---
title: 'California Legacy Survey: Exoplanets & Stellar Activity'
url: https://www.emergentmind.com/topics/california-legacy-survey
type: topic
---

# California Legacy Survey: Exoplanets & Stellar Activity

California Legacy Survey (CLS) is a long-term, high-precision radial-velocity and spectroscopic program developed by the California Planet Search team to deliver a blind, uniform census of exoplanets and long-period companions around nearby FGKM stars, while also using the same spectra to characterize stellar chromospheric activity and magnetic cycles [2105.11583, 2406.17332]. In its core radial-velocity release, the survey assembled 103,991 measurements for 719 stars and produced a uniform catalog of 178 companions, including 164 previously known exoplanets and 14 newly discovered or revised exoplanets and substellar companions [2105.11583]. The broader CLS framework also includes the California-Kepler Survey (CKS), described as the spectroscopic cornerstone of the broader California Legacy Survey, which extends the legacy of uniform stellar characterization to Kepler planet hosts and connects host-star properties, chromospheric activity, stellar rotation, and exoplanet demographics [2401.10864].

## 1. Survey conception, sample definition, and observational scope

CLS was constructed from several “blind” California Planet Search occurrence-rate surveys, most notably the Keck Planet Search with 585 stars, the Eta-Earth sample with 166 stars, and a 25 pc volume-limited subset, supplemented by 31 additional CPS-observed stars meeting uniform quality and statistical-rigor criteria [2105.11583]. The target-selection logic explicitly excluded biases toward metal-rich stars or previously known planet hosts, and also excluded N2K/M2K, Friends-of-Hot-Jupiters, transit-survey targets, young or IR-excess stars, and subgiant surveys [2105.11583]. The resulting stellar sample spans spectral types F–M on the main sequence, with selection cuts requiring at least 20 total radial-velocity measurements, at least 10 post-2004 HIRES observations, and a baseline of at least 8 years [2105.11583].

The sample occupies a broad region of nearby stellar-parameter space: \(V \approx 3\)–11, distances \(\lesssim 60\) pc with median \(\sim 20\) pc, \(T_{\rm eff} \approx 3200\)–6500 K, stellar masses 0.2–1.5 \(M_\odot\) with median 0.93 \(M_\odot\), and \([{\rm Fe/H}]\) from \(-0.8\) to \(+0.5\) [2105.11583]. Stellar activity in the parent sample is low to moderate, with median \(\log R'_{\rm HK} \lesssim -4.7\) [2105.11583]. This construction was designed to support population-level occurrence measurements rather than case-by-case follow-up of already unusual systems.

A parallel CLS activity program targeted slowly rotating FGKM dwarfs within \(\simeq 50\) pc, with median distance \(\sim 30\) pc, chosen to be amenable to \(1\,{\rm m\,s^{-1}}\)-level radial velocities [2406.17332]. That activity sample comprises 710 stars and extends from mid-2005 through 2023 October, or \(\sim 18.5\) years, with the authors citing “over twenty years” when archival data are included [2406.17332]. This dual structure—planet census plus activity monitoring—is central to the CLS design.

## 2. Instrumentation, radial-velocity pipeline, and completeness formalism

CLS combines three major spectroscopic platforms. Keck-HIRES, operating from 1996 to the present, provided \(R \approx 55{,}000\)–86,000 spectra with iodine-cell calibration, with pre-2004 radial-velocity precision of \(\sim 3\,{\rm m\,s^{-1}}\) and post-2004 precision of \(\sim 1\,{\rm m\,s^{-1}}\), contributing \(\approx 49{,}334\) radial velocities [2105.11583]. APF-Levy, in use from 2013 onward, uses the same iodine Doppler code as HIRES and achieves \(\sim 1.5\,{\rm m\,s^{-1}}\), contributing \(\approx 35{,}000\) radial velocities [2105.11583]. Lick-Hamilton, operating from 1987 to 2011, delivered 3–10 \({\rm m\,s^{-1}}\) precision and added \(\approx 19{,}000\) radial velocities [2105.11583]. Overall, the survey reaches per-star medians of \(N_{\rm obs}\approx 41\) and baseline \(\approx 21\) yr, while stars with detected planets were observed more intensively, with median \(N_{\rm obs}\approx 74\) [2105.11583].

