HD 56414 b: A Warm Neptune Transiting an A-type Star

HD 56414 (a.k.a. TOI-1228 or TIC 300038935) was observed by TESS for a total of 24 sectors between 2018 July 18 and 2021 June 24. During sectors 1–13, the target was observed with a cadence of 2 minutes. During sectors 28–36 and 38–39, the target was observed with cadences of both 2 minutes and 20 s. A transiting planet candidate, denoted TOI-1228.01, was identified in this data by the NASA Science Processing Operations Center (SPOC; Jenkins et al. 2016) pipeline on 2019 August 26. The data and related analyses are available for download on the Mikulski Archive for Space Telescopes (MAST). The SPOC pipeline produces two light curves: a light curve produced using simple aperture photometry (SAP) and a light curve produced using simple aperture photometry plus a presearch data conditioning step (PDCSAP; Stumpe et al. 2014). We utilized the latter for our analysis.

The PDCSAP process retains intrinsic stellar variability, which could influence the interpretation of the data by introducing correlated noise. Specifically, stars in the temperature regime of HD 56414 are often δ Scuti variables, which can pulsate at periods under a day with amplitudes of a few parts per thousand (ppt). While we found no evidence of periodic pulsations, we noticed some aperiodic variability of a few ppt that is likely residual background or instrumental noise. We removed long-term variability by fitting the data to a cubic basis spline with a knot distance of 1 day, linearly interpolating over the 7.6 hr-long transits to remove low-frequency trends without altering the transit shape. Next, we removed short-term out-of-transit variability by clipping out the transits and fitting the light curve to a cubic basis spline with a knot distance of 0.1 days. We ensured that this process did not affect the morphologies of the transits by comparing each preflattening transit with its postflattening counterpart. The transits of the planet candidate were identified using the orbital period (P_orb) and time of first transit center (T₀) reported by the SPOC. Lastly, we removed outliers more than 5σ from the median flux. The resulting light curve is shown in Figure 1.

Zoom In Zoom Out Reset image size

Next, we inspected each transit and removed those with only partial coverage and those with poor data quality. Because our flattening procedure requires both pre- and posttransit baselines to properly normalize each transit, it had difficulty recovering the depths of partially detected transits. Consequently, partial transits that were significantly deeper than expected occurred near 1609.774 TBJD (where TBJD = BJD–2,457,000) and 1638.824 TBJD due to gaps in data coverage. We also removed a transit that occurred at 1348.326 TBJD during sector 1, which took place following an incorrectly configured fine pointing calibration after a spacecraft momentum dump, ¹⁹ and all data from sector 4, during which a row of anomalously low pixels, caused by a smear correction applied to adjust for a saturated star located elsewhere on the CCD, passed directly through HD 56414. Our final data set included 14 transits during 24 TESS sectors (see Figure 1).

We obtained reconnaissance spectra of HD 56414 on 2019 October 21, 2021 September 26, and 2022 January 13 using the CHIRON spectrograph on the 1.5 m SMARTS telescope, located at Cerro Tololo Inter-American Observatory (CTIO), Chile (Tokovinin et al. 2013). The three spectra yielded signal-to-noise ratios per resolution element of 36.6, 71.5, and 117.5, respectively, at 550 nm. Because stellar properties can be difficult to extract from spectra of hot, rapidly rotating stars, we primarily used these spectra to determine the line-of-sight rotational velocity of the star. To do so, we obtained a line profile from each spectrum via a least-squares deconvolution (Donati et al. 1997) between the observation and a synthetic nonrotating spectral template generated from the ALTAS-9 model atmospheres (Castelli & Kurucz 2003). We then modeled the resulting line profile via a line-broadening kernel that incorporates the effects of rotational, instrumental, and macroturbulent broadening. This calculation yielded $v\sin {i}_{\star }=59.4\pm 3.0\,\mathrm{km}\,{{\rm{s}}}^{-1}$. We also use the spectra to rule out false-positive-producing (FP-producing) scenarios, which we discuss further in Section 4.

