The formation of planetary systems with SPICA

Abstract

In this era of spatially resolved observations of planet-forming disks with Atacama Large Millimeter Array (ALMA) and large ground-based telescopes such as the Very Large Telescope (VLT), Keck, and Subaru, we still lack statistically relevant information on the quantity and composition of the material that is building the planets, such as the total disk gas mass, the ice content of dust, and the state of water in planetesimals. SPace Infrared telescope for Cosmology and Astrophysics (SPICA) is an infrared space mission concept developed jointly by Japan Aerospace Exploration Agency (JAXA) and European Space Agency (ESA) to address these questions. The key unique capabilities of SPICA that enable this research are (1) the wide spectral coverage $10{-}220\,\mu\mathrm{m}$ , (2) the high line detection sensitivity of $(1{-}2) \times 10^{-19}\,\mathrm{W\,m}^{-2}$ with $R \sim 2\,000{-}5\,000$ in the far-IR (SAFARI), and $10^{-20}\,\mathrm{W\,m}^{-2}$ with $R \sim 29\,000$ in the mid-IR (SPICA Mid-infrared Instrument (SMI), spectrally resolving line profiles), (3) the high far-IR continuum sensitivity of 0.45 mJy (SAFARI), and (4) the observing efficiency for point source surveys. This paper details how mid- to far-IR infrared spectra will be unique in measuring the gas masses and water/ice content of disks and how these quantities evolve during the planet-forming period. These observations will clarify the crucial transition when disks exhaust their primordial gas and further planet formation requires secondary gas produced from planetesimals. The high spectral resolution mid-IR is also unique for determining the location of the snowline dividing the rocky and icy mass reservoirs within the disk and how the divide evolves during the build-up of planetary systems. Infrared spectroscopy (mid- to far-IR) of key solid-state bands is crucial for assessing whether extensive radial mixing, which is part of our Solar System history, is a general process occurring in most planetary systems and whether extrasolar planetesimals are similar to our Solar System comets/asteroids. We demonstrate that the SPICA mission concept would allow us to achieve the above ambitious science goals through large surveys of several hundred disks within $\sim\!2.5$ months of observing time.

Preface

The articles of this special issue focus on some of the major scientific questions that a future IR observatory will be able to address. We adopt the SPace Infrared telescope for Cosmology and Astrophysics (SPICA) design (Roelfsema et al. 2018) as a baseline to demonstrate how to achieve the major scientific goals in the fields of galaxy evolution, galactic star formation, and protoplanetary disks formation and evolution. The studies developed for the SPICA mission serve as a reference for future work in the field, even though the mission proposal has been cancelled by European Space Agency (ESA) from its M5 competition.

The mission concept of SPICA employs a 2.5-m telescope, actively cooled to below $\sim\!8\,\mathrm{K}$ , and a suite of mid- to far-IR spectrometers and photometric cameras, equipped with state-of-the-art detectors (Roelfsema et al. 2018). In particular, the SPICA Far-infrared Instrument (SAFARI) is a grating spectrograph with low ( $R \sim 200{-}300$ ) and medium ( $R \sim 3\,000{-}11\,000$ ) resolution observing modes instantaneously covering the 35– $210\,\mu\mathrm{m}$ wavelength range. The SPICA Mid-infrared Instrument (SMI) has three operating modes: a large field of view ( $10' \times 12'$ ) low-resolution $17{-}36\,\mu\mathrm{m}$ imaging spectroscopic ( $R \sim 50{-}120$ ) mode and photometric camera at $34\,\mu\mathrm{m}$ (SMI-LR), a medium-resolution ( $R \sim 1\,300{-}2\,300$ ) grating spectrometer covering wavelengths of $18{-}36\,\mu\mathrm{m}$ (SMI-MR), and a high-resolution echelle module ( $R \sim 29\,000$ ) for the $10{-}18\,\mu\mathrm{m}$ domain (SMI-HR). Finally, B-BOP, a large field-of-view ( $2'.6 \times 2'.6$ ), three-channel (70, 200, and $350\,\mu\mathrm{m}$ ) polarimetric camera complements the science payload.

1. Introduction

A key challenge to understanding planet formation is that we must explain both our own Solar System, with all its planets and minor bodies, as well as extrasolar planetary systems, which appear to differ vastly from our own. In the past 5 yr, high spatial resolution imaging of planet-forming disks with Atacama Large Millimeter Array (ALMA), Very Large Telescope (VLT)/Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE), and/or Keck/Gemini Planet Imager (GPI) (e.g., Pérez et al. 2014; ALMA Partnership et al. 2015; Benisty et al. 2015; Rapson et al. 2015) has revolutionised our view and our understanding of how disks evolve into planetary systems. These instruments reveal a wealth of substructures within disks, for both targeted (e.g., Andrews et al. 2018; Huang et al. 2018) and unbiased surveys (Long et al. 2018), as well as in the case of protoplanetary disk candidates (e.g., Ginski et al. 2018; Keppler et al. 2018; Pinte et al. 2018) which likely indicate that planet formation is not only starting well before the disks appear as isolated objects (class II phase without strong envelope/jet components), but furthermore that planet formation must also be a very efficient process. Indeed, the Kepler mission has found that the probability of a low-mass star hosting at least one planet is close to 100% (e.g., Tuomi et al. 2014).

In this era of spatially resolved observations of planet-forming disks, we still lack statistically relevant information on the quantity and composition of the material that is building the planets and how it evolves during and beyond the era of planet formation. Key open questions are:

1. 1. How does the disk gas reservoir which is driving planet formation evolve?—Sections 2,3

2. 2. When does the transition from primordial to secondary gas occur?—Sections 2,3

3. 3. Are the extrasolar planetesimals similar to our Solar System comets/asteroids?—Section 4

4. 4. How do water and ice abundances within the disk evolve during the planet-forming era and beyond?—Section 5

5. 5. How does mineral/ice mixing proceed in planet-forming disks?—Section 6

In order to answer these questions, we need measurements that can only be done using very sensitive infrared (IR) spectral observations due to the unique diagnostic lines and features that trace the planet building material and its evolution (HD and $\mathrm{H}_2\mathrm{O}$ lines, emission bands from water ice, and large dust grains with a wide range of mineral composition). Available spatially resolved data capture only a single tracer at once (e.g., mm-sized dust, micron-sized dust, and CO) and lack crucial calibration measurements to quantify the total gas reservoir. For example, dust grains grow from submicron particles into km-sized planetesimals in a gas-rich disk (e.g., Birnstiel et al. 2016); during these steps, the solid material composition (mineralogy, ices) is altered, transported, and mixed through the disk. Our Solar System comets show the presence of highly processed dust, a strong indication for large-scale mixing from the inner Solar System (Nittler & Ciesla 2016). While ALMA clearly shows dust concentrations (e.g., van der Marel et al. 2013; Casassus et al. 2013), we cannot test our understanding of radial migration, settling, and grain growth without quantifying the gas reservoir in which this happens and the relevant dispersal timescales (see Ercolano & Pascucci 2017, for a recent review). Evidence from hydrodynamical simulations (e.g., Paardekooper & Mellema 2006; Dipierro et al. 2015; Zhang et al. 2018) suggest that the gas surface density, in tandem with forming proto-planets, shapes the remaining dust in the disk into intricate substructures such as rings, spirals, and vortices. Thus, the quantitative interpretation of the wealth of observed dust disk substructures requires firm knowledge of gas surface densities and hence gas masses in disks.

The snowline, where water condenses onto the refractory dust, plays a crucial role in planet formation since the solid mass reservoir available to build planets is significantly enhanced beyond it (Hayashi 1981) and the sticking properties of icy dust could be conducive to planet formation (Okuzumi et al. 2012). Several planet formation scenarios consider the water snowline as the prime location for material to overcome growth barriers in planet formation, enabling the formation of planetary cores (e.g., Schoonenberg & Ormel 2017). Also at the snowline, the C/O ratio of the gas changes, with direct implications for planet formation (e.g., Öberg et al. 2011; Helling et al. 2014; Eistrup et al. 2016; Notsu et al. 2020). None of the present facilities providing spatial resolution, however, has the sensitivity or diagnostic power to measure the snowline location across large samples of disks.

The manner in which planetary cores subsequently grow into planets, both rocky and gas/ice giants, depends again on the total gas reservoir of the disk: the total gas mass controls processes such as migration of planetary cores (Baruteau et al. 2014), growth of gaseous envelopes and atmospheres (Lissauer & Stevenson 2007; Lammer & Blanc 2018), and the circularisation of planetary orbits (Muto et al. 2011; Kikuchi, Higuchi, & Ida et al. 2014). The specific water vapour/ice content of the disk is crucial to quantify the degree of hydration of refractory dust (D’Angelo et al. 2019; Thi et al. 2020), the aqueous alteration of larger km-sized bodies (Beck et al. 2014), and the delivery of water to planets at late stages for the build-up of oceans as well as primary/secondary atmospheres (e.g., Massol et al. 2016; Kral et al. 2018). Eventually, the water content is key to assess the origin of life and habitability of the rocky planets forming in these disks.

During the process of planet formation, the primordial gas mass is decreasing as it is accreted onto the star (building it up to its final mass), incorporated into planets (gas giants), and dispersed through winds and jets (magnetically driven or photoevaporative). Late evolutionary stages of young stars (class III) have disks with very low dust masses $(\!{<}0.3\,M_{\rm Earth}$ , Hardy et al. 2015), potentially they already formed planetesimals and planetary cores. Regular planetesimal collisions will replenish small dust grains and produce a secondary gas component that reflects the volatile content (ices) of the parent planetsimals (Wyatt et al. 2015; Lovell et al. 2020). Once a planet-forming disk has lost its primordial gas, giant planet formation will come to a halt and also the primordial atmospheres of rocky planets will be lost (Lammer et al. 2014; Massol et al. 2016).

A missing link within the wealth of data characterising the composition of exoplanets and their atmospheres is the evolution of dust with time, from young ( $1{-}10\,\mathrm{Myr}$ ) planet-forming disks to debris disks with planetesimals (tens of Myr). Existing and upcoming instruments operate in the near- to mid-IR (e.g., VLT MATISSE/VISIR/CRIRES, James Webb Space Telescope (JWST), and ELT METIS) and therefore will not be able to trace dust grains larger than a few micron, which emit at longer far-IR wavelengths. In addition, thermal emission from water vapour and ices are uniquely observed at far-IR wavelengths, revealing a needed window into the evolution of water, the key element for life (as we know it), during the planet build-up.

