Do anomalously dense hot Jupiters orbit stealth binary stars?

ABSTRACT

The Wide Angle Search for Planets (WASP) survey used transit photometry to discover nearly 200 gas-giant exoplanets and derive their planetary and stellar parameters. Reliable determination of the planetary density depends on accurate measurement of the planet’s radius, obtained from the transit depth and photodynamical determination of the stellar radius. The stellar density and hence the stellar radius are typically determined in a model-independent way from the star’s reflex orbital acceleration and the transit profile. Additional flux coming from the system due to a bright, undetected stellar binary companion can, however, potentially dilute the transit curve and radial velocity signal, leading to underestimation of the planet’s mass and radius, and to overestimation of the planet’s density. In this study, we cross-check the published radii of all the WASP planet-host stars, determined from their transit profiles and radial velocity curves, against radiometric measurements of stellar radii derived from their angular diameters (via the infrared flux method) and trigonometric parallaxes. We identify eight systems showing radiometric stellar radii significantly greater than their published photodynamical values: WASPs 20, 85, 86, 103, 105, 129, 144, and 171. We investigate these systems in more detail to establish plausible ranges of angular and radial velocity separations within which such ‘stealth binaries’ could evade detection, and deduce their likely orbital periods, mass ratios, and flux ratios. After accounting for the dilution of transit depth and radial velocity amplitude, we find that, on average, the planetary densities for the identified stealth binary systems should be reduced by a factor of 1.3.

1 INTRODUCTION

The Wide Angle Search for Planets (WASP) project (Pollacco et al. 2006) has published the discoveries of over 178 transiting gas-giant exoplanets in close orbits about their host stars (Southworth 2011).

The validation and characterization of a WASP planet candidate involves photodynamical analysis of the transit light curve to establish the planet/star radius ratio and the stellar density from the transit depth and duration, respectively (Southworth 2010). Since most WASP host stars have masses close to solar, the inverse cube root of the stellar density (in solar units) provides an approximate estimate of the stellar radius. Follow-up spectroscopy yields the stellar effective temperature, surface gravity, and metallicity. This spectroscopic characterization allows the stellar mass to be estimated. Radial velocity (RV) observations of the host star’s orbit then determine the planetary mass.

Since the release of the Gaia Data Release 2 (DR2) and DR3 catalogues (Gaia Collaboration 2021, 2023), the availability of precise parallaxes has made it possible to determine WASP host-star radii independently. The stellar angular diameter can be estimated from the effective temperature and an estimate of the bolometric flux received at Earth, via the infrared flux method (IRFM) of Blackwell & Shallis (1977). The angular diameter and Gaia parallax together yield a direct geometrical estimate of the stellar radius. The radii determined via this method can be compared directly with the radii inferred from photodynamical fits to their planets’ transit profiles.

The stellar radius estimates obtained via these two methods should agree unless the light of the host star is diluted significantly by a stellar binary companion. In such cases, the additional flux dilutes both the transit depth and the RV amplitude. This in turn leads to an overestimation of the planet’s density and an underestimation of its radius and mass. Stellar binaries are usually detectable if the orbit is small enough that the Doppler-shifted spectral lines of the two stars are resolvable or wide enough for the binary to be resolved through direct imaging. We coin the term ‘stealth binaries’ to characterize systems whose orbital separations lie in the range in which they cannot be resolved by either method.

Ciardi et al. (2015) have carried out a similar study, discussing the effects of undetected multiplicity on planetary radii for Kepler objects of interest (KOIs). For each KOI, they found the best-fitting Dartmouth isochrone and considered all stars along the isochrones that had absolute Kepler magnitudes fainter than the primaries as viable companions. Their derivation of the theoretical correction factor |$X_{R}$| – by which the planetary radius would have been underestimated – is similar to the equations derived in Sections 4.3 and 4.4. They derived mean values of |$X_{R}$| for all possible scenarios up to a multiplicity of 3. Payne et al. (2018) developed this concept further, using the relationship between the mean stellar density and stellar effective temperature to identify which of the stellar components in eight marginally resolved multistar systems were the hosts of transiting planets discovered with Kepler/K2.

