1.

INTRODUCTION

With more than 4300 discovered exoplanets and more than 5700 exoplanets still waiting confirmation^∗, we are in a new era of exoplanetology. These exoplanets were mostly detected by the transit and the radial velocity methods. Even if some information about hypothetical atmospheres can be derived, they are unfortunately poorly constrained for most of theses planets. The next big step is clearly to spectrally characterize them and search for biosignatures, especially for rocky planets in the habitable zone of their stars. Nulling interferometry is one of the most promising direct methods to tackle this challenge in the mid-IR (3-20 μm) domain. This high-contrast observation technique removes the dominant flux of the host star and provides the required angular resolution. On Earth, the thermal background of the atmosphere is the main limitation and decreases drastically the potential detection yield.¹ A space-based nulling interferometer is therefore needed.^{2, 3} Such a project is currently under study under the name of LIFE (Large Interferometer For Exoplanets). The idea is to position a free-flying interferometer in the Earth-Sun L2 point. This mission has the potential to detect more than 500 exoplanets including 10-20 Exo-Earth, according the last detection yield estimate.^{4, 5}

Often discussed in the community, a precursor may be needed for this L-class mission.^{3, 6} Such precursors were also discussed in the 2000’s when both Europe and the US were developing their own large free-flying space-based nulling interferometers (resp., Darwin and TPF-I). It was PEGASE^{7, 8} for Europe, Fourier-Kelvin Stellar Interferometer (FKSI)^{9, 10} or Cold Interferometric Nulling Demonstration in Space (CINDIS)¹¹ for the US. Unfortunately, none of them ever flown.¹²

With the cost-effective capabilities of small satellites (< 500 kg) and the emergence of CubeSats in the 2010’s, it is now relevant to analyse this type of platform for astronomy.^{13, 14} In the exoplanet domain, CoRoT (Convection, Rotations et Transits planétaires), from CNES, was a pioneer in 2006¹⁵ and opened the way to Kepler but these two missions were quite larger than S-class missions. TESS (Transiting Exoplanet Survey Satellite) or CHEOPS (CHaracterising ExOPlanets Satellite), both in duty, are smaller and can be considered as small satellites. With even lower costs and smaller size, we can cite ASTERIA, a 6U CubeSat who measured in 2017-2018 the transit of a known exoplanet, 55 Cancri e, and achieved very high stability.¹⁶ Even if a smaller mission cannot, of course, surpass M or L-class missions, it shows that a precursor of a larger mission has scientific capabilities.¹⁷ Today, new projects are being studied, such as FIRST-S, a 3U CubeSat to study exozodiacal light in the habitable zone around the closest stars,¹⁸ based on the lessons learned from the PicSat mission, a 3U CubeSat planned to measured the possible transit of the giant planet β Pictoris b’s Hill sphere.¹⁹ There are also two 6U Cubesat, CUBESPEC, which has the goal to do near-UV/optical/near-IR spectroscopy of massive stars, low and intermediate mass stars or transiting exoplanets²⁰ and CUTE (Colorado Ultraviolet Transit Experiment), which has to goal to quantify atmospheric mass loss and magnetic fields of transiting hot Jupiters in the near-UV.²¹ On a more theoretical and technological project, the Australian National University is looking to demonstrate a linear formation-flying astronomical interferometer in low Earth orbit.²² It also exists high-altitude experiment such as Balloon Experimental Twin Telescope for infrared interferometry (BETTII), a double-Fourier Michelson interferometer placed on a high altitude scientific balloon which flown in 2017²³, or Planetary Imaging Concept Testbed Using a Rocket Experiment (PICTURE), a sounding rocket with a visible nulling coronagraph which flown in 2015.^{24, 25} Astronomical CubeSats, smallsats, or projects will emerge more and more in the future.^{13, 14, 17} In the present project, the idea is to focus first on a science case and then derive constraints on a small platform. The main goal is to know if a CubeSat or a slightly larger spacecraft can be both a scientific mission on its own and a precursor to a larger mission as LIFE. No free-flying is considered, both pupils are located on one spacecraft. As achieving interferometry in space would already be quite challenging on such a small platform, it seems more relevant to have a specific mission for that part or rely on previous missions. In fact, formation flying was already partially demonstrated by the PRISMA mission²⁶ and will be improved by PROBA-3.^{27, 28}

