Draft version August 19, 2020 Typeset using LATEX twocolumn style in AASTeX63

Constraining the Bulk Composition of Disintegrating Using Combined Transmission Spectra from JWST and SPICA Ayaka Okuya,1 Satoshi Okuzumi,1 Kazumasa Ohno,1 and Teruyuki Hirano1

1Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan

ABSTRACT Disintegrating are ultra-short-period exoplanets that appear to have a comet-like dust tail. They are commonly interpreted as low-mass planets whose solid surface is evaporating and whose tail is made of re- condensing minerals. Transmission spectroscopy of the dust tails could thus allow us to directly probe the elementary compositions of the planets. Previous work already investigated the feasibility of such observations using the JWST mid-infrared instrument. In this study, we explore if one can obtain a strong constrain on the tail composition by adding spectroscopy at longer wavelengths using SPICA mid-infrared instrument. We use a simple model for the spatial distribution of the dust tails and produce their synthetic transmission spectra as- suming various dust compositions. We find that combined infrared spectra from JWST and SPICA will allow us to diagnose various components of the dust tails. JWST will be able to detect silicate and carbide absorption features with a feature-to-noise ratio of & 3 in the tail transmission spectrum of a disintegrating located within 100 pc from the Earth with a transit depth deeper than 0.5%. SPICA can distinguish between Fe- and Mg-bearing crystalline silicates for planets at . 100 pc with a transit depth of & 2%. Transit searches with current and future space telescopes (e.g., TESS and PLATO) will provide ideal targets for such spectroscopic observations.

Keywords: planets and satellites: composition — planets and satellites: terrestrial planets — infrared: planetary systems

1. INTRODUCTION ric transit light curves. An example is K2-22b, which is a Constraining the bulk compositions of planets is crucial planet orbiting close to an M-type star and exhibits asymmet- for understanding their formation and evolution history. The ric and highly time-variable transit curves (Sanchis-Ojeda common approach to infer the bulk composition of et al. 2015). Disintegrating planets are thought to have an an is to use its bulk density (e.g., Fortney et al. evaporating solid surface that produces mineral vapor, and 2007; Zeng & Sasselov 2013; Zeng et al. 2019), but this sin- their asymmetric light curves are interpreted as being due to gle quantity alone cannot uniquely constrain the composition a comet-like tail forming from the recondensing vapor (e.g., (e.g. Seager et al. 2007; Rogers & Seager 2010; Dorn et al. Rappaport et al. 2012). Models suggest that they are presum- 2015). For close-in super-Earths, recent studies predict their ably solid planets of Moon to Mercury masses (e.g., Rap- compositions based on the observed planetary radius distri- paport et al. 2012; Perez-Becker & Chiang 2013). Therefore, bution (e.g., Lopez 2017; Owen & Wu 2017), but the compo- by performing transmission spectroscopy of the dust tails, we sitions inferred this way depend on the assumption about how may be able to directly probe the solid composition of low- mass planets. Although there are only a handful of known arXiv:2008.07781v1 [astro-ph.EP] 18 Aug 2020 the radius distribution is sculptured (Owen & Adams 2019). So-called disintegrating planets discovered by the Ke- candidates for disintegrating planets (Rappaport et al. 2012, pler/K2 missions (Rappaport et al. 2012, 2014; Sanchis- 2014; Sanchis-Ojeda et al. 2015; Jones et al. 2020), current Ojeda et al. 2015) could offer a unique opportunity to inves- and future missions for transit searches will discover more tigate exoplanets’ solid compositions. Disintegrating plan- candidates. ets are ultra-short-period exoplanets that exhibit asymmet- Bodman et al.(2018) explored the possibility of inferring the composition of the dust tails of disintegrating planets from infrared observations with the James Webb Space Tele- Corresponding author: Ayaka Okuya scope (JWST). They found that silicate resonant features near [email protected] 10 µm can produce transit depths that are at least as large as those in the visible, and that most of the features will be de- 2 Okuya et al. tectable with the JWST mid-infrared instrument (MIRI) for y the particular case of K2-22b. While JWST will serve as a powerful tool to observe sil- Rt icate features in the wavelength range of 5–14 µm, silicates also produce a number of absorption features at longer wave- x lengths (Kitzmann & Heng 2018; see also Figure4 of this Δθ paper). Therefore, transmission spectroscopy of the dust tails at longer wavelengths should be useful to put stronger con- z straints on what material the dust tails of disintegrating plan- ets are made of. The proposed mission, Space Infrared Tele- scope for Cosmology and Astrophysics (SPICA), can poten- Figure 1. Schematic illustrating showing the geometry of the dust tially make such observations possible. SPICA is a candi- tail. The tail is approximated by a curved cylinder of thickness Rt date space mission envisaged to be launched in the late 2020s orbiting the central star. The z-axis is in the direction of the ob- server, and the y-axis is perpendicular to the orbital plane of the or early 2030s (Roelfsema et al. 2018). Its mid-infrared in- dust tail. strument (SMI) enables low- to high-resolution spectroscopy in the wavelength range of 12–36 µm (Kaneda et al. 2016), cylinder of radius R , trailing with the planet along a circular which is ideally complementary to spectroscopy with JWST. t orbit at distance a from the central star. We employ such a In this paper, we investigate the feasibility of constrain- simple model because the dust tail is expected to be largely ing the composition of disintegrating planets from combined optically thin (see below), for which a time-integrated trans- transmission spectra obtained with future JWST and SPICA mission depth is nearly proportional the total amount of dust observations. We construct a simple model for the spatial dis- grains passing in front of the central star. For the same rea- tribution of the dust tails of disintegrating planets to produce son, we neglect a leading tail that could be associated with a their theoretical transmission spectra. Since the solid com- real disintegrating planet, including K2-22b (Sanchis-Ojeda positions of exoplanets may be diverse (Bond et al. 2010; et al. 2015). As we show at the end of this section, our sim- Jontof-Hutter 2019), we consider various minerals that po- plified model can reasonably reproduce the transit light curve tentially constitute the dust tails. Based on the expected ca- of K2-22b except for its ingress. pability of JWST and SPICA, we quantify the detectability of For simplicity, we assume that the line of sight of an ob- the absorption features of various minerals at infrared wave- server lies on the orbital plane of the planet and dust tail. lengths as a function of the optical transit depth and distance We introduce a Cartesian coordinate system centered on the to the system. We show that combined transmission spec- star with the z and y axes taken to be in the direction of the tra from JWST and SPICA can place stronger constraints on observer and perpendicular to the orbital plane, respectively the composition of disintegrating planets than spectra from (see Figure1). The transit depth δ at a given time and a wave- JWST alone. length λ is then given by The organization of this paper is as follows. In Section2, R we describe our model for the spatial distribution and mineral √ (1 − e−τ(x,y;λ))dxdy x2+y2≤R composition of the dust tails. In Section3, we present the- δ λ star , ( ) = 2 (1) oretical infrared transmission spectra of the tails in the limit πRstar of zero observational noise to identify the absorption features where R is the radius of the central star, τ is the optical of the candidate minerals in the wavelength coverages of the star depth along the line of sight of the observer. We applied our JWST and SPICA mid-infrared instruments. In Section4, dust tail model to the observed light curve for the disintegrat- we account for expected observational noise to quantify the ing planet K2-22b (Sanchis-Ojeda et al. 2015) and found that detectability of mineral features as a function of the transit the model reproduces the half-width of the light curve at an depth and distance to the planet. In Section5, we discuss accuracy of . 40 % when the maximum transit depth of our some uncertainties of the tail model and possible applications model is set equal to the observed depth. of the proposed tail transmission spectroscopy to planet for- The optical depth τ is given by the product of the number mation studies. We summarize our findings in Section6. density and extinction cross section of the dust grains inte- grated over the observer’s line of sight. Following Rappaport 2. MODEL et al.(2014), we simply assume that the tail decays expo- 2.1. Transit Model nentially with the angular distance from the planet, ∆θ (see We use a simple analytic model for the spatial distribution Figure1 for the definition of ∆θ), expressing τ as of the dust tails. Figure1 schematically shows the geom- Z −α∆θ(x,z) etry of a modeled tail. The dust tail is approximated by a τ(x, y; λ) = σext(λ)n0e dz, (2) Transmission Spectra of Disintegrating Exoplanets 3

