Why Phi – the Fibonacci resonances of the TOI-451 exoplanets

NASA’s exoplanet hunter (TESS)
[image credit: MIT]

This three-planet system has orbit periods ranging from under two to over sixteen days, obviously another very compact group. Their star is slightly smaller and less powerful than our Sun.

Planets b and c are a fraction of Jupiter’s size, but planet d is vast with a radius of over four Jupiters, or about 45 Earth radii.

Multiple resonances of exoplanets in the TOI-178 system

Credit: NASA

This six-planet system has orbit periods from 1.9~ to 20.7~ days, all much closer to their star than Mercury is to the Sun.

It was recently ‘upgraded’ from the three planets discovered in 2018 and 2019.

As usual, the key to understanding the timings of the orbits is to look at the conjunction periods of the neighbour pairs.

Two interacting gas giants orbit sun-like star WASP-148

Super-WASP telescope site, La Palma [image credit: lapalma-island.com]

In nearly six years there are 247 b and 63 c orbits. Since 248:62 is 4:1, it can be seen why the observed ‘acceleration and deceleration’ of the planets might occur.
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Astronomers using the SuperWASP-North telescope on La Palma in the Canary Islands, Spain, and the SOPHIE spectrograph at the Observatoire de Haute-Provence, France, have discovered two giant exoplanets circling the G-type dwarf star WASP-148, reports Science News.

WASP-148 is a slowly rotating, inactive G-dwarf star 809 light-years away in the constellation of Hercules.

Also known as TYC 3083-295-1 and 2MASS J16563135+4418095, the star has the same mass and radius as the Sun.

WASP-148 hosts a planetary system composed of at least two giant planets, WASP-148b and c.

Unprecedented ground-based discovery of two strongly interacting exoplanets

Their orbits have a ratio of 247:63, whereas 248:62 = 4:1.
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Several interacting exoplanets have already been spotted by satellites.

But a new breakthrough has been achieved with, for the first time, the detection directly from the ground of an extrasolar system of this type, reports Phys.org.

An international collaboration including CNRS researchers has discovered an unusual planetary system, dubbed WASP-148, using the French instrument SOPHIE at the Observatoire de Haute-Provence (CNRS/Aix-Marseille Université).

The scientists analyzed the star’s motion and concluded that it hosted two planets, WASP-148b and WASP-148c. The observations showed that the two planets were strongly interacting, which was confirmed from other data.

Why Phi? – resonances of exoplanets LHS 1140 b and c

Wikipedia says:
LHS 1140 is a red dwarf in the constellation of Cetus…The star is over 5 billion years old and has 15% of the mass of the Sun. LHS 1140’s rotational period is 130 days…LHS 1140 is known to have two confirmed rocky planets orbiting it, and a third candidate planet not yet confirmed.

Planet b was in the media spotlight in 2017:
LHS 1140b: Potentially Habitable Super-Earth Found Orbiting Nearby Red Dwarf – Sci-News.

“This is the most exciting exoplanet I’ve seen in the past decade,” said Dr. Jason Dittmann, an astronomer at the Harvard-Smithsonian Center for Astrophysics and lead author of the Nature paper.
. . .
“The LHS 1140 system might prove to be an even more important target for the future characterization of planets in the habitable zone than Proxima b or TRAPPIST-1,” concluded co-authors Dr. Xavier Delfosse and Dr. Xavier Bonfils, both at the CNRS and IPAG in Grenoble, France.

Researchers discover a six-planet system with near 3:2 resonance

With orbit periods ranging from only 2-12 days, this must be one of the most compact multi-planet systems found so far.

Almost visible to the naked eye in the Draco constellation, the star HD 158259 has been observed for the last seven years by astronomers using the SOPHIE spectrograph, reports Phys.org.

This instrument, installed at the Haute-Provence Observatory in the South of France, acquired 300 measurements of the star.

The analysis of the data which was done by an international team led by researchers from the University of Geneva (UNIGE), has resulted in the discovery that HD 158259 has six planetary companions: a “super-Earth” and five “mini-Neptunes.”

These planets display an exceptionally regular spacing, which hints at how the system may have formed.

YZ Ceti update: resonant echoes of Pluto’s moons

There’s been a data update for the three planet system of star YZ Ceti, which featured in our 2018 post: Why Phi? – resonant exoplanets of star YZ Ceti. According to NASA the third planet YZ Ceti d is a ‘super Earth’, about 1.14 times the mass of our planet.

The paper:
‘The CARMENES search for exoplanets around M dwarfs.
Characterization of the nearby ultra-compact multiplanetary system YZ Ceti’
(Submitted on 5 Feb 2020)

With an additional 229 radial velocity measurements obtained since the discovery publication, we reanalyze the YZ Ceti system and resolve the alias issues.

Multiple resonances of the eight planet system of Kepler-90, part 2

Kepler-90 Planets Orbit Close to Their Star [credit: NASA/AMES]

In part 1 we looked at the inner four planets: b,c,i and d. Here in part 2 we’ll look at the outer four: e,f,g and h – with a dash of d included.

