<blockquote>
<p>Do narrow lines in the spectra of O- and B- type stars always indicate magnetic fields?</p>
</blockquote>
<p>The narrow lines don't necessarily require a magnetic field, but any star that large will have one.</p>
<blockquote>
<p>I'm wondering two things:</p>
<ul>
<li>Has the presence of such comparatively narrow lines in the spectra of O- and B- type stars been observed in cases where there is no magnetic field present?</li>
</ul>
</blockquote>
<p><a href="https://en.wikipedia.org/wiki/O-type_main-sequence_star" rel="nofollow noreferrer">O-type main-sequence stars</a> have high metallicity, they will have a magnetic field. <a href="https://en.wikipedia.org/wiki/Tau_Scorpii" rel="nofollow noreferrer">Tau Scorpii</a> and <a href="https://en.wikipedia.org/wiki/Theta1_Orionis_C" rel="nofollow noreferrer">Theta<span class="math-container">$^1$</span> Orionis C</a> info at their links. The Phys.Org article: &quot;<a href="https://m.phys.org/news/2016-01-strong-magnetic-fields-majority-stars.html" rel="nofollow noreferrer">Strong magnetic fields discovered in majority of stars</a>&quot; says:</p>
<p>&quot;An international group of astronomers led by the University of Sydney has discovered strong magnetic fields are common in stars, not rare as previously thought, which will dramatically impact our understanding of how stars evolve.&quot;.</p>
<p>This Wikipedia article: &quot;<a href="https://en.wikipedia.org/wiki/Solar_dynamo" rel="nofollow noreferrer">Solar Dynamo</a>&quot; could use some citations, but here's what it says:</p>
<p>&quot;The solar dynamo is the physical process that generates the Sun's magnetic field. A dynamo, essentially a naturally occurring electric generator in the Sun's interior, produces electric currents and a magnetic field, following the laws of Ampère, Faraday and Ohm, as well as the laws of hydrodynamics, which together form the laws of magnetohydrodynamics. The detailed mechanism of the solar dynamo is not known and is the subject of current research.</p>
<p><strong>Mechanism</strong></p>
<p>A dynamo converts kinetic energy into electric-magnetic energy. An electrically conducting fluid with shear or more complicated motion, such as turbulence, can temporarily amplify a magnetic field through Lenz's law: fluid motion relative to a magnetic field induces electric currents in the fluid that distort the initial field. If the fluid motion is sufficiently complicated, it can sustain its own magnetic field, with advective fluid amplification essentially balancing diffusive or ohmic decay. Such systems are called self-sustaining dynamos. The Sun is a self-sustaining dynamo that converts convective motion and differential rotation within the Sun to electric-magnetic energy.</p>
<p>...&quot;.</p>
<blockquote>
<ul>
<li>If so, are there other mechanisms that could be responsible for this in cases without magnetic fields? I'm grasping at straws for ideas, like low collisional broadening.</li>
</ul>
</blockquote>
<p>Our Q&amp;A: &quot;<a href="https://physics.stackexchange.com/questions/257375/different-width-of-spectral-lines-for-different-groups-of-stars">Different width of spectral lines for different groups of stars</a>&quot; has <a href="https://physics.stackexchange.com/a/257471/170832">Rob Jefferies answer</a>.</p>
<p>This seems well explained in section 3.4 of &quot;<a href="https://arxiv.org/abs/1509.06482" rel="nofollow noreferrer">Magnetically Confined Wind Shocks in X-rays - a Review</a>&quot; (22 Sept 2015), by Asif ud-Doula and Yael Nazé, on page 10:</p>
<p>&quot;<strong>3.4. Structure of confined winds, as revealed by high-resolution spectra</strong></p>
<p>High-resolution spectra can yield a wealth of information. With current instrumentation, line widths and shifts can be evaluated with precisions down to a few tens km s<span class="math-container">$^{−1}$</span> in the most favorable cases (a few hundreds km s<span class="math-container">$^{−1}$</span> more typically). Furthermore, the comparison of lines from H-like and He-like ions and of components of <span class="math-container">$f ir$</span> triplets of He-like ions constrain the temperature and location of the emitting plasma. However, such measurements are currently only possible for the brightest X-ray sources, so that few magnetic massive stars have been investigated
in this respect (τ Sco - Mewe et al. 2003; Cohen et al. 2003, θ<span class="math-container">$^1\!$</span> Ori C - Schulz et al. 2000; Gagné et al. 2005a, b, HD 191612 - Nazé et al. 2007, HD 148937 - Nazé et al. 2008, 2012, β Cep - Favata et al. 2009, IQ Aur - Robrade and Schmitt 2011).</p>