In this paper, we compare the stellar radii obtained from the spectral energy distributions and |$Gaia$| parallaxes of a large sample of WASP planet-host stars against those calculated from transit fitting and spectroscopic characterization. In the majority of cases, the host stars are not known a priori to be binaries. However, if previously undetected binaries are present in the WASP catalogue, the photodynamical host-star radii derived from the stellar density via the transit duration will be smaller than those determined from the stellar angular diameter and parallax. In cases where the discrepancy is significant, their planets’ bulk densities will have been overestimated.

Our methods are discussed in detail in Section 2. In Section 3, we present the comparison of results from both methods. In Section 4.1, we examine these systems in more detail to predict the limits on angular separation and the limiting difference in radial velocities of the two stars that would allow the secondary star to remain undetected. These limits can be used to classify these systems as ‘stealth binaries’ and estimate the plausible range of orbital periods of the stellar binaries. Section 4.2 discusses WASP-85AB – a known stellar binary that we use to verify some of our methods. In Section 4.3, we estimate the most probable flux ratio and mass ratio for each stealth binary system. The factor by which the radii from both methods differ gives us information about how much additional flux is being received from the system – and thus an estimate on the luminosity ratio of the two stars in the binary. We then use the evolutionary tracks and isochrone tables of Bressan et al. (2012) to estimate the binary mass ratios from the luminosity ratios. Finally, in Section 4.4, we assess the effect of contamination of observations on the derived system parameters, and hence recalculate them after having accounted for the secondary star. Corrections to parameters for some WASP planets based on similar studies have previously been made by Evans, Southworth & Smalley (2016), Southworth et al. (2020), and Delrez et al. (2018), which will be discussed in Section 4.5. We conclude the study and suggest follow-up observations in Section 5.

2 METHODS

We start by comparing the published radii of a sample of 178 host stars from the WASP survey, obtained by photodynamical modelling of their transit profiles, with radii estimated from their angular diameters and parallaxes.

Photodynamical modelling of planetary transits is carried out routinely as part of the discovery process leading to the announcement of a new planet. Winn (2009) reviewed the planetary and stellar parameters that can be measured from precise photometry of exoplanet transits combined with RV follow-up. The transit duration |$(T)$| gives us an estimate of the stellar density as per equation (1) for central transits, and the transit depth (⁠|$\delta$|⁠) gives us the ratio of the planetary radius |$(R_{\mathrm{ p}})$| to the stellar radius |$(R_{\mathrm{ s}})$|⁠, as per the relation |$\sqrt{\delta }$| = |$R_{\mathrm{ p}}$|/|$R_{\mathrm{ s}}$|⁠.

Here, |$P$| is the orbital period of the planet and |$\rho _{\mathrm{ s}}$| is the stellar density. Since most main-sequence stars of spectral types F, G and K have a mass close to unity, their radius |$R_{\mathrm{ s}}$| can be estimated directly from the density. Dilution of the transit curve due to flux from a potential binary companion will not cause a change in the transit duration – which is why we can rely on the |$R_{\mathrm{ s}}$| calculation from this method (hereon ‘|$R_{\text{trans}}$|’) to compare results from the IRFM. However, it will cause a decrease in |$\delta$| and thus an underestimation of |$R_{\mathrm{ p}}$|⁠.