the disintegrating planet K2-22b (Sanchis-Ojeda et al. 2015). For R = 0.02R and n = 5.6 × 104 m−3, the dust tail is 1 t star 0 sufficiently optically thin and also reproduces the maximum 0.999 transit depth. The slope of the light curve in the transit egress (corresponding to orbital phase ≈ 0–20◦) is best fit with the 0.998 choice α = 1/(0.133 rad). Since our model neglects a leading tail, the ingress shows a less good match than the engress. In 0.997 Section3, we adopt this parameter set to produce noise-free

0.996 theoretical transmission spectra. Relative flux Because the grain extinction cross section depends on 0.995 wavelength, transit light curves at different wavelengths ex- hibit different transit depths. In this study, we define trans- 0.994 Our Model mission spectra as the maximum transit depth as a function Observation of wavelength. -60 -40 -20 0 20 40 60 2.2. Dust Composition Orbital Phase (degrees) We consider 8 candidate minerals for the dust tails of ter- Figure 2. Transit light curve for a dust tail composed of SiO2 restrial and non-terrestrial planets (Figure3 and Table1). By grains from the tail model with R = 0.02R , n = 5.6 × 104 m−3, t star 0 terrestrial planets we mean rocky planets comprised of a crust and α = 1/(0.133 rad). For comparison, the gray line shows an averaged observed light curve for K2-22b, taken from Fig- containing O, Si, and Al; a mantle containing O, Mg, and ure 6 of Sanchis-Ojeda et al.(2015) using WebPlotDigitzer (https: Si; and an iron core. The vapor from the crust, mantle, and //automeris.io/WebPlotDigitizer/). core is assumed to form dust tails made of SiO2 (silica) and Al2O3 (alminium oxide), MgSiO3 (enstatite) and Mg2SiO4 (forsterite), and pure Fe, respectively. Coreless planets are where σext and n0 are the extinction cross section and number density of the grains at ∆θ = 0, respectively, and α(> 0) is hypothetical planets that have no metallic core but have a gi- the factor that characterize the length scale over which the tail ant silicate mantle that is abundant in iron (Elkins-Tanton & decays. The exponential function in Equation (2) encapsulate Seager 2008). The vapor from the mantle of coreless plan- the net effect of the tail’s decay due to grain sublimation on ets would condense into Mg- and Fe-bearing silicates, which the grain number density and on the grain size. This simple we model with MgSiO3, Mg2SiO4, and Fe2SiO4 (fayalite). prescription, although somewhat ad hoc, allows us to take Carbon planets are solid planets with a carbon-to-oxygen ra- tio (C/O) larger than 1. The vapor from this type of planets σext(λ) as constant in space (see Appendix C of Rappaport et al. 2014 for a validation of this prescription). would condense into SiC (silicon carbide) and graphite (e.g., The dust grains are approximated as compact spheres of Woitke et al. 2018). In Section 5.2 we discuss in more detail how the mineral composition of dust tails can be linked to equal radius rd, and their extinction cross section is calcu- lated using the publicly available Mie calculation code LX- the composition of the disintegrating planets themselves. For MIE (Kitzmann & Heng 2018). The complex refractive in- simplicity, our synthetic transmission spectra assume that the dices of the minerals constituting the grains are taken from dust tail is composed of a single mineral species. literature date (see Section 2.2 for details). The typical grain Computation of the grain extinction cross section requires size in the dust tails is observationally inferred to be in the data of the complex refractive index as a function of wave- range 0.1–1 µm from the forward scattering of the tails and length. In principle, the refractive index differs between from the wavelength dependence of the transit depths (Budaj crystalline or amorphous materials, and Table1 summarizes 2013; Rappaport et al. 2014; Sanchis-Ojeda et al. 2015). For which material is considered for each mineral (“cryst.” and “amo.” refer to crystalline and amorphous materials, respec- simplicity, we fix rd = 1 µm in our calculations. tively). The optical constants for amorphous silicates are Our model involves three important parameters: Rt, n0, and α. We choose the parameter values so that the dust similar (see Figure 1 of Kitzmann & Heng 2018), so we ar- tail is optically thin at the wavelength of the Kepler band bitrarily take amorphous Mg2SiO4 as a representative amor- phous silicate. The refractive indices for crystalline Mg SiO (λKepler = 0.42–0.9 µm). If the dust surrounding an evaporat- 2 4 ing planet were optically thick, starlight would not reach the and MgSiO3 are taken from Fabian et al.(2001) and Jaeger planet’s surface and evaporation would be quenched (Rappa- et al.(1998), respectively. The refractive indices for the port et al. 2012; Perez-Becker & Chiang 2013; van Lieshout other minerals are taken from the compilation by Kitzmann et al. 2016). Figure2 illustrates how a transit curve from & Heng(2018). our model compares with a real transmission light curve for 3. THEORETICAL TRANSMISSION SPECTRA 4 Okuya et al.

