Rings and Gaps Everywhere?: Do the Same Planet Formation Patterns Happen at the Same Periods?

Rings and gaps found in disks from Saturn's rings to protoplanetary disks.

How are planets arranged? Disks, of course. Disks are everywhere in the universe, from Saturn's rings to galaxies, but also planetary systems appear to usually come arranged in disks. Centuries ago, astronomers were guessing that planets were formed in disks. Long before we could see any disks forming planets, Laplace pretty much got it right that planets form from disks of dust and gas. Now, new telescopes are finally observing disks where planet formation is likely taking place, in disks called proto-planetary disks (PPDs).

What is often the main features of disks? Gaps and rings, of course. Saturn's rings are not uniform, but come with bright rings of more material, and dark gaps of less material. Now that PPDs are presumably being observed, many are found to have gaps in them. The recent result by ALMA showing the disk material in TW Hydrae, the nearest PPD, is not the first to find a gap in a PPD (Andrews et al., 2016). Our solar system also has a gap in its distribution of planets, with a wide space between Mars and Jupiter where there is no major planet.

So are there gaps in the arrangements of other solar systems? Certainly there would be in multiplanet systems, but could there also be gaps in the arrangements of planetary systems in general? A region where planets do not form?

There certainly are ``rings,'' such as the ``three-day'' pileups of giant planets with periods a little over three days, and the ``1 AU pileup'' of planets with distances from the star, called ``semi-major axes,'' of over 1 AU (the sun to earth distance). There have also been found regions of fewer planets close in to the star, referred to as valleys or deserts.

Now I present a dramatically deep gap a little further out, where since Taylor (2013) I have presented how the pileup past 1 AU is, when looking at planets hosted by stars more rich in iron than the sun but otherwise mostly sunlike, is actually two pileups separated by a surprisingly wide and deep gap. Though I first found a gap of ``fewer planets'' in 2013, in 2014 I found if I select only sunlike single stars, cutting out evolved stars and stars with stellar companions, there are actually zero planets in the current dataset with periods from 656 to 923 days. 

Fig. 1. Artists concept of the protoplanetary disk (PPD) around the star TW Hyadrae (TW Hya). Credit: NAOJ.

Fig. 2. A synthesized image of the submillimeter (radio) emission from the TW Hya disk from Andrews et. al (2016) and inset zooming into the center shows gap and ring structure in this PPD. 

Fig. 3 Gaps and many smaller rings make up the rings of Saturn.

Features in the planet distribution

We show that similarly there are more detailed features than just the short and long period pileups that are obvious in the distribution of planets. We first show the full counts of planets, and then narrow our selection of planets to find peaks and gaps in the population of planets hosted by sunlike stars that have richer iron abundance than the sun. We describe there how the binning was chosen to best show the gap and peaks. We list a couple of conventions: We want to use the best sample for the broadest range of periods, so we use the sample of planets found by radial velocity (RV) here. It is too hard for other methods to probe the region of a few AU: the detection efficiency falls too much for transiting planets, but this range is too close to the star to be observed by direct imaging. Good counts of planets exist for 429 ``RV planets'' up to periods of 5000 days, so we ignore the spotty findings of planets with periods beyond 5000 days. Finally, we refer to the planet plus its host star plus orbit collectively as an ``object,'' where the eccentricity of an ``object'' means the eccentricity of the orbit, while the iron abundance of an ``object'' is the iron abundance of the star, and ``iron-poor'' (rich) objects are those hosted by stars with poorer (rich) iron abundance than the sun (or other value if specified).

The first histogram, Fig. 4, shows all the periods of 429 planet orbits found by radial velocity up to the end of 2015 as compiled by exoplanets.org with periods up to 5000 days. The 429 are separated into 149 ``iron-poor'' and 280 iron-rich objects (149 and 280 planets hosted by stars with less than/the same and more iron abundance than the sun respectively). Here we already see some structure appearing in the iron-rich object population: though both populations are clearly composed in part by broad peaks centered at periods a little under 1000 days, there are two peaks in the iron rich population.

When the binned counts of all 429 planets, or all RV objects, found by this one method are counted by logarithmic period up to period of 5000 days and are shown together as in Fig. 4, we see that there appear to be a shorter period pileup and a longer period broad pileup. The shorter period pileup was one of the first findings made from the early discoveries of exoplanets, and has since been associated with iron-rich objects (Dawson & Murray-Clay, 2013, hereafter DM13), that is, planets of stars with higher iron abundance than the sun. The longer period pileup has long been expected because planet formation was expected to much more readily occur at a distance from the star beyond a ``snow-line'' far enough from the heat of the star that condensation can occur. Indeed, we see these pileups, but  it is uncertain whether there are more detailed features beyond statistical fluctuations. There are smaller ups and downs in the counts that could be worth investigating for whether there could be variations that are significant.

