Results from the automated Design Reference Mission constructor for exoplanet imagers

Results from the automated Design Reference Mission constructor for exoplanet imagers Dmitry Savransky, N. Jeremy Kasdin, David N. Spergel a a Princeton University, Princeton, NJ USA ABSTRACT We use our automated Design Reference Mission construction framework to evaluate the performance of multiple direct exoplanet imager mission concepts on a variety of metrics including: total number of planetary detections, number of unique planets found, number of target stars observed and number of successful spectral characterizations. We evaluate designs of self-contained coronagraphs and co-orbiting occulters. Performance is evaluated on simulated universes with differing frequencies of planets and varying expected occurrence rates of different planet types. Keywords: DRM, exoplanets, mission simulation, coronagraphs, occulters 1. INTRODUCTION While extra-solar planets (or exoplanets) are now a fairly common discovery, the bulk of our knowledge about planets outside of the solar system comes from indirect observational methods, each of which is limited by the inherent properties of the technique. To address the desire for more spectroscopic information and a wider variety of exoplanets, a large number of proposals are currently being evaluated for direct imaging planet-finding instruments. Many of these (especially those with the goal of detecting Earth-like planets) are designed to fly on space-borne observatories. A majority of these can be grouped into one of two general categories: internal coronagraphs self-contained systems which use internal optics to remove extraneous starlight, and external occulters a conventional telescope flying in formation with an occulting spacecraft (or starshade) which blocks the starlight. While each particular design group has its advantages and disadvantages (some of which will be discussed later in this paper), and specific instruments have benefited from intensive performance evaluations, there does not yet exist a large body of work comparing the projected science yields of different instruments. Here, we use the planet-finding mission simulation framework first presented in Ref. 1 along with detailed descriptions of multiple instruments to carry out this type of study. 2. MISSION SIMULATION The mission simulation framework employed here is composed of multiple components, each of which has been previously described in detail. Briefly, the framework constructs an end-to-end simulation of an entire planetfinding and characterization mission. A group of target stars is selected based on an instrument and observatory specification and observations are scheduled based on a rudimentary decision modeling algorithm. 1 Simulated planets are randomly assigned to a subset of the target stars and given physical and orbital characteristics drawn from predefined distributions of parameters. Each observation is modeled by combining the description of an arbitrary planetary observation by a direct imaging instrument 2 with an algorithm for calculating minimum required integration times for confirmed detections. 3 A minimum planetary brightness and separation is assumed to calculate the maximum integration time for each target. A detection is assumed only when a planet exists in the simulated system and is detectable in less than the maximum integration time for that system. In the event of simulated planetary detections, spectral characterization is modeled as a search for specific atmospheric components (biomarkers in the case of terrestrial planets). 4 Repeated observations of each target system are scheduled at times calculated to maximize the probability of detection. The selection of each subsequent star Send correspondence to Dmitry Savransky dsavrans@princeton.edu

