin as a new, separate question. It may not be answerable right away, I'll think about how to word the question. I'm considering something like "What could the author have meant in the following quote..." Surely they would have run down a list of alternatives to a BH themselves, maybe even though about an unusually dense cluster, or an unusual grouping of very massive stars. I wonder if there is more written about this out there somewhere.
uhoh
CC BY-SA 4.0
2019-03-04T13:33:11.453Z
I've just asked [Why does the author believe that the central mass that gas cloud HCN-0.009-0.044 orbits is smaller than our solar system?](https://astronomy.stackexchange.com/q/29853/7982)
uhoh
CC BY-SA 4.0
2019-03-04T08:56:22.520Z
2019-03-04T10:17:34.740Z
2019-03-04T10:17:34.740Z
pela
<p>Phys.org's <a href="https://phys.org/news/2019-03-black-hole.html" rel="nofollow noreferrer">Hiding black hole found</a> says:</p>
<blockquote>
<p>A research team led by Shunya Takekawa at the National Astronomical Observatory of Japan noticed HCN-0.009-0.044, <strong>a gas cloud moving strangely near the center of the galaxy 25,000 light-years away from Earth in the constellation Sagittarius.</strong> They used ALMA (Atacama Large Millimeter/submillimeter Array) to perform high-resolution observations of the cloud and found that it is swirling around a massive invisible object.</p>
<p><strong>Takekawa says, &quot;Detailed kinematic analyses revealed that an enormous mass, 30,000 times that of the sun, was concentrated in a region much smaller than our solar system.</strong> This and the lack of any observed object at that location strongly suggests an intermediate-mass black hole. By analyzing other anomalous clouds, we hope to expose other quiet black holes.&quot;</p>
<p>Tomoharu Oka, a professor at Keio University and coleader of the team, adds, <strong>&quot;It is significant that this intermediate mass black hole was found only 20 light-years from the supermassive black hole at the galactic center.</strong> In the future, it will fall into the supermassive black hole, much like gas is currently falling into it. This supports the merger model of black hole growth.&quot;</p>
<p>These results were published as Takekawa et al. &quot;Indication of Another Intermediate-mass Black Hole in the Galactic Center&quot; in The Astrophysical Journal Letters on January 20, 2019.</p>
</blockquote>
<p>The paper <a href="https://iopscience.iop.org/article/10.3847/2041-8213/aafb07/meta" rel="nofollow noreferrer">Indication of Another Intermediate-mass Black Hole in the Galactic Center</a> (open access) is pretty hard to read as it details the careful analysis of ALMA data reduction and analysis.</p>
<p><strong>Question:</strong> How did the authors determine both the spatial size of gas cloud HCN-0.009-0.044 and the mass of the central object at the same time?</p>

CC BY-SA 4.0
2019-03-03T13:17:25.977Z
I wanted to use an `imaging` tag but it defaults to `photography`.
uhoh
<black-hole><radio-astronomy>
How did the authors determine both the spatial size of gas cloud HCN-0.009-0.044 and its central mass at the same time?
uhoh
# How did the authors determine both the spatial size of gas cloud HCN-0.009-0.044 and its central mass at the same time?

(Asked by: username_0 on 2019-03-03)

Phys.org's [Hiding black hole found](https://phys.org/news/2019-03-black-hole.html) says:

> A research team led by Shunya Takekawa at the National Astronomical Observatory of Japan noticed HCN-0.009-0.044, **a gas cloud moving strangely near the center of the galaxy 25,000 light-years away from Earth in the constellation Sagittarius.** They used ALMA (Atacama Large Millimeter/submillimeter Array) to perform high-resolution observations of the cloud and found that it is swirling around a massive invisible object.
>
> **Takekawa says, "Detailed kinematic analyses revealed that an enormous mass, 30,000 times that of the sun, was concentrated in a region much smaller than our solar system.** This and the lack of any observed object at that location strongly suggests an intermediate-mass black hole. By analyzing other anomalous clouds, we hope to expose other quiet black holes."
>
> Tomoharu Oka, a professor at Keio University and coleader of the team, adds, **"It is significant that this intermediate mass black hole was found only 20 light-years from the supermassive black hole at the galactic center.** In the future, it will fall into the supermassive black hole, much like gas is currently falling into it. This supports the merger model of black hole growth."
>
> These results were published as Takekawa et al. "Indication of Another Intermediate-mass Black Hole in the Galactic Center" in The Astrophysical Journal Letters on January 20, 2019.

The paper [Indication of Another Intermediate-mass Black Hole in the Galactic Center](https://iopscience.iop.org/article/10.3847/2041-8213/aafb07/meta) (open access) is pretty hard to read as it details the careful analysis of ALMA data reduction and analysis.

**Question:** How did the authors determine both the spatial size of gas cloud HCN-0.009-0.044 and the mass of the central object at the same time?

**Tags:** black-hole, radio-astronomy
> **Comments:**
> **username_0**: I wanted to use an `imaging` tag but it defaults to `photography`.  

