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Evangelická Akademie Praha  Praha –    Czech Republic 17 years old, 15 years old   4 / 2

TOI-560c

TOI-560c project description:

This work focuses on the exoplanet TOI-560 c (referred to as a mini-Neptune or super-Earth), one of the two exoplanets orbiting the K-type dwarf star TOI-560, which was observed using the transit method with the CHaracterising ExOPlanets Satellite (CHEOPS) space telescope. The objective of our research was to calculate the fundamental properties of this exoplanet, including its radius, mass, orbital distance, orbital period, density, and average temperature. Based on these findings, the work is aimed to determine whether this exoplanet satisfies the conditions necessary for the existence of life similar to life on Earth. Based on available informations, the existence of life similar to that on Earth on TOI-560 c is considered unlikely.

To calculate the radius of the exoplanet TOI-560 c, the transit method is utilized, which involves observing the planet’s passage in front of its host star. The average radius of the planet in comparison to the radius of the Earth is determined. The mean orbital distance and orbital period were calculated using Kepler’s laws. The density of the exoplanet TOI-560 c was obtained from the volume and mass values based on the estimated radius.

The results indicate that the exoplanet TOI-560 c has a radius approximately 2.37 times bigger than the radius of Earth, a mass approximately 9.7 times that of Earth, a mean orbital distance of about 0.124 AU, and an orbital period of approximately 18.88 days. The estimated density of the exoplanet is approximately 4.004 g/cm3, and the average temperature is estimated to be 225°C.

TOI-560c Results and Analysis

1.    Data analysis
The aim of the analysis is to determine the radius of the exoplanet TOI-560 c, its orbital period, distance from its star, and its density. The methods of calculations are given in the following sections.
3.1. The radius of TOI-560 c
To determine the radius of the planet, it was necessary to know the depth of the transit (i.e., the percentage decrease in the brightness of the star TOI-560 when the planet TOI-560 c was located between the observer and its star). In our calculations, this was estimated to be 0.2%.

Subsequently, the analysis is proceeded with the formula:

(1.1)

R stands for radius; p stands for the exoplanet (TOI-560 c) and s stands for its star (TOI-560).

The following is modification of the formula for calculating the radius:

(1.2)

The known values are substituted into the formula (3.2.):

Calculations of radius follows.

 

 

 

 
(1.3)

Figure 2: Transit light curve of the TOI-560 c [[1]]

Due to the imprecise estimation of the percentage transit depth, however, our result Due to the imprecise estimation of the percentage transit depth, our result turned out slightly higher than it actually was. Referring to the values obtained in the Allesfitter program, we adjusted our result to REarth, and this value is used as the basis for further calculations.

3.2. Orbital period

In the calculation of the orbital period, it was necessary to know the gravitational constant (G) and the mass of the Sun (MS).

We found both values on the Hack an Exoplanet website[[1]]. The values we worked with are as follows:

(1.4)

 

 
(1.5)

From the values obtained from the Allesfitter program, the orbital period of TOI-560 c (18.8797 days) was determined. For further calculations, this value to seconds (1631206.082 s) is converted.

These values were then used in the formula

(1.6)

where d represents the orbital distance.

The work with the formula proceeded as follows:

(1.7)

 

(1.8)

 

(1.9)

Figure 3: The model of the orbit of TOI-560 c around the star TOI-560 (the blue dot in the yellow rectangle represents TOI-560 c) [[1]]

(1.10)

From the calculations, a result of 0.124 AU, which is a shorter distance compared to the Earth’s distance from the Sun (1 AU). The comparison of values related to TOI-560 c with those related to planets in the Solar System will be addressed in a later part of the study. At this point, it is appropriate to mention that based on the orbital period and the distance from the host star, it can be inferred that TOI-560 c is very close to its star and is not located within the habitable zone (Figure 3).
3.3. Temperature
The average temperature on TOI-560 c was determined from the available data obtained by the CHEOPS telescope, as provided on the Hack an Exoplanet website [[2]]. The average temperature on TOI-560 c is approximately 225°C. This significantly surpasses the temperatures of nearly all the planets in the Solar System, with the possible exception of Venus, where the average temperature reaches values around 565°C. The temperature of TOI-560 c is close to the temperature of Mercury, where the average temperature reaches up to 167°C. Such a temperature is inhospitable for life similar to that on Earth, as the average temperature on Earth hovers around 17°C. Additionally, the temperature we have determined for TOI-560 c exceeds the boiling point of water (125°C). One crucial factor is the atmospheric pressure. The boiling point of a substance depends not only on its temperature but also on the pressure exerted on it. On Earth, at sea level, the atmospheric pressure is approximately 1 atmosphere, which allows water to boil at 100°C. On TOI-560 c, however, the atmospheric conditions and composition are substantially different. If the atmospheric pressure is significantly higher than on Earth, water would require a higher temperature to reach its boiling point. The boiling point of a substance is the temperature at which its vapor pressure equals the external pressure acting on it. If the external pressure is higher, as might be the case on TOI-560 c, the boiling point of water would be correspondingly higher.

