Blocking Starlight Much Closer to Home 2: This Year’s Pluto Occultation

Today’s blog is by guest blogger Dr. Jay Pasachoff. Jay is Chair of the International Astronomical Union’s Working Group on Eclipses and is Field Memorial Professor of Astronomy at Williams College. He has viewed 61 solar eclipses, and is an expert on both their use for scientific observations and their use for public education. Jay has has written and several astronomy books including the Field Guide to the Stars and Planets and the textbook The Cosmos: Astronomy in the New Millennium. He last provided a blog post about occultations of stars by Pluto in 2011, about a different way of planetary bodies blocking out star light that’s a little closer to home than the exoplanet transits normally discussed in this blog. He’ll be discussing what we can learn from studying dwarf-planet Pluto blocking out (or occulting) the light from distant background stars and relating it to the forthcoming flyby of Pluto by a NASA spacecraft.

As I write, NASA’s New Horizons spacecraft gets closer to Pluto after a 9 year journey. Soon it will give images BTH: Better than Hubble. Already, it is imaging all five known moons of Pluto (http://pluto.jhuapl.edu).

For the last dozen years, my colleagues, students, and I from Williams College have been working with MIT colleagues to observe Neptune’s moon Triton, Pluto, and Charon occult stars–usually stars ranging from 14th to 17th magnitude. The starlight comes into the solar system as parallel light, so the path on Earth from which the occultation is visible is the same width as the occulting object: about 2400 km wide for Pluto and half that for Charon. Our various occultations observed are discussed at a website I set up at http://stellaroccultations.info.

Our group now extends to include Bryce Babcock and me at Williams College; Michael Person, Amanda Bosh, and Carlos Zuluaga at MIT; Amanda Gulbis at the South African Astronomical Observatory; and Stephen Levine at Lowell Observatory, as well as students and others. Carlos posts the MIT group’s latest predictions at http://occult.mit.edu.

I last blogged about our work at the time of a double Pluto/Charon occultation in 2011, which our group observed from several telescopes in Hawaii as well as from the SOFIA aircraft. Our recently published papers that resulted are as follows:

Gulbis, A. A. S., J. P. Emery, M. J. Person, A. S. Bosh, C. A. Zuluaga, J. M. Pasachoff, and B. A. Babcock, 2015, “Observations of the same-day 2011 stellar occultation by Charon and graze by Pluto,” Icarus 246, 226-236. DOI: 10.1016/j.icarus.2014.05.014

Bosh, A. S., M. J. Person, S. E. Levine, C. A. Zuluaga, A. M. Zangari, A. A. S. Gulbis, G. Schaefer, E. W. Dunham, B. A. Babcock, A. B. Davis, J. M. Pasachoff, P. Rojo, E. Servajean, F. Förster, T. Oswalt, D. Batcheldor, D. Bell, P. Bird, D. Fey, T. Fulwider, E. Geisert, D. Hastings, C. Keuhler, T. Mizusawa, P. Solenski, B. Watson, 2015, “The State of Pluto’s Atmosphere in 2013,” Icarus 246, 237-246. http://dx.doi.org/10.1016/j.icarus.2014.03.048

For the ten minutes or so nearest to the occultation for ground-based telescopes, the object and the star appear merged, and we detect the occultation by the light curve. For Charon, with no atmosphere (and our occultation method is very sensitive), the starlight disappears abruptly. If the star is brighter than the occulting object, the occultation is quite noticeable; if the star is fainter, then just a percentage is subtracted from the total. For Pluto (and, earlier, for Triton), its atmosphere bends and distorts the starlight, and the ingress and egress are slanted on the light curve. These ingresses and egresses can last a minute or so with a central occultation of five minutes or so, depending on the relative speed of Pluto with respect to the star.