|$R_{\mathrm{ s}}$| can also be derived from the spectrum of the star using the IRFM, which gives us the star’s effective temperature (⁠|$T_{\text{eff}}$|⁠). This method was first proposed by Blackwell & Shallis (1977), after which various improved scales have been proposed. The basic idea of the IRFM is to compare the ratio between the bolometric flux (⁠|$f_{\text{bol}}$|⁠) and the flux in a given infrared (IR) bandpass (⁠|$f_{\text{IR}}$|⁠) – both received at the Earth’s atmosphere – to the ratio between the stellar surface bolometric flux (⁠|$\sigma T_{\text{eff}} ^4$|⁠) and the surface flux in the same IR bandpass (⁠|$F_{\text{IR, model}}$|⁠), which is determined theoretically using the stellar |$T_{\text{eff}}$|⁠, stellar surface gravity log |$g$|⁠, and [Fe/H] values from the star’s spectrum (Casagrande et al. 2010). This is shown in equation (2), where |$T_{\text{eff}}$| is the only unknown quantity:

Using |$T_{\text{eff}}$| along with the |$f_{\text{bol}}$| received from the star and the parallax from Gaia DR3 (Gaia Collaboration 2023) extracted using VizieR¹ (Ochsenbein, Bauer & Marcout 2000), |$R_{\mathrm{ s}}$| (hereon ‘|$R_{\text{IRFM}}$|’) can be calculated using equation (3):

Here, |$d$| is the distance to the star given by the inverse of the parallax and |$\sigma$| is the Stefan–Boltzmann constant.

In this study, we estimate the angular diameter by fitting the apparent magnitudes in eight optical/IR bandpasses: Gaia|$BP$|⁠, |$G$|⁠, and |$RP$| (Gaia Collaboration 2023); Two-Micron All-Sky Survey (2MASS)|$J$|⁠, |$H$|⁠, and |$Ks$| (Skrutskie et al. 2006); and Wide-field Infrared Survey Explorer (WISE)|$W1$| and |$W2$| (Wright et al. 2010), with synthetic photometry derived from the stellar model atmospheres of Castelli & Kurucz (2003).While other bandpasses can be used in addition to these, this set has two advantages: they are available for all the WASP host stars, and the angular diameter values derived from them are independent of degeneracies between stellar effective temperature and interstellar reddening (Schanche et al. 2020). At the distances of typical WASP host stars, the parallax and the angular diameter combine to yield the stellar radius to a precision of the order of 1–2 per cent. This is comparable to the precision achievable with asteroseismology (e.g. Silva Aguirre et al. 2015, 2017).

Our aim is to compare the values of |$R_{\mathrm{ s}}$| using both the methods above for all the WASP systems. The stars that have a larger |$R_{\mathrm{ s}}$| from the IRFM than from photodynamical modelling (i.e. |$R_{\text{IRFM}} > R_{\text{trans}}$|⁠) are our targets of interest.

3 RESULTS

We have used the Transiting ExoPlanets Catalogue (TEPCat)² (Southworth 2011) to extract all our data on the WASP systems. Because the discovery papers for the majority of these planets were published prior to the Gaia DR2 and DR3 data releases, the published |$R_{\mathrm{ s}}$| values have in most cases been obtained using the transit duration method. We performed the IRFM calculations using python routines³ developed by the authors, based on the astroquery (Ginsburg et al. 2021), pysynphot (STScI Development Team 2013), and pyphot (Fouesneau 2022) packages, on all the systems to check the consistency with the published values. The inferred stellar radii are plotted against the values catalogued in TEPCat, in Fig. 1, and listed in Appendix A, Table A1. We have also extracted the renormalized unit weight error (RUWE) values for each star from Gaia DR3, which should be |$\simeq$|1 for single sources (Gaia Collaboration 2023). The RUWE is similar in character to the reduced |$\chi ^2$| statistic; Ziegler et al. (2020) note that values in excess of 1.4 are indicative of an extended or binary source in Gaia DR2, while Penoyre, Belokurov & Evans (2022) and Castro-Ginard et al. (2024) suggest a lower threshold of the order of 1.25 for Gaia DR3. The points on the graph in Fig. 1 are colour-coded by their RUWE values to highlight outliers with high RUWE.

