Further Evidence Found by TESS Is Confirming the Orbital Decay of Kepler-1568b

Research Article
Open access

Further Evidence Found by TESS Is Confirming the Orbital Decay of Kepler-1568b

Shi Qiu 1*
  • 1 Guanghua Academy, Shanghai, 201319, China    
  • *corresponding author david_s_que@163.com
TNS Vol.108
ISSN (Print): 2753-8826
ISSN (Online): 2753-8818
ISBN (Print): 978-1-80590-089-4
ISBN (Online): 978-1-80590-090-0

Abstract

The orbital decay of Kepler-1658b remains a mystery to this day. Many previous authors have searched for this hot Jupiter using ground-based telescopes, with no secure results. Here, I present a search for Kepler-1658b with the data from NASA's Transiting Exoplanet Survey Satellite (TESS). By using the most recent TESS data, I have extended the time baseline of previous observations and was able to perform a more sensitive search. I evaluated the latest data and found further evidence to confirm the shrinking orbit of Kepler-1658b and predict the inspiral time of the system.

Keywords:

exoplanets, Kepler 1658, TESS, transits, precise photometry

Qiu,S. (2025). Further Evidence Found by TESS Is Confirming the Orbital Decay of Kepler-1568b. Theoretical and Natural Science,108,57-62.
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1. Introduction

Kepler-1658 was the first planet candidate revealed by the Kepler mission, as KOI-1.01, KOI-2.01, and KOI-3.01 were known before launch [1]. Astronomers have been seeking evidence for the orbital decay Involving Kepler-1658 since at least the work of Vissapragada et al [2]. The authors showed that the orbit of Kepler-1598b should be shrinking constantly like WASP-12b [3] according to the analysis of the previous data from Kepler, WIRC, and TESS. Kepler-1658b is a hot Jupiter with an F-type host star [4]. Compared to some other systems, the data of Kepler-1658 is relatively unstable since its star is faint. As a result, we cannot guarantee the completeness of the study by Vissapragada et al. [2]. Recently, since more data detected by TESS came out, astronomers have further evidence to determine the future trend of changes in its orbit. Because the essay is a further evidence for proving the orbital decay, the introduction is relatively brief. For further introduction, please refer to Vissapragada et al [2].

2. Observations

2.1. Kepler

There are 12 quarters at a 30-minute cadence and three quarters at a 1-minute cadence observed by Kepler spacecraft. This is also a set of data that astronomers have previously studied, and it is mentioned again to be reused and combined with the latest data to find the result. By using lightkurve package [4], I downloaded the Kepler light curve and modeled the data sets by utilizing exoplanet package.

2.2. TESS

Although TESS data is not as high-quality as Kepler data, its database is relatively large. By doing so, errors can be reduced to a certain extent. All the data available is in Table 2.

To be more specific, there is an example from TESS Sector 41 with an orbit number from 1147 to 1153. In Figure 1, the transiting curves look relatively obvious. However, it is easy to notice that there is a breaking point in the middle of the whole curve. As a result, that data set cannot be useful for us to determine the transiting time, as shown in Figure 2.

3. Methods

Compared to Kepler's data, the individual data of TESS fluctuates significantly, but it still has reference value. By unifying the units of the two types of data and combining them with a plot and a residual plot, I found that the most suitable one for them is not linear regression, but quadratic regression. From Figure 1, we can easily see that on the left half of the figure (more precise data from Kepler), the residual plot shows an apparent pattern but not a random distribution. As a result, The data does not best fit with the linear regression line. Thus, a quadratic relationship needs to be needs to be considered. From Figure 2, the individuals are about randomly distributed alone x-axis, which means the quadratic regression fits the data sets. By using the Python program, the quadratic coefficient appears to be \( (-7.23598±1.45176)∙{10^{-9}} \) . Because of its negative sign, the orbital decay of Kepler-1658b can be confirmed.

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Figure 1: The overall light curve of Kepler-1658 (the red sign is where the transiting progress occur)

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Figure 2: More specific steps for finding the transiting time interval

Table 1: For the Kepler data sets, LC and SC refer to long cadence (30-minute exposures) and short cadence (1-minute exposures), respectively. the data from the second column is the calculated results, for unifying the unit with TESS

Data Set

Orbit number (calculated result)

Transit Time (BJD)

Kepler LC Quarter 0

-12

2454959.7314

+0.0014

-0.0015

Kepler LC Quarter 1

-6

2454982.82835

-0.00061

-0.00061

Kepler SC Quarter 2

11

2455048.26751

+000021

-0.00022

Kepler LC Quarter 3

35

2455140.65189

+0.00040

-0.00042

Kepler LC Quarter 4

59

2455233.03736

-0.00033

-0.00035

Kepler LC Quarter 5

83

2455325.42133

+0.00035

+0.00035

Kepler SC Quarter 7

131

2455510.19192

-0.00036

+0.00023

Kepler SC Quarter 8

155

2455602.57708

-0.00023

+0.00027

Kepler LC Quarter 9

178

2455691.11211

-0.00027

+.00033

Kepler LC Quarter 11

228

2455883.58121

-0.00031

+0.00032

Kepler LC Quarter 12

252

2455975.96583

-0.00033

-0.00036

Kepler LC Quarter 13

275

2456064.50087

+0.00036

-0.00036

Kepler LC Quarter 14

325

2456256.97026

-0.00037

-0.00035

Kepler LC Quarter 15

349

245634935438

+0.00038

-0.00039

Kepler LC Quarter 17

365

2456410.94385

+0.00065

+0.00064

/word/media/image3.png

Figure 3: This is the residual plot of the quadratic regression, which contains the uncertainties of each individual.