Astronomical circumstances currently put most of the occultations visible mainly in the southern hemisphere. Last year, in late July 2014, my student Adam Schiff ’15 (Keck Northeast Astronomy Consortium, from Middlebury College), Robert Lucas from Sydney, and I observed from the Mt. John University Observatory of Canterbury University, New Zealand. The observatory is about a 3-hour drive west of Christchurch. We were helped especially by the observatory’s superintendent, Alan Gilmore. Even though the UCAC star catalogue’s values of 15th magnitude for the occulted stars were high by about two magnitudes, we succeeded in observing two occultations by Pluto out of the three we tried. While we were there, we had heard from Wes Fraser of the Herzberg Institute of Astrophysics, Canada (who I knew from when we were both in Mike Brown’s group at Caltech a few years ago) about a prospective occultation by the KBO Quaoar, and also from NZ occultation coordinator David Herald about a prospective occultation by Pluto’s tiny moon Nix; we have flat light curves for both of them–that is, no occultation shadow passed over our site. One needs a dense picket fence of telescopes plus a lot of luck to capture occultations of such small objects. While we were there, we had coordinated observations from Amanda Gulbis with the 4-m telescope on Siding Spring, Australia, and with David Osip on the 6.5-m Clay, Stephen Levine on the 4.1-m SOAR, and Mike Person on the 2.5-m DuPont telescopes in Chile but they, unfortunately, had clouds for the most part.

After our observing run was over in New Zealand, there was another event in Chile, with an especially bright star for us, 12th magnitude. But clouds came in 90 seconds before the predicted ingress. Still, our colleagues noted on the light curve a 2% dip just before the clouds came. Was it from a ring around Pluto? Was it from a hitherto unknown moon of Pluto? It turned out that it was from a previously unknown 15th magnitude star lurking in the Airy disk of the 12th magnitude star, as our colleagues soon confirmed with Keck AO. It was clearly much less exciting to discover a 15th magnitude star than to find a ring around Pluto or to discover a moon. Anyway, we have the light curve of an occultation by that 15th magnitude star, which was the typical brightness of our occultation stars that we were observing anyway. We are about to submit a paper to the Astronomical Journal about our results.

It is important to search in the Pluto system ahead of and behind Pluto itself, since the New Horizons spacecraft’s radio signals are so weak that it will take 18 months or so after the July 14, 2015, flyby to send back all the data (from about 40 au; at 8 light minutes per au, it takes over 5 hours to get signals back at all). So if the spacecraft is killed at flyby by running into a ring particle or other dust, then most of the data–even from closest approach–would be lost. Our earlier occultation observations provided some limits on the dust content, and were among many pieces of evidence considered by the New Horizons team at Southwest Research Institute, headed by Alan Stern, in targeting their spacecraft.

We actually don’t know exactly how big Pluto is, because its lower atmosphere is opaque to starlight during occultations. It could be from haze in the lower atmosphere or thermal inversion. Eris, on the other hand, is so far out that its atmosphere has frozen and snowed onto the surface. We therefore now know from occultation studies by the Bruno Sicardy group from Paris just how big Eris is, and it turns out to be near the lower end of the possible range of Pluto’s size. Would the IAU have reclassified Pluto as a dwarf planet in 2006 if Pluto hadn’t been thought to be smaller than Eris? (It is certainly less massive, since each has at least one moon that has provided an accurate mass value.) Would NASA have launched a spacecraft to Pluto if it hadn’t been thought to be the 9th, and the only unvisited, planet?

We have a prediction this year for the occultation of a 12th magnitude star from the region of New Zealand, and perhaps the lower half of Australia. (http://occult.mit.edu/research/occultations/Pluto/P20150629) If you can observe from the centerline, you might get a central flash from focusing of the starlight all around Pluto–as we once got (with much luck) from Hubble. With this desirable possibility in mind, NASA’s SOFIA (Stratospheric Observatory for Infrared Astronomy) will fly out of Christchurch, with Mike Person from our group on board. Amanda Bosh will be in Flagstaff, coordinating last-minute updates to the astrometry. Bryce Babcock and I will be at Mt. John, with our Williams College undergraduates Rebecca Durst ’17 and Christina Seeger ’16; Alan Gilmore will continue to assist us, even though he has retired. This time, we have not only the 1-m telescope but also an adjacent 0.6-m telescope, for which Stephen Levine will bring down an infrared camera from our Williams College alumnus Henry Roe who is now at the Lowell Observatory. We even have arranged with a Japanese group who use a second 0.6-m telescope to get three-color photometry from it, unless they have an urgent need for it as part of their gravitational-lensing program. Amanda Gulbis will be observing from a different location in New Zealand, to give us a different chord. The Southwest Research Institute (SwRI), especially Leslie Young and Eliot Young, have also arranged observations from telescopes around Australia and New Zealand, just as we are coordinating with other telescopes besides those at Mt. John. The Bruno Sicardy group from Paris also has its own prediction.

