Earth’s atmosphere’s lowest layers probed during a lunar eclipse

Abstract

We report the results of detailed investigation of the Earth’s transmission spectra during the lunar eclipse on UT 2011 December 10. The spectra were taken by using the High Dispersion Spectrograph (HDS) mounted on the Subaru 8.2 m telescope with unprecedented resolution in both time and wavelength (300 s exposure time in umbra and 160000 spectral resolution, respectively). In our penumbra and umbra data, we detected the individual absorption lines of |$\rm O_2$| and |$\rm H_2O$| in transmission spectra and found that they became deeper as the eclipse became deeper. This indicates that the sunlight reaching the Moon passed through lower layers of the Earth’s atmosphere with time, because we monitored a given point on the Moon during the full eclipse duration. From the comparison between the observed and theoretically constructed transmission spectra, the lowest altitude at which the sunlight actually passed through the atmosphere is estimated to be about 10 km from the ground, which suggests the existence of sunlight-blocking clouds below that altitude. Our result can be a test case for future investigations of the atmospheric structure of Earth-like exoplanets via transmission spectroscopy including the refraction effect of the planetary atmosphere.

1 Introduction

Transmission spectroscopy is a useful way to examine an exoplanet’s atmosphere. This method searches for additional absorption features due to planetary atmospheres in a host star’s spectrum; one can detect some species in the planetary atmosphere by observing the stellar light through the atmosphere of the planet during a transit (figure 1). The detection of Na in the transmission spectrum of the hot Jupiter HD 209458b was first reported by Charbonneau et al. (2002) using the Hubble Space Telescope. Some other species like neutral hydrogen (e.g., Vidal-Madjar et al. 2003) and |$\rm H_2O$| (e.g., Deming et al. 2013) were subsequently detected for the planet. Species such as Na and |$\rm H_2O$| were also detected in other hot Jupiters like HD 189733b and HAT-P-1b (Wakeford et al. 2013; McCullough et al. 2014). These results are mainly observed by space telescopes, but ground-based observations have also played an important role in this field, for example in the detection of Na for HD 209458b by Snellen et al. (2008), followed by the detection of Ca and Sc for the same planet (Astudillo-Defru & Rojo 2013).

Fig. 1.

(a) Configuration of a lunar eclipse and (b) configuration for transmission spectroscopy of a transiting exoplanet. S(λ, t), T₁(λ, t), and T₂(λ, t) are the solar spectrum, telluric transmission spectrum, and telluric spectrum above a telescope, respectively.

Although the observations described above are for hot Jupiters, it is particularly interesting to examine terrestrial exoplanets’ atmospheres in order to search for biotic atmospheric species, so-called “biomarkers,” like oxygen and ozone. For this purpose, since the Earth is currently the only planet where life exists to our knowledge, measuring Earth’s transmission spectra could be the first step toward future observations of habitable terrestrial exoplanets. We can obtain a transmission spectrum of the Earth’s atmosphere by observing sunlight reflected by the Moon during a lunar eclipse; the sunlight passes through the Earth’s atmosphere before reaching the Moon (see figure 1; e.g., Pallé et al. 2009).

In analyzing the transmission spectra of Earth-like planets, the refraction of the light in the atmosphere should be properly taken into account. In the case of a planet orbiting very close to the central star, like a hot Jupiter, we can observe the stellar light passing through the entire atmosphere of the planet. However, in the case of a distant planet like the Earth orbiting the Sun, we can only observe the stellar light that transmits above a critical altitude because of the refraction effect. For this reason, the refracted transmission spectrum becomes almost flat over a wide wavelength range, even if no clouds exist in the atmosphere (Bétrémieux & Kaltenegger 2014).

The stellar light that passes through the atmosphere of the planet can actually reach an observer even before the transit begins, owing to the refraction in the atmosphere (Sidis & Sari 2010). Then the stellar light transmits through different layers of the atmosphere with time, which enables us to scan the vertical structure of the atmosphere (García Muñoz et al. 2012). Although it is not possible to apply the method to Earth-like exoplanets at this stage, future ground-based and space-based telescopes will allow us to do so (Misra et al. 2014).

From the above viewpoint, the Earth offers a unique opportunity to obtain accurate transmission spectra of the atmosphere through a lunar eclipse with high temporal (i.e., spatial) resolution using an existing large telescope. The spectra will help us to understand the vertical structure of Earth-like exoplanets in the future, and our observations become test cases to investigate the dependence of transmission spectra on elevation in the atmosphere in a more general sense.

Observations of a lunar eclipse were first pioneered by Pallé et al. (2009) for the optical to near-infrared wavelength range (3600–24000 Å) with low-resolution spectroscopy using LIRIS and ALFOSC spectrographs attached to the 4.2 m William Herschel Telescope (WHT) and the 2.56 m Nordical Optical Telescope (NOT), respectively. This observation resulted in a mainly qualitative identification of the Earth’s atmospheric compounds, though it could not allow us to identify absorbing species in detail because of the low spectral resolution (R ∼ 920–960). Vidal-Madjar et al. (2010) observed the same 2008 lunar eclipse with the SOPHIE high-resolution spectrograph (R ∼ 75000) at the 1.93 m telescope of the OHP (Observatoire de Haute Provence) observatory covering a wavelength range of 3900–7000 Å. They detected broadband signatures of |$\rm O_3$| and Rayleigh scattering, as well as narrowband features of Na i and |$\rm O_2$| at high spectral resolution. However, they did not detect narrowband features of |$\rm H_2O$|⁠. Subsequently, high-resolution broadband observations (3200–10400 Å) using HARPS (R ∼ 115000) at the 3.6 m La Silla telescope and UVES (R ∼ 120000) at the 8.2 m Very Large Telescope (VLT) were conducted in 2010 by Arnold et al. (2014), and they detected broadband absorption lines of |$\rm H_2O$| and |$\rm O_2$|⁠.

