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Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Per-orbit excess absorption spectrum for planet c, in the observations (top) and the fiducial model (bottom). The first orbit is used to compute the out-of-transit spectrum. The white regions are the blue and red wings, the light gray regions are the far wings, and the dark gray region has low flux because of interstellar absorption. The second and third orbits, in addition to the second half of the second orbit, are within the white-light transit.
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Residuals images after SYSREM, for planets c (top) and b (bottom). Colors indicate relative brightness change in percent. The dashed red lines indicate the wavelengths of the helium triplet in the planetary frame. The dashed horizontal black line indicates the beginning of transit, while the solid horizontal black line indicates the end of transit. Note the darkening during the transit of b, which we ascribe to stellar variability (see the text).
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: In black is the excess absorption spectrum in the planetary frame for c (top) and b (bottom). The vertical red lines indicate the positions of the helium triplet. The absorption from planet b is probably stellar variability (see the text, and Figure 4). The injected models (teal) are from the 3D hydrodynamic simulations described in Section 5, and the observed excess absorption spectrum after injection is shown in blue. The gray regions are locations of strong stellar and telluric lines.
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Light curves of the HeI 10833 Å and HI 10941 Å lines, integrated in a 3.2 Å bandpass, for planet c (top) and b (bottom). To normalize out nonstellar variations, the line fluxes are divided by the continuum at 10825 Å (HeI) or 10937 Å (HI), also integrated in a 3.2 Å bandpass. In orange we plot the predictions of the 3D hydrodynamic model.
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Top: best-fit intrinsic stellar X-ray spectrum. The total spectrum as observed from Earth (black) is the sum of a low-temperature component (APEC 1) and a high-temperature component (APEC 2). Bottom: the XMM EPIC spectra measured by the three detectors (MOS1, MOS2, and pn) and the folded models, which take into account the instrumental RMF and ARF (the X-ray equivalents of line-spread function (LSF) and throughput). For clarity, the data are binned so that each bin, except those on the edges, contains at least a 3σ detection.
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Background-subtracted X-ray light curves of HD 63433 recorded by the three EPIC cameras (MOS1, MOS2, and pn). The pn light curve is divided by 2 for clarity.
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Light curve for HD 63433 (“Variable”) in the Johnson V (green; top panel) and B (blue; upper middle) pass bands normalized using a comparison star. Nightly observations are plotted as small gray points, while the annual means are shown as larger colored circles. An equivalent light curve for a less active star, HD 63432 (“Check”), is shown in the lower middle and bottom panels to demonstrate the photometric stability of these data.
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Top: the reconstructed stellar Lyα profile (blue), with uncertainty indicated by the gray shading. Bottom: the model Lyα profile after interstellar absorption and convolution with the instrumental line-spread profile (blue), compared to the data (orange). The data has error bars, but they are too small to see.
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Fiducial stellar spectrum. We binned the X-ray data for better visibility.(The data used to create this figure are available.)
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Neutral hydrogen number density, temperature, and triplet helium density from the time-averaged (over the last ∼10 kinematic timescales) fiducial 3D models, for c (top) and b (bottom). The star is toward the left, and the velocity vector of orbital motion lies in the paper plane and points upward. These plots show the profiles in the orbital plane. The white lines are the streamlines, while the dashed black lines represent the inner sonic surface. Note that the middle column showing metastable helium distribution zooms into the innermost 40 R ⊕ region for clearer presentation.
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Radial profiles of key quantities along the radial lines pointing to the direction of orbital motion. Profiles are calculated for the time-averaged data (over the last 10 kinematic timescales of the simulations) for the fiducial models of planets c and b. Top: number densities of electrons (n  e ), neutral helium (n He), metatstable helium (﹩{n}_{{\mathrm{He}}^{* }}﹩), neutral hydrogen (n H), and ionized hydrogen (n H I ). Bottom: temperature T, radial velocity v  r , sound speed c  s , and hydrogen ionization fraction f ion. Solid lines are for planet c; dashed lines for b.
