Colour–magnitude diagrams of transiting exoplanets – III. A public code, nine strange planets, and the role of phosphine

ABSTRACT

Colour–magnitude diagrams provide a convenient way of comparing populations of similar objects. When well populated with precise measurements, they allow quick inferences to be made about the bulk properties of an astronomic object simply from its proximity on a diagram to other objects. We present here a python toolkit that allows a user to produce colour–magnitude diagrams of transiting exoplanets, comparing planets to populations of ultra-cool dwarfs, of directly imaged exoplanets, to theoretical models of planetary atmospheres, and to other transiting exoplanets. Using a selection of near- and mid-infrared colour–magnitude diagrams, we show how outliers can be identified for further investigation, and how emerging subpopulations can be identified. Additionally, we present evidence that observed differences in the Spitzer’s 4.5 μm flux, between irradiated Jupiters and field brown dwarfs, might be attributed to phosphine, which is susceptible to photolysis. The presence of phosphine in low-irradiation environments may negate the need for thermal inversions to explain eclipse measurements. We speculate that the anomalously low 4.5 μm flux of the nightside of HD 189733b and the daysides of GJ 436b and GJ 3470b might be caused by phosphine absorption. Finally, we use our toolkit to include Hubble Wide Field Camera 3 spectra, creating a new photometric band called the ‘Water band’ (W_JH band) in the process. We show that the colour index [W_JH − H] can be used to constrain the C/O ratio of exoplanets, showing that future observations with James Webb Space Telescope and Ariel will be able to distinguish these populations if they exist, and select members for future follow-up.

1 INTRODUCTION

We have come a long way since Mayor & Queloz (1995) discovered the first hot Jupiter orbiting a Sun-like star. We now know of over 4000 exoplanets and there are over 2000 candidates waiting for confirmation of their planetary status.¹ Our ambition has grown with the broadening scope of the field: We are now not content to simply know of a system’s geometry, but are probing various layers of exoplanetary atmospheres through transit spectroscopy and multiwaveband photometry (for a review, see Madhusudhan 2019). We are able to infer the presence of atomic (e.g. Charbonneau et al. 2002; Redfield et al. 2008) and molecular species (e.g. Kreidberg et al. 2014; McCullough et al. 2014; Sheppard et al. 2017). This in turn reveals some of the chemical and thermal transport processes taking place at different pressure levels within the atmosphere (Stevenson et al. 2014a). A clearer picture of the chemical composition of a planet’s atmosphere allows us to compute useful parameters such as the carbon-to-oxygen (C/O) ratio (Moses et al. 2013a). The C/O ratio is particularly useful to probe the nebular gas in which the planet formed, and hence the location of its formation within a disc (Madhusudhan et al. 2011b; Öberg, Murray-Clay & Bergin 2011).

Inferences for the C/O ratio have regularly been performed on transmission spectra (e.g. Pinhas et al. 2019). However, transmission only probes a special location of the atmosphere of a tidally locked planet, and its terminator, which might not be representative of the whole. In addition, transmission spectra can be strongly affected by opacity on the line of sight, with haze and clouds often masking important features (Sing et al. 2016a). Furthermore, transmission can be affected by stellar contamination (e.g. Jordán et al. 2013; Rackham, Apai & Giampapa 2017).

A solution is to measure a planet’s integrated dayside thermal emission, which is obtained during a secondary eclipse event (or occultation) when the planet passes behind its parent star (Kreidberg 2018). When this has been detected in several photometric bands, a low-resolution emission spectrum emerges (Alonso 2018), which we can use to retrieve atmospheric compositions.

The process of atmospheric retrieval relies on reliable atmospheric models, some of which require accurate chemical networks and complete line lists for all the main opacity sources (see Madhusudhan 2018, for a detailed review of atmospheric retrieval processes). At present, we have access to several state-of-the-art modelling codes, but they are very much still in flux, with chemical networks and line lists being updated frequently (e.g. Baudino et al. 2017; Hobbs et al. 2019; Venot et al. 2019). Retrieval codes being computationally intensive, there is interest in including as small a number of species as possible. However, if a certain molecule is present in the atmosphere, but absent in the code, the retrieved abundances will be inaccurate (Waldmann & Rocchetto 2015; MacDonald & Madhusudhan 2017). Obtaining diagnostics about which atomic or molecular species are present in a spectrum is therefore important. This is where colour–magnitude diagrams can help.

The field of exoplanet physics is in its infancy when compared to the field of stellar physics, and the latter hits a turning point with the plotting of the first Hertzsprung–Russell diagram (H–R; Hertzsprung 1911; Russell 1914). The H–R diagram was crucial as it allowed astronomers to statistically characterize a single object by placing it in the context of a well-studied population. In this way, subpopulations could be identified as well as their formation and evolution mechanisms (Eddington 1920), allowing future observational strategies to be shaped.

We are now approaching a turning point in the field of exoplanetary observations: The launch of the James Webb Space Telescope (JWST), which is scheduled for 2021 March, will allow more detailed characterization of planetary atmospheres than ever before (see Madhusudhan 2019, Fig. 10). As such, it is vital that we use the data already available to select the very best targets for further investigation. Looking further into the future, Ariel is to be launched in 2028, with the goal of observing approximately 1000 planets to compile the planetary equivalent of an H–R diagram (Tinetti et al. 2018). While a bolometric luminosity versus spectral type H–R diagram is not yet achievable for planets, mid- and near-infrared colour–magnitude and colour–colour diagrams are already used in the field to help characterize atmospheres (Kammer et al. 2015; Triaud et al. 2015; Zhou et al. 2015; Alonso 2018; Deming, Louie & Sheets 2019). Additionally, plots similar to colour–magnitude diagrams have been produced, for instance fig. 10 in Molaverdikhani, Henning & Mollière (2019), but they rely on some model-independent parameters (such as temperature). Similar diagrams can also be made using transmission spectra (see Extended Data figs 1 and 2 in Sing et al. 2016b).

Direct imaging of exoplanets yields a straightforward measurement of the planet’s brightness; for planets observed in this way, the use of a colour–magnitude diagram to compare it with objects of similar brightness is intuitive (e.g. Mohanty et al. 2007; Marois et al. 2008; Beatty et al. 2014; Bowler 2016). The use of colour–magnitude diagrams for transiting exoplanets was first produced in Triaud (2014), and later expanded on by Triaud et al. (2014). Colour–magnitude diagrams serve a similar purpose to H–R diagrams in that they allow for planets to be compared to a larger population. In the most recent paper in this series, distance measurements were photometrically estimated due to the lack of availability of parallaxes for most systems.