Terrestrial planets Coreless planets Carbon planets

Crust (O, Si, Al,...) Crust (O, Si, Al,...) Crust (C) SiO2 SiO2 Mantle (O, Mg, Si,...) Mantle (O, Mg, Si, Fe,...) Mantle (C, Si, ...) Core (Fe) Core (Fe) C Al2O3 Al2O3

Fe2SiO4

SiC MgSiO3, Mg2SiO4 MgSiO3, Mg2SiO4

Fe Fe

Time Time Time

Figure 3. Schematic illustration of candidate compositions of the dust tail generated by the evaporation of terrestrial, coreless (Elkins-Tanton & Seager 2008), and carbon (Kuchner & Seager 2005) exoplanets (see also Section 5.2). The time evolution of dust compositions goes along the arrows if the planets evaporate (disintegrate) from their crusts to their cores. Table 1. Candidate Minerals for the Dust Tails of Disintegrating Based on the presence or absence of absorption Planets peaks/features in the wavelength ranges covered by JWST and SPICA, the candidate minerals can be crudely classi- Mineral Planet type Source part fied into three groups as summarized in Table2 (see also SiO (amo.) Terrestrial Crust 2 Figure5). Group (a) includes SiO 2 and silicates (Fe2SiO4, Al2O3 (amo.) Terrestrial Crust Mg2SiO4, and MgSiO3), which show absorption peaks both MgSiO3 (cryst.) Terrestrial/Coreless Mantle in the JWST and SPICA wavelength regions. Group (b) con- Mg2SiO4 (cryst. & amo.) Terrestrial/Coreless Mantle sists of Al2O3 and SiC, which have an absorption peak at Fe2SiO4 (cryst.) Coreless Mantle λ ≈ 10–12µm in the JWST range but not in the SPICA range; Fe (metallic iron) Terrestrial/Carbon Core Group (c) consists of Fe metal and graphite, which are fea- C (graphite) Carbon Crust tureless and only exhibit slopes in both wavelength ranges. SiC (cryst.) Carbon Mantle The above classification already demonstrates the strength of combined transmission spectroscopy with JWST and SPICA in discriminating between the tail composition. The spectral features of the individual minerals can be characterized as follows (see also Figure5). For silicates, the In this section, we present theoretical transmission spectra peaks in the JWST wavelength range are narrowly concen- of the dust tails in the ideal limit of no observational noise trated at ∼ 10 µm. When viewed at a low spectral resolution, and identify spectral features of candidate minerals in the these materials only exhibit a single peak around 10 µm as we JWST and SPICA wavelength ranges. demonstrate in Figure6 in the following section. However, Figure4 shows the theoretical infrared transmission spec- in the SPICA wavelength range, their spectral features are tra from the fiducial tail model for all candidate minerals more diverse; crystalline Mg-bearing silicates have promi- considered in this study. A variety of absorption features nent peaks at 19–23 µm, while crystalline Fe SiO exhibits are visible at wavelengths longer than 5 µm, and some of 2 4 additional strong features at 26–30 µm. This diversity is vis- them fit in the wavelength ranges covered by JWST MIRI and ible even in low-resolution spectra (see Figure6). This im- SPICA SMI. The wiggles appearing in the spectrum curves plies that SPICA could potentially serve as a useful tool to at λ . 5 µm are so-called interference and ripple structures discriminate between silicates in the dust tail. Amorphous characteristic of Mie scattering by spheres with r & λ/2π d silicates (represented by amorphous Mg SiO ) have a peak (see, e.g., Bohren & Huffman 1983). These structures largely 2 4 at 17–18 µm, but this lies at at the edge of the SPICA wave- depend on r and hence are not purely inherited from the bulk d length coverage. This feature would appear as a slope rather optical properties of the materials. For this reason, below we than a peak in low-resolution spectra (see Section4). SiO focus on the absorption features at λ > 5 µm. 2 has a peak at 8.8 µm in the JWST range and at 20.5 µm Transmission Spectra of Disintegrating Exoplanets 5

1 1 SiO2 (amo) Mg2SiO4 (cryst.) Mg2SiO4 (amo.) 1

0.8 0.8 0.8

0.6 0.6 0.6

0.4 0.4 0.4 Transit depth (%) Transit depth (%) Transit depth (%) 0.2 0.2 0.2

0 0 0 1 10 100 1 10 100 1 10 100 Wavelength (µm) Wavelength (µm) Wavelength (µm)