This overview paper on the formation of planetary systems argues for the uniqueness of a cooled infrared space mission such as SPICA in order to

• establish an absolute calibration of disk gas mass estimates using HD,

• measure the gas dissipation timescale,

• determine when the transition from ‘primordial’ to ‘secondary’ gas occurs,

• quantify the evolution of the water vapour and ice reservoirs,

• characterise the evolving mineralogy as dust grains grow into planetesimals,

• characterise the volatile content in planetesimals in late stages of planetary system formation.

These important results will require large statistical surveys of many thousands of systems throughout the planet formation phase (1–500 Myr). Figure 1 shows that SPICA’s wide spectral coverage $10{-}220\,\mu\mathrm{m}$ , high line detection sensitivity of $(1{-}2) \times 10^{-19}\,\mathrm{W\,m}^{-2}$ with $R \sim 2\,000{-}5\,000$ in the far-IR (SAFARI) and $10^{-20}\,\mathrm{W\,m}^{-2}$ with $R \sim 29\,000$ in the mid-IR (SMI, spectrally resolving line profiles), and high far-IR continuum sensitivity of 0.45 mJy (SAFARI) are keys to achieve the above-outlined scientific goals.

Figure 1. Sketch summarising where SPICA provides unique insight into how planetary systems form.

2. Disk gas masses

Over the past three decades, many different observational techniques have been employed to measure disk masses (roughly ordered in time): mm-continuum fluxes, CO line fluxes, mm-continuum and sub-mm line interferometry, CO isotopologue line ratios, [O I] $63\,\mu\mathrm{m}$ + CO sub-mm lines, HD line(s), and wavelength-dependent dust outer radii. Important steps in the disk mass determination were (1) the use of disk models in the interpretation of interferometric data, (2) the recent revision of dust opacities, and (3) the combined interpretation of multi-wavelength datasets. We discuss below the most recently employed techniques to estimate disk masses as well as the advantages and disadvantages of each method.

Continuum mm/sub-mm fluxes: Thermal continuum emission can be used to determine the dust mass within a disk under the assumption of a dust opacity (typically uncertain by at least a factor of 2) and a dust temperature (better modelled as varying with radial location in the disk). Reliable estimates of the dust mass also require attention to the optical depth (Beckwith et al. 1990). Recent ALMA observations raise again the possibility that the inner parts of planet-forming disks are optically thick (Ballering & Eisner 2019; Zhu et al. 2019). Woitke et al. (2016) show how the assumptions of a single-representative dust temperature and an optically thick contribution to the emission affect the dust mass derivation. Once the dust mass is determined, conversion to gas mass requires an estimate of the dust to gas ratio which is usually assumed to be 100 (based on the canonical interstellar medium value).

CO sub-mm and [O I] $\boldsymbol{63\,\mu}\textbf{m}$ : Herschel was able to detect the strongest gas cooling line from planet-forming disks, the [O I] $63\,\mu\mathrm{m}$ line, in a large fraction of young planet-forming disks (Dent et al. 2013; Riviere-Marichalar et al. 2016). The [O I] 63- $\mu\mathrm{m}$ line-emitting region shifts, radially and vertically, with disk mass, making it an indirect tracer in combination with a temperature indicator. Hence, in combination with a CO sub-mm line, these fine structure line fluxes can be used to estimate disk masses within a factor of 3 (Kamp et al. 2011; Meeus et al. 2012). However, for disks with gas masses above $\sim\!10^{-3}\,\mathrm{M}_\odot$ , or for disks with non-solar carbon and/or oxygen abundances, this method becomes highly uncertain.

CO isotopologue sub-mm lines: A more direct estimate of disk gas mass comes from the observations of the rotational lines of CO and its rarer isotopologuesa ( $^{13}\mathrm{CO}$ , $\mathrm{C}^{18}\mathrm{O}$ , $^{13}\mathrm{C}^{18}\mathrm{O}$ , and $^{13}\mathrm{C}^{17}\mathrm{O}$ ) using (sub)-millimetre telescopes. The rarer isotopologues are optically thinner and hence trace disk regions down to the CO iceline. The uncertainty in the gas-phase abundances of these species relative to $\mathrm{H}_2$ molecules, however, limits the measurement reliability. In addition, CO rotational lines predominantly measure the cold gas mass, typically residing beyond 50 au. Processes such as CO freeze-out (Panić & Hogerheijde 2009) and CO isotope selective photodissociation, by stellar and interstellar photons (Miotello, Bruderer, & van Dishoeck 2014; 2016), as well as the gas phase carbon and oxygen abundances (Bruderer et al. 2012; Miotello et al. 2017) affect these gas mass estimates. Williams & Best (2014) consider use of the fluxes of the two rarer isotopologues $^{13}\mathrm{CO}$ and $\mathrm{C}^{18}\mathrm{O}$ to derive disk gas mass estimates. The method was refined by Miotello et al. (2016), accounting self-consistently for isotope selective dissociation. Both grids of models, however, neglect the gas-to-dust mass ratio as a confounding parameter in their study; Woitke et al. (2016) show that the gas-to-dust parameter can strongly affect the CO isotopologue line fluxes; the local gas-to-dust mass ratio determines the disk temperature and affects the location of the CO iceline as well as the gas temperature of the emitting CO isotopologues. Thus, we require an iterative approach, relying on successive dust and the gas mass determinations. And again, chemical effects changing the canonical CO-to- $\mathrm{H}_2$ conversion factor continue to present a significant source of uncertainty (Yu et al. 2017; Molyarova et al. 2017).

HD: The major constituent of the disk gas is molecular hydrogen, $\mathrm{H}_2$ , but its rotational lines are not sensitive to main disk temperature conditions, that is, these lines are not effective disk mass tracers. The deuterated variant, HD, has a very simple chemistry and is expected to have a constant abundance of $2 \pm 0.1 \times 10^{-5}$ (the average local ISM value, Prodanović et al. 2010) throughout the disk. This constancy makes the lowest two HD rotational lines— $J=1{-}0$ at $112\,\mu\mathrm{m}$ ( $E_{\rm up}=128.5\,\mathrm{K}$ ) and HD $J=2{-}1$ at 56 $\mu\mathrm{m}$ ( $E_{\rm up}=384.6\,\mathrm{K}$ )—reliable tracers of the warm gas mass in the inner disk (inside $\sim\!100\,\mathrm{au}$ ). These inner disk regions are of prime importance since the majority of planets are thought to be formed there, rather than in the cold outer disk beyond $\sim\!100\,\mathrm{au}$ where CO sub-mm lines become good tracers of mass. Bergin et al. (2013) and McClure et al. (2016) detected the lower excitation HD line in three planet-forming disks with Herschel/PACS and Kama et al. (2020) derived upper limits to the gas masses for disks around 15 objects from Herschel upper limits on both HD lines.

Figure 2. Distribution of disk masses as a function of the stellar mass for nearby star-forming regions, based on recent millimetre dust continuum observations with the SMA and ALMA (Andrews et al. 2013; Ansdell et al. 2016; Barenfeld et al. 2016; Pascucci et al. 2016; Cieza et al. 2019; Cazzoletti et al. 2019) and assuming a global gas-to-dust mass ratio of 100. The two horizontal lines indicate the detection limits that will be achieved with SAFARI observations of the HD $J=1{-}0$ line fluxes in the case of the shallow (1 h on-source, dashed line) and deep (10 h on-source, dotted) surveys, following the HD line flux predictions from Trapman et al. (2017).

2.1. Disk gas masses from HD lines with SPICA

Over the next decade, we anticipate ALMA to have undertaken complete disk surveys (dust and CO isotopologues) in all relevant nearby star-forming regions (within $500\,\mathrm{pc}$ ). For large, $>\!100\,\mathrm{au}$ , disks in low-mass star-forming regions, most of the disk gas mass is expected to be well below 50 K; with ALMA, we will thus have a good understanding of the cold outer disk component. Planet formation similar to our Solar System, however, happens in the inner regions of the disk, inside 100 au, and Trapman et al. (2017) showed that most of the HD emission is originating along the inner warm disk surfaces ( $50{-}200\,\mathrm{K}$ ). Furthermore, ALMA surveys have shown recently that the majority of disks are likely smaller than 100 au (Ansdell et al. 2018; Long et al. 2019), making HD a direct tracer of the bulk gas mass for those objects. On the other hand, in high-mass star-forming regions, the external radiation field of nearby O/B stars could warm the entire disk surface well above 50 K, enhancing the importance of HD measurements.

Both HD lines ( $J=1{-}0$ and $J=2{-}1$ at 112 and $56\,\mu\mathrm{m}$ , respectively) are only accessible from space/stratosphere and SAFARI is uniquely equipped in terms of spectral coverage and sensitivity to measure them across statistical samples of disks. For an observational estimate of the gas mass in the planet-forming region, within 100 au, the HD line ratio will be a proxy of the ‘disk gas temperature’ and the line fluxes will be used to derive disk mass estimates using model grids, similar to what has been done with ALMA for the CO isotopologues (Miotello et al. 2017; Long et al. 2018). These model grids can be easily refined, taking the disk substructure known from the ALMA surveys into account. Since the HD abundance is not affected by element abundances/chemistry/freeze-out, this remains the most robust technique to estimate disk gas masses.

Figure 2 shows the ALMA disk samples for which dust masses have been measured in five star-forming regions (Taurus, Lupus, Chameleon I, Upper Sco, and Corona Australis, from Andrews et al. 2013; Ansdell et al. 2016; Barenfeld et al. 2016; Pascucci et al. 2016; Cieza et al. 2019; Cazzoletti et al. 2019). We assume here a gas-to-dust mass ratio of 100 and indicate the SAFARI sensitivity limits based on a 1 and 10 h per source deep survey. If all the disks in these surveys are T Tauri disks with disk/stellar properties similar to those modelled by Trapman et al. (2017), the HD line flux predictions reveal that we can detect the gaseous counterpart from all ALMA dust-detected disks. Both HD lines are optically thin for disks as massive as a few $10^{-2}\,M_{\odot}$ (i.e., a few times the value of the minimum mass Solar Nebula, Trapman et al. 2017). The vast majority of the ALMA-surveyed disk population has a total gas mass below this limit, utilising a gas-to-dust ratio of 100. Therefore, HD line flux measurements, together with the constant HD abundance, provide a temperature and gas column density estimate which can be converted into a precise mass estimate of the gas. Figure 3 demonstrates the feasibility of this approach across a grid of T Tauri disk models (Trapman et al. 2017). Combined with ALMA dust continuum fluxes, the SAFARI measurements of the two HD lines will provide the most complete survey for bulk gas mass estimates and gas-to-dust mass ratios for disk planet-forming regions at a sensitivity comparable to that of the current ALMA dust surveys (Ansdell et al. 2016; Barenfeld et al. 2016; Pascucci et al. 2016; Long et al. 2018; Cieza et al. 2019; Cazzoletti et al. 2019). Having HD gas masses for statistically relevant disk samples allows also to calibrate and understand the issues around the CO isotopologue mass estimate.