The radiometric stellar radii were derived from the angular diameter (obtained from the apparent bolometric flux and effective temperature derived from the synthetic photometry via equations 2 and 3) and the Gaia parallax. These were then compared with the photodynamical stellar radii |$R_{\rm trans}$| obtained from TEPCat, which in the source publications had generally been computed under the assumption that no contaminating light was present.

We have identified eight clear outliers in Fig. 1 that lie significantly above the |$R_{\rm trans}=R_{\rm IRFM}$| line, but near or below the |$R_{\rm IRFM}=\sqrt{2}R_{\rm trans}$| line along which binaries with equal-luminosity components should lie. Six of these eight WASP hosts (WASPs 85, 103, 105, 129, 144, and 171) have |$R_{\rm {trans}} \lt R_{\rm {IRFM}} \lesssim \sqrt{2} R_{\rm {trans}}$|⁠, while WASPs 20 and 86 lie above the line. Half of these also have high RUWE values, as indicated by their colours on the graph, which provides further evidence of binarity (Belokurov et al. 2020). We note that WASP-86 (Faedi et al. 2016) has recently been identified as the same star as KELT-12 (Stevens et al. 2017). The apparent discrepancy in the stellar radii reported in these two discovery papers has recently been reconciled by Southworth & Faedi (2022). This star has a long and shallow transit, causing the initial discrepancy in measurement of its properties in the two discovery papers. We will hence not include WASP-86 in our analysis. The revised radius can be found in Southworth & Faedi (2022). Out of the remaining seven stars, WASP-20 and WASP-85 are known binary systems.We will look at WASP-85 in more detail in a later section as we have sufficient information about its binary companion from the discovery paper itself. WASP-20 will be discussed in Section 4.5.

4 DISCUSSION

Since we have identified the systems where we suspect the presence of a bright, unresolved secondary star diluting the transit curve, we can now begin our investigation of these systems in more detail. The next few sections discuss the various studies that we carried out on these seven systems.

We first investigate the reasons why the companion star has not been detected yet.

4.1 Radial velocity difference and angular separation

The transit depth can be diluted due to background stars that may not be bound to the primary star. It is unlikely, however, that such a chance alignment would involve two physically unrelated stars with indistinguishable radial velocities. The absence of two resolvable spectra therefore allows us to assume that the two stars form a wide but bound pair, and that the dilution is caused by a secondary star that has an RV very close to that of the primary. For the two stars’ spectra to be unresolved with an RV spectrometer such as Spectrographe pour l'Observation des Phénomènes des Intérieurs stellaires et des Exoplanètes (SOPHIE), CORALIE, or High-Accuracy Radial-velocity Planet Searcher (HARPS), the Doppler shift between the two stars’ spectral lines would have to be close enough for their cross-correlation function to have a single peak.To estimate the detection threshold for such a binary, we approximated the cross-correlation functions (CCFs) of slowly rotating solar-type stars as Gaussian profiles with the same width as the CCF of the Sun observed with the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) solar telescope feed (Collier Cameron et al. 2019), as shown in Fig. 2.

For RV separations less than |$\Delta$|RV = 8 km s⁻¹, the combined signal appears like that of a single star, with no sign of the presence of a companion. Above that, the combined signal broadens and develops significant kurtosis, before separating into a recognizably bimodal profile. We therefore set our upper limit for stealth binaries at |$\Delta \mathrm{ RV} < 8$| km s⁻¹.

It is also possible for stealth binaries to be mistaken for planet-host systems in the absence of high-resolution spectra, as discussed by Marcussen & Albrecht (2023). They found that the primary false-positive scenario for astrometric exoplanet detections is an unresolved binary system with alike components and a small photocentric orbit.