1 1 1 MgSiO3 (cryst.) Fe2SiO4 (cryst.) Al2O3

0.8 0.8 0.8

0.6 0.6 0.6

0.4 0.4 0.4 Transit depth (%) Transit depth (%) Transit depth (%) 0.2 0.2 0.2

0 0 0 1 10 100 1 10 100 1 10 100 Wavelength (µm) Wavelength (µm) Wavelength (µm)

1 SiC 1 Fe 1 C

0.8 0.8 0.8

0.6 0.6 0.6

0.4 0.4 0.4 Transit depth (%) Transit depth (%) Transit depth (%) 0.2 0.2 0.2

0 0 0 1 10 100 1 10 100 1 10 100 Wavelength (µm) Wavelength (µm) Wavelength (µm)

Figure 4. Theoretical transmission spectra for different minerals from the fiducial tail model. Here, “cryst.” and “amo.” refer to crystalline and amorphous materials, respectively. The cyan and orange shaded regions mark wavelength ranges covered by JWST MIRI/LRS (5–12 µm) and SPICA SMI/LR (17–36 µm), respectively. in the SPICA range. The positions of the peaks are fairly To predict if the spectral features identified in the previ- insensitive to crystallinity because the refractive indices for ous section will be detectable in future observations with silicate and amorphous SiO2 are similar (Kitzmann & Heng JWST and SPICA, we need to estimate how large observa- 2018). As for the minerals belonging to group (b), SiC has a tional noise will be added to real transmission spectra. In this peak at 10.8 µm, whereas Al2O3 has a peak at 12 µm. When section, we quantify the detectability of the mineral features viewed in the SPICA wavelength range, SiC produces very of disintegrating planets by taking into account expected ob- low transit depths, while Al2O3 produces a spectral slope servational noise. whose amplitude is comparable to that of the feature in the Because signals in transmission spectra of low-mass exo- JWST range. These differences might be useful for discrim- planets are generally faint, spectral resolution must be com- inating between the two minerals from transmission spectra. promised to gain sensitivity. Because the spectral features of Obviously, the minerals belonging to group (c) would be in- solid materials are broad compared to molecular lines, low- distinguishable at mid-infrared wavelengths. resolution (R = λ/∆λ ∼ 10, where ∆λ is the spectral resolu- tion) spectroscopy would suffice to spectrally resolve the fea- tures. For this reason, we assume observations using the low- 4. DETECTABILITY OF MINERAL FEATURES WITH resolution mid-infrared spectrometers on JWST (MIRI/LRS; FUTURE OBSERVATIONS λ = 5–12 µm, R = 40–200) and on SPICA (SMI/LR; λ =17– 6 Okuya et al.

Table 2. Classification of the Candidate Minerals Based on the Position of Absorption Peaks

Group Peaks/Features with JWST Peaks/Features with SPICA Minerals

(a) XX SiO2, Fe2SiO4, Mg2SiO4, MgSiO3

(b) X Al2O3, SiC (c) Fe, C

1 1 (a) SiO2 (b) Al2O3 MgSiO3(cryst.) SiC Mg2SiO4 (cryst.) 0.8 0.8 Mg2SiO4 (amo.) Fe2SiO4 (cryst.)

0.6 0.6

0.4 0.4 Transit depth (%) Transit depth (%) 0.2 0.2

0 0 5 10 15 20 25 30 35 5 10 15 20 25 30 35 Wavelength (µm) Wavelength (µm)

1 Fe (c) C 0.8

0.6

0.4 Transit depth (%) 0.2

0 5 10 15 20 25 30 35 Wavelength (µm)

Figure 5. Theoretical transmission spectra from the fiducial tail model classified into three groups (a)–(c) based on the presence or absence of features in the JWST MIRI/LRS and SPICA SMI/LR wavelength ranges (see Table2 for the classification). The absorption features seen at λ ≈ 5 µm are the edges of the interference structure of the 1 µm-sized spherical particles and do not directly reflect the intrinsic bulk absorption properties of the minerals (see text). 36 µm, R = 50–150). Following Bodman et al.(2018), we The detectability estimates shown below are for conserva- also assume binning of observed spectra into coarser spectral tive, single transit observations. A higher signal-to-noise ra- bins of R = 10 to further enhance signal-to-noise ratios. As tio may be achieved by averaging transmission spectra from an example, Figure6 shows theoretical transmission spec- multiple transit events. Because disintegrating planets gener- tra for some selected candidate minerals from the tail model ally have very short orbital periods, multiple transit observa- used in Section3 (see Figure4), but now binned to R = 10. tions of the planets are relatively easy to conduct. However, With this reduced spectral resolution, fine features are largely interpretation of such averaged spectra would require caution smeared out, but broad features are still visible both in the when the tails is highly time-variable. JWST and SPICA bands. We adopt a transit duration of t = 0.8 hr, which is equal to the transit duration of K2-22b (Sanchis-Ojeda et al. 2015). 4.1. Observational Noise for JWST and SPICA Transmission Spectra of Disintegrating Exoplanets 7