<p>Within noise limitations, the X-ray lines of magnetic massive stars were found to be symmetric, and globally unshifted. This agrees well with MHD models. In the case of θ<span class="math-container">$^1\!$</span> Ori C, global fitting however suggests small variations in velocity (Gagné et al., 2005a): from −75 km s<span class="math-container">$^{−1}$</span> when the star is seen pole-on to about 100 km s<span class="math-container">$^{−1}$</span> when seen edge-on. This change needs to be confirmed as the errors are large but also because one cannot exclude a stochastic variation when only a single observation per phase is available. If further observations provide evidence that velocity varies with phase, then refinement of models will be needed, as no such changes are currently predicted (Gagné et al., 2005a).</p>
<p><strong>Reported widths of X-ray lines largely depend on object and ion considered. The narrowest widths, so far, were found for β Cep, whose lines are dominated by instrumental resolution, yielding only upper limit on intrinsic widths (&lt;600 km s<span class="math-container">$^{−1}$</span>, Favata et al., 2009). Larger widths, full width at half-maximum (FW HM) ∼ 600 − 800 km s<span class="math-container">$^{−1}$</span>, were reported for ions with high ionization potential (Mg, Si, S) in τ Sco, θ<span class="math-container">$^1\!$</span> Ori C, and HD 148937, three stars with more rapid winds than β Cep. Such widths are much smaller than observed for “normal” O-type stars (FW HM ∼ v∞), where lines arise in embedded wind shocks distributed all over the wind, hence cover a larger velocity range. They indicate formation in slowly moving plasma, in agreement with the confined winds scenario. However, most MHD models predict even narrower lines (Gagné et al., 2005a).</strong></p>
<p>Furthermore, lines from ions with lower ionization potential, notably oxygen, appear broader (FW HM ∼ 1800−2000 km s<span class="math-container">$^{−1}$</span> Gagné et al., 2005a; Nazé et al., 2007, 2008). These lines are associated with cooler plasma, which could have a different origin than hotter plasma. For example,
the dominant hot plasma in θ<span class="math-container">$^1\!$</span> Ori C is thought to arise in confined winds while the cooler one could arise in embedded wind shocks as in normal O-stars (Gagné et al., 2005a). This dual origin could be supported by the different temperatures derived from the different ions (Schulz et al., 2000). In <a href="https://arxiv.org/abs/1801.06152" rel="nofollow noreferrer">Of?p</a> stars, however, the spectra are dominated by the cooler component, i.e. confined winds emit soft X-rays in these objects (see above), but it cannot be excluded that current errors, which are large, are somewhat blurring the picture.</p>
<p>In He-like triplets, the forbidden line is suppressed when the density is high or the UV radiation is intense. In the case of massive stars, the latter effect is the most important one and, thanks to dilution with distance, enables us to locate the emitting region. In <strong>τ Sco</strong>, <strong>θ<span class="math-container">$^1\!$</span> Ori C</strong>, HD 148937, and <strong>β Cep</strong>, the start of the emitting region is found to be close to the photosphere, at radii r ∼ 1.5 − 3 R<span class="math-container">$_∗$</span> for the first three stars and r ∼ 4 − 6 R<span class="math-container">$_∗$</span> for the latter case. These values are only slightly lower than the corresponding <a href="https://en.wikipedia.org/wiki/Alfv%C3%A9n%27s_theorem" rel="nofollow noreferrer">Alfvén</a> radii of these stars, they thus appear qualitatively compatible with MHD simulations. In IQ Aur, the forbidden line was found to be normal, suggesting a formation radius larger than 7R<span class="math-container">$_∗$</span> (Robrade and Schmitt, 2011) - despite a large value, this also appears compatible with the supposed location of confined winds in this star.&quot;.</p>
<p>Other reading:</p>
<p>&quot;<a href="https://arxiv.org/abs/astro-ph/0606156" rel="nofollow noreferrer">The surprising magnetic topology of <span class="math-container">$\tau$</span> Sco: fossil remnant or dynamo output?</a>&quot; (7 Jun 2006), by JF Donati, ID Howarth, MM Jardine, P Petit, C Catala, JD Landstreet, JC Bouret, E Alecian, JR Barnes, T Forveille, F Paletou, and N Manset</p>
<p>&quot;<a href="https://arxiv.org/abs/astro-ph/0601623" rel="nofollow noreferrer">The magnetic field and confined wind of the O star θ<span class="math-container">$^{1\!}$</span> Orionis C</a>&quot; (26 Jan 2006), by G.A. Wade, A.W. Fullerton, J.-F. Donati, J.D. Landstreet, P. Petit, S. Strasser</p>
<p>&quot;<a href="http://adsabs.harvard.edu/full/2006IAUS..230...45M" rel="nofollow noreferrer">X-ray hardness ratios for stars of different spectral types</a>&quot; (2006), by Meurs, E. J. A., Casey, P., &amp; Norci, L.</p>
<p>Wikipedia - <a href="https://en.wikipedia.org/wiki/Zeeman_effect" rel="nofollow noreferrer">Zeeman Effect</a></p>
<p>&quot;<a href="http://adsabs.harvard.edu/full/1958ApJ...128..228B" rel="nofollow noreferrer">Magnetic Fields of the A-Type Stars</a>&quot; (30 Apr <strong>1958</strong>), by H. W. Babcock</p>