All radial velocities were derived through forward modeling of iodine-superimposed spectra against a deconvolved stellar template, fitting each \(\sim 2\) Å segment for Doppler shifts, line-spread function, and continuum [2105.11583]. The automated search pipeline, RVSearch, performs iterative planet detection and characterization using a likelihood model of the form
$$
\ln \mathcal{L} = -\frac12\sum \left[\frac{(v_i-m(t_i)-\gamma_D)^2}{\sigma_i^2} + \ln(2\pi \sigma_i^2)\right],
$$
with
$$
m(t)=\Sigma_n K_n(t|P_n,e_n,\omega_n,t_{c,n}) + \dot{z}(t-t_0) + \ddot{u}(t-t_0)^2,
$$
including per-instrument zero points, jitter added in quadrature, Keplerian terms, and optional linear and quadratic trends [2105.11583]. The search proceeds through an iterative grid in \(\log P\) from 2 days to \(5\times\) the observational baseline, using \(\Delta{\rm BIC}\) as periodogram power and adopting a detection threshold set at an empirical false-alarm probability of 0.1% [2105.11583]. Posterior sampling uses RadVel plus emcee in the basis \(\{\ln P, K, t_c, \sqrt{e}\sin\omega, \sqrt{e}\cos\omega\}\), while TheJoker is used for sparsely constrained orbits [2105.11583].

Survey completeness is a defining methodological component. For each star, completeness \(C(P,M)\) was computed by injecting Keplerian signals that are log-uniform in period and mass and \(\beta\)-distributed in eccentricity into the real radial-velocity time series, then measuring the fraction recovered above the detection threshold [2105.11583]. Typical 50% completeness curves show sensitivity above 50% to \(M\sin i \sim 0.3\,M_J\) out to 5 AU, above 50% to \(>1\,M_J\) out to 10 AU, and falling to \(\sim 10\,M_J\) beyond 20 AU [2105.11583]. Population occurrence in a region of period–mass space is then written as
$$
\eta = \frac{1}{N_*}\sum_{i=1}^{N_p}\frac{1}{C(P_i,M_i)},
$$
providing the statistical basis for the occurrence studies that followed [2105.11583].

## 3. Giant-planet occurrence across orbital separation

CLS II used the uniform radial-velocity sample to measure giant-planet occurrence as a function of orbital separation from 0.03 to 30 AU and found that giant planets are more prevalent at 1–10 AU than at smaller or larger separations [2105.11584]. In non-parametric form, the survey reports \(f_{\rm Jup}(0.03\text{--}1\,{\rm au}) \simeq 3.5 \pm 0.5\) planets per 100 stars, \(f_{\rm Jup}(1\text{--}10\,{\rm au}) \simeq 14.1^{+2.0}_{-1.8}\) per 100 stars, and \(f_{\rm Jup}(10\text{--}30\,{\rm au}) \simeq 8.9^{+3.0}_{-2.4}\) per 100 stars [2105.11584]. The \(\sim 4\times\) enhancement between \(<1\) AU and 1–10 AU is highly statistically significant, and the decline beyond 10 AU is favored over models with flat or increasing occurrence at the \(\sim 2\sigma\) to \(\sim 2.5\sigma\) level [2105.11584].

The same framework applied to sub-Jovian planets with masses 0.1–1 \(M_J\) yields \(f_{\rm sub\text{-}Jup}(0.03\text{--}1\,{\rm au}) \simeq 7.5 \pm 1.0\) per 100 stars and \(f_{\rm sub\text{-}Jup}(1\text{--}10\,{\rm au}) \simeq 18.4^{+3.5}_{-3.0}\) per 100 stars, with the 10–30 AU rate not well constrained because of few detections [2105.11584]. The survey therefore identifies an orbital region near and just beyond the water-ice line where both Jovian and sub-Jovian planets are enhanced.

