Detectability of extrasolar planets in radial velocity surveys

By A. Cumming. 2004

212 citations recorded by the source corpus.

Radial velocity surveys are beginning to reach the time baselines required to detect Jupiter analogs, as well as sub-Saturn mass planets in close orbits. Therefore it is important to understand the sensitivity of these surveys at long periods an d low amplitudes. In this paper, I derive analytic expressions for the detectability of plane ts at both short and long periods, for circular and eccentric orbits. In the long period regime, th e scaling of the detection threshold with period depends on the desired detection efficiency. The 99% velocity threshold scales as K / P 2 / a 3 , whereas the 50% velocity threshold scales as K / P / a 3/2 . I suggest an extension of the Lomb-Scargle statistic to Keplerian orbits, and describe how to estimate the false alarm probability associated with a Keplerian fit. I us e this Keplerian periodogram to investigate the effect of eccentricity on detectability. A t short periods, detectability is reduced for eccentric orbits, mainly due to the sparse sampling of th e periastron passage, whereas long period orbits are easier to detect on average if they are eccentric because of the steep velocity gradients near periastron. Fitting Keplerian orb its allows the lost sensitivity at short orbital periods to be recovered for e . 0.6, however there remain significant selection effects against eccentric orbits for e & 0.6, and the small number of highly eccentric planets discovered so far may reflect this. Finally, I present a Bayes ian approach to the periodogram which gives a simple derivation of the probability distribu tions of noise powers, clarifies why the periodogram is an appropriate way to search for long period signals, and emphasises the equivalence of periodogram and least squares techniques.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/f720d0fde1912fbe7ba7b695948d86b3af7ddba8

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Citations in the corpus

The Keck Planet Search: Detectability and the Minimum Mass and Orbital Period Distribution of Extrasolar Planets (2008, methodology): “The detectable amplitude depends on the number and duration of the observations, and particularly on the Doppler measurement errors and other noise sources (see Cumming 2004 for a detailed discussion).”
WASP-19b: THE SHORTEST PERIOD TRANSITING EXOPLANET YET DISCOVERED (2010, background): “According to Cumming (2004), the number of independent frequencies can be approximated by the duration of the time-series data times the difference between the highest and lowest frequencies tested (here M = 753).”
DHP Framework: Digital Health Passports Using Blockchain - Use case on international tourism during the COVID-19 pandemic (2004, background): “…to extract with a few missed transits; however, if the outer planet is highly eccentric, then most of the change in transit c© 0000 RAS, MNRAS 000, 000–000 timing may occur for a few transits (e.g. HD37124; a similar selection effect occurs in radial velocity searches as discussed by Cumming 2004).”
The planet search programme at the ESO CES and HARPS - IV. The search for Jupiter analogues around solar-like stars (2012, background): “…de- The final false alarm probability (FAP) for the period search accounts for the number of independent frequenciesM with the simple estimateM ≈ f T (Cumming 2004), i.e. the frequency 19 The corresponding normalisation as z = (χ2constant− χ2)/(ν − νconstant) χ2best/(N − ν) follows a F2,N−5 and…”
The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms (2009, methodology): “For comparison we also show the periodogram with the normalisation by the best fitat eachfrequency (Cumming 2004) zKep(ω) = N − 5 4 χ20 − χ 2(ω) χ2(ω) (30) which is used in the 2DKLS and reveals the power maximum as impressively as in O’Toole et al. (2009, Fig.1b).”
Toward a Deterministic Model of Planetary Formation. IV. Effects of Type I Migration (2008, background): “But the extrapolation of existing data suggests that a higher fraction of solar-type stars may have longer period gas giant planets (Cumming 2004).”
THE LICK–CARNEGIE EXOPLANET SURVEY: A 3.1 M⊕ PLANET IN THE HABITABLE ZONE OF THE NEARBY M3V STAR GLIESE 581 (2010, background): “Additionally, we can also define power in a prominent peak as (Cumming (2004)): p0 = (N − 2) 2 (χ2constant − χ 2 circ) χ2circ , (2) where χ2circ is the reduced chi-squared for a circular fit at/near the period implied by the peak and χ2constant is the reduced chi-squared for a constant RV model of…”
High-cadence spectroscopy of M-dwarfs. I. Analysis of systematic effects in HARPS-N line profile measurements on the bright binary GJ 725A+B (2016, background): “Note a promising signal arising over the 0.1 per cent of the false alarm probability (or FAP, Cumming 2004) threshold at ∼3 d in the RV differential periodogram.”
Search for Axionlike Dark Matter through Nuclear Spin Precession in Electric and Magnetic Fields (2017, methodology): “To calculate the periodogram of the data series, we use the least squares spectral analysis (LSSA) method [72,73], where the amplitude at frequency f is estimated by the amplitude of the best-fit oscillation of that frequency.”
The LCES HIRES/Keck Precision Radial Velocity Exoplanet Survey (2017, methodology): “This value is a similar threshold to a 0.1% FAP (which we have chosen in keeping with the precedent established by Cumming 2004but for five degrees of freedom), as is the case when comparing models with k and k 1+ Keplerian signals.”
Understanding the Lomb–Scargle Periodogram (2017, background): “There have been various attempts to estimate this value more carefully, both analytically and via simulations (see, e.g. Horne & Baliunas 1986; Schwarzenberg-Czerny 1998; Cumming 2004; Frescura et al. 2008), but all such approaches are necessarily only approximations.”