Confirmation of a Sub-Saturn-size Transiting Exoplanet Orbiting a G Dwarf: TOI-1194 b and a Very Low Mass Companion Star: TOI-1251 B from TESS

Since the discovery of PSR 1257+12 c and d in 1992 (Rasio et al. 1992), more than 5000 planets have been confirmed. Ground-based and space-based telescopes have significantly contributed to exoplanet detection and research. The expected efficiency of the transit method for exoplanet search is very optimistic (Horne 2003), but the actual situation in recent years shows that the rate of planet identification and the physical characteristics of the discovered planets are obviously limited by the detection methods and observation strategies. For instance, about 17% of confirmed planets revolve around their host star with an orbital period greater than 100 days, ²⁰ which makes it more challenging to detect long-period and wide-orbit planets. These planets share similarities with our own solar system and require further research. Understanding these exoplanets and their properties can yield valuable insights into planetary formation and evolution. Therefore, the immediate goal is to expand the sample of detected planets through advanced detection methods and observation strategies.

The most efficient way to confirm exoplanets is through space-based surveys and follow-up studies from ground-based telescopes. The nine-year survey by the Kepler mission (Borucki et al. 2010; Howell et al. 2014) gives us a glimpse into the abundance of planets in the universe. Since the launch of Transiting Exoplanet Survey Satellite (TESS) in 2018 April, numerous exoplanet candidates have been discovered and confirmed. However, some candidates with extended periods (≥27 days), or only a single transit detected (called single-transit, Cooke et al. 2018) require further confirmation and research, which may demand a considerable amount of observation time at a single ground-based site. In addition, capturing the full transit can be challenging in certain cases. A well-designed multi-telescope campaign provides a solution to this problem, and the feasibility of this approach has been validated by the studies on long-period planet HD 80606 b, which has a period of 111.43605 days (Naef et al. 2001; Pont et al. 2009). For instance, telescopes located at 40° latitude typically have an average dark time of around 8 hr per observation night. In this case, multiple telescopes spanning a time zone of fewer than eight hours can work together to perform relay observations on exoplanets with transit durations exceeding eight hours. By doing so, more data can be obtained with a single transit for these planets, which have larger orbital radii and a higher probability of being in the habitable zone.

Simultaneous multiband photometry using ground-based telescopes provides a cost-effective and efficient method for identifying exoplanet candidates and reducing false positives (FPs). While space-based telescopes capture the decline in candidate stars' luminosity through long-term sky area monitoring, the satellite orbit and observation conditions limit the available observation time to a single band, ensuring survey efficiency and the robustness of the telescope system. It is worth noting that over half of the exoplanet candidates are subject to stellar luminosity variations or are eclipsing binaries (EBs) (Deleuil & Fridlund 2018). Simultaneous multi-color light curves can effectively eliminate most FPs caused by EBs (Tingley 2004). In contrast, the Kepler mission has shown that low transit signal-to-noise ratios (S/Ns) are more likely to result in FPs, particularly in the case of Earth-like planets (Fressin et al. 2013). Although this issue also affects ground-based telescope detection, the ample observation time provides an opportunity to accumulate more time-series data on transits and enhance the transits' S/Ns by adding multiple transits (Kaltenegger & Traub 2009).

Since the first transit planet was confirmed (Charbonneau et al. 2000), photometry of transits has become the most efficient method for identifying new planet candidates and determining their radius (R_P ) and semimajor axis (a). Achieving 1% precision in radius determination is essential for studies of planetary structure and evolution, and relies heavily on accurate measurements of stellar limb darkening values (Csizmadia et al. 2013). Transit light curve morphology, particularly the ingress and egress fragments, can significantly impact model-estimated parameters. The transit observation cadence is the primary driver for such morphology (Kipping 2010). Ground-based telescopes with meter-scale apertures (called one meter-class telescopes) enable high S/Ns ≥ 100 for follow-up observations, while maintaining an observation cadence that conforms to exposure time constraints.

We want to present some of our latest confirmations of TOI-1194 b and TOI-1251 B through our global follow-up campaign utilizing several telescopes, including the Sino-German multiband photometric campaign. Section 2 offers an introduction to the Sino-German multiband photometric campaign, target selection and the follow-up observation strategy employed during our campaign. Section 3 gives an overview of the observations. Section 4 describes the rapid processing of intensive data generated by campaign telescopes and light curve fitting, while Section 5 details our confirmation of TOI-1194 b and TOI-1251 B. Lastly, Section 6 concludes with a summary and discussion of our findings.

In order to identify a greater number of long-period planets, our Sino-German cooperation team has successfully established a global multiband follow-up observation network. This network incorporates a wide range of optical observational equipment, including both professional-grade instruments and those utilized by amateur astronomers. The network remains distributed across several telescopes in China, Germany and Chile, covering time zones spanning five to twelve hours among the sites, as illustrated in Figure 1. Currently, the network includes fifteen telescopes located at ten observation sites.

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Our follow-up campaign utilizes multiband photometric observations to exclude FPs from Tess Objects of Interest (TOIs) we have observed. Nonetheless, filter systems may differ among several telescopes. For instance, telescopes at Xinglong (Huang et al. 2012; Fan et al. 2016; Bai et al. 2018) and Weihai (Hu et al. 2014; Gao et al. 2016) in China use the Johnson-Cousins filter system, while telescopes at Wendelstein Observatory in Germany (Hopp et al. 2014; Steuer et al. 2021) and Nanshan in China utilize the SDSS $u^{\prime} g^{\prime} r^{\prime} i^{\prime} z^{\prime}$ system. Other amateur telescopes rely on RGB filters or white band (refer to Table 1).

