Polarimetric signature of the oceans as detected by near-infrared Earthshine observations
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Astronomy & Astrophysics manuscript no. EarthshineNIC_astroph3 ©ESO 2021
September 15, 2021
Polarimetric signature of the oceans as detected by near-infrared
Earthshine observations
J. Takahashi1 , Y. Itoh1 , T. Matsuo2 , Y. Oasa3 , Y. P. Bach4, 5 , and M. Ishiguro4, 5
1
Center for Astronomy, University of Hyogo, 407-2 Nishigaichi, Sayo, Hyogo 679-5313, Japan
e-mail: takahashi@nhao.jp
2
Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
3
Faculty of Education / Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama
338-8570, Japan
4
Astronomy Program, Department of Physics and Astronomy, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826,
arXiv:2106.10099v3 [astro-ph.EP] 14 Sep 2021
Republic of Korea
5
SNU Astronomy Research Center, Department of Physics and Astronomy, Seoul National University, 1 Gwanak-ro, Gwanak-gu,
Seoul 08826, Republic of Korea
Received September 03, 2020; accepted June 18, 2021
ABSTRACT
Context. The discovery of an extrasolar planet with an ocean has crucial importance in the search for life beyond Earth. The po-
larimetric detection of specularly reflected light from a smooth liquid surface is anticipated theoretically, though the polarimetric
signature of Earth’s oceans has not yet been conclusively detected in disk-integrated planetary light.
Aims. We aim to detect and measure the polarimetric signature of the Earth’s oceans.
Methods. We conducted near-infrared polarimetry for lunar Earthshine and collected data on 32 nights with a variety of ocean
fractions in the Earthshine-contributing region.
Results. A clear positive correlation was revealed between the polarization degree and ocean fraction. We found hourly variations in
polarization in accordance with rotational transition of the ocean fraction. The ratios of the variation to the typical polarization degree
were as large as ∼0.2–1.4.
Conclusions. Our observations provide plausible evidence of the polarimetric signature attributed to Earth’s oceans. Near-infrared
polarimetry may be considered a prospective technique in the search for exoplanetary oceans.
Key words. Planets and satellites: oceans – Planets and satellites: terrestrial planets – Techniques: polarimetric
1. Introduction The second type of signature was identified from Earth’s
spectra. Robinson et al. (2014) observed Earth from the Lu-
As a solvent, a liquid phase seems more favorable for biochem- nar CRater Observation and Sensing Satellite (LCROSS) and
ical reactions than gas and solid phases (Benner et al. 2004). showed good agreement with the model spectrum that consid-
Therefore, the discovery of planets with a liquid ocean has cru- ered glint. Enhanced intensity contrasts between wavelengths
cial importance in the context of the search for extraterrestrial sensitive to the surface (e.g., ∼1.6 µm) and those insensitive due
life. How can we find an exoplanet with a surface ocean? to strong molecular absorption (e.g., ∼1.4 µm) are key features
With regard to non-polarimetric signatures of oceans, two indicating the contribution of glint from the oceans.
types signature have been confirmed by the astronomical obser- A polarimetric signature of oceans is also expected, and thus,
vations of Earth. These are (i) photometric variations caused by polarimetry has the potential to be another powerful technique.
the rotation of a planet covered by a surface with inhomogeneous Specular reflection (glint) from a smooth liquid surface is highly
reflectances and/or colors, and (ii) the spectroscopic signature of polarized (∼100% when the incident angle equals Brewster’s an-
glint (specular reflection) from an ocean. gle), as expressed by the Fresnel equations. Some researchers
For the first type, model calculations for an Earth-like planet theoretically studied the polarization of light reflected from plan-
expect a diurnal intensity (and color) variation because of the ets with an ocean (McCullough 2006; Stam 2008; Williams &
rotating brighter (redder) continents and darker (bluer) oceans Gaidos 2008; Zugger et al. 2010, 2011; Kopparla et al. 2018).
(Ford et al. 2001; Oakley & Cash 2009; Fujii et al. 2010); how- A common conclusion was that a cloud-free planet with a full
ever, it was also expected that the existence of clouds would ocean coverage exhibits a very high peak polarization degree
make surface-type determination much more difficult than the (>70%), which is significantly larger than that of planets with
cloud-free case (Ford et al. 2001; Oakley & Cash 2009). From other surface types. However, it is commonly noted that diffuse
an examination of the multiband light curves of Earth obtained scattering by clouds, atmospheric Rayleigh scattering, and vari-
from space by the EPOXI (Extrasolar Planet Observation and ous other effects dilute the polarimetric signature of the oceans.
Characterization (EPOCh) + Deep Impact Extended Investiga- Most of these theoretical works calculated the intensity and po-
tion (DIXI)) mission, a correlation between color and ocean frac- larization of the glint considering wind-driven tilts of the ocean
tion was identified (Cowan et al. 2009). surface based on the Cox–Munk model (Cox & Munk 1954).
Article number, page 1 of 20
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One benefit of polarimetry is that the degree of polarization in the Earthshine-contributing region (the region illuminated by
is virtually insensitive to telluric extinction because of the nature sunlight and viewable from the Moon), the dependence of the
of the relative measure (Stam 2008) that makes polarimetry ap- Earthshine polarization degree on the ocean fraction may be ob-
plicable both in space and on the ground. In contrast, the photo- served.
metric and spectroscopic signatures seem to be severely affected In the past, we measured Earthshine polarization degrees in
by telluric extinction and its variability, which make them more visible wavelengths on 19 nights. Although it was implied that
suitable for space observations than ground-based observations. Earthshine from an ocean-dominant Earth surface has a higher
Another benefit is the compatibility with high-contrast ob- polarization degree than that from a land-dominant surface, the
servations. Polarimetric differential imaging (PDI) is a widely difference was not statistically significant because of the large
utilized technique to enhance the contrast performance to de- observational errors (Takahashi et al. 2012).