In Ref. 29, we have presented our first results. We have considered four configurations, from small to medium satellites. The main objective was to develop our tool and present our first analyzes. Based on a planet population synthesis tool, we showed that, even without considering platform stability constraints, CubeSats can hardly detect giant exoplanets. A PROBA-like mission could detect more than 120 putative exoplanets and a more ambitious mission such as the former FKSI could detect 250 exoplanets around 326 nearby main-sequence stars (distance < 20 pc). One of our conclusions is that small platforms are well suited to test and validate critical technological components needed for a larger mission as well as perform scientific observations.²⁹ In Ref. 30, we have updated our results and focused on the optical train temperature, the optical path difference (OPD), and the relative tip/tilt angle wavelength dependencies. We showed that the instrumental operating wavelength has a lower impact as previously thought. We also applied our tool to nearby exoplanets (28 nearest) and applied the same methodology as in Ref. 29 to these planets.³⁰

In this paper, we focus on the instrumental requirements of the platform. In Sec. 2, the mission architecture is defined. It is then followed by our science objectives (Sec. 3). In Sec. 4, we reviewed every important module of a Bracewell nulling space-based interferometer and the related requirements. In Sec 5, an analysis about potential orbits is performed and the target visibility is derived for the closest exoplanets.

2.

MISSION ARCHITECTURE

This section describes briefly our main architecture. Each subelement of the optical train will be defined and reviewed in Sec. 4.

In 1978, R.N. Bracewell proposed a space-based interferometer with two pupils and a recombination of light in phase opposition.³¹ It produces a dark fringe on the line-of-sight and the stellar emission is strongly suppressed. For an off-axis source, the light can be transmitted, depending on the baseline length and observing wavelength, which defines the interferometer transmission map. In the following, we will refer as the Bracewell configuration this 2-aperture configuration.

Table 1:

Three small-sat configurations considered in this study.

Three small satellites are considered in this study. They are chosen to cover the CubeSat and the small satellite family. As for Ref 30, we have decided to put aside the former FKSI. Its size and cost correspond to the medium satellite size range.⁹ The pupil diameter and the baseline length of each configuration are fixed to avoid too many variables in the study. Values are available in Tab. 1. Figure 1 represents a basic design of the three configurations. Both pupils are located on the same spacecraft, no free-flying is sought here. Each module location is of course subject to change, as well as their size.

Figure 1:

Design of each three small-sat configurations considered in this study. These are preliminary concepts to help the reader’s understanding. All modules are related to the optical layout (Fig. 2).

3.

SCIENTIFIC OBJECTIVES

Characterizing exoplanet atmospheres is very challenging due to the high angular resolution needed and the large star/planet contrast. With nulling interferometry, both challenges can be tackled. In the mid-infrared, several molecular absorption features are present (e.g., H₂O, CO₂, O₃, CH₄).³² It corresponds to the spectral band sought by LIFE. The orbital parameters can be derived whatever the spectral band. Depending on the waveband, one can measure the planet temperature (mid-IR) or measure the planet radius (mid-IR) or a combination of the radius and albedo (visible - NIR).³³ The science case was already described in a white paper submitted to ESA for the Voyage 2050 long-term plan⁴ and a coming series of articles about LIFE are currently being written (Konrad et al., in prep.).

For the precursor, the main goal is to validate nulling interferometry in space. The scientific objectives are more focused on pure exoplanet detection. At this stage, no spectroscopy is considered since the Signal-to-Noise Ratio (SNR) is quite low and would not be sufficient in the different spectral channels. In Ref. 29, 30, the minimum integrated SNR over the bandwidth was fixed to at least 5 to detect a planet. Mid-infrared is also out of range due to the instrumental temperature of the spacecraft. The instrumental temperature, simulated as a grey body, dominates all other sources.^{29, 30} The exoplanet yield decreases drastically beyond 4-6 μm. The small sat is indeed considered in Low Earth Orbit (LEO), or at least near the Earth (cf. Sec. 5). To decrease the temperature of each collector, LIFE seeks to be in Earth-Sun L2 point. The precursor, by design, therefore, operates in the near-IR (1-4 μm). Once the design will be fixed, several others science cases can be investigated.