Fig. 4. The number distribution by period of all 429 planets found by radial velocity (RV) by the end of 2016, with periods up to 5000 days (since the statistic cut off beyond that). It appears that there is a single ``1 AU'' pileup at periods from one year to 1000 days. Though the double peak bracketing a gap pattern is visible here, it looks like random jitter rather than the strong feature that it is when a more focused sample is chosen.

Separating the counts of iron-poor from iron-rich objects as in Fig. 5 shows the short period peak to be a feature of iron-rich objects, as found by DM13. The separated collections of iron-poor and rich objects have been shown to be different populations with different distributions. Below, we show that these populations do indeed have different distinct features in the number count by period. We have also begun discussing the eccentricity distribution by period. We find features separate out more distinctly by period than by semi-major axis, likely because the period adjusts some to change in stellar mass. We find features separate out more distinctly by period than by semi-major axis, likely because the period adjusts some to change in stellar mass. A plot of planets orbiting smaller stellar mass stars shows the peak is at shorter periods. The peak in lower stellar mass systems at shorter periods could cover up a gap that in higher mass occurs the same range of period.

Fig. 5. The number distribution by period of all 429 planets as in the previous figure but this time divided into two populations, with red denoting those 280 objects whose stars are more iron-abundant than the sun (which we will call ``iron-rich'' and in astronomer's notation written [Fe/H] > 0), and blue denoting those 149 objects whose stars are iron-poor relative to the sun (``iron-poor''; in astronomer's notation written [Fe/H] <= 0).The double peak bracketing a gap pattern is more visible here, in the iron-rich population, but it still could be taken as random features.

In Fig. 5 the longer period peak in the iron-rich population begins to divide into two peaks, which when we restrict our counting to the 243 ``sunlike'' objects in Fig. 6, this shows that the space in between the two peaks includes at least one gap of zero planets next to a sharply rising ``longer period'' peak. These 243 planets have been chosen for being hosted by stars that are sunlike in temperature, surface gravity, and in being single stars (not having a stellar companion as follows: only objects with effective temperature (of the star) ``T<sub>eff</sub>'' which was chosen to be 4500 to 6500 K, or roughly within 1000 K of 5772 K, the T<sub>eff</sub>  of the sun, and the strength of the surface gravity of at least 10000 cm/sec<sup>2</sup>, which in astronomy jargon means requiring that ``log g'' is greater than 4.0, compared to the solar log g of 4.4. We do not at this time cut objects with different stellar masses due to their small numbers, though may do so in the future.

The bins size and placement was chosen to best show the two peaks in the ``beyond 1 AU pileup'' and the gap in between them. We were able to choose as bin boundaries the boundary between the short period peak and the gap, and the boundary between the gap and the long period peak. We took a bin boundary just beyond the longest period of the short period peak of 493.4 days, choosing on the left side of the gap a bin boundary of 494 days, or 2.69 in log period of 493.4, and we took a bin boundary just shortward of the shortest period in the longer period peak of 923.8 days or 2.97 in log period, choosing on the right side of the gap a bin boundary at 923.5 days. There is a span of 0.27 in log period space, a factor of 1.87, from the period of 493.4 to 923.8 days. The choice of four bins between these two chosen periods allows the most reasonable presentation of detail that appears to be real, without having too much statistical fluctuation that appears in smaller bins. The ratio between each bin, called the ``bin factor'' on exoplanets.org, is then 1.17, which is in 0.067 in ``log 10 period space.'' Though there were only two bins in between the gap in Taylor (2013), we show below that detail may be apparent having the smaller binsize. 

It appears that there could be structure in the gap in between the double peaks, in the form of a small gap separated from a larger gap by a small pileup: All of the six planets in between the two peaks have periods in between 567 and 653 days, a distance of 0.061 in log period space which is small enough to fit into one of the bins that are of width 0.067, but this pileup starts after a small gap slightly smaller than a bin, a gap also spanning 0.061 in log period space. So the pileup goes from 0.22 to 0.44 of the fractional distance in between the two peaks. The pileup then is situated just slightly shortward of the 2nd bin, such that the first planet period falls in the first bin.  To show the gap/pileup/gap features, in Fig. 7 a smaller binsize (``bin factor'') of 1.17 corresponding to a distance in log 10 period of 0.067 is taken, and the same 243 objects as in Fig. 6 are shown in 59 bins. 

