The Activity of a Solar-Type Star TOI-1422 and Mass Loss of the Atmosphere of the Planet TOI-1422b

Abstract

The results of the analysis of the activity of a solar type star G2V TOI-1422 are presented and estimates of the loss of atmospheric matter of the planet TOI-1422b are made. The planet can be attributed to the type of hot Neptunes. Compared to other exoplanets of a similar mass range, it is expected that the planet has an extensive gas envelope. According to the long-term photometric survey of Kamogata Wide-field Survey (KWS) the TOI-1422 activity was analyzed and the existence of possible activity cycles of 1650–1680 days and 2450 days was suggested. The probable value of the rotation period P of the star lies in the range of 27 (+19, –8) days, observations of the KWS survey in the V filter indicate the most possible value for the period P = 32 days. Mass loss of the planet’s atmosphere is determined using an approximation formula corresponding to the model of atmospheric loss with an energy restriction. To estimate the flux of XUV photons analytical dependences were used linking the flux values and the parameter $\log R_{{{\text{HK}}}}^{'}$. Calculations have shown that the atmosphere matter loss of TOI-1422b is $\dot {M} = 9.4 \times {{10}^{8}}$ g/s; considering the existing errors in determining the parameters of the atmosphere it lies in the range from $6.8 \times {{10}^{8}}$ to $1.4 \times {{10}^{9}}$ g/s, and considering the uncertainty in the value of the chromospheric activity index—from $8.3 \times {{10}^{8}}$ to $1.1 \times {{10}^{9}}$ g/s.

1 INTRODUCTION

Neptune-type planets are one of the main types of exoplanets and have chemical and physical characteristics that are between rocky planets and gas giant planets. The study of such exoplanets is relevant for understanding both the mechanisms of their formation and models of their evolution [1]. The authors of [2] studied the exoplanet candidate object TOI-1422b, whose transits were detected by the TESS space telescope, with the main goal of confirming its planetary nature and finding its properties. The solar-type parent star TOI-1422 (spectral class G2 V, $V{{ = 10.6}^{m}}$) is located at a distance of 155 pc from us.

In [2], additional observations of TOI-1422 were made with the HARPS-N spectrograph for 1.5 years to more accurately determine changes in its radial velocity (RV), which were analyzed together with TESS photometry and the results of other observations (including images with high spatial resolution). The performed analysis made it possible to refine the main parameters (mass, radius, luminosity, etc.) of TOI-1422 and to characterize the properties of TOI‑1422b, as well as to suggest the presence of the Neptune-mass planet TOI-1422c in a more distant orbit, which was not detected in the TESS light curves. The inner planet, TOI-1422b, orbits with a period of $12.9972 \pm 0.0006$ days and has an equilibrium temperature of ${{T}_{{eq,b}}} = 867 \pm 17$ K. According to [2], the planet’s radius is ${{R}_{b}} = 3.96_{{ - 0.11}}^{{ + 0.13}}{\kern 1pt} {{R}_{ \oplus }}$, the mass is M_b = $9.0_{{ - 2.0}}^{{ + 2.3}}{\kern 1pt} {{M}_{ \oplus }}$ and, consequently, the density is ρ_b = $0.795_{{ - 0.235}}^{{ + 0.290}}$ g/cm³, i.e., the planet can be attributed to the type of hot Neptunes. Compared to other exoplanets of a similar mass range, TOI-1422b is one of the most “bloated”. The authors of [2] expect that this planet will have an extensive gas envelope surrounding the core with a mass fraction of about 10–25% of the total mass of the planet. The outer planet candidate, TOI-1422c, has an orbital period of $29.29_{{ - 0.20}}^{{ + 0.21}}$ days, its minimum mass, ${{M}_{c}}{\kern 1pt} \sin i$, is $11.1_{{ - 2.3}}^{{ + 2.6}}{\kern 1pt} {{M}_{ \oplus }}$, the equilibrium temperature is ${{T}_{{eq,c}}} = 661 \pm 13$ K, and therefore, if its type is confirmed, it could be considered another hot Neptune.

The first part of this work presents the results of the analysis of TOI-1422 activity manifestations. In the second, the results obtained were used to estimate the loss of matter from the atmosphere of the planet TOI‑1422b.