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Similar to Figure 13 but for important reaction rates. Top: rates of important processes that create or destroy neutral hydrogen, namely photoionization, radiative recombination, and advection. Bottom: rates of processes that create or destroy metastable helium, namely collisional de-excitation, recombination, and photoionization [He* + h ν (>4.8 eV) → He + e −]. Rates for planet c are shown as the solid lines, and those for planet b are shown as the dashed lines. The rates are computed along the radial line pointing to the direction of the planets’ orbital motion.
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Comparison of independent analyses by M.Z., L.D.S., and L.F. The blue wing light curves are shown on the left, and the red wing light curves are shown on the right. Planet c is shown in the top panel, and planet b is shown in the bottom panel. The duration of the white-light transit is indicated by the gray shaded region. We exclude the data from the failed second observation of planet b in this comparison.
Paper: Detection of Ongoing Mass Loss from HD 63433c, a Young Mini-Neptune
Authors: Michael Zhang, Heather A. Knutson, Lile Wang, Fei Dai, Leonardo A. dos Santos, Luca Fossati, Gregory W. Henry, David Ehrenreich, Yann Alibert, Sergio Hoyer, Thomas G. Wilson, Andrea Bonfanti
Figure caption: Same as Figure 15, but breathing corrections are included in the L.F. and L.D.S. analyses. The fiducial analysis remains the same.
Paper: Kepler Bonus: Aperture Photometry Light Curves of EXBA Sources
Authors: Jorge Martínez-Palomera, Christina Hedges, Joseph E. Rodriguez, Geert Barentsen, Jessie Dotson
Figure caption: Example full EXBA mask (four tiles) for channel 48 observed during quarter 5. The image shown here is 36 × 60 pixels, and the flux values are averaged across cadences. Marked with red circles are the 123 sources obtained from the Gaia EDR3 catalog down to G ≤ 20 mag (see Section 3.2). The brightest visible star is G = 13.7 mag. Our pipeline filters out all contaminating sources within 2″ to fit the PRF models. Sources outside the coverage of the mask (up to 4″) are allowed and extracted for photometry.
Paper: Kepler Bonus: Aperture Photometry Light Curves of EXBA Sources
Authors: Jorge Martínez-Palomera, Christina Hedges, Joseph E. Rodriguez, Geert Barentsen, Jessie Dotson
Figure caption: The PRF models across the focal plane computed from Kepler's FFIs, as described in Section 3.1. The models are based on data observed during quarter 5. Each cell in the figure grid represents a single CCD channel (number in red). In a cell, each data point represents the pixel position from the reference source in Cartesian coordinates, while the color represents the pixel flux value normalized by the total flux of the corresponding reference source. As discussed in Hedges et al. (2021a), the PRF profiles show steep gradients and are elongated, particularly as we move away from the center of the focal plane. Note that in this figure, the CCD channels have the axis origin at each cell’s lower left corner; then, the orientations of the plotted PRFs do not reflect the axis origin of the CCD channels on Kepler's focal plane, which are arranged to be invariant under rotation. This is only esthetics and does not affect the use of our models.
Paper: Kepler Bonus: Aperture Photometry Light Curves of EXBA Sources
Authors: Jorge Martínez-Palomera, Christina Hedges, Joseph E. Rodriguez, Geert Barentsen, Jessie Dotson
Figure caption: Number of EXBA sources with the total number of observed quarters. Of the total sources, 46.5% have observations in all 13 quarters in which Kepler used the EXBA masks. The rest have 12 or fewer quarters available.
Paper: Kepler Bonus: Aperture Photometry Light Curves of EXBA Sources
Authors: Jorge Martínez-Palomera, Christina Hedges, Joseph E. Rodriguez, Geert Barentsen, Jessie Dotson
Figure caption: Color–magnitude diagram of the EXBA sources (9327 sources in blue) in comparison with the main targets (213,393 sources) of Kepler's mission (density plot in black). The red symbol represents the location of G...304 (see Section 4.2.3), which falls in the binary sequence.
