Kepler, K2 and TRAPPIST-1

[furrysocks2]

I was interested by the TRAPPIST-1 announcement last month and in particular the science behind it, the analysis of light curves.

Source: https://www.eso.org/public/images/eso1706e/

 

One of my own goals is to observe and record one or more asteroidal occultations which is more of a binary observation than the photometery involved in the study of exoplanets, but related I suppose. I happened across an article today announcing that raw Kepler data is being made available and with renewed interest, fancied having a play.

I'd only heard of Kepler before and thought I'd post a brief summary of my background research here.

Kepler is a 0.95m, 94.6 megapixel telescope (https://en.wikipedia.org/wiki/Kepler_(spacecraft)).

 

Quote

Kepler: A search for Earth-like planets around Sun-like stars

The Kepler spacecraft launched in March 2009 and spent a little over four years monitoring more than 150,000 stars in the Cygnus-Lyra region... The primary science objective of the Kepler mission was transit-driven exoplanet detection with an emphasis on terrestrial (R < 2.5 REarth) planets located within the habitable zones of Sun-like stars.

Kepler exceeded its nominal mission lifetime of three years and continued operating for an additional year as an extended mission. Between the nominal and extended missions, Kepler has discovered thousands of transiting planets and revealed that small planets are abundant in the Galaxy.

Source: https://keplerscience.arc.nasa.gov/objectives.html

 

Failure of a second reaction wheel (https://en.wikipedia.org/wiki/Reaction_wheel) in May 2013 brought and end to the above. It now operates only in the ecliptic plane (https://en.wikipedia.org/wiki/Ecliptic) which minimises the effect of the solar wind to work around the hardware failures. Kepler is now dedicated to a community-driven mission (K2) whereby targets are proposed by the community and campaigns are limited to approximately 80 days.

Quote

K2: Extending Kepler's power to the ecliptic

... the K2 mission represents a new concept for spacecraft operations that enables continued scientific observations with the Kepler space telescope. K2 became fully operational in June 2014 and is expected to continue operating until 2017 or 2018.

The K2 mission entails a series of sequential observing "Campaigns" of fields distributed around the ecliptic plane and offers a photometric precision approaching that of the original Kepler mission. 

Source: https://keplerscience.arc.nasa.gov/objectives.html

The NASA press conference last month announced the discovery of seven planets within the "habitable zone" of another star (https://www.nasa.gov/press-release/nasa-telescope-reveals-largest-batch-of-earth-size-habitable-zone-planets-around). The star, TRAPPIST-1, is an ultra-cool drawf star in the constellation of Aquarius. (https://en.wikipedia.org/wiki/TRAPPIST-1). Three planets had previously been found in 2015 using the Transiting Planets and Planetesimals Small Telescope (TRAPPIST), the following four having been more recently revealed by NASA's Spitzer Space Telescope, setting a new record for greatest number of habitable-zone planets found around a single star outside our solar system.

 

Kepler remains pointed on a single field for the duration of each 80-odd day K2 campaign. The most recent Campaign 12 (Dec 2016 - Mar 2017) has included TRAPPIST-1.

Source: https://keplerscience.arc.nasa.gov/k2-fields.html, modified by me.

 

Source: https://github.com/KeplerGO/k2-footprint-plots/blob/master/k2-c12-field.png

 

The release tomorrow consists of "raw cadence data" from Campaign 12 for TRAPPIST-1. All I've done so far is downloaded some software and a couple of files from Campaign 9 and ran a couple of commands. If I am going to have a play with the data, I should probably go and understand exactly what "cadence" means in this context.

 

Thanks for reading, hope this may be of interest to someone.

[furrysocks2]

This post is for reference, just feeling my way...

 

Cadence

Quote

the frequency with which summed data are read out of the SDA. Short cadence is a 1-minute sum while long cadence is a 30-minute sum.

Source: http://archive.stsci.edu/kepler/manuals/archive_manual.pdf

 

Raw cadence data files

Quote

... provides the pixel counts in that cadence for all those pixels which were pre-selected to be downlinked from the spacecraft (roughly 3% of the 95-megapixel camera).

Source: https://github.com/KeplerGO/kadenza/blob/master/README.md

 

Pixel mapping reference files (PMRFs)

Quote

... these files provide the key to identifying which data values in a given cadence data set belong to which targets.

Source: http://archive.stsci.edu/kepler/manuals/archive_manual.pdf

 

Quote

... specifies the (column, row) CCD coordinates for each value in the one-dimensional cadence data arrays.