to observe is made based on a cost function which incorporates the star s single visit completeness, 6 the amount of time available for observation, 7 and the observatory specific costs of switching the field of view to that star. 1 By varying the weights on the various cost function terms, we can prioritize different science yield metrics and operational costs, and simulate varying mission rules. By executing the simulation multiple times, we produce an ensemble of mission simulations, which generates distributions of science yield metrics for the planet-finding architecture being studied. 2.1 Instrument Design The two classes of direct detection instruments evaluated here have operational properties which lead to direct tradeoffs in science yield. For any starlight suppression system, we can define an inner working angle (IWA) - the angular separation between the star and planet beyond which the planet can be resolved from the suppressed star signal. We assume that all of the instruments studied here are designed such that the optical throughput is a function of the angular separation, having some maximum value at high separations and going smoothly to zero as the separation goes to zero. We thus define the IWA at the angular separation corresponding to the point where the throughput is % of its maximum value. Coronagraph IWAs are wavelength dependent, and extremely precise wavefront control is required to suppress starlight at small angular separations. Occulter IWAs are determined by the starshade size and separation distance from the telescope and are wavelength independent. This removes the wavefront control problem, but introduces a positioning control problem, and requires that much of the mission lifetime be spent on transiting the starshade between targets. This difference has a profound impact on spectral characterization. For an occulter, if the planet is observable, then a full spectrum is always achievable, given enough time. A coronagraph, on the other hand, may not be able to ever see a planet in higher wavelengths, regardless of how much observation time is available. In addition, while the occulter has an effective throughput of 1 for angular separations greater than the angle defined by the starshade diameter and separation distance from the telescope, even the most optimistic coronagraph designs have maximum throughputs of less than unity, which lead to longer integration times for the same telescope diameter. On the other hand, the fact that the occulter must be repositioned in between observations of different stars means that a coronagraph on the same telescope will always be able to perform more observations in the same amount of time. The specific times involved vary with starshade size and propulsion system, but given the state of the art in propulsion and current starshade designs, occulter transfer times are on the order of 1 2 weeks for the smallest starshade considered here, which typically translates to less than % of available mission time going to exoplanet observations. The occulter repositioning also introduces an additional cost starshade propellant mass that must be monitored. Given a fixed launch vehicle payload capacity, the amount of fuel carried by the starshade spacecraft is strictly limited, and may be exceeded during the mission lifetime if steps are not taken to minimize fuel expenditures during transfer slews. Table 1. Occulter Designs. Telescope Occulter Starshade Separation % Throughput Starshade Petal Diameter (m) Type Radius (m) Distance (km) IWA (mas) Mass (kg) Length (m) 4.6 7 9 19 / 7. 337 8 3.2 96 6 71 24 27.2 74/236 3 49 13. 16m 43.2 118/8316 47 22 21. For s, the first separation distance is used for covering 2-7nm, and the second for 7-nm. The same design is used for the 1m telescope. Note that the throughput discussed here relates only to the starlight suppression system and ignores any downstream optics.

To study these various system properties and the science yield tradeoffs, we consider four specific systems - two high-throughput coronagraphs with IWAs at 2 and (wavelength/telescope diameter), a single distance occulter (), which performs all observations at one separation distance from the telescope, and a multiple distance occulter (), which performs planetary detections and covers half of the spectral band at one separation distance and the remainder of the spectral band at a smaller separation. The was originally created to alleviate the very tight tolerances on starshade manufacturing and positioning, and requires a smaller starshade than the for the same telescope size. We pair these starlight suppression systems with circular aperture telescopes of varying diameters. While larger telescopes do not require significant changes in the modeled coronagraphs (we assume that optics of any required size would be available), the size of the starshade needed increases with telescope diameter, which means that the separation distance from the telescope must be increased as well, to produce the same geometric IWA. Of course, if we were to design occulters with IWA scaling inversely with the telescope diameter (as occurs with coronagraphs), we would need even larger starshades than the ones described here. If we assume a fixed propulsion system and launch vehicle payload capacity, this leads to a direct tradeoff between telescope size and occulter efficacy, as the larger occulters will be more massive and have to travel larger distances when retargeting, leaving less time for observation. Table 1 describes the various occulter designs used in this study. Table 2 lists the portion of mission time used for observation, and the total number of stars available for each instrument, about which an Earth-twin in the habitable zone could be observable. Table 2. Observation Times and Target Pools. Telescope Diameter (m) Suppression System Mission Portion Available Targets 19% 112 4 % 117 % 173 % 1 7% 1 8 8% 7 % 3 % 2 4% 242 16 % 38 % 31 This refers to how much of the mission time (on average) is used for planet finding science. For occulters, it is determined by the amount of time required for slewing. For coronagraphs it is set at % to account for time allocations for other instruments sharing the observatory. The same design is used for the 1m telescope so the target list is the same, but due to longer required integration times, this system uses % of the mission time for observations. 2.2 Science Yield Metrics The metrics selected to measure science yield stem from the science goals set for the simulated planet-finding missions. We sought to optimize the science yield of a mission by simultaneously maximizing the number of unique planets discovered, the number of spectral characterizations of discovered planets, the number of planets observed a sufficient number of times to produce orbital fits, and the portion of the target list observed at least once. This last goal was included since there is scientific merit in any observation, whether or not a planet is detected (in the form of disk science and concurrent observations by other instruments on the observatory), and this provides a balance to the inherent decision algorithm bias towards higher completeness stars. This leads to more unique planet detections in the course of a mission, at the cost of a larger number of repeated detections. 3. RESULTS For each of the instruments described in 2.1 an ensemble of mission simulations was generated over simulated universes containing only Earth-twin planets, a fixed mission length of years, and fixed target lists selected

