I seek collaborators to put the following discovery into my paper in preparation on features in the number distribution and eccentricity of the exoplanet population. This is a newer discovery of a ``spike'' in the eccentricity distribution by period of the planets in multiple planet systems. I add this to my finding of the double peak around a gap and my finding of the nature of there being a correlation between eccentricity and iron abundance of the star that changes with period. This includes how there is a region in between 500 and 600 days where the eccentricity of orbits of stars more iron-poor than the sun ``spikes'' in eccentricity.
Do you want to join me in writing this for the full peer reviewed publication?
Introduction
How could there be a ``spike’’ of five high eccentricities clumped
together in period out of one population of planets hosted by sunlike stars
that has 95 planets selected to be sunlike in temperature, surface gravity, and
absence of a stellar companion? Specifically, when the eccentricities versus
period of the population of just planets that are in multiple planets systems,
five eccentricities are clumped together in period that collectively have
higher eccentricities than anywhere elsewhere in the logarithmic period space
of exoplanets. These eccentricities especially stand out above the rest when
looking at the 20 planets with periods from 10 to 100 days by being much higher
than any eccentricities of the other 15 planets. Though among these 95 planets
there is a rise in the spread of eccentricities with increasing period, four of
these five eccentricities are still higher than any of the other 90
eccentricities.
 |
| Fig. 1. The eccentricities
versus periods of all stars. The eccentricities of orbits of
stars more iron abundant than the sun (``iron-rich,'' red open circles) are
higher at most all periods than the eccentricities of orbits of stars less
iron abundant than the sun (` `iron-poor,'' blue filled circles). |
 |
| Fig. 2. Eccentricities of the orbits of planets around only stars that are ``sunlike'' in temperature and surface gravity, and in being single
stars. Symbols same as Fig. 1. The lower eccentricity at most periods of orbits of stars more iron rich than the sun can be seen, as well as the peaking of the eccentricity of orbits of stars that are poor in iron relative to the sun at periods above 500 days. |
Eccentricity as a
function of period for selected populations
All and Sunlike:
The eccentricity as a function of period, with whether iron-abundance is
poorer or richer than solar indicated, are shown in Fig. 1 for the
full and some selections of the 429 orbits of planets found by radial velocity
(RV) found with periods of up to 5000 days, followed by Fig. 2 which shows the
selection of 243 orbits chosen for stars that are more ``sunlike’’. The ``sunlike’’
sample was selected by taking the 243 planets of the 429 available objects
found by RV, where ``objects’’ refers to the set of parameters describing a
planet, its star, and their orbit. Stars with different parameters might not
have the same features or have them at the same period, so only stars similar
to the sun are compared here. Since planet searches have emphasized sunlike
stars, this group of stars has the highest number of objects with similar stars
available for study. Sunlike objects are those which have stars that have no
stellar companion with effective temperatures (or Teff) of 4500 to 6500 K to be
close to the Teff of the sun of 5772 K, and with surface gravity not too
much less than the sun's value given in logarithmic terms of 4.4. We do not at
this time remove stars with very different masses than the sun because not too
many remain in this sample, but it may later be important since the small data
on lower mass stars could indicate that the peaks and gap feature may occur at
shorter periods. Different markers are used to separate orbits by whether the
star is poorer or richer in iron abundance than the sun, [Fe/H] <= 0 or [Fe/H] > 0
respectively, shown by the blue filled or red unfilled circles respectively. Table
1 gives the counts in each cut with each cut divided into how many iron-poor
and iron-rich objects there are.
Features stand out:
Several features stand out, starting with a broad increase in
eccentricity with period at the shorter periods that results from the shortest
period orbits having their eccentricities reduced (commonly said to be
``circularized'') due to tidal interaction with the star. This affects all populations of orbits. When
those orbits of stars that have less or more iron than the sun are separated,
which are referred to as ``iron-poor'' and ``iron-rich'' objects, it can be
seen that the eccentricities of the iron-rich objects rise more rapidly from
zero than do the eccentricities of the iron-poor objects, leading to the
``eccentricity-metallicity’’ correlation found between the eccentricity of
moderately short period planet orbits and iron abundances found by Taylor
(2012, 2013b) and Dawson \& Murray-Clay (2013). This correlation is
strongest at periods of roughly 100 days (the ``valley’’ region) but may
persist more weakly at periods up to 500 days. The eccentricities of the
iron-rich objects have a broader peak, while the eccentricities of the
iron-poor objects come more sharply to a peak, and then decline more. The
result of the peaking of the eccentricities of iron-poor objects is that the correlation
between eccentricity and iron abundance goes away for a middle range of periods
from 500 days (shown in Taylor 2013b) upward into the periods where we are
showing there is a gap in the number distribution of iron-rich objects. We are
preparing work that shows that beyond that gap, the correlation likely returns.
