HATS-4b: A DENSE HOT JUPITER TRANSITING A SUPER METAL-RICH G STAR^*

HATS-4b was first identified as a TEP candidate using a light curve constructed with 33,121 photometric measurements of its host star HATS-4 (also known as 2MASS 06162689-2232487; $\alpha = 06^{\mathrm{h}}16^{\mathrm{m}}26\buildrel{\mathrm{s}}\over{.}90$, δ = −22°32'488; J2000; V = 13.459 ± 0.017 mag; APASS DR5; Henden et al. 2009). The photometric measurements were obtained with the full set of six HS units of the HATSouth project, a global network of fully automated telescopes located at Las Campanas Observatory (LCO) in Chile, at the location of the High Energy Spectroscopic Survey in Namibia, and at Siding Spring Observatory (SSO) in Australia. A detailed description of HATSouth can be found in Bakos et al. (2013). Each of the HATSouth units consists of four 0.18 m f/2.8 Takahasi astrographs, each coupled with an Apogee U16M Alta 4k×4k CCD camera. Observations of 4 minutes were taken through a Sloan r filter, and covered the period between 2009 September and 2011 May. The first six entries in Table 1 summarize the HATSouth discovery observations, and the differential photometry data are presented in Table 4. The large number of 33,121 photometric datapoints acquired for HATS-4 is remarkable, and this was possible due to the fact that this star was located at the intersection of two adjacent fields which were monitored simultaneously by each of the two units at each site. The majority of the datapoints were collected at the LCO stations HS-1 and HS-2, and very few observations were taken by the HS-6 unit in Australia as its cameras were being serviced for a large fraction of the time that the relevant fields were being followed.

The photometric and candidate identification procedures adopted by HATSouth are described in Bakos et al. (2013) and Penev et al. (2013). Briefly, photometry is performed via aperture photometry, and the resulting light curves are detrended using an external parameter decorrelation (EPD) and trend filtering algorithm (TFA; for a description of these procedures, see the Appendix in Bakos et al. 2010, and references therein). The resulting light curves are searched for transits using the box-fitting least squares algorithm (Kovács et al. 2002). The HATS-4b discovery light curve is shown in Figure 1, folded with a period of P = 2.5167286 days. The transit evident in this light curve triggered a follow-up process to confirm its planetary nature which we describe below.

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The process of spectroscopic confirmation for HATSouth candidates is divided into steps of reconnaissance and high precision RV measurements with high resolution spectrographs. Table 2 summarizes all the follow-up spectroscopic observations which we obtained for HATS-4. The relative RVs and bisector span (BS) measurements are presented in Table 3 and shown, along with the best-fit model, in Figure 2. In the reconnaissance step, which utilizes spectrographs with a wide range in resolutions, we are able to exclude most stellar binary false positives. We obtained low and medium resolution reconnaissance observations of HATS-4 with the Wide Field Spectrograph (WiFeS) (Dopita et al. 2007) mounted on the Australian National University (ANU) 2.3 m telescope at SSO. A flux-calibrated spectrum at R ≡ λ/Δλ = 3000 provided an initial spectral classification for HATS-4, confirming it was a dwarf and excluding false positive scenarios that involve giants. Multiple-epoch observations at a higher resolution, R = 7000, allowed us to rule out variations in RV with amplitudes >1 km s⁻¹ which would indicate that the system is an eclipsing binary. Details of WiFeS and the data reduction and analysis procedures adopted for stellar parameters and RV measurements in the HATSouth survey have been presented in Bayliss et al. (2013).

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After HATS-4b had passed the reconnaissance with WiFeS, it was scheduled to be observed on higher resolution facilities capable of delivering high-precision RVs. For HATS-4b, we obtained a total of 57 spectra with four such spectrographs as summarized in Table 2. We now briefly describe the observations and data reduction procedures adopted for each of these spectrographs.

Twenty-four observations were obtained with the Planet Finder Spectrograph (PFS; Crane et al. 2010) mounted on the Magellan II (Clay) telescope at LCO. We obtained two I₂-free templates on the night of 2012 December 28 UT with a slit width of 03, while the remaining observations were taken through an I₂ cell and a slit width of 05 on the nights of 2012 December 28–31. A large number of exposures with PFS were taken in transit with the aim of measuring the R–M effect (see Section 3.2). Exposures were read out using 2 × 2 binning on the CCD in order to increase the signal-to-noise ratio (S/N), which was typically ≈70 per resolution element for the I₂-free templates and in the range 30–90 for the spectra taken through I₂. Reduction of the PFS data was carried out using a custom pipeline and the RVs were measured using the procedures described in Butler et al. (1996).

