Alas, Kepler

The sad news broke this afternoon. By now it's been around the world a few times. The Kepler spacecraft has suffered serious equipment failure, over and above the problems it had last year. For now, and potentially forever, Kepler has lost its ability to point its telescopic apparatus with the precision required to track transiting planets.

“I wouldn’t call Kepler down and out yet,” said John Grunsfeld, a NASA official, but the planet-hunting community has registered extreme dejection anyhow. Geoff Marcy, the godfather of exoplanetary science, was inspired to circulate this variation on a lament by W.H. Auden (as reported in the LA Times):

Stop all the clocks, cut off the internet,
Prevent the dog from barking with a juicy bone,
Silence the pianos and with muffled drum
Bring out the coffin, let the mourners come.

Let jet airplanes circle at night overhead
Sky-writing over Cygnus: Kepler is dead.
Put crepe bows round the white necks of doves,
Let the traffic officers wear black cotton gloves.

Kepler was my North, my South, my East and West,
My working week, no weekend rest,
My noon, my midnight, my talks, my song;
I thought Kepler would last forever: I was wrong.

The stars are still wanted now; let's honor every one,
Pack up the moon and dismantle the sun,
Pour away the ocean and sweep up the woods;
For nothing will ever be this good.

Ah, but we still have so many blessings to count. Look at that poster at the top of this post -- look at all those candidate terrestrial planets! We had nothing like those data just four years ago. Or go to the Kepler Mission page and peruse the confirmed discoveries -- 132 planets and counting. If that isn't amazing, astounding, thrilling, weird, and wondrous, I'd like to know what is!

Kepler survived for the entire lifetime of its original mission, and it has already returned so much data that we can expect scores, if not hundreds, of new planets to emerge from the pipeline over the next few years. Many of them are bound to be cool-ish and Earth-ish, given four years of accumulated coverage. So I'm sad, I'm regretful, but I'm not really desolate.

After all, the Transiting Exoplanet Survey Satellite (TESS) is scheduled to launch in ONLY four years (or so) . . . and that new Star Trek movie is opening tonight . . . .

Postscript on May 27, 2013: On Thursday, May 16 (the day after I uploaded the preceding post), I went to the local university for a presentation by Jon Jenkins, a scientist and engineer who has been part of the Kepler Mission since before it was called Kepler. Jenkins gave an overview of the development of the telescopic apparatus, summarized mission highlights, and answered questions about Kepler’s future. Uppermost in the minds of just about everybody in the audience was whether the problem with the reaction wheel was fixable, and whether the flow of amazing new exoplanet data would continue as it has in the recent past.

Jenkins made it pretty clear that Kepler’s transit mission is finished. There seemed no hope that the spacecraft’s pointing ability could be restored, and nothing I’ve read in the days since then suggests otherwise. Nevertheless, Jenkins stressed that by any measure, Kepler has already proved to be a huge success, and its original mission has been completed more or less as planned. It’s only the extended mission – approved just last year – that had to be scuttled.

He also emphasized that large quantities of data already collected still await analysis. So in terms of new discoveries hitting the press, the next 10 or 12 months will probably be similar to the past 10 or 12. If I had to guess, I’d say we’ll be seeing more interesting new multiplanet systems, more subterrestrials, and more Earth-size planets in or near their systems’ habitable zones. Such planets are likely to orbit stars cooler than our Sun, since habitable planets of M, K, and even late G stars have periods shorter than 365 days, and thus are more easily detectable in the available Kepler datasets. 

Jenkins held out hope that the Kepler apparatus could be repurposed somehow to conduct observations that don’t require precise pointing, but I didn’t get a clear idea of what that alternative would look like.

Evidently we have a long wait until the next major onslaught of unprecedented marvels. CHEOPS, the CHaracterising ExOPlanets Satellite, won’t be launching until 2017. It involves a telescope in Earth orbit optimized to detect transiting planets of 6 Earth radii or less (i.e., telluric and gas dwarf planets) around nearby stars already known to host planets.

TESS, the Transiting Exoplanet Survey Satellite, is also scheduled for launch in 2017 – or maybe 2018, according to an online article I just saw. (As we know, launch dates have an unfortunate tendency to slip.) Unlike Kepler, which studied a limited region of space, TESS will conduct an all-sky survey focusing on planets in the Sun’s back yard, which I think is peachy. I only wish it would launch sooner.