In further work, it will be shown that the correlation of eccentricity
is not simply bimodal with iron abundance but the eccentricity changes gradually
with iron abundance, that is that the eccentricities of objects slightly above
solar have, in periods where the correlation exists, a higher means than
iron-poor objects but lower means than for objects with the highest iron
abundances.
 |
|
Fig. 3. Eccentricity versus period of planet orbits of sunlike stars in single-planets, with marker symbols showing whether the iron abundance is above or below solar ([Fe/H] of 0) as in Fig. 1.
|
 |
| Fig. 4. The ''spike'' in the eccentricity of planet orbits of sunlike stars that are in multiple planets systems can be seen clearly here all being between periods of 44 and 75 days. Symbols as in Fig 1. Four of these five are higher than the eccentricity of any other eccentricity. The eccentricity clearly slowly rises with period for both iron-poor and iron-rich stars, though few iron-poor stars are found in multiple systems at longer periods. |
Different patterns in eccentricity by period of orbits
in single-planet versus Multi-planet systems:
In the next two figures the eccentricity versus period is shown for two
populations formed by further dividing the sunlike sample of 243 objects. Fig.
3 shows the eccentricities for the 148 ``single-planet’’ objects for which the
planet is the only planet found orbiting its host star, and Fig. 4 shows
eccentricities for the 95 ``multi-planet’’ objects for which one or more
additional planets has been found.
The single-planet sample has a distribution that retains more of the
description of the full sample, as this sample has higher mean eccentricities
at most periods. This is expected given that the orbits in multi-planet systems
are constrained from being too eccentric.
The eccentricities of the multi-planet sample do not peak but continue
to rise with period, though the number counts of iron-poor multi-planet objects
drops off such that there are far fewer iron-poor multi-planet objects than
iron-rich multi-planet objects at periods longer than 1000 days.For multiplanet objects in just sunlike systems there is 1 iron poor vs
23 iron-rich objects at periods longer than 1000 days.
Single-planet and
Multi-planet:
We take the 243 sunlike objects separately show the eccentricity versus
period distributions for the 148 orbits of ``single-planet’’ objects, or of
planets that are the only planet found, and of 95 ``mutiple-planet’’, or of
planets for which at least one more planetary companion has been found. The
breakdown of counts into iron-poor and rich objects are given in Table 1.
The two distributions look quite different, with the eccentricities of
the multiple planets lower in general. This is as expected that a planet is
more likely to have a more orderly orbit if there is another planet in the
system. The full description of how different these two populations are will be
given in upcoming work, while the focus here is on the spike in eccentricity in
the multiple planet population. Some qualitative differences besides the spike
jump out, including how in the multiple-planet population, the number of
iron-poor objects drops off at longer periods. This drop off contributes to the
ratio of iron-poor to rich objects being higher for the single planets (40:108
or 0.37) than for multiple planets (23:72 or 0.32).
Whether other than the spike the shape of the eccentricity distributions
in the multiple planet population bear a lower eccentricity resemblance to the
single planet distribution is a subject of current work. The highest
eccentricity point of the iron-poor multiple planet population, HD_192310_c, is
at 0.32 much higher than the 2nd highest eccentricity of 0.21 (the
24.451 day HD_7924_d). Its 525.8 ± 9.2 day period fits within the 500 to 600
day period range of the spike in eccentricity of the general population that is
the subject of Taylor (2014). While it may be difficult to attach too much significance
to one point, it is notable for being such an outlier.
The region of the spike in the eccentricity versus period distribution
of the multiple planet population corresponds to a region without similarly
high eccentricity objects in the same period range of the single planet
population, though if objects that include stars with stellar companions are
not cut, there is one such object in this period range of the iron-rich
population of the full (not sunlike) selection.
This does raise the possibility that perhaps the spike is simply ``cut
out’’ of the single plus multiple planet population by a greater likelihood of
finding a planetary companion for planets within this region. This could be
true of either physical causes or observational effects. It seems unlikely,
though, that the shorter period edge could be a result of not finding
companions to shorter period planets. It is worth further work studying this
possible effect.
Table 1. Counts of numbers of
objects in figures in each cut, with counts of objects divided by whether the abundance of iron of the star is poorer or richer than the sun.
|
Fig Number
|
Selection
|
Total objects
|
Iron-poor objects
|
Iron-rich objects
|
|
1
|
All RV objects
|
429
|
149
|
280
|
|
2
|
``Sunlike’’ objects in
temperature and surface gravity
|
243
|
63
|
180
|
|
3
|
Single-planet sunlike
objects
|
148
|
40
|
108
|
|
4
|
Multiple-planet sunlike
objects
|
95
|
23
|
72
|
Spike Description:
The five planets comprising this spike have orbits with periods from 44
.2 to 75.3 days. Planets orbits tend to be spaced at increasing distances such
that it is best to look at planet orbits in ``log space’’ where it is common to
give the logarithm to the base 10. When looked at in log period space, this is
the very small range of 0.23, going from 1.65 to 1.88 in logarithmic period.
