Kepler-90 f

How do Kepler-90 d and f differ?

The radius of Kepler-90 f is about 2.88 times that of Earth, and the inner planet d is about 2.87 times. The two planets are almost the same size, but the energy f receives is about 37% of that of d. Since they orbit the same star and have similar age and size, they are good candidates to compare how differences in received energy affect the atmosphere. However, the actual masses and atmospheres of the two planets have not yet been measured, so it is unknown what effect this difference has had.

• Approximately 124.91 days Orbital period of f measured by repeated transits
• About 2.88 Earth radii Radius of f calculated from transit depth and the star's size
• About 6.8 times Earth's level Stellar energy calculated to reach f
• About 2.7 times as much Stellar energy received by d compared with f

Why are two planets orbiting the same star useful to compare?

How much a planet blocks starlight is determined by the ratio of the sizes of the planet and the star. Since d and f pass in front of the same star, if the radius of the central star is adjusted, the radii of both planets will change together by almost the same proportion. Even if there is an error in the size of the star, this effect is reduced when comparing the two planets with each other. Calculating with the current representative values, f is about 0.35% larger than d, and the difference in the starlight blocked by the two planets is only about 0.7%.

This difference is much smaller than the measurement errors of the two radii. Therefore, rather than arguing which planet is actually larger, it is more accurate to say that it is difficult to distinguish the sizes of the two planets with current observations. The important point is that the sizes of the two planets orbiting the same star are almost the same within the observational error.

d and f are judged to be almost equal in size because they block the same amount of starlight. However, it is still unknown how much rock core and gas each of the two planets contains.

How were the masses of d and f estimated?

The NASA Exoplanet Archive lists planet d as about 8.60 Earth masses and planet f as about 8.65 Earth masses. Judging by the numbers alone, they appear to be a pair with not only the same radius but also the same mass. However, these values are not the results of measuring the star's wobble or the gravitational effects between planets. They are expected values obtained by applying the same mass-radius relationship to the two radii.

Since the radii of the two planets are nearly the same, applying the same statistical method yields similar masses. Even if you calculate the average density using these estimated masses, the two planets inevitably come out similar. Therefore, this does not mean that their size, mass, and density were each independently measured and found to be identical. In fact, this is the result of calculating mass and density sequentially based on one measured radius.

1. Starlight reduction It is measured that d and f block nearly the same amount of starlight.
2. Radius calculation By applying the star's radius, d is found to be about 2.87 times that of Earth, and f about 2.88 times.
3. Mass estimation From statistics of other planets of similar size, d is estimated to be about 8.60 Earth masses, and f about 8.65 Earth masses.
4. Measurements Needed in the Future The gravitational effects of the two planets on their star or neighboring planets must be observed separately to determine their actual masses.

How much does temperature change when the incoming energy differs?

Planet d receives about 18.2 times the energy that Earth does, and planet f receives about 6.8 times. Although the difference in energy is about 2.7 times, the simply calculated temperatures are approximately 520K for d and 407K for f, a difference of about 1.28 times. Because the higher the temperature, the more rapidly a planet emits heat into space, the temperature does not simply increase 2.7 times even if the received energy is 2.7 times.

This calculation only compares how differently the two planets are heated; it does not measure the actual temperature. The actual temperature difference also depends on factors such as the amount of clouds and the reflectivity of the surface, atmospheric composition, and the extent to which daytime heat transfers to nighttime. The atmospheres and surfaces of the two planets have not been observed yet.

How can intense starlight affect a planet’s atmosphere?

Among the planets discovered by Kepler, those about 1.5 to 2 times the size of Earth are relatively few. Planets that are 2 to 3 times larger are often interpreted as having light gases like hydrogen and helium on top of a rocky core. In the early stages of a star's formation, strong ultraviolet and X-rays can cause a planet's gas to escape into space, and planets closer to the star may be more affected. Planets d and f are good subjects for comparison because they are similar in size but receive very different amounts of energy.

However, being the same size does not mean they started with the same amount of gas. For d to remain the same size as f while receiving more energy, it could have a heavier rocky core or initially had a thicker atmosphere. It is also possible that the two planets were made of different materials from the beginning. With current data alone, it is not possible to determine which explanation is correct. General trends observed in multiple planets should not be taken as the actual history of d and f.

The colors and clouds shown on the page are illustrations to aid understanding, not observational photographs. The radii of d and f were obtained from transit observations, but their masses are estimates derived from statistics of other planets. The received energy and calculated temperatures are results based on the star's properties, orbits, and simple thermal conditions, and do not represent the actual atmospheric state.

What more must we measure to confirm the differences between the two planets?

By measuring the actual masses of d and f, it is possible for the first time to independently compare whether their average densities are the same when their radii are almost equal. If the densities differ, the proportions of rocky cores and gas layers are also likely to differ. There are methods such as analyzing the transit times at multiple points together or measuring the star's motion over a long period due to planetary gravity, but for the distant and faint Kepler-90, it is difficult to distinguish small changes.

If we could observe the starlight passing through the atmospheres of the two planets, we could compare how molecules, clouds, and heat transfer changed depending on the difference in received energy. What we know for certain now is that the two planets are almost the same size, and f receives much less energy than d. It has not yet been confirmed whether the internal structures are the same or whether the atmospheres are different.

Sources

• NASA Exoplanet Archive — Kepler-90 d and f Parameters and Mass Provenance
• Astronomy & Astrophysics — The Planetary System to KIC 11442793
• The Astronomical Journal — A Gap in the Radius Distribution of Small Planets
• The Astrophysical Journal — The Evaporation Valley in the Kepler Planets
• Monthly Notices of the Royal Astronomical Society — Testing Exoplanet Evaporation with Multitransiting Systems
• The Astrophysical Journal — Probabilistic Mass–Radius Relation
• NASA Science — Kepler Transit Method