Thursday, April 10, 2014

Has Kepler Found Other Earths?

Earthlike Planets: Found or Not Found?

For years now, headlines in major newspapers have announced that the Kepler spacecraft has found earthlike planets. These headlines are misleading, trading on the vagueness of the terms “earthlike”, “find”, and “discover”. In fact, Kepler has found no single case known to be very much like the Earth, but rather several cases which may turn out, pending further study, to be earthlike. The purpose of this post is to survey the most promising cases, and what they collectively say about the prevalence of earthlike planets.

Kepler data can be used to determine the size of a planet and how much light it receives from its star. Different researchers have used different standards of how close to Earth’s parameters one chooses to define as earthlike. I will follow some of the more stringent definitions in calling earthlike a size of 0.8–1.25 R⊕ (Earth radius) and an equilibrium temperature (the temperature one would expect given the amount of light it receives from its star) of 185K–303K. It must be noted, though, that Kepler’s measurements of size and temperature have considerable uncertainty. The error (one standard deviation) in size is typically close to half the estimated size, and the error in temperature is often greater than the difference between Death Valley and Antarctica. Therefore, I will include for consideration planets with estimated size 0.7–1.6 R⊕ and estimated equilibrium temperatures from 160K–325K because better measurements may reveal some of these planets to fall in the tighter ranges.

Another kind of uncertainty is whether or not the planet actually exists! Kepler observes the dimming of a star which may be due to a planet transiting in front of it, but false positives (FPs) may be due to other explanations:

Electronic False Positives: Noise in the Kepler instrument may cause random dimming of a star which coincidentally resembles the transits of an earthlike planet. I discussed in my last post how this occurs and how we might diagnose such cases.

Astrophysical False Positives: A real astrophysical eclipse or transit may be taking place involving a background star which coincidentally is aligned so as to be observed by the same pixel in Kepler’s instrument as the brighter star. A real Kepler discovery is shown schematically in case (a) in this figure, whereas cases (b) and (c) show two examples of astrophysical false positives that can look the same as (a) in Kepler data.

The Sample

Kepler discoveries, initiated with algorithmic searches of the data, and proceeding to human inspection of the most promising candidates, are called Kepler Objects of Interest (KOIs). After examination, a KOI may be classified as Confirmed (nearly certain to exist), Candidate (may exist), False Positive (does not exist), or Not Dispositioned (uncertain status at this time). For a sample of sunlike stars, we take the 144,308 Kepler targets with a magnitude of 16.0 or brighter and logg (a measure of density) of 4.0–4.9.

Completeness

It is important to understand the completeness of Kepler's search for planets: For any given star in the sample that does happen to have an earthlike planet circling it, the probability is extremely low that Kepler would have been able to detect that planet. There are three reasons for this:

Geometry: Planets only transit their star if the orbit is aligned so as to appear edge-on as seen from Earth. For a planet orbiting a sunlike star in an earthlike orbit, this probability is about 0.5%.

Temporal: Although Kepler observed many stars for four years, there were short gaps in operations, both planned and unplanned, when observations were not conducted. Some stars were not observed in all quarters, and some earthlike planets could have orbital periods so long that four years was not enough to record the three or more transits required for detection. For a planet with the same orbital period as the Earth, the probability of three or more transits taking place while Kepler observed its star is about 90%.

Signal: Unfortunately, many stars' brightness varies over time by an amount comparable to the dimming that would be caused by an earthlike planet crossing in front of it. In these cases, Kepler could be staring right at the star while a transit occurs, but we would not be able to recognize it in the data. For an earthlike planet orbiting a sunlike star, the probability of the transit signal sufficiently exceeding its star's noise is about 6%.

The probabilities vary considerably from case to case, but they combine to leave only a small fraction of earthlike planets observable. We call the product of these three numbers the completeness, and calculate it for all combinations of orbital period, planet size, and type of star involved in this study. Completeness allows us to use a set of discoveries to estimate how many stars typically have planets of a certain kind.