Figure 3. HD diagnostic diagram: Disk gas masses can be derived from a combination of the two HD lines, based on a grid of T Tauri disk models from Trapman et al. (2017). Open symbols denote disk model predictions for a distance of 140 pc (e.g., the Taurus star-forming region), where SPICA will not be able to detect both HD lines in a SAFARI/HR 1 h integration $(\!<\!5\,\sigma$ ) due to the lower sensitivity at $56\,\mu\mathrm{m}$ (the higher continuum lowers the line sensitivity). The black dot with error bars shows the only object, TW Hya ( $60.1\,\mathrm{pc}$ , put here at a distance of 140 pc), for which both HD lines have been measured with Herschel/PACS. The vertical dotted line indicates the 1 h sensitivity limit ( $5\,\sigma$ ) for the HD $J=1{-}0$ line.

To mitigate the temperature dependence of the HD gas mass estimates, we will use the $^{12}\mathrm{CO}$ and $^{13}\mathrm{CO}$ rotational ladders to derive the 2D temperature structure (see Section 2.2), providing an improvement over the simple HD line ratio ‘disk gas temperature’ estimate. We will thus measure the total gas mass from a simultaneous fit of the two HD line fluxes and the $^{12}\mathrm{CO}$ and $^{13}\mathrm{CO}$ rotational ladders (e.g., Fedele et al. 2016).

Disk flaring is key for the gas heating and disk temperature structure (Kamp et al. 2011, e.g.). Hence, to further refine the disk gas mass estimates, the [O I] fine structure lines have been shown to be sensitive tracers of disk flaring out to $\sim\!100\,\mathrm{au}$ (regions where HD is also predicted to emit, Trapman et al. 2017) and good probes of disk gas temperature (Woitke et al. 2010; Kamp et al. 2011); the [O I] $63\,\mu\mathrm{m}$ line is the brightest cooling line in disks, regularly detected with Herschel, and hence will be detected routinely with SPICA.

Figure 4. Herschel/PACS spectrum of TW Hya showing the detection of the lowest two HD rotational lines at $56\,\mu\mathrm{m}$ and $112\,\mu\mathrm{m}$ (spectra re-reduced by D. Fedele).

ALMA CO surveys can provide radial surface gas density profiles. The combination of ALMA CO and far-IR [O i] together with modelling lines can break degeneracies in the determination of disk masses. Ancillary and routine detection of the [O I] ${63, 145}\,\mu\textrm{m}$ and [C II] ${158}\,\mu\textrm{m}$ lines with SAFARI, can also address the frequently discussed question of the disk C/O abundances being different from typical ISM values, possibly due to planet-forming processes, migration of icy planetesimals, and filtering of sizes due to dust traps (see e.g., Cleeves et al. 2018; Miotello et al. 2019).

The HD lines do not need to be spectrally resolved in the SAFARI wavelength range. However, since molecular lines have a very low line-to-continuum ratio $({\lesssim}0.05$ ), that is, weak narrow gas lines (unresolved) on a strong continuum, we require a spectral resolution of at least a few 1 000 to maximise the line detection rate (see Trapman et al. 2017, for a detailed discussion). The low excitation HD lines, $J=1{-}0$ , $J=2{-}1$ , are expected to have typical widths of $5{-}20\ \mathrm{km\ s}^{-1}$ , dependent also on inclination. Figure 4 shows that even with the Herschel/PACS resolution of $R \sim 1500$ , the HD lines were not blended. Given the higher spectral resolution of SAFARI/Fourier Tranform Spectrometer (FTS) ( $R \sim 7\,300$ and $3\,700$ at 56 and 112 $\mu\mathrm{m}$ respectively) line fluxes can be extracted in a straightforward manner.

From thermo-chemical disk models by Trapman et al. (2017) for T Tauri disks spanning a typical range of disk properties (flaring, disk size, and scale heights), we find HD $J=1{-}0$ line fluxes ranging from $7\!\times\!10^{-20}\,\mathrm{W\,m}^{-2}$ for $10^{-4}\,\mathrm{M}_\odot$ disks (low mass, optically thin) to $2.3 \times 10^{-18}\,\mathrm{W\,m}^{-2}$ for $10^{-1}\,\mathrm{M}_\odot$ disks (massive, optically thick). The HD $J=2{-}1$ line is stronger for low-mass optically thin disks ( $10^{-19}\,\mathrm{W\,m}^{-2}$ ) and fainter for optically thick massive disks ( $10^{-18}\,\mathrm{W\,m}^{-2}$ ).

Since the line fluxes scale with the continuum (see Figure 19 in Appendix A.1), we propose a survey based on the continuum brightness of the sources. The HD $J=1{-}0$ and $J=2{-}1$ lines fall into the long (LW) and medium wavelength band (MW) with a spectral resolution of $R \sim 3\,700$ and $R \sim 7\,300$ , respectively. For sources with a continuum flux $<\!0.1\,\mathrm{Jy}$ (MW) and $<\!1\,\mathrm{Jy}$ (LW), respectively, SAFARI/HR reaches a line sensitivity of $\sim\!1.3 \times 10^{-19}\,\mathrm{W\,m}^{-2}$ in 1 h ( $5\,\sigma$ ); this corresponds to disk gas masses down to $\sim\!10^{-3}\,\mathrm{M}_\odot$ . We will set our integration times in the HD disk gas mass survey such that we can push down to $2 \times 10^{-4}\,\mathrm{M}_\odot$ while still detecting both HD lines. Figure 2 shows that we would be able to provide, in a survey with $1{-}10$ h integration times, reliable gas mass estimates for all disks that are currently detected in dust surveys of star-forming regions with ALMA. The sensitivity limit also overlaps with the upper end of the gas masses detected via CO in debris disks (Moór et al. 2019, see Section 4). Should those disks harbour remnant primordial gas from the younger phase (instead of secondary $\mathrm{H}_2$ -poor gas), we would detect that gas in the HD lines. Including in the survey a statistically significant number of class III disks, potentially young debris disks, we will be able to determine for the first time the transition from primordial to secondary gas.

2.2. Radial temperature profiles—The co-ladder

Disks are not isothermal structures. Rather, they are characterised by a large gradient in the gas temperature, which can go from nearly $10^3\,\mathrm{K}$ in the proximity of the star down to $\sim\!10\,\mathrm{K}$ (or even lower) in the outer part of the disk midplane. Knowledge of the gas temperature gradient is important for the interpretation of both molecular and atomic spectra, as $T_{\rm gas}$ regulates line intensities. The vertical gas temperature gradient is, for example, key to understanding the emission from CO isotopologues which probe successively deeper layers in the disk (Dartois et al. 2003). Moreover, the local gas temperature also controls the gas chemistry, hence the formation of molecules and the resultant chemical enrichment. For example, at warm temperatures ( $>\!200\,\mathrm{K}$ ), neutral-neutral chemistry can proceed to efficiently form water via the radiative association H + OH (Glassgold et al. 2009; Kamp et al. 2013).

An ideal thermometer of disk surface layers is the CO rotational ladder: the CO rotational transitions are optically thick and, due to their low critical density, are quickly thermalised in disks. Moreover, the CO transitions span a large range of upper energy levels, from 5.5 K ( $J=1{-}0$ ) up to a few 1 000 K (for $J_{\rm up} > 20$ ), see Table 1. Rotational lines up to $J=10{-}9$ can be obtained from the ground, but the higher rotational lines are uniquely measured from space. As such the CO rotational ladder provides direct information about the kinetic temperature throughout the entire disk surface. In particular, a simultaneous model fit to the various CO transitions allows us to constrain the 2D temperature structure, not only the radial gradient but also the vertical gradient in the surface. Additional constraints to the vertical gradient reaching deeper into the disk are provided by the $^{13}\mathrm{CO}$ ladder. Due to the lower optical depth with respect to the main isotopologue, the $^{13}\mathrm{CO}$ transitions probe different density and temperature regions inside the disk. Figure 5 shows that we can routinely detect the CO ladder in our HD survey ( $1{-}10\,\mathrm{h}$ exposure times) toward the warm disks around Herbig stars, and typically up to $J=17{-}16$ for the colder T Tauri disks.

Table 1. Wavelengths and upper level energies ( $E_{\rm up}$ ) of CO lines to be observed with SAFARI to constrain the 2D gas temperature structure.

Figure 5. Predicted line flux of high-J CO rotational transitions in protoplanetary disks to be measured with SAFARI. The two models refer to the case of a flat disk with low scale height around a Herbig Ae star (spectral type A0, $20\,L_{\odot}$ ) and to a cold T Tauri disk (K5, $1.5\,L_{\odot}$ ), both located at a distance of 140 pc from the Sun (DALI models, Bruderer et al. 2012; Bruderer 2013 ). The two horizontal lines indicate the limiting line flux ( $5\,\sigma$ detection limit) for a shallow and deep survey, respectively.

2.3. Disentangling disk and shock origin for HD

Often disks and shocks produce the same spectral lines in star-forming regions. In the absence of spatial resolution, spectral resolution can be used to disentangle these components. However, SPICA has only limited spectral resolution. We can overcome this by using diagnostic line ratios for disentangling disk and shocks. This is demonstrated in Figure 6, where we show the line ratio of CO (18-17)/CO (12–11) versus the line ratio of $\mathrm{H}_2\mathrm{O}\,4_{23}{-}3_{12}$ $(78.74\,\mu\mathrm{m})/2_{12}{-}1_{01}(179.53\,\mu\mathrm{m}$ ) for the disk models explored by the DENT (Disk Evolution with Neat Theory) grid (Woitke et al. 2010; Kamp et al. 2011) and for a non-dissociative shock models grid by Flower & Pineau des Forêts (2015). The figure shows that shocks and disks populate relatively separated areas of the line ratio plane. A larger contamination occurs only for dissociative shock models at the highest pre-shock density of $10^4\,\mathrm{cm}^{-3}$ .

Figure 6. Line intensity ratio of CO(18-17)/CO(12-11) versus $\mathrm{H}_2\mathrm{O}\, 78\,\mu\mathrm{m}/179\,\mu\mathrm{m}$ line ratios predicted by the DENT grid of disk models compared with the predictions of J- and C-type shock models of Flower & Pineau des Forets (2015) for different pre-shock densities and pre-shock velocities.

