# Low dispersion spectra of lunar impact flashes

Masahisa Yanagisawa, Yuki Uchida, Seiya Kurihara, Shinsuke Abe, Ryota Fuse, Satoshi Tanaka, Keisuke Onodera, Taichi Kawamura, Ryuhei Yamada

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Masahisa Yanagisawa, Yuki Uchida, Seiya Kurihara, Shinsuke Abe, Ryota Fuse, et al. Low dispersion spectra of lunar impact flashes. Icarus, 2025, 434, 10.1016/j.icarus.2025.116480. insu-05080885

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# Low dispersion spectra of lunar impact flashes

Masahisa Yanagisawa<sup>a,1,*</sup>, Yuki Uchida<sup>a</sup>, Seiya Kurihara<sup>a</sup>, Shinsuke Abe<sup>b</sup>, Ryota Fuse<sup>b</sup>, Satoshi Tanaka<sup>c</sup>, Keisuke Onodera<sup>d</sup>, Taichi Kawamura<sup>e</sup>, Ryuhei Yamada<sup>f</sup>

## ARTICLE INFO

### Keywords:

- Moon
- Impact flashes
- Spectroscopy
- Impact processes

## ABSTRACT

Lunar impact flashes are observed at collisions of meteoroids against the non-sunlit lunar surface. They appear suddenly and usually last only 0.1 s or less in visible light. Using our spectral video cameras, we made observations to obtain their low dispersion spectra from Oct. 2017 to Dec. 13, 2018. We detected five flashes confirmed by multiple site observations and eight unconfirmed flashes. The spectra of the confirmed flashes in the 400–800 nm wavelengths are continuous and red. The best-fitted single blackbody spectra to these spectra show temperatures of 2200–4000 K. The spectrum at the beginning of the brightest confirmed flash may show the optical radiation from the impact-generated vapor plume. The rapid cooling of the impact-generated fine droplets could explain the decrease in brightness and temperature between the subsequent two video frames. The temperature of this flash remained above 2300 K, even 80 ms (milliseconds) after the flash appearance, indicating the existence of coarse incandescent ejecta that cools slowly. This flash’s spectral evolution would show the following three processes of meteoroids’ impact phenomena on the moon: vapor plume generation, rapid cooling of fine droplets that would be later the lunar spherical glasses, and the ejection of incandescent coarse particles probably melt and solid particle aggregates.

## 1. Introduction

The lunar impact flashes by the high-velocity collisions of meteoroids on the lunar surface had been expected to exist, though no one knew how bright and frequent they were (Melosh et al., 1993; Ortiz et al., 1999). After several attempts to detect them (e.g., Ortiz et al., 1999), several flashes were observed and confirmed by multiple observers on Nov. 18, 1999 (UT) during the Leonid meteor activity (Dunham et al., 2000; Ortiz et al., 2000; see also Yanagisawa and Kisaichi, 2002). Flashes associated with the other meteoric showers and sporadic meteoroids were also observed thereafter (e.g., Yanagisawa et al., 2006; Ortiz et al., 2015; Ortiz et al., 2006).

An important purpose of observing the lunar impact flashes is to assess the meteoroid population larger than centimeters or decimeters in diameter. For this purpose, systematic observations started several years after the first confirmed detections (Suggs et al., 2014; Bonanos et al.,

2018). A routine monitoring program at NASA’s Marshall Space Flight Center recorded over a hundred lunar flashes during Sep. 2006–Aug. 2011, a relationship between meteoroids’ flux and kinetic energy was obtained (Fig. 9 in Suggs et al., 2014). NELIOTA campaign using the 1.2 m Kryoneri telescope in Greece (Xilouris et al., 2018) detected about two hundred flashes during Feb. 2017–Aug. 2023 and obtained the mass distribution of meteoroids (Liakos et al., 2024).

However, it should be noted that the luminous efficiency, the ratio of the observed luminous energy to the kinetic energy of a meteoroid used in almost all lunar impact flash studies, is not clearly understood nor established. Bellot Rubio et al. (2000a, 2000b) first derived the efficiency, $2 \times 10^{-3}$, by comparing the numbers of lunar impact flashes and terrestrial meteors during the 1999 Leonids shower. The uncertainty of the value is about an order of magnitude, as mentioned in the papers. Moser et al. (2010) obtained the efficiencies between (1.1–1.6) $\times 10^{-3}$ for the other meteor showers using NASA’s data and Bellot Rubio’s

<footnote><sup>a</sup> Department of Engineering Science, The University of Electro-Communications, Japan</footnote>

<footnote><sup>b</sup> Department of Aerospace Engineering, Nihon Univ., Japan</footnote>

<footnote><sup>c</sup> Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Japan</footnote>

<footnote><sup>d</sup> Earthquake Research Institute, The University of Tokyo, Japan</footnote>

<footnote><sup>e</sup> Institut de Physique du Globe de Paris, University of Paris Diderot, France</footnote>

<footnote><sup>f</sup> School of Computer Science and Engineering, The University of Aizu, Japan</footnote>

<footnote>* Corresponding author at: 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan.
E-mail addresses: yanagi@uec.ac.jp, yanagi.uec@gmail.com (M. Yanagisawa).</footnote>

<footnote n="1">¹ Present address: 5-37-6-202 Tsurumaki, Tama-shi, Tokyo 206-0034, Japan.</footnote>
procedure. The efficiencies derived by the two groups are consistent with each other. However, in Bellot Rubio's procedure, there is a significant uncertainty when one estimates the number of large meteoroids that cause lunar flashes from that of small meteoric particles.

There are limits to directly obtaining the efficiency from laboratory impact experiments because two-stage light-gas guns, usually used in high-velocity impact experiments, cannot accelerate projectiles more than 8 km s⁻¹, much slower than meteoroid velocities. Swift et al. (2010) conducted experiments investigating the efficiency using a lunar regolith simulant as targets and obtained the efficiencies between 10⁻⁷ and 10⁻⁴ at impact velocities less than 6 km s⁻¹. The results are useful for studying the velocity dependence of the efficiency. But, the luminous efficiency at meteoroidal impact velocities cannot be determined only from experimental data.

Swift et al. (2010) proposed a theoretical exponential luminous efficiency model to express the efficiency as a function of impact velocity. However, the theory is not comprehensive and is not widely accepted. Numerical simulations of the radiation from an impact-generated vapor plume were conducted and applied to the Leonids' lunar impact flashes in 1999 (e.g., Artemieva et al., 2000). However, the radiation from hot liquid and solid particles, which could contribute to the lunar impact flashes, is not included.

We do not know much about the efficiency yet. Is the value of (1–2) × 10⁻<fnref n="3" /> correct? Is it almost constant at velocities more than 10 km s⁻¹? How does it depend on the meteoroid densities? To answer these issues and obtain accurate efficiency values, we must study how a lunar impact flash radiates by observing each of them in detail.

Spectral information is useful for improving our knowledge of lunar impact flashes. However, no spectral observation was reported before 2021, though there were some observations in two or three photometric bands to obtain the temperature of the flashes (Avdellidou and Vau-baillon, 2019; Bonanos et al., 2018; Liakos et al., 2020, 2024; Madiedo et al., 2019a; Xilouris et al., 2018).

Yanagisawa and Kakinuma (2022a) made a simple spectral video camera and conducted the first observations between Oct. 2016 and May 2017. They obtained low dispersion spectra in visible and near-infrared wavelengths for nine flashes, though they were not confirmed by multiple observers.

Then, the Japan-France collaborative project, that is, the joint observation of meteoroids' impacts as lunar seismic sources (Yamada et al., 2011; Yamada et al., 2019) started, and an observation campaign was planned for the December Geminids activities in 2018. On Dec. 15, thirteen flashes were detected, and two or three observatories confirmed eleven. The spectral cameras obtained their spectra. Though the resolution of the spectra is relatively low, they appear continuous and red. Single blackbody spectra fitted to the observed spectra show temperatures of 2000–4000 K (Yanagisawa et al., 2021).