---

## 1 answers

### Answer by username_1 on 2019-03-04. Score: 1 | Accepted answer

The gas clouds are much larger than you think: From Fig. 1 of the paper ([Takakawa 2019](https://arxiv.org/abs/1812.10733)), the largest cloud (which they call the "Balloon") is roughly 10 arcsec across. Now they can't actually measure its exact distance, but its projected distance from the Galactic center is only 7 pc, and the authors argue that it's at least 5 kpc away due to absorption from molecular gas which is known at this distance ([Sofue 2006](http://adsabs.harvard.edu/abs/2006PASJ...58..335S)), and since such hot and high density ($\sim 10^7\,\mathrm{cm}^{-3}$) molecular gas is abundant in the Galactic center, it is probably located there, i.e. at a distance of $R=8\,\mathrm{kpc}$.

The cloud's absolute size is thus
$$
D = 10'' \times 8\,\mathrm{kpc} = 80\,000\,\mathrm{AU} \simeq 0.4\,\mathrm{pc}.
$$

The mass is measured from dynamics, i.e. they measure the line-of-sight velocities of several clouds. These velocities depend both on the mass of the dynamical center (i.e. whatever object the clouds orbit), and on the total velocity of this object wrt. us. Since they only know the line-of-sight velocities and not the full, 3D motions, they cannot know with certainty the mass, but performing a chi-square fit of 3D models that fit the 2D observations, they determine the best-fit value of the mass to be $(3.2\pm0.6)\times10^4 M\_\odot$.

Their Fig. 4 shows the model:

[![model](https://i.sstatic.net/nUpeP.png)](https://i.sstatic.net/nUpeP.png)

3D model of the motion of the clouds. The *red* cloud is the Balloon. Other observed clouds are shown in *green*, *blue*, and *orange* colors. The *black* dot indicates the position of the black hole. The actual observation is the 2D projection, seen in the bottom plane.

The model of the velocities also gives the actual trajectories of the clouds around the central mass. Because the radius of the Balloon's orbit is $\sim0.07\,\mathrm{pc}$, it means that this much mass must be concentrated within a region of maximum that size, and probably significantly smaller. This implies a density of $>2\times10^8 M\_\odot\,\mathrm{pc}^{-3}$, at least an order of magnitude larger than even the most densely packed globular clusters, and since no luminous counterpart is observed at that location, the authors consider an intermediate-mass black hole as the most promising candidate for the gravitational source.

> **Comments:**
> **username_1**: @uhoh I thought so, but that's still roughly 3 zeros to much :) Anyway, I'll remove that line.  
> **username_0**: Thanks, *looks great!* It turns out what I really wanted to but failed to ask was how they know the size of the central mass is smaller than the solar system. The third paragraph in block quote. Should I ask that as a separate question?  
> **username_1**: @uhoh I just made an edit where I quoted 0.07 pc (i.e. 15,000 AU) as the max size of the central mass. I see that in the phys.org article they write "much smaller than the Solar System", but I can't really see where they got that from. I suppose it's just their interpretation of "significantly smaller than 0.07 pc".  
> **username_1**: So, to recap: The cloud's orbit around the mass is 0.07 pc, and the whole system is 7 pc (i.e. ~20 lightyears) from the Galactic center.  
> **username_1**: @uhoh I added a bit of detail on how they got the (max) size of the central mass.  
> **username_0**: Okay thanks for all of this! The quote is all over the internet. I have found that [sciencedaily](https://www.sciencedaily.com/releases/2019/02/190228093614.htm) and [iflscience](https://www.iflscience.com/space/intermediatemass-black-hole-discovered-lurking-in-the-core-of-the-milky-way/) link back to the quote on an official NAO page [here](https://www.nao.ac.jp/en/news/science/2019/20190228-nro.html) *Takekawa explains, “Detailed kinematic analyses revealed that an enormous mass, 30,000 times that of the Sun, was concentrated in a region much smaller than our Solar System.”*  
> **username_1**: @uhoh Hmm okay, so it's not in the paper, but from an interview with Takekawa. Maybe they get constraints from their model that aren't explicitly written in the paper, e.g. that some of the clouds' trajectories have "recently" been even closer to the center of mass, but I don't see it reported in the paper. But of course, if indeed it _is_ a black hole, then its Schwarzschild radius is ~100,000 km, which is indeed "much smaller than the Solar System".  
> **username_0**: I'm going to go ahead and ask about the origin and veracity of this quote and the science behind its origin as a new, separate question. It may not be answerable right away, I'll think about how to word the question. I'm considering something like "What could the author have meant in the following quote..." Surely they would have run down a list of alternatives to a BH themselves, maybe even though about an unusually dense cluster, or an unusual grouping of very massive stars. I wonder if there is more written about this out there somewhere.  
> **username_0**: I've just asked [Why does the author believe that the central mass that gas cloud HCN-0.009-0.044 orbits is smaller than our solar system?](https://astronomy.stackexchange.com/q/29853/7982)  

---

