adsabs/AstroCLIMB huggingface dataset:
Paper: Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations
Authors: L.-L. Zhao, G. P. Zank, H. Li
Figure caption: Compensated frequency spectra in the instrument frame for the GS turbulence model from Equation (14). The panels from top left to bottom right represent the spectra at different Alfvén wave propagation speeds, i.e., assuming V A = 0, 50, 250, and 400 km s−1, respectively. The parallel and perpendicular scaling are indicated by the values of θ VB, including 5°, 45°, 60°, 75°, and 90°, respectively. The SC speed relative to the plasma flow V 0 = 400 km s−1 and the fluctuating velocity δ v = 50 km s−1 for all cases.
Paper: Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations
Authors: L.-L. Zhao, G. P. Zank, H. Li
Figure caption: The “observed” frequency (Ω) spectra of the 2D turbulence obtained by integrating its 4D frequency-wavenumber spectral model P(ω,  k ) (Equation (11)) with different broadening functions F(ω,  k ). The tangential SC velocity relative to plasma flow V  x  = 400 km s−1 in all cases. The wavenumber spectrum is set to a broken power law. The solid black lines represent the spectra without broadening effects, where the Dirac delta description of the broadening function F is used. The orange dashed lines denote the spectra calculated using a Gaussian form of the broadening function F, and the blue dotted–dashed lines represent the spectra calculated using a Lorentzian broadening function. Panels (a)–(d) show the cases of different broadening widths Δω = k ⊥ δ v where the fluctuating velocity amplitude δ v = 10, 50, 200, and 400 km s−1, respectively. The insets in panels (a), (b), and (c) show a zoom of the spectral break to illustrate the smoothing effect of two different broadening functions on spectral breaks.
Paper: Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations
Authors: L.-L. Zhao, G. P. Zank, H. Li
Figure caption: Comparison of different spectral models with PSP-observed sub-Alfvénic solar wind flow during Encounter 10. The bottom panels show the comparison between the theoretical cross helicity (﹩{\sigma }_{c}^{M}﹩ and ﹩{\sigma }_{c}^{\mathrm{GS}}﹩) and PSP-observed cross helicity ﹩{\sigma }_{c}^{\mathrm{obs}}﹩. The theoretical cross helicity is computed from the Elsasser spectra, which include both Alfvén frequency and broadening effects. Panel (a) shows the 2D+slab model comparison, and panel (b) shows primarily GS model comparison, but with additional imbalanced slab turbulence imposed on the z + spectrum to better fit the observed cross helicity. The solid black and green, and black dashed lines represent the modeling results, and the blue, yellow, and pink curves represent the observed z ± frequency spectra and cross-helicity ﹩{\sigma }_{c}^{\mathrm{obs}}﹩ spectra. In the bottom of panel (b), the black dashed line represents the cross helicity calculated from the balanced GS model alone, and the black solid line represents the cross helicity calculated with an imbalanced slab component included in the z + mode.
Paper: Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations
Authors: L.-L. Zhao, G. P. Zank, H. Li
Figure caption: Left panel: the “observed” Elsasser frequency spectra P +(Ω) (for z + mode, black line) and P −(Ω) (for z − mode, blue line) and the corresponding cross helicity for the critical-balanced GS turbulence model in a sub-Alfvénic flow when finite Alfvén wave frequency is included. Right panel: the “observed” cross helicity spectrum for the GS model at different sampling angles θ VB from 1° to 90°.
Paper: Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations
Authors: L.-L. Zhao, G. P. Zank, H. Li
Figure caption: Similar to Figure 3, but for GS turbulence calculated using Equation (14). Four cases are considered, (i) without broadening and the Alfvén wave frequency (solid black lines); (ii) without broadening but with the Alfvén frequency (cyan solid lines); (iii) with Gaussian frequency broadening and the Alfvén frequency (orange dashed lines); and (iv) with Lorentzian broadening and the Alfvén frequency (blue dashed–dotted lines). Panels (a) and (b) are for perpendicular scaling with θ VB = 90°, and panels (c) and (d) are for parallel scaling with θ VB = 5°. Two different levels of broadening (e.g., δ v = 50 and 400 km s−1) are presented for the parallel and perpendicular spectra, respectively. The Alfvén velocity used in calculating the Alfvén wave frequency is set to 50 km s−1, and the SC speed relative to the plasma flow V 0 = ∣ V ∣ in all cases is 400 km s−1.
