We present a novel method to derive rotation curves of the inner broad-line region (BLR) of lensed quasars with light-day spatial resolution.The approach exploits microlensing distortions of the broad emission lines (BELs), where the strength of the effect in the line wings traces the size of the emitting region at different velocities.We analyze the high-ionization lines Si IV and C IV in five gravitationally lensed quasars, measuring microlensing amplitudes across several velocity bins.Bayesian inference yields emission-region sizes, which we confront with a Keplerian disk model.We find a smooth, monotonic increase in microlensing with velocity, and the derived velocity-size relations are consistent with disk-like rotation.These results provide the first direct evidence for Keplerian motion in the innermost BLR of quasars.

Microlensing by stars in the lens galaxy of a gravitationally lensed quasar is a phenomenon that can selectively magnify quasar subregions, producing observable changes in the continuum brightness or distortions in the emission line profiles. Hence, microlensing allows us to probe the inner quasar regions. In this paper, we report measurements of the ratio of the broad emission line region (BLR) radius to the continuum source radius in eight lensed quasars, for the C IV, Mg II, and Hα emission lines and their respective underlying continua at λλ 1550 Å, 2800 Å, and 6563 Å. The microlensing-induced line profile distortions and continuum magnifications were observed in the same single-epoch datasets, and simultaneously compared with microlensing simulations. We found that, on average, the inner radius of the BLR starts at the end of the UV-optical continuum source, independently of the line ionization and the wavelength of the continuum. The half-light radius of the BLR is, on average, a factor of six larger than the half-light radius of the continuum source, independently of the quasar’s bolometric luminosity. We also found a correlation between the BLR radius and the continuum source radius, supporting the idea that the dominant contribution to the UV-optical continuum may come from the BLR itself. Our results independently confirm the results of reverberation mapping studies, and extend them to higher-redshift, higher-luminosity quasars.

Microlensing-induced distortions of broad emission line profiles observed in the spectra of gravitationally lensed quasars can be used to probe the size, geometry, and kinematics of the broad-line region (BLR). To this end, single-epoch Mg II or Hα line profile distortions observed in five gravitationally lensed quasars, J1131-1231, J1226-0006, J1355-2257, J1339+1310, and HE0435-1223, have been compared with simulated ones. The simulations are based on three BLR models, a Keplerian disk (KD), an equatorial wind (EW), and a polar wind (PW), with different sizes, inclinations, and emissivities. The models that best reproduce the observed line profile distortions were identified using a Bayesian probabilistic approach. We find that the wide variety of observed line profile distortions can be reproduced with microlensing-induced distortions of line profiles generated by our BLR models. For J1131, J1226, and HE0435, the most likely model for the Mg II and Hα BLRs is either KD or EW, depending on the orientation of the magnification map with respect to the BLR axis. This shows that the line profile distortions depend on the position and orientation of the isovelocity parts of the BLR with respect to the caustic network, and not only on their different effective sizes. For the Mg II BLRs in J1355 and J1339, the EW model is preferred. For all objects, the PW model has a lower probability. As for the high-ionization C IV BLR, we conclude that disk geometries with kinematics dominated by either Keplerian rotation or equatorial outflow best reproduce the microlensing effects on the low-ionization Mg II and Hα emission line profiles. The half-light radii of the Mg II and Hα BLRs are measured in the range of 3 to 25 light-days. We also confirm that the size of the region emitting the low-ionization lines is larger than the region emitting the high-ionization lines, with a factor of four measured between the sizes of the Mg II and C IV emitting regions in J1339. Unexpectedly, the microlensing BLR radii of the Mg II and Hα BLRs are found to be systematically below the radius-luminosity (R − L) relations derived from reverberation mapping, confirming that the intrinsic dispersion of the BLR radii with respect to the R − L relations is large, but also revealing a selection bias that affects microlensing-based BLR size measurements. This bias arises from the fact that, if microlensing-induced line profile distortions are observed in a lensed quasar, the BLR radius should be comparable to the microlensing Einstein radius, which varies only weakly with typical lens and source redshifts.