Fig. 6. The distribution of periods of the 243 planets of single sunlike stars, with objects of 180 iron-rich stars shown in red (not filled) and planets of 63 iron-poor stars in blue (filled). The bins have been placed to fit four bins in the boundary of a gap from periods of 494 to 923 days. There is a deep gap of zero planets from 656 to 923 day periods, which is a little larger than the last two bins in the gap, that has zero planets.

Fig. 7. The same selection of 243 planets as before but shifting the bins slightly to shorter periods, and setting the bins slightly smaller, to show that there could actually be two gaps separated by a small pileup. In the gap from 494 to 923 days, there is a bin with zero planets, then six planets close together in period, then more than two bins with zero planets.

We can answer whether features are due to random chance by using large numbers of computer-generated random numbers to see how often random distributions produce these features. As for whether these features are due to observational effects, a strong case can be made that they are not observational by how these features change due to the parameters of the planet plus star system -- the argument can also be made that the correlation between the features and the selected parameters of the actual system of planet and stars strengthens the case that these features are properties of the systems being observed in space, and not due to observational or selections of randomly produced clustering.

Table 1: Counts of planets in period ranges that have different characteristics

Name of period range		All objects	All separated by [Fe/H]		Sunlike separated by [Fe/H]
			poor	rich	poor	rich
Period range
(days)
Shortest period		60	12	48	8	38
0-10
Valley		61	19	42	14	29
10-100
Beyond valley		87	35	52	11	32
100-365
Shorter period peak		42	16	26	2	17
365-493.71
Shorter period gap		16	10	6	3	0
493.71-568
Mid-gap pileup		20	9	11	1	6
568-656
Longer period gap		31	18	13	5	0
656-923
Longer period peak		53	15	38	8	28
923-1469
Beyond peak		59	15	44	11	30
1469-5001
Total		429	149	280	63	180

Next, we compare the distribution of planets without other planets in the same system in Fig. 8, and with such known ``sibling'' companion planets hosted by the same star in Fig. 9. It is immediately apparent that the two distributions of iron-rich objects are not the same in periods short of the gap: Though the gap and longer period peak exist in both distributions, the period range of the shorter period peak does not have nearly as many planets as the single planet distribution. In the four bins from periods of 267 to 497 days, there are 21 planets in the short period peak of the single planet iron-rich sunlike population, has only five planets. However, four of the six objects in the pileup separating the narrow and wide gaps are in multiple planet systems. It might be expected that planets in multiplanet systems have undergone less planet scattering and less movement of planets crossing from beyond to inside the snow-line, which might account for the shorter period peak being so much smaller.  

Fig. 8. Selecting the 148 planets of the 243 sunlike objects that are in ``single'' planet systems (with no 2nd planet found) shows that the double-peak with a gap pattern is a feature of the 108 single-planet objects around iron-rich stars, while the 40 single-planet planets around iron-poor stars have just a single pileup (though it shows the effects of small-number jitter).

What is the likelihood that the gap is real?

The important question when seeing a gap in a distribution that has a limited number of points is, ``Is this a real gap?’’ To answer this, two rebuttal questions must be asked, ``Is the gap simply due to the random distribution of the data or might the gap be from some observational effect?’’ 

To answer whether the gap could be just the result of random measurements of period, I simulated several random distributions of the period, from a uniform distribution that assumes nothing, not even that the 1 AU pileup is real, and a distribution weighted to assume that there is a single pileup. I am careful to raise the chance of randomly having a gap by looking for a gap anywhere along a wide range of periods. I even consider the most conservative possibility, that there really are two peaks but that the period space in between is really just populated at the same level as outside the two peaks. In the first two cases, only in fewer than one in 10,000 cases is a gap. 