This poses a significant challenge for the emergence of life akin to that on Earth.

Nevertheless, this conclusion is not entirely definitive or conclusive. Despite the inhospitable conditions on the planet’s surface, there is a possibility of liquid water existing in the form of subsurface oceans or deep reservoirs. The high density (see 3.4. Density) of TOI-560 c could indicate the presence of a significant amount of water locked beneath its rocky surface.

 

Figure 4: Data (temperature) from the Hack an exoplanet website [1]

3.4. Density
To calculate the density of the planet, it was necessary to determine its volume. The volume is calculated using the formula

(1.11)

where RP represents the radius of TOI-560 c.

We multiplied RP =2.37 by REarth = 6378 km to convert it to base units. From this, we obtained the value of Rp.

(1.12)

We substituted this value into the aforementioned formula (3.11),

(1.13)

 

The formula then looked as follows:

(1.14)

The value of volume was then substituted into the formula for calculating the density,

(1.15)

where 𝜌 represents the density, M represents the mass, V represents the volume and p represents the exoplanet (TOI-560 c).

The calculation proceeded according the (3.14) as follows:

(1.16)

 

(1.17)

1.1. Results
Table 1: Results of the study

Name
TOI-560 c

Radius
2.378 REarth

Orbital distance
0.124 AU

Orbital period
18.8797 days

Density
4.004 g/cm3

Average temperature
225 degrees Celsius

 

 

 

 

 

 

 

 

Based on the provided information about exoplanet TOI-560 c, hypothesis could be proposed regarding its appearance and potential habitability.

 

Hypothesis 1: Given the average temperature of 225 degrees Celsius, it is likely that TOI-560 c has a hostile environment with extreme heat. The high temperatures suggest the absence of an Earth-like atmosphere capable of sustaining life as we know it. Instead, it may have a predominantly thick and dense atmosphere composed of greenhouse gases, leading to a significant greenhouse effect. This could result in a runaway greenhouse effect, causing the surface temperatures to rise to uninhabitable levels.
Hypothesis 2: The density of TOI-560 c, estimated at 4.004 g/cm3, suggests a high concentration of heavy elements or rocky materials. It is possible that the exoplanet has a rocky composition similar to terrestrial planets in our Solar System. The surface may be characterized by rugged terrain, rocky formations, and potentially active geological processes. However, the extreme temperatures make it unlikely that liquid water exists on the planet’s surface.
Hypothesis 3: Despite the inhospitable conditions on the planet’s surface, there is a possibility of liquid water existing in the form of subsurface oceans or deep reservoirs. The high density of TOI-560 c could indicate the presence of a significant amount of water locked beneath its rocky surface. It is conceivable that, if certain conditions are met, such as geothermal activity and insulation, these subsurface oceans could provide a potential habitat for microbial lifeforms adapted to extreme environments. These organisms might thrive in environments akin to Earth’s deep-sea hydrothermal vents or subsurface habitats.

[1] https://hackanexoplanet.esa.int/wp-content/uploads/2023/04/Hack_an_exoplanet_challenges_Czech.pdf

[2] https://hackanexoplanet.esa.int/wp-content/uploads/2023/04/Hack_an_exoplanet_challenges_Czech.pdf

TOI-560c Conclusions

Based on the provided information, the following conclusions are obtained:

The exoplanet TOI-560 c has a radius of 2.378 times larger than the radius of Earth (REarth). This suggests that TOI-560 c is larger in size compared to Earth. That is also the reason why TOI-560 c is sometimes referred to as a “Super-Earth”. However, the radius of TOI-560 c is much closer to the radius of Neptune (3.88 REarth). That is also why we do not object to the designation “Mini-Neptune” in our study group.
TOI-560 c is situated at an average distance of 124 astronomical units (AU) from its host star. This indicates that it orbits relatively close to its star within the planetary system. For reference, TOI-560 c has a similar orbital distance to Mercury (0.39 AU) or Venus (0.72 AU). Therefore, we can confidently state that it is not located in the habitable zone, considering both the properties of its host star.
Density: With a density of 004 (g/cm3), TOI-560 c possesses a relatively high density. This suggests that the exoplanet is likely composed of dense materials, possibly including heavy elements.
Average temperature: The average temperature on TOI-560 c is approximately 225 °C. This temperature is significantly higher than the average temperature on Earth.

 

Based on the provided data, the values of the radius, volume, density, temperature, orbital distance and period were provided for exoplanet TOI-560 c. It appears to be a hostile environment with extreme temperatures and an inhospitable surface. However, the presence of subsurface water reservoirs or oceans cannot be ruled out entirely, potentially providing a niche for extremophilic lifeforms. Further scientific investigation, including observations and measurements, would be necessary to validate these hypotheses and determine the actual habitability of TOI-560 c.

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