Source: https://github.com/KeplerGO/kadenza/blob/master/README.md

 

Target pixel file (TPF)

Quote

... a file that contains the individual data values for each pixel for each cadence. 

Source: http://archive.stsci.edu/kepler/manuals/archive_manual.pdf

 

Quote

Each row in the table contains timestamps, photometric measurements, astrometric measurements and data quality flags.

Source: https://keplergo.arc.nasa.gov/DataAnalysisTargetPixels.shtml

 

Kepler documentation

• Kepler Archive Manual - http://archive.stsci.edu/kepler/manuals/archive_manual.pdf
• Kepler Data Processing Handbook - http://archive.stsci.edu/kepler/manuals/KSCI-19081-001_Data_Processing_Handbook.pdf
• Kepler Data Characteristics Handbook - http://archive.stsci.edu/kepler/manuals/Data_Characteristics.pdf
• Format Information for Cadence Pixel Files - http://archive.stsci.edu/k2/manuals/KADN-26315.pdf

 

Software

• Kadenza - https://github.com/KeplerGO/kadenza
• KeplerFFI - https://keplergo.arc.nasa.gov/ContributedSoftwareKeplerFFI.shtml
• DS9 - http://ds9.si.edu/site/Home.html
• https://keplergo.arc.nasa.gov/DataAnalysisTools.shtml

 

Other

• Calculating Exoplanet Properties - https://www.sfu.ca/colloquium/PDC_Top/astrobiology/discovering-exoplanets/calculating-exoplanet-properties.html
• PyFITS Documentation - http://www.sal.wisc.edu/~khn/salt/Outgoing/documentation/PySALT/The_PyFITS_Handbook.pdf
• Finding exoplanets: the Transit technique - http://zuserver2.star.ucl.ac.uk/~ingo/Lecture_Notes_files/lect11.pdf

[furrysocks2]

Nothing to do with TRAPPIST-1, just having a play...

 

Every so often (twice per campaign), a full frame image (FFI) is retrieved from Kepler, where every pixel of a single long cadence is read out.

From http://archive.stsci.edu/missions/k2/ffi/, I downloaded a single file (389 MB), loaded it with DS9, changed scale to log and this is the result.

 

Having spotted a fuzzy and manually identified it as NGC 4674 in Stellarium by its RA/Dec coordinates, Astrometry.net gave me this:

 

Although I perhaps cropped it slightly when taking the screenshot, Astrometry.net gives the field center at 191.316, -8.269, which matches up nicely with the center of one of the 84 channels.

Source: https://github.com/KeplerGO/k2-footprint-plots/blob/master/k2-c10-field.png, modified by me.

 

From the web, I was able to identify that modules 3 and 7 had failed by this point and therefore that the image I have is channel 1 (module 2).

Source: http://archive.stsci.edu/kepler/manuals/archive_manual.htm, modified by me.

 

To view each individual channel in DS9, I used the menu option: File > Open as > Multiple Extension Frames... (see https://keplergo.arc.nasa.gov/DataAnalysisInspectionFFI.shtml) fv does show 84 channels although crashes on me with a buffer overflow trying to display any of them.

Browsing through the other channels in DS9, Astrometry.net identified NGC 4593 in 8.4 (channel 24), a barred spiral galaxy in Virgo, 124M light years away. Zoomed in DS9, screenshot and adjusted levels in GIMP (alternatively, you can hold the right mouse button over the image in DS9 and move the mouse left and right to adjust contrast):

 

Interesting, but ultimately it's not FFIs that I'm interested in.

[furrysocks2]

Despite it being off-topic, I still wanted to view/reconstruct a full frame image - DS9 will only show each channel individually.

I started with fits2bitmap, which requires matplotlib. I used the following command to create 84 bitmap files:

for i in `seq 1 84`
do
	fits2bitmap -e $i --stretch log -o $i.bmp <FFI_filename>
done

 

Using the layout diagram in the previous post, I initially tried manually reassembling sensor 2 (channels 1-4) in GIMP but haven't verified if each tile is correctly oriented:

 

Instead, I want to automate cropping and layout. Each bitmap is 1132 x 1070 pixels. 

Quote

Each channel has 1132 columns and 1070 rows.

There are 1100 science columns enumerated as columns 12 through 1111.  Collateral data is enumerated as columns 0 through 11.  Columns 1112 through 1131 are virtual columns used to measure electronic bias levels.