Table 1. Primary Parameters of Telescopes in Sino-German Campaign

Site	Longitude	Latitude	Altitude	Aperture	Filter	FoV.
	(°)	(°)	(m)	(cm)
Nanshan, China	87.1736E	43.4747N	2088	25/60	SDSS $g^{\prime} r^{\prime} i^{\prime}$	62'/25'
Aishan, China	119.9453E	36.1231N	100	10/25	LRGB	50'/87'
Weihai, China	122.0496E	37.5359N	100	60/100	Johnson BVRI	30'/12'
Lijiang, China	100.0300E	26.6951N	3200	30/35	SDSS $g^{\prime} r^{\prime} i^{\prime}$/LRGB	21'/25'
El Sauce, Chile	70.7631W	30.4725S	1525	35/60	LRGB	60'/60'
Xinglong, China	117.5772E	40.3958N	950	60/80/85	Johnson BVRI	37'/11'/30'
Wendelstein, Germany	12.0121E	47.7364N	1838	43	SDSS $g^{\prime} r^{\prime} i^{\prime}$	43'
Ali, China	80.1272E	32.2312N	5360	50	Johnson BVRI	11'
Muztaga, China	74.8967E	38.3297N	4583	50	Johnson V	5'
Minqin, China	103.3152E	38.4141N	1335	60	Johnson BVRI	30'

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2.1. Target Selection and Observation Strategy

To confirm exoplanets, obtaining high-quality data depends upon choosing candidates with full-transit when observation conditions are favorable. More than half of the TOI objects have brightness above 12 mag in the TESS band, making them suitable for observation using one meter-aperture telescopes. During the Sino-German campaign follow-up observations, our strategy aims to maximize the observation efficiency within the limited observation time. Our team achieves this efficient observation strategy by calculating all TOI transits for each observation site during the observable time. The TOIs are then ranked in terms of priorities based on observation parameters such as brightness, transit depth and orbital period. Between 2019 October and 2023 May, we screened and observed a total of 181 TOIs. Through our follow-up data, we confirmed a planet orbiting a solar-type star, TOI-1194 b, and a very low-mass stellar companion, TOI-1251 B.

For one meter-aperture telescopes, the main factor affecting the precision of photometric observation data is S/N. The point source standard S/N formula is as follows

$$\begin{eqnarray*}&&{\rm{S}}/{\rm{N}}=\displaystyle \frac{{R}_{* }\times t}{\sqrt{{R}_{* }\times t+{n}_{\mathrm{pix}}\times ({R}_{\mathrm{sky}}\times t+{\mathrm{RN}}^{2}+D\times t)}}.\end{eqnarray*}$$

In this context, R_* denotes the target flux, t represents exposure time, R_sky indicates the sky background flux, n_pix signifies the number of pixels occupied by a star, RN refers to camera readout noise and D denotes dark current (Howell 2006). Due to the use of a camera cooler with temperature below −80 °C, dark current noise can be ignored. A faster readout speed results in greater readout noise, while a slower readout speed tends to be preferred. Analyses of CoRot and Kepler data by Kipping have revealed that sampling frequency has a particularly crucial effect on planet confirmation and the determination of planetary parameters (Kipping 2010). Longer exposure cadences of photometry images can result in increasing levels of systematic errors concerning physical parameters. On the 60 cm telescope at Xinglong Observatory, we employed an Andor #DZ936N CCD camera with an S/N of 100 for a 12 mag star exposure lasting 10 s. By utilizing a readout speed of 1 MHz, the readout time per image was reduced to 4 s, albeit with a readout noise of 6.5 electrons. Conversely, the readout time was prolonged to 76.8 s and the readout noise reduced to 3.6 electrons at a readout speed of 50 kHz. Furthermore, we selected a gain value closest to 1 to curb readout noise linked to amplification. The CCD/CMOS exposure parameters were tailored to meet these standards and set for the telescope used during our campaign. Consequently, the photometric data obtained achieved an accuracy better than 0.002 mag when the S/N was no less than 100.

It is noteworthy that roughly 20% of the TOIs are brighter than eight in TESS band, making them well-suited for observation with one meter-class telescopes. However, when observing TOIs brighter than 8 mag, the field of view (FoV) of one-meter telescopes is typically limited to approximately 30', making identification of reference stars with similar brightness within the FoV difficult. To ensure optimal data quality, it is imperative to appropriately defocus the target image in order to avoid saturation, while also limiting the exposure time to effectively enhance the S/N of fainter reference stars within the FoV. The efficacy of the observation strategy is critical to successful data acquisition.

We observed two planet candidates from TESS, TOI-1194.01 and TOI-1251.01, by using several ground-based one meter-class telescopes in the Sino-German campaign and TESS Follow-up Observing Program (TFOP). ²¹ The photometric observation parameters are summarized in Tables 3 and 4, followed by a description of the observations by different observatory sites and TESS.

3.1. TESS Observation

3.2. Ground-based Follow-up Photometric Observation

3.2.1. Xinglong Observatory

We obtained data from three telescopes at Xinglong Observatory, in Hebei, China, during the Sino-German follow-up campaign. Specifically, data from the 0.6 m telescope, TNT (0.8 m) (Huang et al. 2012) and NBT (0.85 m) (Bai et al. 2018) resulted in the acquisition of eight series of data (seven primary transits and one secondary transit) of TOI-1194 b and two series of data (all primary transits) for TOI-1251 B. We require that the S/Ns of the images are greater than 1000 pixel⁻¹, and the exposure times of each band are adjusted according to environmental conditions such as sky background and seeing, which are not fixed values.

The selected CCD exposure parameters are outlined in Table 2. Despite our efforts, the primary transit on 2021 December 2nd and secondary transit on 2022 March 1st of TOI-1194 b could not be satisfactorily captured due to poor photometric accuracy. Analysis of planetary parameters and properties was primarily based on the transit data outlined in Tables 3 and 4, which detail the observation date, filters and the number of images.