WFIRST-2.4, another upcoming NASA mission, will use one of the two spare Hubble-quality telescopes that the U.S. Department of Defense recently decided it didn’t need. It’s slated to conduct three different programs relevant to exoplanetary science. According to a brand-new report by Spergel and colleagues, the first program is a microlensing survey of unparalleled scope and precision that will characterize “the demographics of exoplanets.” Another program will directly image planets around nearby stars. A third will image nearby debris disks at high resolution. All that sounds great, but there’s a catch – WFIRST-2.4 doesn’t have a launch date yet. Spergel and colleagues speak vaguely of work that will begin “early in the next decade.”

Meanwhile, I recommend Star Trek Into Darkness. It’s one of the better films in that franchise, and you’re hearing this from a non-Trekkie. (I myself belong to the fast-dwindling species of Barsoomiasts, who remain chained to the allegedly outmoded technology known as books.)

Holy Grail, Earthman!

Figure 1. Artist’s view of Kepler-62f, a likely terrestrial planet orbiting in the habitable zone of an amber K2 star located about 368 parsecs (1200 light years) away in the constellation Lyra.

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It’s happened. The Holy Grail of exoplanetary science has been glimpsed, if not yet grasped. Yesterday the Kepler Mission reported a transiting planet, most likely of rocky composition, orbiting in the habitable zone of its amber host star. This planet, Kepler-62f, has an estimated diameter of 17,985 km (11,140 miles), corresponding to 1.41 Earth radii (Rea), and an equilibrium temperature (Teq) of 205 K, similar to the Teq of Mars. It also has four inner companions, one of which (Kepler-62e) may be a second candidate for habitability. While neither Kepler-62e nor Kepler-62f can honestly be described as “Earth Twins,” The New York Times declares that they’re still “promising places to live.” (And if the Times doesn’t know real estate, who does?)

No transit timing variations have been observed for any of the planets in this system, nor did a radial velocity search detect any variability consistent with planetary motion. These null results mean that we have no secure way to determine the mass of any of these planets, except by using theoretical models to estimate their likely composition and density.

According to the latest mass-radius relationships published by Lissauer et al. (2013), the radius of Kepler-62f is consistent with a range of masses and compositions, depending on whether it is entirely rocky or whether it has a significant icy component. At its likely maximum mass of 3.5 times Earth (3.5 Mea), 62f would have exactly the same iron/silicate composition as our home planet, and thus qualify as a true Super Earth. Exchanging some proportion of rock and metal for ices would result in increasingly lower masses, down to about 1.5 Mea for a planet that is 75% rock and 25% ice, and less than 1 Mea for a half rock, half ice planet. With its larger radius of 1.61 Rea, Kepler-62e might be an iron/silicate planet of 6.5 Mea, or it might be an Earth analog of 1 Mea with a 1% hydrogen atmosphere. If it has an icy component, its mass could range from about 2.5 Mea for a 75% rocky/25% icy composition, down to 1 Mea for a half rock, half ice planet.

Borucki et al. (2013) favor the rocky or icy options, arguing that both planets have probably “lost their primordial or outgassed hydrogen envelope.”   

Table 1. Parameters of the Kepler-62 system

Rea = radius in Earth units; Period = orbital period in days; a = semimajor axis in astronomical units (AU); e = orbital eccentricity; Teq = equilibrium temperature in Kelvin.

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As it turns out, Kepler-62e is just the grown-up name for KOI 701.03, which I discussed three months ago in a posting titled Earth 2. Back then, available data indicated a slightly smaller radius and a slightly lower Teq, making 701.03 one of my favorite candidates for a second Earth. The new data make it less attractive, but they compensate by yielding the unexpected planets 62c  –  a Hot Mars!  – and 62f, our likeliest habitable Super Earth.

Table 1 and Figure 2 summarize the system architecture, which is very interesting. We see five low-mass planets orbiting in a region that is equivalent, temperature-wise, to the Solar System inside the orbit of Mars. Four out of five planets must be less massive than 10 Mea (as constrained by their radii and thermal environment), while the largest planet (62d) has an upper mass limit of 14 Mea.