There are 1024 science rows enumerated as rows 20 through 1043.  Collateral data is enumerated as rows 0 through 19 and 1044 through 1069.

Source: http://archive.stsci.edu/kepler/manuals/archive_manual.htm

 

To crop, I used imagemagick (convert):

for i in `seq 1 84`
do
	fits2bitmap -e $i --stretch log -o $i.bmp <FFI_filename>
	convert -colorspace Gray -crop 1100x1024+12+20 +repage $i.bmp $i.png
done

Two and half minutes later, 389MB is down to 8.7MB.

I used "montage" to generate a very quick composite image and then over-stretched in GIMP - obviously not correctly laid out nor even in order:

There are 8 channels that no longer contain data due to sensor module failures, and some have very bright stars in the field of view. However, layout before balance.

 

First I wrote a small C++ program and hand-coded two datastructures (two dimensional arrays), which I could then iterate over to give me the following output:

	---	---	---		
 | 	---	---	 | 	 | 	
 | 	 | 	 | 	 | 	 | 	
 | 	 | 	---	---	 | 	
	---	---	---	

		4	3	8	7	12	11			
		1	2	5	6	9	10			
15	14	20	19	24	23	25	28	29	32	
16	13	17	18	21	22	26	27	30	31	
35	34	39	38	43	42	45	48	49	52	
36	33	40	37	44	41	46	47	50	51	
55	54	59	58	62	61	66	65	69	72	
56	53	60	57	63	64	67	68	70	71	
		74	73	78	77	82	81			
		75	76	79	80	83	84			

The first is the sensor module orientation, the second is the layout of channels. My understanding from the layout diagram in the previous post is that the orientation of the channels depends on its position on a given module, so I can pre-process the individual bitmaps, independent of the layout stage.

For now, I wish to construct a single image with each tile in the appropriate location.

 

By altering the code that generated the output above to instead output HTML, I was able to screengrab a webpage containing a table of the tile images:

Quick for a first attempt. Note that the gaps between tiles is not at all faithful.

 

To normalise the brightness of the tiles, I simply added "--min_cut 2" to the fits2bitmap command and visually it's much better.

 

I found a Campaign 10 FFI through google, and modified it to give the image below:

Source: https://www.nasa.gov/sites/default/files/styles/full_width/public/thumbnails/image/k2-c10-failed_modules-labels.jpeg?itok=klMmsSrP, modified by me.

This lets me compare against my own, to determine visually which tiles need flipped or rotated, which I've tallied against the sensor layout and orientation diagram I posted earlier. The mapping is straightforward... horizontal and vertical sensors, each yielding 2x2 channels, each have their own patterns of rotation and or reflection.

Using my C++ code and datastructures, I used the rotation/reflection mapping for each 2x2 block and generated the following sequence of commands...

convert -flop 3.png 3.png
convert -flop 7.png 7.png
convert -flop 11.png 11.png
convert -flip 1.png 1.png
convert -flop -flip 2.png 2.png
convert -flip 5.png 5.png
convert -flop -flip 6.png 6.png
convert -flip 9.png 9.png
convert -flop -flip 10.png 10.png
convert -rotate 90 -flop 15.png 15.png
convert -rotate 90 14.png 14.png
convert -flop 19.png 19.png
convert -flop 23.png 23.png
convert -rotate 90 -flop 25.png 25.png
convert -rotate 90 28.png 28.png
convert -rotate 90 -flop 29.png 29.png
...

Now the orientation of the tiles in the HTML render appears to match the FFI I found online:

 

Imagemagick has a tool called "composite" that only works with two files at a time, but I've modified the C++ code to place each channel tile onto a blank canvas.

convert -size XXXXXxYYYYY xc:black composite.png
composite -geometry +XXXX+0 4.png composite.png composite.png
composite -geometry +XXXX+0 3.png composite.png composite.png
composite -geometry +XXXX+YYYY 1.png composite.png composite.png
composite -geometry +XXXX+YYYY 2.png composite.png composite.png
...

It's going to take a wee while to tweak the positions to get the spacing correct.

A good test of my script will be to take another FFI from another campaign and render the whole field in one go.

 

(I'm sure there will be a tool available to do this already, but I didn't readily find it so here I am.)

[furrysocks2]

Fudged the spacings in code - a two line fix but it takes a good while to run.

So I downsampled and manually cut and pasted, stretched and here it is, my first Kepler full field image at 1/2 resolution...