tect polarized objects (planets and disks) around an unpolarized Sterzik et al. (2012) and Sterzik et al. (2019) presented po-
central star. The PDI technique can be used not only to detect larization degree spectra (in the visible wavelengths) of Earth-
planets but also to measure their polarization (Murakami et al. shine observed with the Very Large Telescope in Chile. They
2006; Takahashi et al. 2017). In addition, the fact that multiwave- showed that the polarization degrees of Earth with the Pacific
length observation is not required to detect the polarimetric sig- in view were significantly higher than those with the Atlantic in
nature is favorable for high-contrast observations because high- view. As possible causes of the polarization difference, Sterzik
contrast optics are very sensitive to wavelength, and therefore et al. (2019) suggested two factors: (a) different cloud coverages,
the effective bandwidth is currently limited to 10% of the central and (b) a larger contribution of ocean glint from the Pacific side;
wavelength (N’Diaye et al. 2016; Llop-Sayson et al. 2020). This however, conclusive evidence regarding the the ocean signature
seems advantageous to the polarimetric technique, in compari- has not been presented yet.
son with the techniques based on the photometric (color) varia- Although most of the previous Earthshine polarimetry was
tion and the spectroscopic contrasts. conducted in the visible wavelengths (
J. Takahashi et al.: Polarimetric Signature of Earth’s Oceans
µm), and K s -band (2.15 µm) imaging. In the imaging polarime-
try mode, a rotatable half-wave plate and a polarizing beam dis- (a) 20-04-29 12:00 (wax) (b) 19-11-21 19:00 (wan)
placer are inserted in the optical path (Takahashi et al. 2018;
Takahashi 2019). A pair of ordinary and extraordinary images
with a size of ∼ 2400 × 6900 is obtained with a single exposure.
Observations were conducted between May 2019 and April
2020 (Table A.1). Valid data were obtained for 32 nights. The
Moon was in the waxing phase for 20 nights and in the waning
phase for the other 12 nights. As observed from Japan, Earth-
shine on the waxing Moon is usually contributed by the Eurasian
and African continents and the Indian Ocean, whereas that on the
waning Moon originates from the Pacific Ocean and the Ameri-
cas (Fig. 1). Under our observation conditions, the ocean fraction (c) 20-01-03 10:00 (wax) (d) 20-01-03 14:00 (wax)
(with consideration of the cloud distribution) in the Earthshine-
contributing region ranged from ∼15–40% for the waxing phase,
and ∼20–45% for the waning phase. On average, the ocean frac-
tion is larger in the waning phase than in the waxing phase. We
covered a wide range of ocean fractions (∼15–45%), which al-
lowed us to investigate the possible dependence of the Earth-
shine polarization degrees on the ocean fraction. The ocean and
land fractions also vary on an hourly timescale because of the
Earth’s rotation, as shown in Fig. 1 (c) and (d), and this enabled
us to explore the hourly variations of the Earthshine polarization
degrees.
Fig. 1. Views of cloud-free Earth from the Moon at different observation
To minimize the undesired effects caused by observing dif- times. At each panel, the illuminated hemisphere is the Earthshine con-
ferent lunar locations, we conducted observations according tributing region. These images were created with the Earth and Moon
to the following procedure. On each observing night, we first Viewer3 developed by John Walker.
pointed the Nayuta telescope toward the crater Grimaldi (seleno-
graphic coordinate: 68.6◦ W, 5.2◦ S) in the waxing phase and the
crater Neper (84.5◦ E, 8.8◦ N, east of Mare Crisium) in the wan- The exposure time for a single frame was usually 20–180
ing phase, after correcting the pointing error measured using a seconds depending on the brightnesses of the Earthshine and the
nearby star. Both craters are near the lunar edge (distances . 20 ). sky. A series of four exposures corresponding to four different
Then, we scanned the Moon along the RA axis until the edge rotation angles of the half-wave plate (φhwp = 0◦ , 45◦ , 22.5◦ , and
of the Moon was placed near the center of the field of view 67.5◦ ) produced a set of normalized Stokes parameters q = Q/I
(FOV). An example of the observed (and reduced) images is and u = U/I. We call this single series a “sequence” of obser-
shown in Fig. 2. Our target locations are not on a major maria vations. With a typical interval of ∼30 minutes, we observed a
and near sites repeatedly observed in previous Earthshine pho- blank sky region 6000 –9000 east or west of the observing lunar
tometry because they were expected to have roughly comparable edge. The exposure time for the blank sky observations was set
albedos (Qiu et al. 2003; Pallé et al. 2004; Montañés-Rodríguez to be the same as that for the Earthshine observations.
et al. 2007). Half of the FOV was reserved for the sky, which After basic image processing including flat fielding and the
allows the sky background intensities and their positional gradi- subtraction of the sky background, the maps of normalized
ents to be measured. The position angle of the instrument (φinspa ) Stokes parameters q = Q/I and u = U/I were produced (Fig. 2).
was maintained at 90◦ from the equatorial north, as measured The values of q and u in a region of ∼ 1600 × 800 are extracted
counter-clockwise, so that the long side of the FOV was aligned and averaged. The polarization degree (fractional polarization,
with the RA axis. Telescope tracking was conducted in accor- P) and polarization position angle (Θ) are converted from q and
dance with the sky motion of the Moon, which was calculated u with a correction of positive bias (Plaszczynski et al. 2014).
at the Jet Propulsion Laboratory (JPL) Horizons system1 . Be- We confirm that the derived Θ is almost always perpendicular
cause the tracking was not perfect, we shifted the telescope east to the scattering plane (the plane that includes the Sun, Earth,
or west with a typical interval of ∼30 minutes so that the lunar and Moon), as shown in Fig. 3, and this supports the fact that
edge remained near the center of the FOV. Features on the Moon we successfully extracted the polarization by the reflection of
were hardly recognizable in the raw images because of the dim sunlight by Earth. Details on the data reduction are presented in
Earthshine and strong scattered light from the day side of the Appendix B.