We also observed HATS-4 with the High Dispersion Spectrograph (HDS; Noguchi et al. 2002) mounted on the Subaru telescope on the nights of 2012 September 19–22, obtaining three I₂-free templates and eight spectra taken through an I₂ cell. We used the KV370 filter with a 06×2'' slit, resulting in a resolution R = 60,000 and wavelength coverage of 3500–6200 Å. Exposures were read out using 2 × 1 binning on the CCD in order to increase the S/N, which was typically ≈130 per resolution element for both the I₂-free templates and the ones taken through I₂. RVs were measured using the procedure detailed in Sato et al. (2002, 2012) which was in turn based on the method of Butler et al. (1996). BS measurements were measured following Bakos et al. (2007).

Finally, observations were also obtained with the FEROS spectrograph (Kaufer & Pasquini 1998) mounted on the ESO/MPG 2.2 m telescope and with the CORALIE spectrograph (Queloz et al. 2001b) mounted on the Euler 1.2 m telescope in La Silla. Descriptions of the data reduction procedures for these spectrographs have been detailed in papers reporting previous HATSouth discoveries (Penev et al. 2013; Mohler-Fischer et al. 2013). The CORALIE procedures were only briefly described in Penev et al. (2013). In the Appendix, we describe in more detail the reduction and RV measurement procedures which we have developed and applied in the context of HATSouth follow-up for CORALIE.

HATS-4 is a metal-rich dwarf with low rotation, allowing, in principle, very high precision RVs to be measured, but its relative faint magnitude limits the precision that can be obtained in a single measurement, especially for the spectrographs mounted on smaller telescopes.

In order to discount the possibility that the RV variations detected have a stellar-activity-induced origin, we probed our RV data for correlations between the measured RVs and the BS measurements for the set of all data points that have both quantities measured. We find that the 95% confidence interval for the Pearson correlation coefficient ρ is [ − 0.22, 0.53]. The confidence interval was estimated using a bootstrap procedure whereby we generated 10,000 data sets where the RV and BS values were given by adding Gaussian deviates to the measured values, with standard deviations given by the uncertainties. Based on this exercise, we conclude that there is no significant correlation between RV and BS measurements and that the RV signal is not induced by stellar activity.

High-precision photometric follow-up of HATS-4, necessary to determine precise values of the orbital parameters and the planetary radius, was performed using four facilities: the spectral camera on the 2 m Faulkes Telescope South (FTS) at SSO, the SITe3 camera on the Swope 1 m telescope at LCO, the 0.3 m Perth Exoplanet Survey Telescope (PEST), and the Andor camera on the Perth 0.6 m telescope. We observed three partial and one full transit. The light curves are shown in Figure 3 and the differential photometry for the light curves is presented in Table 4.

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Details of the instruments, observation strategy, reduction, and photometric procedures for Spectral/FTS, SITe3/Swope, and PEST can be found in Bayliss et al. (2013), Penev et al. (2013), and Zhou et al. (2014a), respectively. This is the first time we present data from the Perth 0.6 m: on 2012 November 9, we monitored the transit of HATS-4 with the Andor iKon-L CCD camera coupled to the 0.6 m Perth-Lowell Automated Telescope at Perth Observatory, Australia. We used an r-band filter and exposure times of 100 s. Standard bias, dark, and flat-field corrections were performed using the Perth-Lowell Automated Telescope automated reduction pipeline. Aperture photometry was performed following the methods described in Bakos et al. (2010) with modifications appropriate for this facility.

The stellar parameters for HATS-4b were estimated using the stellar parameter classification (SPC) procedure (Buchhave et al. 2012) using the I₂-free templates obtained with PFS. The initial values of the stellar parameters obtained with SPC were T_eff⋆ =5403 ± 50 K, log g =4.46 ± 0.1, [Fe/H] =0.43 ± 0.08, and vsin i=1.5 ± 0.5 km s⁻¹.