Two groups independently reported observations of the lunar eclipse on UT 2011 December 10, which we also observed using the Subaru telescope. One group, Ugolnikov, Punanova, and Krushinsky (2013), observed it using the 1.2 m telescope at the Kourovka Astronomical Observatory, Russia, with a fiber-fed echelle spectrograph with a wavelength range of 4100–7800 Å and a spectral resolution of R ∼ 30000. They reported the detection of spectral features of |$\rm O_2$|⁠, |$\rm O_3$|⁠, |$\rm O_2 \cdot O_2$| collision induced absorption (CIA), |$\rm NO_2$|⁠, and |$\rm H_2O$|⁠. The other group, Yan et al. (2015a), conducted observations with the fiber-fed echelle High Resolution Spectrograph (HRS) mounted on the 2.16 m telescope at Xinglong Station, China. The wavelength region was 4300–10000 Å and the spectral resolution was R ∼ 45000. They detected the spectral features of Rayleigh scattering, |$\rm O_2$|⁠, |$\rm O_3$|⁠, |$\rm O_2$| · |$\rm O_2$|⁠, |$\rm NO_2$|⁠, and |$\rm H_2O$|⁠, and calculated the column densities of |$\rm O_3$|⁠, |$\rm H_2O$|⁠, and |$\rm NO_2$|⁠. They also detected the different oxygen isotopes clearly for the first time.

Furthermore, one of the latest lunar eclipses was observed with HARPS on 2014 April 15 (Yan et al. 2015b). All 382 exposure frames covered the wavelength range from 3780 to 6910 Å with a spectral resolution of R ∼ 115000. Using these lunar eclipse spectra, they demonstrated that the Rossiter–McLaughlin effect can be a useful tool to characterize an exoplanet’s atmosphere (McLaughlin 1924; Rossiter 1924).

We report here our independent observations of the lunar eclipse on UT 2011 December 10 using the Subaru telescope and the High Dispersion Spectrograph, HDS (Noguchi et al. 2002). Based on a series of spectra with high S/N and higher temporal and spectral resolution (R ∼ 160000) than those of the previous works, we clearly detected temporal variations in telluric transmission spectra, which are attributed to the vertical structure of the Earth’s atmosphere.

The rest of the paper is organized as follows. In sections 2 and 3 we describe our observations and a procedure to extract telluric transmission spectra. In section 4 we develop theoretical transmission spectra of the Earth’s atmosphere, which are compared with the observed ones. In section 5 we discuss temporal variations in the observed transmission spectra and the difference between observed and model transmission spectra. Section 6 is devoted to a summary of this work.

2 Observations

We observed a total lunar eclipse on UT 2011 December 10 with the Subaru 8.2 m telescope and the HDS (Noguchi et al. 2002), which is placed at a Nasmyth focus. The wavelength range was set to cover 5500–8200 Å, which is a non-standard format of HDS, and the slit width was set to |$0{^{\prime\prime}_{.}}2$| corresponding to a spectral resolution (R = λ/Δλ) of ∼160000. This resolving power is higher than those of previous works.

We started to observe the Moon prior to the eclipse and terminated the observation in the middle of the eclipse. We alternately obtained a series of spectra of the sunlight reflected by two points of the lunar surface; one was the Ocean of Storms (point A) and the other was the Sea of Fertility (point B)—see figure 2. The reflectance difference of these two points is known to be small, corresponding to less hubby regions (Wilhelms & McCauley 1971). On point A we took a total of 13 exposures of 30 s prior to the eclipse (i.e., full Moon), 10 exposures of 30–300 s in penumbra, and 5 exposures of 300 s in umbra. On point B we took a total of 15 exposures of 30 s prior to the eclipse (i.e., full Moon), 6 exposures of 100–300 s in penumbra, and 11 exposures of 300 s in umbra. The sequence of the observations is shown in figure 3.

Fig. 2.

Positions of points A and B on the lunar surface.

Fig. 3.

Positional relation between Earth’s shadows and the observation points on the lunar orbit from hour to hour.

Fig. 4.

The black pluses represent the temporal wavelength (velocity) shifts of T₂(λ, t) in full Moon and penumbra spectra relative to the T₂(λ, t) template spectrum. The red, orange, green, and blue lines are the best-fit quintic, quartic, cubic, and quadratic curves to the black pluses, respectively.

Fig. 5.

Left: Full Moon spectrum around |$\rm O_2$| lines (black line in upper panel), and the spectrum from which T₂(λ, t), the red line in the upper panel, is eliminated (bottom panel). Center, Right: Lunar eclipse spectrum around |$\rm O_2$| lines (black line in upper panel), and the spectrum from which T₂(λ, t), the red line in the upper panel, is eliminated (bottom panel).

We note here that the light reaching the observation point comes from an arc of the Earth’s limb seen from the Moon. We found that the point which the sunlight passes in the Earth’s atmosphere is over the region from the center of the southern Indian Ocean (∼20° S, 80° E) to the northern coast of Antarctica (∼65° S, 100° E) at the time of our run. The calculation method of the longitude and latitude at each time is described in the Appendix, and these results are given in table 1.

Table 1.

Latitude and longitude at the typical universal time during eclipse.

Universal time (UT)	Latitude (°)	Longitude (°)
	Point A
12:47	15.9 S	81.6 E
12:54	17.2 S	80.4 E
13:01	18.8 S	79.7 E
13:07	20.4 S	78.6 E
13:14	22.5 S	77.9 E
13:21	24.9 S	77.5 E
13:27	28.1 S	77.5 E
	Point B
13:48	28.8 S	72.7 E
13:54	30.8 S	72.3 E
14:01	33.5 S	72.1 E
14:08	36.6 S	72.4 E
14:14	39.6 S	73.0 E
14:21	43.6 S	74.3 E
14:27	47.4 S	76.3 E
14:34	52.3 S	80.0 E
14:41	57.5 S	86.2 E
14:47	61.7 S	93.9 E
14:54	65.6 S	106.5 E
15:01	67.1 S	114.6 E
15:07	65.9 S	104.9 E

The reduction of echelle data (i.e., bias subtraction, flat-fielding, scattered-light subtraction, spectrum extraction, and wavelength calibration with Th–Ar spectra) was performed using the IRAF¹ software package in the standard way. The reduced spectra of full Moon, penumbra and umbra have SNRs of ∼173, ∼89, and ∼60 per pixel, respectively. These SNR values (for point A at least) are probably biased by light scattered from the bright moon (penumbra or full moon); this is discussed in subsection 5.1.