3. Disk dispersal—Setting the clock for planet formation

One important aspect of star and planet formation is the timescale for the dispersal of the protoplanetary disk. Indeed, it is crucial to determine how fast gas evaporates or gets accreted onto the central star, as the amount of gas available in the disk will set the clock for planet formation (see Alexander, McKeegan, and Altwegg 2014). ALMA provides now increasing evidence that class ii disks may already host giant protoplanets (e.g., Andrews et al. 2018; Pinte et al. 2018). However, the gas dispersal timescale ends the runaway gas accretion onto giant protoplanets and halts their migration.

Broad-band near- to mid-IR excess (optically thick continuum emission from the dust) above the photospheric emission is an easy means to determine if an inner dust disk exists. The mean dispersal time is estimated from the fraction of such disks still observed as a function of the region’s age (e.g., Haisch Karl, Lada, & Lada 2001; Hernández et al. 2008; Mamajek 2009; Richert et al. 2018). Studies across many star-forming regions have allowed for the determination of a mean disk dispersal timescale of a few Myr; however, this method only traces the optically thick inner dust disk component, which comprises about 1% of the disk mass, and not the gas disk component, which drives the dynamics. Ohsawa et al. (2015) showed that this method also leads to a bias in the estimate of the disk dissipation timescale if the disk mass function is not properly taken into account. Alternative studies using $\mathrm{H}\alpha$ emission, as a tracer for ongoing mass accretion and thus of the continued presence of gas in the disk, provide a similar, albeit possibly slightly shorter, timescale (Fedele et al. 2010), suggesting a coevolving dust and gas disk with a somewhat longer-lived dust component. The few Myr timescale is comparable to the timescale expected for planet formation via the core accretion process, as well as to the timescale for giant planets to migrate (see Ercolano & Pascucci 2017 for a detailed review). The exact mechanism of disk dispersal—photoevaporation and/or magneto-hydrodynamic (MHD) winds—and the amount of mass loss through these processes will therefore have important implications for gas giant planet formation, helping to constrain the available time for orbital migration or circularisation (Tanaka & Ward 2004; Kikuchi et al. 2014). Inner disk evolution and dispersal, thus, play a crucial role in the final configuration of planetary systems, and there is a clear need for unbiased gas disk dispersal timescale studies.

One of the challenges of gas dispersal studies is the difficulty to spatially resolve the inner gas disks. ALMA can measure the gas content in the outer disk regions, however, most planets form in the inner disk, that is, inner 50 au. Therefore, we need to directly quantify the dissipation processes in the inner region of the disk. Spectrally resolved molecular line profiles can provide an ideal substitute for the lack of spatial resolution. These gas line profiles reveal both the spatial and physical components contributing to disk gas dispersal, namely fast jets and photoevaporative, or MHD, slow disk winds.

Disk winds can be generated by MHD processes that can also explain jets and outflows, or they can be launched due to photoevaporation (e.g., Shu et al. 1993; Yorke & Welz 1996; Font et al. 2004). Hydrodynamical simulations show that Extreme Ultraviolet (EUV) radiation can result in photoevaporative mass loss rates of order $10^{-10}\,\mathrm{M}_\odot/\mathrm{yr}$ (see Alexander et al. 2014, for a review), while including X-rays can increase the mass loss by a factor of 100, assuming common X-ray luminosities. The mass loss rate in the photoevaporative case is directly proportional to $L_\mathrm{x}$ (the power found in simulations is 1.14). Though observations show a wide scatter for young stars, there exists a strong correlation with the bolometric luminosity, or stellar mass. Line profiles produced by X-ray-induced winds are more extended than those produced by EUV radiation.

Disk winds around T Tauri stars have been extensively studied from the ground via high-resolution optical/IR spectroscopy. In particular, observations of the [O I] 630-nm line profile have shown that components at different velocities likely trace distinct types of winds. In particular, the high-velocity component at $>\!30\,\mathrm{km\ s}^{-1}$ testifies to the presence of a collimated jet, while components at lower velocity originate in disk winds (e.g., Hartigan, Edwards, & Ghandour 1995; Natta et al. 2014; Nisini et al. 2018). The low-velocity component further reveals a broad, blueshifted, component due to emission within the inner 0.5 au of the disk, and associated with MHD winds. In addition, there is also a low-velocity narrower component that has been suggested to trace winds from more distant gas at 0.5–5 au, indicating winds that might be photoevaporative or MHD in nature (Rigliaco et al. 2013; Simon et al. 2016; Banzatti et al. 2019).

The information that can be obtained from the [O I] emission is, however, limited since [O I], and other optical lines, are (1) excited at very high temperatures ( $>\!5000\,\mathrm{K}$ ) and therefore unable to probe colder disk winds (lower than 2 000 K) that might significantly contribute to the mass loss and (2) modelled wind mechanisms do not lead to different [O I] profiles so that the interpretation of those lines is often limited.

Fundamental information necessary to clarify this picture will come from observations in the mid-IR. In particular, over the range covered by SMI/HR many gas tracers are found, that is, molecular emission, such as $\mathrm{H}_2$ rotational lines at 12.3 and $17\,\mu\mathrm{m}$ , HD, $\mathrm{H}_2\mathrm{O}$ , and OH lines, together with diagnostic atomic lines, such as [Ne II] 12.8, [Ne III] 15.6, [Fe II] 17.9, and [S I] $17.43\,\mu\mathrm{m}$ tracing atomic and ionised material at lower excitation temperatures (i.e., below 2 000 K) than probed by optical forbidden lines. SMI, with its high spectral resolution and sensitivity, will break new ground in the study of gas dispersal in protoplanetary disks. Figure 7 shows that SMI/HR can spectrally resolve the the expected photoevaporative wind line profiles as well as detect shifts in the peak and line asymmetries.

Figure 7. Expected profiles of the [Ne II] $12.8\mu\mathrm{m}$ (red), [Ne III] $15.5\mu\mathrm{m}$ (blue), and [Fe II] $17.9\mu\mathrm{m}$ (green) lines excited in a X-ray-induced photoevaporative wind, based on the models of Picogna et al. (2019) and the calculations of Weber et al. (2020). Histograms show how the lines are seen by the SMI instrument. An iron abundance 10 times smaller than solar has been assumed, taking into account the expected Fe depletion onto dust grains.

Pioneering studies with ground observations at high ( $R=17\,000$ ) resolution with VLT/VISIR have revealed the potential of [Ne II], at $12.8\,\mu\mathrm{m}$ , as a key diagnostic tracer of photoevaporative winds, where Ne ionisation occurs by the action of both X-ray and UV photons from the central star and the accretion shocks (e.g., Pascucci et al. 2007; 2011; Baldovin-Saavedra et al. 2012). The limited observations performed with VISIR have shown that this line usually comes as a single component, and that high-resolution ( $R > 20\,000$ ) is needed to discriminate its origin in slow disk winds ( $v \sim 5{-}10\,\mathrm{km\ s}^{-1}$ ), in the high-velocity jet ( $v > 20{-}50\,\mathrm{km\ s}^{-1}$ ), or in the inner gaseous disk.

Molecular line diagnostics originate from regions located at greater distances from the star, that is, $1{-}10\,\mathrm{au}$ . Near-IR ro-vibrational lines trace gas temperatures $>\!1\,000\,\mathrm{K}$ and probe regions in the disk $\sim\!0.5{-}5\,\mathrm{au}$ (gas and dust can thermally de-couple where these lines originate). Spectrally and spatially resolved observations of $\mathrm{H}_2$ in the near-IR have shown that the emission most often comes from wide-angle low-velocity winds; however, evidence for emission from bound gas in the inner disk has been also found (e.g., Bary et al. 2003; Beck et al. 2012). $\mathrm{H}_2$ mid-IR lines originate from a region further out, of the order of $5{-}10\,\mathrm{au}$ , at $T=150{-}1\,000\,\mathrm{K}$ at the disk surface and thus have the unique potential of tracing the gas within the giant planet formation region. Emissions from $\mathrm{H}_2$ mid-IR rotational lines have been searched for in many T Tauri and Herbig sources (from ground-based telescopes and from space); however, positive detections have been obtained only for an handful of objects, mostly via the space-based Spitzer-IRS instrument at low spectral resolution (e.g., Lahuis et al. 2007) and thus without the possibility to separate the disk wind contribution from the overall emission. Indeed, models of $\mathrm{H}_2$ emission from disks (e.g., Nomura et al. 2007) predict flux levels below the detection limit of present instrumentation, but well above the sensitivity limit of SMI. Significantly, a detailed modelling of theses molecular lines using a thermo-chemical treatment for optically thin disk winds is still lacking. Combined, spectrally resolved observations of both near-IR and mid-IR molecular lines should have the potential of tracing the gas temperature stratification of the inner disk.

In the infrared, high-resolution spectra (e.g., VLT/VISIR and CRIRES+, and in the future E-ELT/METIS and TMT/MICHI) can provide very high spectral resolution, but with poorer flux sensitivity than SMI, mainly due to water vapour in the Earth atmosphere and the high thermal background due to the Earth’s atmosphere. Thus, SMI/HR fills a niche ideal to probe, at high spectral resolution, both molecular and atomic lines that trace the disk wind. Furthermore, SMI will probe disk winds across a very large sample of many hundred planet-forming disks, Ideally, the same sample will be observed as undertaken by the disk gas mass survey with SAFARI, providing a census of both the disk conditions and the disk wind properties that cannot be obtained with ground-based observations.

4. Tracing the gas in Debris disks—Volatile content of planetesimals

Gas that is found in debris disk systems is generally thought to be secondary, released from the debris produced in collisions between planetesimals, rather than a direct remnant from the initial star-forming nebula (e.g., Roberge et al. 2006; Matrà et al. 2015; Kral 2016). As such, this secondary gas provides a unique opportunity to study indirectly the composition of the debris (i.e., the volatile/ice content), and hence the planetesimals, the building blocks of planets. In our Solar System, meteorites (carbonaceous chondrites) contain up to 15 weight% waterb and water dominates the volatile content in comets ( $>\!50$ %, Alexander et al. 2018). Hydrous silicates have also been confirmed in C-complex asteroids by AKARI (Usui et al. 2019) and by the sample return missions for Ryugu (Kitazato et al. 2019) and Bennu (Hamilton et al. 2019), both of which are C-type asteroids. It is unclear whether extrasolar systems contain similar levels of water and volatiles or whether they are generally drier than the Solar System.