Another factor that can allow a contaminating secondary star to evade detection during the RV follow-up is the angular separation (⁠|$\theta$|⁠) between the two stars. If |$\theta$| is less than the fibre diameter of the instrument used, then the measured RV of the primary star will be contaminated. Spectroscopic follow-up for the WASP systems is usually done using the SOPHIE (Perruchot et al. 2008) or CORALIE (Baranne et al. 1996; Queloz et al. 2000) instruments. These have fibre-aperture diameters of 3 and 2 arcsec, respectively, which means that any binaries with |$\theta$| significantly less than the fibre diameter would not be detectable. However, the aperture size of the HARPS (Mayor et al. 2003) spectrograph is 1 arcsec and this instrument was used for follow-up on WASP-85, which is why we set our lower limit for detection at |$\theta$| = 1 arcsec.

Given the masses of the two stars and an estimate of the orbital period, the physical separation |$a$| between the two stars follows from Kepler’s third law. Together with the parallax (⁠|$\hat{\pi }$|⁠) from Gaia, this yields the angular separation. In solar units,

The maximum RV separation |$\Delta R V$|⁠, assuming a circular orbit viewed edge-on, follows from energy conservation and Kepler’s third law:

scaling to the Earth’s orbital velocity |$v_{\oplus }\simeq 30$| km s⁻¹.

In Fig. 3, we plot the |$\Delta \mathrm{ RV}$| values obtained using equation (5) as a function of the angular separation |$\theta$| computed with equation (4) for each of the seven WASP host stars with anomalous radii, on a logarithmic grid of periods spanning the range of |$1\!\!-\!\!10^{5}$| yr. The total mass is assumed to be between 1.5 and 2 times that of the planet-hosting star. Planets are preferentially identified around the brighter components of binaries when the observations are signal-to-noise-limited. The mass ratio distribution of binary systems is quite flat, so a reasonable assumption might be that the total mass is on average |$\sim\!\! 1.5$| times that of the planet-hosting star if its stellar companion is bright enough to affect the overall angular diameter. If we also make allowance for cases where the luminosity ratio is close to 1 and the planet orbits the fainter star, an assumed mass ratio closer to 2 might be preferable. Fig. 3 shows that the difference between these two assumptions has little practical impact on the inferred angular and RV separations.

The blue box indicates the limits on |$\Delta \mathrm{ RV}$| and |$\theta$| below which we anticipate the binary to remain undetected, i.e. to lie within the hiding zone. Each point on the curve for any WASP host corresponds to a particular estimate on the period of the two stars. Thus, using the boundaries of our ‘stealth binaries’ box’, we calculate the minimum and maximum periods, as well as the minimum possible angular separation. These are summarized in Table 1. Increasing the assumed system mass to twice that of the primary decreases the maximum period by about 15 per cent and increases the minimum period by 30 per cent. The minimum angular separation increases by about 35 per cent.

The periods obtained are in the range of a hundred to a few thousand years. This explains naturally why none of these systems could have been detected as a spectroscopic binary in the decade or so since their discovery.

4.2 WASP-85

The binary companion of WASP-85A was detected during its discovery by Brown et al. (2014). From the discovery paper, we took the values for the mass of the companion, and the observed angular separation from Gaia DR3 to get the corresponding orbital period from equation (4). To estimate the true orbital separation from the observed angular separation, we must take into account the random orbit orientation. The distribution of apparent angular separation as a fraction of true separation depends on the angle between the line connecting the stellar centres (assumed randomly oriented in space) and the line of sight. Fig. 4 shows this probability distribution, with a mean of 0.79. Thus, on average, we only observe 80 per cent of the true angular separation.

The Gaia DR3 catalogue gives the observed angular separation of the WASP-85AB binary system as |$\theta = 1.28 \ \mathrm{ arcsec}$|⁠; this suggests a true angular separation of about |$1.6 \ \mathrm{ arcsec}$|⁠. On the plot of |$\Delta \mathrm{ RV}$| versus |$\theta$| in Fig. 3, this angular separation corresponds to a |$\Delta \mathrm{ RV}$| of 2.78 km s⁻¹ and an orbital period of 2500 yr, which is in good agreement with the estimate of 2000–3000 yr in the discovery paper.

