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RV Metric New Monday A Science Metric for Direct Characterization of Known Radial-Velocity Exoplanets Robert A. Brown Space Telescope Science Institute [email protected] June 17, 2013 Abstract Known RV exoplanets are viewed as prime targets for a future high-contrast imaging mission, which may be able to detect and characterize these enigmatic objects in reflected starlight. To help define and differentiate the candidates for such a mission on the basis of scientific performance, and to help set realistic expectations, we develop a science metric, NRV, defined as the estimated number of planets that would be detected and characterized by such a mission. In this report, we estimate upper limits to NRV for missions with apertures in the range 1–2.4 m. We treat both star-shade and coronagraphic missions. 1. Introduction We define the science metric NRV to be the number of known RV exoplanets that satisfy four criteria: #1 permitted pointing: during observations, the angle between the host star and the sun (γ ) must be greater than the solar avoidance angle, γ > γ 1 and, for a star- shade mission, it must also be less than the angle at which the star shade appears illuminated, γ < γ 2 #2 systematic limit: the flux ratio of the planet to the host star, expressed in delta magnitudes ( Δmag ), must be better than the systematic limit in delta magnitudes ( Δmag0 ), i.e. Δmag < Δmag0 #3 wavelength: criteria #1–2 must be satisfied at all wavelengths deemed critical for planet detection and characterization, and particularly for the coronagraph, at the longest critical wavelength (λlc) #4 time: criteria #1–3 must be satisfied at some time during the mission for at least as long as the exposure time required for detection or characterization of a planet as faint as the systematic limit. The input catalog of RV exoplanets—plus working assumptions about the photometric properties of exoplanets—provide the natural parameters for evaluating criteria #1–4. The mission design and science operations provide the technical parameters. In this report, we develop the methods for computing NRV from these parameters. The algorithms and methods were developed earlier by Brown (2004a, 2004b, 2005) and Brown & Soummer (2010) for estimating direct-imaging search completeness and for studying design reference missions (DRMs). 2. Natural Parameters: The Input Catalog On May 10, 2013, we drew 423 known RV exoplanets from www.exoplanets.org, comprising all planets satisfying the search term “PLANETDISCMETH == 'RV'.” We reduced the list to 419 planets by dropping three host stars with unknown distances (HD 13189, BD+48 738, and HD 240237) and one planet with missing orbital information (Kepler-68). The final catalog includes 406 planets with unknown orbital inclination angle (i) and 13 planets with known i. The input catalog includes 347 unique host stars. The input catalog includes 13 planets with known i, only one of which—HD 192310 c— achieves sufficient separation to be observed by the optical systems considered in this report. For current purposes, we have simply carried HD 192310 c along as if we did not know its inclination. The input catalog contains the following parameters for each RV exoplanet: (i) stellar right ascension (α in hours) and declination (δ in degrees) (ii) stellar distance (d) in pc (iii) mass of the star (ms) in solar masses (iv) minimum planetary mass (mp sini) in Jupiter masses (v) semimajor axis (a) in AU (vi) orbital eccentricity (ε) (vii) argument of periapsis of the star (ω s ) in degrees. (ωp = ωs + 180°) (viii) orbital period (T) in days (ix) epoch of periapsis (T0) in JD In addition, we introduce the following natural photometric parameters for the planet: (x) geometric albedo of the planet (p) (xi) planetary phase function ( Φ(β)) (xii) planetary radius (Rp) In this report, we choose to investigate NRV using a Jupiter-like exoplanet as the test body: p = 0.5, Φ = ΦL , the Lambert phase function, and Rp = RJupiter . Such an object is a maximal planet in terms of flux of reflected light relative to the host star, which we express in delta stellar magnitudes (Δmag). In their Figure 9, Cahoy, Marley, & Fortney (2010) suggest that p of a Neptune-like exoplanet orbiting at 5 AU would be 40% smaller in the visible to near-infrared wavelength range than a Jupiter-like exoplanet. Also taking relative size into account, a Neptune analog would be 2.9 magnitudes—a factor of 14—fainter than a Jupiter analog at the same phase. Because the maximum brightness of a Jupiter observable by the current program is typically Δmag = 20–21, a Neptune would exhibit Δmag = 24–25 at brightest. In §2, part of the reason for setting the instrumental requirement for the 2 systematic limit of detectability at Δmag0 = 25 is a perceived scientific imperative to reach—find and study—exoplanets at least as small as Neptune. An associated requirement is the ability to accommodate the long exposure times necessary to reach limiting objects—objects at the systematic limit of detectability—with a robust signal-to- noise ratio (S/N). 