Moon, though we were able to visually identify the lunar edge
in most cases2 . Despite our efforts, the actually observed loca-
tion may have varied night by night even within one phase (wax- 3. Results
ing phase or waning phase), or on an hourly timescale during a 3.1. Nightly means
single night. Possible impacts induced by different lunar loca-
tions (namely different degrees of depolarization) are discussed All observed polarization degrees (P) as nightly means are sum-
in Sect. 4.1. marized in Table A.2 and illustrated in Fig. 4. The only previous
near-infrared polarimetry for Earthshine (Miles-Páez et al. 2014)
1
https://ssd.jpl.nasa.gov/horizons.cgi reported a P of ∼3–5% at α ∼ 100◦ , which approximately agrees
2
In cases where it was impossible to identify the lunar edge, we with our results. The observed P increased with the increasing
quickly subtracted sky background intensity from a raw image using
3
a blank sky frame, which helped us to find the edge. http://www.fourmilab.ch/earthview/
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150 6 6
125 4 4
100
intensity (ADU)
2 2
Stokes q0 (%)
Stokes u0 (%)
75 0 0
50
−2 −2
25
−4 −4
0
−6 −6
−25
Fig. 2. Intensity (left), Stokes q0 (middle), and u0 (right) images observed on 2020 January 3. North is right, and east is up. The FOV is ∼ 1900 ×6400
(smaller than original FOV because of trimming). The parallelograms are the sampling regions. The values of q0 and u0 on the sky are scattered
because of division of ∼0 by ∼0.
manner. In general, the polarization degree of reflected light de-
90
Φ=N pends on both properties of the reflecting body and phase angle.
pol. position angle, Θ (deg)
J (waxing) We fit a curved line to all data points (except some outliers) in
60 J (waning) Fig. 4 (see Appendix B.4 for details of the fitting). The fit curve,
H (waxing)
30 H (waning)
denoted by Pmean , corresponds to the polarization phase curve
Ks (waxing) (phase angle dependence of polarization degrees) for the typical
0 Ks (waning) scene combination on the Earthshine contributing region. The
contrast of the observed P to Pmean for the same α represents the
−30 extent to which P deviates from the polarization degree of the
typical Earth scene, and it clarifies the discussion on the depen-
−60 dence of P on the actual Earth scene because the phase-angle
dependence is suppressed.
−90 Figure 5 (top row) displays P/Pmean plotted against the ocean
−90 −60 −30 0 30 60 90
normal to scattering plane, N (deg) fraction. We see a clear positive correlation of P/Pmean with the
ocean fraction for all J, H, and K s bands. In other words, P
tends to be larger when we have a larger ocean fraction if α is
Fig. 3. Observed position angles of Earthshine polarization as plotted fixed. This is probably attributed to the greater contribution from
against position angles normal to scattering plane. highly polarized sea glint. We also plot P/Pmean against land
fraction and cloud fraction (Fig. 5, middle and bottom rows).
In Fig. 5 (middle row), P/Pmean appears to be negatively corre-
Sun-Earth-Moon phase angle (α), and it reached its peak of ∼4% lated with the land fraction, though the correlation is less clear
or larger at an α between 120◦ and 150◦ . The overall shape of the than that for the ocean fraction. In Fig. 5 (bottom row), no clear
P phase curve and α for the peak P agree with theoretical pre- correlation of P/Pmean is found with the cloud fraction.
dictions by Williams & Gaidos (2008), Zugger et al. (2011), and We classified clouds into three types based on the cloud top
Kopparla et al. (2018), who calculated the polarization degree of height (htop ). Following Lamb & Verlinde (2011), we defined
an ocean planet in the near-infrared wavelengths (or considering clouds for htop ≥ 7 km as high clouds, those for 2 km ≤ htop <
no contribution from atmospheric Rayleigh scattering). 7 km as middle clouds, and those for htop < 2 km as low clouds.
Our primary focus is the possible dependence of the polar- Figure 6 explores the possible dependences of P/Pmean on frac-
ization degree on the ocean fraction. The ocean fraction in the tions of high clouds (top row), middle clouds (middle row), and
Earthshine-contributing region is expressed by the darkness of low clouds (bottom row). Although it is interesting that high
the plot colors in Fig. 4. This set of figures provides an interest- clouds and the other types appear to have opposite dependences,
ing impression that data points with a larger ocean fraction tend none of the correlations are as strong as that for the ocean frac-
to have a larger P than those with a smaller ocean fraction at a tion (Fig. 5, top row).
similar α. The stronger correlation with the ocean fraction ( fo ) than that
We performed the following analysis to illustrate the possi- with the land fraction ( fl ) or cloud fraction ( fc ) can be explained
ble dependence of P on the ocean fraction in a more quantitative as follows. The three types of scenes can be divided into two
Article number, page 4 of 20J. Takahashi et al.: Polarimetric Signature of Earth’s Oceans
groups: (i) oceans as a strong polarizer (because of specular re- efficiency, ) of the Moon at the near-infrared wavelengths is
flection), and (ii) lands and clouds as weak polarizers (because not well known. It is known that depends on surface albedo
of multiple scattering). Because polarimetric effects from the (Dollfus 1957; Bazzon et al. 2013), and a medium with a higher
lands and the clouds are (very) roughly similar, the net polar- albedo has a lower . Bazzon et al. (2013) derived an empirical
ization of Earth should be largely determined by the ratio of fo formula (Eq. (9) of that paper) of as a function of albedo and
to ( fl + fc ), regardless of the specific values of fl and fc . Hence, the wavelength, which is valid in the visible wavelengths. When
the strong correlation of P/Pmean with fo was observed. Once fo we extend the formula to near-infrared wavelengths (1.2–2.2
is given, ( fl + fc ) is automatically fixed since we have a relation µm) with typical highland albedos (0.15–0.25 in visible wave-
of fo + fl + fc = 1. In contrast, even if fc (or fl ) is given, the lengths), ∼ 0.2–0.3 is deduced. Hence, the observed Earthshine
ratio of fo to fl ( fc ) should have a significant impact on the net polarization degree of ∼4% at the peak (as shown in Fig. 4) prob-
Earth polarization. This is probably the reason why we observed ably corresponds to Earth’s polarization degree of ∼13–20%.
a weaker correlation with fc ( fl ) than that with fo . The weaker We always show the observational results in (unconverted)
correlation with fc does not deny a major role of clouds in the Earthshine polarization degrees because there is a considerable
net Earth polarization. The type of surface covered by clouds is uncertainty in the conversion from the Earthshine polarization
important. degree to the Earth’s polarization degree. Furthermore, this is
why we avoided relying on the absolute value of the Earthshine
polarization degree in our discussion of the ocean signatures in
3.2. Hourly variations
Sect. 3. Instead, we discuss it in a relative manner (i.e., using
Fractions of scene types on the Earthshine contributing region P/Pmean and ∆P/P̄) because the dependence on disappears as
vary on an hourly timescale corresponding to Earth’s rotation long as is constant. Although we believe the impact from
(see Fig. 1 (c, d) for 2020 January 3). Hence, it is possible to is minimized in this manner, varies if we observe different
observe the hourly variation of P in accordance with the scene lunar locations with different albedos, and thus may cause an
transition. We investigated the time variation of P on six dates, undesired impact on our discussion. Below, we examine its im-
on which we made a valid observation for more than two hours pact on our discussion with respect to the nightly means and the
on a single night. Time-resolved P values from all six dates are hourly variations of Earthshine P. We note that we do not need
divided by Pmean , as obtained from Fig. 4, and plotted against to consider the phase dependence of because the phase angle of
the ocean, land, and cloud fractions in Fig. 7. Similarly to what the depolarizing back-scattering on the Moon (the Earth–Moon–
is seen in Fig. 5, a clear positive correlation of P/Pmean with the Earth angle) is always zero regardless of the lunar phase.
ocean fraction is deduced again.