The companion star (WASP-85B) is about 0.9 mag fainter in the G band than the primary star, with a flux ratio of about 0.5 in most bands. The discovery paper gives a mass |$M_B=0.88 \pm 0.07 \ \mathrm{ M}_{\odot }$| and a radius |$R_B=0.77 \pm 0.13 \ \mathrm{ R}_{\odot }$|⁠. If we take the photodynamical radius of the primary |$R_{A,{\rm trans}}=0.935\ {\mathrm{ R}_\odot }$| and scale it by the square root of the flux ratio |$f_{A+B}/f_A\simeq 1.5$|⁠, we expect to obtain |$R_{\rm IRFM}=1.16 \ \mathrm{ R}_{\odot }$| when the light of both components is combined.

Since Gaia was able to resolve the system, we combined the Gaia magnitudes for the primary and secondary stars to recalculate the total flux coming from the system and hence the combined Gaia|$BP$|⁠, |$G$|⁠, and |$RP$| magnitudes. Combining these with the 2MASS and WISE magnitudes (in which the binary is unresolved), the resulting angular diameter and parallax yielded |$R_{\rm IRFM}=1.16 \ \mathrm{ R}_{\odot }$|⁠. This confirms that the angular radius derived from the combined spectral energy distribution of both binary components is overestimated by an amount that is consistent with our knowledge of the two stars. This means that in cases where |$R_{\rm trans} \lt R_{\text{IRFM}}\lesssim \sqrt{2}R_{\rm trans}$|⁠, there is a strong possibility that the planet orbits the brighter component of a stealth binary. There may indeed be cases where the luminosity ratio is close to 1, and a planet orbiting the fainter component produces detectable transits. In such cases, it would be possible to obtain |$R_{\text{IRFM}}\gtrsim \sqrt{2}R_{\rm trans}$|⁠. This could explain the location of the system WASP-20, above the orange line in Fig. 1, as discussed in Section 4.5.

4.3 Predicting flux and mass ratios

We now use the information we have about the companion star to make estimates on the flux and mass ratios with respect to the primary star for each of our outliers. We use isochrones from Bressan et al. (2012) to relate stellar masses to magnitudes. Table 2 shows some of the parameters of the primary stars that we have used for our analysis in this section. The stellar radii and masses have been taken from TEPCat, while the rough age estimates have been taken from the discovery papers.

Using these isochrones, we estimated the ratio of fluxes of the primary to the companion star. We evaluated the flux ratio for every mass ratio |$q = M_2/M_1$| from 0.7 to 1.2 in intervals of 0.01. We also computed the most probable flux ratio from the factor |$r$| by which |$R_{\text{IRFM}}$| is greater than the actual radius; i.e. |$1+\frac{f_{2}}{f_{1}} = r^{2}$| where |$f_{2}$| and |$f_{1}$| are the fluxes received from the secondary and primary stars, respectively. Each value of |$r$| corresponds to a different value of |$q$|⁠, found by interpolating the isochrone for a star of the same age, assuming that the age of the companion is the same as that of the primary star. These results are summarized in Table 3, while Fig. 5 shows the probability curves for the factor |$r$|⁠, given the value that was observed.

All the most probable mass ratios are within the range of 0.89–1, barring WASP-20. For this system, r has a value greater than |$\sqrt{2}$|⁠, implying that |$f_{2}$| > |$f_{1}$|⁠; i.e. the secondary star is brighter than the primary, and the planet is orbiting the fainter and hence denser star. The identity of the planet-hosting component of the binary is discussed in Section 4.5.