2. Technical Parameters of the Mission Design We adopt the following values for five technical parameters that are relatively noncontroversial: (a) γ 1 = 45° (coronagraph), γ 1 = 45° and γ 2 = 80° (star shade). These values of γ are being used in current NASA-sponsored studies. (b) mission timing: January 1, 2020, to December 31, 2022. A duration of three years seems about right for a 1–2.4 m class mission. The chosen absolute timing seems reasonable for implementing a mission of this scale. (c) Δmag0 = 25. In recent years, NASA-sponsored studies, laboratory tests, and experience with space instruments have built confidence in the community that optical performance at the level of Δmag0 = 25 can now be achieved for usefully small angular separations (s) at visible and near-infrared wavelengths. In practical terms, the achievable Δmag0 is ultimately determined by the brightest unstable speckles of starlight at the field position of the planet (Brown 2005). (d) λlc = 785 nm, which is the red end of the reddest filter, centered at 766 nm. (e) spectral resolving power R = 5 at 550 nm for search exposures, and R =20 for spectroscopy near 730 nm, which approximately matches the width of the CH4 spectral feature (see Figure 10 in Cahoy, Marley, & Fortney 2010). The parameters of limiting search observations (LSOs for detection) and limiting characterization observations (LCOs for characterization) are defined in Table 1. Type Δmag0 λ (nm) R S/Ngoal q min # LSO 25 550 5 5 2 1 LCO 25 693, 730, 766 20 10 2 3 Table 1. Parameters for LSOs and LCOs. q is the required number of exposures in one limiting observation. The observations are always taken in pairs of consecutive exposures at slightly different telescope rolls, and the data are subtracted, shifted, and added to estimate the signal. The science program sets min #, which is the minimum number of limiting observations: one LSO for a search, and three LCOs for spectral characterization of a massive extrasolar planet. Of the latter, one LCO is centered on the absorption feature of CH4 at 730 nm and two LCOs sample the adjacent continuum, centered at 693 3 and 766 nm. The red edge of the reddest filter determines λlc = 785 nm. The single LSO and the three LCOs are assumed to constitute a minimum spectral characterization of an RV exoplanet. NRV depends on the minimum angle at which the suppressive performance Δmag0 is achieved. This angle is called the inner working angle (IWA). For the coronagraph, typical apparent separations of RV exoplanets from their host stars are smaller than a few Airy rings at λlc, and for this reason, IWA for the coronagraph is controversial. In this report, we study various values of the coronagraph’s IWA in the range (f) IWA = 0.134–0.645 arcsec . IWA is commonly expressed IWA = κ λ / D , (1) where κ is a number of Airy rings at wavelength λ, and D is the diameter of the telescope aperture. Equation (1) is nothing more than a degenerate translation between two operational parameters, IWA and λ, and two descriptive parameters ( f1′ ) κ ( f2′ ) D. In Table 2, we use Equation (1) to explore combinations of values of f1′–2 that produce the studied values of IWA for the coronagraph. By recognizing that the range of values IWA = 0.134–0.645 arcsec is compatible with at least some noncontroversial combinations of κ , λ, and D, we implicitly satisfy criterion #3. Nevertheless, it is important to keep in mind that the technical difficulty of achieving a value of IWA for the coronagraph has a negative relationship with the value of κ, and the practicality of achieving κ < 3 is currently controversial. D (m) κ785 IWA(arcsec) comment 4 0.269 conservative 2.4 3 0.202 moderate 2 0.134 controversial 4 0.430 conservative 1.5 3 0.323 moderate 2 0.215 controversial 4 0.645 conservative 1.0 3 0.484 moderate 2 0.323 controversial 4 Table 2. The cases of D, κ785, and IWA for the coronagraph. The comment is about the degree of difficulty in realizing full starlight suppression at κ785 Airy rings. For the star-shade mission, we select IWA = 0.075 arcsec, and D = 1, 1.5, and 2.4 m. 3. Criterion #1: Permitted Pointing We compute γ from α and δ using the fact that the scalar product of the unit vectors from the telescope to the star and the telescope to the sun is equal to cosγ . We calculate the unit vectors in the rectangular ecliptic coordinates for any given time.
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