Paper: Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations
Authors: L.-L. Zhao, G. P. Zank, H. Li
Figure caption: Power spectral density P(k ⊥, k ∥) of GS95 theory assuming the function g in Equation (4) is an exponential function. The white line indicates the critical balance scaling ﹩{k}_{\parallel }={k}_{\perp }^{2/3}﹩ based on the assumption of τ nl = τ A. The brown contour curve represents the power P at k ⊥ = 1/L 0 and k ∥ = 0 and is used below to construct a broken power law.
Paper: Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations
Authors: L.-L. Zhao, G. P. Zank, H. Li
Figure caption: Broadening function F(ω,  k ) associated with the Gaussian (Equation (2); black curve) and Lorentzian (Equation (3); orange curve) assumptions with the same broadening width Δω.
Paper: Predicting the Timing of the Solar Cycle 25 Polar Field Reversal
Authors: Bibhuti Kumar Jha, Lisa A. Upton
Figure caption: The polar field above 60° latitude for the (a) northern and (b) southern hemispheres is shown from the AFT baseline through 2023 August (solid line) and for 30 SARG realizations afterward (light color lines). For reference, the HMI polar field above 60° is also shown (light gray). The median of the 30 realizations is indicated by the solid line after 2023 August. The median polar field measurements for the northern (c) and southern (d) hemispheres are shown in the same manner. Here, the shaded color regions represent the 50% confidence interval between the first (Q1) and third (Q3) quartiles. The timing of the polar field reversal is marked by the vertical lines with the corresponding months noted in the legend.
Paper: Predicting the Timing of the Solar Cycle 25 Polar Field Reversal
Authors: Bibhuti Kumar Jha, Lisa A. Upton
Figure caption: The magnetic butterfly diagram, constructed using AFT baseline map until 2023 August 31 (marked using white dashed vertical line) and after that using one of the realizations of synthetic ARs in AFT’s predictive mode.
Paper: Predicting the Timing of the Solar Cycle 25 Polar Field Reversal
Authors: Bibhuti Kumar Jha, Lisa A. Upton
Figure caption: (a) The monthly average sunspot number for current cycle (Cycle 25), along with monthly average sunspot number for Cycle 13 and the best-fit curve based on Hathaway et al. (1994). (b) The time latitude butterfly diagram for Cycle 25 up to 2023 August and one SARG realization of synthetic ARs from 2023 September onward.
Paper: Predicting the Timing of the Solar Cycle 25 Polar Field Reversal
Authors: Bibhuti Kumar Jha, Lisa A. Upton
Figure caption: The violin plot shows the median timing of the polar field reversal, along with other statistical parameters such as the first (Q1) and third (Q3) quartiles and the median timing of the reversal in the northern (red) and southern (blue) hemispheres. The third violin (brown) represents the distribution for the reversal of the axial dipole moment.
Paper: Investigation of a Magnetic Reconnection Event with Extraordinarily High Particle Energization in Magnetotail Turbulence
Authors: Yi Qi, Robert Ergun, Neha Pathak, Tai D. Phan, James L. Burch, Alexandros Chasapis, Tak Chu Li, Steven J. Schwartz, Narges Ahmadi, Tien Vo, Stefan Eriksson, David Newman, Maria Usanova, Frederick D. Wilder
Figure caption: The context of the EDR crossing event on 2019 September 6. (a) and (b) Magnetic and electric field components in GSE coordinates. (c) Electron density. (d) Omnidirectional electron flux from 60 to 500 keV. (e) Differential electron energy flux from 6 eV to 25 keV. (f) Omnidirectional ion flux from 70 to 600 keV. (g) Differential ion energy flux from 3 eV to 25 keV. (h) Ion flow velocity in GSE. (i) A schematic of the earth’s magnetotail and an approximate MMS trajectory. The L direction is close to GSE x-direction, N is close to GSE z, and the M is close to the GSE y.