This 0.23 is very small given that the range of RV planets that are comparable
can be said to have a length of 2.58 in ``log period space’’, going from below
10 days to 5000 days, which is going from log of 1 to log of 3.70. How could planets that are in multiple planet systems have orbits with
the highest eccentricities be confined to such a small range?
We must evaluate not only whether this spike could be random or
observational, but also whether it could be a result of making the selection of
the parameters, especially on making the selection on multiple planet systems.
We address how could be possible that planets selecting a part of a larger
population, in this case choosing those planets that are in multiple planet
versus single planet systems, could have led to a small range in period of
planets being preferentially put into this multiple-planet population while
planets just outside this range might be preferentially chosen into the
single-planet population. It could be the observational effect that planets in slightly
longer periods would actually still be in multiple systems but at longer
periods that are still too long for them to have been found. A similar
explanation would be that there simply are not further planets at the longer
periods, but this physical explanation would be of interest as it would be
relevant to the existence of peaks in the planet population counted by period.
The presence of high eccentricity orbits in the corresponding period
range shortwards of the spike in the single planet system population argues
against explanation of tidal dissipation in the star creating the short-period
edge of the spike. It also argues against
not having found companions as an observational effect since these
companion would not be expected to have longer periods, unless there is a
physical reason for the companions not to have been found. It is possible that
the longer period companions would have periods within the gap that has been
found in the iron-rich population, but that these companion planets are simply
``not present’’ due to the gap.`
Likelihood Section:
Calculations show a low likelihood that high eccentricity orbits would be so close in
period
The first questions to ask when seeing an apparent feature must be to
determine whether the feature is a real physical feature, starting with asking
if the feature might just be a random fluctuation in a small numbers of data
points.
The chance that the highest planets in eccentricity would be confined
such a small range depends on whether the likelihood is evaluated as being the
chance of five high values occurring in the somewhat local range where all five
are the highest values, or if the chance of the four highest values occurring
over the entire range, but the two give similar results of under one percent and
a few thousandths respectively.
The five orbits can be considered to by five pairs of log period and
eccentricity values. These are listed below, with the (not log) periods in days
preceding each pair for easy reference:
Table 2: Period
(in days and in base 10 logarithm of the period in days)
and eccentricity of the five high eccentricity objects.
|
PER
|
log period
|
ECC
|
|
day
|
|
|
|
44.24
|
1.65
|
0.47
|
|
51.64
|
1.71
|
0.63
|
|
55.01
|
1.74
|
0.68
|
|
58.11
|
1.76
|
0.53
|
|
75.29
|
1.88
|
0.73
|
The calculated likelihood of a certain number of periods occurring
within a larger range depends on the length of the range we consider these
values might have occurred in. Below we will calculate the likelihood for the
five values to be higher in a large part of the full range in period, and then
will calculate the likelihood that four values have higher eccentricity than
any other object at any period. We choose to be conservative by considering
that higher periods are only likely to be larger for longer period orbits, due
to the general pattern for eccentricities to get larger with increasing period
as a general pattern up to periods of several hundred days. We consider that the
eccentricities of shorter period orbits may be lessened by the tidal
interaction with the star that tends to circularize the shortest period orbits,
so to be conservative, we look for the possibility that these eccentricities
randomly occur at some period from shortest period of the spike to one of two
longer periods discussed below. It should be noted that in the population of
planets without planetary companions, there are high-eccentricity planets by
periods of 20 days, so the period ranges given below could have been taken to
be longer, even further reducing the likelihoods given below. Looking at the
values of eccentricity versus period for single planets shows higher
eccentricities for shorter periods in that population, however, leading the
values calculated here to give a higher likelihood of this spike resulting from
chance, but we choose to err on the conservative side. In calculating the probability that these
periods will occur within the spike range, we take the shortest period of the
high eccentricity points, 44.2 days or 1.65 in log-period space, as the shortest
period of the range of the periods just as likely to have high eccentricity
orbits. The next period at which a higher eccentricity than the lowest of the
five occurs is at 567.9 days, or 2.75 in log period space, so these five values
could have occurred anywhere along a log period range of 1.11, but they all
occurred within 0.23. So the likelihood that five points that could have
occurred in 1.11 but occurred in 0.23 can be calculated by finding how often
five values appear in the fraction 0.23/1.11=0.21 of points randomly generated
from 0 to 1.