The orbits of the three inner planets are closely packed within a semimajor axis of 0.12 astronomical units (AU). Among low-mass planets, this configuration is already quite familiar. If 62e and 62f had not been observed in transit, the reduced three-planet system would look much like a dozen other confirmed Kepler systems with two or three planets.

Given their small radii and high Teq, the two inner planets must be rocky. Kepler-62b is probably about 2.5 Mea; it is also hot, desolate, and probably airless. Kepler-62c is a new example of the growing class of extrasolar subterrestrials: similar in diameter to Mars, and probably similar in mass also. We can imagine it as an enlarged Mercury, slightly cooler but just as inhospitable.

Kepler-62d is more difficult to assess. With a very modest hydrogen/helium atmosphere, it could be as lightweight as 4 Mea, although this model is disfavored by Borucki et al. With a composition equivalent to Earth, it would reach its upper limit of 14 Mea. More likely is a mass somewhere between these extremes, with a structure that includes a water layer above a core of rock and metal, and possibly some contribution from hydrogen. 

Figure 2. Orbital architecture of the Kepler-62 system. Planets are shown at their relative sizes. 

The host star is a dim K2 dwarf with a mass of 0.69 Msol, a radius of 0.64 Rsol, an effective temperature of 4925 K, and a luminosity only 21% Solar. The star also has a remarkably low metallicity of -0.37 (all values Borucki et al. 2013). Although stellar enrichment in metals is strongly associated with the formation of gas giants like Jupiter and Saturn, recent findings by radial velocity and transit searches indicate that small rocky planets are likely around stars even less metallic than Kepler-62.

Although the orbits of 62e and 62f are similar in period and semimajor axis to those of Mercury and Venus, respectively, the low effective temperature of the host star means that their respective thermal environments are more reminiscent of Venus and Mars. Lisa Kaltenegger, one of the co-authors of the discovery paper, opined that Kepler-62e – the “Super Venus” – probably has temperatures “like Washington in May” (although she didn’t say whether she meant the balmy District of Columbia or the damp Northwestern state). However, if that planet’s atmosphere has significant greenhouse gases, it would be much hotter than any inhabited region of Earth, even DC in August.

For Kepler-62f, greenhouse gases would make the difference between a frigid environment with limited or nonexistent surface water and a truly biophilic ocean planet like Earth. Naturally, Kepler astronomers favor optimistic scenarios for both planets; Kaltenegger predicts “endless oceans.”

According to models published by Franck Selsis et al. (2007), planets orbiting within 0.5 AU of a K2 star like Kepler-62 will be tidally locked. This constraint applies to all of the system’s planets except for Kepler-62f, which is likely to have a rapid rotation like Earth, Mars, or Jupiter. Even if its hotter sibling, Kepler-62e, has a permanent dayside and nightside, life-friendly environments are still possible there under the right conditions.

As we have seen over the past decades, early exoplanetary data are always tentative, so that subsequent observations and analyses can shatter any rosy mind-picture we may have formed of this or that alien world. Nevertheless, enough solid evidence has now accumulated to demonstrate that Earthlike planets must orbit in the habitable zones of star systems across our Galaxy. And it looks increasingly likely that they can be found even in systems like Kepler-62, which bears no resemblance to home. At last, at last we can celebrate: we have a plausible candidate for Earth 2.

Figure 3. The Ace of Cups, signifier of joy, abundance, fertility, and nourishment

REFERENCES

Lissauer JJ, Jontof-Hutter D, Rowe JF, Fabrycky DC, Lopez ED, Agol E, et al. (2013) All six planets known to orbit Kepler-11 have low densities. In press: http://adsabs.harvard.edu/abs/2013arXiv1303.0227L   

Borucki WJ, Agol E, Fressin F, Kaltenegger L, Rowe J, Isaacson H, et al. (2013) Kepler-62: A Five-Planet System with Planets of 1.4 and 1.6 Earth Radii in the Habitable Zone. Science Express 18 April 2013. 10.1126/science.1234702 http://www.sciencemag.org/content/early/recent.
Selsis F, Kasting JF, Levrard B, Paillet J, Ribas I, and Delfosse X. (2007) Habitable planets around the star Gliese 581? Astronomy & Astrophysics 476, 1373-1387.
 

Kepler-11 Revisited

Figure 1. Configuration of the Kepler-11 system, based on new data. Planetary radii are represented at the same scale, with darker & bluer colors indicating higher density and lighter & greener colors indicating lower density. (Planet g is represented by an open circle because its radius is known but its density is not.) Semimajor axes are measured in astronomical units (AU).

