Main

Kepler-223 is a known four-planet system13 orbiting around a slightly evolved (about 6-Gyr-old), Sun-like star (see Methods, Extended Data Fig. 1). The low observational signal-to-noise ratio initially caused an incorrect identification of the orbital periods of this system13,14, and has hitherto precluded its detailed characterization. For the analysis of transit timing variation (TTV), we use long cadence (29.4-min integrations) data, collected over the full duration of NASA’s Kepler Space Mission from March 2009 to May 2013. Over this window, the ratios of the orbital periods (P) of planets b, c, d and e (named in alphabetic order from the interior, beginning with b) average Pc/Pb = 1.3336, Pd/Pc = 1.5015 and Pe/Pd = 1.3339 (ref. 15). We expect a system with periods so close to resonance to exhibit TTVs due to planet–planet interactions8 (see Methods).

To measure TTVs, we bin the data into 3-month segments based on Kepler’s observing quarters, confirm that the orbital periods are near resonances, and demonstrate the time-variable nature of the transits (Fig. 1, Extended Data Fig. 2, Extended Data Table 1 and Methods). Phase folding the data and removing the TTVs allows the noisy transits to be identified easily by eye (Fig. 2).

Figure 1: Transit timing variations (TTVs) for all four planets with respect to a linear ephemeris.
figure 1

a–d, Calculated transit times for planets b–e, respectively, come from a linear regression of the best-fit model transits. Open grey circles show the transit times from 20 different models that were stable over a 107-year simulation. Black ‘+’ symbols with 1σ error bars indicate the TTVs found by fitting quarterly binned data (see Extended Data Fig. 2), and black diamonds are the corresponding points for the mean of the grey-circle models binned in the same manner. Where the noise causes large uncertainties, the photodynamic model may deviate from the binned data, but more accurately reflects the true TTVs. BJD, barycentric Julian date.

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Figure 2: Binned planet transits.
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a–d, Photometry data near transits of planets b–e, respectively (small black triangles), binned together (large black circles) by phase-folding after removing the measured TTV for each quarter. Systematic trends have been removed and the flux normalized to 1.0 out of transit. The coloured lines are the best-fit transit models to the data.

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The behaviour of the resonant chain can be characterized by its Laplace angles: ϕ1 ≡ −λb + 2λc − λd, ϕ2 ≡ λc − 3λd + 2λe (for mean longitudes λi and planets i = b, c, d, e) and, for the whole system of four planets, ϕ3 ≡ 2ϕ2 − 3ϕ1 = 3λb − 4λc − 3λd + 4λe. Systems that are in resonance possess such librating Laplace angles, which ensures that two planets have a close approach when the other planets are far away, reducing chaotic interactions. The existence of a single four-body Laplace angle demonstrates that all the planets have close dynamical contact (with various three- and two-body resonances also present). We infer variations in the Laplace angles directly from the measured TTVs (see Methods and Extended Data Fig. 3). If we assume nearly circular orbits, the four years of TTVs in the data have recorded both angles performing nearly a full oscillation; ϕ1 librates between approximately 173° and 190° and ϕ2 librates between approximately 47° and 75°.

To improve the treatment of the TTV signal and directly connect it to planetary dynamics, we integrate the N-body equations of motion for the four-planet system and explicitly model the photometric transit signals over the Kepler observing window (photodynamical modelling)16. We determine best estimates and uncertainties for the system parameters by performing five-body integrations of initial conditions from the resulting posterior distribution for more than 107 orbits of the planets and retaining only parameter sets that remain stable (see Methods for details). We find that the planets all have masses of 3M⊕–9M⊕ and radii of 2.5R⊕–5.5R⊕ (M⊕ and R⊕ are the mass and radius of Earth, respectively; see Table 1). On the basis of these values and internal structure models17, we determine that the composition of the planets varies from about 1% to 5% H/He by mass for the innermost planet to more than about 10% by mass for the outermost planet; that is, they are all sub-Neptunes. The density of the planets decreases with orbital semi-major axis, consistent with scenarios involving atmospheric loss due to stellar irradiation or formation in regions of increasingly cooler temperatures18. The eccentricities of the planets are relatively low (about 0.01−0.1) in configurations that are stable for more than 107 orbits of the system. To fit the data acceptably, the eccentricities need to be slightly larger than in other systems of sub-Neptunes such as Kepler-11, whose eccentricities are less than about 0.02 (ref. 19). Because the eccentricities may be excited and stabilized by the resonances, the system can remain stable even though it is compact. The eccentricity of a planet is only loosely negatively correlated with its mass (from the TTVs in the data), so small changes in the allowed eccentricity will have a small effect on the posterior mass estimate, and removing eccentricity constraints would make the planets only slightly less dense.