Joint global modeling of the available photometry and RV data was performed following the procedure described in detail in Bakos et al. (2010). Light curves were modeled using the expressions provided in Mandel & Agol (2002) together with EPD and TFA to account for systematic variations due to external parameters and common trends of the ensemble of stars in a given set of observations. The RV data was modeled with a Keplerian orbit following the formalism of Pál (2009). The best fit parameters are first estimated via a maximization of the likelihood using a downhill simplex algorithm. This is followed by a Markov Chain Monte Carlo (MCMC) analysis to estimate the posterior distribution of the parameters.

Following Sozzetti et al. (2007) we use the values of T_eff⋆ and [Fe/H] obtained from SPC together with the stellar mean density ρ_⋆ inferred from the transit to constrain mass, radius, age, and luminosity of HATS-4 using the Yonsei–Yale (YY) stellar evolution models (Yi et al. 2001). In each step of the MCMC run as part of the global modeling, the current sample values for T_eff⋆, ρ_⋆, and [Fe/H] are used to interpolate from the YY isochrones values for mass, radius, age, and luminosity, thus building posterior distributions for them and derived quantities such as log g. This process usually results in a more precise value of log g than that inferred from spectroscopy alone, and this new estimate for log g can be fixed in a new spectroscopic analysis to infer new values of T_eff⋆, [Fe/H], and vsin i. The new values obtained are also used to update the limb-darkening parameters (taken from Claret 2004) which are needed to model the light curves and are dependent on stellar parameters. This process is iterated until the isochrone-revised log g value is consistent within 1σ with the input estimate. In the case of HATS-4, the isochrone-revised value of log g was consistent with the original SPC value quoted above and, therefore, no iterations were necessary.

The stellar parameter estimates, along with 1σ uncertainties resulting from the process described above, are listed in Table 5. The inferred location of the star in a diagram of a/R_⋆ versus T_eff⋆ is shown in Figure 4. Finally, the global modeling estimates of the geometric parameters relating to the light curves and the derived physical parameters for HATS-4b are listed in Table 6. We find that the planet has a mass of M_p ≈ 1.32 M_J, and a radius of R_p ≈ 1.02 R_J, which results in a planet that is not inflated and has a density of ρ_p = 1.55 ± 0.16 g cm⁻³. Note that we allow the eccentricity to vary in the fit so as to allow our uncertainty on this parameter to be propagated, but we find the eccentricity to be consistent with that of a circular orbit.

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Table 6. Orbital and Planetary Parameters

Parameter	Value
Light Curve Parameters
P (days)	2.516729 ± 0.000002
Tc (BJD)a	2455808.34095 ± 0.00036
T14 (days)a	0.1053 ± 0.0009
T12 = T34 (days)a	0.0112 ± 0.0006
a/R⋆	$8.43_{-0.22}^{+0.17}$
ζ/R⋆b	21.26 ± 0.15
Rp/R⋆	0.1132 ± 0.0029
b ≡ acos i/R⋆	$0.217_{-0.093}^{+0.074}$
i (deg)	88.5 ± 0.6
Limb-darkening coefficientsc
ar (linear term)	0.4675
br (quadratic term)	0.2624
aR	0.4356
bR	0.2718
ai	0.3518
bi	0.2930
RV parameters
K (m s−1)	197.5 ± 3.2
$\sqrt{e}\cos \omega$	0.029 ± 0.039
$\sqrt{e}\sin \omega$	−0.097 ± 0.085
ecos ω	0.003 ± 0.005
esin ω	$-0.010_{-0.022}^{+0.010}$
e	0.013 ± 0.016
ω	275 ± 98
CORALIE RV jitter (m s−1)d	29.0
HDS RV jitter (m s−1)	8.4
FEROS RV jitter (m s−1)	0.0
PFS RV jitter (m s−1)	5.8
Planetary parameters
Mp (MJ)	1.323 ± 0.028
Rp (RJ)	1.020 ± 0.037
C(Mp, Rp)e	0.07
ρp (g cm−3)	1.55 ± 0.16
log gp (cgs)	3.50 ± 0.03
a (AU)	0.0362 ± 0.0002
Teq (K)	1315 ± 21
Θf	0.094 ± 0.004
〈F〉 (108 erg s−1 cm−2)g	6.74 ± 0.44