3 Extraction of telluric transmission spectra

A lunar eclipse spectrum is composed of three kinds of spectra: the solar spectrum S(λ, t), the telluric transmission spectrum T₁(λ, t), and the telluric spectrum above a telescope T₂(λ, t)—see figure 1. Since we are interested in the telluric transmission spectrum T₁(λ, t), we need to eliminate the unnecessary spectra [T₂(λ, t) and |$S(\rm \lambda ,t$|⁠)] from the lunar-eclipse spectrum.

3.1 Eliminating T₂(λ, t)

3.1.1 A template spectrum for T₂(λ, t)

We used a high-resolution spectrum of the rapid rotator HR 8634 (B8V, vsin i = 185 km s⁻¹; Glebocki et al. 2000), which was taken on the same night as the lunar eclipse observations, as a template for T₂. Since the star is rapidly rotating, the stellar absorption lines in the spectrum are largely broadened and the spectrum is almost featureless. Thus the spectrum basically conveys only the telluric spectrum above a telescope, and we can use it as a template for T₂. HR 8634 is also known to have fewer interstellar absorption lines, which makes the star an appropriate target for this purpose. Using this template spectrum, we next evaluate the dependence of T₂(λ, t) on airmass and the wavelength shift of T₂ in order to match the template spectrum with the actual T₂ in the lunar eclipse spectra.

3.1.2 Airmass variation

T  ₂(λ, t) is dependent on the airmass, AM [= |$\sec (z)$|⁠; z is zenith distance]. Assuming a plane parallel atmosphere of the Earth, T₂ can be expressed as

\begin{equation} T_2(\lambda , t) = T_2(\lambda ,t_0)^{AM/AM_0}, \end{equation}

(1)

where T₂(λ, t₀) is the template spectrum taken at time t₀ and airmass AM₀, and T₂(λ, t) is the expected telluric spectrum above a telescope taken at time t and airmass AM assuming that T₂ was constant for the rest of the night. Based on that relation, we can estimate the line depth of T₂ inherent to each lunar eclipse spectrum. The time variation of precipitable water vapor (PWV) can cause depth variation in |$\rm H_2O$| absorption lines. This effect, however, is negligible in this case as the value of PWV obtained from data from the Caltech Submillimeter Observatory² is small and changed little during the observation (PWV ∼ 0.64–1.70 mm).

We adopted a high-S/N spectrum of HR 8634 as T₂(λ, t₀), which was obtained by averaging eight spectra of the star taken prior to the lunar eclipse in a short period of time with a negligible change in airmass of <0.02. The mean time and airmass were 8:35 UT and 1.03, respectively, which were attributed to T₂(λ, t₀).

3.1.3 Wavelength shift

Variations of absorption lines in T₂(λ, t) are found not only in line depth but also in the wavelengths of the lines. The wavelength variation can be caused by wind in the atmosphere, error in wavelength calibration, instability of the spectrograph, and so on. The Earth’s rotation velocity is about 0.5 km s^-1. The wavelength variation caused by the velocity (Doppler shift) is about ±0.0055 Å at a wavelength of 6000 Å. The typical error in wavelength calibration is about 0.0011 Å for HDS, and there could also be temporal variation due to instrumental instability. Unfortunately we cannot discriminate among these causes, and cannot directly derive the wavelength shift in umbra spectra since the telluric transmission spectrum T₁ is easily confused with T₂ in umbra spectra.

Alternatively, we estimated wavelength shifts of T₂ in umbra spectra by using those in the full Moon spectra taken outside of the eclipse. We measured wavelength shifts of telluric |$\rm O_2$| lines between 6306.45 Å and 6306.66 Å in full Moon and penumbra spectra relative to those in the template T₂, and tried to extrapolate the values in umbra by using polynomials. Figure 4 shows the derived wavelength variations of T₂ together with the fitted polynomials as a function of time, and these results are detailed in table 2. We found that all the polynomials gave reasonable estimates of the wavelength shifts in umbra for point A, but this was not the case with point B. Thus we adopted the values derived by a quintic equation for point A, and the value of −0.1 km s^-1, which is the average of the four data points closest to umbra, for point B. These choices of the fitting functions have less impact on the subsequent analyses and results.

Table 2.

Relation between the period elapsed from the first full Moon data and the variation in wavelength of T₂(λ, t) from HR 8634 data.

Universal time (UT)	Variation of wavelength, O2 spectra (km s−1)		Universal time (UT)	Variation of wavelength, O2 spectra (km s−1)
10:54	−0.11		11:49	−0.10
10:56	−0.12		11:51	−0.09
10:58	−0.12		12:14	−0.07
11:01	−0.13		12:16	−0.08
11:03	−0.14		12:18	−0.07
11:05	−0.14		12:20	−0.06
11:22	−0.15		12:22	−0.07
11:24	−0.14		12:24	−0.07
11:26	−0.13		12:26	−0.07
11:28	−0.12		12:29	−0.07
11:30	−0.13		12:31	−0.05
11:32	−0.13		12:33	−0.06
11:34	−0.12		12:36	−0.07
11:36	−0.11		12:39	−0.05
11:38	−0.12		12:42	−0.06
11:40	−0.11		13:33	−0.10
11:43	−0.11		13:36	−0.09
11:45	−0.11		13:39	−0.09
11:47	−0.10		13:43	−0.11

Figures 5 and 6 show the resulting full Moon and lunar eclipse spectra divided by the matched T₂. As shown in the figure, we successfully eliminated T₂ from the spectra down to the photon noise level.