Paper: Kepler Bonus: Aperture Photometry Light Curves of EXBA Sources
Authors: Jorge Martínez-Palomera, Christina Hedges, Joseph E. Rodriguez, Geert Barentsen, Jessie Dotson
Figure caption: Time-based light curve (top two panels) and phase-folded light curve (bottom panel) of G...304. Blue indicates the flux measurements, while black indicates the binned light curves using a time bin size of 1 day for the time light curve. The top and middle panels show the CBV-only corrected and fully detrended (CBVs and splines) light curves, respectively, for observations during quarter 7. The phase-folded light curve contains data from all quarters, as described in Section 4.2.3. The transit U-like shape and depth (∼0.5%) evidence the possibility of a large planet candidate or a substellar companion. The parameters that characterize the best transit model are listed in Table 1.
Paper: Kepler Bonus: Aperture Photometry Light Curves of EXBA Sources
Authors: Jorge Martínez-Palomera, Christina Hedges, Joseph E. Rodriguez, Geert Barentsen, Jessie Dotson
Figure caption: Image in pixel space of the EXBA data (pixel column ≥ 556) and the KIC 7214804 TPF (pixel column < 556) where the host candidate G...304 is located. The flux data are an average of the cadences observed during quarter 7. Red circles show Gaia EDR3 sources, while the filled red circle locates the host candidate. The red squares illustrate the aperture mask used for this work.
Paper: Kepler Bonus: Aperture Photometry Light Curves of EXBA Sources
Authors: Jorge Martínez-Palomera, Christina Hedges, Joseph E. Rodriguez, Geert Barentsen, Jessie Dotson
Figure caption: Posterior distributions of inferred stellar and transit parameters for the transiting signal observed around G...304. The model fitting was performed using the exoplanet Python package following the priors described in Section 4.2.3. The posteriors suggest that the eclipse signal is produced by a large planet with a radius <2 R J.
Paper: Kepler Bonus: Aperture Photometry Light Curves of EXBA Sources
Authors: Jorge Martínez-Palomera, Christina Hedges, Joseph E. Rodriguez, Geert Barentsen, Jessie Dotson
Figure caption: Transit model fitted using the exoplanet tool. The upper panel shows the light-curve data (black symbols), the median model (solid blue line), and the 3rd and 97th percentiles (orange) from the posterior distribution. Residuals are shown in the lower panel with no clear evidence of a remaining signal. The transit shape and depth are typical of a large planet companion.
Paper: Kepler Bonus: Aperture Photometry Light Curves of EXBA Sources
Authors: Jorge Martínez-Palomera, Christina Hedges, Joseph E. Rodriguez, Geert Barentsen, Jessie Dotson
Figure caption: Examples of EBs found in Kepler's EXBA masks. The EAs show well-defined primary and secondary eclipses and are the major source of false positives when looking for exoplanet candidates. The EWs show continuous eclipses and typically have shorter periods than detached EBs.
Paper: K2-79b and K2-222b: Mass Measurements of Two Small Exoplanets with Periods beyond 10 days that Overlap with Periodic Magnetic Activity Signals
Authors: Chantanelle Nava, Mercedes López-Morales, Annelies Mortier, Li Zeng, Helen A. C. Giles, Allyson Bieryla, Andrew Vanderburg, Lars A. Buchhave, Ennio Poretti, Steven H. Saar, Xavier Dumusque, David W. Latham, David Charbonneau, Mario Damasso, Aldo S. Bonomo, Christophe Lovis, Andrew Collier Cameron, Jason D. Eastman, Alessandro Sozzetti, Rosario Cosentino, Marco Pedani, Francesco Pepe, Emilio Molinari, Dimitar Sasselov, Michel Mayor, Manu Stalport, Luca Malavolta, Ken Rice, Christopher A. Watson, A. F. Martinez Fiorenzano, Luca Di Fabrizio
Figure caption: K2 LCs for K2-79 (left) and K2-222 (right). The top panels show the LCs after removing the thruster firings and other high-frequency systematic signals. The teal dashed lines show the best-fit third-degree polynomials, and the second panels show the LCs after subtracting the respective polynomials (discussed in Section 4.1). The third panels show the Everest-reduced LCs (also discussed in Section 4.1). The bottom panels show the flattened LCs after removing all remaining low-frequency signals. In the case of K2-222, both the scatter of flux values and related errors increase in a later subset of the data, beginning at approximately BJD−2400000 = 57,438 days.