Notes. ^aT_c: reference epoch of mid-transit that minimizes the correlation with the orbital period. BJD is calculated from UTC. T₁₄: total transit duration, time between first to last contact. T₁₂ = T₃₄: ingress/egress time, time between first and second or third and fourth contact. ^bReciprocal of the half-duration of the transit used as a jump parameter in our MCMC analysis in place of a/R_⋆. It is related to a/R_⋆ by the expression $\zeta /R_\star = a/R_\star (2\pi (1+e\sin \omega))/(P \sqrt{1 - b^{2}}\sqrt{1-e^{2}})$ (Bakos et al. 2010). ^cValues for a quadratic law given separately for the Sloan g, r, and i filters. These values were adopted from the tabulations by Claret (2004) according to the spectroscopic (SPC) parameters listed in Table 5. ^dThis jitter was added in quadrature to the RV uncertainties for each instrument such that χ²/dof = 1 for the observations from that instrument. ^eCorrelation coefficient between the planetary mass M_p and radius R_p. ^fThe Safronov number is given by Θ = (1/2)(V_esc/V_orb)² = (a/R_p)(M_p/M_⋆) (see Hansen & Barman 2007). ^gIncoming flux per unit surface area, averaged over the orbit.

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One of the most remarkable properties of HATS-4 is its high value of [Fe/H] = 0.43 ± 0.08. Of all the planet-hosting stars listed in exoplanets.org as of 2014 January, only four stars have [Fe/H] >0.43 dex, placing HATS-4 among the 1% of most metal-rich planet-hosting stars. To illustrate the high [Fe/H] of HATS-4, we show in Figure 5 a portion of the PFS spectrum of HATS-4 with a few unsaturated metallic lines and overlay PHOENIX models (Husser et al. 2013) for values of [Fe/H] = 0.0, 0.5 keeping the other stellar parameters fixed to those listed in Table 5. The figure clearly shows that high metal enrichment values are needed to account for the very deep lines present in the spectrum.

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An initial analysis of the FEROS spectra suggested that vsin i was 5 ± 2 km s⁻¹, and based on this information, we scheduled observations with PFS through a well-placed transit event to measure the R–M effect. For a slowly rotating G star like HATS-4 it is critical to distinguish between rotational broadening (parameterized by vsin i) and broadening due to turbulence (parameterized by macroturbulence ζ) when modeling the spectra. Here we describe our procedure for simultaneously measuring both of these parameters from the PFS data.

Both rotation and turbulence are large-scale motions on the surface of the star, with the latter being generated by circulation and convective cells that fill the surface. They result in a Doppler shift of the radiation that emerges from the photosphere producing a broadening of the spectral lines. For F and earlier type stars, the rotational velocity is the principal source of line broadening. On the other hand, for late-type stars like HATS-4, both velocity phenomena are generally of similar magnitude (Gray 2005). For these stars, getting some hold on macroturbulence is necessary because it broadens the lines in a way comparable to rotation, but the R–M effect due to macroturbulence is much smaller (Albrecht et al. 2012; Boué et al. 2013). Any line broadening incorrectly attributed to rotation can thus adversely effect the inferences on the relative alignment of stellar and orbital spins.

Disentangling the value of vsin i from ζ using the width of the lines is a degenerate problem. At the velocity broadening expected for late-type dwarfs (few km s⁻¹), the line profile is usually dominated by the instrumental profile, and in addition, it depends on the atmospheric parameters of the star. The macroturbulence velocity profile is very peaked while the rotational profile is much shallower, and if one is able to observe lines at very high resolution and S/N, a Fourier analysis of single lines can separate both effects (Gray 2005), a methodology that has been applied for bright stars. For fainter systems like HATS-4, this becomes prohibitive, but one can exploit the many lines simultaneously available in our spectra to constrain vsin i and ζ separately.

The approach we followed is to select a large number of isolated, unblended, and unsaturated metal lines based on a PHOENIX synthetic spectrum (Husser et al. 2013) with stellar parameters corresponding to those measured with SPC. Then for the grid of synthetic models, this set of lines is convolved by the effects of vsin i and ζ for a grid of values which, in our case, was given by {0.1, 0.2, 0.3, ..., 7.8, 7.9, 8.0} km s⁻¹ for both quantities. The convolved models were generated following the radial–tangential anisotropic macroturbulence model, which assumes that a certain fraction of the stellar material moves tangential to its surface and the rest of the material moves along the stellar radius (Gray 2005). We assumed that both fractions are equal. To compute the convolved line profile, a numerical disk integration was performed at each wavelength including the macroturbulence Doppler shift at each point on the disk and also the shift due to the stellar rotation. We also include a linear limb darkening law in the disk integration procedure using the coefficients of Claret & Bloemen (2011), performing a linear interpolation to obtain the value at each wavelength.