Paper: Investigation of a Magnetic Reconnection Event with Extraordinarily High Particle Energization in Magnetotail Turbulence
Authors: Yi Qi, Robert Ergun, Neha Pathak, Tai D. Phan, James L. Burch, Alexandros Chasapis, Tak Chu Li, Steven J. Schwartz, Narges Ahmadi, Tien Vo, Stefan Eriksson, David Newman, Maria Usanova, Frederick D. Wilder
Figure caption: (a)–(c) The measured B  L , B  M , and E  N  over the estimated path across the EDR. The gold area represents the EDR. (d) V  e,LN , the measured electron flow velocity projected in the L–N plane. The arrow's color and length indicate the speed and direction. The arrows around the peak speed are set to be thicker to highlight the jet. The purple line is the estimated path. And the background is a cartoon of an ideal reconnection region with the magnetic field lines (gray lines with arrows), EDR (gold area), positive (blue area), and negative (green) Hall magnetic field regions.
Paper: Investigation of a Magnetic Reconnection Event with Extraordinarily High Particle Energization in Magnetotail Turbulence
Authors: Yi Qi, Robert Ergun, Neha Pathak, Tai D. Phan, James L. Burch, Alexandros Chasapis, Tak Chu Li, Steven J. Schwartz, Narges Ahmadi, Tien Vo, Stefan Eriksson, David Newman, Maria Usanova, Frederick D. Wilder
Figure caption: The EDR crossing by MMS3. (a) and (b)  B  and  E  in LMN. (c) Electron density. (d)  V    e   in LMN. (e) Current density in LMN. (f) The energy conversion rate, ﹩{\boldsymbol{J}}\cdot {\boldsymbol{E}}^{\prime} ﹩. The yellow shadow marks the EDR region.
Paper: Investigation of a Magnetic Reconnection Event with Extraordinarily High Particle Energization in Magnetotail Turbulence
Authors: Yi Qi, Robert Ergun, Neha Pathak, Tai D. Phan, James L. Burch, Alexandros Chasapis, Tak Chu Li, Steven J. Schwartz, Narges Ahmadi, Tien Vo, Stefan Eriksson, David Newman, Maria Usanova, Frederick D. Wilder
Figure caption: Sketch of the Poynting flux transportation with the Poynting flux leaving the EDR along positive L (Sout) in the N > 0 quadrant.
Paper: Investigation of a Magnetic Reconnection Event with Extraordinarily High Particle Energization in Magnetotail Turbulence
Authors: Yi Qi, Robert Ergun, Neha Pathak, Tai D. Phan, James L. Burch, Alexandros Chasapis, Tak Chu Li, Steven J. Schwartz, Narges Ahmadi, Tien Vo, Stefan Eriksson, David Newman, Maria Usanova, Frederick D. Wilder
Figure caption: The B and E power spectral density.
Paper: Formation of Fan-spine Magnetic Topology through Flux Emergence and Subsequent Jet Production
Authors: Yadan Duan, Hui Tian, Hechao Chen, Yuandeng Shen, Zheng Sun, Zhenyong Hou, Chuan Li
Figure caption: Overview of the ephemeral region. (A)–(B): AIA 171 Å and CHASE Doppler images showing the third jet. The green arrows denote the remote brightenings associated with the jet. The field of view of (C)–(F) is indicated by the white box in (A). (C)–(D): a time sequence of HMI LOS magnetograms showing the variations of the negative and positive magnetic fields, scaled at ±50 G, respectively. (E)–(F): AIA 1600 Å and Doppler images showing the circular ribbon during the jet.
Paper: Fierce Feedback in an Obscured, Sub-Eddington State of the Seyfert 1.2 Markarian 817
Authors: Miranda K. Zak, Jon M. Miller, Ehud Behar, W. N. Brandt, Laura Brenneman, Paul A. Draghis, Elias Kammoun, Michael J. Koss, Mark T. Reynolds, Abderahmen Zoghbi
Figure caption: The best-fit model for the EPIC spectrum of Mrk 817 in its highly obscured state, and the associated data/model ratio. The pn spectrum is shown in black, the MOS-1 spectrum in red, and the MOS-2 spectrum in blue. The left and right panels show log and linear energy scales, respectively. The model includes neutral partial-covering absorption, three zones of paired photoionized absorption and reemission, and distant, neutral reflection. The absorption affects a direct continuum consisting of a cutoff power law. The three ionized absorbers are part of a UFO, with projected velocities ranging between v/c  = 0.05 and 0.09. This is likely best exemplified by the Fe XXVI line shifted from 6.97 to 7.25 keV. The data were binned for visual clarity. See Table 1 and the text for additional details.