Table 1 Kepler-223 system parameters
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Periods in a ratio close to 3:4:6:8 are maintained in all the stable, data-fitting solutions. The range of the ratios of the osculating periods of the planets implied by the observed TTVs over the Kepler window is typical for a resonant system. This range is narrower than that for a long-lived (more than about 107 orbits), but circulating (non-resonant), solution (Extended Data Figs 4, 5), suggesting that the system is currently in a state of libration. This libration might be temporary, and periods of Laplace-angle circulation might have occurred previously or might occur in the future for this system. However, requiring short-term Laplace-angle libration substantially increases the likelihood that a parameter set that acceptably fits the data represents a long-lived system (see Methods). Because (i) the orbital parameters of Kepler-223 are consistent with it being in a resonant state, (ii) solutions that are stable for 100 Myr exist within the parameter posteriors, and (iii) resonance greatly helps a system this compact to remain stable, we conclude that the system is probably a true resonant chain.

Planetary migration in a disk has been extensively studied and often leads to resonant chains of planets3,4,5,6. To examine the plausibility of the specific resonant chain observed in Kepler-223, we use a previously developed model20 to simulate the migration of four planets within a gas disk. We find that four planets starting well wide of resonance migrate inwards and converge to the 3:4:6:8 chain of periods that we observe with certain choices of simulation parameters (Fig. 3). Thus the Kepler-223 system is a plausible outcome of disk migration, but the full set of disk migration parameters and initial conditions that would lead to this system remains an open question.

Figure 3: A migration simulation that ends in a configuration matching the observed semi-major axis ratios, and libration angle centres and amplitudes.
figure 3

a, Time evolution of orbital-period ratios of planets b and c (Pc/Pb; red), c and d (Pd/Pc; green), and d and e (Pe/Pd; blue) in a migration simulation. b–d, Time evolution of the Laplace angles (ϕ1–3) defined in the text. The resonant angles and libration amplitudes that the planets end up in (indicated by the black horizontal lines) match those observed in the data (see, for example, Extended Data Fig. 3).

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In a migration scenario, systems trapped in resonances for which the orbital semi-major axes are small (less than about 0.5 au) can potentially be used to constrain the rate of disk photoevaporation and the lifetimes of disks, because a gaseous disk must exist in the 0.02–0.2 au range long enough for planets of moderate mass to migrate. It also provides constraints on turbulence and magnetic fields in the disk21, and the structure of the disk that causes the planets to stop migrating22. An alternative to gas-disk migration for trapping planets into resonances is migration via planetesimal scattering23. It is possible for planetesimal scattering to migrate two planets in a convergent manner, establishing a resonance. However, this convergent migration would excite the eccentricities of the planetesimal population, which would probably prevent additional planets from joining the resonance24. The presence of a large volatile (greater than about 10% H/He by mass)17 layer on the outer planets also suggests that the planets formed in the presence of a gas-containing disk at cool temperatures, further suggesting large-scale migration18.

Several other exoplanet systems have (GJ 876; ref. 25), or are speculated to have (HR 8799; ref. 20), resonant chains, but these are composed of planets that are substantially more massive and have much greater orbital distances; hence, these observations may not be relevant to the formation of systems of close-in sub-Neptunes. Several Kepler systems are probably in a true resonance (as opposed to near resonance; for example, the 6:5 system Kepler-50 and the 5:4:3 system Kepler-60; ref. 26); however, owing to the large number of known multi-planet systems, even if the orbital-period ratios of planets are essentially random, consistent with in situ, giant-impact formation, we would expect to observe some systems whose period ratios were near enough to integer values that they entered true dynamical resonances. By contrast, the precise conditions for the four-planet resonant chain of Kepler-223 cannot be accounted for by random selection of period ratios7, and the system is probably too fragile to have been assembled by giant impacts27.