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Metaphors such as “Rosetta stone,” “natural laboratory,” and “testbed” are overused in scientific discourse. For the Kepler-11 planetary system, however, they are completely appropriate. Six planets are known, all with radii measured by transit observations, and five with masses determined by transit timing variations. Their discovery was one of the highlights of 2011 (Lissauer et al. 2011), and their value for the study of planetary composition and system architecture remains unsurpassed. A new study by Kepler mission scientists, based on the much larger dataset resulting from continued observations, provides a revised view of this prototypical system (Lissauer et al. 2013).

Early findings demonstrated that Kepler-11 is a G-type star, similar to our Sun in mass, temperature, radius, and metallicity. The latest data point to a slightly closer resemblance. While the star’s mass and radius were previously reported as 0.95 and 1.1 Solar, respectively, cumulative observations have revised these values to 0.96 Solar masses (Msol) and 1.05 Solar radii (Rsol). Age remains the most striking difference between the two stars: Kepler-11 is somewhere in the range of 7 to 10 billion years, compared to 4.6 billion for our Sun. Nevertheless, Kepler-11 still looks youthful, without the enlargement in radius that develops as stars evolve off the main sequence.

The similarity between this star and our Sun makes the differences in their system architectures all the more striking. Five planets between the masses of Earth and Uranus orbit Kepler-11 inside a radius smaller than the semimajor axis of Mercury, while a sixth planet in the same mass range orbits just beyond. Initial data demonstrated that at least the inner five planets are much lower in density than Earth and Venus.

The revised data are presented in Table 1. Values for orbital period are unchanged, while values for semimajor axis differ only slightly. Orbital eccentricities, formerly unknown, can now be estimated. All are small, as expected: comparable to those of the Solar planets.
 

Table 1. Parameters of the planets around Kepler-11, based on the latest data from Lissauer et al. (2013). Mea = planet mass in Earth units; Rea = planet radius in Earth units; a = semimajor axis in astronomical units; Period = orbital period in days; e = orbital eccentricity.

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The biggest changes appear in the values for mass and radius, which are critical for understanding planet structure and formation. With one exception (Kepler-11d), values for these parameters have been revised downward. In two cases the reductions in mass are substantial – the inner planet, Kepler-11b, is less than half as massive as previously reported, while the second planet, Kepler-11c, is only about 20% as massive.

The five well-constrained planets (b-f) now seem to fall into two sub-populations: smaller planets with masses between 1.9 and 2.9 Earth masses (Mea) and radii between 1.8 and 2.9 Earth radii (Rea), and larger planets with masses above 6 Mea and radii above 3 Rea. Following a taxonomy that I outlined last year, I might be tempted to call the first group the true Super Earths (scaled-up versions of home) whereas I would call the second group gas dwarfs (planets less massive than ~40 Mea with hydrogen atmospheres, such as Uranus, Neptune, and GJ 436 b).

But that would be a mistake. It has always been clear that planets c through g have hydrogen envelopes, and the newly reduced mass of planet b raises the likelihood that it too supports such an atmosphere. (The alternative is a planet less than 50% rock and more than 50% steam.) Therefore, all the well-constrained companions of Kepler-11 now meet my definition of gas dwarfs, even though the heaviest is less than half as massive as Neptune, while the two lightest are only about twice the mass of Earth.

The revised parameters of Kepler-11 are persuasive evidence that the term Super Earth is a misnomer for all but a tiny fraction of the confirmed exoplanets with minimum or measured masses between 2 and 10 Mea.

Remarkably, the distribution of the Kepler-11 planets reveals few regularities in terms of mass, radius, or density. As Lissauer and colleagues observe, planet radii now appear to increase along with planet masses, a pattern that was obscured by the initial data and analyses (Lissauer et al. 2013). Nevertheless, masses and densities seem to be distributed at random: Kepler-11c orbits between 11b and 11d, but it is less dense (i.e., it has retained a larger fraction of hydrogen/helium) than either of its companions, while fluffy Kepler-11e is similarly flanked by denser 11d and 11f. Moreover, although the innermost planet in the system (b) is also the least massive – a typical architectural feature of multiplanet systems – it is almost identical in mass to the fifth planet (f).