It could be particularly important and interesting to be observing so close to the July 14 flyby by New Horizons, since then we can compare results taken at a comparable state of Pluto’s atmosphere. The atmosphere of Pluto, far from snowing out by now even though it passed perihelion in 1989, had warmed slightly and had increased pressure by the time of our 2002 observations, and has since leveled off. There will certainly be enough atmosphere for New Horizons to observe, which had not been clear a dozen years ago. It must start cooling at some point, as Pluto recedes from the Sun. We hope to calibrate our atmospheric models with the new size of Pluto we will get from New Horizons, and to follow Pluto’s atmosphere as it continues to evolve.

Our occultation work at Williams College has been sponsored by grants from NASA’s Planetary Sciences Division, most recently NNX12AJ29G.

13 May 2015

ExoWorld Naming Suggestion Posted!!

Thank you to everyone who has participated up to this point! The votes have been counted and Planet Hunters has submitted the following naming suggestion to the IAU ExoWorld naming contest:

  • PSR 1257 12: Photo – Photo is the Greek word for light. Since it is a pulsar that releases two beams of light, Photo would be suitable as a name that emphasizes the beams of light the pulsar emits.
  • PSR 1257 12b: Lofío – Since b is the least massive exoplanet ever discovered, the Greek word for a plume fits. Naming the least dense exoplanet after a feather honestly seems suitable.
  • PSR 1257 12c: Xekiní̱ste – Since this is one of the first exoplanets discovered, the Greek word for start fits. This name signifies the start of a new era in finding planets outside of our solar system.
  • PSR 1257 12d: Amydrós – Since it is the outermost planet in the system, it has the longest orbit; it blocks the light beams the most. So for that reason, the Greek word for dim fits, as it dims out the pulsar beams the most.

A hardy congratulations to Trent Crespo is in order. It was his name that was decided on by this community to put forward!

Our work is not done though – shortly in June 2015 a sign-up window will open for individuals to register to vote for the IAU naming selection. Watch http://www.nameexoworlds.org/#signup for this window to open!

Exoworld Naming Vote – Last Day!

This is it, the last day to vote on the name that Planet Hunters will submit in the IAU Name that Exoworld project. So don’t delay and vote now!!

http://www.planethunters.org/#/vote

ExoWorld Naming Vote – Final Days!

The group has done a fantastic job voting so far! For the final days of this vote, I have narrowed down the list of options to the top 4! This four options had greater than 10% of the vote. The voting page has been updated once again and we are asking you to select one naming suggestion for us to move forward to the IAU. If you voted previously, you can vote again. Voting for this round will be ended on May 15, 2015, so please vote promptly!

Voting Link:

http://www.planethunters.org/#/vote

Exoplanet Naming Round 3!

On April 16, 2015, the gavel was slapped on round 2. The naming suggestions were reviewed by Planet Hunter moderators for conformance to the IAU criteria and in all the community had generated 33 naming suggestions that appear to conform. Now it is time for round 3! The voting page has been updated once again and we are asking you to select one naming suggestion for us to move forward to the IAU. Voting for this round will be ended on May 15, 2015, so please vote promptly!

Voting Link:

http://www.planethunters.org/#/vote

 

Planet Naming Suggestion Form Open!

In the blog post earlier today, I reported that phase 1 was complete – the IAU (International Astronomical Union) has selected the stars to be named. Phase 2 involves groups providing naming suggestions for the star and all attached planets. The “Vote” button has been updated with a new form to begin taking these suggestions from Planet Hunters! Please provide your naming suggestion by April 16, 2015.

After April 16, 2015, the Planet Hunter’s moderators will review the suggestions for conformance to the stated guidelines for naming suggestions and a poll will be set up for us to select our one naming suggestion that will be put up. So start your suggesting!

 

Proposed names should be:

  • 16 characters or less in length.
  • Preferably one word.
  •  Pronounceable (in some language)
  • Non-offensive
  • Not too similar to an existing name of an astronomical object. Names already assigned to astronomical objects can be checked using the links http://cds.u-strasbg.fr/cgi-bin/sesame (for galactic and extragalactic names), and the MPC database http://www.minorplanetcenter.net/db_search (for names)

In addition it is not allowed to propose:

  • Names of pet animals.
  • Names of a purely or principally commercial nature.
  • Names of individuals, places or events principally known for political, military or religious activities.
  • Names of living individuals.
  • Only names that are not protected by trademarks or other forms of intellectual property claims may be proposed.