2 All Detections 3 1 Spectral Characterizations between 2 and nm 1 1 9 9 8 7 Figure 1. Simulation results for the,, and the 2 and coronagraph mission concepts as functions of with a 4m telescope for Earth-twin planetary populations. The lines represent median values for simulations at each value of. Error-bars represent the one-sided deviations of each distribution. The top left plot shows the total number of planets found (including multiple detections of the same planet), the top right plot shows the number of unique planets found, the bottom left plot shows the number of unique target systems visited during the mission, and the bottom right plot shows the total number of complete spectra (2-nm) acquired. from a pool of real stars within pc of the solar system. Each ensemble consists of simulations with varying assumed frequencies of Earth-like planets ( ). Figures 1 to 3 show the median values of the four science yield metrics for the four instrument designs for telescopes with circular apertures of 4, 8 and 16m diameters. The error-bars represent the one-sided deviations of each distribution. No was evaluated for the 16m telescope because the starshade is so large that little significant science can be achieved during a year mission with the propulsion system used here. These figures illustrate very well the inherent tradeoff between telescope size and achievable science with an occulter. As larger starshades become necessary, unless there is a significant improvement in the propulsion system, the science yield for a fixed mission length decreases. Although it is possible to achieve higher thrust with more power this requires increasing the size and mass of the power subsystem, and leads to another tradeoff. This trade study is an important future task, and one for which this framework is well suited.

All Detections 7 2 1 6 1 4 Spectral Characterizations between 2 and nm 1 1 1 3 1 9 Figure 2. Simulation results for the,, and the 2 and coronagraph mission concepts as functions of with an 8m telescope for Earth-twin planetary populations.. At the 4m scale, the occulter and coronagraph mission concepts are competitive in different science yield metrics. For total number of detections, the coronagraphs are the clear winners, with many times as many detections as either of occulter designs. These results may be slightly misleading, since they represent, for the most part, many repeated detections of a small number (usually fewer than ) highly visible planets. However, this demonstrates the advantage of being able to perform many more observations over the course of the mission and, with improvements to the scheduling algorithm, should be translatable into a larger number of orbital fits for the coronagraphs. The two occulters average less than two detections per unique planet found, which means that they are generally unable to get more than one orbital fit in five years of mission time. For unique planet detections, the two occulters perform almost identically, finding about % fewer planets than the coronagraph and % more than the coronagraph at = 1. This result is almost purely a function of having a limited target list in a universe with a uniform distribution of isotropically positioned stars, we would expect the coronagraphs larger total number of observations over the mission lifetime to produce proportionately more unique detections. As we are limited to existing stars, all of the instruments are able to find all of the easily observable planets within five years and the greater number of visits made by the coronagraphs translates into only a few more unique detections. At this telescope scale, all of the designs consistently find