To describe the semi-major-axis dependence in a compact analytic form, CLS II fit a broken power law,
$$
\Gamma_B(a)=C\,(a/{\rm au})^{\beta}\,\bigl[1-\exp\!\bigl(-\,(a/a_0)^\gamma\bigr)\bigr],
$$
where \(\Gamma_B \equiv d^2N/(d\ln a\, d\ln M)\), obtaining \(C = 350^{+580}_{-220}\), \(a_0 = 3.6^{+2.0}_{-1.8}\) au, \(\gamma = 1.59^{+0.36}_{-0.33}\), and \(\beta = -0.86 \pm 0.41\) [2105.11584]. Because 99.4% of the posterior samples have \(\beta<0\), the data favor a turnover or decline beyond the ice line [2105.11584].

CLS II also corroborates that cold-gas-giant occurrence increases with host-star mass and metallicity. Restricting to planets \(>0.1\,M_J\) between 1 and 5 AU, occurrence rises from \(\lesssim 2\) per 100 stars for \(M_*<0.8\,M_\odot\) to \(\gtrsim 12\) per 100 for \(M_*>1.3\,M_\odot\), and from \(\sim 3\) per 100 for \([{\rm Fe/H}] \lesssim 0.0\) to \(\sim 15\) per 100 for \([{\rm Fe/H}] \gtrsim +0.2\) dex [2105.11584]. The paper further notes statistical consistency with direct-imaging and microlensing surveys when those results are cast into common mass–semi-major-axis bins [2105.11584].

## 4. Planetary architectures, multiplicity, and host-star metallicity

The uniform CLS catalog enabled direct comparison between systems containing a single giant planet and systems containing multiple giant planets. Of the 178 cataloged companions, 134 have minimum masses \(M\sin i \ge 0.1\,M_J\); these include 65 “lonely” giants and 69 giants in 31 multi-giant systems [2310.08707]. Rosenthal et al. modeled the eccentricity distributions of singles and multis with hierarchical Bayesian Beta distributions,
$$
p(e|\alpha,\beta)=\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\,e^{\alpha-1}(1-e)^{\beta-1},
$$
and found that the two populations are distinct at \(\sim 3\sigma\) [2310.08707]. The multiple-giant population has \(e_{90\%}=0.47\pm 0.05\), whereas the single-giant population extends to \(e_{90\%}=0.77\pm 0.04\), while both have \(\sim 3\%\) of orbits at \(e<0.03\) [2310.08707]. The reported morphology is a pile-up of nearly circular orbits plus a long high-eccentricity tail for singles, and a distribution concentrated at modest eccentricity for multis [2310.08707].

Host-star metallicities also differ. High-resolution spectra analyzed by SpecMatch yielded \(\langle [{\rm Fe/H}] \rangle = +0.129 \pm 0.019\) dex for singles and \(+0.228 \pm 0.027\) dex for multis [2310.08707]. Using \(10^4\) realizations of metallicity cumulative distributions and Anderson–Darling testing, the study found \(p<0.01\) in 82.2% of trials; a Kolmogorov–Smirnov test gave similar results [2310.08707]. The occurrence density as a function of semi-major axis further shows a \(\sim 2.3\sigma\) significant hot-Jupiter pile-up at \(a<0.06\) AU among singles that is not seen among multi-giant systems [2310.08707].

The same comparison identified a mass difference and an intra-system mass correlation. The median \(M\sin i\) of giants in singles is 0.92 \(M_J\), versus 1.71 \(M_J\) in multis, with an Anderson–Darling test giving \(p<0.001\) [2310.08707]. For adjacent giants ordered by semi-major axis within multi-giant systems, the Pearson correlation coefficient is \(R=0.476\pm 0.010\); bootstrapping the observed mass catalog yields a 99.71% exclusion of this correlation under reshuffling, and synthetic populations with a uniform \(\ln M\) distribution produce \(R\ge 0.476\) only 1% of the time [2310.08707]. The resulting “giant peas in a pod” effect has \(\sigma_{\ln(M_2/M_1)} \approx 0.5\), implying paired giants tend to lie within a factor of \(\sim 1.6\) in mass [2310.08707].