Microlensing of the broad emission line region (BLR) in gravitationally lensed quasars produces line profile distortions that can be used to probe the BLR size, geometry, and kinematics. Based on single-epoch spectroscopic data, we analyzed the C IV line profile distortions due to microlensing in two quasars, SDSS J133907.13+131039.6 (J1339) and SDSS J113803.73+031457.7 (J1138), complementing previous studies of microlensing in the quasars Q2237+0305 and J1004+4112. J1339 shows a strong, asymmetric line profile deformation, while J1138 shows a more modest, symmetric deformation, confirming the rich diversity of microlensing-induced spectral line deformations. To probe the C IV BLR, we compared the observed line profile deformations to simulated ones. The simulations are based on three simple BLR models, a Keplerian disk (KD), an equatorial wind (EW), and a polar wind (PW), of various sizes, inclinations, and emissivities. These models were convolved with microlensing magnification maps specific to the microlensed quasar images, which produced a large number of distorted line profiles. The models that best reproduce the observed line profile deformations were then identified using a Bayesian probabilistic approach. We find that the line profile deformations can be reproduced with the simple BLR models under consideration, with no need for more complex geometries or kinematics. The models with disk geometries (KD and EW) are preferred, while the PW model is definitely less likely. In J1339, the EW model is favored, while the KD model is preferred in Q2237+0305, suggesting that various kinematical models can dominate the C IV BLR. For J1339, we find the C IV BLR half-light radii to be r1/2 = 5.1−2.9+4.6 light-days and r1/2 = 6.7−3.8+6.0 light-days from spectra obtained in 2014 and 2017, respectively. They do agree within uncertainties. For J1138, the amplitude of microlensing is smaller and more dependent on the macro-magnification factor. From spectra obtained in 2005 (single epoch), we find r1/2 = 4.9−2.7+4.9 light-days and r1/2 = 12−8+13 light-days for two extreme values of the macro-magnification factor. Combining these new measurements with those previously obtained for the quasars Q2237+0305 and J1004+4112, we show that the BLR radii estimated from microlensing do follow the C IV radius–luminosity relation obtained from reverberation mapping, although the microlensing radii seem to be systematically smaller, which could indicate either a selection bias or a real offset.

J1004+4112 is a lensed quasar for which the first broad emission line profile deformations due to microlensing were identified. Detailed interpretations of these features have nevertheless remained controversial. Based on 15 spectra obtained from 2003 to 2018, in this work, we revisit the microlensing effect that distorts the C IV broad emission line profile in J1004+4112. We take advantage of recent measurements of the image macro-magnification ratios, along with the fact that at one epoch, image B was not microlensed, thus constituting a reference spectrum to unambiguously characterize the microlensing effect observed in image A. After disentangling the microlensing in images A and B, we show that the microlensing-induced line profile distortions in image A, although variable, are remarkably similar over a period of 15 years. We find they are characterized by a strong magnification of the blue part of the line profile, a strong demagnification of the red part of the line profile, and a small-to-negligible demagnification of the line core. We used the microlensing effect, characterized by either the full magnification profile of the C IV emission line or a set of four integrated indices, to constrain the broad emission-line region (BLR) size, geometry, and kinematics. For this purpose, we modeled the deformation of the emission lines considering three simple, representative BLR models: a Keplerian disk, an equatorial wind, and a biconical polar wind, with various inclinations with respect to the line of sight. We find that the observed magnification profile of the C IV emission line in J1004+4112 can be reproduced with the simple BLR models we considered, without the need for more complex BLR features. The magnification appears dominated by the position of the BLR with respect to the caustic network – and not by the velocity-dependent size of the BLR. The favored models for the C IV BLR are either the Keplerian disk or the equatorial wind, depending on the orientation of the BLR axis with respect to the caustic network. We also find that the polar wind model can be discarded. We measured the C IV BLR half-light radius as r1/2=2.8−1.7+2.0 light-days. This value is smaller than the BLR radius expected from the radius-luminosity relation derived from reverberation mapping, but it is still in reasonable agreement given the large uncertainties.