Planetesimals that were formed far enough from the star, in regions of the protoplanetary disk that are sufficiently cold, are expected to have a significant volatile component. For example, comets in the Solar System are made up by mass of $\sim\!50$ % $\mathrm{H}_2\mathrm{O}$ and $3{-}10$ % CO (Bockelée-Morvan & Biver 2017). The volatiles locked inside planetesimals may play a key role in the development of life on exoplanets, since these volatiles can be released from the planetesimals and then migrate to the planets and be captured into their atmospheres (Kral et al. 2020a) or be released upon direct impact with the planet, potentially delivering water, a key ingredient in the origin of life as we know it, and replenishing a secondary atmosphere (Chyba et al. 1990; Kral et al. 2018; Wyatt et al. 2020). Understanding this volatile content can also help inform how and where in planet-forming disks planetesimals are able to form; it is for example suggested that planetesimal belts form preferentially at ice lines (Matrà et al. 2018) which should be reflected in a relatively high volatile content in that localised region. Of particular interest is the C/O abundance ratio (Öberg et al. 2011; Helling et al. 2014; Moriarty, Madhusudhan, & Fischer 2014), since the formation of solids and ultimately planets is believed to be sensitively dependent on this ratio. This is directly due to the fact that the condensation sequence forming solids changes dramatically at $\mathrm{C/O}\,\sim\!0.98$ (Larimer 1975). Also, this ratio determines the C/O in primary atmospheres which originate from the accretion of remnant disk material (Massol et al. 2016). The C/O ratio also has an impact on secondary atmospheres, as these depend on the bulk planet composition.

A new technique for probing the volatile content of planetesimals has recently been developed by studying gas in the debris disks found around nearby stars (these are the exo-Kuiper belts found around $\sim\!20$ % of stars). The planetesimals collide and are ground down into dust, observable through infrared emission from the dust itself. This process has been studied extensively over the last few decades (e.g., Wyatt 2008). In this process, the volatiles are also released as gas. The [C I] $610\,\mu\mathrm{m}$ fine structure line and the CO sub-mm lines have been detected by ALMA from debris disks, revealing the spatial distribution of the gas (e.g., Cataldi et al. 2018; Moór et al. 2019) and in some cases strong asymmetries possibly attributed to recent collisions (e.g., Dent et al. 2014, for the case of $\beta\,\mathrm{Pic}$ ).

Assuming the gas is released in a steady-state process, the production rates of CO and dust can then provide their relative quantities in the planetesimals. The systems studied to date, for example, HD 181327 and Fomalhaut, have CO-to-dust compositions that are comparable with Solar System comets (e.g., Marino et al. 2016; Matrà et al. 2017). However, Kral et al. (2020b) report two systems that may have less CO than Solar System comets. While the CO content of the planetesimals can be probed in the above way with ALMA, this technique relies on an assumption that the gas is produced in steady state and that the lifetime of CO is set by photodissociation via the interstellar radiation field with, in some cases, CO self-shielding (Visser, van Dishoeck, & Black 2009; Heays, Bosman, & van Dishoeck 2017). Yet we expect that once CO is destroyed, the C and O atoms will accumulate until they spread through viscous processes to eventually accrete onto the star. Observations of [C I] with ALMA show that in some cases there is sufficient carbon to shield the CO from photodissociating (see Figure 8, Kral et al. 2019). Moreover, the ALMA [C I] observations call into question the steady-state nature of the gas production (Cataldi et al. 2020) and probably do not probe the bulk of the carbon which is likely to be predominantly ionised, at least for the disks that are not shielded. Cataldi et al. (2020) show that a complete knowledge of the gas composition (e.g., $\mathrm{C}^+$ , C, CO) in connection with a detailed photodissociation and ionisation model allows us to time potential large collision events and determine the time since a collisional cascade was initiated. In addition to CO, there may be other volatiles released, in particular $\mathrm{H}_2\mathrm{O}$ which photodissociation turns into OH, H, and O (Kral et al. 2016). Also here, ALMA observations alone cannot constrain the $\mathrm{H}_2\mathrm{O}$ content of the planetesimals since the ‘daughter’ products are only detectable in the far-IR with, for example, SPICA.

Figure 8. Sketch of gas distribution in a debris disk based on a detailed dissociation/ionisation model including an interstellar radiation field (IRF). This illustrates the complementarity of ALMA and SPICA gas observations in debris disks. Figure modified from Kral et al. (2019).

Even though it lacks spectral and spatial resolution, SAFARI is the only instrument that will be able to detect the [O I] lines at 63 and $145\,\mu\mathrm{m}$ and use them to measure the atomic oxygen abundance. Another unique line, [C II] $158\,\mu\mathrm{m}$ , is crucial to measure the carbon budget together with ALMA [C I] $610\,\mu\mathrm{m}$ and CO sub-mm line measurements. This information is not only relevant for debris disks, but also for planet-forming disks (see Section 2.1). The [C II] line, in conjunction with CO and [C I] observations with ALMA, will allow measurement of the carbon mass, the carbon ionisation fraction, and the electron density in debris disks, all of which constrain both the CO content of the planetesimals and the steady-state versus stochastic production process (as well as the mechanism controlling the viscous evolution, e.g., MRI, Kral & Latter 2016). With this information, the [O I] $63\,\mu\mathrm{m}$ line flux can be used to determine the $\mathrm{H}_2\mathrm{O}$ content of the planetesimals (see Kral et al. 2016). In addition, the $\mathrm{H}_2\mathrm{O}$ ( $179.7\,\mu\mathrm{m}$ ) and OH ( $119.3+119.5\,\mu\mathrm{m}$ ) lines can be used to probe the water content directly, though detection requires a high production rate due to the short photodissociation time for these molecules (Matrà et al. 2018).

Previous observations with Herschel (Riviere-Marichalar et al. 2014) only had the sensitivity to detect [O I] and [C II] for a few debris disks, indicated in Figure 9. SAFARI (yellow line) improves significantly on Herschel/PACSc (red line) and opens the possibility to detect the gas component in a statistically significant sample of debris disks (about 100 potential detections), thereby measuring the volatile content of planetesimals. In addition, these observations characterise the nature of the gas production process, steady versus stochastic, thus informing how the late stages of planet assembly and atmosphere build-up proceed in extrasolar systems (Kral et al. 2020a).

With SAFARI, a $\beta$ Pic-equivalent will be detectable with $5\,\sigma$ in 1 h out to 150 pc in [O I] $63\,\mu\mathrm{m}$ and 400 pc in [C II] $158\,\mu\mathrm{m}$ . This increases the volume in which $\beta$ Pic-like gas-rich debris disks can be detected 400- to 1200-fold, compared to Herschel/PACS. In this volume, there are hundreds to thousands of debris systems already known (Cotten & Song 2016), so a careful target selection is possible. To answer the broader question of how the chemical make-up correlates with the stellar spectral type and the presence of planets in the system, linking chemical composition to planet formation, a sample size on the order of 100 systems is required. There are already $\sim\!20$ debris disks with CO detected by ALMA, and this number is predicted to continue to rise steadily over the next decade. The detection thresholds for [O I] and [C II] predicted by Kral et al. (2017) are comparable to those of ALMA observations of CO and [C I]; this should result in detections of $\sim\!100$ debris disks with both ALMA and SPICA.

4.1. Other gas tracers in Debris disks

Other species of importance for planet formation and uniquely available to SPICA are silicon, through the strong [Si II] $35\,\mu\mathrm{m}$ line (using SMI), and molecules such as $\mathrm{H}_2\mathrm{O}$ (ortho line at $179.7\,\mu\mathrm{m}$ ), and OH (doublet at 119.3, $119.5\,\mu\mathrm{m}$ ). Since molecules are quickly dissociated on timescales of days to hundreds of years (see Kral et al. 2019), they will only be found in systems with significant ongoing gas production such as $\beta\,\mathrm{Pic}$ , where CO is observed (Dent et al. 2014). Since the molecular lines are likely optically thick, the emission will depend sensitively on the excitation temperature. Assuming a molecular gas distribution similar to the observed CO distribution in the $\beta\,\mathrm{Pic}$ disk (i.e., a solid angle of $\sim\!1\,\mathrm{arcsec}^2$ at 20 pc), at a velocity dispersion of $4\,\mathrm{km\ s}^{-1}$ and excitation temperatures in the range $20{-}85\,\mathrm{K}$ , we find a predicted line flux of $\sim\!10^{-18}{-}10^{-17}\,\mathrm{W\,m}^{-2}$ , sufficient to detect $\mathrm{H}_2\mathrm{O}/\mathrm{OH}$ with $5\,\sigma$ in 20 min for a $\beta\,\mathrm{Pic}$ -equivalent out to 30–150 pc.

Figure 9. Predicted [C II] (left) and [O I] (right) masses for the sample of 192 debris disks in Kral et al. (2017). Approximate detection thresholds for surveys with Herschel/PACS (red, 1 h, $5\,\sigma$ ) and with SAFARI/HR (yellow, 1 h, $5\,\sigma$ ) are shown; the sensitivity of Herschel was only sufficient to detect (green dots) the most extreme disks in the population in deep integrations (longer than 1 h), whereas with SPICA we can build statistically representative samples of debris disk gas detections. The mass estimates for the few objects that have detections from Herschel are indicated by green dots. Green arrows indicate lower limits of carbon masses related to the large uncertainty on the excitation temperature.

Figure 10. Left: The water vapour line spectra after subtracting the dust continuum, at SMI and SAFARI wavelengths, colour-coded by the energy of the upper levels of the line. Right: The line-emitting regions of various water vapour transitions in a disk around a $1\,M_{\odot}$ T Tauri star for the model in Kamp et al. (2017). The white dashed line is the water snowline indicating where water vapor starts to freeze out.

5. The water trail during planet formation

Understanding the water vapour and ice distribution in planet-forming disks will provide information on the origin of water in planetary systems, including our Solar System. Water can be delivered to rocky planets, including Earth, through icy pebbles, icy planetesimals, comets, and asteroids, supporting the emergence of life on these planets.

Water vapour line emission has been detected from protoplanetary disks using ground-based telescopes at near-infrared wavelength (e.g., Carr et al. 2004). Resolved water line profiles confirmed that they originate in the inner few au of T Tauri disks (Salyk et al. 2011b; Banzatti et al. 2017). The Spitzer Space Telescope detected water vapour lines towards dozens of T Tauri disks (e.g., Carr & Najita 2008; Pontoppidan et al. 2010; Salyk et al. 2011a). More recently, the Herschel Space Observatory detected warm ( $\sim\!1\,000\,\mathrm{K}$ ) and cold water vapour ( $\sim\!50\,\mathrm{K}$ ) in a few disks around T Tauri and Herbig stars (e.g., Hogerheijde et al. 2011; Meeus et al. 2012; Riviere-Marichalar et al. 2012; Fedele et al. 2012). Meanwhile, near-infrared absorption features of water ice have been detected towards some edge-on disks (e.g., Pontoppidan et al. 2005; Aikawa et al. 2012; Terada & Tokunaga 2017) and in scattered light towards some face-on disks (Honda et al. 2009; 2016) using ground-based telescopes. In addition, far-infrared emission features of water ice have been detected by the ISO and the Herschel Space Observatory towards T Tauri and Herbig disks (e.g., Malfait et al. 1999; McClure et al. 2012; 2015; Min, Hovenier et al. 2016b).