Once we have the grid of convolved models, we compute the quantity $X^2 = \sum _{k=1}^K\sum _{i} [m_i(v \sin {i},\zeta)-d_i]^2$, where m_i(vsin i, ζ) is the convolved model, and d_i is the observed spectrum. The index k runs over the set of chosen lines while i runs over the pixels belonging to each of the K lines. The pair of $(\hat{v \sin {i}}, \hat{\zeta })$ values producing the lowest value of X² are taken to be our estimates. Based on the fact that ζ and vsin i only change the shape of the spectral lines, we normalize each line (both for the data and the models) by its total absorbed flux in order to reduce the effect of systematic mismatches between the data and models. Effectively, we are thus fitting for the line shape and not its strength. This normalization also minimizes the effect of errors in the measured log g and [Fe/H] because in the case of non-saturated metal lines, changes in these parameters mainly affect their strength but not their shape or width. To estimate the uncertainties on vsin i and ζ, we applied a bootstrap over the chosen metallic lines. That is, we selected a set of lines with replacements from our list and re-ran the fit, obtaining a sample of bootstrap estimates $\lbrace v \sin {i}_J,\zeta _J\rbrace _{J=1}^B$ where B is the number of bootstrap replications. From the bootstrap sample we can estimate the parameter uncertainties by taking their dispersion.

We applied this method to the two I₂-free templates acquired with PFS (see Section 2.2). We chose 145 lines in the range 5200–6500 Å and, due to the 2 × 2 binning used in the observations, we can sample each line with ≈10 pixels. To get the instrumental response, we used the calibration thorium–argon (ThAr) spectra taken with the same slit we used in the observations. First we computed a global spectral profile median combining all the normalized emission lines of the ThAr spectrum. This global profile was very well fitted by a Gaussian. We then fitted Gaussians to each emission line to trace the instrumental response across our spectral range. A clear trend was identified in each echelle order whereby the spectral resolution increases from blue to red. This trend was accounted for by fitting to each order the width of the ThAr lines as a linear function of wavelength. We note that in observations of stellar objects, the slit is illuminated by the seeing profile, while in a ThAr frame, the slit is fully illuminated, generally leading to different profiles for emission lines in the ThAr frames and stellar objects in science observations. Given that the slit width we used is small compared to the full width at half-maximum (FWHM) of the seeing profiles during our observations, using the ThAr frames to estimate the instrumental response is an adequate approximation.

Our method yielded values of vsin i=0.7 ± 0.5 km s⁻¹ and ζ = 1.3 ± 0.4 km s⁻¹ for HATS-4. To test the sensitivity of our results on the assumed T_eff⋆, we repeated the procedure but with a synthetic model with values of T_eff⋆ ± 1σ from the SPC values, obtaining results fully consistent with the ones we quote. As a validation procedure, we measured vsin i and ζ for τ Ceti following the same procedure as for HATS-4. The stellar parameters for τ Ceti were taken from Maldonado et al. (2012). We measured vsin i=0.5 ± 0.4 km s⁻¹ and ζ = 2.3 ± 0.1 km s⁻¹. The vsin i value is in agreement with current studies which point toward τ Ceti having a rotation axis close to perpendicular to the sky, and the value for ζ is in good agreement with the expected value for the spectral type of τ Ceti (Gray 2005). We note that the total broadening by vsin i and ζ for HATS-4 is consistent with the value of vsin i estimated by SPC.

In Figure 6, we show the RVs during transit measured using PFS on the night of 2012 December 30 (UT). Along with the data, we show the expected behavior of the RVs without considering the R–M effect and the expected behavior assuming the system was aligned and vsin i had the value of 5 km s⁻¹ initially estimated from the FEROS data. The R–M effect was calculated for RVs measured with an I₂ cell using the ARoME library (Boué et al. 2013). It is clear that with vsin i=5 km s⁻¹ the precision afforded by PFS would have allowed us to measure the relative projected angle between the stellar and orbital spins, but with the actual value of vsin i=0.5 ± 0.4 km s⁻¹ the R–M effect is barely noticeable and thus no constraints are possible.