Here, we report the 13 spectra obtained in the project before Dec. 15, 2018. They also show continuous and red with temperatures between 2200 and 4000 K. We could obtain the temporal variation of the spectrum for 80 ms (6 video frames) for one of the flashes. We concentrate our discussion on this flash<fnref n="2" />.

## 2. Observations

We made observations sporadically when the fraction of the lunar disc illuminated by the Sun was less than 0.5. We used two spectral video cameras at the University of Electro-Communications (UEC) in Tokyo, Japan. One was attached to a Newtonian telescope with an aperture of 450 mm and a focal length of 2025 mm. The other was attached to a Schmidt-Cassegrain telescope with a focal reducer. The

telescope's aperture is 280 mm, and its effective focal length is 940 mm. From now on, we call the observation system with the 450 mm telescope "System1" and the other "System2."

We made each spectral camera by gluing a blazed-type grating on the cover glass of an image sensor. The converging light from the telescopes' primary mirrors directly enters the gratings, passes through them, and is focused on the image planes of the silicon sensor arrays. We do not apply collimators that make the converging light from the telescopes' primary mirrors into parallel light rays before the gratings. The no-collimator is not a standard way to use gratings, but it makes spectral images bright while reducing spectral resolutions. The cameras were operated in the 2 × 2 binning mode, and the spectral resolutions are about 48 and 53 nm pixel⁻¹ for System1 and System2, respectively. It is important to note that inter-frame durations are negligible, and the frame interval is almost the same as the exposure time of 16 or 20 ms. It should be noted that the camera in System2 was modified for spectral observations in late Dec. 2017. For details on the cameras, see Yanagisawa and Kakinuma (2022a).

Observations are also conducted at the Institute of Space and Astronautical Science (ISAS) / JAXA in Kanagawa-prefecture, Japan, and Nihon University (NU) in Chiba-prefecture, Japan. The ISAS group used a normal digital video camera attached to a telescope of 235 mm in aperture, and the NU group used a normal analog video camera and a telescope of 280 mm in aperture. The details of the locations and the instrumentation of the observing stations are shown in a table in Appendix A.

## 3. Results

### 3.1. Detection and confirmation of the flashes

The digital video data of the camera was recorded in the SER file format on a computer's hard disk during the observations made by System1 and System2 at UEC. After the observations each night, an application, "ser_scan," developed by us (Yanagisawa and Kakinuma, 2022b), scanned the data to find flashes. Thirteen flash candidates were detected by the spectral cameras on the un-illuminated lunar disk. The detection time and the location on the moon are shown in Table 1 and Fig. 1. The existence of both the zero-order and the spectral images discards the possibility of the cosmic-ray hit on image sensors or the electric noise of cameras. The most significant source of false-positive detections is the reflection of sunlight by artificial satellites or space debris (satellite glint). First, we examined whether cataloged satellites or space debris passed in front of the lunar disk accidentally. We examined the positions of about 16,000 satellites or space debris listed in the two-line element orbital datasets downloaded from Space-Track<fnref n="3" /> using an application, "StellaNavigator 10" by the Astro Arts company. We found no cataloged object that passed closer than 0.4 degrees from the lunar disc center within plus-minus 1 min of the flash-time for all the flashes except Flash 180718. Unfortunately, we do not have the dataset updated around 2018/07/18. Examining the cataloged objects may support the flashes as lunar phenomena.

However, the accuracy of the orbital data could not be accurate enough for some objects. Moreover, many more uncatalogued objects could cause the satellite glints. The best way to distinguish the lunar flashes from the satellite glints is by examining the videos obtained from at least two observatories separated far enough. Most human-made objects orbit in and below geosynchronous orbit. The distance to them from observatories is less than about 40,000 km, while the moon is about ten times far away. Therefore, their positions on the lunar disk differ between the observatories, while a lunar flash appears at the same position.

The observations at ISAS and NU are practical in discarding the

<footnote n="2">² The video of this flash (Flash 171124) is available as a raw SER format file and a converted AVI format file as supplemental files in the web version of this article. SER files can be viewed with some applications, e.g., SER Player.</footnote>

<footnote n="3">³ Space-Track: https://www.space-track.org/</footnote>
<table><caption>**Table 1**

Confirmed lunar impact flashes and their candidates<sup>a</sup>.</caption><thead><tr><th>Flash<sup>b</sup></th><th>confirmed by</th><th>Time<sup>c</sup> (UT)</th><th>latitude<sup>d</sup><br>[degree]</th><th>longitude<sup>d</sup><br>[degree]</th><th>number of frames<sup>e</sup></th><th>exposure<sup>f</sup><br>[ms]</th><th>gain<sup>f</sup><br>[dB]</th></tr></thead><tbody><tr><td>171026</td><td></td><td>09 h 04 m 38 s</td><td>-31</td><td>-43</td><td>1</td><td>20.0</td><td>40</td></tr><tr><td>171124</td><td>ISAS</td><td><strong>09 h 16 m 16 s</strong></td><td>-8</td><td>-26</td><td><strong>10</strong></td><td><strong>16.0</strong></td><td><strong>40</strong></td></tr><tr><td>171213a</td><td>ISAS</td><td><strong>20 h 11 m 20s</strong></td><td><strong>34</strong></td><td><strong>62</strong></td><td><strong>18</strong></td><td><strong>16.0</strong></td><td><strong>40</strong></td></tr><tr><td>171213b</td><td></td><td>20 h 46 m 02 s</td><td>-2</td><td>27</td><td>2</td><td>16.0</td><td>40</td></tr><tr><td>171222</td><td>ISAS, NU</td><td><strong>08 h 33 m 38 s</strong></td><td><strong>2</strong></td><td>-55</td><td><strong>16</strong></td><td><strong>20.0</strong></td><td><strong>40</strong></td></tr><tr><td>171225a</td><td></td><td>08 h 55 m 32 s</td><td>18</td><td>-61</td><td>3</td><td>16.0</td><td>40</td></tr><tr><td>171225b</td><td></td><td>09 h 19 m 19 s</td><td>-45</td><td>-76</td><td>3</td><td>16.0</td><td>40</td></tr><tr><td>180123<sup>h</sup></td><td>NU</td><td><strong>11 h 52 m 32 s</strong></td><td><strong>-69</strong></td><td><strong>-39</strong></td><td><strong>1</strong></td><td><strong>16.0</strong></td><td><strong>24</strong></td></tr><tr><td>180421<sup>h</sup></td><td>ISAS</td><td><strong>11 h 52 m 07 s</strong></td><td><strong>33</strong></td><td>-25</td><td><strong>2</strong></td><td><strong>16.0</strong></td><td><strong>24</strong></td></tr><tr><td>180422</td><td></td><td>10 h 41 m 27 s</td><td>-2</td><td>-67</td><td>1</td><td>16.0</td><td>40</td></tr><tr><td>180718</td><td></td><td>11 h 49 m 37 s</td><td>48</td><td>-35</td><td>2</td><td>16.0</td><td>40</td></tr><tr><td>181115</td><td></td><td>11 h 15 m 05 s</td><td>2</td><td>-27</td><td>1</td><td>16.0</td><td>40</td></tr><tr><td>181213<sup>i</sup></td><td></td><td>10 h 36 m 24 s</td><td>-48</td><td>-43</td><td>1</td><td>16.0</td><td>40</td></tr></tbody></table>

<sup>a</sup> The confirmed five flashes are shown in bold letters.

<sup>b</sup> Flashes are named after dates. A flash observed on Oct. 26, 2017 (UT) is named "171026."

<sup>c</sup> The times of detections. They are accurate to a second.

<sup>d</sup> Selenographic latitudes and east longitudes in degree. They are accurate to a degree except for the longitudes of Flash 171225b.

<sup>e</sup> The number of frames where each flash is recognized by visual inspection.