4. Results

4.1. Calculation

In previous research [5], some constants have been measured. The quadratic coefficient:

\( {C_{2}}=(\frac{P}{2})(\frac{dP}{dt})=(-7.23598±1.45176)\cdot {10^{-9}} \) (1)

Calculation for \( \dot{P}: \)

\( \frac{dP}{dt}=\frac{2}{3.84937 days }(-7.23598)\cdot {10^{-9}} days =3.75956\cdot {10^{-9}} \) (2)

Table 2: Outliers have been excluded

Orbit number (calculated result)

Transit Time (Days)

1147

2421.13999794±0.01107531

1148

2424.99813411+0.01252269

1149

2428.83521579+0.0132554

1151

2436.54138026±0.01111421

1152

2440.38408397+0.0112751

1153

2444.23698355+0.010986721

1238

2771.43875172+0.01222068

1239

2775.28636183±0.01134779

1240

2779.14246938±0.01221257

1242

2786.84010272±0.01180961

1243

2790.68282405±0.01203744

1244

2794.54313956±0.01247402

1245

2798.37506708±0.01198935

1246

2802.23733038±0.01202081

1247

2806.07532384+0.01212042

1249

2813.779754+0.01088812

1250

2817.62376733+0.01163627

1251

2821.47937701±0.01305526

1280

3318.05933387±0.01383833

1381

3321.90925122+0.01175709

1382

3325.7359887±0.01081116

1383

3329.59725668+0.0148565

1384

3333.43871939±0.01360349

1385

3337.285021521+0.01104347

1387

3344.99763735±0.01207266

1388

3348.84104345+0.01181232

1389

3352.67621157+0.0113846

1390

3356.53349542±0.01280488

1391

3360.40621754+0.01279

1392

3364.229641847+0.0111142

Unify the unit to msec/yr:

\( (2)=3.75956\cdot {10^{-9}}\cdot π\cdot {10^{7}}\cdot 1000=118.110±23.6966\frac{mec}{yr} \) (3)

Using data from Kepler, Palomar/WIRC, and TESS, we showed that Kepler-1658b's orbit appears to be shrinking at a rate of \( \dot{P}=118.11_{-23.697}^{+23.697}\frac{mec}{yr} \) , coresponding to an inspiral timescale of P/P≈2.8 Myr. The inspiral timescale has increased compared to the previous research Vissapragada et al. [2].

5. Conclusion

Though the evidence so far points to the confirmation of the shrinking orbit of Kepler-1568b, we still cannot completely conclude that result since the database is still not enough. Astronomers may find different results in the future with the latest data. Following are three possible outcomes of Kepler-1658b. For one, it falls into its host star after about 2.8 million years. For another, its orbit will shrinking to a certain value, and then, it will always stay in that orbit. Last, the orbital decay does not appear.

/word/media/image4.png

Figure 4: The yellow line is the linear regression result and each purple point is the individual data


References

[1]. Borucki, W. J., Koch, D. G., Basri, G., et al. 2011, ApJ, 736, 19, doi: 10.1088/0004-637X/736/1/19

[2]. Vissapragada, S., Chontos, A., Greklek-McKeon, M., et al. 2022, The Astrophysical Journal Letters, 941, L31, doi: 10.3847/2041-8213/aca47e

[3]. Yee, S. W., Winn, J. N., Knutson, H. A., et al. 2019, The Astrophysical Journal Letters, 888, L5, doi: 10.3847/2041-8213/ab5c16

[4]. Lightkurve Collaboration, Cardoso, J. V. d. M., Hedges, C., et al. 2018, Lightkurve: Kepler and TESS time series analysis in Python, Astrophysics Source Code Library. http://ascl.net/1812.013

[5]. Chontos, A., Huber, D., Latham, D. W., et al. 2019, AJ, 157, 192, doi: 10.3847/1538-3881/ab0e8e


Cite this article

Qiu,S. (2025). Further Evidence Found by TESS Is Confirming the Orbital Decay of Kepler-1568b. Theoretical and Natural Science,108,57-62.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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About volume

Volume title: Proceedings of the 4th International Conference on Computing Innovation and Applied Physics

ISBN:978-1-80590-089-4(Print) / 978-1-80590-090-0(Online)
Editor:Ömer Burak İSTANBULLU, Marwan Omar, Anil Fernando
Conference website: https://2025.confciap.org/
Conference date: 17 January 2025
Series: Theoretical and Natural Science
Volume number: Vol.108
ISSN:2753-8818(Print) / 2753-8826(Online)

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References

[1]. Borucki, W. J., Koch, D. G., Basri, G., et al. 2011, ApJ, 736, 19, doi: 10.1088/0004-637X/736/1/19

[2]. Vissapragada, S., Chontos, A., Greklek-McKeon, M., et al. 2022, The Astrophysical Journal Letters, 941, L31, doi: 10.3847/2041-8213/aca47e

[3]. Yee, S. W., Winn, J. N., Knutson, H. A., et al. 2019, The Astrophysical Journal Letters, 888, L5, doi: 10.3847/2041-8213/ab5c16

[4]. Lightkurve Collaboration, Cardoso, J. V. d. M., Hedges, C., et al. 2018, Lightkurve: Kepler and TESS time series analysis in Python, Astrophysics Source Code Library. http://ascl.net/1812.013

[5]. Chontos, A., Huber, D., Latham, D. W., et al. 2019, AJ, 157, 192, doi: 10.3847/1538-3881/ab0e8e