Performing random selections of one million sets of five periods from 0
to one shows that only 0.7% of random selections of five values will be within
a range of 0.21 of each other. We calculate this by taking the difference
between the highest and lowest of the five selected values to allow for the
possibility of the five points grouping anywhere within this range. We repeat
this procedure to consider how likely is it that the highest four points are
within the short range that we find them where we could find them in anywhere
up to the full 5000 days for which RV periods are available, or 1.99 in log
period from the log values of the period range of 51.6 days to 5000 days. Since
the lowest of the five eccentricity values also corresponds to the shortest
period, there are now four points from periods 51.6 to 75.3 days, which is 1.71
to 1.88 in
log period, spanning a range of 0.16 in log period. This is 0.082 of the 1.99.
The chance of randomly having four points within 0.082 randomly generated from
points from 0 to 1 is 0.21%. We conclude that this feature is unlikely due to
random clustering of the periods at the better than 1% level.
Abundance
The five high eccentricity orbits are characterized by much higher iron
abundance in the stars than in the other 15 of the 20 orbits in the full
population in the similar period range from 10 to 100 days, reflecting the
strong correlation between iron-abundance and eccentricity found in this range.
Four of the five have iron abundances higher than all 15 of the stars with low
eccentricity planets in this range, and the lowest iron abundance of the five
is still higher than more than half of the other 15.
Discussion
Simulations of the likelihood that the periods of the four or five
highest eccentricity objects show that the spike is unlikely to be completely
random. It is also unlikely to be completely observational effect, but the presence
of high eccentricities in a small range of period could be influenced by the
interaction between the physical distribution and how additional planets are
found.
It is essential to consider whether this spike is merely ``shaved’’ out
of the full distribution. The short and long period edges are considered
separately. The shorter period edge of the spike could be created by
shorter-period orbits having their eccentricities reduced by tidal dissipation.
For the longer period edge, there is the possibility that there are higher
eccentricity longer-period orbits of planets in systems with more than one
planet for which the additional planets have not yet been found so these
eccentricity values are still showing in the single-planet plot instead. While
both of these possibilities should be researched further, comparison with the
single-planet distribution gives some evidence that these are not the
explanation for the appearance of a spike. This evidence includes how orbital
circularization falls off more quickly allowing higher eccentricities in the
single-planet population with periods shorter than 44 days. The single-planet
distribution has a rise in eccentricities for periods much shorter than 44
days, and it is more of a gradual rise. It must be noted that the region of the
spike shows a possible hole in this region in period space of the
high-eccentricity envelope of the single-planet population.
At slightly longer periods, there is a paucity of high-eccentricity
systems for both single and multiple planet populations from the range of the
spike to over 100 day periods, so there are not enough values there to move
over to the multi-planet population. (It is worth noting this paucity that is
longwards of the spike, but low statistics makes it uncertain that this paucity
is an actual gap feature.)
Does having so many
different sources invalidate these results?
It is important to address that the catalog of planet orbits is
collected from many different surveys which can have very different
efficiencies and standards, which lead many to distrust looking in such a
collected dataset for patterns. It is hard to believe that the appearance of
these features could be from differences between different observers,
especially given how different populations show clearly different patterns that
it is improbable that observers could be selecting for. Any observational
effects should similarly affect measurements of planets hosted by sunlike or
not sunlike stars, and single or multiple planets or stars. For some features
to appear so strongly should give confidence that the quality of RV exoplanet
data is consistently very high.
Further observations to lead to further work:
It appears that, other than the spike, the shape of eccentricity
distribution by period of iron-poor and iron-moderately-high multiple planets
appears to be a ``pushed down’’ version of the single planets distribution.
Future work must address whether both the iron poor objects in the full
population and the iron poor objects in the multiple planet population have a
similar spreading of the spike with increasing iron abundance in the range 0 < [Fe/H] < 0.1 of the in eccentricity
that occurs in the 500-600 day range.
The finding of a spike in eccentricity in the population of planets with
planetary companions again shows that pattern formation and evolution leads to
more uniform distributions than expected. The presence of distinct features in
the eccentricity and number distribution by period shows that the evolution of
planets which could include activity such as planet scattering after formation
that could smooth out these patterns, is likely not to overly disturb patterns
that occur in system after systems.
These results suggest that the pattern of planet formation is like more
predictable and less random from one planet system to the next. The presence of
these features prompts the suggestion that observers of protoplanetary disks
(PPDs) look for whether the rings and gaps in PPDs tend to have repeating
patterns from disk to disk, or if the features now being found in PPDs tend to
be found at random periods. The preservation of features in the number and
eccentricity distribution presents the opportunity to learn about planet
formation through studying features found in the parameters of mature planet
systems.
