Closed-formed ab initio solutions of geometric albedos and reflected light phase curves of exoplanets
Kevin Heng, Brett M. Morris, Daniel Kitzmann
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12 pages, 8 figures, 2 tables. This is a post-peer-review, pre-copyedit version of an article published in Nature Astronomy. The final authenticated version is available online at: https://www.nature.com/articles/s41550-021-01444-7. Equations (1) to (43) have not changed since v1. Differences between v1 and this version (v4) are in Figure 4 and the inferred parameter values associated with it
Studying the albedos of the planets and moons of the Solar System dates back at least a century. Of particular interest is the relationship between the albedo measured at superior conjunction, known as the ``geometric albedo", and the albedo considered over all orbital phase angles, known as the ``spherical albedo". Determining the relationship between the geometric and spherical albedos usually involves complex numerical calculations and closed-form solutions are restricted to simple reflection laws. Here we report the discovery of closed-form solutions for the geometric albedo and integral phase function, which apply to any law of reflection that only depends on the scattering angle. The shape of a reflected light phase curve, quantified by the integral phase function, and the secondary eclipse depth, quantified by the geometric albedo, may now be self-consistently inverted to retrieve globally averaged physical parameters. Fully Bayesian phase curve inversions for reflectance maps and simultaneous light curve detrending may now be performed due to the efficiency of computation. Demonstrating these innovations for the hot Jupiter Kepler-7b, we infer a geometric albedo of $0.25^{+0.01}_{-0.02}$, a phase integral of $1.77 \pm0.07$, a spherical albedo of $0.44^{+0.02}_{-0.03}$ and a scattering asymmetry factor of $0.07^{+0.12}_{-0.11}$.
The characterization of planetary atmospheres is a daunting task, pushing current observing facilities to their limits. The next generation of high-resolution spectrographs mounted on large telescopes -- such as ESPRESSO@VLT and HIRES@ELT -- will allow us to probe and characterize exoplanetary atmospheres in greater detail than possible to this point. We present a method that permits the recovery of the colour-dependent reflectivity of exoplanets from high-resolution spectroscopic observations. Determining the wavelength-dependent albedo will provide insight into the chemical properties and we…
New observational facilities are becoming increasingly capable of observing reflected light from transiting and directly imaged extrasolar planets. In this study, we provide an analytic framework to interpret observed phase curves, geometric albedos, and polarization of giant planet atmospheres. We compute the observables for non-conservative Rayleigh scattering in homogeneous semi-infinite atmospheres using both scalar and vector formalisms. In addition, we compute phase curves and albedos for Lambertian, isotropic, and anisotropic scattering phase functions. We provide analytic expressions f…
We present a catalog of spectra and geometric albedos, representative of the different types of Solar System bodies, from 0.45 to 2.5 microns. We analyzed published calibrated, un-calibrated spectra, and albedos for Solar System objects and derived a set of reference spectra and reference albedo for 19 objects that are representative of the diversity of bodies in our Solar System. We also identified previously published data that appears contaminated. Our catalog provides a baseline for comparison of exoplanet observations to 19 bodies in our own Solar System, which can assist in the prioritiz…
Photometric phase curves provide an important window onto exoplanetary atmospheres and potentially even their surfaces. With similar amplitudes to occultations but far longer baselines, they have a higher sensitivity to planetary photons at the expense of a more challenging data reduction in terms of long-term stability. In this work, we introduce a novel non-parametric algorithm dubbed "phasma" to produce clean, robust exoplanet phase curves and apply it to 115 Neptunian and 50 Terran exoplanets observed by Kepler. We stack the signals to further improve signal-to-noise, and measure an averag…
Diagnostic potential of the spectral signatures of Raman scattering imprinted in planetary albedo spectra at short optical wavelengths has been demonstrated in research on Solar System planets and has recently been proposed as a probe of exoplanet atmospheres, complementary to albedo studies at longer wavelengths. Spectral features caused by Raman scattering offer insight into the properties of planetary atmospheres, such as the atmospheric depth, composition, and temperature, as well as the possibility of detecting and spectroscopically identifying spectrally inactive species, such as H$_2$ a…