Colour–magnitude diagrams presented in Triaud et al. (2014) showed that in general the planets are compatible in magnitude with the M and L sequence of dwarfs, although there is more diversity in colour shown by the exoplanets, most of which were hot Jupiters. In some bands, planets appeared to be equally compatible with the blackbody sequence as they sat at the intersection of the two. Manjavacas et al. (2019) used a near-infrared colour–magnitude diagram to show that in the J and H bands brown dwarfs are good spectral matches for hot Jupiters.

In this work, we expand significantly on the number of planets plotted. We also include new photometric bands and use alternative populations for comparison. Additionally, we have developed a publicly available python toolkit that produces colour–magnitude diagrams, in a variety of formats and in any combination of photometric bands. We also show how a colour–magnitude diagram can be used to make an initial diagnostic, in order to select standout objects for rapid follow-up with upcoming missions.

The structure of our paper is as follows: In Section 2, we outline how we compiled our data sets, as well as how these data are processed in our python tools to produce colour–magnitude diagrams. We then present a selection of new colour–magnitude diagrams plotted with our tools, and describe the results we infer from the positions of planets. Finally, we conclude and discuss the uses of colour–magnitude diagrams in the context of the next generation of telescopes.

2 METHODS

In these sections, we describe the methods we have used to process spectra and secondary eclipse data found in the literature. We also outline the functionality of our python modules, which we are releasing alongside this paper in order to facilitate similar data handling by other astronomers.

We first describe how we have assembled our data set and the data contained therein. We then explain how we processed spectra to produce our comparison samples in Section 2.3 along with our motivations for each choice. Finally, in Section 2.4 we outline the functionality of the three modules that make up our python toolkit.

2.1 Data base of transiting exoplanet emission measurements

Our starting point was the data set compiled by Triaud et al. (2014). Since 2014, a handful of these measurements have been updated; additionally, there have been many secondary eclipses measured for the first time. Alonso (2018) provided a helpful list of planets with secondary eclipse measurements, together with the bands in which the data are available. Garhart et al. (2019) published secondary eclipses for 36 planets in Spitzer’s channels 1 and 2, 27 of which had been measured for the first time. We also made use of the NASA Exoplanet Archive² that provides secondary eclipse data in all bands, and we continuously searched the ADS and Arxiv for new publications containing planetary emissions. All of these resources allowed us to assemble an up-to-date data base of fluxes measured at occultation for a sample of 83 exoplanets.

Once our planet sample was assembled, we searched the 2MASS catalogue (Cutri et al. 2003) for host star apparent magnitudes in the J, H, and K bands. As Spitzer’s IRAC instrument reached the end of its cryogenic lifetime before 2014, there have been no new measurements in the 5.8 or 8 μm channels. In order to obtain host star apparent magnitudes in the 3.6 and 4.5 μm channels, we made use of the WISE All-Sky catalogue (Cutri & et al. 2012) as WISE’s channels W1 and W2 are very similar to Spitzer’s channels 1 and 2. (Triaud et al. 2014). Where a host star’s apparent magnitude was not available in a certain band, we derived synthetic photometry making use of standard spectra from the Pickles Atlas³ (Pickles 1998). For a detailed description of this process, see Appendix A1.

To compute absolute magnitudes, we need distance with Gaia’s DR2 providing the most recent parallaxes (Gaia Collaboration 2016, 2018). The distances could not be determined simply by inverting the parallaxes published in DR2 due to the non-linearity of the process of parallax estimation by Gaia; instead, we used the distances calculated by Bailer-Jones et al. (2018).

Finally, the planetary radii were retrieved from exoplanet.eu (Schneider et al. 2011) where available. Our compilation of planetary secondary eclipse measurements can be found in Appendix D.

2.2 Transforming planetary flux into magnitudes

In addition, we integrate low-resolution emission spectra measured with the G141 grism on the Wide Field Camera 3 instrument (WFC3) onboard the Hubble Space Telescope (HST) to produce additional planetary photometry. This particular instrument covers the wavelength range 1.1–1.7 μm that overlaps with the majority of the J band. By cutting this grism between 1.130 and 1.325 μm and integrating the planetary flux, we were able to compute J-band photometry for 11 planets. The WFC3 grism extends into the H band as well, but cuts short. We integrated the WFC3 spectra to create an H-short band (H_s) between 1.504 and 1.624 μm, as was done in Manjavacas et al. (2019) and Melville, Kedziora-Chudczer & Bailey (2020), and we include this photometry in our data base. However, the difference in magnitudes between the H and H_s is significant, and contrary to Melville et al. (2020), we cannot assume H and H_s to be the same. The locations of the Hubble bands can be seen in Fig. 1. We illustrate the difference between the H and H_s bands in Fig. 2, where we have plotted H_s versus H magnitudes and colours for three planets for which we have H-band photometry and HST WFG3 low-resolution spectra.

The WFC3 instrument is most often used to search for signs of water in emission or transmission spectra due to a key water absorption feature at 1.4 μm (Kirkpatrick 2005). In order to test whether we could diagnose the presence or absence of water using a colour–magnitude diagram, we create a photometric band centred on the water feature between the J and H bands (W_JH band) defined by integrating between 1.325 and 1.495 μm. We therefore also add W_JH-band photometry for 11 planets to our data base.

2.3 Assembling a brown dwarf comparison sample

The beauty of a colour–magnitude diagram is to enable simple comparison between population samples in a given wavelength space. A handful of objects on a colour–magnitude diagram by themselves do not allow us to infer much about these objects. Therefore, it is crucial that we have a large sample of well-studied objects to compare with our planets. As was done in Triaud et al. (2014), we make use of the detailed catalogue of near- and mid-infrared photometry of brown dwarfs produced by Dupuy & Liu (2012) to populate the background of our diagrams. Brown dwarfs are an excellent comparison sample as they overlap with exoplanets in temperature and radius, which leads to comparable luminosities (Triaud 2014). For non-standard bands, and for photometric bands that we defined, such as W_JH, there are no brown dwarfs catalogues we could use. We therefore synthetically create brown dwarf magnitudes and colours by integrating their spectra, which helps us populate the diagram and provide a comparison sample.

The SpeX Prism Library⁴ provides normalized near-infrared spectra of brown dwarfs spanning the wavelength range 0.8–2.5 μm. These data are collected from the ground but are corrected for telluric absorption caused by water in the atmosphere (Rayner et al. 2003).

We integrated the SpeX spectra to produce a catalogue of photometry of 119 brown dwarfs. These were cross-referenced with the parallaxes provided by Dupuy & Liu (2012) in order to include distances in our catalogue. Our process of producing synthetic photometry is explained in Appendix A2, along with how we validated our method. In Appendix F, we have included a table of the photometry we computed in several near- and mid-infrared bands (see Table F1).