Solved:

 

 

[furrysocks2]

The Campaign 12 data has now been released.

 

Quote

TRAPPIST-1 was observed using a 11x11 short-cadence mask with EPIC ID 200164267 from Dec 15th, 2016, through Mar 4th, 2017. To help the community explore this target, the Guest Observer Office reformatted the raw data into a pseudo Target Pixel Files using the Kadenza tool.

Source: https://keplerscience.arc.nasa.gov/raw-data-for-k2-campaign-12-and-trappist-1-now-available.html

There are caveats which I don't full understand, but it's something to play with.

 

The raw cadence files are here - https://archive.stsci.edu/pub/k2/c12_raw_cadence_data/. Using the script I developed today to render FFI, I took a stab...

kadenza-ffi kplr2016350204148_scs-targ.fits ../pmrfs/kplr2016314003001-090-090_scm.fits
compose_ffi.sh ./sparse_cadence_ffi_raw.fits

 

Black was an poor choice of colour for the composite background, so I took a mask from another FFI for this, and downscaled. I believe I have marked in red the targets listed on the campaign 12 footprint plot - I'm not 100% this is what I think it is, though... TRAPPIST-1 appears to me too close to the edge of its subframe to be centered in 11x11.

Source: https://github.com/KeplerGO/k2-footprint-plots/blob/master/k2-c12-field.png

 

The announcement post linked above cites the k2flix tool (http://barentsen.github.io/k2flix/). With this and the pseudo TPF file also made available, I've created an animated gif showing an hour and a half or so worth of short cadence data (of nearly three months worth)...

k2flix --ut --fps 10 --dpi 20 --step 1 --start 0 --stop 100 k2-trappist1-unofficial-tpf-short-cadence.fits.gz

 

I hope to have a chance to play with some light curves over the next few days.

[furrysocks2]

A few links re: processing:

Quote

The community has made iPython notebooks available that show how to analyze the TRAPPIST1 raw data release.

• Tom Barclay has created an iPython notebook that demonstrates how to create a quicklook light curve using the pseudo-TPF file.
• Jim Davenport has created an iPython notebook that demonstrates how to search for flares using the short cadence pseudo-TPF file. Includes an initial plot of flare rate as a function of duration!
• Benjamin Pope has created an iPython notebook that demonstrates how to create quick-look short and long cadence light curves.

Source: http://archive.stsci.edu/k2/trappist1/

 

Also, a comment on the same page by Andrew Vanderburg links to a "processed and roll-systematics-removed quick-look long-cadence light curve" - https://www.cfa.harvard.edu/~avanderb/trappist1lc.txt

 

[furrysocks2]

Using Tom Barclay's python code as a starting point, an overview of the pseudo TPFs:

~/K2/c12/mrtommyb/trappist-lc $ ./TRAPPIST-1-transit-code.py ../../k2-trappist1-unofficial-tpf-long-cadence.fits
3599 cadences
pixel mask is (11, 11)
~/K2/c12/mrtommyb/trappist-lc $ ./TRAPPIST-1-transit-code.py ../../k2-trappist1-unofficial-tpf-short-cadence.fits
107968 cadences
pixel mask is (11, 11)
majp@moth ~/K2/c12/mrtommyb/trappist-lc $ 

 

Later in his script, using the long cadence data, three plots are generated:

Quote

lets make some plots

• undetrended light curve
• undetrended and the detrending model of the spots [it's a silly median filter]
• final product

Source: https://github.com/mrtommyb/trappist-lc/blob/master/TRAPPIST-1-transit-code.ipynb

 

After this, the data used to plot the third is saved off into a CSV file, which I've graphed here:

And the first 200 points only:

 

Continuing with his script, the planets are modelled based on this data. My results (first column) are close, but not identical to his:

Planet 0
--------
impact          0.5788222878	0.6621764957	
period          1.5109560382	1.5110095181	0.0035%
T0              7322.4911295	7322.47509808	
rprs            0.0905966784	0.0939323244	
			
Planet 1
--------
impact          0.6040065365	0.6389695202	
period          2.4218960537	2.4219412999	0.0019%
T0              7282.78981588	7282.78051711	
rprs            0.0974216208	0.097827176	
			
Planet 2
--------
impact          -0.3391178663	-0.0035611957	
period          4.0504570437	4.0502947595	-0.0040%
T0              7670.12866035	7670.13210989	
rprs            0.0647747732	0.0618048291	
			