Table 2. CCD Parameters of Telescopes at Xinglong Observatory Used in TOIs Follow-up Observations

Telescope	CCD Type	Readout Noise	Gain	Pixel Scale
		(e− Rms)	(e− per A/D)	('' pixel−1)
60 cm	Andor DZ936N	6.5	1.1	1.10
80 cm	PYL1300BX	4.02	1.36	0.51
85 cm	Andor DZ936N	7.0	0.97	0.93

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Table 3. Ground-based Photometric Follow-up Observation of TOI-1194 b

Date	Telescope	Band	Duration	Number of Images
			(minutes)
2019/10/16	PvdK 0.6 m	SDSS $i^{\prime}$	200	58
2019/12/05	GdP 0.4 m	SDSS $z^{\prime}$	295	107
2019/12/28	CROW 0.35 m	SDSS $g^{\prime}$	249	58
2020/01/14	FLWO 1.2 m	B	244	424
2020/04/22	Xinglong 0.8 m	BVRI	246	314
2021/03/23	Xinglong 0.6 m	BVRI	149	182
2021/04/06	Xinglong 0.6 m	BVRI	128	190
2021/04/13	Xinglong 0.8 m	BVRI	144	424
2021/12/02 a	Xinglong 0.8 m	BVRI	75	100
2022/02/21	Xinglong 0.85 m	BVRI	131	720
2022/02/28	Xinglong 0.6 m	BVRI	138	156
2022/03/01 b	Xinglong 0.6 m	BVRI	165	476
				Total images: 3209

Notes.

^a Ignored because of poor photometric quality. ^b Secondary transit.

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Table 4. Ground-based Photometric Follow-up Observation of TOI-1251 B

Date	Telescope	Band	Duration	Number of Images
			(minutes)
2019/10/12	AUKR 0.8 m	R	315	1267
2019/10/18	TCS 1.52 m	SDSS $g^{\prime} r^{\prime} i^{\prime} z^{\prime}$	77.2	3060
2020/04/02	Xinglong 0.6 m	BVRI	257	807
2020/08/17	AUKR 0.8 m	SDSS $g^{\prime}$, $z^{\prime}$	363	706
2021/08/28	Xinglong 0.85 m	BVRI	243	845
				Total images: 6685

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3.2.2. Canela's Robotic Observatory (CROW)

We conducted an observation of TOI-1194 b on 2019 December 28th in the SDSS $g^{\prime}$ band using the CROW 0.35 m telescope located in Portugal. The telescope is equipped with an ST-10XME camera and a pixel scale of 066. The exposure time of each image is 180 s and the S/N value of the target star is greater than 850 pixel⁻¹. We obtained 58 data points throughout the entire transit, which yielded photometric data analyzed using AstroImageJ (Collins et al. 2017) with rms = 0.001 mag precision.

3.2.3. Grand-Pra Observatory (GdP)

Our observation of TOI-1194 b on 2019 December 5th was conducted in the SDSS $z^{\prime}$ band using the RCO 0.4 m telescope located at the GdP in Switzerland. The telescope features an FLI4710 camera with a pixel scale of 073. The exposure time is 150 s and S/N value of the target star is greater than 540 pixel⁻¹. We acquired 107 data points throughout the entire transit, enabling successful photometric analysis using AstroImageJ (Collins et al. 2017) with rms = 0.002 mag precision.

3.2.4. Fred Lawrence Whipple Observatory (FLWO)

On 2020 January 14th, we observed TOI-1194 b in the B band using the KeplerCam instrument mounted on the FLWO 1.2 m telescope, located at Mt. Hopkins in Arizona, USA. KeplerCam is a wide-field CCD camera constructed to provide multiband follow-up photometry for the Kepler Input Catalog (KIC), with a pixel scale of 067; the four output amplifiers are read out in unison at 200 kHz; the total readout time and instrument overhead are 11 s when binned 2 × 2 (Szentgyorgyi et al. 2005). The exposure time is 15 s and S/N value of the target star is greater than 300 pixel⁻¹. We acquired 424 data points throughout the entire transit, which enabled us to conduct successful photometric analysis using AstroImageJ (Collins et al. 2017) with rms = 0.002 mag precision.

3.2.5. Peter Van De Kamp Observatory (PvdK)

We observed TOI-1194 b on 2019 October 5th, in the SDSS $i^{\prime}$ band by using the PvdK telescope, an f/7.8 Ritchey–Chrétien telescope located in Pennsylvania, USA, with an aperture of 0.6 m. The telescope employed an Apogee U16M camera, and the pixel scale is 076 with 2 × 2 binning (Beatty et al. 2012). The exposure time was 98 s and S/N value of the target star was greater than 350 pixel⁻¹. The observation spanned the entire transit and yielded 58 data points, which were processed using AstroImageJ (Collins et al. 2017) with rms = 0.002 mag precision.

3.2.6. Ankara University Kreiken Observatory (AUKR)

We observed TOI-1251 B using the 0.8 m Prof. Dr. Berahitdin Albayrak Telescope (hereafter T80 Telescope) on 2019 October 12th and on 2020 August 17th from the AUKR Observatory in Turkey; both observations encompassed the entire transit. The T80 Telescope is equipped with an Apogee Alta U47 camera, and the pixel scale is 08. The filter used on 2019 October 12th was R band, and the exposure time was 12 s so that the S/N value of the target star is greater than 200 pixel⁻¹. The observation on 2020 August 17th utilized SDSS $g^{\prime}$ and $z^{\prime}$ bands, and the exposure time in $g^{\prime}$ is 10 s so that the S/N value of the target star is greater than 100 pixel⁻¹ and the exposure time in $z^{\prime}$ is 30 s so that the S/N value of the target star is greater than 250 pixel⁻¹. The images were analyzed using AstroImageJ (Collins et al. 2017) with rms = 0.004 mag precision in each band.

3.2.7. Teide Observatory (OT)

We observed TOI-1251 B on 2019 October 18th in the SDSS $g^{\prime} r^{\prime} i^{\prime} z^{\prime}$ bands using the MuSCAT2 camera mounted on the 1.52 m Telescopio Carlos Sánchez (TCS) telescope located at the OT in Tenerife, Spain. The primary mirror is fixed in an equatorial structure with a Cassegrain focus and focal length of f/13.8 in a Dall–Kirkham type configuration. MuSCAT2 has a capability of 4-color simultaneous imaging in SDSS $g^{\prime} r^{\prime} i^{\prime} z^{\prime}$, with a pixel scale of 044 (Narita et al. 2019). The exposure time is 3 s in each band so that the S/N value is greater than 300 pixel⁻¹. Our observation covers full transit and yielded 765 points in each band, which were analyzed using AstroImageJ (Collins et al. 2017) with the best rms = 0.004 mag precision.