Time-series P on the six dates is presented in Figs. 8–9, with 4.1.1. Impact on nightly-mean P
scene fractions and the observed position angle of polarization.
Among the six dates, we observed significant variations in P on In Sect. 3.1, we treat the combined dataset of Earthshine P from
three dates (2019 December 18, 2020 January 3, and 2020 March both the waxing and waning lunar phases, and we found a corre-
2) in all three bands (Fig. 8, left). The ratios of peak-to-peak vari- lation of P with the ocean fraction, as shown in Figs. 4 and 5. For
ation (∆P) to the averaged polarization degree (P̄) range from Earthshine observations, we must point to the opposite (western
∼0.2 to ∼1.4 (Table 1). The position angle of the polarization and eastern) sides of the Moon between the waxing and wan-
was almost constant and it was confined to be perpendicular to ing phases because the opposite sides are illuminated by sun-
the scattering plane for all six dates and all three bands (Figs. 8– light. If two different lunar locations for the waxing and waning
9, right). phases have different albedos, an apparent difference of Earth-
We attempted to reproduce the observed hourly variations shine P may be induced by different . Indeed, the near-infrared
in P (including the non-variations) based on scene fractions at spectro-polarimetry of Earthshine by Miles-Páez et al. (2014)
the time, by referring to a model of planetary reflected light showed a contrast with a factor of 1.8 ± 0.3 between polariza-
(Williams & Gaidos 2008). The detailed description of the model tion degrees observed on two separate lunar locations. Because
is provided in Appendix C. We see an excellent (2020 January 3 the ocean fraction is tied to the waxing-or-waning phases (on av-
and 2020 March 2) or fairly good (2019 November 21, 2019 De- erage, the ocean fraction is larger for the waning phase than for
cember 19, and 2020 April 29) agreement between the observed the waxing phase), there is a potential risk that the effect from
P and modeled P, except for on 2019 December 18 (Figs. 8–9). different values may be wrongly interpreted as the effect from
The disagreement on 2019 December 18 may be attributed to the oceans.
insufficient time resolution of the referred data of cloud distribu- Figure 10 displays the same (P, α) dataset as Fig. 4; however,
tion (see Appendix C). We discuss other possible causes (such it distinguishes the waxing and waning phases by plot styles. It
as lunar depolarization, telluric polarization, and artificial polar- is barely recognizable that P is likely to be higher for the waning
ization) in Sect. 4. We observe a resemblance between the time- phase than for the waxing phase. However, the dependence of
variation of the ocean fraction and that of the modeled P (Fig. 8); P on the ocean fraction as shown in Fig. 4 seems more obvious
this indicates that mainly the ocean fraction controls the hourly than the difference between the waxing and waning phases as
variation in the polarization degree of Earth. shown in Fig. 10.
If the Earthshine P were severely affected by a significant
difference in between two different lunar locations correspond-
4. Impacts of misleading factors ing to the waxing- and waning-phase observations, the difference
4.1. Depolarization at the lunar surface in Fig. 10 between the two phases should be more distinct. The
indistinct waxing-or-waning difference is easily understood by
The polarization of Earthshine is not the same as the polariza- accepting that Earthshine P is affected by the ocean fraction. Al-
tion of Earth as observed from outside the planet. The light from though the ocean fraction is larger in the waning phase than in
Earth is depolarized when it is back-scattered from the lunar the waxing phase on average, it is often similar between the two
surface (Dollfus 1957). The depolarizing factor (or polarization phases depending on the date and time. During our observations,
Article number, page 5 of 20A&A proofs: manuscript no. EarthshineNIC_astroph3
10
J band
40 10
H band 40 10
Ks band
40
mean (w=0.27, s=0.13) mean (w=0.30, s=0.15) mean (w=0.18, s=0.09)
ocean faction, fo (%)
ocean faction, fo (%)
ocean faction, fo (%)
35 35 35
pol. degree, P (%)
pol. degree, P (%)
pol. degree, P (%)
8 8 8
30 30 30
6 6 6
25 25 25
4 4 4
20 20 20
2 15 2 15 2 15
0 10 0 10 0 10
0 30 60 90 120 150 180 0 30 60 90 120 150 180 0 30 60 90 120 150 180
phase angle, α (deg) phase angle, α (deg) phase angle, α (deg)
Fig. 4. Earthshine polarization degrees (P) in J (left), H (middle), and K s (right) bands, plotted against Sun-Earth-Moon phase angle (α). The ocean
fraction was calculated with concentrated weighting (see Appendix B.5 for details on the derivation of the fractions). The dashed lines represent the
polarization phase curve for the typical Earth scene. They are derived from fitting a curved line to all data points (with some exceptions described
below) with free parameters w (single scattering albedo) and s (scaling factor). The crosses represent data points corresponding to |Θ − N| > 15◦
(where Θ denotes the position angle of polarization and N denotes the position angle normal to the scattering plane) or α < 50◦ , which were
excluded from the fitting (see Appendix B.4 for details on the fitting). These figures give an impression that P for a larger ocean fraction (plots
with a darker color) tends to be larger than those for a smaller ocean fraction at a similar α, which suggests that the contribution from the sea glint
(specular reflection) enhances the polarization degree of Earth.