fewer than half of the available planets in a given universe. All Detections 2 9 7 6 1 1 Spectral Characterizations between 2 and nm 16 1 9 7 6 1 6 Figure 3. Simulation results for the, and the 2 and coronagraph mission concepts as functions of with a 16m telescope for Earth-twin planetary populations. The coronagraphs large number of detections is balanced by their relatively poor performance in terms of spectral characterization. Because of their wavelength dependent IWA, and the fact that detections for Earth-like planets will occur at relatively low separations, 6 in most cases the coronagraphs are capable of only a partial spectrum between 2 and nm. We see that the gets slightly fewer full spectra than the (which has difficulties getting full spectra due to the extra required slew for the longer wavelength characterizations), but both are outperformed by the single distance occulter. The coronagraph is highly IWA limited, and gets many fewer full spectra than any of the other designs. From these metrics, we can conclude that for a 4m telescope, coronagraphs and occulters are both viable options, as long as a IWA is achievable, and that the decision as to which instrument to build should be made based on other considerations, including the relative difficulties of wavefront control versus starshade manufacturing and positioning. For the 8m telescope, we start to see significant disparity between occulter and coronagraph performance, due completely to the smaller amount of observation time available to the occulters as more time is spent slewing between targets. Even so, the occulter designs still produce non-negligible science yield, with the finding as many as 37 unique planets at = 1. The is now outperforming the, since the starshade

required to cover the entire spectral band at one separation distance is much larger than the. At this scale, coronagraphs clearly produce higher yields in all four science metrics. However, the problems of telescope stability and wavefront control become more difficult with larger telescopes. It may turn out that achieving even is exceedingly difficult. If this is the case, then occulter are still a viable alternative, even if there are no improvements in propulsion technology beyond what is modeled here. All Detections 1m 4m 8m 16m 3 1m 4m 8m 16m Spectral Characterizations between 2 and nm 9 9 8 18 16 14 12 1m 4m 8m 16m 7 8 7 6 6 1m 4m 8m 16m 6 4 2 Figure 4. Simulation results for s with 1, 4, 8, and 16m telescopes for Earth-twin planetary populations. With the 16m telescope, the disparity between coronagraphs and occulters is so great that it becomes very difficult to argue for the benefits of an occulter, as modeled here. The extremely large starshade required even by the makes transit slews take so long that less than % of a mission is typically spent on observation. This leads to multiple instances of zero detections at lower values of, meaning that this mission design could be a complete failure in terms of finding planets in this population. Of course, these results would be very different if we considered a system of multiple starshades operating with one telescope, as proposed in Ref. 8. With each additional starshade, the average transit slew time decreases, improving the science yield. In fact, one can design a constellation of starshades such that there is a guaranteed maximum retargeting time, in which case the occulter would operate much like a coronagraph system, with near constant overhead time per observation. Compared with an 8 or 16m telescope, the cost of each starshade is relatively low, making multiple starshades a reasonable approach. Thus, we conclude that at current propulsion technology levels, an occulter system with