Another way of addressing whether the gap is either observational or could be produced randomly is to look at all the objects in the gap. A comparison is made of the values in Table 1, which gives the numbers of sunlike objects versus all objects in period ranges chosen to show important features of the distribution of planets. In the ``wide gap,'' from periods of 654 to 923 days, there are 13 objects, not one of which makes the cut of being ``sunlike,'' with 11 having log g less than 4 and three being binary (one fails both cuts). This compares to less than half of the full population not being sunlike, with even a smaller fraction failing these cuts in the next two or next three bins (comprising the longer period peak). Within the deep gap, there are 13 objects that are not in the sunlike population plus18 sunlike but iron-poor objects, for a total of 31 objects, zero of which are fe-rich sunlike single-star, compared to 113 of the 307 objects from 100 to 5000 days. (Again, the 13 that are not in the sunlike population are hosted by stars with a stellar companion, have too low of surface gravities such that they might be further evolved stars, or are too different from the sun in temperature.) If there is a chance of each object being an iron-rich sunlike object, then the chance of 31 objects having zero iron-rich sunlike objects is 

(1 - 113/307)³¹=6.62x10^-7 , 

which is less than one in a million.

Fig. 9. Selecting the 95 planets of the 243 sunlike objects that are in ``multiple'' planet systems (where a 2nd planet has been found) shows that the shorter period peak is much less apparent even though the longer period pileup and the gap are still features here. The distribution of the multiple-planet planets is quite different than the single planet distribution, with the three day pileup absent from this distribution as well. Notice the paucity in iron-poor objects with periods longer than 1000 days. 

Discussion: What might cause the gaps and peaks?

The hypothesis can be made that higher eccentricity results from more planet-planet scattering where planets are more crowded fits with where how there is higher eccentricity where there is likely to be the most planet formation. There may be so much planet formation in the most iron-rich systems that the result planets are so crowded that they undergo so much scattering that they produce the high eccentricities across a broad range of periods that we measure today.

The observation that higher eccentricity orbits are found in iron-poor systems with stellar companions right at the period that could be where the highest density of planets (most crowded period region) suggests that having a stellar companion could increase the odds of planets scattering, resulting in a narrow period region where ``excited’’ scattering leaves a ``spike’’ of eccentricity among orbits of stars  having less iron than the sun but having stellar companions.

This brings us back to what could cause the gap(s). The wider gap is in the region of where there may be the most intense planet scattering, as evidenced by higher eccentricities in these period ranges even in cases that at other periods there are fewer high eccentricity orbits. In the iron-rich population, the periods that include the most high eccentricities are found in the region of the two peaks, as shown in Fig. 10. 

We will be exploring the patterns of eccentricity in upcoming posts that will expand on features of the how the eccentricity distribution as a function of period depends on iron abundance, going from the correlation of the eccentricity distribution at moderately shorter periods (Taylor 2012, DM13) to how this correlation changes by period (Taylor 2013), to how there is a region of high eccentricity planet orbits of iron-poor stars. We will discuss the spike in eccentricity of iron-poor systems at periods from 511 days to 592 days found in 2013 (Taylor 2014) that roughly corresponds to the shorter part of the gap in planets of iron-rich stars. The previous post gives the finding of a new spike in the distribution of planets in systems where more than one planet has been found (High-eccentricity-spike-in-multiple-planets).

Fig. 10. The eccentricity as a function of period for all planets found by radial velocity, with filled blue circles for iron-poor objects, and open red circles for iron-rich objects. Note how in the iron-rich population the eccentricity reaches a maximum where the planet count is highest.

We note that the presence of these patterns shows the high quality of the collected exoplanet data. Though some worry that the differences in how different authors do their analysis would make it impossible to study the combined data, these results show that most of the reported parameter values have a consistency that evidences good quality results.

It is a surprise that if by taking a sufficiently similar sample of the exoplanet data, that planet formation and evolution is close enough to being the same from system to system that such strong patterns as these pileups, gaps, as well as detail in the eccentricity show up. Planet formation must follow similar storylines from system to system for these patterns to show up in the cumulative dataset.  

References:

Andrews, S.M. et al., 2016, arXiv 1603.09352.

Dawson, R.I., and Murray-Clay, R.A., 2013, Giant planets orbiting metal-rich stars show signatures of planet-planet interactions, ApJL, 767, L24. 

Taylor, S.F., 2012, Flow of Planets Raises Short Period Fall Off, in ``Formation, Detection, and Characterization of Extrasolar Habitable Planets,'' N. Haghighipour, Chief Editor, Proceedings of the International Astronomical Union, IAU Symposium, 293, (available as arXiv:astro-ph/1211.1984)..

Taylor, S.F., 2013, Iron abundance correlations and an occurrence distribution discrepancy from ongoing planet migration, arXiv:astro-ph/1305.5197.

Taylor, S.F., 2014, Eccentricity Dependence on Iron Abundance, Exploring the Formation and Evolution of Planetary Systems, Proceedings of the International Astronomical Union, IAU Symposium, 299, pp. 397-398.