Abstract The distortions of absorption line profiles caused by photospheric brightness variations on the surfaces of cool, main-sequence stars can mimic or overwhelm radial velocity (RV) shifts due to the presence of exoplanets. The latest generation of precision RV spectrographs aims to detect velocity amplitudes ≲ 10 cm s−1, but requires mitigation of stellar signals. Statistical techniques are being developed to differentiate between Keplerian and activity-related velocity perturbations. Two important challenges, however, are the interpretability of the stellar activity component as RV models become more sophisticated, and ensuring the lowest-amplitude Keplerian signatures are not inadvertently accounted for in flexible models of stellar activity. For the K2V exoplanet host ϵ Eridani, we separately used ground-based photometry to constrain Gaussian processes for modeling RVs and TESS photometry with a light-curve inversion algorithm to reconstruct the stellar surface. From the reconstructions of TESS photometry, we produced an activity model that reduced the rms scatter in RVs obtained with EXPRES from 4.72 to 1.98 m s−1. We present a pilot study using the CHARA Array and MIRC-X beam combiner to directly image the starspots seen in the TESS photometry. With the limited phase coverage, our spot detections are marginal with current data but a future dedicated observing campaign should allow for imaging, as well as allow the stellar inclination and orientation with respect to the debris disk to be definitively determined. This work shows that stellar surface maps obtained with high-cadence, time-series photometric and interferometric data can provide the constraints needed to accurately reduce RV scatter.

Line profile distortions are commonly observed in gravitationally lensed quasar spectra. These distortions are caused by microlensing from the stars in the lensing galaxy, which produce differential magnification of spatially and kinematically separated parts of the broad line region (BLR). The quasi-simultaneous visible and near-infrared spectroscopy of the lensed quasar Q2237+0305 reveals strong microlensing-induced line deformations in the high-ionization C IVλ1549 Å and the low-ionization Hα emission lines. We use this effect to constrain the BLR size, geometry, and kinematics in Q2237+0305. For this purpose, we modeled the deformation of the emission lines for three representative BLR models: a Keplerian disk, an equatorial wind, and a biconical polar wind. We considered various inclinations with respect to the line of sight. We find that the observed microlensing effect, characterized by a set of four indices, can only be reproduced by a subsample of the considered BLR models. The microlensing analysis favors a Keplerian disk model for the regions emitting the C IV and the Hα emission lines. A polar wind model remains possible for the C IV BLR, although it is less likely. The equatorial wind model is totally excluded. A preferred inclination of the BLR of 40° is found, in agreement with expectations for a type 1 AGN and past constraints on the accretion disk inclination. The half-light radius of the BLR is r1/2 ≃ 47 ± 19 light-days, with no significant difference between the C IV and Hα BLRs. The size of the C IV BLR agrees with the radius-luminosity relation derived from reverberation mapping, while the size of the Balmer line BLR is one order of magnitude smaller, possibly revealing different quasar properties at high luminosities and high accretion rates.

Aims. We study the 2D spectral line profile of the High Accuracy Radial Velocity Planet Searcher (HARPS), measuring its variation with position across the detector and with changing line intensity. The characterization of the line profile and its variations are important for achieving the precision of the wavelength scales of 10−10 or 3.0 cm s−1 necessary to detect Earth-twins in the habitable zone around solar-like stars. Methods. We used a laser frequency comb (LFC) with unresolved and unblended lines to probe the instrument line profile. We injected the LFC light – attenuated by various neutral density filters – into both the object and the reference fibres of HARPS, and we studied the variations of the line profiles with the line intensities. We applied moment analysis to measure the line positions, widths, and skewness as well as to characterize the line profile distortions induced by the spectrograph and detectors. Based on this, we established a model to correct for point spread function distortions by tracking the beam profiles in both fibres. Results. We demonstrate that the line profile varies with the position on the detector and as a function of line intensities. This is consistent with a charge transfer inefficiency effect on the HARPS detector. The estimate of the line position depends critically on the line profile, and therefore a change in the line amplitude effectively changes the measured position of the lines, affecting the stability of the wavelength scale of the instrument. We deduce and apply the correcting functions to re-calibrate and mitigate this effect, reducing it to a level consistent with photon noise.

ABSTRACT The radial velocity (RV) of the Sun as a star is affected by its surface convection and magnetic activity. The moments of the cross-correlation function between the solar spectrum and a binary line mask contain information about the stellar RV and line-profile distortions caused by stellar activity. As additional indicators, we consider the disc-averaged magnetic flux and the filling factor of the magnetic regions. Here we show that the activity-induced radial-velocity fluctuations are reduced when we apply a kernel regression to these activity indicators. The disc-averaged magnetic flux proves to be the best activity proxy over a time-scale of one month and gives a standard deviation of the regression residuals of 1.04 m s−1, more than a factor of 2.8 smaller than the standard deviation of the original RV fluctuations. This result has been achieved thanks to the high-cadence and time continuity of the observations that simultaneously sample both the RV and the activity proxies.

