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ANALYTIC MODELING OF STARSHADES

External occulters, otherwise known as starshades, have been proposed as a solution to one of the highest priority yet technically vexing problems facing astrophysics-the direct imaging and characterization of terrestrial planets around other stars. New apodization functions, developed over the past few years, now enable starshades of just a few tens of meters diameter to occult central stars so efficiently that the orbiting exoplanets can be revealed and other high-contrast imaging challenges addressed. In this paper, an analytic approach to the analysis of these apodization functions is presented. It is used to develop a tolerance analysis suitable for use in designing practical starshades. The results provide a mathematical basis for understanding starshades and a quantitative approach to setting tolerances.

79 ASTRONOMY AND ASTROPHYSICS↗

Microcracking Study of Carbon Fiber Composite Materials for Starshade Petals

We have conducted materials tests of representative carbon composite materials for starshade petals. The principal goal of these tests is to assess whether the level of microcracking of the materials as the petals are stowed or deployed (or even as they are handled during assembly) is likely to cause a problem with meeting the tight dimensional tolerances required for starlight suppression. Cracking can cause unexpected deformation, and the cracks can act as reservoirs for gases. It may also lead to roughening of the optical edge whose sharpness minimizes undesirable scattering of light. We use mechanical tests, microscopy, acoustic tomography and small‐angle x‐ray scattering to characterize the microcracking. These tests have found no large cracks (>100 microns) at bending strains up to 0.005, the strain at which audible popping occurred. The stress‐strain curves did not display any anomalies until a precipitous drop in stress at a strain of ~0.012 due to the formation of a transverse crack. Analysis of SAXS data is on‐going which will quantify microcrack distributions at the sub‐micron level. We find no large cracks (>100 microns) at the design strain tolerance for non‐critical structural elements (0.005); analysis is on‐going to quantify nanoscale cracking at the strains of critical structural elements (0.0005).

36 MATERIALS SCIENCE↗

NEW COMPLETENESS METHODS FOR ESTIMATING EXOPLANET DISCOVERIES BY DIRECT DETECTION

We report on new methods for evaluating realistic observing programs that search stars for planets by direct imaging, where observations are selected from an optimized star list and stars can be observed multiple times. We show how these methods bring critical insight into the design of the mission and its instruments. These methods provide an estimate of the outcome of the observing program: the probability distribution of discoveries (detection and/or characterization) and an estimate of the occurrence rate of planets ({eta}). We show that these parameters can be accurately estimated from a single mission simulation, without the need for a complete Monte Carlo mission simulation, and we prove the accuracy of this new approach. Our methods provide tools to define a mission for a particular science goal; for example, a mission can be defined by the expected number of discoveries and its confidence level. We detail how an optimized star list can be built and how successive observations can be selected. Our approach also provides other critical mission attributes, such as the number of stars expected to be searched and the probability of zero discoveries. Because these attributes depend strongly on the mission scale (telescope diameter, observing capabilities and constraints, mission lifetime, etc.), our methods are directly applicable to the design of such future missions and provide guidance to the mission and instrument design based on scientific performance. We illustrate our new methods with practical calculations and exploratory design reference missions for the James Webb Space Telescope (JWST) operating with a distant starshade to reduce scattered and diffracted starlight on the focal plane. We estimate that five habitable Earth-mass planets would be discovered and characterized with spectroscopy, with a probability of zero discoveries of 0.004, assuming a small fraction of JWST observing time (7%), {eta} = 0.3, and 70 observing visits, limited by starshade fuel.

79 ASTRONOMY AND ASTROPHYSICS↗

Multi-orbital-phase and Multiband Characterization of Exoplanetary Atmospheres with Reflected Light Spectra

Direct imaging of widely separated exoplanets from space will obtain their reflected light spectra and measure atmospheric properties. Previous calculations have shown that a change in the orbital phase would cause a spectral signal, but whether this signal may be used to characterize the atmosphere has not been shown. We simulate starshade-enabled observations of the planet 47 UMa b, using the present most realistic simulator Starshade Imaging Simulation Toolkit for Exoplanet Reconnaissance to estimate the uncertainties due to residual starlight, solar glint, and exozodiacal light. We then use the Bayesian retrieval algorithm ExoReL{sup R} to determine the constraints on the atmospheric properties from observations using a Roman- or Habitable Exoplanet Observatory (HabEx)-like telescope, comparing the strategies to observe at multiple orbital phases or in multiple wavelength bands. With a ∼20% bandwidth in 600–800 nm on a Roman-like telescope, the retrieval finds a degenerate scenario with a lower gas abundance and a deeper or absent cloud than the truth. Repeating the observation at a different orbital phase or at a second 20% wavelength band in 800–1000 nm, with the same integration time and thus degraded signal-to-noise ratio (S/N), would effectively eliminate this degenerate solution. Single observation with a HabEx-like telescope would yield high-precision constraints on the gas abundances and cloud properties, without the degenerate scenario. These results are also generally applicable to high-contrast spectroscopy with a coronagraph with a similar wavelength coverage and S/N, and can help design the wavelength bandwidth and the observation plan of exoplanet direct-imaging experiments in the future.