A separate CLS analysis addressed whether distant giant companions are enhanced around systems hosting close-in small planets, especially in metal-rich stars. Using the Rosenthal et al. 2021 sample filtered to 594 Sun-like stars with \(M_*>0.6\,M_\odot\), measured \([{\rm Fe/H}]\), and at least 20 radial-velocity observations, and adopting the same planet definitions as Bryan and Lee (2024), the study found \(P({\rm DG}|{\rm CS},[{\rm Fe/H}]>0)=14^{+12}_{-8}\%\) and \(P({\rm DG}|[{\rm Fe/H}]>0)=16.4^{+2.5}_{-2.4}\%\) [2410.23071]. The conditional rate is therefore statistically indistinguishable from, or slightly lower than, the field rate, and a factor-of-two enhancement is in the 97.5% upper tail of the posterior, constituting a \(\approx 2\sigma\) tension with Bryan and Lee’s result [2410.23071]. The paper attributes the discrepancy to small-number statistics, sample inhomogeneity, and completeness-correction methodology, and states that larger, homogeneous samples will be required to settle the question at \(>3\sigma\) confidence [2410.23071].

## 5. Chromospheric activity monitoring and stellar magnetic cycles

CLS V repurposed the long time-series HIRES archive to construct a chromospheric activity survey of 710 main-sequence stars, based on 52,372 Ca II H and K spectra after quality cuts [2406.17332]. The spectra were obtained mainly with the B5 and C2 deckers, giving \(R\approx 60{,}000\), with occasional B1 and B3 templates at \(R\approx 80{,}000\) [2406.17332]. S-values on the Mount Wilson scale were measured from the H and K cores and two 20-Å continuum windows according to
$$
S = \alpha\,\frac{N_H+N_K}{N_R+N_V} + \beta,
$$
with \(\alpha\) and \(\beta\) determined from standard stars and individual-observation uncertainties on \(S\) of \(\lesssim 0.001\) [2406.17332]. The corresponding dimensionless chromospheric metric was then computed as
$$
R'_{\rm HK}=C_{\rm cf}(B-V)\,[S-S_{\rm phot}(B-V)],
$$
with \(\log R'_{\rm HK}=\log_{10} R'_{\rm HK}\) [2406.17332].

For cycle searches, the survey required at least 45 post-2005 observations, producing a cycle-search subsample of 285 stars [2406.17332]. Periods from 100 to 10,000 days were scanned with a generalized Lomb–Scargle periodogram, after which the strongest peak was fit with a zero-eccentricity sinusoid,
$$
S(t)=S_0 + A\,\sin[2\pi\,(t-t_0)/P_{\rm cycle}],
$$
and subjected to robustness filters: peak power \(>0.5\), second-tallest peak \(<75\%\) of the main peak, and \(({\rm STD}_i-{\rm STD}_f)/({\rm STD}_i\times {\rm median}(S))>1.20\) [2406.17332]. Under those criteria, 138 stars, or 48% of the sufficiently sampled subsample, show robust cycles [2406.17332].

The detected cycle periods span 2.3–23 yr, with a broad peak near 7–12 yr, and amplitudes \(A_S \approx 0.05\)–1.6, corresponding to \(\Delta\log R'_{\rm HK} \approx 0.05\)–0.4 dex [2406.17332]. A particularly tight empirical relation appears for main-sequence stars with \(\log R'_{\rm HK}\) between \(-4.7\) and \(-4.9\): cycle period increases systematically as \(T_{\rm eff}\) decreases, with 300 K bins yielding \(P_{\rm cycle}=4.4\pm 0.5\) yr for 5800–6100 K, \(6.0\pm 0.7\) yr for 5500–5800 K, \(7.2\pm 1.1\) yr for 5200–5500 K, and \(7.8\pm 2.0\) yr for 4900–5200 K [2406.17332]. For stars less active than \(R'_{\rm HK}\approx -4.9\), the correlation breaks down and periods scatter to 10–20 yr [2406.17332]. The Sun, with \(T_{\rm eff}=5777\) K, \(\langle \log R'_{\rm HK}\rangle \approx -4.90\), and \(P_{\rm cycle}\simeq 11\) yr, sits squarely on the G-star trend line [2406.17332]. Within exoplanet surveys, these S-value and \(\log R'_{\rm HK}\) time series are used as chromospheric diagnostics that correlate with radial-velocity jitter and can be incorporated through regression or quasi-periodic Gaussian-process modeling [2406.17332].