3.3. Ground-based Follow-up Spectroscopic Observation

4.1. Data Reduction Pipeline: QLCP

4.2. Creation of Light Curves

4.3. Planet Transit Model Fitting

We performed data fitting of transit data using the EXOFASTv2 online service, supported by the NASA Exoplanet Science Institute (Eastman et al. 2013; Eastman 2017). In order to efficiently identify potential planets from a vast amount of observed TOI transit data, we initially visually detected distinguishable transits after generating light curves and prioritized multiband light curve fitting for these targets. However, for TOIs with transit depths below the photometry accuracy threshold, their transits necessitate phase folding in an attempt to uncover the transit signal. Following data reduction and flux normalization, we input each band transit photometric data and prior distribution of parameters (see Table 5) into EXOFASTv2, which employs Markov chain Monte Carlo (MCMC) analysis to perform model fitting and parameter analysis of both the host star and planet. The convergence criteria for MCMC independent sampling here are described in Eastman et al. (2013).

Table 5. The Prior Distribution of Transit-only Fit

Parameter	Description(Unit)	TOI-1194	TOI-1251
[Fe/H]	Metallicity (dex) a	${ \mathcal N }$(0.28, 0.05)	${ \mathcal N }$(−0.24, 0.05)
Teff	Effective temperature (K) a	${ \mathcal N }$(5553.93, 140)	${ \mathcal N }$(6038.91, 140.00)
log(g)	Surface gravity (cgs) a	${ \mathcal N }$(4.5, 0.1)	${ \mathcal N }$(4.2, 0.1)
Tc	Time of conjunction (BJDTDB) b	${ \mathcal N }$(2459632.287997, 0.0001554)	${ \mathcal N }$(2459759.178675, 0.0001791)
Rp /R*	Ratio of Planet to Stellar Radius	${ \mathcal N }$(0.1, 0.05)	${ \mathcal N }$(0.006, 0.003)
i	Inclination (degree)	${ \mathcal N }$(90, 20)	${ \mathcal N }$(90, 20)
P	Planetary orbital period (days) b	${ \mathcal N }$(2.3106444, 0.0000007)	${ \mathcal N }$(5.9630544, 0.0000015)

Notes.

^a Starhorse (Anders et al. 2019, 2022). ^b ExoFOP-TESS, https://exofop.ipac.caltech.edu/tess/.

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5.1. Multiband Light Curve Fitting

Comparative analysis of multiband light curves is the core of planet identification in this work. Prior to this work, detailed stellar parameters were lacking for both the host stars of TOI-1194 b and TOI-1251 B, and were therefore supplemented based on the analysis of transit photometric data and high-resolution spectra. The best-fit models for the two targets were obtained by reducing and analyzing TOI-1194 observation data obtained on 2022 February 21st and TOI-1251 observation data obtained on 2021 August 28th. Remaining observation data were fitted using these best-fit models (see Figures 2 and 3). The transit depth (δ) and limb-darkening coefficients (u₁, u₂) obtained by fitting the transit light curve of each band are shown in Table 6. Both candidates are achromatic in the measurement accuracy of better than 1%.

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Table 6. Fitted Transit Depth and Limb-darkening Coefficient of Each Band

Parameter	Description (Unit)	TOI-1194	TOI-1251
Transit Depth
δB	Transit depth of Johnson-Cousins B band (ppm)	${6684}_{-79}^{+80}$	${9975}_{-356}^{+358}$
δV	Transit depth of Johnson-Cousins V band (ppm)	${6694}_{-81}^{+82}$	${9759}_{-349}^{+349}$
δR	Transit depth of Johnson-Cousins R band (ppm)	${6700}_{-80}^{+81}$	${10370}_{-293}^{+291}$
δI	Transit depth of Johnson-Cousins I band (ppm)	${6701}_{-79}^{+78}$	${9620}_{-351}^{+354}$
${\delta }_{{g}^{{\prime} }}$	Transit depth of SDSS $g^{\prime}$ band (ppm)	${6691}_{-79}^{+80}$	${10178}_{-328}^{+321}$
${\delta }_{{r}^{{\prime} }}$	Transit depth of SDSS $r^{\prime}$ band (ppm)	...	${10017}_{-356}^{+370}$
${\delta }_{{i}^{{\prime} }}$	Transit depth of SDSS $i^{\prime}$ band (ppm)	${6693}_{-79}^{+82}$	${9804}_{-388}^{+395}$
${\delta }_{{z}^{{\prime} }}$	Transit depth of SDSS $z^{\prime}$ band (ppm)	6690 ± 80	${10748}_{-304}^{+306}$
Limb-darkening Coefficient
u1(B)	Linear limb-darkening coeff of Johnson-Cousins B band	0.781 ± 0.051	${0.667}_{-0.051}^{+0.050}$
u2(B)	Quadratic limb-darkening coeff of Johnson-Cousins B band	0.061 ± 0.050	0.158 ± 0.050
u1(V)	Linear limb-darkening coeff of Johnson-Cousins V band	${0.563}_{-0.052}^{+0.051}$	0.459 ± 0.051
u2(V)	Quadratic limb-darkening coeff of Johnson-Cousins V band	0.192 ± 0.050	${0.256}_{-0.049}^{+0.050}$
u1(R)	Linear limb-darkening coeff of Johnson-Cousins R band	${0.450}_{-0.052}^{+0.050}$	${0.370}_{-0.049}^{+0.051}$
u2(R)	Quadratic limb-darkening coeff of Johnson-Cousins R band	${0.231}_{-0.049}^{+0.051}$	${0.282}_{-0.050}^{+0.048}$
u1(I)	Linear limb-darkening coeff of Johnson-Cousins I band	${0.349}_{-0.050}^{+0.051}$	${0.278}_{-0.050}^{+0.049}$
u2(I)	Quadratic limb-darkening coeff of Johnson-Cousins I band	${0.247}_{-0.049}^{+0.050}$	${0.268}_{-0.049}^{+0.051}$
u1($g^{\prime}$)	Linear limb-darkening coeff of SDSS $g^{\prime}$ band	0.696 ± 0.051	0.585 ± 0.051
u2($g^{\prime}$)	Quadratic limb-darkening coeff of SDSS $g^{\prime}$ band	0.119 ± 0.051	0.221 ± 0.050
u1($r^{\prime}$)	Linear limb-darkening coeff of SDSS $r^{\prime}$ band	...	${0.386}_{-0.051}^{+0.049}$
u2($r^{\prime}$)	Quadratic limb-darkening coeff of SDSS $r^{\prime}$ band	...	${0.277}_{-0.050}^{+0.051}$
u1($i^{\prime}$)	Linear limb-darkening coeff of SDSS $i^{\prime}$ band	0.377 ± 0.050	0.316 ± 0.050
u2($i^{\prime}$)	Quadratic limb-darkening coeff of SDSS $i^{\prime}$ band	0.246 ± 0.050	${0.282}_{-0.051}^{+0.050}$
u1($z^{\prime}$)	Linear limb-darkening coeff of SDSS $z^{\prime}$ band	0.304 ± 0.050	${0.273}_{-0.051}^{+0.050}$
u2($z^{\prime}$)	Quadratic limb-darkening coeff of SDSS $z^{\prime}$ band	0.254 ± 0.050	${0.291}_{-0.050}^{+0.049}$