2 MANIFESTATIONS OF TOI-1422 ACTIVITY

According to the results of [2], the effective temperature of the star is $5840 \pm 62$ K, the logarithm of the acceleration of gravity $\log g = 4.41 \pm 0.11$, the radius is $R{\text{/}}{{R}_{ \odot }} = 1.019 \pm 0.14$, the luminosity is $L{\text{/}}{{L}_{ \odot }} = 1.116 \pm 0.037$ and the mass is $M{\text{/}}{{M}_{ \odot }} =$ 0.981 ± 0.06. The age of TOI-1422 is $5.1 \pm 3.9$ billions of years. The object is identified with the source Gaia EDR3 192 0333 4491 6951 6288, its parallax is $\pi = 6.4418 \pm 0.0138$ mas.

According to the long-term KWS,¹ we analyzed the manifestations of TOI-1422 activity. The review presents observations of the star in filters $V$ and $Ic$. First of all, we analyzed the data for the filter $V$, which has a longer observation interval, 4142 days (11.3 years) (HJD 245 5777.3–9919.9). A total of 1355 star brightness estimates in the $V$ filter were considered. Presented in Fig. 1 (top), the data clearly indicate the presence of cyclicity in the change in its brightness. Based on the constructed power spectrum for TOI‑1422, we can assume the existence of possible activity cycles 1650^d and 2450^d (middle diagram). The vertical dotted lines represent periods corresponding to annual and double annual variability. The bottom diagram of Fig. 1 shows the power spectrum for the interval of periods 1–140^d, which includes the probable rotation period of the star. According to the authors of [2], for TOI-1422, it should be expected that the rotation period $P$ of the star lies within an interval of $27_{{ - 8}}^{{ + 19}}$ days. On the bottom diagram of Fig. 1, the specified interval is marked with vertical thin dotted lines, and the possible value of $P$ is marked with a thick dotted line. The dashed line corresponds to the maximum amplitude peak in the considered interval ($P{{ = 32}^{d}}$).

Fig. 1.

Top panel: filtered photometric observations of TOI-1422 from the Kamogata Wide-field Survey (KWS). Middle panel: power spectrum for this data, vertical lines refer to activity cycles 1650^d and 2450^d (4.5 and 6.7 years, respectively). Dashed lines are the peaks corresponding to seasonal (about 365^d) and double seasonal periods. Below is the power spectrum for the interval of periods 10–140^d. The interval of possible values of the rotation period P is marked with thin dotted lines, and the possible value P itself is marked with a thick dotted line. The dashed line corresponds to the maximum amplitude peak for P = 32^d in the considered interval.

Less numerous are the data on the brightness of the object in the filter Ic. There are a total of 1170 estimates of star brightness in this filter. Presented in Fig. 2 (top), the data undoubtedly indicate the presence of a change in its brightness in the considered time interval. We can assume the presence of possible activity cycles of the order of 1680^d and 4600^d (the latter is unlikely to be real, its magnitude is comparable to the duration of the observation interval) (Fig. 2, middle diagram), and variability on the time scale of the order of 1–140^d (Fig. 2, lower diagram). In the time interval characterizing the probable rotation period of the star, one can point to a set of peaks, among which there is no dominant one. Manifestations of details pointing to $P{{ = 27}^{d}}$ or ${{32}^{d}}$ were not found. Photometric observations of TOI-1422 were also made in 2004, 2006 and 2007 during research under the WASP tr-ansit-search program [3]. In total, more than 20 000 photometric estimates were obtained over several observation periods with a total duration of 120 days per year. The authors of [2] searched for the presence of manifestations of rotational modulation in the observational data, but found no significant periodicity in the range between 1 and 100^d. The TESS light curve also shows no modulation, confirming the star’s rather quiet behavior during the interval ~100^d.

Fig. 2.

Upper panel: photometric observations of TOI-1422 in the Ic filter from the KWS survey data. Middle panel: power spectrum for this data, vertical lines refer to activity cycles 1680^d and 4600^d (4.6 and 12.6 years respectively). Dashed lines are the peaks corresponding to seasonal (about 365^d) and double seasonal periods. Below is the power spectrum for the interval of periods 10–140^d. The interval of possible values of the rotation period P is marked with thin dotted lines, and the possible value of P itself is marked with a thick dotted line. The dashed line corresponds to the period P = 32^d in the interval under consideration (see Fig. 1).