4.4 Recalculating planetary parameters

Using the most probable flux ratios calculated in the previous section, we can obtain the value of the factor ‘|$r$|’ and use this to correct the planet’s radius |$R_{\mathrm{ p}}$|⁠, mass |$M_{\mathrm{ P}}$|⁠, and density |$\rho _{\mathrm{ P}}$|⁠. We know that

where |$\delta$| is the transit depth. From Collier Cameron (2016),

|$K$| is the RV amplitude, whose observed value is the flux-weighted average of all the |$K$| values for each star. Using the above relations and the published values of these quantities, we recalculated the planetary parameters, as summarized in Table 4.

The surface gravity of the planet varies directly with its mass and inversely with the square of its radius. After accounting for the stealth binarity, the mass goes up by |$r^{2}$| while the radius goes up by |$r$|⁠, which means that the planet’s surface gravity remains unchanged. This is an interesting result, as it tells us that the planetary surface gravity is immune to stealth binaries.

4.5 WASP-20 and WASP-103

The binary companion of WASP-20A was discovered at a separation of 0.26 arcsec by Evans et al. (2016) using near-IR adaptive-optics imaging with the Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) instrument on the Very Large Telescope (VLT) of the European Southern Observatory (ESO) on Cerro Paranal, Chile.They inferred an increase in planetary mass |$M_{\mathrm{ P}}$| and radius |$R_{\mathrm{ p}}$| by |$4\sigma$| and |$1\sigma$|⁠, respectively, after having accounted for the dilution to the transit curve and RV amplitude. They concluded that the planet orbits the brighter of the two stars, on the grounds that the inferred stellar density in the planet-orbits-fainter-star scenario yielded an implausibly old stellar age of 16 Gyr. The inferred separation of 61 au and system mass of the order of 2 |$\mathrm{ M}_\odot$| implies a period of the order of 340 yr, and hence an RV separation |$K_A+K_B\simeq 5.3$| km s⁻¹, placing it within the blue box in Fig. 3.

Southworth et al. (2020) made further corrections to these parameters using updated light curves and spectroscopic data. They were unable to rule out the planet-orbits-fainter-star scenario, finding a density 1.08 times solar and an age of 3.3 Gyr. In both cases, the planet’s density is reduced relative to that obtained by assuming that the host star is single. In our own study, the balance of probability in Fig. 5 suggests that the ratio of the angular and photodynamical radii is greater than 1.4 for an assumed age of 4 Gyr. Our study thus favours the planet-orbits-fainter-star scenario.

The planetary parameters for WASP-103b were also corrected in the analysis by Delrez et al. (2018) for the presence of a stellar companion at a separation of 0.23 arcsec. This companion was discovered in a lucky-imaging survey by Wöllert & Brandner (2015). It is 3.1 mag fainter than the brighter star in the |$i^{\prime }$| band and 2.6 mag fainter in the |$z^{\prime }$| band. We find that a discrepancy remains between |$R_{\rm IRFM}$| and the value of |$R_{\rm trans}$| found by Delrez et al. (2018) even after this correction, so we infer that the host star may have another brighter and closer companion.

In their study of the tidal deformation and orbital decay rate of WASP-103b, Barros et al. (2022) recently found that the faint visual companion of the host star was too distant and insufficiently massive to explain the inferred positive RV acceleration |$a=+0.113 \pm 0.058$| m s⁻¹ d⁻¹, whose sign is contrary to expectations for tidal orbit decay. This suggests that the unresolved stellar companion responsible for the observed excess in the stellar angular diameter could also be the cause of the anomalous observed acceleration. Using our derived value |$q=0.92$| for the stealth companion of WASP-103, we get |$M_{2}=1.11 \pm 0.10 \ \mathrm{ M}_{\odot }$|⁠, where |$M_{2}$| is the mass of the companion. If we assume that the unseen companion is close to superior conjunction, the host star should be accelerating away from the observer. Using the observed acceleration and the inferred secondary mass, assuming a circular orbit and a high inclination we obtain an approximate estimate of the orbital separation:

where |$d$| is the binary separation. At maximum elongation, this would give an angular separation |$\theta =0.15\pm 0.04$| arcsec and an orbital period |$P\simeq 400$| yr. The maximum RV separation of the two stars would then be |$K_1+K_2=2\pi d/P \simeq 1.1$| au yr⁻¹, or 5.2 km s⁻¹. These inferred maximum angular and RV separations lie comfortably within the blue region in Fig. 3, explaining why the inferred binary companion has thus far evaded detection.