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5.2. Radial Velocity Fitting

Determining the mass of the companions enables direct confirmation of their planetary status. To accomplish this, we reduced the high-resolution spectra of TOI-1194 and TOI-1251 captured by the TRES, FIES and HRS instruments, calculated their RVs and derived their phase-RV variation curves, before analyzing their orbital solutions. Reduction and multi-order spectrum analysis from TRES and FIES were conducted using the method described in Buchhave et al. (2010). We utilized the Stellar Parameters Classification (SPC) tool to estimate the stellar parameters. The SPC tool relies on synthetic grid library spectra and simultaneously derives the effective temperature, surface gravity, metallicity and rotational velocity by matching the models with the observed spectra originating from different instruments (Buchhave et al. 2012, 2014). (The reference stellar atmospheric models are from Kurucz (1992).) High-resolution RV data obtained from follow-up observations by HRS were reduced using GAMSE ²² for one-dimensional spectral extraction from double-fiber high-resolution spectra. We employed IRAF to fit nine lines in Order93 and Order98 for calculating RV in 600–700 nm (Tody 1986). We utilized barycorrpy (Kanodia & Wright 2018) to calculate the barycentric RV correction. Three points of HRS RV data obtained on 2021 November 22nd were disregarded, due to poor S/Ns and insufficient identifiable lines. To enable fitting of all RV points collected from the three instruments, we shifted the systemic velocity (γ) of each instrument to 0 m s⁻¹. Table 7 shows RV data of TOI-1194 b, while Table 8 displays RV data of TOI-1251 B, within best models obtained when the χ²/dof value is lowest.

Table 7. Ground-based Follow-up Radial Velocities for TOI-1194 b

BJDTDB	RV	eRV	Instrument
	(m s−1)	(m s−1)
2458829.952974	129.80	20.77	FLWO 1.5 m TRES
2458830.979613	−47.76	22.29	FLWO 1.5 m TRES
2459980.881301	30.22	20.77	FLWO 1.5 m TRES
2459981.855344	−38.24	25.88	FLWO 1.5 m TRES
2459982.837025	46.81	23.01	FLWO 1.5 m TRES
2459983.853953	−91.88	19.20	FLWO 1.5 m TRES
2459984.855371	60.96	17.91	FLWO 1.5 m TRES
2459985.938541	−0.69	16.18	FLWO 1.5 m TRES
2459987.909966	−3.17	17.74	FLWO 1.5 m TRES
2459991.837408	40.57	21.77	FLWO 1.5 m TRES
2460000.815599	−43.86	21.72	FLWO 1.5 m TRES
2460001.824999	32.74	24.48	FLWO 1.5 m TRES

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Table 8. Ground-based Follow-up Radial Velocities for TOI-1251 B

BJDTDB	RV	eRV	Instrument
	(m s−1)	(m s−1)
2458776.68854	−10363.24	67.18	FLWO 1.5 m TRES
2458779.66325	10356.45	67.18	FLWO 1.5 m TRES
2459026.64331	−7527.15	67.48	NOT 2.56 m FIES
2459036.54954	9326.95	91.73	NOT 2.56 m FIES
2459038.61436	−8007.87	53.32	NOT 2.56 m FIES
2459093.47847	−8041.56	108.67	NOT 2.56 m FIES
2459093.50021	−7818.58	79.84	NOT 2.56 m FIES
2459095.45703	9096.31	56.86	NOT 2.56 m FIES
2459105.47225	−7720.50	72.90	NOT 2.56 m FIES
2459119.42068	9566.68	62.45	NOT 2.56 m FIES
2459123.37912	−7229.17	83.26	NOT 2.56 m FIES
2459124.38530	2216.98	98.45	NOT 2.56 m FIES
2459132.39111	6631.18	52.06	NOT 2.56 m FIES
2459134.34215	−9398.61	50.26	NOT 2.56 m FIES
2459539.93873	−9629.71	107.67	Xinglong 2.16 m HRS
2459539.96100	−9357.86	107.67	Xinglong 2.16 m HRS
2459631.39846	3962.04	126.91	Xinglong 2.16 m HRS
2459631.42052	3814.53	126.91	Xinglong 2.16 m HRS
2459639.38316	4519.53	116.19	Xinglong 2.16 m HRS
2459639.39846	4748.09	116.19	Xinglong 2.16 m HRS
2459754.20779	−7892.08	135.92	Xinglong 2.16 m HRS
2459754.22996	−7582.42	135.92	Xinglong 2.16 m HRS
2459890.93302	−6189.59	158.63	Xinglong 2.16 m HRS
2459890.95543	−5610.81	158.63	Xinglong 2.16 m HRS
2459890.97752	−6190.05	158.63	Xinglong 2.16 m HRS
2459890.99957	−6025.26	158.63	Xinglong 2.16 m HRS

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We utilized both EXOFASTv2 and Exo-Striker (Trifonov 2019) to fit RV points for two TOIs, with best-fitted models visualized in Figures 4 and 5. The calculated RV amplitude for TOI-1194 b is K = ${69.4}_{-7.3}^{+7.9}$ m s⁻¹, with a derived minimum mass of M_p sin i = ${0.453}_{-0.051}^{+0.055}\,{M}_{{\rm{J}}}$, which appears close to Saturn in terms of mass and orbits its host star on a nearly circular orbit.

