<p><a href="https://arxiv.org/abs/2002.10463" rel="nofollow noreferrer">Betelgeuse Just Isn’t That Cool: Effective Temperature Alone Cannot Explain the Recent Dimming of Betelgeuse</a> suggests that the recent dimming might be caused by increased optical absorption by dust around the star, based on a spectral analysis. </p>

<p><strong>Question:</strong> The images below show absorption features assigned to titanium oxide (TiO) around Betelgeuse. Why are these features saw-tooth shaped? When I think of absorption edges the transmitted light <em>drops</em> when crossing from lower to higher energy photons, but here the measured light <em>increases</em> from lower to higher energy.</p>

<p><strong>note 1:</strong> A <a href="http://www.stsci.edu/~inr/ldwarf.html" rel="nofollow noreferrer">quick check</a> shows that these shapes are typical, so it's really just a matter of me not understanding why these features have the particular shapes that they do. </p>

<p><strong>note 2:</strong> There is some discussion of Betelgeuse's titanium lines in the second half of Scott Manley's <a href="https://youtu.be/mnE4RTk3MCU" rel="nofollow noreferrer">Astronomers Think They Know Why Betelgeuse Got Dimmer</a></p>

<p><a href="https://i.sstatic.net/qAMsp.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/qAMsp.png" alt="Fig. 1.— Optical spectrophotometry of Betelgeuse from 2020 (black) and 2004 (red)"></a></p>

<blockquote>
  <p>Fig. 1.— Optical spectrophotometry of Betelgeuse from 2020 (black) and 2004 (red).</p>
</blockquote>

<p><a href="https://i.sstatic.net/Fne1v.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Fne1v.png" alt="Fig. 2.— Normalized and continuum-flattened spectra of Betelgeuse from 2020 and 2004"></a></p>

<blockquote>
  <p>Fig. 2.— Normalized and continuum-flattened spectra of Betelgeuse from 2020 (black) and 2004
  (red dashed), illustrating the relative depths of the T<sub>eff</sub>-sensitive TiO bands (labeled) in both spectra. </p>
</blockquote>