Paper: Fierce Feedback in an Obscured, Sub-Eddington State of the Seyfert 1.2 Markarian 817
Authors: Miranda K. Zak, Jon M. Miller, Ehud Behar, W. N. Brandt, Laura Brenneman, Paul A. Draghis, Elias Kammoun, Michael J. Koss, Mark T. Reynolds, Abderahmen Zoghbi
Figure caption: The recent Swift/XRT light curve is shown in the top two panels, and the X-ray hardness ratio is shown in the two panels below. Data are plotted for two 700-day time intervals separated by a 700-day gap in monitoring. The top left panel shows extreme variability, likely due to a combination of intrinsic variability and strong intermittent disk winds. The top right panel shows the deep low-flux state that we have explored with NuSTAR and XMM-Newton. The bottom right panel shows the observed increase in X-ray hardness, as expected from the absorption in the soft X-ray band by disk winds. Each data point in the hardness ratio represents the average hard photon count (2.0–10.0 keV) divided by the average soft photon count (0.3–2.0 keV) in a 10-day period. The vertical yellow and cyan lines indicate the time of the NuSTAR and XMM-Newton exposures that are analyzed in this paper.
Paper: Fierce Feedback in an Obscured, Sub-Eddington State of the Seyfert 1.2 Markarian 817
Authors: Miranda K. Zak, Jon M. Miller, Ehud Behar, W. N. Brandt, Laura Brenneman, Paul A. Draghis, Elias Kammoun, Michael J. Koss, Mark T. Reynolds, Abderahmen Zoghbi
Figure caption: The best-fit model for the XMM-Newton spectra is shown here, including additive components. For simplicity, only the pn spectrum is shown in gray, and the total best-fit model is shown in solid black. Dashed black: the heavily absorbed direct continuum (higher flux), and distant reflected flux. Dashed red: the unpaired additive wind reemission component, potentially from the NLR. Dashed cyan, green, and blue (respectively): wind reemission from zones 1, 2, and 3 (respectively).
Paper: Fierce Feedback in an Obscured, Sub-Eddington State of the Seyfert 1.2 Markarian 817
Authors: Miranda K. Zak, Jon M. Miller, Ehud Behar, W. N. Brandt, Laura Brenneman, Paul A. Draghis, Elias Kammoun, Michael J. Koss, Mark T. Reynolds, Abderahmen Zoghbi
Figure caption: Left: XMM-Newton/EPIC-pn spectra of Mrk 817 in 2009 (red) and 2022 (black). The data are shown in the host frame and are binned for visual clarity. A fiducial, unabsorbed, broken power-law model (shown in blue) was fit to the spectrum in 2009 and then shifted to match the 2022 spectrum in the 7–10 keV band. The 2022 spectrum is clearly marked by extremely strong, broad absorption and (re)emission. Right: the 2022 EPIC-pn (black), MOS-1 (red), and MOS-2 (blue) spectra of Mrk 817 jointly fit with a model consisting of neutral partial covering of a cutoff power-law direct continuum and neutral distant reflection (in XSPEC terminology, tbpcf × cutoffpl + pexmon). This model clearly fails to account for strong absorption and emission lines across the full passband, pointing to the need for more complex, ionized absorption.
Paper: Fierce Feedback in an Obscured, Sub-Eddington State of the Seyfert 1.2 Markarian 817
Authors: Miranda K. Zak, Jon M. Miller, Ehud Behar, W. N. Brandt, Laura Brenneman, Paul A. Draghis, Elias Kammoun, Michael J. Koss, Mark T. Reynolds, Abderahmen Zoghbi
Figure caption: The source light curves from the three EPIC cameras aboard XMM-Newton, over the full spectral fitting band (0.3–10.0 keV). The pn light curve is shown in black, the MOS-1 light curve in red, and the MOS-2 light curve in blue. Note that the MOS-2 light curve is artificially shifted by +0.2 counts s–1 for visual clarity. The data were binned to have a resolution of 1000 s. Periods of zero flux are due to the exclusion of instrumental flaring. The zero-point is measured relative to the start time of the MOS-1 exposure, which slightly preceded the start of the pn exposure.