4.

PLATFORM REQUIREMENTS

In this section, a review of each element of the optical train is performed. The block diagram in Fig. 2 represents the optical layout of a fibered Bracewell interferometer.

Figure 2:

Block diagram of a fibered Bracewell interferometer optical layout (simplified version of the one shown in Ref. 40).

4.2

Tip/tilt and OPD correction stage

One of the main concerns for nulling interferometry is the stability of the null. It means that tip/tilt errors and optical path differences (OPD) need to be monitored and controlled in real-time. After the telescope module, and before injecting in the single mode fiber, a correction stage is needed.

4.2.1

Tip/tilt correction

Tip/tilt errors can have multiple origins. They can be decomposed in global and differential tip/tilt errors.

The first one occurs when the spacecraft does not point perfectly at the star and wobbles around it. It is therefore directly related to the RMS pointing stability and the absolute pointing accuracy of the spacecraft. A fine attitude controller on the platform is necessary. The outer working angle of our instrument (OWA) is given by 0.514λ/D where λ is the wavelength and D the aperture diameter. Above this angular separation, there is no transmission and therefore no planet signal. For both CubeSats, with λ = 1.5 μm and D = 0.08 m, OWA = 2000 mas while for the PROBA-size sat, with λ = 2.0 μm and D = 0.25 m, OWA = 850 mas. It means that the spacecraft needs to operate in that range of pointing accuracy and stability. Both apertures need to be equipped with angle steering mirrors to compensate pointing errors. These mirrors will also compensate the differential tip/tilt errors as discussed below.

An attitude control with pointing accuracy and pointing stability around the arcsec is quite challenging, especially for CubeSats. ASTERIA is able to perform pointing stability of 1.8 to 4.6 arcseconds RMS over 20 minutes and 0.5 arcseconds with a pointing control subsystem (PCF) inside the payload.⁴² This result is impressive and ASTERIA has, to this date, the best pointing stability performance for a CubeSat. With improvements, and without the PCF, ASTERIA’s team thinks that they can achieve 1.6 arcseconds RMS over 20 minutes for both axes.⁴² It means that this type of attitude controller is well suited for both CubeSats. However, for our application, a longer integration time is needed and it adds some requirements on the stability duration. CUBESPEC uses the same technique, a coarse attitude control of the satellite (0.1 deg) and a pointing control subsystem (fast steering mirror) inside the payload (2 arcsec around each axe).²⁰

For FKSI, preliminary studies show that that 1 arcsecond was achievable.⁴³ Even if the PROBA size is considered in this study, we can not rely on the previously flown attitude control system of the three past missions. PROBA-1 achieved an absolute pointing accuracy of 150 arcsec and a relative pointing stability of 10 arcsec (10 s), PROBA–2 an absolute pointing accuracy of 75 arcsec and a relative pointing stability of 1 arcsec (60 s), and PROBA-V an absolute pointing accuracy of < 20 arcsec and a relative pointing stability of < 1.5s (1.5 s)^‖. It may seem quite large but these missions had no need of a more precise attitude controller. The attitude control of CINDIS was thought to provide a spacecraft platform pointing accuracy better than 3 arcsec in the plane parallel to the target and 30 arcsec along the target direction.¹¹

For the differential tip/tilt errors, the requirements are even more stringent. In that case, the satellite has a zero-mean tip/tilt angle, but it exists an RMS differential tip/tilt angle between both pupils. During the integration time, the two pupils are therefore misaligned by this angle, which is converted to a translation of the PSF in the image plane, i.e., at the tip of the fiber. It creates an intensity imbalance at the output. This value has an impact on the null capability of the instrument.