• Ocean fraction
J band H band Ks band
4 waxing 4 waxing 4 wa ing
waning waning waning
a=3.4, b=0.1, r=+0.64 a=4.1, b= 0.1, r=+0.69 a=4.9, b=−0.3, r=+0.72
3 3 3
P Pmean
P/Pmean
P/Pmean
2 2 2
/
1 1 1
0 0 0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
ocean fraction, fo (%) ocean fraction, fo (%) ocean fraction, fo (%)
• Land fraction
J band H band Ks band
4 waxing 4 waxing 4 waxing
waning waning waning
a=−1.3, b=1.3, r=−0.42 a=−1.4, b=1.3, r=−0.43 a= 1.7, b=1.3, r= 0.44
3 3 3
P Pmean
P/Pmean
P/Pmean
2 2 2
/
1 1 1
0 0 0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
land fraction, fl (%) land fraction, fl (%) land fraction, fl (%)
• Cloud fraction
J band H band Ks band
4 waxing 4 waxing 4 waxing
waning waning waning
a=0.3, b=1.0, r=+0.07 a=0.2, b=1.0, r=+0.06 a=0.2, b=1.0, r=+0.04
3 3 3
P Pmean
P/Pmean
P/Pmean
2 2 2
/
1 1 1
0 0 0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
cloud fraction, fc (%) cloud fraction, fc (%) cloud fraction, fc (%)
Fig. 5. Dependence of polarization degree on ocean (top), land (middle), and cloud (bottom) fractions (in J, H, and K s bands from left to right).
Each polarization degree (P) in Fig. 4 is divided by typical polarization (Pmean : dashed line in Fig. 4) at the phase angle, and then plotted against
the ocean, land, or cloud fraction ( fo , fl , or fc , respectively). The filled and open plots correspond to observations in the waxing and waning phases,
respectively. The dashed lines are regression lines of the form a f + b with a correlation coefficient r. The crosses correspond to those in Fig. 4 and
were excluded from the linear regression. The fractions was calculated with concentrated weighting.
Article number, page 6 of 20J. Takahashi et al.: Polarimetric Signature of Earth’s Oceans
• High-cloud fraction
J band H band Ks band
4 waxing 4 waxing 4 waxing
waning waning waning
a=−0.9, b=1.4, r=−0.25 a=−0.6, b=1.3, r=−0.15 a=−0.6, b=1.2, r=−0.13
3 3 3
P Pmean
P/Pmean
P/Pmean
2 2 2
/
1 1 1
0 0 0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
high-cloud fraction (%) high-cloud fraction (%) high-cloud fraction (%)
• Mid-cloud fraction
J band H band Ks band
4 waxing 4 waxing 4 waxing
waning waning waning
a=4.7, b=0.3, r=+0.37 a=1.3, b=0.9, r=+0.11 a=1.1, b=0.9, r=+0.09
3 3 3
P Pmean
P/Pmean
P/Pmean
2 2 2
/
1 1 1
0 0 0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
mid-cloud fraction (%) mid-cloud fraction (%) mid-cloud fraction (%)
• Low-cloud fraction
J band H band Ks band
4 waxing 4 waxing 4 waxing
waning waning waning
a=2.1, b=0.8, r=+0.37 a=1.8, b=0.8, r=+0.28 a=1.8, b=0.8, r=+0.25
3 3 3
P Pmean
P/Pmean
P/Pmean
2 2 2
/
1 1 1
0 0 0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
low-cloud fraction (%) low-cloud fraction (%) low-cloud fraction (%)
Fig. 6. Dependence of polarization degree on high- (top), middle- (middle), and low-cloud (bottom) fractions (in J, H, and K s bands from left to
right). The legends are the same as those in Fig. 5.
the ocean fraction was ∼15–40% for the waxing phase and ∼20– waxing- and waning-phase observations, but are instead caused
45% for the waning phase. There is a large overlap in the ocean by the Earth’s oceans.
fractions. In this section, we discuss a possible impact of the differ-
Furthermore, Fig. 5 (top row) supports our interpretation. We ence in between the waxing and waning phases. Within one
consider two cases where Earthshine P is affected by two differ- or the same phase (waxing phase or waning phase), we invested
ent values corresponding the waxing and waning phases. our best effort to observe the same lunar location as described in
First, we assume that Earthshine P is affected by different Sect. 2. However, the actually observed location may be slightly
depolarizing factors, but it is not affected by ocean fractions. In different from night to night because of the limited pointing ac-
this case, the data plots in Fig. 5 (top row) should be split into curacy, and this can cause night-to-night differences in . In con-
two levels, rather than showing a linear correlation. For instance, trast to the difference between the waxing and waning phases,
if is smaller (i.e., more depolarizing) in the waxing phase than the night-to-night differences in (caused by telescope point-
in the waning phase, the plots should be distributed on a lower ing) is not coupled with Earth’s ocean fraction. Therefore, it is
level (a smaller P/Pmean ) for the waxing phase and in a higher unlikely that the night-to-night differences cause the linear cor-
level (a larger P/Pmean ) for the waning phase. relation shown in Fig. 5 (top row). Nonetheless, the deviations
Second, we assume that Earthshine P is affected by both of from the regression line in Fig. 5 (top row) may be caused in
the different depolarizing factors and the ocean fractions. In this part by the night-to-night differences in .
case, we can draw two separate regression lines for the waxing
and waning phases in Fig. 5 (top row). In reality, however, the 4.1.2. Impact on hourly variation of P
data points from both phases appear to roughly fall on a single
regression line. Because different lunar locations may have different albedos, im-
Based on the above discussions, we are convinced that the perfect telescope tracking can lead to a false hourly variation in
retrieved linear correlations in Fig. 5 (top row) do not result from P that does not correspond to any of Earth’s properties. We at-
the difference (if any) in the lunar depolarizing factors between tempt to estimate the possible variation of P caused by the shift
Article number, page 7 of 20A&A proofs: manuscript no. EarthshineNIC_astroph3
• Ocean fraction
J band H band Ks band
4 waxing 4 waxing 4 waxing
waning waning waning
a=2.7, b=0.3, r=+0.77 a=2.5, b=0.3, r=+0.67 a=3.4, b=0.0, r=+0.85
3 3 3
P Pmean
P/Pmean
P/Pmean
2 2 2
/
1 1 1
0 0 0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
ocean fraction, fo (%) ocean fraction, fo (%) ocean fraction, fo (%)
• Land fraction
J band H band Ks band
4 waxing 4 waxing 4 waxing
waning waning waning
a= 1.0, b=1.2, r= 0.50 a=−0.8, b=1.1, r=−0.42 a=−1.4, b=1.2, r=−0.64
3 3 3
P Pmean
P/Pmean
P/Pmean
2 2 2
/
1 1 1
0 0 0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
land fraction, fl (%) land fraction, fl (%) land fraction, fl (%)
• Cloud fraction
J band H band Ks band
4 waxing 4 waxing 4 waxing
waning waning waning
a=0.3, b=0.9, r=+0.10 a=0.3, b=0.8, r=+0.11 a=0.8, b=0.6, r=+0.24
3 3 3
P Pmean
P/Pmean
P/Pmean
2 2 2
/
1 1 1
0 0 0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
cloud fraction, fc (%) cloud fraction, fc (%) cloud fraction, fc (%)
Fig. 7. Same figure as Fig. 5, except the data source is the time-resolved data on 2019 November 21, 2019 December 18, 2019 December 19, 2020
January 3, 2020 March 2, and 2020 April 29. The data on the same date are connected by lines.