The dynamical fragility of Kepler-223 suggests that resonant chains were precursors to some of the more common, non-resonant systems and that planet–planet scattering post-formation is probably an important step in creating the observed period distribution10. A model of the formation of the Solar System that has parallels with observed exoplanets involves the four giant planets entering a series of resonances, reaching their current configuration only after destabilization hundreds of millions of years later12. Numerical simulations for Kepler-223 indicate that only a small mass of orbit-crossing planetesimals is needed to move Kepler-223 off resonance28, but that it could escape this fate if intrinsic differences in protoplanetary disks resulted in the lack of such a planetesimal population. In fact, various mechanisms including disk dissipation9, planet–planet scattering10, tidal dissipation5 and planetesimal scattering11 could break migration-induced resonances in the majority of exoplanet systems. It has been suggested that some multi-resonant systems (for example, Kepler-80, which has planetary pairs near, but not in, two-body resonances) might have undergone resonant disruption as a result of tidal dissipation, which would explain most of the period ratios that are slightly greater than resonant values in Kepler data29,30. It is possible that the Kepler-223 resonance has survived as a result of its relatively more distant innermost planet. Overall, we suggest that substantial migration of planets, including epochs of resonance that are typically only temporary, rather than in situ formation, leads to the final, observed planetary orbits for many close-in sub-Neptune systems.

Methods

Stellar properties

To improve our knowledge of the Kepler-223 system, we obtained a spectrum of the host star on 10 April 2012 using the HIRES spectrometer31 at the Keck-1 10-m telescope. These data are now publicly available at http://cfop.ipac.caltech.edu. After normalizing the continuum, we model the observed spectrum using synthetic spectra. Model spectra are generated by interpolating within a grid of synthetic spectra32. The resulting spectroscopic parameters for Kepler-223 are Teff = 5,821 ± 123 K, log(g) = 4.070 ± 0.096 dex and [Fe/H] = 0.060 ± 0.047 dex (where g is the surface gravity in cm s−2 and the metallicity [Fe/H] is the logarithm of the ratio of iron to hydrogen in the star relative to that ratio in the sun).

To determine an age and mass of the star, we match the measured properties to Y2 isochrones33. We ran a Markov chain Monte Carlo (MCMC) using the spectroscopic data and an interpolation of the Y2 grid values as the model to obtain an age of and mass of (see Extended Data Fig. 1). Combining these values with log(g), we measure the stellar radius, , and stellar density, We also derive a distance from Earth of to Kepler-223 and find the mean flux S on the planets to be Sb = (492 ± 47)S0, Sc = (335 ± 32)S0, Sd = (195 ± 19)S0 and Se = (133 ± 13)S0, where S0 = 1,377 W m−2 is the average insolation of Earth.

To determine the size of model-dependent uncertainties, we compare our results to an independently developed, publicly available method for computing , and age using the Dartmouth isochrones34 (https://github.com/timothydmorton/isochrones). All three values are consistent within the 1σ error bars, so we conclude that our measurements are robust and that model-dependent errors are small compared to our quoted uncertainties. We also use a stellar population synthesis model, TRILEGAL35, with the default galaxy stellar distribution and population as described therein, to demonstrate that the best-fit mass and uncertainties described above are essentially unaffected by reasonable priors; so, we keep flat priors for all stellar parameters.

TTVs

To measure TTVs, we begin by detrending the simple aperture photometry (SAP) flux data from the Kepler portal on the Mikulski Archive for Space Telescopes (MAST). For long-cadence data (quarters 1–8), we fit the amplitudes of the first five co-trending basis vectors (largest magnitude vectors from a singular value decomposition of the photometry for a given CCD channel) to determine a baseline. We discard points marked as low quality (quality flag of ≥16). For short-cadence data (58.8-s integrations, quarters 9–17), co-trending basis vectors are not available. Instead, we first masked out the expected transit times of a preliminary model, plus 20% of the full duration of each transit intending to account for possible additional timing variations; then we fit a cubic polynomial model with a 2-day width centred within half an hour of each data point to determine its baseline. In both cases, the baseline remains dominated by instrumental systematics that are time-variable; thus, we divide the flux by this baseline.