Paper: K2-79b and K2-222b: Mass Measurements of Two Small Exoplanets with Periods beyond 10 days that Overlap with Periodic Magnetic Activity Signals
Authors: Chantanelle Nava, Mercedes López-Morales, Annelies Mortier, Li Zeng, Helen A. C. Giles, Allyson Bieryla, Andrew Vanderburg, Lars A. Buchhave, Ennio Poretti, Steven H. Saar, Xavier Dumusque, David W. Latham, David Charbonneau, Mario Damasso, Aldo S. Bonomo, Christophe Lovis, Andrew Collier Cameron, Jason D. Eastman, Alessandro Sozzetti, Rosario Cosentino, Marco Pedani, Francesco Pepe, Emilio Molinari, Dimitar Sasselov, Michel Mayor, Manu Stalport, Luca Malavolta, Ken Rice, Christopher A. Watson, A. F. Martinez Fiorenzano, Luca Di Fabrizio
Figure caption: K2-79 HARPS-N RV and stellar-activity-indicator (contrast, cross-correlation function area, full-width at half-maximum, bisector inverse span, and S-index) observations.
Paper: K2-79b and K2-222b: Mass Measurements of Two Small Exoplanets with Periods beyond 10 days that Overlap with Periodic Magnetic Activity Signals
Authors: Chantanelle Nava, Mercedes López-Morales, Annelies Mortier, Li Zeng, Helen A. C. Giles, Allyson Bieryla, Andrew Vanderburg, Lars A. Buchhave, Ennio Poretti, Steven H. Saar, Xavier Dumusque, David W. Latham, David Charbonneau, Mario Damasso, Aldo S. Bonomo, Christophe Lovis, Andrew Collier Cameron, Jason D. Eastman, Alessandro Sozzetti, Rosario Cosentino, Marco Pedani, Francesco Pepe, Emilio Molinari, Dimitar Sasselov, Michel Mayor, Manu Stalport, Luca Malavolta, Ken Rice, Christopher A. Watson, A. F. Martinez Fiorenzano, Luca Di Fabrizio
Figure caption: K2-222 HARPS-N RV and stellar-activity-indicator (contrast, cross-correlation function area, full-width at half-maximum, bisector inverse span, and S-index) observations.
Paper: K2-79b and K2-222b: Mass Measurements of Two Small Exoplanets with Periods beyond 10 days that Overlap with Periodic Magnetic Activity Signals
Authors: Chantanelle Nava, Mercedes López-Morales, Annelies Mortier, Li Zeng, Helen A. C. Giles, Allyson Bieryla, Andrew Vanderburg, Lars A. Buchhave, Ennio Poretti, Steven H. Saar, Xavier Dumusque, David W. Latham, David Charbonneau, Mario Damasso, Aldo S. Bonomo, Christophe Lovis, Andrew Collier Cameron, Jason D. Eastman, Alessandro Sozzetti, Rosario Cosentino, Marco Pedani, Francesco Pepe, Emilio Molinari, Dimitar Sasselov, Michel Mayor, Manu Stalport, Luca Malavolta, Ken Rice, Christopher A. Watson, A. F. Martinez Fiorenzano, Luca Di Fabrizio
Figure caption: K2 LCs for K2-79 (left) and K2-222 (right). The top panels show the LCs after removing the thruster firings and other high-frequency systematic signals. The teal dashed lines show the best-fit third-degree polynomials, and the second panels show the LCs after subtracting the respective polynomials (discussed in Section 4.1). The third panels show the Everest-reduced LCs (also discussed in Section 4.1). The bottom panels show the flattened LCs after removing all remaining low-frequency signals. In the case of K2-222, both the scatter of flux values and related errors increase in a later subset of the data, beginning at approximately BJD–2400000 = 57,438 days.