Figure 3 represents the number of detections as a function of the wavelength and the RMS differential tip/tilt for the three considered configurations. The number of detections is derived from the Monte-Carlo simulation tool (Sec. 3-2). Above 25 mas, already half of the 6U CubeSats detections are not available and for the PROBA-size, 35 − 40 mas seems to be the goal to not loose any detections. These requirements lead to specific optics, as angle steering mirrors to compensate the errors. In CINDIS, the tip/tilt actuator was thought to achieve ±1.5 arcsec equivalent sky angle.¹¹ For FKSI, thanks to a good control model, it results in less than 10 mas of spacecraft attitude error in roll and pitch.⁴³

Figure 3:

Number of detected planets with the three configurations defined in Tab. 1 as a function of the operating wavelength (spectral resolution, R = 1.2) and the RMS differential tip/tilt. A planet is considered as detected if the SNR is a least 5 with an integration time of 24 h. Instrumental temperature: 200K for both CubeSats and 150K for PROBA. No OPD perturbations considered.

In 2008, a performance study of both PEGASE and FKSI was performed. Thanks to a end-to-end simulation and vibrational studies of both satellites, the control loop performances were derived. Tip/tilt errors can be reduced down to 15 mas for PEGASE and 20 mas for FKSI.⁴⁴

4.2.2

OPD correction

The first order optical path difference (OPD) is a pure piston that is not corrected by the single-mode waveguide. Higher-order aberrations are corrected by the fiber and converted into an intensity imbalance at the output of the fibers. They are not considered in this study.

Figure 4 represents how the residual OPD affects the number of exoplanet detections. The wavelength dependency is also presented. The impact on the exoplanet yield is important and a maximum of 5nm of OPD RMS is allowed for the PROBA-size configuration to avoid any large drop of detections. For the two CubeSats, any large deviation will lead to a non-detection scenario.

Figure 4:

Mean number of detected planets with the three configurations defined in Tab. 1 as a function of the operating wavelength (resolution parameter, R = 1.2) and the residual optical path difference. A planet is considered as detected if the SNR is a least 5 with an integration time of 24 h. Instrumental temperature: 200K for both CubeSats and 150K for PROBA. No tip/tilt considered.

On small space-based platforms, OPD error can be corrected by a piezo mounted mirror and not by large delay lines as on the ground. FKSI had two corrector stages, one coarse just after the siderostat and one fine (only 2 microns of stroke) in the nuller part. Both are cats eye delay line mechanisms (two confocal parabolas).43, 45 Their Matlab Simulink simulations show a correction on the order of 3.5−5 nm. For Pegase, only one stage was planned before the tip/tilt correction. The cat’s eye system had a ±1 cm stroke and 1nm rms resolution.⁴¹ For CINDIS, the system was thought to be an actuator on a flat relay mirror with a stroke of ±15 μm.¹¹

In the same 2008 study as the tip/tilt, control loop performances for the OPD for both PEGASE, and FKSI were derived. PEGASE OPD can go down to 1.7nm RMS and FKSI down to 2nm RMS.⁴⁴

4.3

Fiber injection

Both apertures of the interferometer focus the light into single-mode optical fibers of the same length to avoid any chromatic dispersion.³⁵ They were not present in the Bracewell proposal, but their addition leads the correction of phase defects of the incoming wavefront, except a relative piston.^{31, 36} Each single-mode waveguide has a coupling efficiency, ρ_i, and only the fundamental mode is propagated if we work close to or below the cutoff frequency.⁴⁶ This fundamental mode can be approximated by a Gaussian pattern and the circular pupil creates an Airy pattern on the focal plane. Due to the mismatch between both profiles, the coupling efficiency reaches a maximum value of ≈ 81% and not 100 %. A real fiber tends to achieve this value, but due to approximations (not a pure Gaussian pattern) and due to Fresnel reflections on the fiber head, it is reduced to a maximum of 78 %.⁴⁷ Any aberrations, geometrical or physical, like a tip/tilt or central obstruction, decrease the coupling efficiency and can lead to very low transmission.³⁶

