A decade of transit photometry for K2-19: Revised system architecture

TL;DR

The study reexamines the K2-19 system with a 10-year transit dataset to precisely constrain the masses and orbital eccentricities of its resonant Neptunian pair. Using a comprehensive photodynamical framework based on $n$-body dynamics (REBOUND with WHFast) and light-curve modeling, the authors derive $m_b=30.8\pm1.3\,M_\oplus$ and $m_c=11.12\pm0.44\,M_\oplus$, with modest free eccentricities ($e_b=0.043\pm0.024$, $e_c=0.067\pm0.017$) and distinct forced components ($e_b^{(+)}\approx0.015$, $e_c^{(+)}\approx0.045$). They show that earlier high-eccentricity inferences were likely caused by a twilight ingress timing error in a partial transit, and they confirm the system is near the primary fixed point of the $3:2$ resonance, supported by a resonance parameter framework and Fourier analysis of the TTVs. The work also reports a possible exterior planet candidate and performs interior structure retrieval with GASTLI, finding a predominantly rocky core with a substantial H/He envelope and heavy-element enrichment consistent with core-accretion formation. Overall, the findings reinforce disk-driven migration as a plausible formation pathway for K2-19, while highlighting the value of long-term transit photometry and joint dynamical analyses for constraining exoplanetary architectures.

Abstract

The star K2-19 hosts a pair of Neptunian planets deep inside the 3:2 resonance. They induce strong transit-timing variations with two incommensurate frequencies. Previous photodynamical modeling of 3.3 years of transit and radial velocity data produced mass estimates of 32.4 +/- 1.7 M_E and 10.8 +/- 0.6 M_E for planets b and c, respectively, and corresponding eccentricity estimates of 0.20 +/- 0.03 and 0.21 +/- 0.03. These high eccentricities raise questions about the formation origin of the system, and this motivated us to extend the observing baseline in an attempt to better constrain their values. We present a photodynamical analysis of 10 years of transit data that confirms the previous mass estimates (30.8 +/- 1.3 M_E and 11.1 +/- 0.4 M_E), but reduces the median eccentricities to 0.04 +/- 0.02 and 0.07 +/- 0.02 for b and c, respectively. These values are more consistent with standard formation models, but still involve nonzero free eccentricity. The previously reported high eccentricities appear to be due to a single transit for which measurements taken at twilight mimicked ingress. This resulted in a 12-minute error in the midtransit time. The data that covered 1.3 and 5 so-called super and resonant periods were used to match a Fourier analysis of the transit-timing variation signal with simple analytic expressions for the frequencies and amplitudes to obtain planet mass estimates within 2% of the median photodynamical values, regardless of the eccentricities. Theoretical details of the analysis are presented in a companion paper. Additionally, we identified a possible planet candidate situated exterior to the b-c pair. Finally, in contrast to a previous study, our internal structure modeling of K2-19 b yields a metal mass fraction that is consistent with core accretion.

Figures (26)

• Figure 1: Detection of the candidate planet e. Left: Gray data points represent the K2 data without the transits of planets b, c, and d. The orange data points show the mean GP model. The black light curve indicates the four transits we found. Center: Periodogram of the nuance algorithm. Right: Phased light curve without the noise model (gray points), binned (dark gray), and transit model (black line).
• Figure 2: Photodynamical modeling of the transit photometry. Each dataset is shown in a different panel, labeled with the midtransit date (or the start date of the observation for K2 and TESS) and the telescope (or instrument). The error bars, in different colors for each telescope, represent the observations. The black line shows the MAP model that combines transits and noise. The gray line shows the transit model.
• Figure 3: Correlation of the eccentricities of K2-19 b and K2-19 c. The dots represent the posterior samples at $t_{\mathrm{ref}}$, and the color scale shows their $\log$-posterior value. The evolution during the observations for 1000 random draws from the posterior distribution is shown in light gray (black for a random sample), light red (red for a random sample), and light blue (blue for the MAP model). The color coding depends on whether $\varpi_b-\varpi_c$ circulates, librates around $\pi$, or librates around zero (the same scheme as in Fig. \ref{['figure:ecc_longperi']}). The blue dot represents the MAP model values at $t_{\mathrm{ref}}$ (and from there, it starts to move upward), and similarly for the two random samples in red (left) and black (upward). Section \ref{['section:TTVs_ecc']} discusses the shape of the domain and resonance angle behavior.
• Figure 4: Correlation of the eccentricity of K2-19 b (left panel) and K2-19 c (right panel) with the difference in the longitudes of periastron over the time span covered by the observations for 1000 random draws from the posterior distribution. Samples that circulate are shown in light gray (one random sample is shown in black), those that librate around $\varpi_{\mathrm{b}}-\varpi_{\mathrm{c}} = 0\degree$ are shown in light blue, and those that librate around $\varpi_{\mathrm{b}}-\varpi_{\mathrm{c}} = 180\degree$ are shown in light red (one random sample is shown in red). The MAP model, which librates around 0, is shown in blue. The dots, with the same color code, represent the positions at $t_{\mathrm{ref}}$.
• Figure 5: Posterior TTV predictions of K2-19 b (blue band) and K2-19 c (orange band) computed relative to a linear ephemeris (2456813.386969 + 7.9209002 $\times$ epoch [BJD$_{\rm TDB}$], 2456817.280436 + 11.8983248 $\times$ epoch [BJD$_{\rm TDB}$] for planet b and c, respectively). We used 1000 random draws from the posterior distribution to estimate the TTV median value and its uncertainty (68.3% CI). In the upper panel, the posterior TTV values are shown and compared with individual transit-time determinations (Sect. \ref{['section:transit_times']}, open and filled error bars). The filled error bars were used as data in the modeling. In the lower panel, the posterior median transit-timing value was subtracted to visualize the uncertainty of the distribution. The posterior median transit time was also subtracted from each observed epoch for the individual transit-time determinations to allow a better comparison with the posterior of the photodynamical modeling.