Fig. 6.

Left: Full Moon spectrum around |$\rm H_2O$| lines (black line in upper panel), and the spectrum from which T₂(λ, t), the red line in the upper panel, is eliminated (bottom panel). Center, Right: Lunar eclipse spectrum around |$\rm H_2O$| lines (black line in upper panel), and the spectrum from which T₂(λ, t), the red line in the upper panel, is eliminated (bottom panel).

Fig. 7.

Left: Full Moon spectrum around |$\rm O_2$| lines (black line in upper panel) from which T₂(λ, t) is eliminated, and the spectrum from which S(λ, t), the red line in the upper panel, is eliminated (bottom panel). Center, Right: Lunar eclipse spectrum around |$\rm O_2$| lines (black line in upper panel) from which T₂(λ, t) is eliminated, and the spectrum from which S(λ, 0), the red line in the upper panel, is eliminated (bottom panel). A telluric transmission spectrum, T₁(λ, t), is clearly seen in the bottom panel.

Fig. 8.

Left: Full Moon spectrum around |$\rm H_2O$| lines (black line in upper panel), and the spectrum from which S(λ, t), the red line in the upper panel, is eliminated (bottom panel). Center, Right: Lunar eclipse spectrum around |$\rm H_2O$| lines (black line in upper panel), and the spectrum from which S(λ, 0), the red line in the upper panel, is eliminated (bottom panel). A telluric transmission spectrum, T₁(λ, t), is clearly seen in the bottom panel.

3.2 Eliminating S(λ, t)

A full Moon spectrum from which T₂(λ, t) is eliminated is equivalent to the solar spectrum S(λ, t), assuming that the moon has a perfect flat reflectance spectrum. The effect of the moon characteristic should be negligible, as our observation points have small reflection characteristics. We obtain T₁(λ, t) by dividing the T₂-eliminated lunar eclipse spectrum by S(λ, t). In practice, the wavelength of S(λ, t) temporally varies according to the mutual velocities of the Sun, Earth, and Moon. Thus we correct the variations by measuring wavelength shifts of some unblended solar absorption lines in the ranges 6260.93–6261.25 Å, 6327.39–6327.78 Å, and 6470.5–6472.5 Å relative to the full Moon spectrum (table 3).

Table 3.

Relation between the time elapsed from the first full Moon data and the variation in wavelength of S(λ, t) from the first full Moon data.

Universal time (UT)	Wavelength shift, O2 spectra (km s−1)	Wavelength shift, H2O spectra (km s−1)		Universal time (UT)	Wavelength shift, O2 spectra (km s−1)	Wavelength shift, H2O spectra (km s−1)
12:29	−0.84	−0.83		13:39	−1.05	−1.02
12:31	−0.90	−0.89		13:43	−1.11	−1.09
12:33	−0.97	−0.95		13:48	−1.05	−1.02
12:36	−1.03	−1.01		13:54	−0.35	−0.35
12:39	−1.10	−1.08		14:01	−0.18	−0.15
12:42	−1.17	−1.12		14:08	−0.12	−0.07
12:47	−1.16	−1.13		14:14	−0.09	−0.09
12:54	−0.56	−0.51		14:21	−0.04	−0.05
13:01	−0.50	−0.43		14:27	0.00	−0.01
13:07	−0.56	−0.46		14:34	0.11	0.10
13:14	−0.61	−0.45		14:41	0.12	0.05
13:21	−0.66	−0.52		14:47	0.16	0.30
13:27	−0.59	−0.53		14:54	0.51	0.46
13:33	−0.94	−0.93		15:01	0.41	0.62
13:36	−0.98	−0.97		15:07	0.57	0.65

Figures 7 and 8 show the resultant T₂- and S-eliminated full Moon and lunar eclipse spectra. We successfully eliminated S from the spectra well below the signal level of T₁.

3.3 O₂ and H₂O transmission spectrum

Figures 9 and 10 show the thus-extracted T₁ spectra for penumbra and umbra. We can clearly see |$\rm O_2$| absorption lines in 6275–6330 Å, and |$\rm H_2O$| absorption lines in 5870–5930 Å and 6465–6495 Å. We can also see that the absorption lines become deeper as the eclipse becomes deeper.

4 Model spectra

We found that the telluric transmission spectra vary in depth with time. This is because we see the sunlight passing through a lower-altitude region in the Earth’s atmosphere as the eclipse becomes deeper. In order to evaluate the variations quantitatively, we construct theoretical transmission spectra for the Earth and compare them with the observed ones.

4.1 Altitude

The lowest surface altitude of the Earth’s atmosphere, z_min, through which the sunlight passes towards the Moon can be calculated from the positional relation between the Sun, the Earth, and the observation point on the lunar surface by using the Geometric Pinhole Model (Vollmer & Gedzelman 2008).

However, the model only works for umbra (not penumbra), and assumes that the refraction angle in the Earth’s atmosphere is 70΄ for z_min = 0 km. The value is based on analytical approximation, but in fact it is not valid in the case of such a small z_min (i.e., large refraction angle). Alternatively, we calculate z_min for both umbra and penumbra using the fourth-order Runge–Kutta method, following Tsumura et al. (2014).

First, we calculate and trace refraction of the sunlight that enters the Earth’s atmosphere in parallel to the line connecting the center of the Earth shadow on the lunar surface with the center of the Earth (figure 11). The refractive index at each point in the atmosphere is calculated from geometric optics, and rays with a variety of incident altitudes (i.e., impact parameter) are traced. The calculation is based on the assumption that the Earth’s atmosphere is spherically symmetric. The number-density distribution in the vertical direction is given by the T–P profile for mid-latitude in the MIPAS Model Atmosphere of the Earth (2001)³ because we observed the sunlight passing over the center of the southern Indian Ocean and the northern coast of Antarctica this time. As a result of the calculation, we obtain the distance (d) from the center of the Earth shadow to the point that the refracted sunlight reaches the lunar orbit. This distance is related to the lowest surface altitude (z_min) on the Earth at which the sunlight passes. The relation between d and z_min is shown in figure 11. Since we know the distance from the center of the Earth shadow to points A and B on the lunar surface from hour to hour (see the Appendix), we can determine z_min at each observing time.