Earthlike KOIs

In our sample, 59 KOIs fall into the ranges of consideration we defined above. Of those, only 8 have earthlike estimates of both size and equilibrium temperature, which consist of 5 Candidates, 3 Not Dispositioned, and none Confirmed.

In this graph, we see the 59 KOIs that are possible earthlike planets. Orbital period is on the horizontal axis and the size of the planet, in terms of Earth, on the vertical. Cases with the estimated equilibrium temperature in the earthlike range are white; those cooler are blue, and those hotter are red.

The size of the circle is based on factors that relate to how likely the planet is to exist. Larger circles are used for:

• Confirmed planets
• Candidates with
            -Five or more transits (unlikely to be evenly spaced in time by chance) or:
            -Low observational noise as defined in my post about seasonal variations in noise. This is the noise in the quarters where transits were observed divided by the noise over the three least-noisy quarters the star was observed. If this is below 1.15, the observational noise is considered low. Higher noise is associated with higher probability that the object is an electronic false positive.

Areas in the graph where completeness is greater than 0.0001 are shaded pink.
Completeness of 0.0001 on a sample of 144,308 stars translates into a frequency of about 7%, which is near the 5.7% frequency of earthlike planets around sunlike stars derived by [Petigura, et al], although the comparison is not so straightforward since this chart shows false positives and the definitions of "earthlike" are not identical. In any case, it can be seen that most earthlike KOIs fall near or into the shaded region, whereas the lower completeness region at lower right makes the detection of such worlds difficult. For illustrative purposes, the symbols for Venus and Earth have been placed at the appropriate locations.

As the graph shows, there are five cases where the estimated parameters agree exactly with the narrow definition of “earthlike”. There are many more cases where the size, temperature, or existence of the planet is particularly in question. In an almost insidious fashion, each of these qualities tends to be doubtful precisely when the others are better established, as we can see in the cluster of large white circles with periods less than 100 days and sizes of about 1.3 R⊕. These worlds appear to be the right temperature, but are larger than our cutoff of 1.25 R⊕. Just below those, we see many large red circles that indicate an earthlike size but higher temperature. Elsewhere, we see many small white circles which are the right temperature but may not exist. It is not a coincidence that earthlike size and temperature are rarely found together in Kepler results, because each of those qualities lowers the completeness of the observations, and in combination, earthlike size and temperature greatly reduce the completeness. As a result, we have at present no case which is known to exist and be earthlike in size and temperature. But there are many cases which look favorable. How many of these are real?

Expectations

If we integrate completeness as explained above across the entire parameter space, we can consider how many earthlike planets we should expect to find in Kepler data as a function of how common such worlds actually are.

If 100% of stars had one real earthlike planet, then we would expect Kepler’s data to include 4.0 of them circling class M stars, 4.2 around class K stars, 7.9 around class G stars like the Sun, and only 0.6 around class F stars, whose habitable zone is largely out at longer periods with resulting low temporal completeness.

But nobody expects 100% of stars to have earthlike planets, because even if many stars have a planet in an earthlike orbit, many of those will not earthlike in size (in our solar system, only 2 out of 8 planets are earth-sized). [Petigura, et al] estimate, by extrapolation from larger and hotter Kepler discoveries, that 5.7% of sunlike stars have an earthlike planet. As noted earlier, their definition of earthlike is different than the one I use here, but it has a similar area in parameter space, and is useful for setting approximate expectations. If that 5.7% held true for our purposes, then the K, G, and F stars on the list should have a total of 0.7 such planets, which is a tantalizing number, indicating that there is probably an earthlike planet, but maybe none, and probably not more than one. [Dressing & Charbonneau] concluded that about 15% of class M stars (red dwarfs) have earthlike planets, which would lead us to an estimate of 0.7 such earthlike planets on the KOI list, for a total of 1.4 across the four stellar classes.