<sup>f</sup> The exposure time for a frame and the electrical gain of the cameras. The exposure time is almost equal to video frame intervals.

<sup>g</sup> Image blurring may reduce the number of frames.

<sup>h</sup> System2 observed these two flashes. System1 observed the others.

<sup>i</sup> This flash was observed by System1 in the non-binning mode. The others were observed in the 2 × 2 binning mode.

possibility of the satellite glints. Five flashes in Table 1 were detected at UEC, and simultaneously at ISAS, NU, or both. For these flashes, we calculated the parallax $\theta$ for a satellite 40,000 km away from UEC (Obs. 1 in Fig. 2). Obs. 2 in the figure represents ISAS or NU. Obs. 1 and Obs. 2 are approximated to be located on a flat ground plane because the distance between the observatories is 63 km at most. We know the vector $r_1$ by approximating that the directions of the satellite and the lunar disc center are the same. The vector $d$ is obtained from the latitudes and longitudes of the observatories. Then, we calculated $r_2 = r_1 - d$. By approximating that the directions to the moon seen from Obs. 2 and Obs. 1 are the same; that is, the direction is parallel to $r_1$, we derived $\theta$ the angle between $r_1$ and $r_2$. For the five flashes, $\theta$ distributed between 45 and 160 arcsec, corresponding to 2.5–9.1 % of the moon’s angular diameter. We examined the positions of the flash images on the lunar

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Locations of the five lunar impact flashes (solid symbols) and the eight candidates (open symbols). They are named after dates; e.g., one observed on Nov. 24, 2017 (UT) is named "171124." The dashed two rectangles show the field of view of our telescope-camera systems (the smaller one for System1 and the larger one for System2). The lunar image was obtained by using the Virtual Moon Atlas<sup>4</sup>.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Parallax $\theta$ for a satellite observed from two sites on the ground. The satellite is 40,000 km away from Obs. 1 (UEC).</figcaption></figure>

disk on the frames obtained by two observatories. They agree with the accuracy of one-hundredth of the lunar angular diameter. The possibility of satellite glints thus is discarded for these five flashes.

Flashes 171026, 171213b, and 181213 were undetected at ISAS or NU. They were probably too faint to be observed by the small telescopes at these stations with an aperture of less than 280 mm. Lunar monitorings were not made at ISAS nor NU for the five flashes (171225a, 171225b, 180422, 180718, and 181115). Therefore, although these eight flashes were not confirmed, they could also be actual lunar flashes. Hereafter, we denote the confirmed and unconfirmed flashes by "flashes."

The times at which the flashes appear are listed in Table 1. The clocks of the computers that stored video signals were adjusted manually, and the times were accurate to a second. The selenographic latitudes and longitudes of the flashes (Table 1) were determined from the flash positions in a video frame relative to prominent features (e.g., the bright Aristarchus region, the dark Grimaldi crater), which we could recognize on the night side of the moon illuminated by the Earth (Yanagisawa

<footnote n="4"><sup>4</sup> Virtual Moon Atlas: https://www.ap-i.net/avl/en/start/</footnote>
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Temporal variation of a spectral image of the confirmed Flash 171124. The time interval between these successive frames is 16 ms. The lunar background due to the Earthshine was subtracted from the images. The grayscale was adjusted in the same way for the three frames to show the images clearly. We show the position corresponding to some wavelengths (unit nm). The temporal shift of the spectral image to the longer wavelengths can be seen.</figcaption></figure>

et al., 2021; Yanagisawa and Kakinuma, 2022a).

## 3.2. Spectral analyses

As an example of the spectral images obtained by our cameras, we show the successive three images of the confirmed Flash 171124 in

**Fig. 3**, where the frame interval is 16 ms. The lunar background due to the Earthshine was subtracted from the images. The grayscale was adjusted similarly for the three images to show the images clearly. It should be noted that the original images were not saturated except for a pixel in the zero-order image in **Fig. 3b**. We flipped the original images horizontally to show the spectral image on the right side of the zero-order image and show the position corresponding to 400–800 nm in wavelength. The temporal shift of the spectral image to the longer wavelengths can be seen.

The spectral flux densities of a flash were obtained by comparing the spectral image of the flash with that of a comparison star. We approximated the spectrum of a comparison star to a blackbody spectrum at its effective temperature. The characteristics of the comparison star for each flash are listed in **Table 2**, where spectral types and magnitudes are obtained from SIMBAD<fnref n="5" />. For details on the derivation of the spectral flux densities, see Yanagisawa and Kakinuma (2022a) and Yanagisawa et al. (2021).

The spectral flux densities at the Earth without atmospheric absorption are shown in **Fig. 4**. These spectra are reliable between 400 nm and 800 nm in wavelengths. The analyses of the subsequent video frames are possible for four flashes, and we also show their spectra. We calculated the standard deviations of the temporally varying pixel values in background lunar images before and after each flash. The spatial average of the standard deviations was used to derive the 1-σ error bars shown in the figures. Error bars are not shown except for the 1st frame but are almost the same as for the 1st frame at the same wavelength. Here, “the 1st frame” means a video frame where a flash suddenly appears.

To evaluate the effect of atmospheric scintillation on the observed spectra, Yanagisawa and Kakinuma (2022a) examined the temporal variation of the spectrum of a star by System1. They found that the variation of the ratios of the spectral flux densities at some wavelength to another wavelength was 6% on average. However, it should be noted that the effect increases with the zenith angle of an observed object, and the degree of scintillation depends on the atmospheric condition, which varies daily. Therefore, 6% should be considered as a very rough estimate.

We fitted a blackbody spectrum, $a \times B(\lambda, T)$, to spectral flux densities plotted in **Fig. 4**, $\bar{F}_{\text{flash}}(\lambda_i)$ to minimize

$$ \chi^2 = \sum \frac{(\bar{F}_{\text{flash}}(\lambda_i) - a \times B(\lambda_i, T))^2}{\sigma_i^2} \quad (1) $$

where a and T (temperature) are free parameters. $B(\lambda, T)$ is the Planck function and $\sigma_i$ is the 1-σ error (a standard deviation) for each plot at a

<table><caption>**Table 2**
Comparison stars for deriving flash spectraª.</caption><thead><tr><th>Flashes</th><th>Tycho-2 Catalog No.</th><th>Spectral type</th><th>B-magnitude</th><th>V-magnitude</th><th>Effective temperature<sup>b</sup><br>/ K</th></tr></thead><tbody><tr><td>171026</td><td>6291-204-1</td><td>K1 III/IV</td><td>10.39</td><td>9.37</td><td>4806</td></tr><tr><td>171124</td><td>6333-2111-1</td><td>K0 III</td><td>7.62</td><td>6.56</td><td>4731</td></tr><tr><td>171213a,b</td><td>5554-1443-1</td><td>F5 V</td><td>8.31</td><td>7.82</td><td>6324</td></tr><tr><td>171222</td><td>6350-595-1</td><td>K1/2 III</td><td>11.10</td><td>9.75</td><td>4234</td></tr><tr><td>171225a,b</td><td>5258-491-1</td><td>G5 V</td><td>8.34</td><td>7.69</td><td>5717</td></tr><tr><td>180123</td><td>19-1437-1</td><td>A8 IV</td><td>6.32</td><td>6.07</td><td>7481</td></tr><tr><td>180421</td><td>1339-632-1</td><td>B8</td><td>7.64</td><td>7.73</td><td>11376</td></tr><tr><td>180422</td><td>1370-834-1</td><td>A0</td><td>8.28</td><td>8.20</td><td>8625</td></tr><tr><td>180718</td><td>4948-634-1</td><td>F3 V</td><td>10.29</td><td>9.94</td><td>6964</td></tr><tr><td>181115</td><td>6361-190-1</td><td>K1 III</td><td>9.90</td><td>8.83</td><td>4713</td></tr><tr><td>181213</td><td>5808-1420-1</td><td>F3/5 V</td><td>7.54</td><td>7.12</td><td>6632</td></tr></tbody></table>

<footnote>ª Spectral types and magnitudes are obtained from SIMBAD⁵.</footnote>

<footnote>ᵇ Effective temperatures are obtained from B-V color indexes according to Table 3 in Flower (1996).</footnote>

<footnote n="5">⁵ SIMBAD: http://simbad.u-strasbg.fr/simbad/</footnote>
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** The spectral flux densities at the Earth without atmospheric absorption of the five confirmed and eight unconfirmed lunar impact flashes. The flash names are shown in each plot area with bold letters for the confirmed ones. Smooth curves with their temperatures show blackbody spectra that best fit the plots in the non-shaded area. The exposure time and the frame interval of the camera are 16 ms, except for Flashes 171026 and 171222. They are 20 ms for the two flashes.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 4. (continued).</figcaption></figure>

wavelength $\lambda_i$. The plots in the reliable wavelength ranges were used in the fittings. The blackbody spectrum is drawn as a smooth line, and we show the blackbody temperature in each panel in Fig. 4.