To begin with, we calculate the 1σ noise levels σN 0.8 (a) SiO2 (amo.) Mg2SiO4 (cryst.) MgSiO (cryst.) Fe SiO (cryst.) expected for a single transit observation with JWST and 0.6 3 2 4 SPICA. Mg2SiO4 (amo.) For both JWST MIRI and SPICA SMI, the sensitivity is 0.4 largely if not entirely determined by the shot noise on zodi- 0.2 acal light emission (Glasse et al. 2015; Sakon et al. 2016), Transit depth (%) 0 the level of which depends on where the target is on the sky. 5 10 15 20 25 30 35 0.8 The mid-infrared zodiacal emission near the ecliptic plane (b) Al2O3 SiC is ≈ 80/15 ≈ 5 times higher that that near the ecliptic pole 0.6 (Sakon et al. 2016). Unless otherwise noted, we consider tar- 0.4 gets near the ecliptic pole. For targets near the ecliptic plane, 0.2 we augment the noise levels at all wavelengths by the factor Transit depth (%) 0 of 5. 5 10 15 20 25 30 35 For JWST MIRI/LRS, Glasse et al.(2015) provide ana- Wavelength (µm) lytic fits to the expected 10σ sensitivity for a spectrally un- Figure 6. Theoretical transmission spectra for candidate minerals resolved point source and to the spectral resolution ∆λ (their shown in Figures5 (a) and (b), but here binned to R = 10. The error Equations 17 and 18, respectively) for a t = 104 s obser- bars show expected 1σ noise for single transit observations with vation as a function of wavelength. The fit for the sensitiv- JWST MIRI/LRS (5–12 µm; shaded in cyan) and SPICA SMI/LR ity, however, slightly underestimates the up-to-date expected (17–36 µm; shaded in orange) assuming d = 60 pc. sensitivity available online1. We correct for the difference by multiplying the fit by a factor of exp[0.04(14 − λ[µm])1.5]. is comparable to the noise level, suggesting that these fea- We then compute the 1σ noise level for the flux density by di- tures might be barely detectable. The detectability is more viding the corrected 10σ sensitivity for spectrally unresolved quantitatively discussed in the following subsections. targets by 10∆λ. We finally obtain the 1σ noise level for R = 10 and t = 0.8 hr by assuming that the noise simply 4.2. Feature-to-noise Ratio 1/2 −1/2 obeys Poisson statistics, i.e., σN ∝ R t . To quantify the significance of mineral features relative to For SPICA SMI, the expected 5σ noise level for an 1- observational noise, we introduce a metric, which we call the hr observation using SMI/LR, when scaled to R = 80, is feature-to-noise ratio (F/N), defined as ≈ 25 µJy according to the latest version of the SPICA SMI Fact Sheet2. Again assuming Poisson noise, we ob- δ(λpeak) − δ(λfloor) F/N = . (4) tain a 1σ noise level of σ ≈ 5(t/1 hr)−1/2(R/80)1/2 µJy ≈ q N σ (λ )2 + σ (λ )2 2(t/0.8 hr)−1/2(R/10)1/2 µJy. N peak N floor To translate the noise in the flux density into the noise in where λpeak is the wavelength at which the mineral feature the transit depth, one needs to assume the flux density of the under consideration is peaked and λfloor is the wavelength at emission from the central star. Assuming blackbody radia- which the transit depth takes a local minimum just outside tion, the flux density Fstar of the starlight is given by the feature. In the right-hand side of Equation (4), the nu- R2 merator is the relative transit depth of the feature, whereas F (λ) = star πB(λ, T ), (3) star d2 star the denominator is the root sum square of the observational noises at λ = λpeak and λfloor. A feature with a higher F/N where d is the distance from the Earth to the star, Teff is the is more detectable. For each mineral and for each of the two stellar effective temperature, and B is the Planck function. observational bands, we calculate the F/N of the strongest In this section, we fix Rstar = 0.55 R and Tstar = 3800 K, feature in the binned model spectrum. Crystalline Mg SiO which apply to K2-22 (Sanchis-Ojeda et al. 2015), but vary 2 4 and Fe SiO are exceptional because they have multiple fea- the value of d to be able to predict the detectability of mineral 2 4 tures that are comparable in magnitude. We take the 21–25 features for as yet undiscovered disintegrating planets. µm feature for the former and 24–32 µm feature for the latter. For illustration, the error bars in Figure6 indicate the 1 σ Figure7 illustrates the definition of F /N works for the 24–32 observational uncertainties for the binned transmission spec- µm feature of crystalline Fe SiO . tra expected for d = 60 pc. For this particular example, 2 4 the signal level of the silicate features in the SPICA band 4.3. Detectability Prediction We evaluate F/N for representative mineral features as a 1 MIRI Sensitivity - JWST User Documentation function of the transit depth in the Kepler band δ(λKepler) and 2 https://www.ir.isas.jaxa.jp/SPICA/SPICA HP/SMI/instrument-en.html distance to the system d. We vary δ(λKepler) by adjusting the 8 Okuya et al.

∼ 0.4 1%, one can observe the features with F/N 1 for SiO2, crys- talline Mg2SiO4, and crystalline Fe2SiO4, and F/N ∼ 0.3 for amorphous Mg2SiO4 in the SPICA band. F/N ∼ 1 would 0.3 be a minimum requirement to detect the features. There- σ λ fore, one would need to observe the disintegrating planet with 0.2 ( ) N peak δ(λKepler) & 1% located at d < 100 pc in order to detect the F features in the SPICA band confidently.

Transitdepth (%) 0.1 We here assess the detectability of mineral features for σ (λ ) N floor the nearest candidate of disintegrating exoplanets, K2-22b

0 (d=225 pc and δKepler ∼ 0.55%). Since K2-22b is located near the ecliptic plane, we adopt noise levels 5 times higher 18 20 22 24 26 28 30 32 34 36 than for planets near the ecliptic pole (see Section 4.1). The Wavelength (μm) F/N maps for this high noise case is shown in Figure9. In a