of the observation location on the Moon. Although our target ∆P/P̄ = 1 − min /¯ . The results from the calculations are listed
locations are not on the major maria, we occasionally recog- in Table 1.
nize a dark patch on the reduced lunar images. From the vi- For comparison, we determine ∆P/P̄ in the observed values.
sual inspection of the intensity (I) images on the three dates Time-series P (Fig. 8; left column) is fit by a linear function. We
when a P variation is detected, we approximately determined take the difference of P at the two ends of the fit line as ∆P and
the intensity contrasts between a dark region and the surround- the average as P̄. This derivation aims to avoid the overestima-
ing typical region (Idark /Ityp ) in addition to the maximum area tion of ∆P caused by a single extreme data point. The derived
ratio of the dark region within the sampling region (S dark /S smpl ). ∆P/P̄ in the observed values is summarized in Table 1.
Then, assuming that the albedo is proportional to the observed The ∆P/P̄ estimated based on the variation in lunar depolar-
intensity, we estimate the possible highest
albedo contrast for ization is ∼0.1 at the maximum. That variation is significantly
smaller than the observed ∆P/P̄, which ranges from ∼0.2 to
the night by Amin /Ā 1 − S dark /S smpl 1 − Idark /Ityp , where
A denotes the effective albedo of the sampling region (Amin is ∼1.4. Therefore, the variation in lunar depolarization cannot ex-
the minimum and Ā is the mean)4 . From the difference be- plain the observed variation of P.
tween Eq. (9) in Bazzon et al. (2013) for Amin and Ā, we have Even if the depolarization variation caused by the tracking
log(min /¯ ) = −0.61 log(Ā/Amin ). Although the albedo in Eq. error contributes part of the hourly variations in the observed
(9) in Bazzon et al. (2013) is at wavelength of 602 nm, we as- Earthshine P, it is very unlikely that the tracking error, which is
sumed that the ratio of two albedos has a negligible wavelength independent of the scene fractions, can create clear correlations
dependence. Then, we estimate the relative variation of P by with the ocean fraction as shown in Fig. 7.
S smpl −S dark
4
From the assumption, we have Ā ∝ Ityp and Amin ∝ S smpl
Ityp + 4.2. Telluric and telescope polarization
S dark
The equation for Amin /Ā is derived by dividing the latter for-
I .
S smpl dark The term “telluric” in this article refers to the Earth’s atmosphere
mula by the former. on the path from a celestial body to a ground-based observer.
Article number, page 8 of 20J. Takahashi et al.: Polarimetric Signature of Earth’s Oceans
2019-12-18 ( aning, α = 97 ∘ ) 2019-12-18 × lunar EL 2019-12-18
5 80 90 90
lunar elevation (deg)
N
position angle (deg)
∘odel (ε = 0.25)
pol. degree, P (%)
4 60
60
fraction (%)
ocean
land 60 30
3
40 cloud 0
2
30 −30
1
20
−60
0 0 0 −90
15 16 17 18 19 15 16 17 18 19 15 16 17 18 19
UT (h) UT (h) UT (h)
2020-01-03 (waxing, α = 94 ) 2020-01-03 × lunar EL 2020-01-03
5 80 90 90
lunar elevation (deg)
N
position angle (deg)
∘odel (ε = 0.25)
pol. degree, P (%)
4 60
60
fraction (%)
ocean
land 60 30
3
40 cloud 0
2
30 −30
1
20
−60
0 0 0 −90
10 11 12 13 14 15 10 11 12 13 14 15 10 11 12 13 14 15
UT (h) UT (h) UT (h)
2020-03-02 (wa ing, α = 86 ∘ ) 2020-03-02 × lunar EL 2020-03-02
5 80 90 90
lunar elevation (deg)
ocean N
position angle (deg)
∘odel (ε = 0.25)
pol. degree, P (%)
4 land 60
60 cloud
fraction (%)
60 30
3
40 0
2
30 −30
1
20
−60
0 0 0 −90
9 10 11 12 13 9 10 11 12 13 9 10 11 12 13
UT (h) UT (h) UT (h)
Fig. 8. Time-series polarization degrees (left column), scene fractions (middle column), and polarization position angles (right column) for dates
when significant hourly variation of polarization degree is detected. (Left) Polarization degrees: Squares, circles, and triangles represent data in the
J, H, and K s bands, respectively. Open plots represent data points with |Θ−N| > 15◦ . The dashed line is the model curve for Earthshine polarization
calculated based on the ocean, land, and cloud fractions. The applied lunar polarization efficiency (depolarizing factor, ) is shown in the inset.
(Middle) Scene fractions: Ocean, land, and cloud fractions are exhibited as solid, dashed, and dotted lines, respectively (left y-axes). Fractions
were calculated with concentrated weighting (see Appendix B.5). The crosses correspond to lunar elevation (right y-axes). (Right) Polarization
position angles: Solid lines in the right panels show the position angle normal to the scattering plane.
Table 1. Estimates of possible polarization variation caused by lunar depolarization.