It is also important to verify whether exoplanet atmospheric models match observations. We produce synthetic photometry from atmospheric model spectra. In this paper, we chose to use the publicly available model spectra produced by Mollière et al. (2015) as they cover a wide parameter space, most importantly carbon–oxygen ratios of 0.35–1.40, effective temperatures of 1000–2500 K in 250 K increments, and five metallicity values, ranging from −0.5 to 2.0. While we chose the Molliére models to demonstrate our code, it can adapt to use others as well. The data were processed using an adapted version of the code we used to produce magnitudes from the SpeX data.

2.4 Description of our python toolkit

We have produced a selection of python tools that automate all of the data analysis methods described above. Data handling is packaged into three modules: Synth.py to produce synthetic photometry of brown dwarfs from SpeX spectra; Models.py to produce synthetic photometry from model exoplanetary spectra; and ExoCMD.py: a plotting module that computes planetary magnitudes and plots colour–magnitude diagrams. Users can interact with the modules via a Jupyter Notebook; the code and the notebook can be accessed at https://github.com/gdransfield/ExoCMD.

Below we give a brief outline of the modules; more detailed information can be found in Appendix C, which also includes a walkthrough tutorial.

2.4.1 SYNTH.PY

This module provides a user with the flexibility to define bespoke photometric bands, in much the same way as we created our W_JH band. New bands should be designed to coincide with interesting absorption features, which can be selected by inspection of brown dwarf spectra, or from line lists (e.g. Polyansky et al. 2018). Fig. 1 shows model brown dwarf emission spectra (Allard et al. 2001; Baraffe et al. 2003) on which we have highlighted the 2MASS J, H, and K bands in lilac, along with Spitzer’s mid-infrared bands in shades of red. The hatched area corresponds to the G141 grism we used, with the light blue hatched area indicating the position of our W_JH band. This plot shows how the 1.4 μm water absorption widens and deepens with decreasing temperature.

It is important to bear in mind that a new band might not necessarily be useful for the full temperature range of brown dwarfs: The spectra of cooler objects are likely to be dominated by molecular species while hotter objects could have molecular, atomic, or even ionized absorbers present. These changes are evident in the spectra shown in Fig. 1, as well as the changing width of absorption features. Cooler objects are likely to need wider photometric bands to detect molecular features, whereas narrower bands are increasingly useful for the narrow absorption features seen in objects with higher temperatures.

Our Synth.py module contains seven built-in photometric bands, and all synthetic photometry will be produced in these bands along with a user-defined band. As well as the three 2MASS bands and our W_JH band, we have included HAWK-I’s two narrow bands (NB1090 and NB2190) and Sloan’s z’ band.

While this module has been written with SpeX spectra in mind specifically, it can easily be adapted to work with any other brown dwarf spectra. The function outputs either a text file or a spreadsheet with photometry in the desired bands, along with spectral types and astrometric distances.

2.4.2 MODELS.PY

The Models.py module computes photometry from Mollière’s model spectra. Although the code has been written with this particular set of models in mind, it can be used for any model spectra that are produced in physical units. The functions make use of the map provided by Mollière et al. (2015) to search for the spectrum that matches with the chosen parameters. The inputs required are constraints on metallicity, surface gravity, C/O ratio, effective temperature, and host star spectral type. These constraints can be single values or lists of values; it is also possible to leave a parameter open that will result in all possible values being computed for that parameter. The two functions within the module output photometric magnitudes or colours, respectively. There are 11 built-in near- and mid-infrared bands that can be called by name, and once again users can define bespoke bands if required.

2.4.3 EXOCMD.PY

This module reads the planet data base we have assembled and computes colours and magnitudes of exoplanets. There are five plotting functions that use these data to produce colour–magnitude diagrams.

The first plotting function (ExoCMD|$\_$|1) produces diagrams in the style of those presented in Triaud et al. (2014). We have added a keyword argument to this and all other plotting functions (adjusted) that when called will adjust the absolute magnitudes of the exoplanets to a size of 0.9R_J. This is to allow for a better comparison between planets, and to brown dwarfs. We chose this particular radius since typically brown dwarfs have a radius of ≈0.9R_J (Kirkpatrick 2005) while hot Jupiters are more diverse in size. This only corrects the measurement with a simple translation up or down in absolute magnitude. See Appendix B and Fig. B1 for an illustration of the effect of different adjustment factors.

The second and third plotting functions (ExoCMD|$\_$|2 and ExoCMD|$\_$|3) both show a polynomial to represent the mean trend of brown dwarfs in order to clarify and de-clutter the diagrams; this is especially valuable in colours where we now have many planets plotted. The polynomials are positioned using coefficients computed by Dupuy & Liu (2012). The key difference between the second and third plotting functions is a keyword argument (highlight) present in ExoCMD|$\_$|3 that greys out all planets except those called by name. This allows objects of particular interest to be highlighted when needed.

The remaining two plotting functions make use of our new comparison samples. They call the functions from Synth.py and Models.py in order to compute the necessary photometry for the bands requested. When using the model plotting function (ExoCMD|$\_$|model), the model atmospheres can be coloured according to any of the five model parameters (C/O ratio, metallicity, surface gravity, effective temperature, or host star spectra type); in the synthetic brown dwarf function (ExoCMD|$\_$|synth), the ultra-cool dwarfs are coloured according to spectral type.

All plotting functions additionally include the ability to plot the position of a blackbody of comparable radius to the objects plotted on the diagram.

3 RESULTS

In the sections that follow, we present a selection of our colour–magnitude diagrams along with some of the key inferences we have been able to make from them. These are designed to be illustrative of how powerful it can be to view results for individual planets in context.

We begin with a brief explanation of how to read a colour–magnitude diagram, along with some of the terminology to expect. In Section 3.2, we show how a colour–magnitude diagram can allow us to select standout objects for rapid follow-up, and Section 3.3 outlines how inconsistency between colours of planets and brown dwarfs led us to investigate the absence of phosphine in irradiated objects. In Section 3.4, we demonstrate how a colour–magnitude diagram can be used to get a quick constraint on the C/O ratio.

3.1 Notes on terminology

The x-axis of a colour–magnitude diagram is a colour index, calculated as the difference in magnitude between two photometric bands. It is conventional to subtract a longer wavelength magnitude from a shorter wavelength magnitude; this convention is observed throughout our paper.

In a conventional colour–magnitude diagram, objects can therefore be compared in terms of their x-position on the plot: An object on the left-hand side would be described as ‘bluer’ than one on the right-hand side. This is due to it having more flux, and therefore a higher magnitude, in the shorter, bluer wavelength than in the longer, redder wavelength. The converse is true of ‘redder’ objects. When describing the spread of objects on our colour–magnitude diagrams, we will therefore use the terms ‘bluer’ and ‘redder’ to refer to placements on the left- and right-hand sides, respectively.

3.2 Outliers and emerging subpopulations

In this section, we go through a few examples on how colour–magnitude diagrams can be used to select target for additional observations, asking questions about patterns in the data, and diagnosing molecular signatures.