In computing TTVs, we use only those data for which the transits do not overlap with another planetary transit (that is, two transit mid-times fall within 1 day of each other) according to a preliminary model (data with overlapping transits is modelled directly by the photodynamic method described later). To determine transit times, we first fit transit parameters (period, transit mid-time, planet-to-star radius ratio, transit duration, impact parameter and limb-darkening coefficient) to the entire long-cadence dataset. Second, we refit each quarter using the globally determined values for all parameters except for transit mid-time, which is solved for. Third, we refine the transit shape parameters and slide the refined transit model in time through the data for each planet in each quarter, computing the goodness-of-fit statistic χ2 in steps of 0.001 days. The values of the numerical χ2 function that are within 1.0 of the minimum are fit with a parabola, the minimum of which we adopt as our best estimate of the mid-time. The time shifts in each direction at which the χ2 function rises by 1 and 9 above the minimum are adopted as narrow and conservative error bars. If the likelihood surface of the mid-time parameter was Gaussian, these values would correspond to 1σ and 3σ estimates. Extended Data Table 1 reports the average time of the transits that were combined to make each measurement, the best-estimate and uncertainty estimates of these time shifts. Once phased at these transit times, the transit light curves are shown in Fig. 2. These transit times are also represented graphically in Extended Data Fig. 2 as the horizontal error bar. Planets c, d and e all have visible fluctuations over the dataset. These data constitute our transit timing measurement, which does not depend on the photodynamical model we develop subsequently; also, the data are not used in this model.

We use these transit times to estimate the Laplace critical angles36 and their evolution. To do so, we note that for circular orbits the mean longitude, λ, is a linear function of time, t, related to the transit period, P, and a specific mid-time, , as

In place of we may use T0 + ΔT0, where P and T0 define the linear ephemeris on which the quarterly ΔT0 of Extended Data Table 1 are based. Then, for Laplace’s critical angles we have

where t is given in units of days in terms of the barycentric Julian date (BJD), and similarly

These values are plotted in Extended Data Fig 3. The values are not constant, and the data appear to have sampled a minimum and maximum value of a libration cycle, which indicates a restoring torque. The specific values are sensitive to phase shifts due to eccentricity-vector precession; the libration centres may be different by about 30° if the eccentricities are as high as 0.1.

Photodynamic inputs

A Newtonian photodynamic model similar to existing models37, but developed independently, was used for a dynamical analysis of this system. To find the most likely parameter values and uncertainties in the system, we run a differential-evolution Markov chain Monte Carlo (DEMCMC)38 to compare model output for different system parameters to observed long- and short-cadence Kepler data, as well as spectroscopic data of the star. The TTV signal (Fig. 1), which here is constrained by the photometry directly, detects the gravitational perturbations due to planet mass. Combined with transit shape information, this constrains the eccentricities and provides positive mass detections at >2.5σ for all bodies with uncertainties approximately 10–30% of the fitted values.

Each planet (i = b, c, d, e) has seven parameters: pi = [P, T0, ecos(ω), esin(ω), i, Ω, Rp/, Mp/] in which P is the period, T0 is the mid-transit time, e is the eccentricity, i is the inclination, ω is the argument of periastron, Ω is the nodal angle, Rp/ is the planet-to-star radius ratio and Mp/ is the planet-to-star mass ratio. The star has five parameters:  = [, , c1, c2, dilution], in which ci are the two quadratic limb-darkening coefficients and ‘dilution’ is the amount of dilution from other stars. Because photometry constrains only stellar density, and not mass and radius individually, we fix at the best-fit value found from spectroscopy and convolve the mass distribution with the DEMCMC posteriors when reporting final values.

We fix Ω = 0 for all planets because the data do not sensitively measure mutual inclinations. The typical mean mutual inclination (MMI) of Kepler systems, approximately 1.8°, implies near coplanarity7. Additionally, multi-planet systems with higher mutual inclinations between planetary orbital planes are correlated with instability39, and we expect any observed system to be at least quasi-stable. Although, for some pairs of planets, photometry determines whether their inclinations are on the same side of 90° (refs 40, 41), in preliminary runs we find no preference for either conclusion. Therefore, we explore only i > 90° for each planet to reduce the volume of the symmetric parameter space. The value for the stellar limb-darkening coefficient c2 was chosen as 0.2 because this value is close to the median value for stars in the 4,000–6,500-K range in the Kepler bandpass42, and for low signal-to-noise ratio transits such as that in Kepler-223, a single limb-darkening parameter is sufficient to match transit shape43,44.