The field of exoplanets has rapidly expanded from the exclusivity of exoplanet detection to include exoplanet characterization. A key step towards this characterization will be retrieval of planetary albedos and rotation rates from highly undersampled imaging data. The Deep Space Climate Observatory (DSCOVR) provides a unique opportunity to test such retrieval methods using high cadence data of the sunlit surface of the Earth. There are two NASA instruments on board DSCOVR that can be used to achieve this task: the NASA instruments Earth Polychromatic Imaging Camera (EPIC) and the National Ins…
Bright features have been recently discovered by Dawn on Ceres, which extend previous photometric and Space Telescope observations. These features should produce distortions of the line profiles of the reflected solar spectrum and therefore an apparent radial velocity variation modulated by the rotation of the dwarf planet. Here we report on two sequences of observations of Ceres performed in the nights of 31 July, 26-27 August 2015 by means of the high-precision HARPS spectrograph at the 3.6-m La Silla ESO telescope. The observations revealed a quite complex behaviour which likely combines a …
The upcoming launch of the James Webb Space Telescope (JWST) means that we will soon have the capability to characterize the atmospheres of rocky exoplanets. However, it is still unknown whether such planets orbiting close to M dwarf stars can retain their atmospheres, or whether high-energy irradiation from the star will strip the gaseous envelopes from these objects. We present a new method to detect an atmosphere on a synchronously rotating rocky exoplanet around a K/M dwarf, by using thermal emission during secondary eclipse to infer a high dayside albedo that could only be explained by br…
We present revised near-infrared albedo fits of 2835 Main Belt asteroids observed by WISE/NEOWISE over the course of its fully cryogenic survey in 2010. These fits are derived from reflected-light near-infrared images taken simultaneously with thermal emission measurements, allowing for more accurate measurements of the near-infrared albedos than is possible for visible albedo measurements. As our sample requires reflected light measurements, it undersamples small, low albedo asteroids, as well as those with blue spectral slopes across the wavelengths investigated. We find that the Main Belt s…
Identifying liquid water on the surface of planets is a high priority, as this traditionally defines habitability. One proposed signature of oceans is specular reflection ("glint"), which increases the apparent albedo of a planet at crescent phases. We post-process a global climate model of an Earth-like planet to simulate reflected lightcurves. Significantly, we obtain glint-like phase variations even though we do not include specular reflection in our model. This false positive is the product of two generic properties: 1) for modest obliquities, a planet's poles receive less orbit-averaged s…
Reflected light curves observed for exoplanets indicate bright clouds at some of them. We estimate how the light curve and total stellar heating of a planet depend on forward and backward scattering in the clouds based on Pioneer and Cassini spacecraft images of Jupiter and Saturn. We fit analytical functions to the local reflected brightnesses of Jupiter and Saturn depending on the planet's phase. These observations cover broad bands at 0.59-0.72 and 0.39-0.5 μm, and narrow bands at 0.938 (atmospheric window), 0.889 (CH4 absorption band), and 0.24-0.28 μm. We simulate the images of the planet…
Direct-imaging spectra hold rich information about a planet's atmosphere and surface, and several space-based missions aiming at such observations will become a reality in the near future. Previous spectral retrieval works have resulted in key atmospheric constraints under the assumption of a gray surface, but the effect of wavelength-dependent surface albedo on retrieval has not been shown. We explore the influence of the coupling effect of cloud and wavelength-dependent surface albedo on retrieval performance via modeling suites of Earth-like atmospheres with varying cloud and surface albedo…
Basic atmospheric properties such as albedo and heat redistribution between day and nightside have been inferred for a number of planets using observations of secondary eclipses and thermal phase curves. Optical phase curves have not yet been used to constrain these atmospheric properties consistently. We re-model previously published phase curves of CoRoT-1b, TrES-2b and HAT-P-7b and infer albedos and recirculation efficiencies. These are then compared to previous estimates based on secondary eclipse data. We use a physically consistent model to construct optical phase curves. This model take…
One significant difference between the atmospheres of stars and exoplanets is the presence of condensed particles (clouds or hazes) in the atmosphere of the latter. The main goal of this paper is to develop a self-consistent microphysical cloud model for 1D atmospheric codes, which can reproduce some observed properties of Earth, such as the average albedo, surface temperature, and global energy budget. The cloud model is designed to be computationally efficient, simple to implement, and applicable for a wide range of atmospheric parameters for planets in the habitable zone. We use a 1D, cloud…