3.2.1 Identifying oddball systems and measurements

Fig. 3 is a colour–magnitude diagram made with our plotting function ExoCMD|$\_$|3. As we are comparing planets and brown dwarfs, we have used the key word argument adjusted to scale the magnitudes to the size of a typical brown dwarf. On this plot, we have highlighted two objects that are clear outliers and one that is not.

On the top left, we have HAT-P-2b, a highly eccentric planet (e ≈ 0.5; Lewis et al. 2013) that is speculated to have a dayside temperature inversion. In [3.6–4.5 μm], it is consistent with both the L-Dwarf sequence and the mean position of other planets, which indicates that the 5.8 μm flux is the one causing its very blue colour. The surprisingly shallow secondary eclipse in Spitzer’s channel 3 was noted at the time of measuring, as it yields a brightness temperature of ∼700 K lower than the secondary eclipses measured in channels 1, 2, and 4. If this low flux in the 5.8 μm band is caused by processes unique to eccentric hot Jupiters, then it is possible that further eccentric systems will be similarly blue in this colour.

Further down on the same plot, we have GJ 436b. This object is also eccentric (e ≈ 0.14; Maciejewski et al. 2014b), yet in this case the problematic flux is in the 3.6 μm band. This is confirmed by its position on an M_5.8 versus [5.8–8.0 μm] where it intersects exactly with the brown dwarf sequence.

GJ 436b is a hot Neptune with an equilibrium temperature of ≈700 K (Turner et al. 2016), while HAT-P-2b is a hot Jupiter with an equilibrium temperature of 1540 K (Pál et al. 2010). Following up on both of these objects will allow us to determine whether their blue colours in [3.6–5.8 μm] are in any way caused by their eccentricity, and if so it could point to key population differences between Jupiter- and Neptune-sized objects.

We have highlighted one other planet on Fig. 3: XO-3b is the only other planet with a significant eccentricity (e significant >0.1) on this plot (e ≈ 0.28; Machalek et al. 2010). The 3.6 and 5.8 μm fluxes for XO-3b have not been updated since 2010, and the values come from single eclipse measurements. When the 4.5 μm flux was remeasured in 2014 by Wong et al. (2014), they calculated a deeper eclipse of 0.158 |${{\rm per\, cent}}$| that differs by 2.1σ from the original. This new eclipse depth was derived from 12 consecutive secondary eclipse events, and the mean variation between them of just 5|${{\text{ per cent}}}$| indicates no consequential orbit-to-orbit variation. XO-3b’s location within the population of circular planets throws a doubt on our initial hypothesis, an example on how a colour–magnitude diagram can be used.

Both of the HAT-P-2b fluxes were also calculated from single secondary eclipse events. For GJ 436b, the 3.6 μm flux has been remeasured since the first observations of its thermal emission, but the 5.8 μm flux has not; this latter value also came from a single-eclipse event. Hansen, Schwartz & Cowan (2014) has claimed that these flux ratios measured from single events have low reproducibility and underestimated errors as they do not adequately account for instrument systematics. This throws into question the significance of results inferred from single-eclipse photometry.

A further standout system can be seen in Fig. 4: On the far left with a colour of −0.9 we find WASP-65b. WASP-65b is one of the densest known hot Jupiters in its mass regime (R = 1.112R_J, M = 1.55M_J); it orbits in an area where inflated radii are the norm (a = 0.0334 au) yet it is denser than Jupiter itself (Gómez Maqueo Chew et al. 2013). It has been suggested that its uninflated radius could be evidence of the advanced age of the system, and that if this is the case, the contraction of its atmosphere could lead to changes in its temperature–pressure profile giving rise to unexpected spectral features. The measurements for WASP-65b also result from observations of a single-eclipse event (Garhart et al. 2019).

These four planets are clear candidates for follow-up. While at first look, the data so far are indicative that eccentricity and density might cause an important difference in atmospheric properties in two cases, it is, however, more likely that a lack of repeated measurement is the root cause. Regardless of what the answer turns out to be, using a colour–magnitude diagram simplifies the process of target selection.

3.2.2 Planets near the T spectral class

In Fig. 4, we present a colour–magnitude diagram in M_3.6 versus [3.6–4.5 μm]. The five planets we have highlighted all have equilibrium temperatures between 800 and 1000 K, with HAT-P-18b and WASP-80b being the coolest of the set. Triaud et al. (2015) pointed out that WASP-80b was the first planet whose measured dayside flux fell in a position consistent with the L–T transition experienced by ultra-cool dwarfs between 1100 and 1500 K. This transition is characterized by the emerging spectral signature of methane, which has its fundamental band at 3.3 μm and is therefore detectable by Spitzer’s channel 1. Triaud et al. (2015) suggested that this could be indicative that planets undergo a similar transition but at a lower temperature. The fact that we now have fluxes measured for HAT-P-18b, which is comparable in temperature and radius (Wallack et al. 2019), yet is significantly bluer, indicates that perhaps this is not true of all cool exoplanets.

One way in which these two planets differ is in mass: WASP-80b is approximately three times more massive than HAT-P-18b (0.55M_J versus 0.183M_J). Additionally, we find that WASP-67b, whose colour is also consistent with that of an early T-dwarf, is more than twice as massive as HAT-P-18b (Kammer et al. 2015). HAT-P-19b (0.292M_J) and WASP-69b (0.25M_J) fall between the others in both colour and mass. This is still too small a sample for a proper inference; however, so far, there is an interesting indication in the transition from L to T class [carbon monoxide (CO) to CH₄ chemistry] that increased mass might be correlated with a redder colour in [3.6–4.5 μm].

This ties in well with the conclusions of Zahnle & Marley (2014), who showed that the temperature of transition from CO-dominated to CH₄-dominated atmospheres scales with gravity. As the densest of the five, WASP-80b also has the highest surface gravity, which would point to a higher temperature to undergo the planetary version of an L–T transition.

An alternative interpretation for the range of colour that these planets cover might arise as differences in metallicity and C/O ratio. Kammer et al. (2015) sought to find a link between mass, metallicity, and C/O ratio for cool exoplanets, with HAT-P-19b and WASP-67b included in their sample. They found a tentative link between the masses of cool planets and the ratio of 3.6 and 4.5 μm magnitudes, which is consistent with the suggestion that less massive planets have higher metallicities (Moses et al. 2013b). More recently, Wallack et al. (2019) found that for cool planets, extreme values of C/O ratio lead to big shifts in atmospheric chemistry, having large effects on the [3.6–4.5 μm] colour. Our synthetic photometry of model atmospheres shows a very similar trend.