Kepler-11 now looks a little more like Kepler-20, the only other system that hosts a comparable number of transiting planets with well-constrained masses. In both systems, low-mass planets are found adjacent to higher-mass planets, on exterior as well as interior orbits, and low-density planets are similarly intermixed with high-density planets. By contrast, our bizarre Solar System segregates its planet populations, with a handful of dense rocky planets in the inner system, a pair of gas giants in the middle system, and a pair of gas dwarfs in the outer system.

REFERENCES

Lissauer JJ, Fabrycky DC, Ford EB, Borucki WJ, Fressin F, Marcy GW, et al. (2011) A closely packed system of low-mass, low-density planets transiting Kepler-11. Nature 470, 53-58. Abstract: http://adsabs.harvard.edu/abs/2011Natur.470...53L

Lissauer JJ, Jontof-Hutter D, Rowe JF, Fabrycky DC, Lopez ED, Agol E, et al. (2012) All six planets known to orbit Kepler-11 have low densities. In press: http://adsabs.harvard.edu/abs/2013arXiv1303.0227L  

Lopez ED, Fortney J, Miller N. (2012) How thermal evolution and mass loss sculpt populations of super-Earths and sub-Neptunes: Application to the Kepler-11 system and beyond. Astrophysical Journal 761, 59. Abstract: http://adsabs.harvard.edu/abs/2012ApJ...761...59L

Migaszewski C, Slonina M, Gozdziewski K. (2012) A dynamical analysis of the Kepler-11 planetary system. Monthly Notices of the Royal Astronomical Society 427, 770-789. http://adsabs.harvard.edu/abs/2012MNRAS.427..770M

 

Subterrestrials

 Figure 1. Subterrestrial planets orbiting Sun-like stars, with the Earth included for comparison.

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Over the past few weeks, Kepler Mission scientists have reported two new transiting systems containing members of a tiny but growing extrasolar population: planets smaller than Earth, which I christen “subterrestrials” (Figure 1). Although objects of this size account for more than one-third of the planets and all of the spheroidal moons and dwarf planets in the Solar System, they represent only 2% of all transiting planets, and less than 1% of the vaguely defined census of confirmed exoplanets. (I say “vaguely” because the Extrasolar Planets Encyclopaedia currently lists 861 exoplanets discovered by all methods, but it omits some of the newest and smallest transiting subterrestrials. Qui peut dire pourquoi?)

The two newest systems are especially interesting (Figure 2). Kepler-68, the subject of a forthcoming article by Ronald Gilliland and colleagues, centers on a G-type star almost identical in mass to our Sun, although it is evidently older, hotter, and more bloated in radius. The star’s three companions define an inner system that includes two transiting low-mass planets (b and c) and an outer system that includes a single non-transiting gas giant (d) whose orbital period is about 580 days. Kepler-68 therefore meets my definition of a mixed-mass system. Still better, it joins the exclusive club of extrasolar systems that contain at least one gas giant and at least two low-mass planets (like our Solar System). Since most known mixed-mass systems (e.g., 55 Cancri, Mu Arae) contain only one low-mass planet, that club previously included just three members: GJ 876, HD 10180, and Kepler-30. Even with its enlarged membership, only two systems, HD 10180 and Kepler-68, present low-mass planets in adjacent orbits plus a gas giant on a wider orbit. This arrangement is one of the most distinctive features of the architecture of our Solar System.

Figure 2. Kepler-37 and Kepler 68, two new systems with subterrestrial and Super Earth planets, represented at the same scale. Orbital dimensions are measured in astronomical units (AU). Red lines mark the planets of Kepler-68; blue lines mark those of Kepler-37. Pink fill indicates rock/metal composition; purple indicates an additional water or hydrogen envelope, or both. Only one of these objects has an estimated mass: Kepler-68b, at 8.3 Earth masses (Mea). Kepler-68 also harbors a third planet, a Jupiter-mass giant with a semimajor axis of 1.4 AU, similar to the orbit of Mars.