For estimating the 1-σ errors in T, we searched for Ts, lower and higher temperatures, which increases $\chi^2$ by one. The actual temperature would be between the lower and the higher temperatures with 68.3 % confidence (Section 14.5 in Press et al., 1989). The temperatures with their 1-σ errors are listed in Table 3, and their temporal variations are shown in Fig. 5.

Blackbody spectra generally approximate the observed spectra well. Then, we can estimate the source areas that radiated the flashes on the lunar surface as described in Yanagisawa et al. (2021). Here, we define the source area as the cross-section perpendicular to the observers' line of sight. Table 3 shows the areas with 1-σ errors corresponding to the 1-σ temperature errors. The errors are significant as the radiation intensity from a blackbody's unit area strongly depends on its temperature. The spectral flux densities for the 1st frames could be underestimated because the flashes could start near the end of a camera's exposure duration. Then, the area for the 1st frames could also be underestimated.

### 3.3. Magnitudes

The magnitudes $m_{flash}$ were calculated according to the following formula for the V- and R-bands independently;

$$m_{flash} - m_{sun} = -2.5 \log_{10} \left[ \frac{\int \bar{F}_{flash}(\lambda)R(\lambda)d\lambda}{\int F_{sun}(\lambda)R(\lambda)d\lambda} \right] \quad (2)$$

where $m_{sun}$ is the solar magnitude; -26.8 and -27.3 for the V- and R-bands, respectively. $R(\lambda)$ is the response function for a band (Bessell, 2005). The integrals were calculated numerically. In the numerator in Eq. (2), we used the plot intervals in Fig. 4 as $d\lambda$. In the denominator, $F_{sun}(\lambda)$ denotes the solar spectral flux density approximated by a black-body spectrum at 5777 K whose bolometric flux is 1370 W m$^{-2}$ (the solar constant) and $d\lambda = 10$ nm. We did not truncate the integration at 800 nm for the R-magnitude calculations, though the reliability of the spectral flux densities is poor above the wavelength. The magnitudes are shown in Table 3. Errors (1-σ) in the magnitudes were calculated from the errors in the spectral flux densities (see Fig. 4).
<table><caption>**Table 3**
Temperatures and brightnesses of the lunar flashes and their candidates<sup>a</sup>.</caption><thead><tr><th>Flash</th><th>Blackbody temperature / K</th><th>V-magnitude</th><th>R-magnitude</th><th>Effective area of radiating source<sup>b</sup> / m<sup>2</sup></th></tr></thead><tbody><tr><td>171026</td><td>3800<sup>-900</sup><sub>-700</sub></td><td>10.2<sup>-0.2</sup><sub>+0.3</sub></td><td>9.3<sup>-0.2</sup><sub>+0.3</sub></td><td>0.19<sup>-0.14</sup><sub>+0.56</sub></td></tr><tr><td>171124<sup>c</sup></td><td>4000<sup>+100</sup><sub>-100</sub></td><td>8.1<sup>-0.0</sup><sub>+0.0</sub></td><td>7.2<sup>-0.0</sup><sub>+0.0</sub></td><td>1.1<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td></td><td>3100<sup>-100</sup><sub>-100</sub></td><td>8.0<sup>+0.0</sup><sub>-0.0</sub></td><td>6.8<sup>+0.0</sup><sub>-0.0</sub></td><td>7.8<sup>+1.2</sup><sub>-1.5</sub></td></tr><tr><td></td><td>2500<sup>+300</sup><sub>-300</sub></td><td>9.8<sup>-0.2</sup><sub>+0.2</sub></td><td>8.5<sup>+0.1</sup><sub>-0.1</sub></td><td>8.6<sup>+5.3</sup><sub>-16.4</sub></td></tr><tr><td></td><td>2300<sup>-400</sup><sub>-400</sub></td><td>11.0<sup>+0.5</sup><sub>+1.0</sub></td><td>8.8<sup>+0.2</sup><sub>-0.2</sub></td><td>9.7<sup>+39.4</sup><sub>-7.4</sub></td></tr><tr><td></td><td>2700<sup>+500</sup><sub>-500</sub></td><td>10.3<sup>+0.3</sup><sub>-0.4</sub></td><td>8.8<sup>+0.2</sup><sub>-0.2</sub></td><td>2.7<sup>+2.0</sup><sub>+8.1</sub></td></tr><tr><td></td><td>2800<sup>-400</sup><sub>-400</sub></td><td>10.3<sup>+0.4</sup><sub>-0.4</sub></td><td>8.7<sup>+0.2</sup><sub>-0.2</sub></td><td>2.1<sup>+1.4</sup><sub>+4.5</sub></td></tr><tr><td>171213a</td><td>3600<sup>+500</sup><sub>-400</sub></td><td>9.1<sup>-0.2</sup><sub>+0.2</sub></td><td>7.8<sup>+0.1</sup><sub>-0.1</sub></td><td>0.84<sup>+0.46</sup><sub>-1.06</sub></td></tr><tr><td>171213b</td><td>2500<sup>+500</sup><sub>-400</sub></td><td>10.9<sup>-0.4</sup><sub>+0.7</sub></td><td>9.1<sup>-0.2</sup><sub>+0.2</sub></td><td>4.6<sup>+3.7</sup><sub>-21.4</sub></td></tr><tr><td>171222</td><td>2800<sup>+100</sup><sub>-100</sub></td><td>9.0<sup>+0.1</sup><sub>-0.1</sub></td><td>7.6<sup>+0.1</sup><sub>-0.1</sub></td><td>7.7<sup>+2.5</sup><sub>-3.7</sub></td></tr><tr><td></td><td>2400<sup>+300</sup><sub>-200</sub></td><td>10.0<sup>+0.2</sup><sub>-0.2</sub></td><td>8.4<sup>+0.1</sup><sub>-0.1</sub></td><td>10<sup>+6</sup><sub>+15</sub></td></tr><tr><td></td><td>2500<sup>-400</sup><sub>-300</sub></td><td>10.4<sup>-0.3</sup><sub>+0.4</sub></td><td>8.8<sup>+0.1</sup><sub>-0.2</sub></td><td>5.6<sup>+3.9</sup><sub>-15.2</sub></td></tr><tr><td>171225a</td><td>4600<sup>-200</sup><sub>-200</sub></td><td>8.4<sup>+0.1</sup><sub>+0.1</sub></td><td>7.7<sup>+0.1</sup><sub>+0.1</sub></td><td>0.30<sup>+0.07</sup><sub>-0.09</sub></td></tr><tr><td></td><td>2400<sup>+700</sup><sub>-600</sub></td><td>11.1<sup>-0.4</sup><sub>+0.8</sub></td><td>9.6<sup>+0.3</sup><sub>-0.3</sub></td><td>3.2<sup>+2.8</sup><sub>-43.7</sub></td></tr><tr><td>171225b</td><td>4200<sup>+100</sup><sub>-100</sub></td><td>7.3<sup>-0.0</sup><sub>+0.0</sub></td><td>6.4<sup>+0.0</sup><sub>-0.0</sub></td><td>1.6<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td>180123</td><td>2200<sup>+300</sup><sub>-300</sub></td><td>8.7<sup>+0.2</sup><sub>-0.2</sub></td><td>7.4<sup>+0.1</sup><sub>-0.1</sub></td><td>57<sup>+40</sup><sub>-153</sub></td></tr><tr><td>180421</td><td>2200<sup>+500</sup><sub>-500</sub></td><td>8.7<sup>+0.4</sup><sub>+0.6</sub></td><td>7.4<sup>+0.3</sup><sub>+0.2</sub></td><td>76<sup>+65</sup><sub>-783</sub></td></tr><tr><td></td><td>2700<sup>+700</sup><sub>-600</sub></td><td>8.5<sup>+0.4</sup><sub>-0.6</sub></td><td>7.2<sup>+0.2</sup><sub>-0.3</sub></td><td>12<sup>+10</sup><sub>-76</sub></td></tr><tr><td>180422</td><td>3900<sup>+1000</sup><sub>-700</sub></td><td>9.6<sup>-0.2</sup><sub>+0.3</sub></td><td>8.4<sup>+0.2</sup><sub>-0.2</sub></td><td>0.27<sup>+0.20</sup><sub>+0.78</sub></td></tr><tr><td>180718</td><td>2400<sup>+600</sup><sub>-600</sub></td><td>11.5<sup>-0.8</sup><sub>+5.7</sub></td><td>9.3<sup>+0.2</sup><sub>-0.2</sub></td><td>4.9<sup>+3.9</sup><sub>-26.2</sub></td></tr><tr><td>181115</td><td>4400<sup>+1000</sup><sub>-700</sub></td><td>9.1<sup>+0.2</sup><sub>-0.2</sub></td><td>8.4<sup>+0.2</sup><sub>+0.3</sub></td><td>0.20<sup>+0.13</sup><sub>+0.36</sub></td></tr><tr><td>181213</td><td>3300<sup>+1100</sup><sub>-700</sub></td><td>10.5<sup>-0.4</sup><sub>+0.6</sub></td><td>9.2<sup>+0.3</sup><sub>-0.3</sub></td><td>0.45<sup>+0.38</sup><sub>-2.67</sub></td></tr></tbody></table>