Figure 7. Illustration showing the definition of F = δ(λpeak) − single transit observation of K2-22b with JWST, the feature δ(λfloor), σN(λpeak), and σN(λfloor) in the expression for F/N (Equa- of SiO2 may be detectable with F/N ∼ 3. The other features tion (4)) for the case of the 24–32 µm peak of Fe2SiO4. The solid in the JWST band have F/N ∼ 1, so detection of these fea- curve shows the binned theoretical transmission spectrum, while the tures may benefit from multiple transit observations. In con- vertical bars represent observational noise (see also Figure6). trast, all the features in the SPICA band have F/N < 0.1, sug- gesting that detection of these features with SPICA is highly value of Rt, while fixing α = 1/(0.133 rad) and n0 = 5.6 × challenging for K2-22b. 104 m−3 as in the previous section. As discussed in Section Current and upcoming dedicated missions for transit 5.1, adjusting the value of n0 with fixed Rt gives essentially searches such as TESS and PLATO would be able to pro- the same results for F/N, except that there is an upper limit vide optimal targets for the JWST and the SPICA transmis- on transit depth set by the tail’s optical thickness. sion spectroscopy. Since N is smaller for closer planets, even Figure8 shows the calculated F /N of each mineral for a small F and hence even small δ(λKepler) provide the detec- single transit observation as a function of δ(λKepler) and d. tion with F/N & 3. According to the estimation of Barclay Over the entire range of δ(λKepler) explored here, the dust tail et al.(2018), about 70 % of exoplanets found by TESS are is optically thin both at optical and infrared wavelengths, and expected to be located within as near as 200 pc. Moreover, hence F/N increases monotonically with δ(λKepler), or Rt. For TESS and PLATO will survey nearly the entire sky, allowing planets at d = 100 pc, the features of SiO2, Mg2SiO4, SiC, us to detect disintegrating planets far away from the eclip- and Al2O3 in the JWST band have F/N & 3 if δ(λKepler) & tic plane with high background noise. Although the optical 0.5%. For those planets, the features of SiO2, Mg2SiO4, and transit depth is much smaller than that of K2-22b, a potential Fe2SiO4 in the SPICA band achieve F/N & 3 if δ(λKepler) ex- new candidate of the disintegrating planet has been recently ceeds 2%. discovered by TESS in the nearby system of DMPP-1 at 60 More specifically, taking d = 100 pc and δ(λKepler) = 1% pc from the Earth (Jones et al. 2020). as an example, one can detect the spectral features with F/N 5. DISCUSSION > 30 for SiO2,F/N > 10 for Mg2SiO4 and SiC, and F/N ∼ 7 for Al2O3 in the JWST band. Among the mineral features 5.1. Effects of Varying n0 on F/N in the spectra in the JWST band, SiO2 has the largest fea- In our model, we have produced dust tails of different opti- ture at 8.8 µm, resulting in the highest F/N. The absorption cal transit depths δ(λKepler) by varying the tail radius Rt while features of crystalline Mg2SiO4 and SiC are as detectable as 4 −3 fixing the grain number density n0 to be 5.6 × 10 m . Al- amorphous Mg2SiO4. Although the features of crystalline though this value of n0 is consistent with the dust tail of K2- Mg2SiO4 and SiC, located at & 10 µm, are larger than those 22b inferred to be optically thin (see Section 2.1), the choice of amorphous Mg2SiO4, high observational noise of JWST is rather arbitrary. For completeness, we study below how at & 10 µm results in the similar F/N for these minerals. The the countour map of F/N as shown in the previous section high observational noise yields the lowest F/N for the fea- depends on the choice of n0. ture of Al2O3, located to ∼ 12 µm, as compared to the other We here take the feature of SiO2 in the SPICA band as an mineral features in the JWST band. example and calculate its detectability (F/N) by taking n0 as Overall, F/N for mineral features in the SPICA band tend a free parameter while fixing the tail radius to Rt = 0.02Rstar. to be lower than those for features in the JWST band. This Figure 10 maps the values of F/N calculated for different sets is simply because the central star is fainter at longer wave- of n0 and d on the d-δ(λKepler) plane. The map is bounded at lengths. For the planet located at d = 100 pc with δ(λKepler) = δ(λKepler) ≈ 2.5% because a dust tail of fixed Rt cannot have Transmission Spectra of Disintegrating Exoplanets 9

10 10 10 SiO2(amo), JWST Mg2SiO4 (cryst), JWST Mg2SiO4 (amo), JWST

1 1 1

3.0 3.0 Transit depth [%] 1.0 1.0 3.0 30 100 30 100 30 100 Distance [pc] 10 10 SiC, JWST Al2O3, JWST

1000.0

1 1 3.0 300.0 3.0

Transit depth [%] 1.0 1.0

30 100 30 100 100.0

10 10 SiO2 (amo), SPICA Mg2SiO4 (cryst), SPICA 30.0

10.0 1 1 1.0 3.0 1.0 3.0 Transit depth [%]

3.0 30 100 30 100

10 10 Mg SiO (amo), SPIC3.0A Fe SiO (cryst), SPICA 2 4 2 4 1.0 Feature-to-noise ratio (F/N)

0.3 1 1 1.0 3.0 1.0

Transit depth [%] 0.1

30 100 30 100 Distance [pc] Distance [pc]

Figure 8. Feature-to-noise ratios (F/N) for different minerals from a single transit observation with JWST or SPICA as a function of the distance to the system, d, and the optical transit depth δ(λKepler). The white contours mark F/N = 1 and 3. 10 Okuya et al.