CC BY-SA 4.0
2018-06-13T05:28:13.173Z
Only a small fraction of O-type stars have magnetic fields (as ud-Doulda & Naze, which you cite early on, confirms!), perhaps 10-15%. Really, stars like $\theta^1$ Orionis C are in the minority (additional citation: I work with one of the coauthors of some of those papers you mention). That article stating that a large fraction of stars have magnetic fields applies only to red giants (coming from mid- to late- type main sequence stars), not stars of the early spectral types I'm interested in.
HDE 226868
CC BY-SA 4.0
2018-06-13T05:41:43.983Z
Take your time, definitely - it's not urgent for me to know, and I appreciate your work on it. But I think you might have misread it slightly; both the article and the paper state that the results only apply to stars "that have masses of about 1.5-2.0 times that of the Sun" - not greater than that. Again, though, no need to make edits right away, and thanks for spending time on this.
HDE 226868
CC BY-SA 4.0
2018-06-13T13:03:45.927Z
That figure was just off the top of my head, but I can point you to a number of sources detailing that the fraction is extremely low (e.g. measurement of [7%](https://arxiv.org/pdf/1411.3604.pdf) - see page 7). [Theory predicts that it should be very difficult for these fields to form](https://www2.hao.ucar.edu/sites/default/files/users/whawkins/Wed_Magnetic%20Fields%20in%20Early-Type%20Stars.pdf) in O-type stars due to turbulence, so it's not surprising that most of them don't have fields; it's surprising that a handful of them *do*.
HDE 226868
CC BY-SA 4.0
2018-06-13T13:40:00.973Z
Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/78824/discussion-between-hde-226868-and-rob).
HDE 226868
CC BY-SA 4.0
2018-06-13T05:03:34.300Z
2018-06-13T07:51:27.570Z
2020-06-17T09:47:40.653Z
Rob
<p>I was reading <a href="http://adsabs.harvard.edu/abs/2005ApJ...627..953W" rel="nofollow noreferrer">a paper</a> on the differential emission measures of a set of hot O- and B- type stars. As the authors discuss in Section 3 (page 959), two stars, <a href="https://en.wikipedia.org/wiki/Tau_Scorpii" rel="nofollow noreferrer">$\tau$ Sco</a> and <a href="https://en.wikipedia.org/wiki/Theta1_Orionis_C" rel="nofollow noreferrer">$\theta^1$ Ori C</a>, have narrow emission lines compared to other stars of the same spectral type. There is a good amount of evidence that both stars are young and have magnetic fields; the stellar winds travel along the field lines and collide at the magnetic equator, producing shocks and, indirectly, X-ray emission. This is in contrast to the mechanism behind shock formation in other O- and B- type stars, where shocks come from the line instability transition.</p>