Paper: K2-79b and K2-222b: Mass Measurements of Two Small Exoplanets with Periods beyond 10 days that Overlap with Periodic Magnetic Activity Signals
Authors: Chantanelle Nava, Mercedes López-Morales, Annelies Mortier, Li Zeng, Helen A. C. Giles, Allyson Bieryla, Andrew Vanderburg, Lars A. Buchhave, Ennio Poretti, Steven H. Saar, Xavier Dumusque, David W. Latham, David Charbonneau, Mario Damasso, Aldo S. Bonomo, Christophe Lovis, Andrew Collier Cameron, Jason D. Eastman, Alessandro Sozzetti, Rosario Cosentino, Marco Pedani, Francesco Pepe, Emilio Molinari, Dimitar Sasselov, Michel Mayor, Manu Stalport, Luca Malavolta, Ken Rice, Christopher A. Watson, A. F. Martinez Fiorenzano, Luca Di Fabrizio
Figure caption: Auto-correlation function (ACF) curves for the polynomial-reduced (top) and Everest-reduced (bottom) K2 LCs of K2-79 (left) and K2-222 (right). The dark purple points show the ACF. The solid orange line shows the result of the underdamped simple harmonic oscillator function fit to the ACF curves, as described in Section 4.1. The ACF shows repeating peaks separated by P quasi, a timescale often related to P rot, with the correlation power of each peak dropping off at a rate related to the evolution timescale of magnetic active regions, τ. The P quasi values returned by successful fits for both targets are similar to each other and the strongest signals in all LC periodograms (Figure 4). The τ values are also all quite long relative to P quasi. We therefore cannot rule out, for either target, the potential that the ACF signal is the result of instrumental systematics.
Paper: K2-79b and K2-222b: Mass Measurements of Two Small Exoplanets with Periods beyond 10 days that Overlap with Periodic Magnetic Activity Signals
Authors: Chantanelle Nava, Mercedes López-Morales, Annelies Mortier, Li Zeng, Helen A. C. Giles, Allyson Bieryla, Andrew Vanderburg, Lars A. Buchhave, Ennio Poretti, Steven H. Saar, Xavier Dumusque, David W. Latham, David Charbonneau, Mario Damasso, Aldo S. Bonomo, Christophe Lovis, Andrew Collier Cameron, Jason D. Eastman, Alessandro Sozzetti, Rosario Cosentino, Marco Pedani, Francesco Pepe, Emilio Molinari, Dimitar Sasselov, Michel Mayor, Manu Stalport, Luca Malavolta, Ken Rice, Christopher A. Watson, A. F. Martinez Fiorenzano, Luca Di Fabrizio
Figure caption: Correlation plots and strengths (Spearman r coefficients, r  s ) between the K2-79 RVs and various activity indicators (contrast, cross-correlation function area, FWHM, bisector inverse span, and S-index). All RVs and error bars are plotted in dark purple, with season 1 RVs overplotted in turquoise and season 2 RVs in magenta. P-value is a measure of how probable it is that the observed correlation is due to random chance.
Paper: K2-79b and K2-222b: Mass Measurements of Two Small Exoplanets with Periods beyond 10 days that Overlap with Periodic Magnetic Activity Signals
Authors: Chantanelle Nava, Mercedes López-Morales, Annelies Mortier, Li Zeng, Helen A. C. Giles, Allyson Bieryla, Andrew Vanderburg, Lars A. Buchhave, Ennio Poretti, Steven H. Saar, Xavier Dumusque, David W. Latham, David Charbonneau, Mario Damasso, Aldo S. Bonomo, Christophe Lovis, Andrew Collier Cameron, Jason D. Eastman, Alessandro Sozzetti, Rosario Cosentino, Marco Pedani, Francesco Pepe, Emilio Molinari, Dimitar Sasselov, Michel Mayor, Manu Stalport, Luca Malavolta, Ken Rice, Christopher A. Watson, A. F. Martinez Fiorenzano, Luca Di Fabrizio
Figure caption: Correlation plots and strengths (Spearman r coefficients, r  s ) between the K2-222 RVs and various activity indicators (contrast, cross-correlation function area, FWHM, bisector inverse span, and S-index). All RVs and error bars are plotted in dark purple, with season 1 RVs covered in turquoise and season 2 RVs covered in magenta. P-value is a measure of how probable it is that the observed correlation is due to random chance.