Water vapour observations from the ground are intrinsically difficult due to the Earth’s atmosphere and thus limited to very narrow windows of high-excitation water lines and low abundance water isotopologues. The Earth’s atmosphere is opaque to the rotational transitions of water, especially the low-J transitions which trace the bulk of the cold gas reservoir in disks. Water remains mostly inaccessible even to air-borne facilities, like SOFIA.

SPICA will characterise the main reservoirs of warm and cold water vapour (see Figure 10) and the far-infrared crystalline and amorphous water ice features, giving unique access to the time evolution of the water throughout the entire disk. SPICA will trace the time evolution of the water snowlines in the planet-forming disks which divide the regions between rocky and gas giant planet formation (Notsu et al. 2016; 2017). SPICA will characterise how the water vapour and ice reservoirs change in the presence of strong accretion events and substructures such as the inner cavities, gaps/rings, and spiral arms, which are related to the disk evolution and planet formation. SPICA will enable the water trail to be traced into the phase of mature planetary systems.

5.1. Tracing the water vapour and ice reservoir

Together, SAFARI and SMI cover a wide range of wavelength and many water vapour emission lines from the mid- to far-IR, as well as water ice features at far-IR wavelengths (45 and $63\,\mu\mathrm{m}$ ). In particular, the wavelength range of 30–50 $\mu\mathrm{m}$ opens new spectroscopic windows with SPICA. SAFARI and SMI provide access to more than a thousand ro-vibrational water vapour transitions spanning a wide range of excitation energies from $E_{\rm up} \sim\!100\,\mathrm{K}$ to several 1 000 K (Figure 10, left). Given this wide range of the energy levels, these transitions are ideal to trace the gaseous reservoirs in a variety of regions within planet-forming disks. Figure 10 (right) shows the dominant emitting regions for four $\mathrm{H}_2\mathrm{O}$ transitions in a planet-forming disk around a $1\,M_{\odot}$ T Tauri star: the $\mathrm{H}_2\mathrm{O}$ transitions in the SMI/SAFARI wavelength range originate at different radial location in the disk.

SPICA has a sensitivity which is a factor of 50 higher than that of either the Spitzer Space Telescope or the Herschel Space Observatory. This enables the detection of both water vapour and ice with disks across a variety of evolutionary stages. Figure 11 shows the flux from the 179.5- $\mu\mathrm{m}$ water vapour line as a function of the underlying dust continuum flux, for models with a variety of parameters such as the gas-to-dust mass ratio, the stellar luminosity, and the disk mass (DENT grid, Woitke et al. 2010; Kamp et al. 2011). The sensitivity levels of SPICA/SAFARI are shown for shallow and deep surveys, revealing that the water vapour line emission from disks with dust continuum fluxes above $1\,\mathrm{Jy}$ are detectable. The embedded histogram of dust continuum fluxes for a sample of disks observed by the Herschel Space Observatory reveals that there exists sufficient detectable targets in nearby star-forming regions. The fluxes of various water vapour lines are plotted in Figure 10 (left), showing that many of the lines will be detectable together with the 179.5- $\mu\mathrm{m}$ line. Thus, SAFARI and SMI have the potential to trace the evolution of the distribution of water vapour in disks.

Figure 11. The 179.5- $\mu\mathrm{m}$ water vapour line fluxes as a function of the dust continuum fluxes for the DENT grid of disk models with a variety of parameters (Woitke et al. 2010; Kamp et al. 2011). The sensitivity levels of SAFARI for a 1 h (shallow) and 10 h (deep) survey and the histogram of observed Herschel dust continuum fluxes (red) from selected star-forming regions are also shown.

5.2. Tracing the water snowlines

The high-resolution mode of SMI is unique for locating the water snowline near the midplane in planet-forming disks. Since the line emission is Doppler-shifted due to the Keplerian rotation, the velocity profiles of the water lines are sensitive to the radial distribution of the water line-emitting region within the disks. SMI/HR ( $R \sim 30,000$ ) spectra enable us to spectroscopically resolve the water line profiles originating in the inner few au of the disk and thus locate kinematically the line-emitting regions, that is, the water snowlines in disks (Figure 12, see also Figure 10 showing the 17.75- $\mu\mathrm{m}$ line-emitting region is located inside the white dashed snowline). Since water vapour is distributed not only inside the water snowline, but also in the warm (a few 100 K) surface layer and the cold outer regions (Figure 12, see also Figure 10 showing the 78.74 and $179.53\,\mu\mathrm{m}$ lines trace the outer disk), we need to select specific transitions in order to only trace the water vapour inside the water snowline.

Figure 12. (Left:) Water profiles of the 17.75- $\mu\mathrm{m}$ line convolved with $R=29,000$ ( $\Delta v \sim 10\,\mathrm{km\ s}^{-1}$ ) and (centre) the 37.98- $\mu\mathrm{m}$ line convolved with $R=10,000$ ( $\Delta v \sim 30\,\mathrm{km\ s}^{-1}$ ), emitted from a Herbig Ae disk with inclination angle of $45^\circ$ at a distance of 140 pc. An integration time of $\sim\!10\ \mathrm{min}$ is assumed. (Right:) The $\textbf{water vapour abundance distribution}$ ( $n_{\rm H_2O}/n_{\rm H}$ ) in a disk around a $2.5\ \mathrm{M}_{\odot}$ Herbig Ae star (Notsu et al. 2017)

Sophisticated physical and chemical disk models show that the transitions with low emissivity, that is, low Einstein A coefficient of $10^{-6}{-}10^{-3}\ \mathrm{s}^{-1}$ , and an excitation energy of $E_{\rm up}\sim 1\,000\,\mathrm{K}$ are suitable to trace the water snowline (Notsu et al. 2016; Notsu et al. 2017). These transitions exist at wavelengths ranging from mid-IR to sub-millimetre, and the $17.75\,\mu\mathrm{m}$ line, which satisfies the condition to trace the water snowline, is the best candidate transition in the wavelength range of SMI/HR ( $12{-}18\,\mu\mathrm{m}$ ). The $37.98\,\mu\mathrm{m}$ line in the wavelength range of SAFARI is similarly suited, but the spectral resolution even with the FTS is lower ( $R \sim 10\,000$ ). Thus, SAFARI will not be able to resolve the double peak structure of this emission line but will enable us to measure the line width. This will give us additional information on the location of the snowline (Figure 12).

These water lines cannot be accessed from ground-based telescopes due to telluric absorption. The sensitivity of the Spitzer Space Telescope was not high enough to detect these lines (Antonellini et al. 2015; 2016; Antonellini 2016). JWST will be able to detect the 17.75- $\mu\mathrm{m}$ line, but its highest spectral resolution ( $R \sim 3\,000$ ) is not high enough to resolve the line profiles. However, JWST observations will be key in measuring line strengths, a key input for the planning of future observations by SPICA. Suitable water lines to trace snowlines with ALMA require long integration times to detect the line profiles (Carr et al. 2018; Notsu et al. 2018; 2019) and thus it will not be possible to study the time evolution of the location of water snowlines across large samples of disks.

The detection of the 17.75- $\mu\mathrm{m}$ water line profiles towards Herbig Ae stars with enough sensitivity to locate the snowline requires only short integration times ( $\sim\!30\,\mathrm{min}$ ) with SMI/HR even if the disks are located at the distance of the Orion Molecular Clouds ( $\sim\!420\,\mathrm{pc}$ ). T Tauri disks in nearby star-forming regions ( $<\!300\,\mathrm{pc}$ ) will require typically $\sim\!1\,\mathrm{h}$ exposure times to achieve the required sensitivity for a reliable snowline estimate.

5.3. Tracing the thermal history of water ice

Water ice has multiple bands in the infrared, each of which are sensitive to the temperature of the ice. In the far-IR, two prominent features exist around $45\,\mu\mathrm{m}$ and $63\,\mu\mathrm{m}$ . The thermal history of water ice is imprinted in the peak strength and shape of the $45\,\mu\mathrm{m}$ feature that is narrower in the crystalline phase compared to the amorphous form. In situ formation and mass transport from the inner disk has been discussed by Min et al. (2016a) as potential origin of crystalline water ice in planet-forming disks. Such mixing of material between hot inner regions and cold outer regions of the disks has been also discussed based on the presence of crystalline silicates in comets (e.g., Watson et al. 2009).

Observing water bands in the far-IR also allows to trace deeper regions within planet-forming disk due to the lower opacity at longer wavelengths. The mid-IR ice bands at 3, 6, and $13\,\mu\mathrm{m}$ are mostly optically thick under typical disk conditions and therefore do not probe the reservoir where most of the ice is located (Rocha & Pilling 2020). Hence, the 45- $\mu\mathrm{m}$ feature is an excellent tracer of the formation of ice and transport of icy material within disks. Water ice formed in the warm region near the snowline and transported to the cold outer region (cooldown) has a different structure (and thus spectral appearance) compared to water ice formed in cold regions and transported into warm regions (warmup, e.g., Smith et al. 1994). The model calculations around a $0.7\,M_{\odot}$ T Tauri star show that ice features with these different thermal histories are distinguishable through observations with a spectral resolution of $R=250$ (Figure 13). SOFIA/HIRMES also will be able to detect this ice feature; however, SOFIA will require long exposure times, $\sim\!1\ \mathrm{hr}$ for the most nearby star-forming regions. SPICA/SAFARI can achieve the same sensitivity with much shorter integration times ( ${\sim}10\ \mathrm{min}$ ) and thus will be a unique instrument to perform large surveys of water ice features towards young objects in various evolutionary stages (Kamp et al. 2018).

Figure 13. Simulated water ice spectra at $45\,\mu\mathrm{m}$ with different thermal histories. Using a 10-min integration (SAFARI noise level) and spectral resolution of $R=250$ , these are distinguishable. The ‘Reference’ case is for using constant temperature crystalline ice opacities (140 K).

6. From pristine dust to planetesimals/comets

While only 1% of the matter in disks is solid, dust grains play a crucial role in the formation of planetary systems. In order to understand the properties of planets, it is important to constrain the chemical composition of their building blocks: these are small dust particles that enter the disk from the molecular cloud and grow as they are transported inwards. In the inner disk, annealing of the amorphous interstellar grains causes the lattice structure to become ordered, forming crystalline silicates.

Crystalline grains can also be produced by gas phase condensation. Radial mixing transports these hot grains from the inner disk outwards, and they become part of planetesimals and eventually planets. In the inner disk, collisions between dust particles result in a constant cycling of grains between larger and smaller particles, including larger parent bodies. Collisions dominate in the gas-poor debris disk environment, allowing a unique view on the composition of parent bodies. All these processes alter the chemical composition of dust. Infrared spectroscopy can be used to constrain the chemical composition of dust particles.

