Spectroscopic temperature determination of M-giant stars in the K-band

Abstract

Determining the effective temperature (Teff) of stars is fundamental to further study stellar populations. For cool M-giants this is a challenge due to their crowded optical spectra, caused by closely spaced absorption lines from molecular bands. These complicate existing spectroscopic methods, limiting observations to the near-infrared (NIR). This is further motivated by the fact that NIR wavelengths can penetrate dust-obscured regions such as the Galactic center, where M-giants can serve as important probes of stellar populations.

The project investigates whether the temperature-sensitive neutral scandium (Sc I) lines in the K-band can be used to determine Teff empirically. Due to its unique atomic structure, resulting in hyperfine splitting of energy levels and a metastable lower state, its spectral lines are especially strong. This combined with the lines' temperature sensitivity in the 3000–4000 K range makes them promising candidates for a spectroscopic thermometer. Nine Sc I lines in the 2.17–2.27 µm range were selected and their strength measured by the area under a Gaussian profile fitted to the lines. This was done for 44 M-giant stars provided by Nandakumar et al. (2023). Empirical calibration equations of the form Teff = a1 · area + a2 · [M/H] + a0 were derived for each line using two calibration sets, from Nandakumar et al. (2023) and APOGEE.

The resulting equations were tested against 19 stars from Thorsbro et al. (2020), and the calculated Teff agreed with the literature values within the uncertainty of ±150 K for most stars. Metallicity was found to have a small but noticeable effect on the line areas, corresponding to a Teff difference of 50–100 K per 0.5 dex in metallicity. The method provides a simple and practical tool for estimating Teff of M-giant stars from K-band spectra, with applications for large stellar surveys and studies of dust-obscured regions.

Popular Abstract

Have you ever wondered how astronomers can tell you so much about stars without ever touching them? You could try to touch a star, but you would burn yourself. Instead the answer lies in starlight. Although stars appear as simple points of light in the night sky, their light contains a detailed "barcode" of information. When this light is spread out into a spectrum, like a rainbow, it reveals dark lines where specific wavelengths are missing. These lines are caused by atoms and molecules in the stellar atmosphere that absorbs light at precise wavelengths depending on the element. Each star has a unique set of lines in its spectrum, which acts like a fingerprint. By studying these fingerprints, astronomers can determine several fundamental properties of stars, such as their temperature, surface gravity and chemical composition. The temperature is especially important, since it controls many physical processes inside a star, and hence reveals key information.

For stars like our Sun, this method performs very well. However, for cooler stars, such as the large and evolved red giants, their spectra become much more complex. Their atmospheres contain large amounts of molecules, which due to their complexity, make bands of closely spaced lines rather than single lines. This makes the spectra very cluttered in the visual wavelengths and very difficult to work with. It is like a barcode that has been smudged. To study these stars, you need to look at wavelengths not visible to the human eye, namely infrared, which contains much fewer molecular bands. Red giants are also particularly bright in the infrared due to their large size. In fact, some red giants are so large that they would extend beyond Earth's orbit around the Sun. Their enormous size makes them shine brightly, which makes them visible from large distances. It also makes them visible through large clouds of dust, which there is a lot of in the center of the Milky Way. Unlike visible light, infrared can pass right through this dust, revealing what lies behind. Even when we can see a star, measuring its temperature remains a challenge.

There are several existing infrared spectroscopic methods that are able to determine the temperature of a star. However, they all have their own limitations. Surprisingly, a new possible method may have arisen from something that once puzzled some astronomers. In 2018, researchers studying stars near the center of the Milky Way noticed unusually strong spectral lines of the element scandium. At first, the explanation for this was thought to be an anomalously high abundance of scandium, which would suggest a unique chemical evolution history of these stars. However, later studies show that this is not the case. Instead, the solution lies in the physics of the scandium atoms themselves. Additionally, it turns out that the strength of the scandium lines for red giants are very temperature sensitive in the temperature range 3000-4000 K. The combination of the specific atomic physics and this temperature sensitivity makes these scandium lines a promising candidate for a stellar thermometer.

The goal of this project is to explore this possibility. By observing a set of scandium lines in the near-infrared spectra of cool red giant stars, my aim is to determine whether the strength of the lines can be related reliably to the temperature of the star. This way I hope to develop a set of equations where you give me the line strength and I give you the temperature. If successful, this new method could provide a powerful tool for analyzing large numbers of cool stars, and help studying stars that would otherwise remain hidden.

• author: Lilliequist Palm, Kevin
• supervisor: Brian Thorsbro; Nils Ryde
• organization: Department of Physics; Astrophysics
• course: FYSK04 20261
• year: 2026
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• keywords: infrared spectroscopy, M-giant stars, effective temperature, scandium, hyperfine splitting
• report number: 2026-EXA261
• other publication id: 2026-EXA261
• language: English
• id: 9241341
• date added to LUP: 2026-06-19 17:44:34
• date last changed: 2026-06-19 17:46:45