The largest and most close-in exoplanets would reflect enough star light to enable its ground-based photometric detection under the condition of a high to moderate albedo. We present the results of an observing campaign of secondary eclipse light curves of three of the most suitable exoplanet targets, WASP-43b, WASP-103b, and TrES-3b. The observations were conducted with meter-sized telescopes in the blue optical broadband filters Johnson B and Johnson V. We do not detect a photometric dimming at the moment of the eclipse, and derive a best-fit eclipse depth by an injection-recovery test. Thes…
An important source of opacity in exoplanet atmospheres at short visible and near-UV wavelengths is Rayleigh scattering of light on molecules. It is accompanied by a related, albeit weaker process -- Raman scattering. We analyze the signatures of Raman scattering imprinted in the reflected light and the geometric albedo of exoplanets, which could provide information about atmospheric properties. Raman scattering affects the geometric albedo spectra of planets in following ways. Firstly, it causes filling-in of strong absorption lines in the incident radiation, thus producing sharp peaks in the…
In anticipation of future flagship missions focused on the goal of achieving direct imaging of rocky exoplanets, we have developed a database of models to help the community examine the potential spectral characteristics of a broad range of rocky planet atmospheres. Using the publicly available Planetary Spectrum Generator (PSG), we have computed a grid of 141,600 rocky exoplanet geometric albedo spectra across a 7-dimensional parameter space. Using this grid, we have performed a color-color analysis seeking to identify the most useful near-ultraviolet and red or near-infrared photometric foll…
Future space telescopes will directly image extrasolar planets at visible wavelengths. Time-resolved reflected light from an exoplanet encodes information about atmospheric and surface inhomogeneities. Previous research has shown that the light curve of an exoplanet can be inverted to obtain a low-resolution map of the planet, as well as constraints on its spin orientation. Estimating the uncertainty on 2D albedo maps has so far remained elusive. Here we present exocartographer, a flexible open-source Bayesian framework for solving the exo-cartography inverse problem. The map is parameterized …
[Abridged] If both the day-side and night-side effective temperatures of a planet can be measured, it is possible to estimate its Bond albedo, 0<A_B<1, as well as its day-night heat redistribution efficiency, 0<epsilon<1. We attempt a statistical analysis of the albedo and redistribution efficiency for 24 transiting exoplanets that have at least one published secondary eclipse. For each planet, we show how to calculate a sub-stellar equilibrium temperature, T_0, and associated uncertainty. We then use a simple model-independent technique to estimate a planet's effective temperature from planet…
Rotational mapping and glint are two proposed methods to directly detect liquid water on the surface of habitable exoplanets. However, false positives for both methods may prevent the unambiguous detection of exoplanet oceans. We use simulations of Earth as an exoplanet to introduce a combination of multiwavelength, multiphase, time-series direct-imaging observations and accompanying analyses that may improve the robustness of exoplanet ocean detection by spatially mapping the ocean glint signal. As the planet rotates, the glint spot appears to "blink" as Lambertian scattering continents inter…
There are now many known exoplanets with Msin(i) within a factor of two of Neptune's, including the transiting planets GJ436b and HAT-P-11b. Planets in this mass-range are different from their more massive cousins in several ways that are relevant to their radiative properties and thermal structures. By analogy with Neptune and Uranus, they are likely to have metal abundances that are an order of magnitude or more greater than those of larger, more massive planets. This increases their opacity, decreases Rayleigh scattering, and changes their equation of state. Furthermore, their smaller radii…
Recent work has shown that sulfur hazes may arise in the atmospheres of some giant exoplanets due to the photolysis of H$_{2}$S. We investigate the impact such a haze would have on an exoplanet's geometric albedo spectrum and how it may affect the direct imaging results of WFIRST, a planned NASA space telescope. For temperate (250 K $<$ T$_{\rm eq}$ $<$ 700 K) Jupiter--mass planets, photochemical destruction of H$_{2}$S results in the production of $\sim$1 ppmv of \seight between 100 and 0.1 mbar, which, if cool enough, will condense to form a haze. Nominal haze masses are found to drastically…