At this stage, there is no central obstruction due to a secondary mirror in the telescope design. If it may be necessary, it will lead to a drop of coupling efficiency as shown in Fig 5. In Figure 5a, the wavelength dependency is presented. The numerical aperture of the fiber is 0.16 and the cut-off wavelength is λ_c = 1.5 μm. The coupling efficiency is optimized (maximum) for λ_opt = 2.5 μm. Three central obstructions are selected: 0 (no obstruction), 0.25 (Hubble Space Telescope) and 0.436 (ESO 3.6m telescope).⁴⁸ As expected, the coupling efficiency is mainly achromatic over a band [λ_c, 2λ_c] and decreases afterwards, whatever the central obstruction.³⁶ However, a high α has a drastic impact on the coupling efficiency, unless an additional optic is added to reshape the Point-Spread-Function (PFS) before the injection to match the Gaussian pattern of the fiber. Figure 5b shows the drop of maximum coupling efficiency as a function of the central obstruction. Since only a few planetary photons reach the instrument, we have decided to focus on a no obstructed design. Aberrations related to this choice (mainly coma) will be assessed in a future work. It also means that some fold mirrors will be necessary to keep a small compactness. FKSI, PEGASE and CINDIS were also fibered but with injection after the recombination stage since this part was done using classical bulk optics.^{11, 41, 45}

Figure 5:

Coupling efficiency of the single-mode fiber (N.A. = 0.16) as a function of (a) the wavelength with varying central obstruction α and (b) the central obstruction at the optimal wavelength (λ_opt = 2.5 μm).⁴⁸

5.

MISSION ORBITS

The orbit of such a mission is a key factor since it dictates the sky availability as well as all environmental factors to which the spacecraft is submitted. CubeSats are mostly deployed in Low-Earth Orbit (LEO), protected from the harsh conditions of deep space by the Van Allen Belts. Even with that natural protection, space radiation is one of the main contributors to CubeSats failures. For small satellites, like the PROBA-ones, one can think about more peculiar orbit but due to cost issues, we have restricted our analyze to classical Earth orbits. FKSI and PEGASE were heading the Earth-Sun L2 point^{41, 45} but it seems quite optimistic and unrealistic for a small mission to target this location. Even if a classical Sun-synchronous orbit was analyzed for CINDIS, they decided to go to a Earth-Trailing orbit. They estimated, at that time, that the cost saving of classical LEO was not sufficient regarding the advantages of a drift-away orbit (temperature, sky-visibility, etc.).

In our study, we have considered two main orbit families : circular orbits (Hubble, ISS, geostationary, Sun-synchronous, and polar orbits) and elliptical orbits (Molnya, XMM-Newton, geostationary transfer, and SMILE orbits).⁵⁵

For each orbit, we looked to the sky availability. The question is to know if the satellite can target an exoplanet without any obstruction (Sun, Earth and Moon) and for how long. For that, the five most promising systems closest to the Earth, at the time of the study, were selected (Proxima Centauri, Barnard’s Star, Epsilon Eridani, Ross 128, and Tau Ceti) and five figures of merit were derived:⁵⁵

As expected, FoM1 tells us that all elliptical orbits offer better visibility performance. The higher the altitude, the better the performance. It means that for LEO orbit, like typical Sun-synchronous orbits, an altitude of 800km is more favorable. Figure 6 shows the percentage of visibility during 1 year for all considered orbits. To be conservative, an antisolar constraint is taken. It means that the spacecraft can not target towards the sun (a virtual cone with a half aperture angle of 90 deg is selected).²⁹

Figure 6:

Mean observation time with the antisolar constraint. The calculated percentage is the ratio of observable time to total time. XMM = XMM-Newton, SMI = SMILE (120 or 0 is the right ascension angle), MOL = Molnya, GEO = geostationary transfer orbit, GTO = geostationary orbit, POL = polar orbit (896 km), SSO = Sun-synchronous (800 or 400 is the altitude in km), HUB = Hubble, and ISS = International Space Station.⁵⁵

To go deeper, and even if FoM1 gives a good overall picture, FoM2 tells us when and where the satellite is obstructed by the Sun, the Earth or the Moon. In our radiometric model, the integration time is limited to 24 h.^{29, 30} It means that no obstruction is needed during that time. It leads to the FoM3. In fact, some orbits, like the International Space Station (ISS) orbit, never allow more than one hour of continuous visibility. Sun-Synchronous orbits are a better choice since most of the star systems can be observed during quite a long time. Elliptical orbits are of course more suited for long observations as the Earth obstruction is reduced. Nevertheless, the antisolar constraint leads inevitably to a drop of 50% of visibility on each target since during 6 months, the Sun is blocking the view.⁵⁵