ExoWorld Selection Complete – Next Up, Obtaining Name Suggestions!

As you are likely aware, Planet Hunters is taking part in an IAU (International Astronomical Union) project to name several ExoWorlds. A few months back we provided the IAU a list of ExoWorlds which we thought should be named. The IAU took this list, plus all of the lists provided by other groups and determined which ExoWorlds will be named. In total, 15 stars and 32 planets will be named. The list:

 

 

Host Star (catalogue) # Planet (designation) Planet Mass (Jupiter mass) Planet Mass (Earth mass) Orbital Period (day) Semi Major Axis (au) Discovery (year) Constellation (English) Visibility V magnitude
1 exoplanet (5 systems)
Ain (epsilon Tauri) epsilon Tauri b 7.6 2415.5 594.9 1.93 2007 the Bull Visible to the naked eye 3.5
Edasich (iota Draconis) iota Draconis b 8.82 2803.3 510.7 1.275 2002 the Dragon Visible to the naked eye 3.3
Errai (gamma Cephei) gamma Cephei b 1.85 588 903.3 2.05 2003 the King Visible to the naked eye 3.2
Fomalhaut (alpha Piscis Austrini) Fomalhaut b 3 953.5 320000 115 2008 the Southern Fish Visible to the naked eye 1.2
Pollux (beta Geminorum) beta Geminorum b 2.9 921.7 589.64 1.69 2006 the Twins Visible to the naked eye 1.2
1 star + 1 exoplanet (10 systems)
14 Andromedae 14 Andromedae b 5.33 1694 185.84 0.83 2008 the Chained Maiden Visible to the naked eye 5.2
18 Delphinis 18 Delphinis b 10.3 3273.6 993.3 2.6 2008 the Dolphin Faint to the naked eye 5.5
42 Draconis 42 Draconis b 3.88 1233.2 479.1 1.19 2008 the Dragon Visible to the naked eye 4.8
51 Pegasi 51 Pegasi b 0.47 148.7 4.23 0.052 1995 the Winged Horse Visible to the naked eye 5.5
epsilon Eridani epsilon Eridani b 1.55 492.6 2502 3.39 2000 the River Visible to the naked eye 3.7
HD 104985 HD 104985 b 6.3 2002.3 198.2 0.78 2003 the Giraffe Faint to the naked eye 5.8
HD 149026 HD 149026 b 0.36 113.1 2.88 0.04288 2005 the Hercules Visible through binocular 8.2
HD 81688 HD 81688 b 2.7 858.1 184.02 0.81 2008 the Great Bear Visible to the naked eye 5.4
ksi Aquilae ksi Aquilae b 2.8 889.9 136.75 0.68 2008 the Eagle Visible to the naked eye 4.7
tau Bootis tau Bootis b 5.9 1875.2 3.31 0.046 1996 the Herdsman Visible to the naked eye 4.5
1 star + 2 exoplanets (1 system)
47 Ursae Majoris
47 Ursae Majoris b 2.53 804.1 1078 2.1 1996 the Great Bear Visible to the naked eye 5.1
47 Ursae Majoris c 0.54 171.6 2391 3.6 2001 the Great Bear Visible to the naked eye 5.1
1 star + 3 exoplanets (2 systems)
PSR 1257 12
PSR 1257 12 b 7.00E-05 0.022 25.26 0.19 1992 the Maiden
PSR 1257 12 c 0.01 4.1 66.54 0.36 1992 the Maiden
PSR 1257 12 d 0.01 3.8 98.21 0.46 1992 the Maiden
upsilon Andromedae
upsilon Andromedae b 0.62 197.1 4.62 0.059 1996 the Chained Maiden Visible to the naked eye 4.1
upsilon Andromedae c 1.8 572.1 237.7 0.861 1999 the Chained Maiden Visible to the naked eye 4.1
upsilon Andromedae d 10.19 3238.7 1302.61 2.55 1999 the Chained Maiden Visible to the naked eye 4.1
1 star + 4 exoplanets (1 system)
mu Arae
mu Arae b 1.68 532.7 643.25 1.5 2000 the Altar Visible to the naked eye 5.2
mu Arae c 0.03 10.6 9.64 0.09094 2004 the Altar Visible to the naked eye 5.2
mu Arae d 0.52 165.9 310.55 0.921 2004 the Altar Visible to the naked eye 5.2
mu Arae e 1.81 576.5 4205.8 5.235 2006 the Altar Visible to the naked eye 5.2
1 star + 5 exoplanets (1 system)
55 Cancri
55 Cancri b 0.8 254.3 14.65 0.1134 1996 the Crab Faint to the naked eye 6
55 Cancri c 0.17 53.7 44.34 0.2403 2002 the Crab Faint to the naked eye 6
55 Cancri d 3.84 1218.9 5218 5.76 2002 the Crab Faint to the naked eye 6
55 Cancri e 0.03 8.3 0.74 0.0156 2004 the Crab Faint to the naked eye 6
55 Cancri f 0.14 45.8 260.7 0.781 2007 the Crab Faint to the naked eye 6