The potential habitability of known exoplanets is often categorized by a nominal equilibrium temperature assuming a Bond albedo of either 0.3, similar to Earth, or 0. As an indicator of habitability, this leaves much to be desired, because albedo on other planets can be very different, and because surface temperature exceeds equilibrium temperature due to the atmospheric greenhouse effect. We use an ensemble of 3-dimensional general circulation model simulations to show that for a range of habitable planets, much of the variability of Bond albedo, equilibrium temperature, and even surface temp…
First generation optical coronagraphic telescopes will obtain images of cool gas and ice giant exoplanets around nearby stars. The albedo spectra of exoplanets at planet-star separations larger than about 1 AU are dominated by reflected light to beyond 1 μm and are punctuated by molecular absorption features. We consider how exoplanet albedo spectra and colors vary as a function of planet-star separation, metallicity, mass, and observed phase for Jupiter and Neptune analogs from 0.35 to 1 μm. We model Jupiter analogs with 1x and 3x the solar abundance of heavy elements, and Neptune analogs wit…
The disk-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motion coupled with an inhomogeneous albedo map. We have previously derived analytic reflected lightcurves for spherical harmonic albedo maps in the special case of a synchronously-rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard 2013). In this paper, we present analytic reflected lightcurves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points ($δ$-maps)…
The Radius, Composition, Albedo, and Absolute Magnitude of Planet Nine Based on Exoplanets with Teq less than 600 K and the Planet Nine Reference Population 3.0
Light curves show the flux variation from the target star and its orbiting planets as a function of time. In addition to the transit features created by the planets, the flux also includes the reflected light component of each planet, which depends on the planetary albedo. This signal is typically referred to as phase curve and could be easily identified if there were no additional noise. As well as instrumental noise, stellar activity, such as spots, can create a modulation in the data, which may be very difficult to distinguish from the planetary signal. We analyze the limitations imposed by…
Unlike previously explored relationships between the properties of hot Jovian atmospheres, the geometric albedo and the incident stellar flux do not exhibit a clear correlation, as revealed by our re-analysis of Q0 to Q14 Kepler data. If the albedo is primarily associated with the presence of clouds in these irradiated atmospheres, a holistic modeling approach needs to relate the following properties: the strength of stellar irradiation (and hence the strength and depth of atmospheric circulation), the geometric albedo (which controls both the fraction of starlight absorbed and the pressure le…
There has been growing observational evidence for the presence of condensates in the atmospheres and/or comet-like tails of extrasolar planets. As a result, systematic and homogeneous tables of dust properties are useful in order to facilitate further observational and theoretical studies. In this paper we present calculations and analysis of non-isotropic phase functions, asymmetry parameter (mean cosine of the scattering angle), absorption and scattering opacities, single scattering albedos, equilibrium temperatures, and radiative accelerations of dust grains relevant for extrasolar planets.…
In order to recognize a habitable exoplanet from future observed spectra, we present new model reflected spectra and geometric albedo for modern and prebiotic (3.9 Ga) Earth-like exoplanets orbiting within the habitable zone of stars of spectral types F, G, K and M. We compute this for various atmospheric and surface compositions of the planets. Molecules that are potential biosignatures and act as greenhouse agents are incorporated in our model atmosphere. Various combinations of solid and liquid materials such as ocean, coast, land consisting of trees, grass, sand or rocks determine the surf…
It is challenging to measure the starlight reflected from exoplanets because of the extreme contrast with their host stars. For hot Jupiters, this contrast is in the range of $10^{-6}$ to $10^{-4}$, depending on their albedo, radius and orbital distance. Searches for reflected light have been performed since the first hot Jupiters were discovered, but with very limited success because hot Jupiters tend to have low albedo values due to the general absence of reflective cloud decks. The aim of this study is to search for reflected light from $τ$ Boo b, a hot Jupiter with one of the brightest hos…
We use a planetary albedo model to investigate variations in visible wavelength phase curves of exoplanets. The presence of clouds on these exoplanets significantly alters their planetary albedo spectra. We confirm that non-uniform cloud coverage on the dayside of tidally locked exoplanets will manifest as changes to the magnitude and shift of the phase curve. In this work, we first investigate a test case of our model using a Jupiter-like planet, at temperatures consistent to 2.0 AU insolation from a solar type star, to consider the effect of H2O clouds. We then extend our application of the …