FoM3 gives us the average duration of the observation period. Results are available in Tab. 2. It shows that LEO offers quite low visibility over time and that 24 h of integration over a target is on average not feasible. However, since it is a mean value, during some periods of the year, it is possible to target continuously a star during 24 h (FoM4). Figure 7 represents, in an annuli way, the performance of 6 best orbits. Each of the annuli accounts for a star. If the ring portion is white, the star cannot be observed more than 24 hours continuously at this time of the year. If the portion is green, it means that the line of sight is clear all day long. Red sectors represent periods in which the star is not visible due to the antisolar constraint. Even if the average duration of the observation period is not optimal (Tab. 2), Sun-synchronous orbits, especially at high altitude, are still good candidates. They offer visibility on stars all over the years and they are accessible for CubeSats and small satellites. With an altitude below the Van Allen belts, they also offer protections from radiations unlike elliptical orbits (FoM5).

Figure 7:

Annulus representation of the visibility for six orbits in the antisolar case. If portion of the annulus is green, the target is observable all day long without interruption. If the sector is white, there is at least one occultation within the day. Numbers in some sectors represent the duration of the segment. Red sectors are the green sectors of the ideal case affected by the antisolar constraint. XMM = XMM-Newton, SMI = SMILE (120 or 0 is the right ascension angle), GEO = geostationary transfer orbit, SSO = Sun-synchronous (800 or 400 is the altitude in km).⁵⁵

Table 2:

Average duration of the observation period (m = minutes, h=hour, d=days and y=year) Duration: 1 year. XMM = XMM-Newton, SMI = SMILE (120 or 0 is the right ascension angle), MOL = Molnya, GEO = geostationary transfer orbit, GTO = geostationary orbit, POL = polar orbit (896 km), SSO = Sun-synchronous (800 or 400 is the altitude in km), HUB = Hubble, and ISS = International Space Station.

At this stage, this preliminary orbital study, by taking only 5 planetary systems, gives us some clues on the satellite design. Of course, lots of parameters, as the eclipse time, the temperature (study on-going) or a more general sky visibility needs to be completed to have a refined model.

6.

CONCLUSION

Nulling interferometry is one of the most promising solutions to spectrally characterize exoplanets. In this paper, we investigated three space-based mission architectures using nulling interferometry in a Bracewell configuration that could be a precursor to an L-class mission such as LIFE. It will demonstrate the feasibility of a nulling interferometer in space. The considered spacecraft architectures are two CubeSats, with small apertures and a moderate baseline length (max 1 m) and a PROBA-like satellite with larger apertures (25 cm) and a longer baseline length (5 m).

Thanks to a state-of-the-art exoplanet synthesis tool (P-POP) and a previously presented radiometric budget, we derived instrumental requirements on the optical path difference and the differential tip/tilt angle. The OPD RMS has to be corrected down to 3-5nm and the differential tip/tilt down to 25 − 40 mas to keep a significant exoplanet detection yield.

All main components of the classical optical layout of a Bracewell interferometer are discussed and compared to previous studies about smaller space-based nulling interferometers (i.e., FKSI, PEGASE, and CINDIS) thought to be the precursors of the L-class Darwin (ESA) and TPF-I (NASA) missions. The optical layout study, presented as a block diagram, is on-going and this proceeding is the first step to a more complex study.

Orbits are also a key parameter for a space-based platform. As a precursor and low-cost mission, heading the Earth-Sun L2 point seems unrealistic. Therefore, classical Low Earth Orbits were analysed and presented. Due to the quite long integration time needed, a Sun-synchronous orbit, especially at high altitude, seems to be the more adequate orbit. More peculiar orbits, as high elliptical ones, offer better star visibility but are less common for small satellites. The emphasis was put on the sky visibility but thermal constraints have also to be considered. The thermal behaviour (and stability) is still an on-going study.

A full analysis of the control subsystem (OPD and tip/tilt), with a fine modelization, is needed. These are critical components since the drastic requirements on them for this mission. A 3-apertures interferometer may also be a solution. Thanks to its higher null order (4 compared to 2 with a classical Bracewell), this configuration is less sensitive to tip/tilt errors. However, the complexity of such a configuration needs to be well studied.