Earth Two

The table below summarizes the properties of the 59 possible earthlike planets in the KOI list. The six most promising cases are coded white. Cases with an equilibrium temperature (eqt) that is too cold or too hot are coded blue or red, respectively. The remaining cases, where the size is well outside the range 0.8-1.25 R⊕, the KOI is not dispositioned, or the Observational Noise is greater than 1.15, are coded gray. The three terrestrial planets with atmospheres in our solar system are included for comparison’s sake, at the top, coded yellow.

We should expect that about 1 or 2 earthlike planets are among these KOIs, but that number is not guaranteed. Systematic or Poisson errors could make the true count as low as zero or as high as several. And if some of the worlds on this list are truly earthlike planets, we don't know which ones. The most likely possibilities are the six coded with white which I will briefly discuss as a group.

First, all six are Candidates, none Confirmed. Each is the only KOI detected in its system. This is important, because it has been estimated that a significant fraction of Candidates are actually false positives but that the FP rate is much lower for multiple-KOI systems and consequently higher for single-KOI systems. This is compatible with the estimate that approximately two of these Candidates are real.

Four of the six were observed making five or more transits, which is evidence that they are real astrophysical objects, whether astrophysical false positives or not. The other two made three transits each, and are subject to suspicion of being electronic false positives.

The uncertainties in size and equilibrium temperature, not shown, allow for any of these worlds that does exist to be outside the ranges defined as earthlike. The uncertainty in equilibrium temperature is relatively small in most cases. However, the uncertainty in size is often considerable – larger than the size estimate itself in most cases – so it is possible that any world listed here, if real, could actually be larger than 1.25 R⊕. Size and equilibrium temperature don’t pin down the climate these worlds might have. For example, Venus is, strictly speaking, earthlike as we have defined it, but in reality is famously hellish, with a surface temperature much hotter than its equilibrium temperature due to a runaway greenhouse effect. It has been theorized that planets orbiting a red dwarf star experience tidal phenomena that could make them un-earthlike in various ways. The range of climates of other terrestrial planets remains a topic for further study.

The Path Ahead

It is possible, then, that the first earthlike planet humanity will find (or has found) is on this list, but it would require more work to establish which of these Kepler discoveries qualify as such. It may be that the distance to Kepler discoveries, typically over 1,000 light years, will preclude or seriously postpone opportunities for meaningful follow-up science. The next steps may, instead, focus on other exoplanets located closer to Earth. It may also be that digging deeper into Kepler data will result in a confirmed earthlike planet that is not on this list. Whatever comes next, Kepler has given us a sense of how common earthlike planets are, and if its discoveries don’t provide our first known example, they certainly assist in planning any further studies.

Acknowledgements

Great thanks are due to Peter Plavchan and Phil Horzempa for their comments and assistance along the way.