United Kingdom Infrared Telescope (UKIRT) archives reveal that there are two objects within 2″ of the position specified by the Kepler Input Catalog (KIC)45. The brighter of the two objects is less than 0.2″ from the KIC position and has a predicted Kepler magnitude of 15.4932, which is based on the formula used within the UKIRT archives to convert the measured J-band magnitudes to a Kepler magnitude46. This value is 0.1492 magnitudes fainter than that reported in the KIC (15.344). The second object is 1.937″ away from the KIC location, but is about 8 times fainter. The sum of these two objects has a predicted intensity in the Kepler bandpass equal to 98.2% of the intensity of the object reported by the KIC. Faulkes Telescope North (FTN) imaging confirms the dual nature of the Kepler-223 object47. Speckle imaging done at WIYN observatory indicates no additional bodies between approximately 0.2″ and 1.9″ of the brighter object48. Because the fainter of the two objects contributes approximately 11.202% of the light in the Kepler bandpass, we perform our DEMCMC runs with the dilution fixed at 0.11202.

Photodynamic fits

Beginning the DEMCMC by distributing parameters over the entire 30-dimensional prior is computationally untenable for this problem because it would take an excessively long time for the parameter sets, { pi}, of the DEMCMC to escape local minima and reach the global minimum. Instead we begin the DEMCMC by taking a four-planet solution found by exploration using migration-assembly solutions, p0, which approximately matches the observed data, and forming a set of 48 30-parameter vectors, { p0}, by adding 30-dimensional Gaussian noise to p0. We allow each set to explore the parameter space and, to eliminate any effects of the choice of p0, we wait until the DEMCMC chains have converged and then remove a ‘burn-in’ period, that is, the portion that is dependent on the choice of { p0}.

In the DEMCMC, a given choice of planetary parameters is accepted or rejected one the basis of the data over the Kepler observing window (about 4 years), and does not take into account the long-term evolution of a system with such parameters. It is not computationally tenable to numerically integrate each model for the age of the Kepler-223 system during the DEMCMC run. Therefore, the DEMCMC posterior includes solutions that acceptably fit the data, but that become unstable shortly after. To prevent our posterior parameter estimates from representing unstable solutions, we take two steps to encourage stability. First, we do not allow the DEMCMC to explore any solutions where the orbits of two adjacent planets cross (which generates a posterior we call ). This was implemented by allowing the DEMCMC to explore a limited range of eccentricities for each planet, (eb,max, ec,max, ed,max, ee,max) = (0.212, 0.175, 0.212, 0.175), with the symmetry of values due to the resonant-chain structure of the periods (posteriors can be found in Extended Data Table 2 and best-fits in Extended Data Table 3). Retrospectively, this eccentricity prior is justified because mean eccentricities greater than 0.1 are very rarely stable (Extended Data Fig. 6). Further, the similarity between the 106-year eccentricity-stability distribution and the 107-year distribution indicates that using either as a proxy for stable solutions will yield comparable results.

To assess the stability of the solutions in the posterior distribution, we selected 500 random draws from the C1 posterior and numerically integrated each of these solutions for 107 years, which corresponds to more than 108 orbits of the outermost planet. We used the MERCURY symplectic integrator49 and stopped integration if a close encounter between any two bodies occurred. 30% of systems lasted the entire 107-year integration. We randomly selected 25 of the systems that lasted 107 years and numerically integrated them for an additional 9 × 107 years, or until a close encounter, with 64% of them lasting 108 years. The age of the Kepler-223 star is about 6 × 109 years. We expect the planets to have reached their current configuration by migration through a disk within only a few million years, which corresponds to the lifetimes of gas disks50, suggesting that the current planet configuration has also survived for about 6 × 109 years. However, integrating for this long is not computationally feasible for this study. Other numerical stability studies10 predict that systems are approximately equally likely to become unstable in bins of log(time), implying that approximately 12% of the tested systems (and thus approximately 12% of the systems in the posterior) remain stable on timescales of billions of years. This fraction is high compared to a modelled population of compact, sub-Neptune systems, which are destabilized by mean motion resonances (MMRs) on a shorter timescale10. However, in such simulations there are generally a few bodies not engaged in the resonance; here all four bodies are involved in the resonance, remaining stable despite MMRs exciting eccentricities. Also, MERCURY is a Newtonian physics integrator, but adding a suitable general relativistic potential term, UGR = −3(/(cr))2, where G is the gravitational constant, c is the speed of light and r is the distance from a planet to the star51, does not change our long-term stability results from 100 trials (32 stable, 68 unstable).