a The confirmed five flashes are shown in bold letters.

b The cross-sectional area of a radiating source.

c Results for multiple successive frames are shown from top to bottom.

<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Time variations of the blackbody temperatures of the confirmed flashes. The temperature for a frame where a flash appears first (1st frame) is plotted at around zero in the horizontal axis. The variations are not obtained for subsequent frames in the two flashes plotted at –5 ms. The abscissa does not necessarily represent the time after the beginning of a flash, and there is an uncertainty of a frame interval.</figcaption></figure>

### 3.4. Impact energies, meteoroid masses, and crater diameters

For each observed spectral flux density in Fig. 4, we calculated the flux in the 400–800 nm wavelength range [W m⁻² in SI unit]. The flux multiplied by the exposure time is the luminous energy received per unit area at the Earth [J m⁻²] during the exposure of a video frame. We summed up the luminous energies for the frames, in which we could obtain the spectra, and obtained the total luminous energy received per unit area at the Earth [J m⁻²]. We assumed a flash is an isotropic radiation into 4π steradians at the moon and calculated the total luminous

<table><caption>**Table 4**
Meteoroid masses and impact crater diameters estimated for the lunar flashes and their candidates<sup>a</sup>.</caption><thead><tr><th>Flash</th><th>meteoroid source candidate and its probability<sup>b</sup></th><th>impact velocity<sup>c</sup> / km s<sup>-1</sup></th><th>impact angle<sup>d</sup> / degree</th><th>mass / g</th><th>crater diameter / m</th></tr></thead><tbody><tr><td>171026</td><td>ORI (66 %)</td><td>66</td><td>55</td><td>13</td><td>2.7</td></tr><tr><td>171124</td><td>NTA (59 %)</td><td>29</td><td>45</td><td>1100</td><td>6.1</td></tr><tr><td>171213a</td><td>GEM (93 %)</td><td>35</td><td>60</td><td>120</td><td>4.3</td></tr><tr><td>171213b</td><td>GEM (90 %)</td><td>35</td><td>35</td><td>35</td><td>2.6</td></tr><tr><td>171222</td><td>SPO</td><td>17<sup>e</sup></td><td>45<sup>e</sup></td><td>1300</td><td>4.9</td></tr><tr><td>171225a</td><td>SPO</td><td>17<sup>e</sup></td><td>45<sup>e</sup></td><td>710</td><td>4.1</td></tr><tr><td>171225b</td><td>SPO</td><td>17<sup>e</sup></td><td>45<sup>e</sup></td><td>2000</td><td>5.5</td></tr><tr><td>180123</td><td>SPO</td><td>17<sup>e</sup></td><td>45<sup>e</sup></td><td>800</td><td>4.2</td></tr><tr><td>180421</td><td>LYR (83 %)</td><td>49</td><td>62</td><td>150</td><td>5.2</td></tr><tr><td>180422</td><td>LYR (81 %)</td><td>49</td><td>20</td><td>34</td><td>2.5</td></tr><tr><td>180718</td><td>SPO</td><td>17<sup>e</sup></td><td>45<sup>e</sup></td><td>110</td><td>2.4</td></tr><tr><td>181115</td><td>SPO</td><td>17<sup>e</sup></td><td>45<sup>e</sup></td><td>310</td><td>3.2</td></tr><tr><td>181213</td><td>GEM (83 %)</td><td>35</td><td>31</td><td>32</td><td>2.5</td></tr></tbody></table>

a The confirmed five flashes are shown in bold letters.

b IAU meteor shower code (SPO denotes sporadic meteor). For the probabilities, see text.

c Geocentric velocities of meteoroids V<sub>∞</sub> in “List of Meteor Showers for Observation Session<sup>6</sup>.”

d The angles are measured from the local horizon on the lunar surface.

e The assumed impact velocity and angle for the sporadic meteoroids.

energy at the lunar surface [J]. The energy was divided by the luminous efficiency of lunar impact flashes (Bellot Rubio et al., 2000a, 2000b; Moser et al., 2010) to obtain the impact energy, that is, the kinetic energy of a meteoroid. We adopted 0.2 % as the efficiency.

Next, we calculated the flashes' probability of being associated with some meteor showers listed in the “List of Meteor Showers for Observation Session<sup>6</sup>” according to the formulae proposed by Madiedo et al. (2015, 2019b). If the probability is more than 50 % for a shower, we inferred that a meteoroid associated with it caused the flash and obtained the impact velocity and angle on the lunar surface (Table 4). Here, we neglected the acceleration and the deflection of the meteoroid motion by the lunar gravity. We inferred sporadic background meteoroids as the source for the flashes, for which we could not find such showers. We supposed that the orbital distribution is the same between the sporadic meteoroids and Near-Earth Objects (NEOs). A NEO orbital distribution model by Greenstreet et al. (2012) shows the average impact velocity onto the Earth, 20.6 km s⁻¹. Without the Earth's gravity acceleration, this velocity reduces to 17 km s⁻¹, and we adopted this value as the sporadic meteoroids' impact velocity onto the lunar surface. The impact angle was supposed to be 45°, the most probable angle of impact (Section 4.3 in a textbook by Melosh, 1989). For further descriptions of the probability calculation, see Appendix B.