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To rule out the possibility that HATS-4 is a blended stellar eclipsing binary system, we conducted a blend analysis as described in Hartman et al. (2011b). This analysis attempts to model the available light curves, photometry calibrated to an absolute scale, and spectroscopically determined stellar atmospheric parameters, using combinations of stars with parameters constrained to lie on the Girardi et al. (2000) evolutionary tracks. We find that the data are best described by a planet transiting a star. Moreover, the only non-planetary blend models that cannot be rejected with greater than 5σ confidence, based on the photometry alone, would have easily been rejected as double-lined spectroscopic binary systems, or would have exhibited very large (∼1 km s⁻¹) RV and/or BS variations. Such large BS variations can be ruled out based on the Subaru/HDS measurements which show an rms scatter of only ∼22 m s⁻¹.

The pipeline starts with the classification of the different image frames present in a directory into the following types: bias, quartz (fiber flats), thorium–argon (ThAr) frames (object or comparison fiber illuminated by the wavelength reference lamp), and science frames (in our case, with the object fiber illuminated by a star and the comparison fiber by the wavelength reference lamp). Master bias and flat frames are constructed by median combining biases and fiber flats. The master bias is used to subtract the bias structure while the master flats are used to trace all echelle orders for both the object and comparison fibers. Orders are identified by an order finding algorithm which starts by median filtering the central column of the master flat with a 45 pixel window. Then, a robust mean and standard deviation of this baseline-subtracted column is obtained and an order is considered detected if a given pixel and two consecutive ones have a signal of more than five standard deviations from the mean. The positions of these consecutive pixels are saved and then their signals are cross-correlated with a Gaussian in order to find robust pixel positions for the center of the profile of each order at the central column. The process is repeated for adjacent columns, and the centers for each order are finally fitted with a fourth-degree polynomial to determine the trace for each order. Once orders have been traced we proceed to extract the flux of the science and ThAr frames. For the latter, we perform a simple extraction, i.e., just summing the flux in a region ±3 pixels around the trace. The same is true of the comparison fiber of the science frames which is illuminated by the ThAr lamp. For the object fiber in the science frames we perform optimal extraction for distorted spectra as presented in Marsh (1989).

Wavelength calibration is computed based on the emission lines of the spectrum of a ThAr lamp. The pipeline only identifies lines contained in the line list presented in Lovis & Pepe (2007). Reference files are created once for every echelle order. In these reference files, each line is associated with an approximate pixel position along the trace. The pipeline then fits Gaussians around these zones after determining an offset in pixel space between the positions in the reference file and the lines of a given echelle order in the frame under processing via cross-correlation. The Gaussian means give precise pixel positions of the lines, allowing us to determine the relation between wavelength, pixel, and echelle order for each emission line. In the case of blended lines, multiple Gaussians are fitted. An individual wavelength solution is first computed for each echelle order and ThAr lines that deviate significantly from the fit are rejected iteratively until the rms is below 75 m s⁻¹. Then a global wavelength solution in the form of an expansion of the grating equation (see Section 2.6 in Baranne et al. 1996) using Chebyshev polynomials is fitted and more lines are iteratively rejected until the rms of the global solution is below 100 m s⁻¹. Our global wavelength solution takes the form

$$\begin{equation} \lambda (x,m) = \frac{1}{m}\sum _{i=0}^{3}\sum _{j=0}^{4} a_{ij} c^i(m) c^j(x), \end{equation} \tag{ A1 }$$

where x and m refer to the pixel value and echelle order number, respectively, cⁿ denotes the Chebyshev polynomial of order n, and a_ij are the coefficients that are fitted to obtain the wavelength solution. The echelle order numbers in CORALIE range from m_i = 89 (reddest) to m_f = 159 (bluest).

Wavelength solutions are first computed for object and comparison fibers of all ThAr calibration frames and each science frame is associated with the closest ThAr frame in time. Then, the pipeline determines the instrumental velocity shift δv between the science frame and the associated ThAr frame by fitting a velocity-shifted version of the wavelength solution of the comparison fiber of the associated ThAr frame to the comparison fiber of the science frame. Finally, the object fiber wavelength solution of the associated ThAr frame is applied to the science object fiber shifted by the instrumental velocity shift δv computed with the comparison fibers. In general, the instrumental shifts are smaller than 10 m s⁻¹ on timescales of ∼1 hr.