ISO-SWS, Spitzer-IRS, and JWST-MIRI have studied or will study the dust emission from the inner, warmer disk regions, probing temperatures down to about 100–150 K. The ISO and Spitzer observations show clear evidence for grain growth and the presence of both Mg-rich olivines ( $\mathrm{Mg}_{2x}\mathrm{Fe}_{(2-2x)}\mathrm{SiO}_4$ ) and pyroxenes ( $\mathrm{Mg}_{x}\mathrm{Fe}_{1-x}\mathrm{SiO}_3$ ), with up to 10% of Fe contained in some of the crystalline pyroxenes (see, Juhász et al. 2010; Sargent et al. 2009). Spitzer spectra also reveal that olivines are more abundant in the outer disk, and pyroxenes in the inner disk (Juhász et al. 2010). Radial mixing models (e.g., Gail 2004) suggest an opposite trend, with olivines (specifically forsterite $\mathrm{Mg}_2\mathrm{SiO}_4$ ) more abundant in the inner disk.

Much less is known about the composition of the cold dust reservoir. Solar system comets that were formed in the outer regions of the proto-solar nebula contain significant amounts of refractory materials (crystalline silicates, FeS) that require high formation temperatures, that are more typical for the inner disk. (e.g., Crovisier et al. 1997; Brownlee 2014; Wooden et al. 2017). In contrast, the molecular and volatile content of comets provides strong evidence that these objects never experienced high temperatures (e.g., Calmonte et al. 2016). The outer regions of the proto-solar nebula may have experienced substantial mixing of solids from high-temperature regions in the disk. However, it is not clear such radial mixing is a common process in the disk during planet formation.

Both ISO-LWS and Herschel have searched for solid-state features in the far-IR spectra of Herbig Ae/Be disks, and they were successful in detecting the 69- $\mu\mathrm{m}$ crystalline olivine band (Malfait et al. 1998; Bowey et al. 2002; Sturm et al. 2010; 2013; Maaskant et al. 2015, see Figures 14 and 15). For Herbig Ae/Be proto-planetary disks, Sturm et al. (2013) found eight detections of the 69 $\mu\mathrm{m}$ band of, almost pure, forsterite ( $\mathrm{Mg}_2\mathrm{SiO}_4$ ) in a sample of 32 Herbig Ae/Be disk observations. For debris disks, only one detection of the 69 $\mu\mathrm{m}$ band was found out of a set of eight observations (de Vries et al. 2012). The observations so far tell us about the diversity of the crystalline silicate abundance in the cold disk region, implying a variety of disk mixing histories. To directly compare with our Solar System radial mixing history, observations of T Tauri stars are required. However, such observations have been limited due to the sensitivity of previous instruments and issues with the pointing and base-line stability over a broad wavelength range.

Figure 14. The effect of radial mixing of forsterite (crystalline silicate) grains in the disk on the infrared spectra. When fosterite resides only within 5 au, the $69\,\mu\mathrm{m}$ forsterite feature is very weak. On the other hand, when forsterite appears within the 0–50 au radius of the disk, astrong $69\,\mu\mathrm{m}$ feature appears (Maaskant et al. 2015).

Figure 15. (Top) The 69- $\mu\mathrm{m}$ resonance of $\mathrm{Mg}_2\mathrm{SiO}_4$ for a range of temperatures. The band position broadens and shifts redwards with increasing temperature. Note that the band also shifts redwards with increasing Fe content. Optical constants from Suto et al. 2006, using a distribution of hollow spheres (DHS) grain model (Min et al. 2005) with $f=0.7$ and a grain size of $1\,\mu\mathrm{m}$ . (Bottom) Forsterite 69- $\mu\mathrm{m}$ feature peak and Full Width Half Maximum (FWHM) dependence on Fe content in olivine ( $\mathrm{Mg}_{2x}\mathrm{Fe}_{(2-2x)}\mathrm{SiO}_4$ ) and temperature. Only 1% inclusion results in $\sim\!0.3\,\mu\mathrm{m}$ shift to longer wavelengths (this figure has been modified from de Vries et al. 2012, Springer Nature).

SPICA will be able to observe solid-state resonances from dust particles in the far-IR with unprecedented sensitivity and will have the full mid- to far-IR spectral coverage to identify and characterise minerals that show vibrational resonances over a wide wavelength range (Figure 16). Far-IR resonances of minerals are invaluable since they allow the determination of mineral properties within the low-temperature regions where comets are formed. By using the many resonances of these dust species, the spatial distribution of olivines and pyroxenes can be derived. Figure 14 illustrates how FIR is important to understand the radial mixing history. The relative abundance of olivines to pyroxenes as a function of radius in the disk can be used as a probe of the relative importance of different processes in the disk that produce crystalline silicates, such as chemical equilibrium gas-phase condensation, thermal annealing of molecular cloud amorphous silicates, and (local) flash heating events caused by activities such as stellar outbursts, lightning, and planet formation.

Figure 16. Opacities of forsterite, enstatite, calcite, and the hydrosilicates montmorillonite and serpentine, showing the potential of SPICA to detect these dust species over the full SMI and SAFARI wavelength range. Optical constants from Suto et al. (2006), Zeidler, Mutschke, and Posch (2015), and Koike & Shibai (1990) using a ‘distribution of hollow spheres’ grain model (Min et al. 2005) with a vacuum fraction of $f=0.7$ and a grain size of $0.1\,\mu\mathrm{m}$ .

Far-infrared resonances also allow us to measure the Fe/Mg ratio in crystalline olivine and pyroxene with very high precision (down to an error of better than a percent). For example, the wavelength position and width of the $69\,\mu\mathrm{m}$ band of olivine ( $\mathrm{Mg}_{2x}\mathrm{Fe}_{(2-2x)}\mathrm{SiO}_4$ ), is strongly dependent on the Fe/Mg ratio and grain temperature(see Figure 15). This allows a precise determination of the composition of olivine and pyroxene grains. The Fe/Mg ratio of (crystalline) olivine and pyroxene is sensitive to parent body processing and can be used to constrain the size and formation timescale of parent bodies. In the case of a small parent body $(\!<\!10\ \mathrm{km}$ ), the composition of the mineral is unaltered since its formation in the proto-planetary disk and we expect a very low Fe content (Fe/(Fe + Mg) $\sim 0$ ). In slightly larger parent bodies ( $\sim\!10\,\mathrm{km}$ to several hundreds of kilometres), the minerals undergo equilibration (Fe/(Fe + Mg) $\sim 0.3$ ) and for large planetesimals and planets ( $>\!200\,\mathrm{km}$ ) igneous processes will strongly impact the minerals (Fe/(Fe + Mg) $> 0.5$ . As in gas-rich disks, the mineralogy of $\mu\mathrm{m}$ -sized dust particles in debris disks directly probes the composition of their parent bodies: extra-solar asteroids and comets.

Furthermore, a search for carbon-bearing solids such as calcite and dolomite will be interesting. Carbon-bearing minerals like calcite ( $\mathrm{CaCO}_3$ ) and dolomite (CaMg)( $\mathrm{CO}_3$ ) $_2$ only form under specific conditions, on Earth requiring the presence of liquid water or biogenic processes. Carbonates have been detected in evolved stars (Kemper et al. 2002) and protostars (Ceccarelli et al. 2002). Several formation mechanisms have been proposed (e.g., Toppani et al. 2005), such as gas-grain chemical reactions and non-equilibrium gas-phase condensation, all requiring a $\mathrm{CO}_2$ and $\mathrm{H}_2\mathrm{O}$ -rich environment. The detection of such minerals in planetary systems would strongly impact our current view on the early presence of environments that are essential for life.

7. The first true Kuiper belt analogue

While all stars presumably host debris disks at some level, only the thermal continuum of the brightest 20% are currently detectable, and we know neither our rank in the remaining 80%, nor how this rank is related to the Solar System’s history or planetary architecture. A decade from now we will have detected or set stringent limits on planets around most nearby stars, but the limits on small body populations will be as poor as they are now (see Figure 17). SPICA provides our only opportunity to detect true Kuiper belt analogues.

Figure 17. Sensitivity to Kuiper belt analogues at 5 pc. The blackbody radius is the stellocentric radius obtained from the dust temperature by assuming the dust behaves as a blackbody. Grey dots are known disks around nearby stars. Disks that lie above a given instrument’s line are detectable. The SPICA sensitivity at 50– $70\,\mu\mathrm{m}$ is very similar, so only one line is shown. Thus, only SPICA can detect debris disks at Kuiper belt (and fainter) levels.

A true Kuiper belt (KB) analogue is defined here as a debris disk with a fractional luminosity $L_{\rm disk}/L_{\star} \sim 10^{-7}$ and a radius of $\sim\!45\,L_\star^{0.2}\,\mathrm{au}$ (i.e., scaling with $L_\star$ as suggested by mm-wave imaging of bright debris disks, Matrà et al. 2019). With temperatures of $\sim\!50\,\mathrm{K}$ , KB analogues emit essentially all of their energy at far-IR wavelengths, but their low luminosities imply that this emission is at most 1% of the stellar flux. To detect a debris disk requires: (1) sensitivity sufficient to detect the disk flux, (2) unresolved disks to be brighter than some fraction of the stellar flux due to calibration uncertainties, (3) resolved disks to have surface brightness greater than the local uncertainty in the stellar Point Spread Function (PSF), and (4) disks to be brighter than the confusion limit. The typical calibration limit (2) is $\sim\!10$ %, explaining why it is not possible to detect unresolved KB analogues (e.g., with Spitzer or Herschel), while the sensitivity and PSF limits (1) and (3) preclude the detection of resolved KB analogues with ALMA, JWST, or in scattered light. These points are illustrated in Figure 17 which shows the detectability of debris disks with different radii and fractional luminosities for a Sun-like star at 5 pc. Disks can be detected above the lines indicated for a given instrument, and essentially all known disks lie above the Herschel $100\,\mu\mathrm{m}$ limit, with no current or planned instruments able to detect KB analogues, except SPICA.