Planets larger than Earth and smaller than Neptune are some of the most numerous in the galaxy, but observational efforts to understand this population have proved challenging because optically thick clouds or hazes at high altitudes obscure molecular features (Kreidberg et al. 2014b). We present models of super Earths that include thick clouds and hazes and predict their transmission, thermal emission, and reflected light spectra. Very thick, lofted clouds of salts or sulfides in high metallicity (1000x solar) atmospheres create featureless transmission spectra in the near-infrared. Photochem…
Reflected light photometry of terrestrial exoplanets could reveal the presence of oceans and continents, hence placing direct constraints on the current and long-term habitability of these worlds. Inferring the albedo map of a planet from its observed light curve is challenging because different maps may yield indistinguishable light curves. This degeneracy is aggravated by changing clouds. It has previously been suggested that disk-integrated photometry spanning multiple days could be combined to obtain a cloud-free surface map of an exoplanet. We demonstrate this technique as part of a Bayes…
Giant exoplanets located >1 AU away from their parent stars have atmospheric environments cold enough for water and/or ammonia clouds. We have developed a new equilibrium cloud and reflected light spectrum model, ExoREL, for widely separated giant exoplanets. The model includes the dissolution of ammonia in liquid water cloud droplets, an effect studied for the first time for exoplanets. While preserving the causal relationship between temperature and cloud condensation, ExoREL is simple and fast to enable efficient exploration of parameter space. Using the model, we find that the mixing ratio…
Context: Detecting moons around exoplanets is a major goal of current and future observatories. Moons are suspected to influence rocky exoplanet habitability, and gaseous exoplanets in stellar habitable zones could harbour abundant and diverse moons to target in the search for extraterrestrial habitats. Exomoons will contribute to exoplanetary signals but are virtually undetectable with current methods. Aims: We identify and analyse traces of exomoons in the temporal variation of total and polarised fluxes of starlight reflected by an Earth-like exoplanet and its spatially unresolved moon acro…
The depth of a secondary eclipse contains information of both the thermally emitted light component of a hot Jupiter and the reflected light component. If the dayside atmosphere of the planet is assumed to be isothermal, it is possible to disentangle both. In this work, we analyze 11 eclipse light curves of the hot Jupiter HAT-P-32b obtained at 0.89 $μ$m in the z' band. We obtain a null detection for the eclipse depth with state-of-the-art precision, -0.01 +- 0.10 ppt. We confirm previous studies showing that a non-inverted atmosphere model is in disagreement to the measured emission spectrum …
A space telescope capable of high-contrast imaging has been recognized as the avenue toward finding terrestrial planets around nearby Sun-like stars and characterizing their potential habitability. It is thus essential to quantify the capability of reflected light spectroscopy obtained through direct imaging for terrestrial exoplanets, and existing work focused on planetary analogs of modern Earth. Here we go beyond Earth analogs and use a Bayesian retrieval algorithm, ExoReL$^\Re$, to determine what we could learn about terrestrial exoplanets from their reflected light spectra. Recognizing th…
[Abridged] Distant stars and planets will remain spatially unresolved for the foreseeable future. It is nonetheless possible to infer aspects of their brightness markings and viewing geometries by analyzing disk-integrated rotational and orbital brightness variations. We compute the harmonic lightcurves, F_l^m(t), resulting from spherical harmonic maps of intensity or albedo, Y_l^m(theta,phi), where l and m are the total and longitudinal order. Notably, odd m>1 are present in an inclined lightcurve, but not seen by an equatorial observer. We therefore suggest that the Fourier spectrum of a the…
The detection of reflected light from an exoplanet is a difficult technical challenge at optical wavelengths. Even though this signal is expected to replicate the stellar signal, not only is it several orders of magnitude fainter, but it is also hidden among the stellar noise. We apply a variant of the cross-correlation technique to HARPS observations of 51 Peg to detect the reflected signal from planet 51 Peg b. Our method makes use of the cross-correlation function of a binary mask with high-resolution spectra to amplify the minute planetary signal that is present in the spectra by a factor …