Kepler ID
Classs
Name
Dispositionon
Period (d)d)
Size (R)
eqt (K)
SNR
Noise

G
Earth

365.3
1.00
255



G
Venus

224.7
0.95
301



G
Mars

687.0
0.53
207


11465869
G
K05904.01
Candidate
322.5
0.77
219
8.33
1.09
6497146
M
K03284.01
Candidate
35.2
0.93
273
12.39

8570210
G
K05545.01
Candidate
541.1
1.05
206
7.30
1.04
5091808
G
K05123.01
Candidate
288.9
1.09
265
7.24

11654039
G
K05927.01
Candidate
436.4
1.24
245
7.48
1.10
5942112
K
K05210.01
Candidate
126.0
1.24
286
6.45

8120608
M
K00571.05
Candidate
129.9
1.02
180
10.64

7416016
K
K05387.01
Candidate
297.8
1.25
167
7.38

4247991
G
K02311.01
Candidate
191.9
0.95
310
8.30

12020376
G
K05950.01
Candidate
109.4
0.99
315
7.22

11462341
K
K02124.01
Candidate
42.3
1.05
313
24.10

7619667
G
K05405.01
Candidate
103.2
1.09
314
7.11

10905746
M
K01725.01
Candidate
9.9
1.15
320
7.10

8652997
F
K05554.01
Candidate
362.2
1.16
312
7.58
1.11
7033233
K
K02339.02
Candidate
65.2
1.23
312
4.30

4172805
M
K04427.01
Candidate
147.7
1.46
164
11.02

8294683
K
K05499.01
Candidate
122.6
1.33
279
7.61

6149553
M
K01686.01
Candidate
56.9
1.33
246
5.20

5709014
F
K05194.01
Candidate
287.5
1.35
297
7.38

9292100
K
K05652.01
Candidate
91.5
1.37
302
7.38

11768142
M
K02626.01
Candidate
38.1
1.39
288
17.30

11497958
M
K01422.05
Confirmed
34.1
1.40
297
17.20

3642335
M
K03010.01
Candidate
60.9
1.41
264
18.70

9002278
K
K00701.04
Confirmed
267.3
1.46
205
13.45
1.07
9002278
K
K00701.03
Confirmed
122.4
1.54
255
47.80

8036863
G
K05465.01
Candidate
476.8
1.55
227
7.78
1.04
6106282
M
K04087.01
Candidate
101.1
1.58
201
16.82

8352009
F
K05506.01
Candidate
641.6
1.59
230
6.69
1.11
3540873
G
K04986.01
Candidate
444.1
1.60
211
6.68
1.11
8890150
M
K02650.01
Confirmed
35.0
1.28
312
15.70

9205938
F
K02162.02
Candidate
199.7
1.29
306
12.05

9674789
K
K05704.01
Candidate
96.2
1.29
313
8.20
1.08
11457664
G
K05902.01
Candidate
150.7
1.51
321
7.85

5353137
M
K03447.01
N/A
31.5
0.75
253
11.27

10579570
M
K05809.01
N/A
216.1
1.13
184
6.38

7592339
F
K05401.01
N/A
229.9
1.13
301
7.16

3641216
F
K04996.01
N/A
358.5
1.18
280
5.98
1.08
6608090
G
K05303.01
N/A
438.6
1.25
202
6.88
1.40
3865815
G
K05022.01
N/A
117.3
0.97
313
7.12

6447372
K
K05285.01
N/A
405.3
1.44
166
7.79
1.17
6364582
G
K03456.02
N/A
486.1
1.28
250
7.00
1.10
10663976
G
K05819.01
Candidate
381.4
1.29
213
7.06
1.24
4139254
G
K06108.01
N/A
485.9
1.29
226
7.26
1.05
8678345
G
K05560.01
N/A
365.0
1.31
241
7.54
1.19
10552263
G
K05806.01
Candidate
313.8
1.33
272
7.61
1.17
12645262
G
K05975.01
N/A
545.5
1.34
228
6.66
1.21
9412267
F
K05670.01
N/A
542.2
1.37
239
7.25
1.14
6946708
G
K06151.01
N/A
431.8
1.40
211
9.73
1.05
9463329
F
K05679.01
N/A
615.9
1.40
221
7.37
1.24
10977671
G
K05846.01
N/A
199.1
1.42
279
9.94

9941136
G
K05737.01
N/A
376.2
1.43
254
6.63
1.08
5529385
G
K05176.01
Candidate
215.7
1.51
292
8.33
1.40
3548044
G
K02194.03
N/A
445.2
1.55
240
9.72
1.13
11462969
G
K06239.02
N/A
491.6
1.55
221
6.61
1.05
5271637
G
K05147.01
N/A
471.4
1.55
267
8.18
1.04
12007270
G
K05948.01
Candidate
398.5
1.57
223
7.66
1.22
9024568
G
K05601.01
N/A
124.1
1.35
305
7.57

9935983
G
K05736.01
N/A
161.7
1.43
314
9.89

7041972
G
K05350.01
N/A
222.1
1.56
319
6.91



1 comment :

  1. ~5,500 billion billion earth-sized planets going around sun-like suns in the habitable zone in the universe by my calculations.

    ReplyDelete