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The RV amplitude of TOI-1251 is notably distinctly different from that of TOI-1194, due to the former being a very low-mass star. We calculate the RV amplitude caused by TOI-1251 B to be K = ${9849}_{-40}^{+42}$ m s⁻¹, with a minimum mass of M₂sin i = 96.3 ± 1.5 M_J. The fitted RV curve suggests that TOI-1251 B orbits its host star on a nearly circular orbit, consistent with parameters obtained in fitted light curves.

5.3. Joint Analysis

The parameters of TOI-1194 b and TOI-1251 B were derived through a joint analysis of all available ground-based photometric and spectroscopic data. We employed Exo-Striker to conduct the joint MCMC analysis (Foreman-Mackey et al. 2013), initializing 20 walkers and generating 2000 steps for the burn-in phase, and a further 10,000 steps to sample the posterior parameter distribution of stellar and planetary parameters from the MCMC process.

In addition to the transit epoch (T_c ) and period (P) in Table 5, the prior parameters used also include metallicity ([Fe/H]), surface gravity (log g) and effective temperature (T_eff), which were obtained by fitting stellar spectra (Section 5.2). Since planets appear to be in nearly circular orbits based on the RV curve fitting, we assigned a Gaussian distribution ${ \mathcal N }$(0, 0.1) as a prior.

The process ultimately converged to the maximum likelihood estimate. The joint analysis results, presented at the 1σ confidence interval in Tables 9 and 10, indicate that the mass of TOI-1194 b is ${0.456}_{-0.051}^{+0.055}\,{M}_{{\rm{J}}}$, while the mass of TOI-1251 B is 96.5 ± 1.5 M_J.

Table 9. TOI-1194 Host Stellar and Planetary Parameters at 68% Confidence Intervals

Parameter	Description (Units)	Value
Host Stellar Parameters
R.A.	R.A. coordinate (J2000.0) a	11h11m1691
Decl.	Decl. coordinate (J2000.0) a	+69d57m5294
B [mag]	Johnson-Cousins B band magnitude b	11.833 ± 0.081
V [mag]	Johnson-Cousins V band magnitude c	11.185 ± 0.042
G [mag]	Gaia G band magnitude d	10.9887 ± 0.0004
I [mag]	Johnson-Cousins I band magnitude c	10.289 ± 0.020
M*	Mass (M⊙)	${1.007}_{-0.048}^{+0.050}$
R*	Radius (R⊙)	${0.963}_{-0.051}^{+0.056}$
L*	Luminosity (L⊙)	${0.732}_{-0.081}^{+0.095}$
ρ*	Density (cgs)	${1.59}_{-0.22}^{+0.26}$
$\mathrm{log}g$	Surface gravity (cgs)	${4.473}_{-0.042}^{+0.043}$
TTIC	Effective Temperature from TIC (K) e	${5323.0}_{-156.1}^{+92.9}$
TGaia	Effective Temperature from Gaia (K) d	${5339.90}_{-116.23}^{+207.10}$
Teff	Best fitting Effective Temperature (K)	${5446}_{-48}^{+51}$
[Fe/H]	Metallicity (dex)	0.290 ± 0.078
vsini	Minimum rotational velocity (km s−1)	2.4 ± 0.5
ϖ	Parallax (mas) a	6.6527 ± 0.0126
d	Distance (kpc) a	${0.148508}_{-0.003278}^{+0.003023}$
Planetary Companion Parameters		TOI-1194 b
P	Period (days)	2.310644 ± 0.000001
RP	Radius (RJ)	${0.767}_{-0.041}^{+0.045}$
MP	Mass (MJ)	${0.456}_{-0.051}^{+0.055}$
ρP	Density (cgs)	${1.25}_{-0.21}^{+0.26}$
$\mathrm{log}({g}_{{}_{P}})$	Surface gravity	3.281 ± 0.064
MP /M*	Mass ratio	${0.000432}_{-0.000046}^{+0.000050}$
RP /R*	Radius of planet in stellar radii	0.08196 ± 0.00047
a/R*	Semi-Major Axis in stellar radii	${7.65}_{-0.37}^{+0.39}$
δ	Transit depth (fraction)	0.006717 ± 0.000078
K	RV Semi-Amplitude (m s−1)	${69.4}_{-7.3}^{+7.9}$
T0	Time of conjunction (BJDTDB)	2459632.28801 ± 0.00015
a	Semimajor axis (au)	0.03428 ± 0.00055
i	Inclination (Degrees)	83.98 ± 0.50
b	Transit Impact parameter	${0.802}_{-0.027}^{+0.025}$
e	Eccentricity	${0.076}_{-0.043}^{+0.032}$
ω	Argument of Periastron (Degree)	${76.7}_{-39.5}^{+49.7}$
T14	Total transit duration (hours)	${1.684}_{-0.058}^{+0.063}$
Teq	Equilibrium temperature (K)	${1391}_{-37}^{+38}$
${\chi }_{\mathrm{RV}}^{2}$	RV fitting χ2 value	3.89
rmsRV	RV fitting rms value (m s−1)	31.8

Notes.

^a Gaia DR3. ^b All-sky compiled catalog of 2.5 million stars (ASCC-2.5 V3) (Kharchenko 2001). ^c TASS Mark IV Photometric Survey of the Northern Sky (Droege et al. 2006). ^d Gaia DR2 (Gaia Collaboration 2018). ^e TIC v8.2 (Paegert et al. 2021).