Fig. 5 shows a colour–magnitude diagram created using ExoCMD_model(). The Molliére spectra chosen correspond to a planet with T_eff = 1000 K, log g = 3.0, and host star spectral type = G5. We found that this colour was not sensitive to host star spectral type, but showed some changes for values of log g ≥ 4. We can see that in this temperature regime, planets with a metallicity of >0 (which we expect) experience a dramatic shift in colour with very small changes in oxygen abundance (between C/O = 0.7 and 0.85).

This shows that, in principle, we could diagnose limits on both C/O ratio and metallicity for exoplanets under 1000 K simply by measuring thermal emission in these two bands, and without extensive retrieval methods. For example, the only objects with colours of 0.25 or lower are oxygen-rich ones. We also see that the very bluest colours only occur with a combination of oxygen richness and high metallicity. Colours close to 1 indicate both a high metallicity and a C/O ≥ 0.85.

At the time of writing, this relationship is not yet calibrated. In Section 4.3, we outline the problem of model spectra that are not fully calibrated to real data. To account for this, the colours in Fig. 5 have been offset by −1 mag. This offset is an approximation from inspection of the mean offsets in M_3.6 and M_4.5 as can be seen in Fig. 11. We also note that the relationships outlined above are true for the Molliére model spectra used in this paper. An interesting next step would be to see if the same relationship holds for other model sets.

3.3 Identifying molecular signatures

One interesting prospect for colour–magnitude diagram would be their ability to diagnose the presence of certain molecules, which would help setting up certain retrieval schemes.

A plot similar to Fig. 6 appeared in Triaud et al. (2014), who highlighted a large discrepancy between the colours of brown dwarfs and hot Jupiters. Even with our improved distance measurements and absolute magnitudes adjusted to 0.9R_J, we can clearly see that planets are systematically bluer than brown dwarfs. This is in contrast with most near- and mid-infrared colour–magnitude diagrams where the planets are largely consistent in both colour and magnitude with the L-dwarf sequence (see Appendix E for up-to-date colour–magnitude diagrams). In Triaud et al. (2014), we suggested that the discrepancy in [4.5–5.8 μm] could perhaps be explained by an additional absorber within the 4.5 μm band, present for the brown dwarfs but not for the exoplanets. We reached this conclusion because 5.8 μm measurements of exoplanets appear consistent with brown dwarfs.

An important difference between brown dwarfs and hot Jupiters is that while brown dwarfs are self-luminous, hot Jupiters are irradiated objects. We searched the literature to find out what irradiation could produce in relation to the 4.5 μm band. We identified phosphine, PH₃, as a molecule present within brown dwarf atmospheres, but most likely absent in hot Jupiters (due to photolysis), as the cause of the discrepancy.

Phosphine has a strong absorption feature at approximately 4.3 μm (Sharp & Burrows 2007) and is identified as the most likely Phosphorus-carrying gas in the observable atmospheres of hot T-dwarfs and cool L-dwarfs, with temperatures in the range of 1000–1400 K (Visscher, Lodders & Fegley 2006). Visscher et al. (2006) also note that while in the atmospheres of warmer L-dwarfs PH₃ may be replaced by other phosphorus-bearing species, it may still be possible to detect the 4.3 μm PH₃ feature if it can be distinguished from the 4.5 μm CO feature. However, PH₃ is highly susceptible to irradiation (Sousa-Silva et al. 2019), and if present in the atmospheres of hot Jupiters, we expect it to be photodissociated and therefore not detectable. This would also then be true of other highly irradiated objects such as brown dwarf secondary to high-mass or high-temperature primaries.

We sought to verify our hypothesis by searching for an irradiated brown dwarf with an eclipse measurement in the bands that we considered. There is only one such object to our knowledge, WD0137-349B (Casewell et al. 2015). This object is part of a white dwarf–brown dwarf binary and as such its dayside is subject to high levels of irradiation. We plot WD0137-349B’s irradiated side on Fig. 6 (Casewell et al. 2015). Its position on the colour–magnitude diagram is more consistent with the most irradiated exoplanets rather than the ultra-cool dwarfs. We interpret this as indication that irradiation is likely the cause of a higher than usual flux in the 4.5 μm channel. Since phosphine does absorb in that particular band, and is expected to be within brown dwarfs’ atmospheres, but not within hot Jupiter, we deduce that a lack of phosphine may provide a good explanation for the 4.5 μm measurements.

To further investigate whether phosphine can have the effect we thought, we used model spectra of GJ 504b produced with and without PH₃ present (Baudino et al. 2017). We integrated these spectra and found that the removal of PH₃ from the atmosphere causes a blueward shift of 0.65 mag in [4.5–5.8 μm]. We have added an arrow of this size to Fig. 6 to illustrate the impact of PH₃ in this colour, which has an amplitude consistent with the difference between brown dwarfs and hot Jupiters, and between the irradiated brown dwarf WD0137-349B and its field brethren.

One further interesting feature of Fig. 6 is that the amplitude of the colour offset between brown dwarfs and hot Jupiters increases with decreasing absolute magnitude (i.e. increasing equilibrium temperature). Equilibrium temperature is obviously related with insolation. If the bluer colours of planets are caused by the photodissociation of PH₃, then higher levels of insolation would be expected to lead to higher PH₃ depletion.

Could it be something else? Madhusudhan & Seager (2011) describe how Spitzer fluxes, and therefore our colours, can be interpreted based on knowledge of the location of spectral features of the key absorbers present in an atmosphere. Most notably, they state that these interpretations are based on the assumption that H₂O, CH₄, CO, and CO₂ are the four dominant molecules in all Spitzer bands. Of these four, both CO and CO₂ have strong absorption features in the 4.5 μm channel, so low fluxes in this band are usually attributed to one or both of these molecules. However, thermal equilibrium predicts that both brown dwarfs and hot Jupiters should have most of their atmospheric carbon locked into CO in this temperature regime. We therefore return to our ‘additional absorber’ hypothesis.

An alternative explanation is to invoke thermal inversions in the vast majority of the hot Jupiters depicted in Fig. 6. With such an inversion, CO would be in emission and increase the flux in the 4.5 μm band. However, as we discuss in Section 4.2, planets with compelling evidence for a thermal inversion are scarce, and their existence is doubted by several authors.

One other possibility worth considering is the effect of clouds. Clouds are believed to be the cause of the significant colour change seen in brown dwarfs close the L–T transition in near- and mid-infrared colours (Patten et al. 2006), as the disappearance of silicate and iron condensates reveals atmospheric methane absorption (Triaud et al. 2014). It is unclear as yet whether similar colour changes in exoplanets could also be caused by clouds since very few planets corresponding to a T spectral class have been measured. In transmission spectroscopy, spectral features can present lower amplitudes than expected due to the presence of clouds and haze opacities (Wakeford & Sing 2015), which can lead to incorrect abundances being inferred. This is less the case when considering secondary eclipse data, as the daysides of planets as the spectrum probes at a higher altitude (Madhusudhan 2018). Nevertheless, better understanding of the role of clouds and hazes in exoplanetary atmospheres is needed to rule this out as a contributing factor since difference in irradiation and gravity between brown dwarfs and hot Jupiters might produce differing cloud coverage, altitude, and dynamics. From visual inspection of Fig. E1, and particularly of Fig. E2, we note that irradiated hot Jupiters and field brown dwarfs do follow a similar behaviour in the near-IR, over the L-type range, where clouds are thought to dominate brown dwarf atmospheres.