## 6. The California-Kepler Survey within CLS and the survey’s long-term legacy

The California-Kepler Survey represents the spectroscopic cornerstone of the broader California Legacy Survey, and its eleventh installment extended CLS methodology to Kepler planet hosts by extracting chromospheric activity measurements from CKS Gaia survey spectra [2401.10864]. The parent sample comprises 1189 Kepler Objects of Interest with confirmed or candidate planets, selected to be among the brighter hosts in the Kepler field with \(Kp \lesssim 14.2\), of which 879 stars have sufficient signal-to-noise in the blue chips to measure the cores of the Ca II H line at 3968 Å and the K line at 3934 Å [2401.10864]. All spectra were obtained with HIRES on Keck I at resolving power \(R \simeq 60{,}000\) over \(\lambda \approx 3650\)–8000 Å [2401.10864].

Using Spectroscopy Made Easy and an updated line list, the survey homogeneously derived \(T_{\rm eff}\) with typical uncertainties \(\sigma_T \approx 60\) K, \(\log g\) to \(\sigma_{\log g}\approx 0.10\) dex, \([{\rm Fe/H}]\) to \(\sigma_{[{\rm Fe/H}]}\approx 0.04\) dex, and isochronal ages from Dartmouth tracks with median uncertainties of order 25–30%, or roughly \(\sigma_{\rm age}\approx 1.5\) Gyr for a 5 Gyr star [2401.10864]. The Mount Wilson S-index was computed from triangular bandpasses of full-width at half-maximum 1.09 Å centered on the Ca II H and K cores and two 20 Å pseudocontinuum windows, achieving an external precision of \(\lesssim 0.005\) after calibration to the Mount Wilson scale [2401.10864]. In practical form, the pure chromospheric flux ratio is written as
$$
R'_{\rm HK}=1.34\times10^{-4}\;C_{\rm cf}\;S - R_{\rm phot},
$$
where \(R_{\rm phot}\) is the dimensionless photospheric contribution [2401.10864].

Rotation periods were inferred by inverting the empirical \(R'_{\rm HK}\)–Rossby relation of Mamajek and Hillenbrand (2008), with \(P_{\rm rot}=Ro(R'_{\rm HK})\times \tau_c\), and convective turnover times obtained from the Noyes et al. polynomial
$$
\log \tau_c = 1.362 - 0.166x + 0.025x^2 - 5.323x^3,\quad x=1-(B-V),
$$
valid for \(0.4\le B-V\le 1.2\) [2401.10864]. Comparing activity-derived rotation periods to photometric rotation periods from Kepler light curves revealed a systematic offset along the “Rossby Ridge,” \(0.2\lesssim Ro \lesssim 1\), with stars older than \(\sim 2\) Gyr spinning down more slowly than predicted by standard Skumanich-type braking laws, in direct support of weakened magnetic braking [2401.10864]. The same analysis found no statistically significant metallicity trend in the \(R'_{\rm HK}\)–\(Ro\) relation for \(-0.2\le [{\rm Fe/H}] \le +0.3\), and identified approximately 25 stars with \(\log R'_{\rm HK}<-5.1\) that lie slightly below the main sequence in the \(M_V\) versus \(T_{\rm eff}\) plane as potential Maunder Minimum analogs, while noting that multi-year time series are not yet available to verify those states [2401.10864].

Taken together, the CLS data products comprise radial velocities from Keck-HIRES, APF-Levy, and Lick-Hamilton, Ca H&K S-values, APT photometry, machine-readable stellar and planetary tables, completeness contours, and the public RVSearch codebase [2105.11583]. The survey has therefore become a benchmark dataset for giant-planet occurrence measurements, differential studies of single and multiple giant-planet systems, chromospheric cycle statistics, age–activity–rotation calibrations, and host-star characterization for exoplanet demographic analyses [2105.11583, 2401.10864]. A plausible implication is that CLS functions not only as a planet catalog, but as an integrated empirical framework linking planetary architectures, stellar magnetic evolution, and survey completeness over decadal baselines.

Source: https://www.emergentmind.com/topics/california-legacy-survey