The largest planet in the system is h, the outermost of the eight so far found, and it’s about the same size as Jupiter. It’s ‘an exoplanet orbiting within the habitable zone of the early G-type main sequence star Kepler-90’, says Wikipedia. However, ‘it is a gas giant with no solid surface’, so probably no aliens lurking there.

It wasn’t that easy to find synodic patterns of interest, but here we have two examples, both involving planet h.

Multiple resonances of the eight planet system of Kepler-90, part 1

Golden rectangle: Fibonacci spiral

Unusually, the eight planets in the Kepler-90 system were found using machine learning. “It’s very possible that Kepler-90 has even more planets that we don’t know about yet,” NASA astronomer Andrew Vanderburg said.
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From Wikipedia’s Near resonances section on exoplanet Kepler-90:

“Kepler-90’s eight known planets all have periods that are close to being in integer ratio relationships with other planets’ periods; that is, they are close to being in orbital resonance.

The period ratios b:c, c:i and i:d are close to 4:5, 3:5 and 1:4, respectively (4: 4.977, 3: 4.97 and 1: 4.13) and d, e, f, g and h are close to a 2:3:4:7:11 period ratio (2: 3.078: 4.182: 7.051: 11.102; also 7: 11.021).

f, g and h are also close to a 3:5:8 period ratio (3: 5.058: 7.964). Relevant to systems like this and that of Kepler-36, calculations suggest that the presence of an outer gas giant planet facilitates the formation of closely packed resonances among inner super-Earths.”
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Let’s look at it another way i.e. at the synodic periods rather than the orbit ratios, as these tend to deliver more clear-cut results, starting with a model for the first four planets: b,c,i and d, which we’ll call the inner planets. Their orbits of the star are in a range of 7-60 days.

NASA’s TESS satellite claims its first Earth-size exoplanet in the habitable zone

Having one side of the planet constantly facing the star due to tidal locking could make habitability tricky though. There are three known planets in the system.
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From Wikipedia:
NASA’s Transiting Exoplanet Survey Satellite (TESS) has discovered its first Earth-size planet in its star’s habitable zone, the range of distances where conditions may be just right to allow the presence of liquid water on the surface.

Scientists confirmed the find, called TOI 700 d, using NASA’s Spitzer Space Telescope and have modeled the planet’s potential environments to help inform future observations.

Six hot rocky exoplanets orbiting very close to their stars could shed light on the geology of planets in our solar system

A researcher said of one of the new finds: “It is hard to see how the planet got there!”
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Six ‘very hot’ rocky exoplanets orbiting stars in the local region of the Milky Way hold the key to understanding more about how the Earth was formed, astronomers claim.

Researchers from the Open University have been studying planets discovered by the European Space Observatory’s planet-hunting telescope in Chile.

They are orbiting stars between 160 and 440 light years from Earth and all have hot surfaces with temperatures of around 2,012F to 3,272F.

The new findings could shed light on the geology of Earth and other rocky planets in the Solar System including Mercury, Venus and Mars, researchers say.

Full Daily Mail report here.

Resonances of the first (pulsar) exoplanetary system ever found

Poster from the NASA Exoplanets Exploration Program’s Exoplanet Travel Bureau [credit: NASA/JPL-CalTech]

Before we start – ‘Pulsar planets are planets that are found orbiting pulsars, or rapidly rotating neutron stars.’

Wikipedia tells us:
‘PSR B1257+12, previously designated PSR 1257+12, […] is a pulsar located 2,300 light-years from the Sun in the constellation of Virgo. It is also named Lich, after a powerful, fictional undead creature of the same name.

The pulsar has a planetary system with three known planets, named “Draugr” (PSR B1257+12 b or PSR B1257+12 A), “Poltergeist” (PSR B1257+12 c, or PSR B1257+12 B) and “Phobetor” (PSR B1257+12 d, or PSR B1257+12 C), respectively.

They were both the first extrasolar planets and the first pulsar planets to be discovered; B and C in 1992 and A in 1994.

A is the lowest-mass planet yet discovered by any observational technique, with somewhat less than twice the mass of Earth’s moon.’

One of the closest exoplanet pairs to the 3:2 mean motion resonance: K2-19b and c

Artist’s impression of the Kepler telescope [credit: Wikipedia]

So said researchers in their 2015 study which had that title. Then a third planet was seen.

In the abstract they say:

Methods. Our search through two separate pipelines led to the independent discovery of K2-19b and c, a two-planet system of Neptune-sized objects (4.2 and 7.2 R⊕), orbiting a K dwarf extremely close to the 3:2 mean motion resonance. The two planets each show transits, sometimes simultaneously owing to their proximity to resonance and the alignment of conjunctions.

Resonances of the Kepler-184 three-planet system

There doesn’t seem to be any online discussion of this planetary system, first seen in 2014 – but it turns out be interesting anyway.

This is a Lucas series set-up, the planets being b, c, and d in order of proximity to the star.

Starting with the orbits:
19 b = 203.006394 days
10 c = 203.03005
7 d = 203.1565
(data: exoplanet.eu)

Lucas resonances in six-planet Kepler-20 system

In 2011, astronomers were saying:
“We’ve crossed a threshold: For the first time, we’ve been able to detect planets smaller than the Earth around another star.”