This unique capability of SPICA is possible because of its combination of photometric sensitivity and resolution at wavelengths around the peak KB emission. Constraint (2) can be avoided by observing stars close enough that a KB analogue would be resolved (see Figure 18, left panels), and constraint (4) is partially or wholly avoided by observing at $\leq\!70\,\mu\mathrm{m}$ , rather than at $100\,\mu\mathrm{m}$ where a KB analogue would be well below the confusion limit. This means that, once the resolution constraint is met, sensitivity (1) and PSF stability (3) constraints on SPICA’s imaging performance determine the number of stars for which it will be feasible to detect true KB analogues, as shown in the right panels of Figure 18. Here we consider surveys at $34\,\mu\mathrm{m}$ (upper panels) and $70\,\mu\mathrm{m}$ (lower panels). Both require that the SPICA PSF be very well understood, but the shorter wavelength is preferred as the higher spatial resolution means that more stars can be observed (compare for example the number of stars closer than the resolution limit in the left panels of Figure 18).

Figure 18. Kuiper Belt sample selection. The top row shows the 34- $\mu\mathrm{m}$ SMI survey, and the bottom row shows the 70 $\mu\mathrm{m}$ B-BOP survey. (Left panels:) Volume-limited sample of nearby stars (Phillips et al. 2010). The KBs of targets falling below the solid line would be resolvable by SPICA. (Right panels:) The surface brightness of resolvable KB analogues is used to determine a further selection based on a 3 $\sigma$ detection in a 2-h observation assuming the sensitivity (dashed lines) and confusion limits (dot-dashed lines), and disk to star contrast assuming the PSF is known at 1% accuracy near the first Airy ring (dotted lines). Stars with detectable KBs lie above and right of all lines. Here disks have been assumed to be face-on; inclined disks would move up and to the right on this plot. Detection for the top left target in the upper right panel, $\alpha$ Cen, should still be possible as the angular size of a KB for this target is well beyond 1.2 $\lambda/D$ . KBs around M-type stars cannot be detected at 34 $\mu\mathrm{m}$ unless the contrast is better than $1.7 \times 10^{-4}$ , or at 70 $\mu\mathrm{m}$ because their surface brightness is below the confusion limit (unless stellar proper motion is used to subtract the background).

The sensitivity limit (1) is shown on the right panels of Figure 18 as horizontal dashed lines assuming a 2-h observation per star, and using the nominal sensitivities (e.g., $10\,\mu\mathrm{Jy}$ , $5\,\sigma 1\,\mathrm{h}$ for SMI). A longer observation is not warranted at 70 $\mu\mathrm{m}$ because this already reaches the confusion limit (horizontal dash-dot line), while at 34 $\mu\mathrm{m}$ the sample is more constrained by the PSF stability. For the PSF stability limit (3), consider that the surface brightness of a star’s first Airy ring is 1.7% of the star. The right panels of Figure 18 show that at both wavelengths face-on KB analogues are 10-100 times fainter than this at a comparable location (though these could be in the minima). Thus to detect such disks, the surface brightness of the PSF wings must be known to $\sim\!1$ % accuracy, resulting in a PSF stability requirement of $1.7 \times 10^{-4}$ of the peak near the first Airy ring. This is the vertical dotted line shown on the right panels of Figure 18. This PSF stability constraint can be relaxed by a factor of a few at 70 $\mu\mathrm{m}$ because the star is fainter but the disk similarly bright compared with the shorter wavelength (meaning that sensitivity, or more accurately confusion is the limiting factor). Assuming that this PSF requirement can be met, surveys at each of the wavelengths would be able to detect KB analogues around the stars in the top right quadrants of the right panels of Figure 18. These limits are somewhat pessimistic in the sense that an inclined KB analogue would have higher surface brightness, and higher disk to star contrast, than assumed.

The frequency of Kuiper belt analogues is unknown but might be expected to be several tens of percent. Deriving the incidence with a precision of a few percent, comparable with that for brighter disks, would allow characterisation of the entire brightness distribution down to sub-KB levels, thus placing the Solar System’s debris disk in context for the first time. This level of precision requires observing several tens of stars. Figure 18 left shows that the KBs around $>\!100$ nearby stars would have a large enough angular size to be resolved by SPICA at 34 $\mu\mathrm{m}$ , and 14 at 70 $\mu\mathrm{m}$ . Of these, Figure 18 right shows that KB analogues around M-types would be too faint given the sensitivity, confusion, and/or PSF stability limits, leaving an unbiased sample of $\sim\!100$ targets at 34 $\mu\mathrm{m}$ and 11 at 70 $\mu\mathrm{m}$ . Furthermore, $\sim\!7$ from the 34 $\mu\mathrm{m}$ sample and 4 from the 70 $\mu\mathrm{m}$ sample are already known to host detected disks (i.e., they are in the 20% of the population that have KBs bright enough to be detected by photometry). Thus, while a survey at 70 $\mu\mathrm{m}$ could achieve the first detection of a true KB analogue, a survey at 34 $\mu\mathrm{m}$ would be better suited to determining the frequency of dust at KB analogue levels.

Table 2. Summary of the reference mission. Surveys in brackets use the data acquired by the main survey and do not require a different sample and/or longer exposure times. Exposure time estimates are derived using SAFARI simulator version 1.2 issue 6.2 and SMI simulator version 4.

^aThis is the exposure time without instrument and observatory overheads.

^bThese times were derived using issue 3.0 of the SAFARI time estimator (w/o background).

To summarise, the proposed observing strategy is to image systems at 34 and/or 70 $\mu\mathrm{m}$ with SMI or B-BOP (if the latter includes a 70- $\mu\mathrm{m}$ detector), but the goal of detecting true KB analogues would only be feasible if the above PSF stability constraint can be met.

8. A reference observing programme

In the context of the ESA M5 process, we studied the feasibility of achieving the science goals outlined in this paper within the typical lifetime of a space mission. We rely here on the detailed instrument descriptions, wavelength ranges, spectral resolution and sensitivities, outlined in Roelfsema et al. (2018) for the mid- and far-IR instruments SMI (Kaneda et al. 2020) and SAFARI (Roelfsema et al. 2018) and briefly summarised in the preface.

Table 2 summarises a potential reference observing programme consisting of six surveys with strongly overlapping samples. Details of how the surveys are compiled can be found in Appendix A. These surveys would provide the data required to answer the key science questions outlined in this white paper. The total exposure time required for such a reference programme is 1.5 months. If we add typical overheads such as 10% calibration time, slew times (3 min per source) and assume an overall efficiency of the observatory of 60% (based on Herschel experience), we estimate the full reference observing programme to take $\sim\!77\,\mathrm{d}$ , or ${\sim\!2.5}$ months. This is eminently feasible within a mission lifetime of3 yr.

9. Beyond SPICA

We now let loose the mission design of SPICA and comment in the following subsections on a couple of interesting capabilities that should be considered for future infrared instrumentation development.

9.1. Mid-IR spectral resolution

The spectral resolution of $R \sim 30\,000$ is crucial to resolve line profiles from the inner warm disk and to separate the peaks of the Keplerian profiles (see Section A.3). Increasing the resolution further can help disentangling more complex lines profiles (more than two peaks), but the true gain arises once line profiles can fully resolve disk wind kinematic features. Figure 7 shows that the spectral resolution of $R \sim 30\,000$ is enough to detect a shift of the wind profile with respect to the disk rest frame. However, a full study of the line asymmetries, including accurate peak determination, arising from various disk dispersal processes warrants a resolution of $R \sim 100\,000$ , or $\sim\!3\,\mathrm{km\ s}^{-1}$ , such as available on the ground with VLT CRIRES.

9.2. Far-IR spectral resolution

The limited SAFARI spectral resolution will make it difficult to kinematically separate the individual components contributing to the emission lines and thus to isolate the emission within the disk from that in the disk wind and outflow. In practice, it will only be possible to distinguish atomic emission in fast jets, that is, $v_{\rm jet} > 50\,\mathrm{km\ s}^{-1}$ , contributing to the [O I] line at $63\,\mu\mathrm{m}$ , where the resolution is $R > 5\,000$ . To properly discriminate between the various components potentially contributing to the far-IR lines (disk, wind), we require a spectral resolution of $30\,000$ , close to that which SMI offers at shorter wavelengths.

9.3. Wavelength coverage

The only water line excited by cold gas in the SAFARI wavelength range is the 179.5 $\mu\mathrm{m}$ ortho- $\mathrm{H}_2\mathrm{O}$ line ( $T_{\rm up}=114.4\,\mathrm{K}$ ). However, going to slightly longer wavelengths than presently envisioned for SAFARI, the 269.27 $\mu\mathrm{m}$ para-water line ( $T_{\rm up}=53.43\,\mathrm{K}$ ), one of the three ground state lines of water could be included. Furthermore, due to this increase in spectral coverage, the gap in the CO ladder would close with respect to the ground-based sub-millimetre facilities. This would be beneficial for measuring the radial temperature gradients in disks, especially to gain accuracy at the spatial scales of a few to a few 10 au.

9.4. Mirror size

Finally, a larger primary mirror would undoubtedly increase the sensitivity and diminish confusion at far-IR wavelengths. This increase in angular resolution is very interesting for detecting a true Kuiper Belt analogue (Section 7). The higher the spatial resolution, the larger the ‘volume’ and hence potential sample size available for searching for true Kuiper Belt analogues (Figure 18). The most stringent constraint here is in fact the level of PSF stability for far-IR imaging that is required to detect the faint disk emission with sufficient confidence (see Section 7).

10. Conclusions

This white paper describes the unique science questions that a spectroscopic infrared space mission such as SPICA can answer. Mid- to far-IR infrared spectra will uniquely measure the gas masses of disks (HD, CO ladder) and the water/ice content and determine how these evolve during the planet-forming period. The key measurements of infrared lines (e.g., HD, OH, water, mid- to far-IR fine structure lines) will pinpoint the crucial transition when disks exhaust their primordial gas and further planet formation may use secondary gas produced from planetesimals. The mid-IR high spectral resolution is also unique in determining indirectly from the water line profiles the location of the snowline dividing the rocky and icy mass reservoir in the disk and how this evolves during the build-up of planetary systems. Infrared spectroscopy (mid- to far-IR) of key solid state bands (e.g., forsterite, enstatite, hydrosilicates, calcite) is crucial for assessing whether extensive radial mixing, which is part of our Solar System history, is a general process occurring in all planetary systems. The combined gas, dust, and ice observations of debris disks will assess whether extrasolar planetesimals are similar to our Solar System comets/asteroids.

With SPICA being taken out of the M5 competition, there is no other facility within the next 20 yr that will be able to measure these fundamental quantities in statistically relevant samples of planet-forming disks. Among the facilities that the infrared community is constantly pushing forward are the Origins Space Telescoped proposed as part of the US Decadal Survey and a potential new instrument on the Stratospheric Observatory for Infrared Astronomy (SOFIA) filling the niche of medium- to high-resolution spectroscopy in the 30–120 $\mu\mathrm{m}$ wavelength range. This latter instrument would have less sensitivity compared to SPICA but could serve as a key pathfinder for the brighter objects.