 

At this point, Planet Hunters can submit one naming suggestion. A suggestion consists of the name for one star, all attached planets and the basis for this recommendation. We are working to set up a Google form to select submissions and then we will have a round of voting to select the candidate to be submitted. This will all take place prior to May 31, 2015.

Extracted Lightcurves From Vanderburg & Johnson (2014) Now Available at MAST

epic_201363707

A new MAST High Level Science Product from K2 has been delivered that includes extracted lightcurves. Courtesy of Vanderburg & Johnson (2014), long-cadence targets from Campaigns 0 and 1 now have detrended, extracted lightcurves available at MAST, including 20 different photometric apertures. There’s a MAST Classic Search Interface so you can get lightcurves based on target IDs, coordinates, EPIC catalog fluxes, etc. You can also use our interactive plotter to explore the lightcurves using any of the photometric apertures before downloading the FITS files. Check out all the details here: http://archive.stsci.edu/prepds/k2sff/

Name That ExoWorld!!

This is exciting! The International Astronomical Union (IAU) is working Zooniverse, astronomical clubs and the public at large to name some number of exoworlds and host stars. Some of the work has already been done, some work is yet to do. The exciting part is that Planet Hunters will be assisting in some of the next steps! Let’s break down their milestones:

  • July 2014: IAU compiled a list of 305 exoworlds confirmed prior to December 31, 2008 as candidates for naming.
  • October 2014: The IAU opened http://www.nameexoworlds.org to permit astronomy organizations to register to take part. Planet Hunters completed this and was confirmed!
  • January 2015: Planet Hunters, along with other clubs, will vote for the ExoWorlds they wish to name out of the list provided by the IAU.
  • February 2015: Planet Hunters, along with other clubs, will send in proposals for the names of members of these selected ExoWorlds (including the host star), based on the rules in the IAU Exoplanet Naming Theme, together with a detailed supporting argument for their choice. Each group is allowed to name only one ExoWorld. More details on this stage will be given later.
  • June 2015: the general public votes to rank the proposed names.
  • July 2015: the IAU, via its Executive Committee Working Group on the Public Naming of Planets and Planetary Satellites, oversees the final stages of the contest, and validates the winning names from the vote.
  • 3–14 August 2015: the results are announced at a special public ceremony held during the IAU XXIX General Assembly in Honolulu, USA

We are in the January 2015 milestone. You may have noticed that there is a new “Vote” button on the Planet Hunters classification ribbon. This button takes you to a poll which has been set up to collect Planet Hunter community input. We want your participation! So let’s name an ExoWorld!!!

A Recipe for Making a K2 Light Curve

Today we have a post by Andrew Vanderburg. Andrew is a graduate student at Harvard University who works on producing and correcting K2 light curves and searching them for planets. He recently joined the Planet Hunters team to provide K2 light curves for classification.

As readers of this blog are probably well aware, the K2 mission is an exciting new opportunity for the Kepler spacecraft to continue searching for exoplanets, even after the failure of two reaction wheels ended the original Kepler mission. Making K2 work is in several ways more complicated than Kepler, and previous posts have already discussed how Kepler is stabilized by balancing against solar radiation and pointing itself opposite the sun in the ecliptic plane. Even with this very clever strategy for data collection, getting high quality data from K2 is not straightforward.