We obtained meteoroid masses from the impact energies and velocities. Next, we estimate the crater diameters associated with the impact flashes. Although some sophisticated crater diameter scaling laws exist, we adopted an easy-to-use formula for lunar craters up to roughly 100 m in diameter in loose soil or regolith developed by Gault (1974). This formula is introduced in Section 7.8 in Melosh (1989). In the calculation, we used the bulk density of meteoroids in Babadzhanov and Kokhirova (2009) and lunar regolith density of 1.6 × 10³ kg m⁻³ (McKay et al., 1991). It should be noted that the diameters in Table 4 are at the level of the pre-existing lunar surface and are called “apparent diameters.”

<footnote n="6">⁶ IMO's List of Meteor Showers for Observation Session: https://www.imo.net/members/imo_showers/working_shower_list/</footnote>
# 4. Discussion

## 4.1. Spectra recorded in the 1st video frames

The spectra of the five confirmed flashes shown in Fig. 4 are continuous and increase monotonically with wavelengths. This spectral feature leads to the blackbody temperatures of 2200–4000 K, lower than the Sun’s surface temperature (Table 3). The spectra of the eight unconfirmed flashes are much noisier but show the same tendency. The confirmed eleven Geminid flashes also show continuous and red spectra except one (M-flash in Yanagisawa et al., 2021).

Overall, the temperatures derived from the spectra and brightnesses decrease with time when flashes are observed in successive video frames (Yanagisawa et al., 2021). The temperatures obtained from the color index by the almost-simultaneous observation at the R- and I-bands in the lunar monitoring project NELIOTA (Xilouris et al., 2018) also generally decrease with time (Avdellidou and Vaubaillon, 2019; Bonanos et al., 2018; Liakos et al., 2020, 2024). The incandescent ejecta generated by an impact would be the primary source of the flashes, and their cooling would decrease the brightness.

The temperature would decrease rapidly in the early phase of a flash, with the time constant much shorter than the video exposure time (e.g., 16 ms). If a flash begins, e.g., 1 ms before the end of a video exposure (late beginning in an exposure, Fig. 6b), the spectrum obtained from the 1st video frame shows high temperature, though its recorded brightness may be low. On the other hand, if it begins near the start of an exposure

<figure><img src="image_10.png" /><figcaption>**Fig. 6.** (a) The spectral evolution of Flash 171124. The smooth, solid red line shows a blackbody spectrum best fitted to the plots in the 600–800 nm wavelength range of the 1st frame. (b) A possible timing of the beginning of Flash 171124 relative to our video camera’s exposures. Because of the late beginning in the 1st frame exposure, the vapor cloud spectrum is more prominent than the case of the early beginning in an exposure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

(early beginning in an exposure), it appears bright in the 1st frame because of the light accumulation over 16 ms. However, the spectrum average of over 16 ms would show the temperature lower than the case of the late beginning.

The decrease in temperature and the increase in brightness between the 1st and 2nd frames for Flash 171124 (Table 3, Fig. 4b) indicate the late beginning case (Fig. 6b), whereas the decrease of both the temperature and brightness for Flash 171222 could show the early beginning case. For a confirmed Flash 180421, the temperature and brightness do not change significantly between the two frames. The significant errors prevent how to interpret its temperature and brightness evolution.

If only the incandescent ejecta were the source of the flashes, the temperature would not exceed the evaporation temperatures of major lunar minerals of 3800 K (feldspars and pyroxenes, Table II in Ahrens and O’Keefe, 1972; Tabel 1 in Cintala, 1992), because the evaporation would act as a buffer against further increases in flash temperatures. Nevertheless, the 1st frames of some flashes in Table 3 show temperatures exceeding 3800 K.

A higher temperature of 5700 K was reported for a confirmed flash by examining the R (red)-, G (green)-, and B (blue)-images recorded by a

<figure><img src="image_11.png" /><figcaption>**Fig. 7.** (a) Early stage of an impact cratering. The radiation from the expanding vapor plume would be a source of a lunar impact flash. If the plume is optically thin, many line spectra from the constituent of the vapor, e.g., Fe, would be radiated. If it is optically thick, it radiates as a blackbody. The duration of this stage would be less than 1 ms for the flashes reported in this paper. This figure is modified from Fig. 5.6 in a textbook (Melosh, 1989). (b) Early excavation stage. Melted fine droplets less than 3800 K in temperature would be the primary source of the flashes. (c) Later excavation stage. After the fine droplets get cold, coarse particles would be the primary source.</figcaption></figure>
color video camera (Madiedo et al., 2019a). Unfortunately, its temperature is not reported for the subsequent video frames because of the low sensitivity of their color observation system, e.g., the telescope aperture is only 10 cm. Its brightness of 4.2 in V-magnitude, duration of 0.28 s observed by the other telescopes, and the expected meteoroid mass of 45 kg show that it is one of the most significant impacts observed thus far as the lunar flashes. In such a significant impact, an impact-generated vapor plume (or vapor cloud, see Fig. 7a) may be optically thick, and the plume hotter than the evaporation temperatures may radiate approximately as a single blackbody. However, Fuse et al. (2020) revealed that vapor plumes radiate about a thousand times less efficiently than ejecta in their laboratory experiments using quartz sand targets and polycarbonate projectiles. Though the contribution of the vapor plume radiation would be more intense at higher impact velocities than their laboratory impacts at 6.5 km s⁻¹, the radiation from ejecta, recorded in a video frame with the vapor plume radiation, would not be ignored. Therefore, it is natural to think that both the hot vapor and the ejecta less than 3800 K in temperature could be the source of the flash. Combining the two sources of different temperatures may lead to the 5700 K. The assumption of a single blackbody spectrum would not be appropriate in the analyses for the 1st frames. It is thus better to consider the 1st frame temperatures as “apparent temperatures.”

Even if the vapor plume is optically thin, adding emission lines from the plume to an ejecta’s blackbody spectrum may lead to high apparent temperature when we fit a single blackbody spectrum to the observed spectrum. Terrestrial meteors show many lines and band spectra of Fe and Mg, significant meteoroid and lunar material elements, in the shorter wavelength range of 400–600 nm (Espartero et al., 2018; Koten et al., 2019). Though our cameras’ spectral resolution is too low to identify these lines and bands, their addition to a blackbody spectrum of ejecta increases the spectral flux densities in the wavelength range. It could lead to a high temperature exceeding the evaporation temperature of 3800 K.

In Fig. 6a, a blackbody spectrum best fitted to the plots in the 600–800 nm wavelength range is shown for the 1st frame of Flash 171124. The observed spectrum may consist of this 3000 K blackbody spectrum and the flux excess in the 400–600 nm range. The excess could be the contribution of a vapor plume. In the 400–800 nm range, the excess is 7 % of the sum of the 1st and 2nd frames’ observed fluxes. Therefore, the excess would not appear as prominent as our observations if the flash began at the start of the 1st frame’s exposure. The excess is 5 % of the sum of the 1st–6th frames’ observed fluxes. The vapor plume’s contribution to the flash could be much more significant than expected from the laboratory impact experiments (Fuse et al., 2020). It should be noted that some 1st frames’ spectra of the Geminids lunar impact flashes in 2018 also indicate that the spectra could consist of low-temperature components of about 2000 K and high-temperature components of about 6000 K (Yanagisawa et al., 2021).

Much higher temperatures exceeding 7000 K were reported by analyzing the NELIOTA data (e.g., Avdellidou et al., 2021; Liakos et al., 2024). The NELIOTA temperatures would not be affected by the possible excess in 400–600 nm because they were derived from the observations in the longer wavelengths, i.e., the effective wavelengths of the R- and I-bands are 640 nm and 800 nm (Bessell, 2005). However, because of the imperfect synchronization between the R- and I-bands exposure of up to 6 ms (Liakos et al., 2024), the R-band camera could preferentially get more flash-light than the I-band camera, as shown in Fig. 8. Then, the R-I index could inappropriately show the color bluer than in reality, and lead to the high temperature.