Paper: Fierce Feedback in an Obscured, Sub-Eddington State of the Seyfert 1.2 Markarian 817
Authors: Miranda K. Zak, Jon M. Miller, Ehud Behar, W. N. Brandt, Laura Brenneman, Paul A. Draghis, Elias Kammoun, Michael J. Koss, Mark T. Reynolds, Abderahmen Zoghbi
Figure caption: The broad SED of Mrk 817. The spectrum shown in black is the EPIC-pn spectrum shown in Figures 2–5, fit with the model shown in Figures 4 and 5 and detailed in Table 1. The six optical and UV flux points are Swift/UVOT filter fluxes derived from a simultaneous observation. In order of ascending energy, the B, V, U, UVW1, UVM2, and UVW2 filters are shown in red, green, blue, cyan, magenta, and yellow, respectively. The fit to the EPIC-pn spectrum was extended to longer wavelengths with the addition of a reddened disk blackbody function. When the broad unabsorbed flux is translated into a bolometric luminosity, an Eddington fraction of λ = 0.008–0.016 is implied (the uncertainty reflects a range of reported black hole mass values).
Paper: Fierce Feedback in an Obscured, Sub-Eddington State of the Seyfert 1.2 Markarian 817
Authors: Miranda K. Zak, Jon M. Miller, Ehud Behar, W. N. Brandt, Laura Brenneman, Paul A. Draghis, Elias Kammoun, Michael J. Koss, Mark T. Reynolds, Abderahmen Zoghbi
Figure caption: These panels show simulated 100 ks XRISM spectra of Mrk 817, made assuming the best-fit model detailed in Table 1. At CCD resolution, the fastest outflows in Mrk 817 are apparent, but the anticipated 5 eV resolution of the Resolve calorimeter spectrometer makes the strong, highly blueshifted absorption lines in the Fe K band especially clear. These panels can be directly compared with those in Figure 4.
Paper: Fierce Feedback in an Obscured, Sub-Eddington State of the Seyfert 1.2 Markarian 817
Authors: Miranda K. Zak, Jon M. Miller, Ehud Behar, W. N. Brandt, Laura Brenneman, Paul A. Draghis, Elias Kammoun, Michael J. Koss, Mark T. Reynolds, Abderahmen Zoghbi
Figure caption: The joint best-fit models for the NuSTAR FPMA (black) and FPMB (red) spectra of Mrk 817 in the range 3–25 keV. The model fits well despite its relative complexity compared to the spectral resolution of the NuSTAR data.
Paper: TOI-4201: An Early M Dwarf Hosting a Massive Transiting Jupiter Stretching Theories of Core Accretion 
Authors: Megan Delamer, Shubham Kanodia, Caleb I. Cañas, Simon Müller, Ravit Helled, Andrea S. J. Lin, Jessica E. Libby-Roberts, Arvind F. Gupta, Suvrath Mahadevan, Johanna Teske, R. Paul Butler, Samuel W. Yee, Jeffrey D. Crane, Stephen Shectman, David Osip, Yuri Beletsky, Andrew Monson, Leslie Hebb, Luke C. Powers, John P. Wisniewski, Jaime A. Alvarado-Montes, Chad F. Bender, Jiayin Dong, Te Han, Joe P. Ninan, Paul Robertson, Arpita Roy, Christian Schwab, Guđmundur Stefánsson, Jason T. Wright
Figure caption: Figure including all photometric and RV observations used in the analysis of TOI-4201 b. (a) Time series of RV observations of TOI-4201 b with NEID (red) and PFS (green). The best-fitting model from the joint fit is plotted in blue, and residuals after subtracting the fit are included below. (b) NEID and PFS observations phase-folded on the best-fit orbital period from the joint fit, with the model in blue and 16%–84% confidence levels in light blue. (c)–(i) Photometric observations of TOI-4201 b; in all plots, the detrended data are in gray, and the model and 16%–18% confidence levels are in blue. In each figure, the point at x = −0.075 represents the median uncertainty in the photometric data.