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Nevertheless, it was the second new subterrestrial system that got all the headlines: Kepler-37, announced in Nature (Barclay et al. 2013), featured in Wikipedia news, and reported in global media outlets ranging from the Los Angeles Times to the Malaysia Chronicle. The system’s primary appears to be a K-type star whose mass is 80% of Solar (0.80 Msol). Three low-mass planets have been detected, all transiting and all confined within an astrocentric radius of 0.21 astronomical units (AU). The international flood of headlines originated in the fact that Kepler-37b is the smallest exoplanet yet detected (der kleinste Exoplanet! il più piccolo esopianeta!) – so small that it barely exceeds the diameter of the Earth’s Moon. Its characterization represents a new frontier in exoplanetary astronomy.

With these additions we now have at least seven subterrestrial exoplanets, orbiting in four different Kepler multiplanet systems (Table 1). Their host stars include a very small M dwarf, Kepler-42, which is similar in mass to GJ 1214 and Barnard’s Star; a K-type star, Kepler-37; a G-type star, Kepler-20, which is similar in metallicity to our Sun but less massive by 9%; and a more massive and metal-rich G-type star, Kepler-68. The range of masses and metallicities represented by this group implies that low-mass rocky planets like those in our Solar System are common in the Milky Way Galaxy, whether in habitable orbits or not. 

Table 1. All confirmed subterrestrial exoplanets. Column 2 lists the planet radius in Earth units (Rea); column 3, the orbital period in days; column 4, the semimajor axis in AU; column 5, the estimated equilibrium temperature in Kelvin; column 6, the distance of the star in parsecs; column 7, the stellar metallicity; column 8, the stellar mass in Solar units (Msol); and column 9, the stellar radius in Solar units (Rsol).

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With their high equilibrium temperatures and small radii, most or all of the objects in Table 1 must be rocky. Planets so lightweight have difficulty retaining volatiles; they cannot sustain hydrogen envelopes. Most, if not all, are also too warm to retain ices. They may be cousins of Mercury, which after all is one of the Earth’s siblings.

Another potential subterrestrial object, KIC 12557548 b, has been interpreted as a solitary companion to a K-type star of 0.70 Msol located about 470 parsecs away (Rappaport et al. 2012). The star exhibits unusual transits at intervals of less than 16 hours: regular in period but irregular in depth. Two studies have explained this behavior as the signature of a low-mass rocky planet undergoing catastrophic disintegration (Rappaport et al. 2012, Perez-Becker & Chiang 2013). In these models, the disintegrating planet is less massive than Mars. Successive transits vary in depth because the planet constantly sheds a cloud of dust that streams after it like a comet’s tail. As the cloud disperses semi-chaotically, it varies in size, and the area of the star occulted during each transit varies along with it. Perez-Becker & Chiang detail a scenario in which the planet was originally similar to Mercury (0.06 Mea) but by now has lost 80% of its mass, so that it is as lightweight as the Moon. At the implied rate of loss, this object will disappear completely within 100 million years. Given its peculiar physical status, I don’t include it in my personal census of subterrestrials.

The emergence of this new subpopulation of small planets adds substantially to our understanding of the likely distribution of Earth-like planets in the Galaxy. We now know that low-mass planets can range continuously from less than the mass of Mercury to twice the mass of Uranus. They occur preferentially alongside similar planets, so that a single system (e.g., Kepler-20 or Kepler-68) can harbor both rocky terrestrial planets (like Venus) and more massive gas dwarfs (like Uranus) in close proximity. Unfortunately, the known terrestrials and subterrestrials are still confined to short-period orbits, with very few detected on orbits longer than 100 days. Further collection and analysis of Kepler data should correct at least some of that bias.

REFERENCES

Barclay T, Rowe JF, Lissauer JJ, Huber D, Fressin F, Howell SB, and 58 others. (2013) A sub-Mercury-sized exoplanet. Nature 494, 452-454.

Gilliland RL, Marcy GW, Rowe JF, Rogers L, Torres G, Fressin F, and 27 others. (2013) Kepler-68: Three planets, one with a density between that of Earth and ice giants. Astrophysical Journal, in press.

Perez-Becker D, Chiang E. (2013) Catastrophic evaporation of rocky planets. Monthly Notices of the Royal Astronomical Society, in press.

Rappaport S, Levine A, Chiang E, El Mellah I, Jenkins J, Kalomeni B, Kotson M, Nelson L, Rousseau-Nepton L, Tran K. (2012) Possible disintegrating short-period Super-Mercury orbiting KIC 12557548. (2012) Astrophysical Journal 752, 1.