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Table 10. TOI-1251 Host and Companion Stellar Parameters at 68% Confidence Intervals

Parameter	Description (Units)	Value
Host Stellar Parameters
R.A.	R.A. coordinate (J2000.0) a	18h14m0707
Decl.	Decl. coordinate (J2000.0) a	+62d51m2971
B [mag]	Johnson-Cousins B band magnitude b	12.020 ± 0.127
V [mag]	Johnson-Cousins V band magnitude c	11.318 ± 0.037
G [mag]	Gaia G band magnitude d	11.0942 ± 0.0010
I [mag]	Johnson-Cousins I band magnitude c	10.505 ± 0.021
M*	Mass (M⊙)	${1.057}_{-0.049}^{+0.050}$
R*	Radius (R⊙)	${0.986}_{-0.024}^{+0.025}$
L*	Luminosity (L⊙)	${0.968}_{-0.062}^{+0.066}$
ρ*	Density (cgs)	${1.553}_{-0.059}^{+0.061}$
$\mathrm{log}g$	Surface gravity (cgs)	${4.4737}_{-0.0093}^{+0.0096}$
TGaia	Effective Temperature from Gaia (K) d	${5759.71}_{-209.53}^{+163.69}$
Teff	Best fitting Effective Temperature (K)	${5769}_{-50}^{+49}$
[Fe/H]	Metallicity (dex)	0.019 ± 0.080
vsini	Minimum rotational velocity (km s−1)	9.2 ± 0.5
ϖ	Parallax (mas) a	3.6550 ± 0.3382
d	Distance (kpc) a	${0.246147}_{-0.011126}^{+0.010750}$
Companion Stellar Parameters		TOI-1251 B
P	Period (days)	5.963054 ± 0.000001
R2	Radius (RJ)	${0.947}_{-0.035}^{+0.037}$
M2	Mass (MJ)	${96.47}_{-1.47}^{+1.50}$
ρ2	Density (cgs)	${141}_{-12}^{+13}$
$\mathrm{log}({g}_{2})$	Surface gravity	${5.425}_{-0.025}^{+0.024}$
M2/M*	Mass ratio	${0.0876}_{-0.0008}^{+0.0007}$
R2/R*	Radius of planet in stellar radii	0.0987 ± 0.0022
a/R*	Semi-Major Axis in stellar radii	14.69 ± 0.19
δ	Transit depth (fraction)	${0.00975}_{-0.00042}^{+0.00043}$
K	RV Semi-Amplitude (m s−1)	${9849}_{-40}^{+42}$
T0	Time of conjunction (BJDTDB)	${2459759.17874}_{-0.00018}^{+0.00017}$
a	Semimajor axis (au)	0.0674 ± 0.0010
i	Inclination (Degrees)	${92.3}_{-0.11}^{+0.08}$
b	Transit Impact parameter	${0.469}_{-0.030}^{+0.027}$
e	Eccentricity	${0.028}_{-0.001}^{+0.002}$
ω	Argument of Periastron (Degree)	${341}_{-5}^{+6}$
T14	Total transit duration (hours)	${3.086}_{-0.040}^{+0.041}$
${\chi }_{\mathrm{RV}}^{2}$	RV fitting χ2 value	3.37
rmsRV	RV fitting rms value (m s−1)	390.7

Notes.

^a Gaia DR3. ^b All-sky compiled catalog of 2.5 million stars (ASCC-2.5 V3) (Kharchenko 2001). ^c TASS Mark IV Photometric Survey of the Northern Sky (Droege et al. 2006). ^d Gaia DR2 (Gaia Collaboration 2018).

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5.4. Potential Contamination

Apart from the EBs mentioned in Section 1, the eclipses of nearby EBs are usually responsible for the high FP probability in exoplanet surveys as well. Approximately half of all discovered planets orbit stars with stellar companions (Howell et al. 2021; Lester et al. 2021a). However, follow-up photometric data and Gaia DR3 catalogs alone are not sufficient to distinguish such companions in regions between 10 and 100 au around the host stars. High-resolution imaging data have the potential to exclude some companions around the host stars (Lester et al. 2021b). The resolution of ground-based optical telescopes without adaptive optics depends on the atmosphere seeing conditions. At Xinglong Observatory, the median seeing value is around 17 (Zhang et al. 2015), incapable of ruling out stellar contaminations from stars present in this sky region via aperture photometry alone. We used the 'Alopeke instrument on the Gemini North 8 m telescope to observe TOI-1194 on 2020 February 17th and obtained high-resolution speckle images in the 562 and 716 nm bands to search for nearby stellar companions (see Figure 6). The data were reduced using the standard speckle interferometry pipeline as described in Howell et al. (2011). From the 5σ contrast curves shown in Figure. 6, we found that within the angular and magnitude limits achieved, there is no close companion star within 5–7 mag and between 002 (the diffraction limit of the device) and 1''. These angular limits correspond to 2.96–148 au around TOI-1194, which is located 148 pc away.

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The 562 and 832 nm speckle images of TOI-1251 from the WIYN telescope revealed the presence of a star located 022 away from the host star (equivalent to a projected separation of about 41 au), with Δmag = 1.66 in the 562 nm band and Δmag = 1.36 in the 832 nm band (Howell et al. 2021). However, from follow-up photometric and spectroscopic RV data, we discerned the existence of only one stellar companion, which orbits the host star in a nearly circular orbit with a semimajor axis of a = 0.0674 ± 0.0010 au. While the angular separation between the companion and the host star observed from the Earth's perspective is 00002, high-resolution imaging cannot currently observe it. This in turn indicates that the star located within 41 au of the host star is not dynamically associated with it.