## 4.2. Spectra recorded in the subsequent video frames

We could obtain the spectra for multiple frames in the four flashes (Fig. 4). The spectra after the 1st frames are well approximated by single blackbody spectra and show temperatures less than 3200 K (Table 3). They are less than 2800 K for the 2018 Geminids flashes (Yanagisawa

<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Imperfect synchronization between the R- and I-bands exposure of the NELIOTA camera system. The exposure time of the cameras is 23 ms, followed by a readout time of 10 ms. The synchronization accuracy between the R- and I-band cameras is 6 ms. The time constant of the brightness variation of the flashes at their beginning is shorter than 10 ms. Therefore, if the I-band exposure lags behind the R-band exposure, as is depicted in this figure, the R-band camera gets more light than the I-band camera, and the underestimated R-I index value leads to an apparent high temperature. The time constant in the subsequent stage of the flashes would be longer, and the temperatures derived for the 2nd and 3rd video frames would be more reliable.</figcaption></figure>

et al., 2021).

The time constant of the brightness and temperature variations would be longer in the subsequent frames than in the 1st frame. Therefore, the temperatures derived from the NELIOTA observations would be more accurate for the subsequent frames than the 1st frame. The temperatures in the subsequent frames derived by Avdellidou and Vaubaillon (2019) are less than 2800 K. They are less than 3200 K in Liakos et al. (2020, 2024).

These temperatures are less than the approximate evaporation temperatures of silicate minerals (Table II in Ahrens and O’Keefe, 1972). In the subsequent frames, the emission from the vapor would be negligible, and the source of the flashes must be the thermal radiation from the melt or solid particles ejected by meteoroid impacts (Fig. 7b, c). To estimate the ejecta particle size, we made two ejecta cooling models and fit them to the spectral evolution of Flash 171124.

In our single-size model, the particles are spheres of the same diameter and initial temperature. Here, the time zero is defined as the beginning of the 2nd frame exposure. The temperature is uniform inside each particle, which cools by the blackbody radiation from the surface. In this case, the temperature as a function of time has been analytically obtained (Eq. (14) in Bouley et al., 2012). We calculated the temperature evolution with the fixed parameters: the density of 2.4 × 10³ kg m⁻³ and

<table><caption>**Table 5**

Parameters of ejecta cooling models that best fit the spectral evolution of Flash 171124.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">single-size model</th><th colspan="2">dual-size model</th></tr><tr><th>fine particles</th><th>coarse particles</th></tr></thead><tbody><tr><td>diameter [mm]</td><td>0.22</td><td>0.063</td><td>2.2</td></tr><tr><td>initial temperature [K]</td><td>3300</td><td>3700</td><td>2700</td></tr><tr><td>total volume [m³]</td><td>1.2 × 10<sup>-3</sup></td><td>4.2 × 10<sup>-4</sup></td><td>6.4 × 10<sup>-3</sup></td></tr></tbody></table>
<figure><img src="image_13.png" /><figcaption>**Fig. 9.** (a) Light-curve of Flash 171124. The ordinate shows the energy flux obtained by integrating the spectral flux densities in Fig. 4b over the wavelength between 400 nm and 800 nm. (b) Time variation of the blackbody temperature of the flash. Time variations of the flux and temperature for the two ejecta cooling models described in the text are also shown by smooth curves. In the single-size model, the diameter of the spherical particle is 0.22 mm. In the dual-size model, the diameters are 0.063 mm and 2.2 mm.</figcaption></figure>

the specific heat capacity of $1.3 \times 10^3 \text{ J kg}^{-1} \text{ K}^{-1}$. The diameter and the initial temperature are free parameters. While we calculated the temperature evolution, we obtained the spectral flux density observed at the Earth as a function of time by setting the third free parameter, the total volume of ejecta.

We searched for values of the three free parameters as the time-evolved spectral flux densities of the model best fit the observed time-evolved spectral flux densities, specifically, 10 plots in the 2nd spectrum and 11 plots in each of the 3rd through 6th spectra in Fig. 4b. For the fitting, we used the Solver tool in Microsoft Excel. The results are shown in Table 5. The temperature evolution is shown by a dotted line in Fig. 9b. For the flux in the wavelength range of 400–800 nm, the light curve calculated from the model is shown by a dotted line in Fig. 9a. The particle must be small to reproduce the rapid decrease of the temperature and brightness between the 2nd and 3rd frames. On the other hand, the fine particle cannot reproduce the nearly constant temperature and brightness between the 3rd and 6th frames. Therefore, the fitting is not satisfactory, as seen in Fig. 9.

In our dual-size model, we added particles of another size. We

searched for the values of the six free parameters as the time-evolved spectral flux density best fits the 2nd to 6th spectra in Fig. 4b. The results are shown in Table 5. It should be noted that Bouley et al. (2012) noticed the particle diameter to be less than 1 mm when applying the uniform temperature model. Our coarse particles may be too large for their cooling to be accurately calculated. Nevertheless, the dual-size model reproduces the observed spectral evolution better than the single-size model (Fig. 9) and suggests the existence of the coarse particles, the total volume of which is about an order of magnitude larger than the fine particles (Table 5).

The size of the fine particles is typical in impact glasses in the lunar regolith samples (McKay et al., 1991). We must observe incandescent melted droplets, which are later the lunar impact glasses, in the 1st and 2nd frames of Flash 171124. On the other hand, the glass particles of the size of our coarse particles are rare in the lunar regolith (McKay et al., 1991). This disagreement could be due to simplifying the size-frequency distribution of ejected particles by two sizes. Nevertheless, the coarse particles in our model suggest the existence of radiating materials that cool slowly with low initial temperatures. The coarse particles may substitute the melt and solid particle aggregates that cool slowly. Such aggregates are common in the lunar regolith (McKay et al., 1991).

The other flashes we observed do not permit us to examine the spectral evolution in detail due to our systems' low sensitivity for the spectral image (Yanagisawa and Kakinuma, 2022a). Besides, some of the flashes observed by NELIOTA show temperatures that did not decrease clearly for more than 100 ms (Avdellidou and Vaubaillon, 2019; Liakos et al., 2020, 2024). The spectral evolution of these flashes could be similar to that of Flash 171124.

## 5. Conclusions

Two simple spectral cameras at UEC recorded 13 lunar impact flashes between 6.4 and 9.3 in R-magnitude from Oct. 2017 to Dec. 13, 2018. Simultaneous observations at ISAS and NU discriminate lunar flashes from satellites' glints and confirmed 5 of them. We derived their low-dispersion spectra of about 50 nm in spectral resolution with a 16 or 20 ms time resolution. Their spectra at wavelengths between 400 nm and 800 nm are continuous and red. Best-fitted single blackbody spectra show temperatures of about 2200–4000 K for the confirmed flashes. These temperatures are almost concordant with the results obtained previously by our spectral observations and obtained from multi-wavelength-band observations.

We could obtain the spectral evolution for six successive video frames for Flash 171124. Because of the probable exposure timing shown in Fig. 6b, the 1st frame spectrum could show the radiation from the vapor plume with that from the fine melted droplets. The droplets would be the primary source in the 2nd frame (Fig. 7b). The temperature and brightness decrease significantly between the 2nd and 3rd frames. Our dual-size cooling model suggests the rapid decrease is due to the cooling of the incandescent fine particles of about 60 µm in diameter. These particles would be later the lunar glasses.

The fine particles cool so rapidly (Fig. 7c) that they cannot be the source of the afterglow of about 2600 K in the 3rd–6th frames. The radiation source must cool more slowly than the fine particles. In our model, coarse particles of 2 mm in diameter with a lower initial temperature than the fine particles represent the source of the afterglow. However, the lunar glass of this size is rare in the lunar regolith. They may be the melt and solid particle aggregates that cool slowly in reality.