We obtained I-band speckle interferometric observations of HD 56414 on 2019 March 17 with HRCam mounted on the 4.1 m Southern Astrophysical Research (SOAR) telescope, located at Perro Pachón, Chile. These observations and their related analyses are outlined in Ziegler et al. (2020, 2021), to which we direct the reader for more information. The observations achieved a contrast of 5.2 magnitudes at 1''. The speckle autocorrelation function, which covers a field of view of 3'' × 3'', and the corresponding contrast curve are shown in Figure 2. We use these observations to constrain the possibility of FP-producing scenarios, which we discuss further in Section 4.

Zoom In Zoom Out Reset image size

Our adopted stellar parameters were obtained using a number of sources and methods (see Table 1). We adopted the stellar R.A. (α), decl. (δ), proper motion in R.A. (μ_α ), proper motion in decl. (μ_δ ), and parallax (π) from Gaia eDR3 (Gaia Collaboration et al. 2021).

Table 1. Adopted Stellar and Planet Parameters

Parameter	Value	Source
Identifiers
HD	56414
TOI	1228
TIC	300038935
2MASS	J07112249−6850006
Gaia DR2	5268547016621360768
Astrometry and Position
α	07:11:22.48	Gaia eDR3
δ	−68:50:00.03	Gaia eDR3
μα (mas yr−1)	−0.735 ± 0.019	Gaia eDR3
μδ (mas yr−1)	35.120 ± 0.015	Gaia eDR3
π (mas)	3.735 ± 0.013	Gaia eDR3
Distance (pc)	267.74 ± 1.07	From parallax
Photometry
GBP	9.2908 ± 0.0006	Gaia eDR3
GRP	9.0508 ± 0.0006	Gaia eDR3
B	9.390 ± 0.002	APASS
V	9.22 ± 0.03	APASS
J	8.89 ± 0.03	2MASS
H	8.85 ± 0.05	2MASS
Ks	8.82 ± 0.02	2MASS
W1	8.78 ± 0.02	ALLWISE
W2	8.80 ± 0.02	ALLWISE
W3	8.82 ± 0.02	ALLWISE
W4	9.1 ± 0.2	ALLWISE
Stellar Physical Properties
M⋆ (M⊙)	1.89 ± 0.11	This paper
R⋆ (R⊙)	1.751 ± 0.065	This paper
Teff (K)	8500 ± 150	This paper
L⋆ (L⊙)	14.39 ± 0.34	This paper
[Fe/H] (dex)	${0.0}_{-0.0}^{+0.3}$	Houk & Cowley (1975)
AV (mag)	0.22 ± 0.03	Kounkel & Covey (2019)
$v\sin {i}_{\star }$ (km s−1)	59.4 ± 3.0	This paper
vmac (km s−1)	3.2 ± 1.0	This paper
Fbol (erg cm−2 s−1)	(6.44 ± 0.15) × 10−9	This paper
${P}_{\mathrm{rot}}/\sin {i}_{\star }$ (days)	1.49 ± 0.09	This paper
Age (Myr)	420 ± 140	This paper
Best-fit Planet Model Parameters
T0 (BJD)	2458348.324 ± 0.005	This paper
Porb (days)	29.04992 ± 0.00021	This paper
Tdur (hours) a	7.58 ± 0.14	This paper
Rp (R⊕)	3.71 ± 0.20	This paper
b	0.34 ± 0.19	This paper
i (◦)	89.3 ± 0.4	This paper
a (AU)	0.229 ± 0.004	This paper
e	< 0.68 (3σ)	This paper
u⋆,0	0.54 ± 0.27	This paper
u⋆,1	0.19 ± 0.37	This paper
Teq (K) b	1133 ± 30	This paper
ESM	1.9 ± 0.2	This paper
TSM c	30.0 ± 1.7	This paper

Notes.

^a Calculated as the total transit duration, T₁₄. ^b Calculated assuming zero Bond albedo and full day–night heat redistribution. ^c Planet mass estimated using the mass–radius relation defined in Chen & Kipping (2017) for Neptunian worlds.