3 MATTER LOSS OF THE ATMOSPHERE OF TOI-1422b

As mentioned above, TOI-1422b is a Neptune-type planet with a mass on the order of $M = 9{\kern 1pt} {{M}_{ \oplus }}$ and an orbital semi-major axis of 0.108 AU. According to the authors of [2], the density of TOI-1422b is about 0.8 g/cm³, which is close to the density of Saturn and lower than that of most exoplanets in this mass range. The planet is located closer to the upper left corner of the mass–radius diagram [2], Fig. 12, making it very similar to the exoplanets Kepler-36c and Kepler-11e. According to [2], TOI-1422b may have an extensive gas envelope surrounding a massive core. It is expected that the mass fraction of this shell will be about 10–25% of the total mass of the planet, unless some of the atmosphere was previously blown away by the stellar wind. The nature of this vast shell requires further study, most likely based on observations with the JWST. A hot Neptune-type exoplanet loses its helium-hydrogen atmosphere over time. To calculate such a loss (without detailed modeling of processes in the star–planet system), our study used an approximation formula (see, e.g., [4, 5]), usually referred to in the literature as an energy-limited atmospheric loss model. This model assumes that the flux of hard UV radiation is absorbed in a thin layer of radius ${{R}_{{{\text{XUV}}}}}$, where the optical depth for stellar XUV photons is equal to unity, and takes into account the tidal effect:

$$\dot {M} = \frac{{{{\epsilon }_{{{\text{XUV}}}}}{\kern 1pt} \pi {\kern 1pt} {{F}_{{{\text{XUV}}}}}{\kern 1pt} {{R}_{p}}{\kern 1pt} R_{{{\text{XUV}}}}^{2}}}{{G{\kern 1pt} {{M}_{p}}{\kern 1pt} {{K}_{{{\text{tide}}}}}(\xi )}},$$

(1)

where ${{\epsilon }_{{{\text{XUV}}}}}$ is the heating efficiency parameter (${{\epsilon }_{{{\text{XUV}}}}} = 0.2 \pm 0.1$ for mini-Neptunes and super-earths); $G$ is the gravitational constant; ${{F}_{{{\text{XUV}}}}}$ is the flux of XUV photons; ${{R}_{p}}$ is the radius of the planet; ${{M}_{p}}$ is the mass of the planet; ${{R}_{{{\text{XUV}}}}}$ is the absorption radius of XUV photons; ${{K}_{{{\text{tide}}}}}(\xi )$ is the tidal parameter. Details of the use of relation (1) can be found in many literature sources, including [1, 4–6].

The main data on the planet TOI-1422b were taken from [2]. Calculations by formula (1) require estimates of the XUV photon flux ${{F}_{{{\text{XUV}}}}}$. For this purpose, we used the analytical dependences obtained in [7] and relating the values of the flux ${{F}_{{{\text{XUV}}}}}$ and the parameter $\log R_{{{\text{HK}}}}^{'}$ for stars of spectral types from F to M. As was pointed out in [2], TOI-1422b is a fairly old star with an age of about 5 Gyr. The authors of [2] found that the value of the index of stellar chromospheric activity of a star $\log R_{{{\text{HK}}}}^{'}$, measured by them from the Ca II H and K lines in their HARPS-N spectra, is equal to $- 4.95 \pm 0.03$. This value generally agrees with the assumption of the authors of [2] that the star is comparable in age to the Sun, and its activity is only slightly higher than that of the Sun (for the Sun $\log R_{{{\text{HK}}}}^{'} = - 5.021$ [8]). According to [7], we previously obtained an estimate of the value $\log ({{F}_{{{\text{XUV}}}}}{\text{/}}{{F}_{{{\text{bol}}}}})$, it is shown in Fig. 3 together with data for other objects considered in [7, Table 1]. The flux of XUV photons was $4.6 \times$ 10^–15 erg/(cm^–2 s). Calculations using relation (1) showed that the loss of atmospheric matter by the planet TOI-1422b for the value $\log R_{{{\text{HK}}}}^{'} = - 4.95$ is $9.4 \times {{10}^{8}}$ g/s. The value of the tidal parameter is ${{K}_{{{\text{tide}}}}}(\xi ) = 0.88$. The values of atmospheric parameters according to the data of [2], Table 2 (${{M}_{p}} = 9{\kern 1pt} {{M}_{ \oplus }}$, ${{R}_{p}} = 3.96{\kern 1pt} {{R}_{ \oplus }}$), were used in the calculations.

Fig. 3.

Dependence of $\log ({{F}_{{{\text{XUV}}}}}{\text{/}}{{F}_{{{\text{bol}}}}})$ values for objects from [7] on their effective temperature. Light circle—data for TOI-1422.