However, as the sun has a finite size, the sunlight that passes the minimum altitude actually illuminates a finite area, ω, on the lunar surface (figure 11). The area can be considered to be circular because of the projection of the Sun. In this case, we can estimate the range of d whose corresponding ω include the observation point with various position angles ϕ (figure 11) using the same method as the pinhole model. The minimum and the maximum d are calculated as

\begin{equation} d_{\rm max,min}(\phi ) = d_0 \cdot \cos \phi \pm \sqrt{r^2-(d_0 \sin \phi )^2}, \end{equation}

(2)

where d₀ is the distance between the center of the Earth shadow and the observation point, and r is the radius of the Earth shadow on the lunar surface. d_max and d_min are converted into the maximum and minimum of z_min, respectively, by using the relation presented in the right panel of figure 11.

Figure 12 shows the derived ranges of z_min for point A (left) and point B (right) at each observing time. In this figure, we can see that (1) the sunlight reaching the observation point is transmitted through lower layers of the Earth’s atmosphere with time; (2) the sunlight that is transmitted through the opposite side with respect to the Earth center also reaches the observation point at the middle of the eclipse; and (3) the bottom of the range of z_min is not 0 km but 1.8 km (table 4) due to refraction.

Table 4.

Altitude range at the typical universal time during eclipse.

Observation point A or B	Observation time (UT)	Altitude range (km)
A	12:47	8.1–(penumbra)
A	12:54	7.3–82.4
A	13:01	6.6–22.4
A	13:07	6.0–18.0
A	13:14	5.5–15.2
A	13:21	5.0–13.6
A	13:27	4.5–12.2
		1.8–2.0 (other side)
B	13:48	7.7–(penumbra)
B	13:54	7.1–35.4
B	14:01	6.5–21.6
B	14:08	5.9–17.7
B	14:14	5.6–15.7
B	14:21	5.1–14.1
B	14:27	4.9–13.2
B	14:34	4.6–12.3
		1.8–2.0 (other side)
B	14:41	4.3–11.5
		1.8–2.2 (other side)
B	14:47	4.2–11.2
		1.8–2.3 (other side)
B	14:54	4.1–11.0
		1.8–2.3 (other side)
B	15:01	4.1–10.9
		1.8–2.4 (other side)
B	15:07	4.1–11.0
		1.8–2.3 (other side)

We can also see that the sunlight passed through similar layers of the atmosphere for points A and B. However, the line depth of the transmission spectrum for point A is much shallower than that for point B (figure 9). We discuss this difference in subsection 5.1.

Fig. 9.

Transmission spectrum [T₁(λ, t)] of |$\rm O_2$| (left). The |$\rm O_2$| absorption lines of 6305.80 Å and 6306.56 Å are expanded in the right panels. The upper figures show the spectra observed at point A and the lower figures show the spectra observed at point B.

Fig. 10.

Transmission spectra [T₁(λ, t)] of |$\rm H_2O$| (left). The |$\rm H_2O$| absorption lines of 6487 Å and 6489.5 Å are expanded in the right panels. The upper figures show the spectra observed at point A and the lower figures show the spectra observed at point B.

Fig. 11.

Relation between the distance from the center of the Earth shadow to the point which the sunlight reaches (d) and the minimum altitude at which the sunlight passes in the Earth’s atmosphere (z_min). R_moon means the lunar radius.

4.2 Creating a modeled spectrum

A theoretical transmission spectrum [T₁(λ, t)] is obtained from the Beer–Lambert law:

\begin{equation} T_{1} (\lambda ,t) = e^{-\int ( u \cdot \sigma )dx}, \end{equation}

(3)

where u, σ, and x are the number density and cross section of each species and the path length in the atmosphere, respectively. Hereafter we only calculate |$\rm O_2$| absorption lines because |$\rm H_2O$| absorption lines largely depend on the climate variation in the transmitted atmosphere. The |$\rm O_2$| absorption line [|$T_{1{\rm O_2}} (z_{\rm min})$|] made by the light passing at an altitude z_min is expressed as

\begin{equation} T_{1{\rm O_2}} (z_{\rm min}) = e^{-\int [u_{{\rm O_2}} (z) \cdot \sigma _{{\rm O_2}} (z)]dx}, \end{equation}

(4)

where |$u_{{\rm O_2}} (z)$| and |$\sigma _{{\rm O_2}} (z)$| are the number density and cross section of |$\rm O_2$| in the atmosphere, respectively, and the summation in the exponent is taken along the ray.

The cross section has been developed with the rational polynomial of Kuntz (1997), which was revised by Ruyten (2003) for the approximation of the Voigt profile function. The FWHM of the Stokes function is estimated using the data of HITRAN 2012 (Rothman et al. 2013), and the FWHM of the Doppler function (γ_D) is determined by the line position ν, the molecular mass m, and the temperature T as

\begin{equation} \gamma _{\rm D} = \nu \sqrt{\frac{2kT}{mc^2}} \approx 7.6 \cdot 10^{-8} \nu \sqrt{T \ \rm [K]} \ \ (m = 32 \, {\rm a.m.u.}), \end{equation}

(5)

where k is Boltzmann’s constant and c is speed of light.

The number density is calculated from the equation of state using the temperature (T), pressure (P), and |$\rm O_2$| abundance at each point along the ray. As the cross section and number density depend on T and P, these values are calculated at each altitude assuming the vertical structure of Earth atmosphere based on the MIPAS model. As T, P, and molecule abundance are given for every 1 km in height from 0 to 120 km from the surface in the MIPAS model, we calculate the number density every kilometer. The number density at an arbitrary altitude is obtained by linear interpolation between these values.