3.4 Seeking to constrain the C/O ratio with colour–magnitude diagrams

In Fig. 7, we present colour–magnitude diagrams featuring our new W_JH band, made with our ExoCMD|$\_$|synth() function. On the left-hand panel, we have plotted nine of the planets that have low-resolution spectra measured with HST, combining W_JH photometry with H_s. We include this as there are significantly more planets available than those with H-band photometry, but we see that their positions are shifted in colour with respect to the left-hand panel. On the right-hand panel, we have plotted three planets: from brightest they are WASP-12b, HAT-P-32Ab, and WASP-43b. We computed the brown dwarf photometry for both the panels with our Synth.py code, and we computed photometry for the three planets by integrating low-resolution emission spectra measured with the HST’s G141 grism.

We have yet to identify a colour index where objects with confirmed water detections are easily distinguishable from those without; however, we can see that three objects in 7 are widely spread in colour. Incidentally, all three of these planets have firm detections of water using these data.

In objects cooler than 1000 K, the left-hand side of the equation is favoured and methane is the dominant carbon-bearing molecule. For objects hotter than 1000 K, carbon is found mainly in the form of CO. However, if a hotter atmosphere is also oxygen rich, we would expect the excess oxygen to react with the H₂ to form water. This indicates that C/O ratio should be the biggest indicator of both [W_JH − H] colour and water abundance: More excess oxygen will cause more water to be produced. This will deepen the absorption at 1.4 μm leading to increased W_JH magnitude, and therefore a redder colour. This is consistent with the retrieved water abundances for WASP-12b and WASP-43b by Line et al. (2014): WASP-43b’s abundance was found to be greater than WASP-12b’s by a factor of 10³.

Figs 8 and 9 are colour–magnitude diagrams featuring Mollière model atmospheres. Both have been plotted for four values of log g from 2.3 to 5.0, seven values of effective temperature from 1000 to 2500 K, and a host star spectral type of G5. Fig. 8 features atmospheres with a metallicity of −0.5, while in Fig. 9 we have assigned a metallicity of 2.0. The models have been coloured according to their C/O ratio.

We can see from Fig. 8 just how much [W_JH − H] colour is affected by the C/O ratio, and for two of the planets here plotted we can attempt to infer whether they are consistent with oxygen- or carbon-rich model spectra.

Within its uncertainties, WASP-43b colours and magnitudes are consistent with an oxygen-rich atmosphere for all values of surface gravity, and retrievals of its metallicity have found it to be (0.3–1.7) × Solar (Kreidberg et al. 2014; Stevenson et al. 2017). Therefore, it is best matched by Fig. 9, and we can see that its colour is indicative of an oxygen-rich atmosphere. This is in agreement with the upper limit set by Benneke (2015) and indeed with the recent retrieval by Irwin et al. (2019).

In contrast, WASP-12b’s eclipse measurements coincide with the carbon-rich model atmospheres for both extremes of metallicity and all values of surface gravity. This is in agreement with Madhusudhan et al. (2011a), who found C/O ≥ 1 using the Spitzer secondary eclipse data. This has since been contested, with Kreidberg et al. (2015) finding that the atmosphere was best fitted by C/O ≈ 0.5 using the HST transit data, but omitting Spitzer transits due to instrument systematics. Benneke (2015) also retrieved an oxygen-rich atmosphere with C/O < 0.9 for WASP-12b, even though analysis of previously unpublished Spitzer measurements by Stevenson et al. (2014b) had confirmed the original findings. We need a better understanding of the physical processes that lead to WASP-12b appearing consistent with carbon-rich model atmospheres; additionally, in order to confirm this consistency, we need to ensure that the models are well calibrated to the data in this colour. See Section 4.3 for more details.

We were unable to find a constraint on HAT-P-32Ab’s C/O ratio in the literature, and due to the large errors on the colour we find that it is equally compatible with carbon-rich and oxygen-rich model atmospheres.

4 DISCUSSION

In the following sections, we discuss the implications of our results, placing them in the context of unexplained low fluxes and exciting upcoming missions.

4.1 Phosphine

The recently updated line list for phosphine published by Sousa-Silva et al. (2015) puts us in a favourable position to identify planets where this gas may be present. Over the lifetime of Spitzer, there have been many unexplained low fluxes measured in channel 2. In this section, we speculate about the impact that phosphine may have for a number of eclipse measurements, and planetary environments.

The absence of PH₃ on the daysides of hot Jupiters due to high levels of irradiation would not preclude the possibility of its presence on the cooler and less irradiated nightsides. One such candidate is HD 189733b that has a puzzlingly low nightside flux in 4.5 μm (Knutson et al. 2012; Steinrueck et al. 2019). The lack of irradiation on the nightside may have prevented photodissociation of the molecule, and the lower temperatures would be indicative of PH₃ accounting for most of the atmospheric phosphorus budget (Visscher et al. 2006). Even if photodissociated on the dayside, phosphorus might recombine with phosphine on the nightside, after being transported by winds.

Alternative explanations were made for this low 4.5 μm flux. For instance, CO also has a deep absorption feature in the 4.5 μm band (Sharp & Burrows 2007), and when the phase curve for HD 189733b was first observed in Spitzer’s channel 2, the low nightside flux was attributed to this molecule (Knutson et al. 2012). It was initially thought that non-equilibrium chemistry would be able to explain the fact that CO was the main carbon-bearing molecule, despite the low temperature. However, recently Steinrueck et al. (2019) showed that this is not the case: Disequilibrium processes alone cannot account for the low fluxes in Spitzer’s channel 2 as excess CO is balanced by a drop in H₂O.

Two other hot Jupiters with similarly low 4.5 μm nightside fluxes are HD 209458b (Zellem et al. 2014) and WASP-43b (Stevenson et al. 2017). Here too, models predict that they should be significantly brighter than they are in Spitzer’s channel 2, as equilibrium chemistry would point to CH₄ being the main carbon-bearing molecule on the cooler nightside. The inclusion of PH₃ in these models could revise our understanding of these planets.

Considering PH₃ in atmospheric composition may additionally help us to shed light on surprisingly shallow 4.5 μm secondary eclipses measured on the daysides of far cooler planets. GJ 436b has had consecutive non-detections in Spitzer’s channel 2 (Stevenson et al. 2010; Lanotte et al. 2014; Morley et al. 2017), pointing to a CO/CH₄ ratio that is considerably higher than what equilibrium chemistry would predict for an object of this temperature (≈700 K; Turner et al. 2016). ‘Additional absorbers’ have been postulated for GJ 436b by Morley et al. (2017) in order to resolve the apparent low flux in this wavelength, and PH₃ could be that absorber.