After obtaining the wavelength-calibrated spectrum of a star, the pipeline determines the barycentric correction and applies it to the wavelength solution using routines from the Jet Propulsion Laboratory ephemerides (JPLephem) package. We then apply a fast and robust stellar parameter determination to each stellar spectrum. In order to estimate the stellar parameters (T_eff⋆, log g, [Fe/H], vsin i) we cross-correlate the observed spectrum against a grid of synthetic spectra of late-type stars from Coelho et al. (2005) convolved to the resolution of CORALIE and a set of vsin i values given by {0, 2.5, 5, 7.5, 10, 15, ..., 45, 50} km s⁻¹. First, a set of atmospheric parameters is determined as a starting point by ignoring any rotation and searching for the model that produces the highest cross-correlation using only the Mg triplet region. We use a coarse grid of models for this initial step (ΔT_eff⋆ = 1000 K, Δlog g = 1.0, Δ[Fe/H] = 1.0). A new cross-correlation function (CCF) between the observed spectrum and the model with the starting point parameters is then computed using a wider spectral region (4800–6200 Å). From this CCF we estimate RV and vsin i values using the peak position and width of the CCF, respectively. New T_eff⋆, log g, and [Fe/H] values are then estimated by fixing vsin i to the closest value present in our grid and searching for the set of parameters that gives the highest cross-correlation, and the new CCF is used to estimate new values of RV and vsin i. This procedure is continued until convergence on stellar parameters is reached. For high S/N spectra, uncertainties of this procedure are typically 200 K in T_eff⋆, 0.3 dex in log g, 0.2 dex in [Fe/H], and 2 km s⁻¹ in vsin i. These uncertainties were estimated from observations of stars with known stellar parameters from the literature. Results of our stellar parameter estimation procedure are obtained in about 2 minutes using a standard laptop. Fast and robust atmospheric parameters are estimated in order to make efficient use of the available observing time because in this way some false positives or troublesome systems, such as fast rotators and giants, can be identified on the fly during the follow-up process.

The radial velocity of the spectrum is computed using the cross-correlation technique against a binary mask (Baranne et al. 1996) that depends on the spectral type. The available masks are for G2, K5, and M5, and are the same ones used by the HARPS (Mayor et al. 2003) data reduction system but with the transparent regions made wider given that the resolution of CORALIE is ≈0.5 times that of HARPS. If a target is being observed for the first time, first a query to the SIMBAD database is made to see if the spectral type is known and otherwise our estimate of T_eff⋆ is used to assign the mask to calculate the RV. Future observations of the same target will always use this same mask to compute the RV. The CCF is computed for each echelle order and then a weighted sum is applied to get the final CCF. Weights are given by the mean S/N on the continuum for each echelle order. A simple Gaussian is fitted to the CCF, and the mean is taken as the RV of the spectrum. The pipeline also infers the presence of moonlight contamination in the CCF. If there is a secondary peak on the CCF due to the moon, the pipeline computes the position and width of this peak and fits for the intensity to correct the RV determination. BSs are also measured using the CCF peak as described in Queloz et al. (2001a). Uncertainties on the RV and BS are determined from the width of the CCF and the mean S/N close to the Mg triplet zone using empirical scaling relations (as in, e.g., Queloz 1995) whose parameters are determined using Monte Carlo simulations where Gaussian noise is artificially added to high S/N spectra. The exact equations used to estimate the errors are

$$\begin{equation} \sigma _{\rm RV} = b + \frac{a(1.6 + 0.2 \sigma _{\rm ccf}) }{ {\rm SN}_{5130}} \end{equation} \tag{ A2 }$$

$$\begin{equation} \sigma _{\rm BS} = \frac{d}{{\rm SN}_{5130}} + c, \end{equation} \tag{ A3 }$$

where a, b, c, d are the coefficients obtained via the Monte Carlo simulations and depend on the applied mask, SN₅₁₃₀ is the continuum S/N at 5130 Å and σ_ccf is the dispersion of the Gaussian fit to the CCF. For illustration, the values of the coefficients for the G2 mask are a = 0.06544, b = 0.00146, c = 0.00181, and d = 0.24416. If the estimated uncertainty σ_RV < 9 m s⁻¹ we assign it a value of 9 m s⁻¹ given that the long-term RV precision we achieve is ≈9 m s⁻¹ over a timescale of several years. We determined this value by monitoring three RV standard stars (HD 72673, HD 157347, and HD 32147) starting around 2010. Figure 8 shows the RV time series for all the CORALIE measurements we have taken of the standards, whose spectra have SN₅₁₃₀ in the range ∼50–150.

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