We divide the ray into small segments and calculate z, u, σ, and x for each segment. Then we take the summation of the product of u, σ, and x along the ray, and obtain the transmission spectrum as

\begin{equation} T_{1{\rm O_2}} (z_{\rm min}) = e^{- {\displaystyle \sum_{i}} u_{{\rm O_2}} (z_i) \cdot \sigma _{{\rm O}_2} (z_i) \cdot \Delta x (z_i)}, \end{equation}

(6)

where z_i is the altitude of the ith segment and Δx(z_i) is the length of the ith segment.

Then, we also consider |$\rm O_3$| absorption and |$\rm O_2$| · |$\rm O_2$| CIA, which contribute to the spectra at broad-band wavelengths, around the |$\rm O_2$| absorption lines (6275–6330 Å), and Rayleigh scattering, which prevents all sunlight from passing through the lowest layer of Earth’s atmosphere. We calculate these transmission spectra by combining each cross section and number density along the ray.

Therefore, we use the cross section for 223K, which corresponds to the altitude where the number density of |$\rm O_3$| reaches a maximum in the Earth’s atmosphere. The number density is calculated from the equation of state using temperature (T), pressure (P), and |$\rm O_3$| abundance. The |$\rm O_2$| · |$\rm O_2$| absorption cross sections are taken from the HITRAN database (Richard et al. 2012).

For Rayleigh scattering, we utilize the number density of all particles in the atmosphere and the cross section of the Rayleigh scattering for the Earth’s atmosphere from Bodhaine et al. (1999):

\begin{eqnarray} \sigma _{\rm Rayleigh} = \frac{1.054 - 341.29 \lambda ^{-2} - 0.9023 \lambda ^{2}}{1+0.002706 \lambda ^{-2} - 87.9686 \lambda ^{2}} \, (\times 10^{-28} \, \rm cm^{2}), \nonumber\\ \end{eqnarray}

(7)

where λ is in |$\rm \mu m$|⁠.

Finally, we calculate all the transmission spectra attributed to the various rays that reach the observation point on the lunar surface, and integrate them weighted by the limb darkening (quadratic law; u1 = 0.5524, u2 = 0.3637) on the solar disk. The synthetic spectrum thus obtained is shown in figure 13. As seen in the figure, it is deeper and wider than the observed one.

5 Discussion

We conducted spectroscopic observations of an eclipse using Subaru/HDS with higher resolutions in time and wavelength than previous works. As a result, we successfully detected temporal variations in individual absorption lines of |$\rm O_2$| and |$\rm H_2$|O in Earth’s transmission spectra.

The lines, however, show large differences in depth between those obtained at point A and point B, as seen in figure 9. Furthermore, there is apparently a discrepancy between the observed and synthetic transmission spectra, as seen in figure 13. We discuss these issues in the following subsections.

5.1 Transmission spectra at points A and B

We alternately observed points A and B during the lunar eclipse, and obtained a series of telluric transmission spectra for each point. As is clearly seen in figure 9, the depth of the absorption lines in the transmission spectra differs considerably between the two points, despite the fact that the sunlight passed through nearly the same atmospheric layers of the Earth before reaching the lunar surface (figure 12). Considering the fact that the difference is not seen in the solar spectra S but in the transmission spectra T₁, full Moon and penumbra light were scattered into point A, increasing the background and making the transmission absorption lines shallower.

Fig. 12.

Solar images as observed from the Moon at different times during lunar eclipse on point A (left) and point B (right). These images mean the ranges of the altitudes, z_min, at which the sunlight passes through the Earth’s atmosphere. Point Z is the lowest point of each image.

Actually, as shown in figure 3, point A is ahead of the rest of the lunar surface toward the shadow of the Earth. Therefore, when point A enters into the Earth shadow, the rest of the lunar surface, which is part of the full Moon, is still bright. On the other hand, point B is located at the back edge of the lunar surface, and thus the rest of the lunar surface is already faint in the shadow when point B enters into the shadow.

5.2 Comparison between observed and modeled transmission spectra

In this section we deal with the transmission spectra obtained at both points in umbra.

Figure 15 shows a comparison between the observed and the synthetic transmission spectrum of |$\rm O_2$| (subsection 4.2). As seen in the figure, the synthetic absorption line is deeper and wider than the observed one. Considering that the observed spectrum may be affected by background scattered light, we first adjusted the line depth of the synthetic spectrum by adding a constant to it and renormalizing it to the continuum level. However, the width of the absorption line still shows a discrepancy between the observed and the modeled spectrum. We discuss possible causes of the discrepancy in more detail below.

The first possible cause is uncertainty in the adopted vertical structure of the Earth’s atmosphere. We used that of the mid-latitude of the MIPAS model since the lowest altitude at which the sunlight passed is from the center of the southern Indian Ocean to the northern coast of Antarctica. However, the actual region where the sunlight passed through is much wider (see figure 12). In order to evaluate how the vertical structure affects the resultant transmission spectrum, we tested five different thermal structure models: polar winter, polar summer, and equatorial models of MIPAS, and mid-latitude summer and subarctic summer models of FASCODE/ICRCCM (Clough et al. 1992). As a result, the vertical structures cannot account for the difference between the modeled and observed spectrum.

The second possibility is uncertainty in the model spectrum. HITRAN has uncertainties in intensity, air-broadened half-width, self-broadened half-width, and the coefficient for the temperature dependence of the air-broadened half-width. In our observational wavelength, the uncertainty range of intensity is 5%–10% and that of air-broadened half-width, self-broadened half-width, and the coefficient for the temperature dependence of the air-broadened half-width is 10%–20% or over 20%. The uncertainty in the final model spectra caused by the factors described above is shown in figure 13. This shows that we cannot explain the difference between model and observation by the uncertainty in the HITRAN database. We omit the absorption lines with an uncertainty range of over 20% in the HITRAN database from the following discussion since we cannot estimate the uncertainty in the final model spectra.

Fig. 13.