It should be considered that we do not yet have accurate data on the cyclic variability of the star’s chromospheric activity, which can lead to a scatter in the estimates of the values of $\log R_{{{\text{HK}}}}^{'}$ and, as a consequence, in the values of the matter loss rate. In this case, with the value of the uncertainty of the index $\log R_{{{\text{HK}}}}^{'}$ equal to 0.03, the value $\dot {M}$ will vary from $8.3 \times$ 10⁸ to $1.1 \times$ 10⁹ g/s.

On the other hand, considering the existing errors in determining the parameters of the TOI-1422b atmosphere, it can be found that the value of the matter loss rate lies in the range from $6.8 \times {{10}^{8}}$ to $1.4 \times$ 10⁹ g/s. The estimates obtained differ by about 2 times, which clearly demonstrates how the errors in determining the parameters of the planet, regardless of whether they are used in approximate estimates (for example, by formula (1)) or in accurate modeling, affect the final result. The high rate of outflow of matter is a consequence of a sufficiently high level of XUV photon flux from a solar-type star, and also due to the fairly close location of the planet from the parent star (about 0.1 AU). Considering the influence of the tidal parameter ${{K}_{{{\text{tide}}}}}(\xi )$ also leads to a higher value of the estimated outflow rate.

According to [2], the star has another exoplanet candidate, TOI-1422c, with an orbital period of 29.29^d and a minimum mass of ${{M}_{c}}\sin i = 11.1\,{{M}_{ \oplus }}$. According to the same authors, the equilibrium temperature of the planet’s surface is close to 660 K, and, if the observational data are confirmed, the planet can be classified as a hot Neptune. The lack of estimates of the parameters of the planet TOI-1422c (for example, radius) does not currently allow us to study the loss of matter from its atmosphere.

4 CONCLUSIONS

The article presents the results of an analysis of the manifestations of the activity of the star TOI-1422 and estimates of the loss of matter from the atmosphere of the planet TOI-1422b. The solar-type star TOI-1422 (spectral type G2 V, $V{{ = 10.6}^{m}}$) is located at a distance of 155 pc from us. Planet TOI-1422b orbits with a period of about 13^d, the radius of the planet is $3.96{\kern 1pt} {{R}_{ \oplus }}$, and the mass is $9.0{\kern 1pt} {{M}_{ \oplus }}$. The planet can be classified as a hot Neptune type, compared to other exoplanets of a similar mass range, this planet is expected to have an extensive gas envelope. According to the long-term photometric survey KWS (observations in the $V$ and $Ic$ filters), we analyzed the manifestations of TOI-1422 activity. Based on the constructed power spectra for TOI-1422, we can assume the existence of possible activity cycles 1650–1680^d (the $V$ and $Ic$ filters) and 2450^d (the $V$ filter). According to the literature estimates for TOI-1422, it should be expected that the rotation period $P$ of the star lies in the interval $27_{{ - 8}}^{{ + 19}}$ days. However, in the power spectrum, a set of peaks falls into the interval characterizing the probable rotation period of the star, among which the peak for $P{{ = 32}^{d}}$ (observations in the $V$ filter) is probably dominant. To calculate the loss of matter by the planet’s atmosphere in our study, we used an approximation formula corresponding to the energy-limited atmospheric loss model. To estimate the value of the flux of XUV photons, analytical dependencies were used that relate the values of the flux and the parameter $\log R_{{{\text{HK}}}}^{'}$. Calculations have shown that the loss of matter from the atmosphere of TOI-1422b for the value $\log R_{{{\text{HK}}}}^{'} = - 4.95$ is $9.4 \times {{10}^{8}}$ g/s. Considering the existing errors in determining the parameters of the TOI-1422b atmosphere, it can be found that the value of the matter loss rate lies in the range from $6.8 \times {{10}^{8}}$ to $1.4 \times {{10}^{9}}$ g/s, and considering the uncertainty in the value of the chromospheric activity index, from $8.3 \times {{10}^{8}}$ to $1.1 \times {{10}^{9}}$ g/s.

The estimates obtained differ by about 2 times and demonstrate how the errors in determining the parameters of the planet affect the final result. The star has another exoplanet candidate, TOI-1422c, with an orbital period of 29.29^d and a minimum mass of 11.1 Earth masses. The absence of other estimates of its parameters (for example, the radius) does not currently allow studying the loss of matter from its atmosphere.