A similar non-detection in the 4.5 μm band for WASP-29b prompted claims of possible non-equilibrium abundances of CO (Hardin et al. 2012). WASP-29b is a Saturn-sized object with an equilibrium temperature of 980 K; PH₃ could yet again provide an explanation for this excess absorption. Most recently, GJ 3470b had a minute 4.5 μm flux measured by Benneke et al. (2019); this is a low metallicity, sub-Neptune sized planet with an equilibrium temperature of approximately 600 K. Equilibrium chemistry once again points to methane accounting for most of its atmospheric carbon budget, and phosphine as a convenient molecule to explain the observations.

4.2 Upcoming missions

The JWST is scheduled for launch in 2021 and is intended as a successor to the HST. A recent simulation of JWST spectra by Wang, Miguel & Lunine (2017) assessed the detectability of PH₃ by the telescope’s NIRCam instrument and found that it could be detectable in emission spectra for objects of around 500 K, and in transmission spectra for objects cooler than 1000 K. Although they concluded that for objects of 1000 K or more PH₃ could not be resolved with a secondary transit, we speculate that objects of intermediate temperatures, such as GJ 436b, might have detectable PH₃ due to their low 4.5 μm fluxes. Additionally, the MIRI instrument will cover the wavelength range of Spitzer’s 5.8 μm band (Rieke et al. 2015); we can therefore use photometry taken in this instrument’s channel 1 to add objects highlighted in Fig. 4 to our PH₃ diagnostic colour–magnitude diagram. The extent to which these objects are offset from the brown dwarfs will indicate whether we should follow up on them using NIRCam to search for PH₃.

While in this paper we propose that phosphine could be responsible for some of the differences in colours seen between hot Jupiters and brown dwarfs, this is not without its issues. Phosphine is hard to distinguish from CO in hotter objects, and in some of the coolest brown dwarfs, where PH₃ is expected to dominate the 4.5 μm band, the evidence for its presence is still scarce. JWST will therefore also allow us to explore the spectra of brown dwarfs in more detail in order to confirm the presence or absence of phosphine in these objects. The first M-band (4.5–5.1 μm) spectrum of WISE 0855, the coldest known brown dwarf, rather surprisingly did not reveal evidence of phosphine absorption; this is despite being very similar to Jupiter in other respects (Skemer et al. 2016). This was interpreted as evidence that WISE 0855 might not share Jupiter’s turbulent vertical mixing, which is responsible for the large abundances of PH₃ present in its observable atmosphere. Morley et al. (2018) later presented an L-band (3.4–4.14 μm) spectrum of WISE 0855; this too lacked the expected footprint of PH₃. This work was recently extended to six other brown dwarfs in the temperature range of 250–750 K, and phosphine absorption was still not clearly present in any of them (Miles et al. 2020). The authors do point out that the wavelength ranges where phosphine would be most detectable (the end of the L band and start of the M band) coincide with the lowest signal-to-noise in their data. It is also worth noting that the centre of the phosphine absorption feature is at 4.3 μm, which falls precisely in the gap between the L and M bands. Fortunately, JWST’s NIRCam will have both the spectral coverage and the resolution to shed new light on this mystery.

JWST will also be equipped with a Near Infrared Spectrograph (NIRSpec; Dorner et al. 2016) with wavelength a coverage of 0.6–5.3 μm. We will therefore be able to use our photometry tools to make diagnostics about the planets’ atmospheres, using colour–magnitude diagrams by integrating JWST spectra. While this does not replace a full atmospheric retrieval, the goal will be to identify objects that appear to be, for instance, carbon rich or outlying the main population for one reason or other, and propose them for a more detailed follow-up as was simulated by Schlawin et al. (2018).

The C/O ratio is essential to our understanding of how and where a planet formed (e.g. Madhusudhan et al. 2011b; Öberg et al. 2011; Madhusudhan 2012; Madhusudhan et al. 2017). It can also tell us whether or not a thermal inversion is likely, as carbon-rich atmospheres favour low abundances of the two molecules thought to be producing inversions (Madhusudhan & Seager 2011): TiO and VO (Fortney et al. 2008). Additionally, the C/O ratio can give an indication about the habitability of a planet (Johnson et al. 2015), as a C/O≥1 causes depletion of water, even if the planet is within the habitable zone.

The detailed spectra that JWST will be capable of producing will also help us to shed light on the atmospheres of controversial planets such as WASP-12b. This planet is predicted to have a stratosphere due to its very hot temperature (Hebb et al. 2009); however, so far TiO and VO have not been detected with any certainty as measurements of eclipse depths in relevant bands have been inconsistent (Sing et al. 2013; Hooton et al. 2019). Most recently, there has been close scrutiny of the orbit of WASP-12b due to the changing transit mid-points; the data now available point to orbital decay over apsidal precession (Bailey & Goodman 2019; Yee et al. 2020). There is also no consensus as yet on whether WASP-12b is carbon or oxygen rich: The detections of water in transmission (Kreidberg et al. 2015) point to an oxygen-rich atmosphere, yet the shallow 4.5 μm eclipse depth indicates CO in absorption rather than emission (Stevenson et al. 2014b).

If WASP-12b does have a thermal inversion caused by TiO, VO, or another mechanism, then its position on Figs 8 and 9 might be misleading. Parmentier et al. (2018) explains how the dissociation of H₂O in the atmospheres of ultra-hot Jupiters with stratospheres leads to free hydrogen atoms capturing electrons. The resulting H⁻ ions produce absorption features in the same spectral region as H₂O, which can lead to confusion when interpreting low-resolution spectra in the 1.4 μm band. In the era of JWST, we will be able to refine our interpretations of positions of ultra-hot Jupiters on our colour–magnitude diagrams in order to improve our use of them as diagnostic tools.

Looking further into the future, Ariel is planned for launch in 2028. Like JWST, it will be equipped with near- and mid-infrared spectrographs that will allow for detailed atmospheric characterization.⁵ In particular, the NIRSpec covers the wavelength ranges of the H and W_JH bands that will enable us to get an initial diagnostic on the C/O ratio, while the Ariel InfraRed Spectrometer covers the 1.95–7.8 μm range allowing us to choose targets to follow up on to find PH₃.