The planets in question were Kepler-20 e and Kepler-20 f.

In the end six planets were detected: b,e,c,f,d, and g (in order of proximity to their star). Orbit periods range from about 9.38 to 63.55 days, all the planets being closer to the star than Mercury is to the Sun.

A NASA article had the title: Kepler-20, An Unusual Planetary System — referring to the alternate large/small sizes of the planets.

NASA quip: ‘Honey I Shrunk the Planetary System’

The Kepler-42 system as compared to the Jovian system [credit: NASA/JPL-Caltech]

The headline was NASA’s joke about both the size and the short orbit periods (all less than two days) of the three planets in the Kepler-42 system.

The discovery of this system dates back to 2012, but there don’t seem to be any numbers on resonant periods, so we’ll supply some now.

Wikipedia says:
‘Kepler-42, formerly known as KOI-961, is a red dwarf located in the constellation Cygnus and approximately 131 light years from the Sun. It has three known extrasolar planets, all of which are smaller than Earth in radius, and likely also in mass.’

‘On 10 January 2012, using the Kepler Space Telescope three transiting planets were discovered in orbit around Kepler-42. These planets’ radii range from approximately those of Mars to Venus. The Kepler-42 system is only the second known system containing planets of Earth’s radius or smaller (the first was the Kepler-20 system). These planets’ orbits are also compact, making the system (whose host star itself has a radius comparable to those of some hot Jupiters) resemble the moon systems of giant planets such as Jupiter or Saturn more than it does the Solar System.’

The three planets in order of distance from their star (nearest first) are c,b and d. They all have very short orbit periods ranging from under half a day to less than two days, and the star has only 13% of the power of our Sun.

A nearby binary star system with four planets

Pairs or multiple systems of stars which orbit their common center of mass. If we can measure and understand their orbital motion, we can estimate the stellar masses.

Relatively nearby, that is…

‘Upsilon Andromedae is located fairly close to the Solar System… (44 light years). Upsilon Andromedae A has an apparent magnitude of +4.09, making it visible to the naked eye even under moderately light-polluted skies, about 10 degrees east of the Andromeda Galaxy.’ – Wikipedia

The larger of the binary stars is ups_And A, which has 4 planets orbiting it: b,c,d and e.

The information on this star system was recently updated, so let’s have a look.

TESS discovers habitable zone planet in GJ 357 system

Credits: NASA’s Goddard Space Flight Center/Chris Smith

Following the report we analyse the orbital data for evidence of resonances.

A planet discovered by NASA’s TESS has pointed the way to additional worlds orbiting the same star, one of which is located in the star’s habitable zone, reports SciTechDaily.

If made of rock, this planet may be around twice Earth’s size.

The new worlds orbit a star named GJ 357, an M-type dwarf about one-third the Sun’s mass and size and about 40% cooler that our star. The system is located 31 light-years away in the constellation Hydra.

In February, TESS cameras caught the star dimming slightly every 3.9 days, revealing the presence of a transiting exoplanet — a world beyond our solar system — that passes across the face of its star during every orbit and briefly dims the star’s light.

Why Phi? – exoplanetary resonances of HD 40307

Moons of Pluto

This one may have slipped through the net, so to speak. The link to Pluto is explained below.

Star HD 40307 has six planets orbiting between 7 and 198 days, but here the focus will be on the outer three: e, f and g. These were reported in 2012 (whereas b, c, and d were found in 2008).

However, it seems the resonances described below have been overlooked, if lack of related internet search results can be relied on.

NASA’s TESS discovered three new planets nearby, including temperate ‘sub-Neptune’

Credit: NASA’s Goddard Space Flight Center / Scott Wiessinger

Quoting from the abstract of the study in Nature Astronomy:
‘The planets orbit close to a mean-motion resonant chain, with periods (3.36 days, 5.66 days and 11.38 days, respectively) near ratios of small integers (5:3 and 2:1).’

One of the astronomers said: “For TOI-270, these planets line up like pearls on a string. That’s a very interesting thing because it lets us study their dynamical behavior. And you can almost expect, if there are more planets, the next one would be somewhere further out, at another integer ratio.”

“There is a good possibility that the system hosts other planets, further out from planet d, that might well lie within the habitable zone. Planet d, with an 11-day orbit, is about 10 million kilometers out from the star.”

In fact the distance-to-star ratios of the planets (named b,c and d) are very similar:
b:c = 1:1.542 and c:d = 1:1.553 (for comparison Earth:Mars is 1:1.524).

NASA’s Transiting Exoplanet Survey Satellite, or TESS, has discovered three new planets that are among the smallest, nearest exoplanets known to date, reports Tech Explorist.

The planets circle a star only 73 light-years away and incorporate a small, rough super-Earth and two sub-Neptunes — planets about a large portion of the size of our own icy giant.

The sub-Neptune farthest out from the star seems, by all accounts, to be inside a temperate zone, implying that the highest point of the planet’s atmosphere is inside a temperature extend that could support a few types of life.