Recent studies have shown that line profile distortions are commonly observed in gravitationally lensed quasar spectra. We investigate the effect of gravitational microlensing on quasar broad emission line profiles and their underlying continuum, combining the emission from simple representative BLR models with generic microlensing magnification maps. Specifically, we considered Keplerian disk, polar, and equatorial wind BLR models of various sizes. The effect of microlensing has been quantified with four observables: $\mu^{BLR}$, the total magnification of the broad emission line; $\mu^{cont}$, the magnification of the underlying continuum; as well as red/blue, RBI and wings/core, WCI, indices that characterize the line profile distortions. The simulations showed that distortions of line profiles, such as those recently observed in lensed quasars, can indeed be reproduced and attributed to the differential effect of microlensing on spatially separated regions of the BLR. While the magnification of the emission line $\mu^{BLR}$ sets an upper limit on the BLR size and, similarly, the magnification of the continuum $\mu^{cont}$ sets an upper limit on the size of the continuum source, the line profile distortions mainly depend on the BLR geometry and kinematics. We thus built (WCI,RBI) diagrams that can serve as diagnostic diagrams to discriminate between the various BLR models on the basis of quantitative measurements. It appears that a strong microlensing effect puts important constraints on the size of the BLR and on its distance to the high-magnification caustic. In that case, BLR models with different geometries and kinematics are more prone to produce distinctive line profile distortions for a limited number of caustic configurations, which facilitates their discrimination.

Planetary rings produce a distinct shape distortion in transit lightcurves.\nHowever, to accurately model such lightcurves the observations need to cover\nthe entire transit, especially ingress and egress, as well as an out-of-transit\nbaseline. Such observations can be challenging for long period planets, where\nthe transits may last for over a day. Planetary rings will also impact the\nshape of absorption lines in the stellar spectrum, as the planet and rings\ncover different parts of the rotating star (the Rossiter-McLaughlin effect).\nThese line-profile distortions depend on the size, structure, opacity,\nobliquity and sky projected angle of the ring system. For slow rotating stars,\nthis mainly impacts the amplitude of the induced velocity shift, however, for\nfast rotating stars the large velocity gradient across the star allows the line\ndistortion to be resolved, enabling direct determination of the ring\nparameters. We demonstrate that by modeling these distortions we can recover\nring system parameters (sky-projected angle, obliquity and size) using only a\nsmall part of the transit. Substructure in the rings, e.g. gaps, can be\nrecovered if the width of the features ($\\delta W$) relative to the size of the\nstar is similar to the intrinsic velocity resolution (set by the width of the\nlocal stellar profile, $\\gamma$) relative to the stellar rotation velocity ($v$\nsin$i$, i.e. $\\delta W / R_* \\gtrsim v$sin$i$/$\\gamma$). This opens up a new\nway to study the ring systems around planets with long orbital periods, where\nobservations of the full transit, covering the ingress and egress, are not\nalways feasible.\n

JRB and CAH were supported by the Science and Technology Facilities Council (STFC) under the grant ST/L000776/1. SVJ acknowledges research funding by the Deutsche Forschungsgemeinschaft (DFG) under grant SFB 963/1, project A16. HRAJ MT and FF are supported by the Leverhulme Trust grant, RPG-2014-281, and the STFC grant, ST/M001008/1. JSJ acknowledges funding by Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) through grants 1161218 and 3110004, and partial support from CATA-Basal (PB06, Comisión Nacional de Investigación Científica y Tecnológica (CONICYT)), the GEMINI-CONICYT FUND and from the Comité Mixto ESO-GOBIERNO DE CHILE.