Download table as:  ASCIITypeset image

Next, we used the broadband spectral energy distribution (SED) and Gaia eDR3 parallax of the star to determine the bolometric flux (F_bol), effective temperature (T_eff), and radius (R_⋆) of the star (following the procedures described in Stassun & Torres 2016; Stassun et al. 2017, 2018). We obtained G_BP and G_RP from Gaia eDR3, our B and V magnitudes from APASS (Henden et al. 2016), our J, H, and K_s magnitudes from 2MASS (Skrutskie et al. 2006), and our W1 − W4 magnitudes from ALLWISE (Cutri et al. 2014). We constrained the interstellar extinction (A_V ) using the analysis by Kounkel & Covey (2019) and stellar metallicity ([Fe/H]) based on the designation of HD 56414 as a metallic-line star by Houk & Cowley (1975). We fit the Kurucz stellar atmospheric models (Kurucz 1993), resulting in a reduced χ² of 1.7 (see Figure 1). We calculated the luminosity of the star (L_⋆) directly using F_bol together with the Gaia distance and stellar mass (M_⋆) using the empirical relations presented in Torres et al. (2010). All of our derived properties are consistent with those quoted in version 8.2 of the TESS Input Catalog (Stassun et al. 2019).

Lastly, we extracted the $v\sin {i}_{\star }$ and macroturbulent velocity (v_mac) from the CHIRON spectra (Section 2.2). Using this $v\sin {i}_{\star }$ and the R_⋆ calculated above, we calculated ${P}_{\mathrm{rot}}/\sin i$ (where P_rot is the stellar rotation period). The rotation rate of the star is not informative of the stellar age because the star is hotter than the Kraft break. However, we assign an age of 420 ± 140 Myr based on its Theia 797 membership assigned in Kounkel & Covey (2019), who identified stellar strings and calculated their ages using a combination of machine-learning analysis and isochrone fitting with a typical uncertainty of 0.15 dex.

We fit the TESS photometry to a transit model using exoplanet (Foreman-Mackey et al. 2021). The transit model was initialized with a quadratic limb-darkening law (with coefficients u_⋆,0 and u_⋆,1) and the following priors: (1) Gaussian priors for M_⋆, R_⋆, T_eff, K_s magnitude, T₀, the logarithm of P_orb, the logarithm of the transit depth, and the flux zero-point of the light curve; (2) a uniform prior on the transit impact parameter (b); and (3) a prior on eccentricity (e) based on Kipping (2013). In addition, we included a Gaussian process model with a simple harmonic oscillator kernel to account for residual variability in the light curve. ²⁰ We ran a 10 walker ensemble with 20,000 steps and discarded the first 10,000 steps as burn in. The best-fit phase-folded model is shown in Figure 1.

As shown in Table 1, we fit for the following physical and orbital parameters: T₀, P_orb, the transit duration T_dur, the planet radius (R_p), b, the orbital inclination (i), the orbital semimajor axis (a), e, u_⋆,0, and u_⋆,1. In addition, we estimated the planet equilibrium temperature assuming zero Bond albedo and full day–night heat redistribution (T_eq) and the planet emission spectroscopy and transmission spectroscopy metrics (ESM and TSM) assuming a circular orbit. ²¹ The best-fit model is a planet with R_p = 3.71 ± 0.20 R_⊕ on a 29.04992 ± 0.00021 day orbit with e < 0.68 (3σ).

