Dimming Titan Revealed by the Cassini Observations

Here we report the temporal variation of Titan's emitted energy with the Cassini/CIRS observations. In the northern hemisphere, the hemispheric-average emitted power decreased from 2007 to 2009 and increased from 2009 to 2012–13, which make the net change insignificant (0.1 ± 0.2%) during the period 2007–2013. The decrease from 2007 to 2009 is mainly due to the cooling around the stratospause, and the increase from 2009 to 2012–13 is probably related to temporal variation of atmospheric temperature around the tropopuase in the northern hemisphere. In the southern hemisphere, the emitted power continuously decreased by 5.0 ± 0.6% from 2.40 ± 0.01 W/m2 in 2007 to 2.28 ± 0.01 in 2012–13, which is mainly related to Titan's seasonal variation. The asymmetry in the temporal variation between the two hemispheres results in the global-average emitted power decreasing by 2.5 ± 0.6% from 2.41 ± 0.01 W/m2 in 2007 to 2.35 ± 0.01 W/m2 in 2012–13. The solar constant at Titan decreased by ~13.0% in the same period 2007–2013, which is much stronger than the temporal variation of emitted power. The measurements of Titan's absorbed solar power are needed to determine the temporal variation of the global energy budget.

years is shown in Fig. 1 (Panels A, B, and C). Figure 1 shows that there are still some observational gaps, which are filled by linear interpolation used in our previous studies [10][11][12] . The coverage after filling the observational gaps is shown in panels D, E, and F of Fig. 1. After filling the observational gaps, we can integrate the thermal radiance in the direction of emission angle to get the emitted power at each latitude, which is shown in panel A of Fig. 2. The uncertainty in Fig. 2 is estimated by combining the error sources from filling observational gaps and the CIRS data calibration, as we discussed in the previous studies 10 . Panel A shows that there are significant temporal variations of emitted power from 2007 to 2013 at most latitudes, which are larger than the corresponding uncertainty. Titan's emitted power continuously decreased from 2007 to 2013 not only in the southern hemisphere (SH) but also in the low latitudes (0-30uN) of the northern hemisphere (NH). In particular, the emitted power decreased by 12.1 6 1.7% from 2.28 6 0.02 W/m 2 in 2007 to 2.00 6 0.03 W/m 2 in 2012-13 in the southern polar region (75-85uS). In the mid southern latitudes (30-60uS) and the tropical region (30uN-30uS), Titan's emitted power decreased 6.3 6 0.8% and 2.9 6 0.6% respectively during the period of 2007-2013. In the high latitudes (45-85uN) of the NH, Titan's emitted power increased ,4.8 6 1.1% from 2007 to 2012- 13. In order to understand the temporal variation of emitted power, we further compute the emitted power at different wavelengths. The Cassini/CIRS has three focal planes: FP1 (10-695 cm 21 ), FP3 (570-1125 cm 21 ), and FP4 (1025-1430 cm 21 ). To decrease the CIRS observational noise around the ends of the wavenumber interval covered by each focal plane, we choose wavenumber ranges 10-600 cm 21 for FP1, 600-1050 cm 21 for FP3, and 1050-1430 cm 21 for FP4 to compute Titan's emitted power. It is possible to compute the emitted power by organizing the spectra in narrower spectral ranges than the wavenumber range covered by each focal plane, but the thermal radiance averaged over a narrower wavenumber range generally has more noise and larger uncertainty. Here, we integrate the thermal radiance over wavelengths covered by each of the three focal planes to compute the emitted power. The inversion kernels of temperature soundings of Titan by the Cassini/CIRS 9 suggest that the radiances at a few FP1 wavenumbers (e.g., 15 cm 21 , 60 cm 21 , and 90 cm 21 ) emit from the pressure levels around Titan's tropopause (i.e., ,100 mbar). The FP1 also includes a wavenubmer (i.e., 530 cm 21 ), in which the surface radiance can escape to space [17][18][19] . The radiances at most FP3 wavenumbers emit from the middle stratosphere, and the radiances at most FP4 wavenumbers emit from the upper stratosphere and lower mesosphere 9 .
The thermal radiance recorded by each of the three CIRS focal planes is shown in panels B, C, and D of Fig. 2. The continuing decrease of Titan's total emitted power from 2007 to 2013 in the middle and high latitudes of the SH (30-85uS) and the tropical region (30uN-30uS), which is visible in panel A of Fig. 2, originated mainly in the wavenumber intervals of focal planes FP3 and FP4 (panels C and D). Therefore, the cooling in the stratosphere and lower mesosphere, which are recorded by FP3/4, contributes to the temporal variation of emitted power from 2007 to 2013 in the SH and the tropical region. The continuing decrease of emitted power in the   20,21 . It is also possible that other factors (e.g., heat transport by the atmospheric circulation 22 ) contribute to the temporal variation of emitted power in the middle and high northern latitudes. In the northern polar region (60-85uN), the decrease of emitted power from 2007 to 2009 (panel A of Fig. 2) is mainly due to a cooling around the stratospause around 0.1 mbar, which was measured by a previous study 22 and panel D of Fig. 2 (FP4). In summary, the temporal variation of emitted power is more complicated in the NH than in the SH. The solar constant at Titan decreased from 2007 to 2013 due to the increased Sun-Titan distance (Fig. 3). At the same time, the seasonal change in which the sub-solar latitude moved from the SH to the NH helped to increase the solar irradiance in the NH during the period 2007-2013 (Table 1). The combined effects make the temporal variation of atmospheric temperature complicated, which contributes to the different behaviors of emitted power in the different latitudes of the NH. In addition, atmospheric circulation also helps modify the atmospheric temperature and hence the emitted power 22,23 .
Assuming the emitted power in the latitude band of 86-90uN/S, in which the observations are too few to get measurements of emitted power, has the same value and uncertainty as the value at 85uS/N, we can integrate the profile of emitted power in the meridional direction to get the global-average emitted power. The observational gaps in the polar regions do not significantly contribute to the uncertainty of the global-average emitted power, because the area covered by the latitudinal band of 86-90uN/S occupies only ,0.3% of the global   (Table 1). Therefore, the large temporal variation from 2007 to 2012-13 suggests that Titan's global-average emitted power varies at least 2.5% at the timescale of one season. On Earth, the seasonal cycle of emitted power is very small at a magnitude of 0.1% 3,4 . Therefore, the temporal variation of global emitted power seems to be significantly larger on Titan than on Earth. Titan's hemispheric-average emitted power is also computed, which is shown in panel B of Fig. 3