Due to its proximity to Earth, Jupiter of the Solar System serves as a unique case study for gas-giant exoplanets. In the current study, we perform fits of ab initio, reflective, semi-infinite, homogeneous model atmospheres to 61 phase curves from 0.40 to 1.00 $μ$m, obtained from the Cassini spacecraft, within a Bayesian framework. We reproduce the previous finding that atmospheric models using classic reflection laws (Lambertian, Rayleigh, single Henyey-Greenstein) provide poor fits to the data. Using the double Henyey-Greenstein reflection law, we extract posterior distributions of the singl…
Seeing oceans, continents, quasi-static weather, and other surface features on exoplanets may allow us to detect and characterize life outside the solar system. The Proxima b planet resides within the stellar habitable zone allowing for liquid water on its surface, and it may be Earth-like. However, even the largest planned telescopes will not be able to resolve its surface features directly. Here, we demonstrate an inversion technique to image indirectly exoplanet surfaces using observed unresolved reflected light variations over the course of the exoplanets orbital and axial rotation: ExoPla…
Here we present the first open-source radiative transfer model for computing the reflected light of exoplanets at any phase geometry, called PICASO: Planetary Intensity Code for Atmospheric Scattering Observations. This code, written in Python, has heritage from a decades old, well-known Fortran model used for several studies of planetary objects within the Solar System and beyond. We have adopted it to include several methodologies for computing both direct and diffuse scattering phase functions, and have added several updates including the ability to compute Raman scattering spectral feature…
Photosynthesis offers a convenient means of sustaining biospheres. We quantify the constraints for photosynthesis to be functional on the permanent nightside of tidally locked rocky exoplanets via reflected light from their exomoons. We show that the exomoons must be at least half the size of Earth's moon in order for conventional oxygenic photosynthesis to operate. This scenario of photosynthesis is unlikely for exoplanets around late-type M-dwarfs due to the low likelihood of large exomoons and their orbital instability over long timescales. Subsequently, we investigate the prospects for pho…
Thermal phase curves of exoplanet atmospheres have revealed temperature maps as a function of planetary longitude, often by sinusoidal decomposition of the phase curve. We construct a framework for describing two-dimensional temperature maps of exoplanets with mathematical basis functions derived for a fluid layer on a rotating, heated sphere with drag/friction, which are generalizations of spherical harmonics. These basis functions naturally produce physically-motivated temperature maps for exoplanets with few free parameters. We investigate best practices for applying this framework to tempe…
We present an optical eclipse observation of the hot Jupiter WASP-12b using the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope. These spectra allow us to place an upper limit of $A_g < 0.064$ (97.5% confidence level) on the planet's white light geometric albedo across 290--570 nm. Using six wavelength bins across the same wavelength range also produces stringent limits on the geometric albedo for all bins. However, our uncertainties in eclipse depth are $\sim$40% greater than the Poisson limit and may be limited by the intrinsic variability of the Sun-like host star -…
Future space telescopes now in the concept and design stage aim to observe reflected light spectra of extrasolar planets. Assessing whether given notional mission and instrument design parameters will provide data suitable for constraining quantities of interest typically requires time consuming retrieval studies in which tens to hundreds of thousands of models are compared to data with a given assumed signal to noise ratio, thereby limiting the rapidity of design iterations. Here we present a novel machine learning approach employing five Multilayer Perceptron's (MLP) trained on model albedo …
Unmixing the disk-integrated spectra of exoplanets provides hints about heterogeneous surfaces that we cannot directly resolve in the foreseeable future. It is particularly important for terrestrial planets with diverse surface compositions like Earth. Although previous work on unmixing the spectra of Earth from disk-integrated multi-band light curves appeared successful, we point out a mathematical degeneracy between the surface colors and their spatial distributions. Nevertheless, useful constraints on the spectral shape of individual surface types may be obtained from the premise that albed…
The high-contrast imaging technique is meant to provide insight into those planets orbiting several astronomical units from their host star. Space missions such as WFIRST, HabEx, and LUVOIR will measure reflected light spectra of cold gaseous and rocky planets. To interpret these observations we introduce ExoReL$^\Re$ (Exoplanetary Reflected Light Retrieval), a novel Bayesian retrieval framework to retrieve cloud properties and atmospheric structures from exoplanetary reflected light spectra. As a unique feature, it assumes a vertically non-uniform volume mixing ratio profile of water and ammo…