Based on the rapid rotational rate of HD 56414, we might expect to see an asymmetrical transit profile due to gravity darkening, which can be modeled to independently measure the true spin–orbit angle (Ψ; Barnes 2009). To test this, we also fit the TESS light curve to a gravity-darkened model following Hooton et al. (2022) in which we additionally fit for the stellar inclination (i_⋆) and sky-projected stellar obliquity (λ). We fixed the stellar polar temperature, stellar equatorial radius, and $v\sin {i}_{\star }$ to the median values in Table 1, and fixed the gravity-darkening coefficient β according to Claret (2017). In addition, we derived P_rot, Ψ, and the stellar oblateness. The parameters shared between the gravity-darkened and non-gravity-darkened fits agreed well, while the gravity-darkened-specific model parameters were only weakly constrained. We constrained the stellar inclination to i_⋆ > 19° at the 3σ level, which rules out configurations with the rotation axis pointing toward the observer. This result is intuitive, as P_rot would need to be very short to explain the spectroscopically inferred $v\sin {i}_{\star }$ for small i_⋆. Values of i_⋆ between 45° and 90° were equally likely, resulting in ${P}_{\mathrm{rot}}={1.33}_{-0.45}^{+0.23}$ days. For λ and Ψ, all angles are plausible, although polar orbits are slightly preferred. Better constraints on these angles may be obtainable with future transit observations. In addition, λ could be obtained independently via the Rossiter–McLaughlin effect (e.g., Collier Cameron et al. 2010), although this would be difficult to accomplish given the shallow transit depth.

We utilized the ground-based follow-up observations described in Section 2 to search for evidence of unresolved stellar-mass companions that would imply that TOI-1228.01 is an FP. We began by using our spectra to search for single-lined and double-lined spectroscopic binaries. The two high-signal-to-noise-ratio spectra were collected at 2483.8406 and 2592.6828 TBJD, which correspond to orbital phases of 0.09 and 0.84 using the orbital parameters in Table 1. These observations yielded RVs of 0.79 ± 0.73 km s⁻¹ and 1.35 ±0.73 km s⁻¹, respectively. At these orbital phases, a 0.1 M_⊙ stellar companion on a circular 29 day orbit would produce a ΔRV > 6 km s⁻¹. These observations therefore rule out the possibility that the transit-like event is caused by a stellar-mass companion. This was corroborated by a search for double-lined spectroscopic binaries, which produced no evidence of excess stellar lines.

We searched for evidence of longer-period stellar companions using our speckle interferometric observations. Our observations rule out companion stars with ΔI < 1 at orbital separations >01 and ΔI < 4.5 at orbital separations >02, indicating that stellar-mass companions with brightnesses comparable to HD 56414 are unlikely to be present beyond 25 au.

Nonetheless, these observations alone are not sufficient to validate TOI-1228.01 because some FP scenarios can evade detection by these methods. For instance, FPs can occur when the transit originates from a nearby source that is known but is unresolved in the TESS data. To illustrate, Figure 2 shows that several additional stars lie near the aperture used to extract the light curve. We investigated these FP scenarios via the following statistical analyses.

FPs due to signals originating from nearby sources often cause offsets between in-transit and out-of-transit centroids, the photocenters of the target star in the TESS images (e.g., Bryson et al. 2013; Twicken et al. 2018). We searched for centroid offsets in the TESS data using the open-source tool vetting (Hedges 2021), which calculates a p-value for each TESS sector indicating whether or not an offset has been detected. For each sector in which a transit occurred, we obtained a p-value >0.05, indicating no significant centroid offset. On average, the in-transit centroids agree well with the out-of-transit centroids (see Figure 2), providing strong evidence that the signal observed by TESS originates from HD 56414.

TRICERATOPS (Giacalone et al. 2021) is a Bayesian tool that can be used to validate TESS planet candidates by calculating an FP probability (FPP; the overall probability that the signal originates from something other than a planet transiting the target star) and a nearby FP probability (NFPP; the probability that the the signal originates from a known nearby source that is listed in the TIC), where the criteria for validation are FPP < 0.015 and NFPP < 10⁻³. Folding in the speckle imaging data for an added constraint on the presence of unresolved FP-inducing stars, we ran TRICERATOPS 50 times and calculated the mean and standard deviation of the FPP and NFPP. ²² We obtained FPP = 0.004 ± 0.006 and NFPP = (1.6 ± 3.5) × 10⁻⁷, which are sufficient for validation. ²³ Hereafter, we refer to TOI-1228.01 as HD 56414 b.