Discussion
This study examines the temporal variation of Titan's emitted power. The meridional profiles of emitted power suggest that the temporal variation of emitted power behaves differently at different latitudes. In particular, the seasonal change of emitted power is different between the two hemispheres during the period of 2007-2013. Our study also suggests that Titan's global-average emitted energy significantly decreased by 2.5 6 0.6% from 2007 to 2013. The extended Cassini observations from 2014 to 2017 will further help us examine if the trend of decreasing global emitted power will continue.
Titan's radiant energy budget is determined by the emitted power and the absorbed solar power. The latter is further determined by the solar flux at the top of the atmosphere (i.e., solar constant) and the Bond albedo. Saturn has the large orbital eccentricity (,0.057), which results in a large variation of Sun-Titan distance at the seasonal scale. Therefore, the solar constant decreased by ,13% from 16.1 W/m 2 in 2007 to 14.0 W/m 2 in 2013 (panel A of Fig. 3). Titan's Bond albedo must be measured to determine the absorbed solar power with the known solar constant. Previous studies suggest that Titan's brightness and hence albedo displayed north-south asymmetry 24 and temporal variation [25][26][27] . The temporal variation of Titan's brightness and albedo is mainly due to the temporally-varying hazes and clouds [25][26][27][28][29][30] . These previous observations of seasonal photometric variability are limited to a few phase angles and wavelengths [25][26][27] . The solar energy mainly comes from the spectral range of ,0.1-3.0 mm. Therefore, the precise measurements of Titan's Bond albedo and its temporal variation require observations covering the whole spectral coverage from 0.1 mm to ,3.0 mm, because the reflection of solar radiance displays different temporal behaviors at different wavelengths 25,26 . In addition, the measurements of Bond albedo require observations with the coverage of phase angle from 0u to 180u. The observations recorded by the Imaging Science Subsystem and the Visual and Infrared Mapping Spectrometer onboard the Cassini spacecraft basically provide such observations. We are processing the Cassini observations to measure Titan's Bond albedo. Then we can determine the absorbed solar energy, which will be combined with this study to investigate Titan's global energy budget and its temporal variation.
Some recent studies of Earth's energy budget suggest that Earth is experiencing a small energy imbalance with the absorbed solar energy greater than the emitted thermal energy 4-6 . The small energy imbalance at the top of Earth's atmosphere significantly contributes to climate change, adding to the effects from greenhouse gases 5,6 . It will be interesting to investigate the effects of the possible energy imbalance, if discovered, on the temporal evolution of Titan's atmosphere besides the greenhouse effects (e.g., H 2 and CH 4 ) and antigreenhouse effects (e.g., high-altitude haze) 8 .