Comparison between the observational and modeled |$\rm O_2$| absorption line for 14:47 UT, when the whole lunar disk moved into the Earth’s shadow and the effect of the scattered light is the lowest. The thickness of the line shows the uncertainty of the model spectrum.

Furthermore, in order to validate our calculation of the model spectrum, we tried to reproduce the T₂ spectra, telluric spectra above the telescope, which are extracted from spectra of rapid rotators (sub-subsection 3.1.1.). As a result, the modeled T₂ spectra are well matched with the observed ones (figure 14), and thus the uncertainty in the model spectra cannot account for the discrepancy, either.

Fig. 14.

Modeled (red) and observed (black) |$\rm O_2$| absorption lines of Earth’s atmosphere (T₂). The synthetic lines are only 1.1 deeper than the observed ones.

Finally, we consider the effect of clouds on transmission spectra. If clouds exist in the atmosphere, the sunlight may be blocked by the clouds and cannot reach the lunar surface. Since clouds can exist up to ∼13 km in the Earth’s atmosphere, we may not have seen the sunlight passing the lower atmosphere, i.e., denser and higher-pressure layers. To examine this effect, we created theoretical transmission spectra that only pass through the atmosphere above some critical elevation, below which no sunlight is transmitted.

As seen in figure 15, the model spectrum with the critical elevation of 9–10 km reproduces the observed one well. In this figure we show only one absorption line, but we obtain the same results from all observed absorption lines and all observing times. In addition, the model spectra with critical elevation lower than 4–5 km are identical to the original one without considering any critical elevations (the purple dotted line in figure 15). This indicates that the Rayleigh scattering can prevent the sunlight from probing the lowest layer (<4–5 km) of Earth’s atmosphere regardless of the existence of clouds. This result is apparently inconsistent with the previous works (Vidal-Madjar et al. 2010; Arnold et al. 2014) showing that the Rayleigh scattering prevents the sunlight from probing the lower layer of the atmosphere of about <20 km at 6300 Å. The inconsistency probably comes from the fact that we observed different altitudes of Earth’s atmosphere from the previous observations. As these previous works observed the limb of the Earth shadow, they can observe the upper atmosphere and most of the sunlight comes from altitudes higher than ∼20 km where extinction by Rayleigh scattering is smaller. On the other hand, as we observed the center of the Earth shadow, we can only observe the sunlight passed through the atmosphere under about 20 km. Although the amount of sunlight that passes through the atmosphere below 20 km is lower than that above 20 km due to Rayleigh scattering, it is still detectable as shown by our observations, and we can reveal detailed structure of the lower atmosphere by only probing this part. We also prove that the existence of |$\rm O_2 \cdot O_2$| and |$\rm O_3$| spectra have little influence on |$\rm O_2$| absorption lines.

Fig. 15.

Comparison between observational and modeled |$\rm O_2$| absorption line for 14:47 UT when the whole lunar disk moved into the Earth’s shadow and the effect of the scattered light is the lowest. The thickness of the line shows the uncertainty of the model spectrum.

To verify our results, we examine the cloud-top pressure in the sunlight-transmitted area (from the center of the southern Indian Ocean to the northern coast of Antractica) during the observation time using Moderate Resolution Imaging Spectroradiometer (MODIS) data acquired from the Level-1 and Atmosphere Archive & Distribution System (LAADS) Distributed Active Archive Center (DAAC).⁴ These data indicate that the cloud-top pressure is about 200–450 hPa (i.e., the cloud-top height was about 6–11 km), which is consistent with our results.

6 Summary

Using Subaru HDS on UT 2011 December 10, we obtained high-resolution transmission spectra of Earth by fixed-point observation at two points (point A, point B) on the lunar surface. We clearly detected temporal variations in |$\rm O_2$| and |$\rm H_2O$| absorption lines of the transmission spectra. In order to investigate the cause of the temporal variations, the minimum altitude (z_min) at which the light was transmitted in the Earth’s atmosphere was calculated by taking account of the atmospheric refraction at each observation time. We found that sunlight was transmitted on the lower altitude range with time at both observation points. We also found that the spectra of point A, which show much shallower absorption lines than those of point B, are probably affected by the scattered light from other bright parts of the lunar surface.

Furthermore, we made a synthetic transmission spectrum of the Earth with the Voigt function by taking account of the limb-darkening, refraction, and dependence of the spectrum on the atmospheric altitude at which the sunlight passes. The model spectra turned out to show wider absorption lines than those of the observed ones even after the correction of the line depth that may be suffered from the scattered light. We found that the width is matched with the observed one if we assume that the sunlight only transmits above 9–10 km of the Earth’s atmosphere. The result suggests the existence of clouds below 9–10 km that may block the sunlight.

Our results will be useful for the investigation of teh atmospheric structure of Earth-like exoplanets when the time variation of their transmission spectra can be obtained in the future.

Acknowledgments

We thank the referee, Dr. Luc Arnold, for many valuable comments that greatly improved this paper. We are grateful for the support of our Subaru/HDS observation by Akito Tajitsu, Naruhisa Takato, Daigo Tomono, and Ruka Misawa. We also acknowledge the people who supported the proposal of the observation and the people who discussed this study, especially Masato Katayama, who advised how to obtain the longitude of the lowest point in the Earth’s atmosphere. Part of our data analysis was carried out on the common-use data analysis computer system at the Astronomy Data Center, ADC, of the National Astronomical Observatory of Japan. This work was supported by Japan Society for Promotion of Science (JSPS) KAKENHI Grant Numbers JP16K17660, 15H02063 and 18H01265. Y.K. is supported by a Grant-in-Aid for JSPS Fellows (JSPS KAKENHI No. 15J08463) and the Leading Graduate Course for Frontiers of Mathematical Sciences and Physics. The cloud-top pressure above the limb Earth region of interest during the observation time is based on Terra and Aqua MODIS Cloud Subset 5-Min L2 Swath 5 km and 10 km data. These data were acquired from the Level-1 and Atmosphere Archive & Distribution System (LAADS) Distributed Active Archive Center (DAAC), located in the Goddard Space Flight Center in Greenbelt, MD (〈https://ladsweb.nascom.nasa.gov/〉). We acknowledge LAADS Web search. We acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous people in Hawai’i.