<p>Now, the plasma at the magnetic equator is roughly stationary because of the collision; this means - if I'm interpreting things correctly - that there is little to no broadening of the lines, and so they are comparatively narrow. Other spectral characteristics and observations support this model.</p>

<p>I'm wondering two things:</p>

<ul>
<li>Has the presence of such comparatively narrow lines in the spectra of O- and B- type stars been observed in cases where there is no magnetic field present? Very few O-type stars have significant magnetic fields, and theory predicts that none should, so these stars are the few exceptions to the rule.</li>
<li>If so, are there other mechanisms that could be responsible for this in cases without magnetic fields? I'm grasping at straws for ideas, like low collisional broadening.</li>
</ul>

<hr>

<p>I talked with my advisor, and we briefly discussed colliding wind shocks (CWS), which form at the interface between the stellar winds in a binary system. It's thought that these shocks contribute only a small amount to the total X-ray production of the system (see <a href="http://adsabs.harvard.edu/abs/2011ApJS..194....5G" rel="nofollow noreferrer">Gagné et al. (2011)</a>), though, so any narrow lines produced in that plasma - if any exist - wouldn't have much influence over the measured spectra. So that seems to be ruled out.</p>

<star><magnetic-field><spectra><solar-wind><x-ray>
Do narrow lines in the spectra of O- and B- type stars always indicate magnetic fields?
HDE 226868
# Do narrow lines in the spectra of O- and B- type stars always indicate magnetic fields?

(Asked by: username_0 on 2018-06-04)

I was reading [a paper](http://adsabs.harvard.edu/abs/2005ApJ...627..953W) on the differential emission measures of a set of hot O- and B- type stars. As the authors discuss in Section 3 (page 959), two stars, [$\tau$ Sco](https://en.wikipedia.org/wiki/Tau_Scorpii) and [$\theta^1$ Ori C](https://en.wikipedia.org/wiki/Theta1_Orionis_C), have narrow emission lines compared to other stars of the same spectral type. There is a good amount of evidence that both stars are young and have magnetic fields; the stellar winds travel along the field lines and collide at the magnetic equator, producing shocks and, indirectly, X-ray emission. This is in contrast to the mechanism behind shock formation in other O- and B- type stars, where shocks come from the line instability transition.

Now, the plasma at the magnetic equator is roughly stationary because of the collision; this means - if I'm interpreting things correctly - that there is little to no broadening of the lines, and so they are comparatively narrow. Other spectral characteristics and observations support this model.

I'm wondering two things:

* Has the presence of such comparatively narrow lines in the spectra of O- and B- type stars been observed in cases where there is no magnetic field present? Very few O-type stars have significant magnetic fields, and theory predicts that none should, so these stars are the few exceptions to the rule.
* If so, are there other mechanisms that could be responsible for this in cases without magnetic fields? I'm grasping at straws for ideas, like low collisional broadening.

---

I talked with my advisor, and we briefly discussed colliding wind shocks (CWS), which form at the interface between the stellar winds in a binary system. It's thought that these shocks contribute only a small amount to the total X-ray production of the system (see [Gagné et al. (2011)](http://adsabs.harvard.edu/abs/2011ApJS..194....5G)), though, so any narrow lines produced in that plasma - if any exist - wouldn't have much influence over the measured spectra. So that seems to be ruled out.

**Tags:** star, magnetic-field, spectra, solar-wind, x-ray


---

## 1 answers

### Answer by username_1 on 2018-06-13. Score: -1

> Do narrow lines in the spectra of O- and B- type stars always indicate magnetic fields?

The narrow lines don't necessarily require a magnetic field, but any star that large will have one.

> I'm wondering two things:
>
> * Has the presence of such comparatively narrow lines in the spectra of O- and B- type stars been observed in cases where there is no magnetic field present?

[O-type main-sequence stars](https://en.wikipedia.org/wiki/O-type_main-sequence_star) have high metallicity, they will have a magnetic field. [Tau Scorpii](https://en.wikipedia.org/wiki/Tau_Scorpii) and [Theta$^1$ Orionis C](https://en.wikipedia.org/wiki/Theta1_Orionis_C) info at their links. The Phys.Org article: "[Strong magnetic fields discovered in majority of stars](https://m.phys.org/news/2016-01-strong-magnetic-fields-majority-stars.html)" says:

"An international group of astronomers led by the University of Sydney has discovered strong magnetic fields are common in stars, not rare as previously thought, which will dramatically impact our understanding of how stars evolve.".