Paper: TOI-4201: An Early M Dwarf Hosting a Massive Transiting Jupiter Stretching Theories of Core Accretion 
Authors: Megan Delamer, Shubham Kanodia, Caleb I. Cañas, Simon Müller, Ravit Helled, Andrea S. J. Lin, Jessica E. Libby-Roberts, Arvind F. Gupta, Suvrath Mahadevan, Johanna Teske, R. Paul Butler, Samuel W. Yee, Jeffrey D. Crane, Stephen Shectman, David Osip, Yuri Beletsky, Andrew Monson, Leslie Hebb, Luke C. Powers, John P. Wisniewski, Jaime A. Alvarado-Montes, Chad F. Bender, Jiayin Dong, Te Han, Joe P. Ninan, Paul Robertson, Arpita Roy, Christian Schwab, Guđmundur Stefánsson, Jason T. Wright
Figure caption: Upper left: we include TOI-4201 b (circled in black) on a mass–radius plane, with planets colored by host star temperature. We include planets around FGK stars in the background, and gray contours indicate bulk densities of 0.3, 1.0, and 3.0 g cm−3 (left to right). Upper right: TOI-4201 b in an insolation–radius plane for the same sample of planets. Lower: planet-to-star mass ratio vs. host star mass, colored by equilibrium temperature. Planets with a true mass measurement from transit observations are represented by circles, and planets with a true mass measurement from astrometry are squares, while triangles are minimum masses (RV only). Around M dwarfs, TOI-4201 b has the highest mass ratio for transiting planets, and the planet with the highest mass ratio overall is GJ 463 b (Endl et al. 2022; Sozzetti 2023).
Paper: TOI-4201: An Early M Dwarf Hosting a Massive Transiting Jupiter Stretching Theories of Core Accretion 
Authors: Megan Delamer, Shubham Kanodia, Caleb I. Cañas, Simon Müller, Ravit Helled, Andrea S. J. Lin, Jessica E. Libby-Roberts, Arvind F. Gupta, Suvrath Mahadevan, Johanna Teske, R. Paul Butler, Samuel W. Yee, Jeffrey D. Crane, Stephen Shectman, David Osip, Yuri Beletsky, Andrew Monson, Leslie Hebb, Luke C. Powers, John P. Wisniewski, Jaime A. Alvarado-Montes, Chad F. Bender, Jiayin Dong, Te Han, Joe P. Ninan, Paul Robertson, Arpita Roy, Christian Schwab, Guđmundur Stefánsson, Jason T. Wright
Figure caption: The radius evolution of a planet with the same mass and equilibrium temperature as TOI-4201 b assuming different H/He equations of state, following the models described in Müller et al. (2020b), Müller & Helled (2021), and S. Müller et al. (2023, in preparation). The gray shaded region represents ±1σ for TOI-4201 b. As there are no indications that this is a particularly young system, we include a dashed line at 1 Gyr to suggest a lower limit on the age of the planet.
Paper: TOI-4201: An Early M Dwarf Hosting a Massive Transiting Jupiter Stretching Theories of Core Accretion 
Authors: Megan Delamer, Shubham Kanodia, Caleb I. Cañas, Simon Müller, Ravit Helled, Andrea S. J. Lin, Jessica E. Libby-Roberts, Arvind F. Gupta, Suvrath Mahadevan, Johanna Teske, R. Paul Butler, Samuel W. Yee, Jeffrey D. Crane, Stephen Shectman, David Osip, Yuri Beletsky, Andrew Monson, Leslie Hebb, Luke C. Powers, John P. Wisniewski, Jaime A. Alvarado-Montes, Chad F. Bender, Jiayin Dong, Te Han, Joe P. Ninan, Paul Robertson, Arpita Roy, Christian Schwab, Guđmundur Stefánsson, Jason T. Wright
Figure caption: The radius evolution of a planet with the same mass and equilibrium temperature as TOI-4201 b assuming different (a) atmospheric metallicities and (b) grain opacities, following the models described in Müller et al. (2020b) and Müller & Helled (2021). The gray shaded region represents ±1σ for TOI-4201 b. As there are no indications that this is a particularly young system, we include a dashed line at 1 Gyr to suggest a lower limit on the age of the planet.