79 ASTRONOMY AND ASTROPHYSICS↗

Probing the Capability of Future Direct-imaging Missions to Spectrally Constrain the Frequency of Earth-like Planets

A critical question in astrobiology is whether exo-Earth candidates (EECs) are Earth-like, in that they originate life that progressively oxygenates their atmospheres similarly to Earth. We propose answering this question statistically by searching for O{sub 2} and O{sub 3} on EECs with missions such as HabEx or LUVOIR. We explore the ability of these missions to constrain the fraction, f {sub E}, of EECs that are Earth-like in the event of a null detection of O{sub 2} or O{sub 3} on all observed EECs. We use the Planetary Spectrum Generator to simulate observations of EECs with O{sub 2} and O{sub 3} levels based on Earth’s history. We consider four instrument designs—LUVOIR-A (15 m), LUVOIR-B (8 m), HabEx with a starshade (4 m, “HabEx/SS”), and HabEx without a starshade (4 m, “HabEx/no-SS”)—as well as three estimates of the occurrence rate of EECs (η {sub earth}): 24%, 5%, and 0.5%. In the case of a null detection, we find that for η {sub earth} = 24%, LUVOIR-A, LUVOIR-B, and HabEx/SS would constrain f {sub E} to ≤0.094, ≤0.18, and ≤0.56, respectively. This also indicates that if f {sub E} is greater than these upper limits, we are likely to detect O{sub 3} on at least one EEC. Conversely, we find that HabEx/no-SS cannot constrain f {sub E}, due to the lack of a coronagraph ultraviolet channel. For η {sub earth} = 5%, only LUVOIR-A and LUVOIR-B would be able to constrain f {sub E}, to ≤0.45 and ≤0.85, respectively. For η {sub earth} = 0.5%, none of the missions would allow us to constrain f {sub E}, due to the low number of detectable EECs. We conclude that the ability to constrain f {sub E} is more robust to uncertainties in η {sub earth} for missions with larger aperture mirrors. However, all missions are susceptible to an inconclusive null detection if η {sub earth} is sufficiently low.

74 ATOMIC AND MOLECULAR PHYSICS↗

Characterizing Earth Analogs in Reflected Light: Atmospheric Retrieval Studies for Future Space Telescopes

Space-based high-contrast imaging mission concepts for studying rocky exoplanets in reflected light are currently under community study. We develop an inverse modeling framework to estimate the science return of such missions given different instrument design considerations. By combining an exoplanet albedo model, instrument noise model, and ensemble Markov chain Monte Carlo sampler, we explore retrievals of atmospheric and planetary properties for Earth twins as a function of signal-to-noise ratio (S/N) and resolution (R). Our forward model includes Rayleigh-scattering, single-layer water clouds with patchy coverage, and pressure-dependent absorption due to water vapor, oxygen, and ozone. We simulate data at R = 70 and 140 from 0.4 to 1.0 μm with S/N = 5, 10, 15, and 20 at 550 nm (i.e., for HabEx/LUVOIR-type instruments). At these same S/Ns, we simulate data for WFIRST paired with a starshade, which includes two photometric points between 0.48 and 0.6 μm and R = 50 spectroscopy from 0.6 to 0.97 μm. Given our noise model for WFIRST-type detectors, we find that weak detections of water vapor, ozone, and oxygen can be achieved with observations with at least R = 70/S/N = 15 or R = 140/S/N = 10 for improved detections. Meaningful constraints are only achieved with R = 140/S/N = 20 data. The WFIRST data offer limited diagnostic information, needing at least S/N = 20 to weakly detect gases. Most scenarios place limits on planetary radius but cannot constrain surface gravity and, thus, planetary mass.

79 ASTRONOMY AND ASTROPHYSICS↗

Refined Telluric Absorption Correction for Low-resolution Ground-based Spectroscopy: Resolution and Radial Velocity Effects in the O{sub 2}A-band for Exoplanets and K i Emission Lines

Telluric correction of spectroscopic observations is either performed via standard stars that are observed close in time and airmass along with the science target, or recently growing in importance, by theoretical telluric absorption modeling. Both approaches work fine when the telluric lines are resolved, i.e., at a spectral resolving power larger than about 10,000, and it is sufficient to facilitate the detection of spectral features at lower resolution. However, a meaningful quantitative analysis also requires the reliable recovery of line strengths. Here, we show for the Fraunhofer A-band of molecular O{sub 2} that the standard telluric correction approach fails in this at lower spectral resolutions, as an example for the general problem. Doppler-shift-dependent errors of the restored flux may arise, which can amount to more than 50% in extreme cases, depending on the line shapes of the target spectral features. Two applications are discussed: the recovery of the O{sub 2} band in the reflected light of an Earth analog atmosphere, as facilitated potentially in the future using an orbiting starshade and a ground-based extremely large telescope; and the recovery of the intrinsic ratio of the K i lines in the post-nova V4332 Sgr tracing the optical depth of the emitting region, to exemplify the relevance using present-day instrumentation. We show how one should derive correction functions for the compensation of the error in dependence of radial velocity shift, spectral resolution, and target line-profile function by use of high-resolution atmospheric transmission modeling, which has to be solved for the individual case.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