10 10 10 SiO2(amo), JWST Mg2SiO4 (cryst), JWST Mg2SiO4 (amo), JWST

1 1 1 3.0 3.0 3.0 1.0 1.0 Transit depth [%]

30 100 30 100 30 100 Distance [pc] 10 10 SiC, JWST Al2O3, JWST

1000.0

1 1 3.0 300.0 3.0 1.0 1.0 Transit depth [%]

30 100 30 100 100.0

10 10 SiO2 (amo), SPICA Mg2SiO4 (cryst), SPICA 3.0 3.0 30.0

10.0 1 1

1.0 1.0 Transit depth [%]

3.0 30 100 30 100

10 10 Mg SiO (amo), SPICA Fe SiO (cryst), SPIC3.0 A 2 4 2 4 1.0 Feature-to-noise ratio (F/N)

3.0 0.3

1 1.0 1 1.0

Transit depth [%] 0.1

30 100 30 100 Distance [pc] Distance [pc]

Figure 9. Same as Figure8 except that the noise level is augmented by a factor of 5. The F /N shown here applies to targets lying near the ecliptic plane. K2-22b is placed on the red cross symbol. Transmission Spectra of Disintegrating Exoplanets 11

10 1000.0 position of the dust tail from such a planet would tell us about SiO2 (amo), SPICA which part of the planet is currently evaporating. For exam- 300.0 ple, vapor of the bulk silicate Earth (BSE) elemental would 100.0 form mineral clouds dominated by Mg2SiO4 and MgSiO3 30.0 (Mahapatra et al. 2017). In contrast, vapor of a crust-like 10.0 elemental composition would yield clouds of SiO2 and SiO (see Figure 11 of Mahapatra et al. 2017) because Si is an or- 1 3.0 der of magnitude more abundant than Mg. Vapor from crust-

1.0 1.0 like materials may also yield dust dominated by Al, Ca, and Transit depth [%] 3.0 0.3 Na-bearing minerals, which are abundant in the Earth’s crust (Rudnick & Gao 2003). A disintegrating planet that has al- 0.1 Feature-to-noise ratio (F/N) ready lost its crust and mantle would produce a tail of Fe 30 100 Distance [pc] metal grains. We summarize the candidate composition of the dust tails produced by each part of a in

Figure 10. F/N map for amorphous SiO2 obtained by varying n0 Figure3. to adjust the optical transit depth δ(λKepler). The solid white lines mark F/N = 1 and 3. For comparison, the white dotted line shows 5.2.2. Coreless Planets the contours of F/N = 1 and 3 shown in the corresponding map in Coreless terrestrial planets are hypothetical planets in Figure8 (left column, third row). which oxidization of iron inhibits the formation of an iron core (Elkins-Tanton & Seager 2008). In principle, such a an arbitrary large projected area by varying n0. In general, planet could form if it initially contains some materials that δ(λKepler) increases linearly with n0 as long as the tail is op- can quickly oxidize iron before it sinks to to the planetary tically thin in the visible. However, as n0 becomes so high center. Because such a planet likely contains Fe in addition that the tail becomes partially optically thick, δ(λKepler) starts to Si and Mg, one can expect that a disintegrating coreless to saturate. In the limit of high optical thicknesses, the ab- planet forms a dust tail composed of iron-bearing silicates, sorption cross section of the dust tail projected on the stellar such as Fe2SiO4, as well as Mg2SiO4 and MgSiO3. A trans- surface approaches the geometric projected area 2Rt × 2Rstar mission spectrum showing strong features of iron-bearing (note that the tail length is assumed to be  Rstar; see Fig- minerals will potentially serve as evidence for this (as yet ure1), giving the upper limit on the optical transit depth of hypothetical) type of planet. × 2 ≈ (2Rt 2Rstar)/πRstar, which is 2.5% for this example. Although how coreless planets can form is poorly under- Apart from the upper boundary, the map of F/N shown in stood, they could potentially form by accreting materials Figure 10 is approximately identical to that shown in Figure outside the H2O snowline in protoplanetary disks. Elkins- 8, which was obtained by varying Rt while fixing n0 (see the Tanton & Seager(2008) suggested that a coreless planet dashed lines in Figure 10). This means that unless the tail could form when the planetary building blocks contain water- is optically thick, the detectability of mineral features sim- rich materials. Water oxidizes iron via metal-water reactions ply scales with the optical transit depth δ(λKepler), and there- such as (e.g., Lange & Ahrens 1984) fore either Rt or n0 can be taken as a parameter controlling

δ(λKepler). Fe + H2O → FeO + H2. (5)