Edwards et al. (2019) recently produced a list of potential targets for Ariel along with their radii and equilibrium temperatures. We searched the literature for their surface gravities, host star metallicities, and host star spectral types; we were able to find all three data for 210 of the potential targets. We used this information to select the most appropriate model spectrum from Mollière et al. (2015) and plotted them on an M_W versus [W_JH − H] colour–magnitude diagram, assigning C/O ratio values of 0.55, 1, and 1.40. As the Mollière models are only available in 250 K increments, we interpolated the magnitudes in order to get a more realistic spread of colours. We did not have access to the Ariel Radiometric Model (Mugnai et al. 2019) to estimate the errors on the magnitudes; we therefore assigned an error of ±0.1 mag. This choice was not arbitrary; when computing photometry from HST/WFC3 spectra, the data with resolution comparable to what Ariel will produce yielded a signal-to-noise ratio of 10, equivalent to a tenth of a magnitude. We present the resulting plot in Fig. 10.

While the values for surface gravity, metallicity, and host star spectral type had to be rounded to fit the model grid, we can see that objects with a C/O ratio of ≥1 are distinguishable from oxygen-rich objects.

A recent paper by Melville et al. (2020) also attempted to use colour–magnitude and colour–colour diagrams to constrain the atmospheric properties of exoplanets. In this paper, model spectra were computed using VSTAR (Versatile Software for Transfer of Atmospheric Radiation; Bailey & Kedziora-Chudczer 2012) for a range of values of metallicity, log g, and C/O ratio. Model atmospheres were then compared with hot Jupiters in near- and mid-infrared colours using photometry in the JHK_s bands and Spitzer’s channels 1 and 2. While planets were seen to cluster around solar values of C/O and metallicity, no definitive constraints were found as the error bars were too large.

4.3 Model calibrations

Our C/O ratio diagnostic tools rely on the availability and reliability of model spectra. We chose to use the models presented in Mollière et al. (2015) as they covered a very wide parameter space and were publicly available. However, those models have limitations that impact the validity of our inferences.

The first limitation we find is simply the range of temperatures available. Both JWST and Ariel will observe objects cooler than 1000 K in more detail than ever before, and in order to use models to characterize these objects it is essential that we have model spectra in this temperature range.

The second limitation comes from the quality of the fit for different wavelengths. In their paper, Mollière et al. (2015) showed a comparison between their retrieved model spectrum for HD-179833b and the many thermal emission measurements available for this planet. They showed that Spitzer photometry at 8 μm was well fitted by their model, while the shorter wavelength channels were not. They also showed that while the pattern for the HST data was well fitted, the measured eclipse depths were larger than those retrieved by the model.

We illustrate the disparity between the measured data and the model spectra in IRAC channels in Fig. 11. It is clear from these plots that there is a systematic offset in all four Spitzer bands when we compare with a large enough sample. However, this also demonstrates that colour–magnitude diagrams, and indeed our tools to produce them, are especially valuable to modellers to validate their model spectra. It is also a cautionary note since similar spectra used for retrieval would be unlikely to lead to correct abundances.

The completeness of the chemistry included into the models impacts the outcome of retrievals. In particular, Baudino et al. (2017) showed how an incomplete line list for PH₃, let alone its exclusion from models altogether, can lead to this crucial molecule not being detected at all. We would also need oxides of titanium and vanadium included in radiative transfer calculations in order to ensure that possible thermal inversions are explored.

5 CONCLUSIONS

In this paper, we have presented a public python toolkit for the plotting of near- and mid-infrared colour–magnitude diagrams. To demonstrate the functionality of the toolkit, and the usefulness of colour–magnitudes of transiting exoplanets, we have presented a selection of our newly plotted diagrams. From these, we have identified some trends:

• Two objects (HAT-P-2b and GJ 436b) are very blue in [3.6–5.8 μm] colour. Despite the fact that for each of these planets the blue colour is caused by excess emission in different bands, what they have in common is high eccentricity. Further follow-up could reveal if their colours are related to their eccentricity, and if so, whether mass and eccentricity are linked to cause excess brightness in different photometric bands. Remeasuring the mid-infrared photometry of XO-3b will also confirm why this planet does not share the blue colours of HAT-P-2b and GJ 436b.

• Objects cooler than 1000 K show a wide spread in colours in [3.6–4.5 μm] colour, which could be attributed to mass, metallicity, and C/O ratio. By comparing the positions of five planets to the colours of model atmospheres, we find that for a C/O ratio of ≥0.85, high metallicity causes reddening. At C/O ratios of ≤0.75, increasing metallicity causes increasing blueness. For the planets we plotted, we also find that increasing surface gravity corresponds to redder colours.

• We attribute the comparative blueness of planets in [4.5–5.8 μm] colour to missing PH₃, which absorbs prominently in the 4.5 μm band. Field brown dwarfs in this temperature range could be expected to have Phospine account for most of their atmospheric phosphorus budget, yet as PH₃ is susceptible to photolysis by ultraviolet radiation, we believe it is feasible that hot and ultra-hot Jupiters would be missing this absorber. We propose that PH₃ might have been overlooked to explain several low 4.5 μm fluxes, including on the dayside of GJ 436b and the nightside of HD 189733b.

• The [W_JH − H] colour index can be used to diagnose the C/O ratio of exoplanets. Magnitude increases in the Wband with increased water absorption, which we attribute to lower C/O ratios. From its position on an M_W versus [W_JH − H] diagram, we find WASP-12b to be carbon rich.

In order to further refine constraints that we derive from comparisons with model magnitudes, model spectra need to be calibrated to real data to the greatest extent possible. Our colour–magnitude diagrams are very well suited to this purpose.

With the launch of JWST now close, our colour–magnitude diagrams will be an invaluable tool for target selection in this new era of exoplanet atmospheric characterization. Additionally, ESA’s Ariel mission will enable us to begin to study populations as a whole. Here colour–magnitude diagrams can prove essential to identify various subpopulations, and to select targets from Tier 1 observations to the more detailed and higher signal-to-noise Tier 2 and 3.

SUPPORTING INFORMATION

Supplementary data are available at MNRAS online.

Appendices_CMD.pdf

Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.

ACKNOWLEDGEMENTS

We would like the thank Joanna Barstow for her considerate and insightful review of our paper. Her feedback helped us to significantly improve and clarify the manuscript. GD acknowledges funding from the University of Birmingham that made this research possible. Many thanks also go to Jean-Loup Baudino for supplying the model spectra for GJ 504b, and to Vivien Parmentier for the very helpful discussions on thermal inversions. We also thank Emil Tersiev and Brigitta Sipocz for early exploration of colour–magnitude diagrams. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC; https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This research has benefitted from the SpeX Prism Spectral Libraries, maintained by Adam Burgasser at http://pono.ucsd.edu/~adam/browndwarfs/spexprism. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Programme. Amaury HMJ Triaud has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 803193/BEBOP).

DATA AVAILABILITY

The data used in this article are available in tables in the appendices of the article, and on Github together with the python toolkit developed for this article at https://github.com/gdransfield/ExoCMD.

Footnotes

REFERENCES