Date Idark /Ityp S dark /S smpl ∆P/P̄ ∆P/P̄
depol obs
(year-month-day) J H Ks
2019-12-18 0.6 ≤ 0.3 ≤ 0.08 0.19 1.30 0.43
2020-01-03 0.8 ≤ 0.9 ≤ 0.11 1.09 0.84 1.35
2020-03-02 0.8 ≤ 0.5 ≤ 0.06 0.39 0.77 1.17
Telluric effects should be eliminated because we are only in- the Canary Islands under a relatively strong effect from the Sa-
terested in the Earth’s properties as observed from outside the haran dust (Bailey et al. 2008), provides a good upper limit to
planet. Although it is usually assumed that telluric extinction telluric polarization.
does not polarize celestial light because of isotropy, extremely In addition, both of the above-mentioned telluric polarizing
precise polarimetry by Bailey et al. (2008) indicated that telluric effects tend to be larger for a larger airmass (i.e., a lower eleva-
airborne dust can polarize celestial light because of the dichroic tion) (Kemp et al. 1987; Bailey et al. 2008). However, all our ob-
extinction caused by the dust. Nonetheless, the observed maxi- served variations in P exhibited the opposite transition: on 2019
mum polarization caused by this effect is as small as ∼ 5 × 10−5 , December 18, P increased with time while the Moon ascended;
which is much smaller than our observed P and its variations. on 2020 January 3 and 2020 March 2, P decreased with time
Based on very sensitive solar polarimetry, Kemp et al. (1987) while the Moon descended (Fig. 8; left and middle columns).
identified telluric polarization attributed to double scattering by Therefore, we are convinced that polarization caused by telluric
aerosols and molecules in the Earth’s atmosphere. However, the effects does not significantly affect our observations.
measured polarization degree by this effect was ∼ 8 × 10−6 at the When the telescope pointing elevation is below 22◦ , part of
maximum. Although other telluric polarizing sources may exist, the light beam incident onto the primary mirror is blocked by
we believe that a ∼ 5 × 10−5 polarization degree, measured from the enclosure wall. This breaks symmetry with respect to the
Article number, page 9 of 20A&A proofs: manuscript no. EarthshineNIC_astroph3
2019-11-21 (waning, α = 64 ∘ ) 2019-11-21 × lunar EL 2019-11-21
5 80 90 90
lunar elevation (deg)
ocean N
position angle (deg)
∘odel (ε = 0.30)
pol. degree, P (%)
4 land 60
60 cloud
fraction (%)
60 30
3
40 0
2
30 −30
1
20
−60
0 0 0 −90
18 19 20 21 22 18 19 20 21 22 18 19 20 21 22
UT (h) UT (h) UT (h)
2019-12-19 (waning, α = 82 ) 2019-12-19 × lunar EL 2019-12-19
5 80 90 90
lunar elevation (deg)
N
position angle (deg)
∘odel (ε = 0.30)
pol. degree, P (%)
4 60
60
fraction (%)
ocean
land 60 30
3
40 cloud 0
2
30 −30
1
20
−60
0 0 0 −90
18 19 20 21 18 19 20 21 18 19 20 21
UT (h) UT (h) UT (h)
2020-04-29 (waxing, α = 74 ∘ ) 2020-04-29 × lunar EL 2020-04-29
5 80 90 90
lunar elevation (deg)
ocean N
position angle (deg)
∘odel (ε = 0.20)
pol. degree, P (%)
4 land 60
60 cloud
fraction (%)
60 30
3
40 0
2
30 −30
1
20
−60
0 0 0 −90
10 11 12 13 14 15 10 11 12 13 14 15 10 11 12 13 14 15
UT (h) UT (h) UT (h)
Fig. 9. Same as Fig. 8, but for dates when significant hourly variation of the polarization degree is not detected.
10
J band
10
H band 10
Ks band
mean (w=0.27, s=0.13) mean (w=0.30, s=0.15) mean (w=0.18, s=0.09)
waxing waxing waxing
pol. degree, P (%)
pol. degree, P (%)
pol. degree, P (%)
8 8 8
waning waning waning
6 6 6
4 4 4
2 2 2
0 0 0
0 30 60 90 120 150 180 0 30 60 90 120 150 180 0 30 60 90 120 150 180
phase angle, α (deg) phase angle, α (deg) phase angle, α (deg)
Fig. 10. Same as Fig. 4, except plot styles are distinguished by waxing-or-waning lunar phases. The filled and open plots represent observations in
the waxing and waning phases, respectively.
telescope optical axis and can induce significant telescope polar- of previous near-infrared polarimetry forces us to rely on results
ization. The degree of the telescope polarization should increase at the visible wavelengths.
as the pointing elevation decreases. However, P varied in the op- Anti-correlation between the albedo and polarization degree
posite sense, as described above. Thus, we exclude this effect of the reflected light is known as the Umov effect (Hapke 2005).
from the causes of the observed variation in P. The polarimetry of the integrated disk of the Moon showed dif-
ferent P at the peak of phase curves between the waxing and
waning phases (Lyot 1929; Coyne & Pellicori 1970): the waning
5. Implications Moon was more polarized than the waxing Moon. The western
5.1. Distinctiveness of polarimetric signature (in selenographic coordinates) part of the Moon, illuminated in
the waning phase, has a larger fraction of maria, and therefore it
One of the issues we should address is whether it is possible has a larger polarization than the eastern part. According to past
to distinguish between planets with an ocean and those without observations (Coyne & Pellicori 1970), P at the effective wave-
an ocean based on the observations of rotational variations in length of 534 nm was 10.9% at its peak in the waning phase,
polarization. Comparison with near-infrared polarization of the whereas it was 8.1% in the waxing phase. This implies that we
Solar System objects would help the discussion; however, a lack will obtain ∆P/P̄ 0.3 when we observe a rotation of the Moon
Article number, page 10 of 20J. Takahashi et al.: Polarimetric Signature of Earth’s Oceans
from outside the Earth-Moon system (above the lunar equator). ∆Pfeature ∆Ptime and Pcont P̄). Although the target signa-
These previous observations by Coyne & Pellicori (1970) were ture in the previous work was a spectro-polarimetric feature with
performed at several different wavelengths between 336 nm and a feature width of ∆λ 0.05 µm, in the current work it is a
534 nm; the corresponding ∆P/P̄ values at different wavelengths broad-band signature. Hence, we can set ∆λ 0.15 µm assum-
do not exhibit an obvious wavelength dependence. Therefore, we ing the coronagraph bandwidth to be ∼10% of the H-band cen-
expect that the near-infrared ∆P/P̄ of the Moon will not differ tral wavelength (∼1.6 µm). This reduces the required exposure
significantly from that at visible wavelengths (i.e., ∼0.3). time to 15 × 0.05/0.15 = 5 hours. In the meantime, planets in the
Asteroid (4) Vesta is the only asteroid known to exhibit habitable zone around M-type stars, which are the main target
a convincing rotational variation in the polarization degree of the in-development ground-based extremely large telescopes,
(Cellino et al. 2016) owing to the inhomogeneous albedo dis- are likely to be tidally locked (Kasting et al. 1993). Thus, a com-
tribution. In previous visible polarimetry for Vesta, ∆P/P̄ was parison of polarization between the waxing and waning near-
in the range 0.06–0.24 (Degewij et al. 1979; Broglia & Manara quadrature phases will be effective for searching an inhomoge-
1989; Lupishko et al. 1999; Wiktorowicz & Nofi 2015). These neously distributed ocean in the star-facing hemisphere, as long
values were observed at phase angles of less than 20◦ when the as the system is not face-on. In this case, the five-hour exposure
polarization is negative (parallel to the scattering plane). It is not time is sufficient to compare the two orbital phases.