5 CONCLUSION AND SUGGESTED WORK

Various properties of transiting exoplanets can be derived from their transit photometry and RV measurements. If these get contaminated by other stars that are bound to the host star, then the calculated parameters need to be corrected by accounting for the additional flux in the system. We find that the surface gravity of the planet is a quantity that is not affected by the dilution of the transit and RV observations. We have recalculated the masses, radii, and densities for seven WASP planets (Table 4) where we suspect that the host star has a hidden stellar companion. Our estimate of the flux ratio and orbital period for the WASP-85 binary system is consistent with that obtained in the discovery paper of Brown et al. (2014). Dilution of observations for WASP-20 and WASP-103 had been accounted for previously in the literature. Our comparisons of the |$R_\text{IRFM}$| values with estimates of the host-star radius based on the photodynamical stellar density suggest that the planet in the WASP-20 system may orbit the fainter of the two stars, and that the stealth companion of WASP-103’s host star may be responsible for the apparent secular increase in the planet’s orbital period.

Overall, the densities of the planets have gone down on average by a factor of 1.3. We also made estimates on the orbital periods, mass ratios, and flux ratios for all seven stealth binary systems, which have been outlined in Tables 1 and 3. The most probable flux ratios range from about 0.5 to 1, and mass ratios from 0.89 to 1 – barring WASP-20, which is an exception wherein both ratios are above 1 implying that the planetary host star is the denser and fainter of the two stellar binary components. The orbital periods range from a hundred to a few thousand years, which explains why the secondary stars have not been detected in RV observations yet. None the less, the example of WASP-103 discussed above suggests that long-term RV monitoring could reveal secular accelerations in systems with companions of unequal luminosities.

These binary systems appear to have angular separations below 1 arcsec but are not close enough to give resolvable Doppler shifts. We also suggest that follow-up observations be made using speckle imaging, lucky imaging, or adaptive optics. Speckle imaging removes effects of turbulence in the atmosphere and provides simultaneous photometric and astrometric data at sub-arcsecond precisions (Matson, Howell & Ciardi 2019). The ‘Differential Speckle Survey Instrument’ (Horch et al. 2009) has successfully detected binary companions to stars in the ‘Kilodegree Extremely Little Telescope’ survey (Coker et al. 2018), and can thus be used for these WASP systems as well – as was done for WASP-103 (Wöllert & Brandner 2015).

ACKNOWLEDGEMENTS

TG thanks Siddharth Rangnekar for helpful discussions and assistance with the preparation of the manuscript. ACC and TGW acknowledge support from STFC consolidated grant numbers ST/R000824/1 and ST/V000861/1, and UKSA grant number ST/R003203/1. This research has made use of NASA’s Astrophysics Data System. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France.

DATA AVAILABILITY

The stellar and planetary data for the WASP systems investigated in this research are available in the TEPCat data base curated by Dr John Southworth at the University of Keele. All other research data underpinning this publication and the python code and notebook used to prepare all diagrams in this paper will be made available through the University of St Andrews Research Portal. The research data supporting this publication can be accessed at https://doi.org/10.17630/1ceff0e3-c2aa-40d0-996a-0d3f8d81cf19 (Goswamy, Collier Cameron & Wilson 2024a). The code supporting this publication can be accessed at https://doi.org/10.17630/72a692c8-dd85-4078-99d3-8a5551727ff9 (Goswamy, Collier Cameron & Wilson 2024b).

Footnotes

REFERENCES

APPENDIX