CC BY-SA 4.0
2020-03-08T03:09:43.810Z
Currently unanswered: [Does the current “fainting” of Betelgeuse show any spectral trends that differ from it's normal variability?](https://astronomy.stackexchange.com/q/34545/7982) and also [Why do these photometric observations of Betelgeuse look “quantized” in 0.1 magnitude steps?](https://astronomy.stackexchange.com/q/34482/7982)
uhoh
CC BY-SA 4.0
2020-11-20T14:38:26.640Z
From the first look at 1D spectrum, it reminds me of when trace is not perfectly parallel to x or y axis and the periodic sawtooth shape like that can happen when you do integer approximation (because pixel is integer but trace can land at any continuous values) during the aperture extraction. This effect is mitigated by using larger aperture, or using interpolation to avoid integer approximation.
Kornpob Bhirombhakdi
CC BY-SA 4.0
2020-11-21T03:13:48.970Z
@KornpobBhirombhakdi that's an interesting thought, thanks! This is mostly unrelated, but is another example of an artificial texture in a distribution caused by rounding [Why did the distribution of asteroids discovered in 2010 have a radial modulation?](https://astronomy.stackexchange.com/q/25736/7982)
uhoh
CC BY-SA 4.0
2022-08-14T20:40:00.067Z
@PeterErwin well I was wrong, I did do it a third time!
uhoh
CC BY-SA 4.0
2022-08-15T19:46:54.280Z
I could be totally off base here, but maybe it’s the result of asymmetrical line broadening? Perhaps instead of increasing and then dropping like it appears to, the peak is the continuum, and up until that point it was being pulled down by the previous TiO line being broadened in just one direction. This would be inconsistent with figure two, so it’s definitely not the sole perpetrator here, but might play a role?
Justin T
CC BY-SA 4.0
2022-08-26T00:45:50.650Z
Just bumped into this, pertaining to the TiO bands being sawtooth shaped: https://britastro.org/observations/observation.php?id=20201216_234948_8cabda965bfe692f. See the last sentence of the second paragraph. Apparently due to rotation and vibration of TiO molecules in relatively cool stellar atmospheres. But I still do not know why the bands are sawtooth shaped.
Ed V
CC BY-SA 4.0
2022-08-26T01:04:48.503Z
I do not have a copy of the book, but maybe the answer is in Gerhard Herzberg’s classic text: Molecular Spectra and Molecular Structure: I. Spectra of Diatomic Molecules. (Krieger, 1989, ISBN 0-89464-268-5).
Ed V
CC BY-SA 4.0
2022-05-06T12:10:25.790Z
This sort of shape is typical of absorption/emission features of asymmetric diatomic molecules (e.g., CO, TiO); it has everything to do with the quantum mechanics of molecules and nothing to do with aperture extraction.
Peter Erwin
CC BY-SA 4.0
2022-05-09T21:08:59.513Z
@PeterErwin I've bountied this again, I don' think I'll do it a third time. I think you have some insight into this, if there's enough for even a partial answer that can shed some light on this shape, that would be most welcome!
uhoh
CC BY-SA 4.0
2023-02-01T19:45:02.600Z
Just found this paper: https://academic.oup.com/mnras/article/488/2/2836/5536948. Way beyond me, but the sawteeth are there!
Ed V
CC BY-SA 4.0
2023-02-01T21:20:09.183Z
@EdV That's a beautiful paper with a very nice looking sawtooth pattern reproduced, thanks! Yes I don't know what it is saying either. I think it's time for a new question post, now deciding between [Chemistry SE](https://chemistry.stackexchange.com/) and [Matter Modeling SE](https://mattermodeling.stackexchange.com/) and will probably choose the latter because your paper is the result of exactly the kin of modeling they talk about there.
uhoh
CC BY-SA 4.0
2023-02-01T22:25:20.313Z
This reminds me of an old joke. An experimentalist is puzzled by their spectrum on a sheet of paper (told you it was old), so they take the spectrum to a theorist and ask if the theorist can explain it. The theorist smiles and says it is easy. They then proceed to give a highly detailed explanation. Whereupon the experimentalist slaps their head and says “Whoops, the paper is upside down. Sorry!” Then they rotate the paper to proper orientation and give it back to the theorist, who then exclaims “That is even easier!”
Ed V
<spectroscopy><photometry><dust><astrochemistry><betelgeuse>
Why does titanium oxide around Betelgeuse produce this particular sawtooth-shaped absorption spectrum?
uhoh
# Why does titanium oxide around Betelgeuse produce this particular sawtooth-shaped absorption spectrum?

(Asked by: username_0 on 2020-03-08)

[Betelgeuse Just Isn’t That Cool: Effective Temperature Alone Cannot Explain the Recent Dimming of Betelgeuse](https://arxiv.org/abs/2002.10463) suggests that the recent dimming might be caused by increased optical absorption by dust around the star, based on a spectral analysis.

**Question:** The images below show absorption features assigned to titanium oxide (TiO) around Betelgeuse. Why are these features saw-tooth shaped? When I think of absorption edges the transmitted light *drops* when crossing from lower to higher energy photons, but here the measured light *increases* from lower to higher energy.

**note 1:** A [quick check](http://www.stsci.edu/~inr/ldwarf.html) shows that these shapes are typical, so it's really just a matter of me not understanding why these features have the particular shapes that they do.

**note 2:** There is some discussion of Betelgeuse's titanium lines in the second half of Scott Manley's [Astronomers Think They Know Why Betelgeuse Got Dimmer](https://youtu.be/mnE4RTk3MCU)

[![Fig. 1.— Optical spectrophotometry of Betelgeuse from 2020 (black) and 2004 (red)](https://i.sstatic.net/qAMsp.png)](https://i.sstatic.net/qAMsp.png)

> Fig. 1.— Optical spectrophotometry of Betelgeuse from 2020 (black) and 2004 (red).