To develop a second posterior based on parameters that are more likely to lead to stability, we randomly drew 5,000 parameter sets from the posterior of , and numerically integrated each of these solutions for 106 years (corresponding to more than 107 orbits of the outermost planet). This allows the problem to be computationally feasible, while still allowing for a large enough number of draws that we have sufficient statistics for parameter estimates. We retained only those parameter sets that remained stable at least this long (2,008 in total) to form a second posterior representative of physical (stable) solutions and call it . Future discussions of parameters and the data in the main text (Table 1 and Fig. 1) use this posterior () because we judge it to be the optimal combination of selecting stable solutions that match the observed Kepler data, while avoiding discarding plausible parameter space as a result of further assumptions. The general shape of the eccentricity distribution remaining after 106 years does not change markedly compared to solutions that are stable for an order of magnitude longer (see Extended Data Fig. 6) and is thus unlikely to change noticeable over the ~6-Gyr age of the system. The instability regions near the best-fit values discovered by our parameter fits suggest the ease with which the system, and others like it, could be moved out of resonance by small perturbations such as evaporation of the protoplanetary disk9,28.

Kepler-223 appears to possess two librating Laplace angles between the inner three and outer three planets, as discussed earlier. Migration simulations suggest that a very large Laplace-angle libration amplitude is unlikely in stable solutions. Further, in stable solutions in the posterior, long-lived (up to about 105 years) Laplace-angle libration is likely to occur. To get another estimate of the parameters of the system while balancing computational efficiency and a stricter stability constraint, we ran a third DEMCMC. For this run, at every step in the DEMCMC we integrate the parameter initial conditions for 100 years (corresponding to more than about 5 secular oscillations) and penalize Laplace-angle oscillation amplitudes that grow too large, in addition to fitting the data. We call the posterior from this run . Our Laplace-angle criteria in are designed to penalize large libration amplitudes and the speed at which the amplitudes grow. If the total range in Laplace angles, Δϕ1 or Δϕ2, exceeds a cut-off value K1 over the integration time (Tmax, in years), then the time at which this occurs is recorded (Trunaway). A value −1 + (Trunaway/Tmax)−2 is added to the χ2 value. All χ2 values were also penalized by an additional term equal to (Δϕ − Vi)2 if Δϕi > Vi and to 0 if Δϕi < Vi for specified angles Vi, i = 1, 2, in degrees and with Δϕ = ϕmax − ϕmin. This way, if the Laplace angles were well behaved enough not to run away, but either or both still grew in amplitude above specified values for each angle (V1 and V2), then a χ2 penalty was assigned and the parameters were less likely to be accepted. We do not impose a direct eccentricity constraint. We report with (Tmax, K1, V1, V2) = (100 yr, 170°, 30°, 50°), for which the numbers are roughly based on the results of migration and DEMCMC results that had long-term libration (see Extended Data Table 2).

Running a similar stability check for as for by choosing 300 chains from the posterior distribution resulted in 100% of the parameter sets leading to stable behaviour lasting 107 years. Ten parameter sets were numerically integrated for 108 years, and 100% of those also lead to a system that survives with no close encounters. These results indicate that this method is effective at finding stable solutions. Comparing this to the stability results for , in which only 19% of solutions were stable for 108 years (as described above), our argument that resonance does encourage stability is strengthened. Nevertheless, this method cannot be guaranteed to reject all unstable systems (because they might pass this test) or to include all stable ones (because some systems could remain stable for a very long time, but have large changes in Laplace angle); see Extended Data Fig. 4. This posterior has lower eccentricities, but because we assume short-term resonance for this fit, we do not take it as our nominal fit.

Future observations

We predict future transit times and uncertainties by averaging the predicted transits from 152 solutions from the posterior that are stable for 107 years. We report transit times quarterly for 10 years, including over the Kepler observing window, in Supplementary Information.

Code availability

The code used for migration simulations is available as Supplementary Information. The code used to generate the TTV and photodynamic analyses is available upon request and will be made publicly available once further analyses have been completed.50