This Wikipedia article: "[Solar Dynamo](https://en.wikipedia.org/wiki/Solar_dynamo)" could use some citations, but here's what it says:

"The solar dynamo is the physical process that generates the Sun's magnetic field. A dynamo, essentially a naturally occurring electric generator in the Sun's interior, produces electric currents and a magnetic field, following the laws of Ampère, Faraday and Ohm, as well as the laws of hydrodynamics, which together form the laws of magnetohydrodynamics. The detailed mechanism of the solar dynamo is not known and is the subject of current research.

**Mechanism**

A dynamo converts kinetic energy into electric-magnetic energy. An electrically conducting fluid with shear or more complicated motion, such as turbulence, can temporarily amplify a magnetic field through Lenz's law: fluid motion relative to a magnetic field induces electric currents in the fluid that distort the initial field. If the fluid motion is sufficiently complicated, it can sustain its own magnetic field, with advective fluid amplification essentially balancing diffusive or ohmic decay. Such systems are called self-sustaining dynamos. The Sun is a self-sustaining dynamo that converts convective motion and differential rotation within the Sun to electric-magnetic energy.

...".

> * If so, are there other mechanisms that could be responsible for this in cases without magnetic fields? I'm grasping at straws for ideas, like low collisional broadening.

Our Q&A: "[Different width of spectral lines for different groups of stars](https://physics.stackexchange.com/questions/257375/different-width-of-spectral-lines-for-different-groups-of-stars)" has [username_1 Jefferies answer](https://physics.stackexchange.com/a/257471/170832).

This seems well explained in section 3.4 of "[Magnetically Confined Wind Shocks in X-rays - a Review](https://arxiv.org/abs/1509.06482)" (22 Sept 2015), by Asif ud-Doula and Yael Nazé, on page 10:

"**3.4. Structure of confined winds, as revealed by high-resolution spectra**

High-resolution spectra can yield a wealth of information. With current instrumentation, line widths and shifts can be evaluated with precisions down to a few tens km s$^{−1}$ in the most favorable cases (a few hundreds km s$^{−1}$ more typically). Furthermore, the comparison of lines from H-like and He-like ions and of components of $f ir$ triplets of He-like ions constrain the temperature and location of the emitting plasma. However, such measurements are currently only possible for the brightest X-ray sources, so that few magnetic massive stars have been investigated
in this respect (τ Sco - Mewe et al. 2003; Cohen et al. 2003, θ$^1\!$ Ori C - Schulz et al. 2000; Gagné et al. 2005a, b, HD 191612 - Nazé et al. 2007, HD 148937 - Nazé et al. 2008, 2012, β Cep - Favata et al. 2009, IQ Aur - username_1rade and Schmitt 2011).

Within noise limitations, the X-ray lines of magnetic massive stars were found to be symmetric, and globally unshifted. This agrees well with MHD models. In the case of θ$^1\!$ Ori C, global fitting however suggests small variations in velocity (Gagné et al., 2005a): from −75 km s$^{−1}$ when the star is seen pole-on to about 100 km s$^{−1}$ when seen edge-on. This change needs to be confirmed as the errors are large but also because one cannot exclude a stochastic variation when only a single observation per phase is available. If further observations provide evidence that velocity varies with phase, then refinement of models will be needed, as no such changes are currently predicted (Gagné et al., 2005a).

**Reported widths of X-ray lines largely depend on object and ion considered. The narrowest widths, so far, were found for β Cep, whose lines are dominated by instrumental resolution, yielding only upper limit on intrinsic widths (<600 km s$^{−1}$, Favata et al., 2009). Larger widths, full width at half-maximum (FW HM) ∼ 600 − 800 km s$^{−1}$, were reported for ions with high ionization potential (Mg, Si, S) in τ Sco, θ$^1\!$ Ori C, and HD 148937, three stars with more rapid winds than β Cep. Such widths are much smaller than observed for “normal” O-type stars (FW HM ∼ v∞), where lines arise in embedded wind shocks distributed all over the wind, hence cover a larger velocity range. They indicate formation in slowly moving plasma, in agreement with the confined winds scenario. However, most MHD models predict even narrower lines (Gagné et al., 2005a).**