Once it became clear in early 2014 that Kepler would be able to continue gathering data, one of the biggest uncertainties about the K2 mission was: “How well can Kepler measure photometry in this new operating mode?” If Kepler’s worsened ability to point itself degrades the quality of its data, it may be harder for the K2 mission to accomplish its goals of finding exoplanets in new environments and around different types of stars. When the Kepler team released data from a 9 day engineering test of the new operation mode taken in February 2014, we attempted to answer that question.

keplervsk2

Hot Jupiter light curves from Kepler (red, bottom) and K2 (blue, top). K2 data is dominated by jagged noise that was not present during the original Kepler mission.

After four years of being spoiled by ultra-high-quality photometry from Kepler, our first look at the K2 data came as a bit of a shock. Unlike the pristine Kepler data, K2 data (shown compared to Kepler in the first image) had wild jagged features contaminating the light curve, which made it hard to see all but the deepest planet transits. In order to continue searching for small planets in the K2 mission, something would have to be done to improve the quality of the photometry.

We started out by trying to figure out what was causing the jagged features in K2 data. Since nothing had changed with the spacecraft other than the reaction wheel failure, it was a pretty good bet that the jagged noise was due to the decreased stability of the spacecraft. We checked to see if this was the case by measuring the apparently position of stars in the images Kepler took (shown in the second image), and comparing them to the measured brightness.

Screen Shot 2015-01-07 at 4.03.59 PM

Measured brightness and image position versus time (Vanderburg & Johnson 2014). The jagged noise in K2 data is caused by the spacecraft’s jittery pointing.

 

The top panel shows the brightness of one particular star called EPIC 60021426 over the course of a week of the engineering test, and the bottom two panels show the horizontal and vertical position of the star, as seen by Kepler, over the same time period. It turns out that just like a cell phone video taken by a person with shaky hands, the images Kepler took were jittering back and forth. And more importantly, the jagged pattern in the location of the star in the image looked very much like the pattern seen in the brightness data.

We concluded that the additional noise in the data was caused by Kepler moving back and forth ever so slightly as it rolled due to a slight imbalance between the spacecraft and the Solar wind. Every six hours or so, Kepler’s thrusters fired to bring the telescope back to its original position. But the most important thing we concluded was that the additional noise in K2 data is very predictable. If the noise is predictable, then it’s correctable.
The third image shows the brightness of a particular star (once again, EPIC 60021426) measured by K2 on the vertical axis, and the position of the star on the horizontal axis. The blue dots indicate brightness measurements during normal K2 operations, and they form a tight relation with the image position. The jagged noise in K2 data depends only on where the image falls on the Kepler camera. With this realization, it’s simple to draw a line through the points (the orange line in the image), and divide it away. The red points are points taken while Kepler’s thrusters were firing, and don’t fit the pattern of the rest of the points. We simply throw them out.

flatfield-1

Measured brightness versus image position (Vanderburg & Johnson 2014). The jagged noise is very predictable, and depends only on where the star is located in the Kepler images.

After dividing the orange line from the data and removing points taken during thruster fires, we are left with a “corrected” light curve. The fourth image shows the result of the correction. The top light curve (blue) shows the raw, uncorrected K2 data, and the bottom, orange light curve shows the corrected K2 data. The correction substantially improves the quality of the K2 data.

f5

K2 light curve of EPIC 60021426 (Vanderburg & Johnson 2014). The correction improves the quality of the data by a factor of 5 in this case.

This type of processing improves the precision of K2 to where it’s close to that of Kepler — within a factor of two for most stars. This makes it possible to detect small planets, even when the planetary signals are much smaller than the jagged variations removed by this process. We discovered the first K2 exoplanet, HIP 116454, using this exact technique, and the one transit we found was totally obscured in the raw K2 data (as shown in the fifth image).

sfflc

Raw and corrected K2 light curve of HIP 116454 (Vanderburg et al. 2014), also known as EPIC 60021410. Without removing the jagged noise from the K2 light curve, this transit would be totally undetectable.

Even now, however, this process is not perfect, and we’re still working to make it better. There are quite frequently glitches and other errors that affect the light curves and make it difficult for computer algorithms to pick out all of the transit signals. Trained human eyes like yours will be crucial for picking out all of the exciting exoplanets that K2 will observe.

 

 

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