These three phases of radiation could be observed more effectively if the camera's framing rate and sensitivity were higher than our systems. If these phases are observed for many flashes during meteor shower activity, e.g., Geminids, we could investigate how the partition of radiation energies among the phases depends on flash brightness and impact angle. We may derive the size-frequency distribution of ejected particles with their initial temperatures. This knowledge must help us obtain accurate values of the luminous efficiency.
### CRediT authorship contribution statement

Masahisa Yanagisawa: Writing – original draft, Formal analysis.
Yuki Uchida: Investigation. Seiya Kurihara: Investigation. Shinsuke Abe: Validation, Investigation. Ryota Fuse: Investigation. Satoshi Tanaka: Project administration. Keisuke Onodera: Validation, Investigation. Taichi Kawamura: Project administration. Ryuhei Yamada: Supervision, Project administration.

### Declaration of Competing Interest

The authors declare that they have no known competing financial

interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

We are indebted to the students of the Univ. Electro-Comm. and Nihon Univ. for their efforts in the observations. The Bilateral Joint Research Program, Japan Society for the Promotion of Science, supported MY, SA, ST, TK, and RY. The Nihon University College of Science and Technology Leading Research Grant supported SA. We are greatly indebted to Prof. J. M. Madiedo and another reviewer for their useful comments.

## Appendix A. Observing stations, telescopes, and cameras

Acronyms for the three observing stations are shown in Table A1. The distances between the stations are 17.4 km (UEC-ISAS), 47.0 km (UEC-NU), and 62.8 km (ISAS-NU).

The image sensor of the ASI174MM camera is SONY IMX174MM (1936 × 1216 pixels, Pixel size: 5.86 × 5.86 µm). The image sensor of the GS3-U3-15S5M-C camera is SONY ICX825 (1384 × 1032 pixels, Pixel size: 6.45 × 6.45 µm). The specifications of the WAT-910HX camera do not describe its image sensor, but it is probably SONY ICX248AL (768 × 494 pixels, Pixel size: 8.4 × 9.8 µm). The angular spatial resolution [radians pixel⁻¹] is obtained by dividing the pixel size by the telescope’s focal length. One obtains the angular field of view in radians by multiplying the resolution by the number of pixels. Operating the camera in 2 × 2 binning mode doubles the size of the binned pixels and halves the number of binned pixels in both the vertical and horizontal directions.

<table><caption>**Table A1**
Observing stations, telescopes, and cameras.</caption><thead><tr><th>Observing station</th><th>Location</th><th>Telescope</th><th>Camera</th></tr></thead><tbody><tr><td>The University of Electro-communications (UEC)</td><td>Tokyo, Japan<br>lat.: 35°39'28" N<br>long.: 139°32'37" E<br>altitude: 80 m</td><td>System1: Newton (JMI NGT-18), D<sup>a</sup> = 450 mm, f = 2025 mm.<br>System2: Schmidt-Cassegrain (Celestron C11) with a focal reducer, D = 280 mm, effective f = 940 mm.</td><td>System1: Black and white digital 1/1.2" CMOS video camera (ZWO ASI174MM) modified for spectral observations<sup>c</sup>.<br>System2: Black and white digital 2/3" CCD video camera (Point Grey GS3-U3-15S5M-C). This camera was modified for spectral observations<sup>c</sup> in late Dec. 2017.</td></tr><tr><td>Institute of Space and Astronautical Science (ISAS)</td><td>Kanagawa, Japan<br>lat.: 35°33'30" N<br>long.: 139°23'43" E<br>altitude: 140 m</td><td>Schmidt-Cassegrain (Celestron NexStar Evolution 9.25-J) with a focal reducer, D = 235 mm, effective f = 1480 mm.</td><td>Black and white digital 1/1.2" CMOS video camera (ZWO ASI174MM)</td></tr><tr><td>Department of Aerospace Engineering, Nihon University (NU)</td><td>Chiba, Japan<br>lat.: 35°43'31" N<br>long.: 140°03'32" E<br>altitude: 28 m</td><td>Schmidt-Cassegrain (Celestron HD1100) with HyperStar, D = 280 mm, effective f = 560 mm.</td><td>Black and white analog 1/2" CCD video camera (Watec WAT-910HX)</td></tr></tbody></table>

## Appendix B. Association with meteoroid streams

We made some simplifications in Madiedo’s formula and calculated the probability of a flash associated with a stream as

$$P^{ST} = \frac{N^{ST}}{N^{ST} + N^{SPO}} = \frac{\nu^{ST}\gamma^{ST}\cos\phi \times ZHR^{ST}}{\nu^{ST}\gamma^{ST}\cos\phi \times ZHR^{ST} + \nu^{SPO}\gamma^{SPO} \times HR^{SPO}} \quad (B-1)$$

where the superscripts ST and SPO respectively denote “stream” and “sporadic background.” N is the number of lunar impacts of the stream or sporadic meteoroids that can produce observable flashes in an hour and a certain area. ZHR (Zenithal Hourly Rate) and HR (Hourly Rate) are the meteoroid fluxes on the Earth. ν represents the flux ratio of large meteoroids that cause observable lunar flashes to the small ones that cause terrestrial meteors. This parameter strongly depends on the so-called population index of meteors related to the size-frequency distribution of meteoroids. γ, the correction factor for the different gravitational focusing effects for the moon and the Earth depends on the meteoroid’s heliocentric velocity. The incident angle of a meteoroid measured from the local vertical at the impact point on the lunar surface is denoted by φ (90° – impact angle).

The ZHRs for the stream meteors are reported as preliminary results as functions of the solar longitude (e.g., Molau et al., 2018). We calculated the solar longitude observed from the moon and obtained these values from the figures in the reports. HR for the sporadic meteors varies between 7 and 13 (Dubietis and Arlt, 2010), and we assumed that it was constant, 10 meteors h⁻¹. We used the population indexes for the stream meteoroids in the IMO’s “List of Meteor Showers for Observation Session⁶.” The index for the sporadic was assumed to be constant of 3.0 (Rendtel, 2003, 2006). Some parameters used in our calculation are listed in Table B1.

<footnote>a aperture.</footnote>

<footnote>b focal length.</footnote>

<footnote>c For the modification details, see Yanagisawa and Kakinuma (2022a).</footnote>
<table><caption>**Table B1**

ZHRs and population indexes used for examining the association with meteor showers.</caption><thead><tr><th>Flashes</th><th>Meteoroid source</th><th>λ<sub>0</sub><sup>a</sup><br/>/ degree</th><th>ZHR<sup>b</sup><br/>/ meteors h<sup>-1</sup></th><th>population index of the stream<sup>c</sup></th></tr></thead><tbody><tr><td>171026</td><td>ORI</td><td>212.8</td><td>23</td><td>2.5</td></tr><tr><td>171124</td><td>NTA</td><td>241.9</td><td>1.6</td><td>2.3</td></tr><tr><td>171213a,b</td><td>GEM</td><td>261.9</td><td>75</td><td>2.6</td></tr><tr><td>180421</td><td>LYR</td><td>31.0</td><td>3</td><td>2.1</td></tr><tr><td>180422</td><td>LYR</td><td>31.9</td><td>7</td><td>2.1</td></tr><tr><td>181213</td><td>GEM</td><td>270.0</td><td>43</td><td>2.6</td></tr></tbody></table>

a Solar longitudes observed from the moon at the times of flashes.

b ZHR at $\lambda_0$ (see e.g., Molau et al., 2018).

c Indexes in “List of Meteor Showers for Observation Session 6.”

It should be noted that these probabilities are rough estimates. We are unsure whether the population index obtained for millimeter-size meteoroids could be used to estimate the number of centimeter or decimeter-size meteoroids. Brown et al. (2002) examined the near-Earth flux of meteoroids larger than 1 m in diameter and found the power-law index of 0.90 in the impact energy vs cumulative number relationship. The index is the same in the mass vs cumulative number relationship. Then, the index corresponds to the population index of 2.3. If we re-calculate the probability with the population index of 2.3 for both the stream and sporadic meteoroids, all the probabilities in Table 4 decrease to less than 50 %, except for three flashes associated with Geminids.

## Appendix C. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.icarus.2025.116480.

## Data availability

Data will be made available on request.

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