Furthermore, lines from ions with lower ionization potential, notably oxygen, appear broader (FW HM ∼ 1800−2000 km s$^{−1}$ Gagné et al., 2005a; Nazé et al., 2007, 2008). These lines are associated with cooler plasma, which could have a different origin than hotter plasma. For example,
the dominant hot plasma in θ$^1\!$ Ori C is thought to arise in confined winds while the cooler one could arise in embedded wind shocks as in normal O-stars (Gagné et al., 2005a). This dual origin could be supported by the different temperatures derived from the different ions (Schulz et al., 2000). In [Of?p](https://arxiv.org/abs/1801.06152) stars, however, the spectra are dominated by the cooler component, i.e. confined winds emit soft X-rays in these objects (see above), but it cannot be excluded that current errors, which are large, are somewhat blurring the picture.

In He-like triplets, the forbidden line is suppressed when the density is high or the UV radiation is intense. In the case of massive stars, the latter effect is the most important one and, thanks to dilution with distance, enables us to locate the emitting region. In **τ Sco**, **θ$^1\!$ Ori C**, HD 148937, and **β Cep**, the start of the emitting region is found to be close to the photosphere, at radii r ∼ 1.5 − 3 R$\_∗$ for the first three stars and r ∼ 4 − 6 R$\_∗$ for the latter case. These values are only slightly lower than the corresponding [Alfvén](https://en.wikipedia.org/wiki/Alfv%C3%A9n%27s_theorem) radii of these stars, they thus appear qualitatively compatible with MHD simulations. In IQ Aur, the forbidden line was found to be normal, suggesting a formation radius larger than 7R$\_∗$ (username_1rade and Schmitt, 2011) - despite a large value, this also appears compatible with the supposed location of confined winds in this star.".

Other reading:

"[The surprising magnetic topology of $\tau$ Sco: fossil remnant or dynamo output?](https://arxiv.org/abs/astro-ph/0606156)" (7 Jun 2006), by JF Donati, ID Howarth, MM Jardine, P Petit, C Catala, JD Landstreet, JC Bouret, E Alecian, JR Barnes, T Forveille, F Paletou, and N Manset

"[The magnetic field and confined wind of the O star θ$^{1\!}$ Orionis C](https://arxiv.org/abs/astro-ph/0601623)" (26 Jan 2006), by G.A. Wade, A.W. Fullerton, J.-F. Donati, J.D. Landstreet, P. Petit, S. Strasser

"[X-ray hardness ratios for stars of different spectral types](http://adsabs.harvard.edu/full/2006IAUS..230...45M)" (2006), by Meurs, E. J. A., Casey, P., & Norci, L.

Wikipedia - [Zeeman Effect](https://en.wikipedia.org/wiki/Zeeman_effect)

"[Magnetic Fields of the A-Type Stars](http://adsabs.harvard.edu/full/1958ApJ...128..228B)" (30 Apr **1958**), by H. W. Babcock

> **Comments:**
> **username_0**: Only a small fraction of O-type stars have magnetic fields (as ud-Doulda & Naze, which you cite early on, confirms!), perhaps 10-15%. Really, stars like $\theta^1$ Orionis C are in the minority (additional citation: I work with one of the coauthors of some of those papers you mention). That article stating that a large fraction of stars have magnetic fields applies only to red giants (coming from mid- to late- type main sequence stars), not stars of the early spectral types I'm interested in.  
> **username_0**: Take your time, definitely - it's not urgent for me to know, and I appreciate your work on it. But I think you might have misread it slightly; both the article and the paper state that the results only apply to stars "that have masses of about 1.5-2.0 times that of the Sun" - not greater than that. Again, though, no need to make edits right away, and thanks for spending time on this.  
> **username_0**: That figure was just off the top of my head, but I can point you to a number of sources detailing that the fraction is extremely low (e.g. measurement of [7%](https://arxiv.org/pdf/1411.3604.pdf) - see page 7). [Theory predicts that it should be very difficult for these fields to form](https://www2.hao.ucar.edu/sites/default/files/users/whawkins/Wed_Magnetic%20Fields%20in%20Early-Type%20Stars.pdf) in O-type stars due to turbulence, so it's not surprising that most of them don't have fields; it's surprising that a handful of them *do*.  
> **username_0**: Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/78824/discussion-between-hde-226868-and-rob).  

---