certain whether ∆P/P̄ in the negative polarization regime is sim- Although forthcoming extremely large ground-based tele-
ilar to that near the peak of positive polarization. scopes will not be optimized for polarimetry, some envisioned
The previous observations of the Moon and Vesta suggest high-contrast instruments — namely, the Planetary Camera and
that for airless rocky bodies ∆P/P̄ are likely to be ∼0.3 or less. Spectrograph (PCS, Kasper et al. 2021) for ELT, and the Plane-
For comparison, the near-infrared ∆P/P̄ of the Earth was 0.2– tary Systems Imager (PSI, Fitzgerald et al. 2019) for the Thirty
1.4 when P was highly variable (Table 1). Hence, we believe Meter Telescope (TMT) — will have imaging polarimetry capa-
that the ∆P/P̄ of a planet with an Earth-like ocean fraction can bilities. It is worth seriously considering a search for an exoplan-
be significantly larger than that of airless rocky planets. etary ocean using these instruments.
For small icy bodies, we notice that some satellites exhibit Although we demonstrated an estimate of the feasibility of
a large difference in polarization depending on the central lati- ground-based detection, it does not imply that this technique
tude (Rosenbush 2002; Ejeta et al. 2013). An analysis of the pre- cannot be implemented by space telescopes. The space-based
vious polarimetry of Jupiter’s satellite Callisto showed a ∆P/P̄ time-series polarimetry for habitable-zone planets orbiting G-
of ∼0.3–0.5 at visible wavelengths (Rosenbush 2002). Spectro- type stars is also worth considering when detecting the rotational
polarimetry results of Saturn’s satellite Iapetus for both its lead- variability of polarization caused by the existence of a partial
ing and trailing hemispheres correspond to a ∆P/P̄ of ∼0.8–1.5 ocean.
at a wavelength ∼900 nm (Ejeta et al. 2013), which is com-
parable to values from our Earthshine polarimetry in the near-
infrared. These results suggest that the surface of the icy plan- 6. Conclusions
etary bodies can have an extraordinarily distinctive albedo con-
Our near-infrared polarimetry of Earthshine indicated the po-
trast that causes a large ∆P/P̄ comparable to that of a planet with
larimetric signature of Earth’s oceans: we found a clear posi-
a partial ocean. This should be considered when we interpret the
tive correlation of P with the ocean fraction on the Earthshine-
polarization of planets near the outer edge of the habitable zone
contributing region (Figs. 4, 5 and 7); furthermore, we observed
or beyond.
hourly variations of P in accordance with the rotational transi-
tion of the ocean fraction (Fig. 8). Although our simple model
5.2. Feasibility estimate reproduced the observed hourly variation of P (Figs. 8 and 9)
fairly well, modeling in a more sophisticated manner and in-
The comprehensive feasibility evaluation of the polarimetric puting more appropriate Earth scene data (hourly time-resolved
technique is beyond the scope of this work, though we briefly cloud maps) may resolve the exceptional observation-model dis-
discuss it by referring to our previous work (Takahashi et al. agreement and confirm the indicated ocean signature. The ob-
2017), in which we demonstrated the feasibility of the ground- served relative variation, ∆P/P̄, reached as large as ∼0.2–1.4.
based detection of a near-infrared spectro-polarimetric feature of An effective observation is estimated to be possible using a 40-m
water vapor in an exoplanetary atmosphere. We showed that the class ground-based telescope with a five-hour exposure. There-
feature with a strength of ∆Pfeature 10% and continuum level fore, we propose near-infrared polarimetry as a prospective tech-
of Pcont 10% was detectable for 5–14 known exoplanets with nique for the detection of an exoplanetary ocean.
a total exposure time of 15 hours using a 40-m class telescope
such as the Extremely Large Telescope (ELT). In the estimate, Acknowledgements. This work was supported by the Japan Society for the Pro-
motion of Science (JSPS) KAKENHI Grant Numbers 15K21296, 17K05390,
we assumed that the high-contrast instrument suppressed stellar and 21K03648; Tokubetsu Kenkyu Joseikin (2019–2021), funded by University
light down to 10−8 –10−9 , and its total throughput was 10%. of Hyogo; and the Optical and Near-Infrared Astronomy Inter-University Coop-
In the current case for ocean detection, the target signature eration Program, funded by Ministry of Education, Culture, Sports, Science and
is the polarization time variation of ∆Ptime 10% with a mean Technology (MEXT), Japan. Part of this work was presented at the IAU Sym-
posium 360 and awarded as one of the best presentations. We acknowledge that
polarization level of P̄ 10% (converted from the Earthshine discussions at the symposium refined this work.
polarization of ∼2.5% near the quadrature phase assuming a lu-
nar depolarization factor5 of ∼0.25 and ∆Ptime /P̄ 1), which
is similar to the previous case for water vapor detection (i.e., Note added in proof. Model simulations by Trees & Stam (2019)
showed P phase curves of ocean planets with realistic ocean sur-
5
Applied depolarization factor (or polarization efficiency, ) of 0.25 is faces and Earth-like atmospheres. Our observations (Fig.4) seem
based on a simple extrapolation of the formula of Bazzon et al. (2013) consistent with their simulations (at λ = 865 nm, the longest
to the near-infrared; it is consistent with our observation-model com- wavelength in their calculations) for partly cloudy ocean planets
parison (see Appendix C for details). with fc = 0.25 and 0.50.
Article number, page 11 of 20A&A proofs: manuscript no. EarthshineNIC_astroph3
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