a single starshade is not a suitable starlight suppression system for telescopes greater than 8m in diameter. The coronagraphs continue to perform well at the larger scales, with the wavelength dependence of the IWA becoming much less of a problem for this specific planetary population Figure 4 compares all of the designs, including one for a 1m telescope. This smaller class of telescope represents a much less expensive option, which has previously been evaluated as a possibility for a smaller scale planet-finding mission. 9 At this aperture size, a coronagraph is essentially useless for terrestrial planet-finding since an IWA at even the telescope s diffraction limit would completely cover the habitable zone for most target stars. Since the occulter s IWA is determined solely by the starshade geometry, this problem does not exist, and the 1m simulated here can use the same starshade and target list as the 4m version. The scheduling algorithm is able to produce a large number of detections with the 1m (about % fewer than the 4m ) by visiting a smaller number of unique target stars during the mission. Of course, there is no way to improve the longer integration times required by the smaller telescope aperture, which means that the 1m gets relatively few full spectra in the course of a mission, performing on par with the 16m version. Still, these results are encouraging, suggesting that a 1 or 1.m telescope with an occulter could provide useful science while proving the technology for larger scales at a much lower cost. Figure compares all of the coronagraph designs, showing the progressive improvements in all metrics with telescope size, and the decreasing importance of the IWA wavelength dependence for this planetary population. Another point of interest is how quickly we will be able to tell whether an instrument is working as designed. Figure 6 shows histograms of first planet discoveries as a function of mission time for the 4 and 8m telescope. For high values of, most of the instruments usually have their first detection in the first month of the mission, but as we see in the figure, at =.3, it may take many months before an initial detection. The two coronagraphs still have their first detections within the first month, but the and designs may take up to 6 months before having the same probability of a first detection. The results are essentially the same for the 4 and 8m telescope instruments with two interesting exceptions. The coronagraph appears to actually have a lower probability of a first detection in the first month with an 8m telescope than with a 4m telescope. This is due to the expanded target list available to the 8m telescope. Because there are now many more targets to consider, and we ve assumed a constant rate of planet occurrence, it is unsurprising that it takes more visits, on average, before a detection is made. The second interesting feature of these histograms is that the appears to have a higher probability of first detection in the first month than the. Again, this is due to the available pool of targets and the number of visits made by each. At the 8m scale, the is able to make significantly more visits than the. Since the makes fewer total detections than the, and visits to high completeness stars (which have highest probabilities of detections) occur early in the mission, the at this scale either gets its first detection early on, or much later in the mission during revisits to these stars or at lower completeness targets. This is evidenced by the large percentage of first detections which occur more than 1 year into the mission for the 8m. Besides varying telescope scales, we can also explore the performance of the same instruments on varying planetary populations. As a first step, we improve slightly on the overly simplistic Earth-twin only population by including habitable zone Super-Earths - rocky planets of 1 to M and radii determined by randomly generated ice-rock-iron proportions. Unsurprisingly, the trends found with this planetary population (Figure 7) are, for the most part, the same as those seen in Figure 1 with an Earth-twin only population, but with larger values for most of the metrics, since Super-Earths are, on average, easier to detect than Earth-twins. With this population, in terms of unique planet detections, the two occulters and the coronagraph are virtually indistinguishable, with the coronagraph finding about % fewer unique planets. Due to the larger number of detections (which translates to longer observation times for characterization), a slightly smaller subset of the target list is typically visited than with the Earth-Twin only population. For spectral characterizations, we find that the coronagraph does much better than before, nearly matching the performance of the coronagraph. Again, this is most likely due to the differing available targets for each, and suggests that the coronagraph s performance in this metric could be improved with scheduling and target selection optimization. The same size starshade is required for both the 1 and 4m telescopes because the smaller telescope aperture spreads the point spread function, requiring a relatively larger level of suppression to produce the required contrast at the same IWA.

All Detections 2 1 4m 4m 8m 8m 16m 16m 9 7 6 4m 4m 8m 8m 16m 16m 1 Spectral Characterizations between 2 and nm 17 16 1 1 1 1 1 9 4m 4m 8m 8m 16m 16m 9 7 6 4m 4m 8m 8m 16m 16m Figure. Simulation results for coronagraphs with 4, 8, and 16m telescopes for Earth-twin planetary populations. 4. CONCLUSIONS In comparing occulter and coronagraph based planet-finding architectures in terms of unique planets discovered and spectrally characterized, we find that the relative performance depends significantly on telescope aperture. At the 4m diameter aperture scale, we find comparable performance between the systems, with the coronagraphs producing more total detections due to more available observation time, but fewer spectra due to wavelengthdependent IWA limitations. While coronagraphs are not a viable option for Earth-twin detection with telescopes smaller than 2m, we find that an occulter system with a 1m diameter aperture is able not only to find Earth-twins, but also spectrally characterize up to planets when = 1. We find that at the 8m scale, coronagraphs begin to outperform single starshade occulter designs in all science metrics, and that at the 16m scale, occulter designs with our assumed propulsion system do not justify their cost unless the system includes multiple starshades. Before occulters may be considered as suitable for larger telescopes, significant progress needs to be made in propulsion systems, and a trade study carried out to find the optimum balance between delivered thrust and power plant mass. At the same time, further work needs to be done in designing and simulating constellations of starshades. A detailed cost-benefit analysis must be carried out to select the optimum number of starshades, and the scheduling algorithm used here must be reformulated to take advantage of a constellation occulter system. However, if insurmountable difficulties are encountered