In our efforts to follow-up on TOIs, we organized a Sino-German campaign group that collected multiple transit photometric data observed in multiband to validate them as planets. The first three years of observation and current data analysis demonstrate that the one meter-class telescopes in our campaign can provide valuable transit and RV data for the identification and planetary property analysis of TESS candidates. Through processing and fitting of these data, we confirmed the presence of a planet, TOI-1194 b, and a very low-mass star, TOI-1251 B, each orbiting G-type hosts. Identifying a planet using only single-band photometric observations collected over a long time baseline is quite difficult due to differences in transit depth across multiband light curves displayed by EBs. In addition to improving observational accuracy and increasing transit data availability, multiband simultaneous photometric observation data are also helpful for the rapid elimination of FP caused by EBs. Moreover, one meter-class telescopes are more accessible and offer cheaper observational resources compared to spectral observation equipment. The ability to conduct multiband photometric observation of exoplanets through a multi-site campaign can also enable faster response times and feedback on follow-up observation results for candidates detected through space-based observations like TESS, enhancing the efficiency and accuracy of exoplanet confirmation.

TOI-1194 b has a density of ρ = ${1.25}_{-0.21}^{+0.26}\,{\rm{g}}\,{\mathrm{cm}}^{-3}$, suggesting that this hot Saturn is comparable in density to Jupiter and is located in the Neptune desert described in Mazeh et al. (2016) (see Figure 7). Figure 8 illustrates the mass–radius diagram of confirmed hot Jupiters with mass under 2 M_J, with TOI-1194 falling into a relatively dense and sparsely populated region (Espinoza et al. 2017). As statistics on ultra-short period planet (USP) samples and the evolution model of hot gas giant planets, it is hypothesized that planets with this nature, exposed to strong ultraviolet and thermal radiation from their host stars, may experience expansion and gradual loss of their outer envelope over time (Owen & Wu 2013). The radial expansion of the planet also increases with enhanced radiation from the host star, and this radiation-induced inflation mechanism is evident at T_eq ≥ 1000 K (Demory & Seager 2011). The T_eq of TOI-1194 b is ∼1400 K, but the radius does not show a significant expansion effect, so it is relatively dense. The higher density of TOI-1194 b may be attributed to its higher proportion of heavy elements (Miller & Fortney 2011), and the relationship between planet and metal-rich host star may be reasonably explained by protoplanetary disk evolution theories.

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TOI-1251 B is an M-dwarf and is located remarkably close to its host star, with an extremely low mass ratio q = M₂/M^* = 0.088, but positioned outside the Roche limit (0.00025 au). M dwarfs are widely distributed in the universe. Due to the smaller radius and mass of M dwarfs, the transit depth and RV variation caused by smaller planets (such as Neptune and Earth-like planets) are more pronounced than those around Sun-like stars (Tuomi et al. 2019), and these small planets are more likely to be detected by one meter-class telescope, so they have attracted much attention in recent years. The statistical results demonstrate a significantly high occurrence rate of low-mass planets around M dwarfs, with a correspondingly high likelihood of super-Earths (3–10M_⊕) existing within their habitable zones (Tuomi et al. 2014; Dressing & Charbonneau 2015). Although most M-dwarfs identified in EB systems exhibit mass similar to that of another star in the system, there are fewer than 100 M-dwarfs orbiting F/G/K-type stars known with an extremely low mass ratio (q ≤ 0.15) (Grieves et al. 2021). Due to the limited sample, the origin and evolution of these EBs lack a systematic explanation. TOI-1251 B expands the sample as a new eclipsing binary with low-mass (EBLM), with the period obtained from this work being consistent with that provided within the Gaia DR3 non-single stars catalog. This consistency indicates that it is a single-lined spectroscopic binary (SB) (Gaia Collaboration 2022). Direct observations of very low mass stars are challenging due to their low surface luminosity compared to massive stars. Nonetheless, the methods employed in exoplanet follow-up observation are well-suited to the observation of these types of stars. Therefore, identifying new EBLMs in TOI candidates using follow-up photometric and spectroscopic observations may become easier.

We thank Dr. David W. Latham and the TRES team for providing the TRES results and helpful suggestions that improved the manuscript. This work is supported by National Natural Science Foundation of China (NSFC, Grant Nos. U1831209 and U2031144) and the research fund of Ankara University (BAP) through the project 18A0759001. This paper refers to some data which are publicly available from the Mikulski Archive for Space Telescopes (MAST), collected by the TESS mission. The TESS mission is funded by NASA's Science Mission directorate. We acknowledge the TESS Follow-up Observing Program (TFOP) SG1, SG2, SG3 and SG4 for the disposition of candidates, and the use of public TOI Release data from pipelines at the TESS Science Office (TSO) and at the TESS Science Processing Operations Center. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products. This research has made use of data obtained from the portal exoplanet.eu of The Extrasolar Planets Encyclopaedia. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.

This article is partly based on observations made with the FLWO/TRES, NOT/FIES and MuSCAT2. We acknowledge the support of the staff of the Xinglong 60 cm, 80 cm, 85 cm and 2.16 m telescopes. This work was partially supported by the Open Project Program of the CAS Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences. We acknowledge the support of the staff of Qingdao Aishan Observatory, Nanshan Observatory, Weihai Observatory, Skyline Observatory, Muztaga Observatory, Lijiang Gemini Observatory and Xingming Observatory. Some of the observations in this paper made use of the High-Resolution Imaging instrument 'Alopeke and were obtained under Gemini LLP Proposal Number: GN/S-2021A-LP-105. 'Alopeke was funded by the NASA Exoplanet Exploration Program and built at the NASA Ames Research Center by Steve B. Howell, Nic Scott, Elliott P. Horch, and Emmett Quigley. 'Alopeke was mounted on the Gemini North telescope of the international Gemini Observatory, a program of NSF's OIR Lab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation, on behalf of the Gemini partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovções e Comunicações (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea).

This work made use of Astropy ²³ : a community-developed core Python package and an ecosystem of tools and resources for astronomy (Astropy Collaboration et al. 2013, 2018, 2022). This work made use of Matplotlib (Hunter 2007), Numpy (van der Walt et al. 2011), PyEphem and PyTransit (Parviainen 2015). This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

This paper makes use of EXOFAST (Eastman et al. 2013) as provided by the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.