Starspots are an important manifestation of stellar activity and yet their distribution patterns on the lowest mass stars is not well known. Time series spectra of fully convective M dwarfs taken in the red-optical with UVES reveal numerous line profile distortions which are interpreted as starspots. New Doppler images of HU Del (GJ 791.2A; M4.5V), BL Ceti (GJ 65A; M5.5V) and UV Ceti (GJ 65B; M6V) at two epochs separated by three nights are presented. We find that contrast ratios corresponding to photosphere-spot temperature differences of only 100-400 K are sufficient to model the time series spectra of M4.5V - M9V stars. Starspots are reconstructed at a range of phases and latitudes with mean spot filling factors of only a few per cent. The distribution and low-contrast of the spots/spot-groups that we recover are likely to be responsible for the low amplitude photometric variability seen in late-M dwarfs. The stability of the spot patterns in the two sets of timeseries observations enables us to measure the latitude dependent differential rotation, which we find to be consistent with zero

We present the discovery of HAT-P-57b, a P = 2.4653 day transiting planet around a V = 10.465 +- 0.029 mag, Teff = 7500 +- 250 K main sequence A8V star with a projected rotation velocity of v sin i = 102.1 +- 1.3 km s^-1. We measure the radius of the planet to be R = 1.413 +- 0.054 R_J and, based on RV observations, place a 95% confidence upper limit on its mass of M < 1.85 M_J . Based on theoretical stellar evolution models, the host star has a mass and radius of 1.47 +- 0.12 M_sun, and 1.500 +- 0.050 R_sun, respectively. Spectroscopic observations made with Keck-I/HIRES during a partial transit event show the Doppler shadow of HAT-P-57b moving across the average spectral line profile of HAT-P- 57, confirming the object as a planetary system. We use these observations, together with analytic formulae that we derive for the line profile distortions, to determine the projected angle between the spin axis of HAT-P-57 and the orbital axis of HAT-P-57b. The data permit two possible solutions, with -16.7 deg < lambda < 3.3 deg or 27.6 deg < lambda < 57.4 deg at 95% confidence, and with relative probabilities for the two modes of 26% and 74%, respectively. Adaptive optics imaging with MMT/Clio2 reveals an object located 2.7" from HAT-P-57 consisting of two point sources separated in turn from each other by 0.22". The H and L -band magnitudes of the companion stars are consistent with their being physically associated with HAT-P-57, in which case they are stars of mass 0.61 +- 0.10 M_sun and 0.53 +- 0.08 M_sun. HAT-P-57 is the most rapidly rotating star, and only the fourth main sequence A star, known to host a transiting planet.

Since M4.5 - M9 dwarfs exhibit equatorial rotation velocities of order 10\nkm/s on average, radial velocity surveys targeting this stellar population will\nlikely need to find methods to effectively remove starspot jitter. We present\nthe first high resolution Doppler images of the M4.5 dwarf, GJ 791.2A, and the\nM9 dwarf, LP 944-20. The time series spectra of both objects reveal numerous\nline profile distortions over the rotation period of each star which we\ninterpret as starspots. The transient distortions are modelled with\nspot/photosphere contrast ratios that correspond to model atmosphere\ntemperature differences of Tphot-Tspot = 200 and 300 K. GJ 791.2A is a fully\nconvective star with vsini = 35.1 km/s. Although we find more starspot\nstructure at high latitudes, we reconstruct spots at a range of phases and\nlatitudes with a mean spot filling of ~3%. LP 944-20 is one of the brightest\nknown late-M dwarfs, with spectral type M9V and vsini = 30.8 km/s. Its spectral\ntime series exhibits two dominant transient line distortions that are\nreconstructed as high latitude spots, while a mean spot filling factor of only\n1.5% is found. The occurrence of low-contrast spots at predominantly high\nlatitudes, which we see in both targets here, is in general likely to be\nresponsible for the low amplitude photometric variability seen in late-M\ndwarfs. For GJ 791.2A, the radial velocities induced by the starspot features\nyield an rms velocity variability of 138 m/s, which can be reduced by a factor\nof 1.9 using our reconstructed surface brightness distributions.\n

Transiting planets around rapidly rotating stars are not amenable to precise radial velocity observations, such as are used for planet candidate validation, as they have wide, rotationally broadened stellar lines. Such planets can, however, be observed using Doppler tomography, wherein the stellar absorption line profile distortions during transit are spectroscopically resolved. This allows the validation of transiting planet candidates and the measurement of the stellar spin-planetary orbit (mis)alignment, an important statistical probe of planetary migration processes. We present Doppler tomographic observations which provide a direct confirmation of the hot Jupiter Kepler-13 Ab, and also show that the planet has a prograde, misaligned orbit, with lambda = 58.6 +/- 2.0 degrees. Our measured value of the spin-orbit misalignment is in significant disagreement with the value of lambda = 23 +/- 4 degrees previously measured by Barnes et al. (2011) from the gravity-darkened Kepler lightcurve. We also place an upper limit of 0.75 solar masses (95% confidence) on the mass of Kepler-13 C, the spectroscopic companion to Kepler-13 B, the proper motion companion of the planet host star Kepler-13 A.