First Detection for =.3 First Detection for =.3 Percent Cases 6 Percent Cases 6 1 2 3 4 6 7 8 9 11 12 >1 year Months after Mission Start 1 2 3 4 6 7 8 9 11 12 >1 year Months after Mission Start Figure 6. Histograms of first planet detections vs. months after mission start for the 4m (left) and 8m (right) telescope instrument designs. in attempting to construct a small IWA coronagraph for large telescopes, we believe that multiple starshade occulter systems could represent a viable alternative. At the present technology levels, we find that occulters are much better suited for smaller scale telescopes than coronagraphs and predict that the an occulter represents the best chance of finding Earth-like planets with a telescope smaller than 4m in diameter. Finally, in studying a population of Super-Earths we find that the increased number of targets made available by this population is actually larger than can be fully searched and characterized in a year mission. In this case the scheduling algorithms that produce near-optimal results for Earth-twin populations (simultaneously maximizing all metrics) do not perform as well in terms of the planet detection and characterization metrics, mostly due to the mission goal of maximizing the number of targets visited. Because this population increases the total number of targets and introduces more targets with relatively low completeness values, it becomes necessary to either put tighter restrictions on the target pool, or weight the importance of the unique detection metric much more than the unique target system metric. Our simulations suggest that the best performance may be achieved when the target list is restricted based on a given architecture s number of possible observations per mission. ACKNOWLEDGMENTS The authors would like to thank Eric Cady for his work on occulter design, Doug Lisman for his starshade propulsion system design, and Don Lindler for helpful discussion and model validation. This work was supported by the NASA ASMCS program as part of the THEIA study. REFERENCES [1] Savransky, D. and Kasdin, N. J., Design reference mission construction for planet finders, in [Space Telescopes and Instrumentation 8: Optical, Infrared, and Millimeter], J. M. Oschmann, J., de Graauw, M. W. M., and MacEwen, H. A., eds., Proc. SPIE 7, SPIE (8). [2] Brown, R. A., Obscurational completeness, ApJ 67, 3 17 (4). [3] Kasdin, N. J. and Braems, I., Linear and bayesian planet detection algorithms for the terrestrial planet finder, ApJ 646, 126 1274 (6). [4] Des Marais, D., Harwit, M., Jucks, K., Kasting, J., Lin, D., Lunine, J., Schneider, J., Seager, S., Traub, W., and Woolf, N., Remote sensing of planetary properties and biosignatures on extrasolar terrestrial planets, Astrobiology 2(2), 3 181 (2).

All Detections 2 1 4 3 Spectral Characterizations between 2 and nm 1 1 9 3 9 8 7 7 Figure 7. Simulation results for the,, and the 2 and coronagraph mission concepts as functions of with a 4m telescope for Super-Earth planetary populations.. [] Savransky, D. and Kasdin, N. J., Return visit optimization for planet finding missions, in [AAS Bulletin], 39(4), 134, AAS (7). [6] Brown, R. A., Single-visit photometric and obscurational completeness, ApJ 624, 24 (). [7] Lindler, D. J., TPF-O design reference mission, in [UV/Optical/IR Space Telescopes: Innovative Technologies and Concepts III], MacEwen, H. A. and Breckinridge, J. B., eds., Proc. SPIE 6687, 14 1 14 9 (7). [8] Hunyadi, S., Lo, A., and Shaklan, S., The dark side of TPF: detecting and characterizing extra-solar earthlike planets with one or two external occulters, in [Proc SPIE], 6693, 6693 (7). [9] Hunyadi, S., Shaklan, S., and Brown, R., The lighter side of TPF-C: evaluating the scientific gain from a smaller mission concept, in [Proc SPIE], 6693, 669Q (7). [] Fortney, J. J., Marley, M. S., and Barnes, J. W., Planetary radii across five orders of magnitude in mass and stellar insolation: application to transits, Astrophysical Journal 69, 1661 1672 (7).