5.2. Links to Planetary Composition If such reactions proceed in the magma ocean rapidly, they In this section, we discuss possible applications of the tail could prevent the formation of an iron core (Elkins-Tanton & transmission spectroscopy to inferring the composition and Seager 2008). Obviously, the building-block materials for a formation process of disintegrating exoplanets. We also re- coreless planet would have to contain a significant amount of view what formation processes are likely to yield these types water. Therefore, if coreless disintegrating planets do exist, of planets, and further discuss possible implications for plan- they would be most likely to have formed outside the snow- etary formation studies derived from their detection. Based line and then migrated to an ultra short-period orbit, or alter- on the above discussion, we finally present how transmission natively, formed in-situ by accreting oxidized materials de- spectra of the dust tails could distinguish between these types livered from outside the snowline. of planets with different formation background. Depending on the initial water fraction and the oxidation rate of iron, some amount of water originally contained in- 5.2.1. Terrestrial Planets side a could be left intact. This is potentially The crust, mantle, and core of differentiated rocky planets important for observational identification of water-rich (but like Earth have distinct elementary compositions. The com- not necessarily coreless) disintegrating planets because the 12 Okuya et al. mantle of such planets may produce water vapor in addition tion features at ≈ 7–10 µm and & 30 µm (Ito et al. 2015). to mineral vapor when it evaporates. We come back to this Water vapor also produces absorption features in the infrared point in Section 5.2.4. wavelength ranges covered by JWST and SPICA (Deming et al. 2009; Greene et al. 2016; Madhusudhan 2019). These 5.2.3. Carbon Planets molecular features could be useful to discriminate between The mineralogy of planets crucially depends on their C/O. disintegrating terrestrial planets and waterworlds. Since Carbon-rich (C/O & 1) rocky planets could have a mantle of molecular features can be narrow in wavelength, their iden- SiC and TiC and a crust of graphite (e.g., Kuchner & Sea- tification may require high-resolution spectroscopy. Outside ger 2005; Bond et al. 2010; see Figure3). This is expected the midinfrared range, Lyman-α lines in the ultraviolet (e.g., because if C/O & 1, CO locks up the majority of the oxy- Vidal-Madjar et al. 2003; Lecavelier Des Etangs et al. 2010; gen and thereby suppresses condensation of oxygen-bearing Ehrenreich et al. 2015) and the absorption feature of excited minerals (e.g., Larimer 1975). The super-Earth 55 Cancri e metastable helium at 1083 nm (Seager & Sasselov 2000; Ok- is a candidate for such carbon planets (Madhusudhan et al. lopciˇ c´ & Hirata 2018; Spake et al. 2018) are potentially use- 2012; Wilson & Militzer 2014). Carbon planets can poten- ful to study whether the disintegrating planets possess an es- tially form in a carbon-rich disk around a carbon-rich star caping atmosphere of hydrogen and helium. Detection of the or in a particular disk location where carbon-rich grains are line absorption features of sodium and calcium atoms would locally concentrated (Kuchner & Seager 2005, see also refer- give us constraints on the gas loss and sublimation processes ences therein). Silicate grains coated by soft organic mantles at work on disintegrating planets (Ridden-Harper et al. 2019). are sticky and may preferentially form carbon-rich planetes- imals (Kouchi et al. 2002; Homma et al. 2019). 6. CONCLUSION Because their formation environments require special con- ditions, carbon planets are commonly assumed to be rare. We have investigated the feasibility of constraining the Data for pollutions also suggest that the solids composition of the dust tail with combined spectroscopy with in extrasolar systems are depleted in carbon (e.g.,G ansicke¨ JWST MIRI and SPICA SMI. We have constructed a simple et al. 2012; Jura & Young 2014). Transmission spectroscopy model of the dust tail that calculates transit light curves and of the dust tails of disintegrating planets will provide inde- transmission spectra of disintegrating planets. pendent constrains on how rare carbon planets are. Accord- We have found that the combination of JWST (5–12 µm) ing to equilibrium mineral sequences for carbon-rich vapor and SPICA (17–36 µm) wavelength regions can provide (e.g., Wood & Hashimoto 1993; Woitke et al. 2018), carbon stronger constraints on the composition of disintegrating disintegrating planets likely produce tails consisting mainly planets than JWST alone (Table2 and Figure5). Although of SiC and graphite grains. crystalline and amorphous silicates, SiC, and Al2O3 have a feature at similar wavelengths in the JWST range, crystalline 5.2.4. Inferring the Planet Types from Tail Transmission Spectra silicates have additional features in the SPICA range that are Finally, we discuss how one can discriminate between ter- absent for SiC and Al2O3. Moreover, crystalline Mg2SiO4 restrial, coreless, and carbon disintegrating planets by look- and crystalline Fe2SiO4 have peaks at different wavelengths ing at their transmission spectra. If the silicates in their dust in the SPICA range. Thus, observations with SPICA in addi- tails are crystalline, combination of JWST and SPICA trans- tion to JWST would greatly help to disentangle the degener- mission spectra will allow us to infer their mineral composi- acy of the candidate minerals of disintegrating planets. tion (see also Figure6). In the JWST band, silicates and SiC We have also discussed how to infer the composition have an absorption feature at similar wavelengths ∼ 10 µm. and formation process of disintegrating planets from the In contrast, in the SPICA band, their spectral features are tail transmission spectra. According to previous studies, more diverse; Mg-bearing and Fe-bearing crystalline silicates Mg-bearing minerals, Fe-bearing minerals, and SiC are po- showing features at 19–23 µm and 26–30 µm, respectively, tentially representative condensates of mantels of terrestrial and SiC is featureless. Therefore, a tail transmission spec- planets, coreless planets, and carbon planets, respectively. trum showing a feature at λ ∼ 10 µm in the JWST band and One would be able to distinguish between these planets from no feature in the SPICA band would be an indication of a car- tail transmission spectra in the JWST and SPICA bands be- bon disintegrating planet. A tail spectrum exhibiting strong cause different types of disintegrating planets produce dust features at ∼ 10 and 30 µm may indicate a coreless planet tails of different spectral features. containing abundant Fe in its mantle. Based on the expected observational noise of the low- While our study has focused on dust, transmission spec- resolution spectrographs of JWST MIRI and SPICA SMI, we troscopy of gas from disintegrating planets may also provide have quantified the detectability of absorption features of the us with additional constraints of the planets’ bulk composi- candidate minerals in the tail transmission spectra at R = 10. tions. For example, SiO vapor produces molecular absorp- For a disintegrating planet located within the distance of 100 Transmission Spectra of Disintegrating Exoplanets 13 pc from the Earth with an optical depth deeper than ∼ 0.5%, posed of a single mineral species, as a first step to examine tail transmission spectra in the JWST band show significant the feasibility of such spectroscopic observations. The de- absorption features of minerals with feature-to-noise ratio of tectability in the case of the dust tails composed of multiple & 3, in a single transit (Fig8). On the other hand, one can mineral species is left for future work. easily identify the mineral features in a single transit obser- vation with SPICA if a disintegrating planet is located within 100 pc with a transit depth deeper than 2%. Multiple transit ACKNOWLEDGMENTS observations K2-22b’s dust tail with JWST will allow us to We thank Akemi Tamanai for providing optical con- constrain the minerals composition of the tail, although de- stant data, and Aki Takigawa, Shota Notsu, and Shigeru tection of mineral features with SPICA would be challenging Ida for useful discussions. This work was supported by for this particular object. Current and upcoming dedicated JSPS KAKENHI Grant Numbers JP18J14557, JP19K14783, missions for transit searches, such as TESS and PLATO, JP18H05438, and JP19K03926. would be able to provide ideal targets for future transmis- sion spectroscopy with JWST and SPICA. In this study, we Software: LX-MIE (Kitzmann & Heng 2018) have evaluated the detectability assuming the dust tails com-

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