Appendix 1.

Terrestrial coordinates of the sunlight-transmitting regions in Earth’s atmosphere

A.1.1. Latitude

Earth’s spin axis is inclined at about |${23{^{\circ}_{.}}4}$| from the perpendicular to the ecliptic (figure 16). Therefore, latitudes on the Earth are projected onto the shadow of the Earth as shown in figure 17. The sunlight that passes through the Earth’s atmosphere at the minimum lowest altitude (point Z; figure 12) on the terminator (point 1 on figure 17) finally reaches a point (point 2 on figure 17) on the line connecting the center of the Earth’s shadow and point 1. Thus we can know the latitude on the Earth where the sunlight passes through at the lowest altitude by reading the projected latitude of point 1 on the Earth shadow.

Fig. 16.

Schematic view showing the relation between the axis of the Earth and the RA of the shadow of the Earth.

Fig. 17.

Schematic view showing the projected latitude on the shadow of the Earth. The light-blue lines are the projected latitude on the shadow of the Earth, the black point is the center of the shadow of the Earth, and the red and pink points are point A (point 2) at 13:21 UT set on the lunar surface and the point corresponding to where the sunlight passes at the terminator of the Earth, respectively.

A.1.2. Longitude

The longitude of point Z (figure 12) at the Earth’s terminator also changes with time because of the Earth’s spin. Here, we try to determine the longitude of the point |$\rm Z_{\rm g}$|⁠, which is on the Earth’s surface just beneath point Z, at a given point in time.

The altitude h and azimuth A of a celestial object at time t is expressed by the following three equations:

\begin{equation} \cos h \cdot \sin A = - \cos \delta \cdot \sin H, \end{equation}

(A1)

\begin{equation} \cos h \cdot \cos A = \cos \phi \cdot \sin \delta - \sin \phi \cdot \cos \delta \cdot \cos H, \end{equation}

(A2)

\begin{equation} \sin h = \sin \phi \cdot \sin \delta + \cos \phi \cdot \cos \delta \cdot \cos H, \end{equation}

(A3)

where δ and H are the declination and hour angle of the object, and ϕ is the latitude of the point |$\rm Z_{\rm g}$|⁠. H is expressed as

\begin{equation} H = \theta _0 + t \times 1.0027379 + \lambda - \alpha , \end{equation}

(A4)

where λ is the longitude of the point |$\rm Z_{\rm g}$|⁠, θ₀ is Greenwich sidereal time when universal time is 0^h, t is the observation time in UT, and α is the right ascension of the object. Here we regard point 2 in figure 17 as the celestial object, which is a point on the Moon that the sunlight passing through point Z reaches. The α and δ of point 2 are given by JPL’s HORIZONS system⁵ at the time t, and θ₀ is also given by “chronological scientific tables.” ϕ is given by the method described above. Therefore, if we know h and A for point 2, we can know H and thus λ.

h is derived in the following way. The refraction angle at point Z is the largest because point Z is at the minimum of the lowest altitude from the surface. The ray passing through point Z comes from the bottom of the Sun since the ray enters the Earth’s atmosphere with the largest incident angle. Therefore, at point Z on the terminator we see point 2 on the Moon, and the bottom of the Sun is in the exact opposite direction in a horizontal fashion. In addition, since the effect of atmospheric refraction makes the elevation of point 2 seen from point |$\rm Z_{\rm g}$| higher, we should subtract the refraction angle (Φ) from the parallax (p) of point 2 to correct h. Assuming that point Z is z km above the Earth’s surface, we obtain h as

\begin{eqnarray} h = p - \Phi = \frac{z}{38400} - \Phi \ \left( p = \frac{z_{{\rm Point} \ Z}}{d_{\rm EM}} \approx \frac{z}{38400} \,\, [{\rm rad}] \right), \!\!\!\!\!\nonumber\\ \end{eqnarray}

(A5)

where d_EM is the distance between the Earth and the Moon.

Next, A and H are calculated as follows. We rewrite equations (12)– (14) as

\begin{eqnarray} \sin A = C \sin H, \end{eqnarray}

(A6)

\begin{eqnarray} \cos H = F, \end{eqnarray}

(A7)

\begin{eqnarray} \cos A = D \cos H + E = D \cdot F + E, \end{eqnarray}

(A8)

where C = −cos δ/cos h, D = −(sin ϕ · cos δ)/cos h, E = (cos ϕ · sin ϕ)/cos h, and F = (sin h − sin ϕ · sin δ)/(cos ϕ · cos δ). Now all of the C, D, E, and F are functions of the known variables. We assume here that A takes a value between 0 and π, because the Moon is seen in the east from the terminator at the beginning of the lunar eclipse. It should be noted that the value of H depends on the signs of sin H and cos H in the following way:

(i) cos H > 0, sin H > 0	(ii) cos H < 0, sin H > 0
0° < H < 90°W	90°W <H < 180°W
(iii) cos H > 0, sin H < 0	(iv) cos H < 0, sin H < 0
0° < H < 90°E	90°E < H < 180°E

We finally obtain λ, the longitude of the point |$\rm Z_{\rm g}$|⁠, from equation (10).

Table 1 lists the thus-determined latitude and longitude of the point |$\rm Z_{\rm g}$|⁠, just beneath point Z on the Earth, for points A and B. The results show that point Z is above the center of the Indian Ocean in the southern hemisphere during our observations.

Footnotes

1

IRAF is distributed by the National Optical Astronomy Observatories, which is operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation, USA.

2

〈http://cso.caltech.edu/tau/〉.

3

〈http://eodg.atm.ox.ac.uk/RFM/atm/〉.

4

〈https://ladsweb.modaps.eosdis.nasa.gov/search/〉.

5

〈https://ssd.jpl.nasa.gov/horizons.cgi〉.