We present a detailed temperature and magnetic investigation of the T Tauri star V410 Tau by means of a simultaneous Doppler- and Zeeman-Doppler Imaging. Moreover we introduce a new line profile reconstruction method based on a singular value decomposition (SVD) to extract the weak polarized line profiles. One of the key features of the line profile reconstruction is that the SVD line profiles are amenable to radiative transfer modeling within our Zeeman-Doppler Imaging code iMap. The code also utilizes a new iterative regularization scheme which is independent of any additional surface constraints. To provide more stability a vital part of our inversion strategy is the inversion of both Stokes I and Stokes V profiles to simultaneously reconstruct the temperature and magnetic field surface distribution of V410 Tau. A new image-shear analysis is also implemented to allow the search for image and line profile distortions induced by a differential rotation of the star. The magnetic field structure we obtain for V410 Tau shows a good spatial correlation with the surface temperature and is dominated by a strong field within the cool polar spot. The Zeeman-Doppler maps exhibit a large-scale organization of both polarities around the polar cap in the form of a twisted bipolar structure. The magnetic field reaches a value of almost 2 kG within the polar region but smaller fields are also present down to lower latitudes. The pronounced non-axisymmetric field structure and the non-detection of a differential rotation for V410 Tau supports the idea of an underlying $\alpha^2$-type dynamo, which is predicted for weak-lined T Tauri stars.

We analyze the profiles of iron emission lines observed in solar coronal\ndimmings associated with coronal mass ejections, using the EUV Imaging\nSpectrometer on board Hinode. We quantify line profile distortions with\nempirical coefficients (asymmetry and peakedness) that compare the fitted\nGaussian to the data. We find that the apparent line broadenings reported in\nprevious studies are likely to be caused by inhomogeneities of flow velocities\nalong the line of sight, or at scales smaller than the resolution scale, or by\nvelocity fluctuations during the exposure time. The increase in the amplitude\nof Alfv\\'en waves cannot, alone, explain the observed features. A\ndouble-Gaussian fit of the line profiles shows that, both for dimmings and\nactive region loops, one component is nearly at rest while the second component\npresents a larger Doppler shift than that derived from a single-Gaussian fit.\n

Abstract Theories of planet formation predict the birth of giant planets in the inner, dense, and gas-rich regions of the circumstellar disks around young stars. These are the regions from which strong CO emission is expected. Observations have so far been unable to confirm the presence of planets caught in formation. We have developed a novel method to detect a giant planet still embedded in a circumstellar disk by the distortions of the CO molecular line profiles emerging from the protoplanetary disk's surface. The method is based on the fact that a giant planet significantly perturbs the gas velocity flow in addition to distorting the disk surface density. We have calculated the emerging molecular line profiles by combining hydrodynamical models with semianalytic radiative transfer calculations. Our results have shown that a giant Jupiter-like planet can be detected using contemporary or future high-resolution near-IR spectrographs such as VLT/CRIRES or ELT/METIS. We have also studied the effects of binarity on disk perturbations. The most interesting results have been found for eccentric circumprimary disks in mid-separation binaries, for which the disk eccentricity - detectable from the asymmetric line profiles - arises from the gravitational effects of the companion star. Our detailed simulations shed new light on how to constrain the disk kinematical state as well as its eccentricity profile. Recent findings by independent groups have shown that core-accretion is severely affected by disk eccentricity, hence detection of an eccentric protoplanetary disk in a young binary system would further constrain planet formation theories.

We present a method of modeling the radial velocity (RV) measurements which can be useful in searching for planets hosted by chromospherically active stars. We assume that the observed RV signal is induced by the reflex motion of a star as well as by distortions of spectral line profiles, measured by the Bisector Velocity Span (BVS). The RVs are fitted with a common planetary model including RV correction term depending linearly on the BVS, which accounts for the stellar activity. The coefficient of correlation is an additional free parameter of the RV model. That approach differs from correcting the RVs before or after fitting the "pure" planetary model. We test the method on simulated data derived for single-planet systems. The results are compared with the outcomes of algorithms found in the literature.