[![Fig. 2.— Normalized and continuum-flattened spectra of Betelgeuse from 2020 and 2004](https://i.sstatic.net/Fne1v.png)](https://i.sstatic.net/Fne1v.png)

> Fig. 2.— Normalized and continuum-flattened spectra of Betelgeuse from 2020 (black) and 2004
> (red dashed), illustrating the relative depths of the Teff-sensitive TiO bands (labeled) in both spectra.

**Tags:** spectroscopy, photometry, dust, astrochemistry, betelgeuse

> **Comments:**
> **username_0**: Currently unanswered: [Does the current “fainting” of Betelgeuse show any spectral trends that differ from it's normal variability?](https://astronomy.stackexchange.com/q/34545/7982) and also [Why do these photometric observations of Betelgeuse look “quantized” in 0.1 magnitude steps?](https://astronomy.stackexchange.com/q/34482/7982)  
> **username_1**: From the first look at 1D spectrum, it reminds me of when trace is not perfectly parallel to x or y axis and the periodic sawtooth shape like that can happen when you do integer approximation (because pixel is integer but trace can land at any continuous values) during the aperture extraction. This effect is mitigated by using larger aperture, or using interpolation to avoid integer approximation.  
> **username_0**: @KornpobBhirombhakdi that's an interesting thought, thanks! This is mostly unrelated, but is another example of an artificial texture in a distribution caused by rounding [Why did the distribution of asteroids discovered in 2010 have a radial modulation?](https://astronomy.stackexchange.com/q/25736/7982)  
> **username_4**: This sort of shape is typical of absorption/emission features of asymmetric diatomic molecules (e.g., CO, TiO); it has everything to do with the quantum mechanics of molecules and nothing to do with aperture extraction.  
> **username_0**: @PeterErwin I've bountied this again, I don' think I'll do it a third time. I think you have some insight into this, if there's enough for even a partial answer that can shed some light on this shape, that would be most welcome!  
> **username_0**: @PeterErwin well I was wrong, I did do it a third time!  
> **username_2**: I could be totally off base here, but maybe it’s the result of asymmetrical line broadening? Perhaps instead of increasing and then dropping like it appears to, the peak is the continuum, and up until that point it was being pulled down by the previous TiO line being broadened in just one direction. This would be inconsistent with figure two, so it’s definitely not the sole perpetrator here, but might play a role?  
> **username_3**: Just bumped into this, pertaining to the TiO bands being sawtooth shaped: https://britastro.org/observations/observation.php?id=20201216_234948_8cabda965bfe692f. See the last sentence of the second paragraph. Apparently due to rotation and vibration of TiO molecules in relatively cool stellar atmospheres. But I still do not know why the bands are sawtooth shaped.  
> **username_3**: I do not have a copy of the book, but maybe the answer is in Gerhard Herzberg’s classic text: Molecular Spectra and Molecular Structure: I. Spectra of Diatomic Molecules. (Krieger, 1989, ISBN 0-89464-268-5).  
> **username_3**: Just found this paper: https://academic.oup.com/mnras/article/488/2/2836/5536948. Way beyond me, but the sawteeth are there!  
> **username_0**: @EdV That's a beautiful paper with a very nice looking sawtooth pattern reproduced, thanks! Yes I don't know what it is saying either. I think it's time for a new question post, now deciding between [Chemistry SE](https://chemistry.stackexchange.com/) and [Matter Modeling SE](https://mattermodeling.stackexchange.com/) and will probably choose the latter because your paper is the result of exactly the kin of modeling they talk about there.  
> **username_3**: This reminds me of an old joke. An experimentalist is puzzled by their spectrum on a sheet of paper (told you it was old), so they take the spectrum to a theorist and ask if the theorist can explain it. The theorist smiles and says it is easy. They then proceed to give a highly detailed explanation. Whereupon the experimentalist slaps their head and says “Whoops, the paper is upside down. Sorry!” Then they rotate the paper to proper orientation and give it back to the theorist, who then exclaims “That is even easier!”  

---

## 0 answers