Planet 3
--------
impact          0.5226553153	0.5869507443	
period          6.0995287285	6.0995098181	-0.0003%
T0              7660.37048634	7660.37109219	
rprs            0.0747846706	0.0757751546	
			
Planet 4
--------
impact          0.3814110999	0.4490460861	
period          9.2078787079	9.2079228576	0.0005%
T0              7671.36108154	7671.3607597	
rprs            0.0735907859	0.0739321437	
			
Planet 5
--------
impact          0.7690563264	0.7954852762	
period          12.3544362537	12.3545208344	0.0007%
T0              7665.35565404	7665.35474277	
rprs            0.0970050102	0.0982995763	

 

 

Taking the mass of TRAPPIST-1 as 0.08 ± 0.009 (source: https://en.wikipedia.org/wiki/TRAPPIST-1), and the following constants with Kepler's third law, I've tried calculating the orbital distances of the six planets.

• AU - 149597870700
• Solar Mass - 1.99E+30
• G - 6.674E-011

The periods and distances all appear to be consistent with published figures.

[furrysocks2]

The planetary characteristics in the previous post (see ktransit) give a value "rprs", which I understand to be a ratio of planetary radius to stellar radius. I plotted these against the my orbital distances for a visual representation:

A very quick comparison with published data suggests the fifth planet shown here appears smaller than perhaps it should, but otherwise not too dissimilar.

Taking planetary sizes and the radius of TRAPPIST-1 from https://en.wikipedia.org/wiki/TRAPPIST-1 and the rprs values from above, I can estimate planetary size and compare with the published planetary sizes:

• Solar radius - 6.96E+008
• Earth radius - 6371000
• TRAPPIST-1 radius - 0.114 ± 0.006

 

An interesting comparison might be to use Andrew Vanderburg's data (https://www.cfa.harvard.edu/~avanderb/trappist1lc.txt) to re-model the planets.

[furrysocks2]

I removed the header line and trailing "," from https://www.cfa.harvard.edu/~avanderb/trappist1lc.txt and ran the following:

my_data = genfromtxt('trappist1lc.txt', delimiter=',')

t1 = numpy.array([i[0] for i in my_data])
cfflux = numpy.array([i[2]-1. for i in my_data])

print ('Number of samples: ' + str(len(cfflux)))
print ('Duration: ' + str(t1[-1]-t1[0]) + ' days')

time, flux, fitT = transit_fit(t1, cfflux)
fitT.print_results()

 

Some small differences between this data set and the previous, but consistently out for planets c, f and g.

Another interesting comparison might be to use the calibrated data set in a few months time, or the short cadence data available now.

[furrysocks2]

On 08/03/2017 at 23:46, furrysocks2 said:

TRAPPIST-1 appears to me too close to the edge of its subframe to be centered in 11x11.

Looking back at channel 68 from my sparse full frame composite, I can see that there is indeed an 11x11 mask, 2 pixels from the edge of frame. I mistakenly made the above comment based on a downscaled image.

However, it could have been worse:

[furrysocks2]

The short cadence pseudo TPF file contains 107968 cadences and crashes before generating the CSV.

I wrote a small python script to extract a range of samples from a TPF file:

low = int(sys.argv[2])
high = int(sys.argv[3])

f = pyfits.open(sys.argv[1])

tbhdu = pyfits.BinTableHDU.from_columns(
        [pyfits.Column(name='TIME', format='E', array=f[1].data['TIME'][low:high]),
         pyfits.Column(name='FLUX', format='121E', dim='(11,11)', array=f[1].data['FLUX'][low:high,:])])

tbhdu.writeto(sys.argv[1][:-5] + '.' + str(low) + '-' + str(high) + '.fits', overwrite=True)

Then I ran a bash loop to split the full short cadence data into several 1000-sample files:

for i in `seq 0 1000 100000`
do
	../../software/tpf_subset.py ./k2-trappist1-unofficial-tpf-short-cadence.fits $i `echo "$i + 999" | bc`
done

For each new fits file, a csv is generated:

for i in *0-*fits
do
	echo $i
	../mrtommyb/trappist-lc/TRAPPIST-1-transit-code.py $i
done | tee log.txt

These CSV files are then concatenated and re-sorted by time, yielding 95518 samples:

cat *.csv | sort > all.csv.tmp; mv all.csv.tmp all.csv

These were then graphed, and run through modelling:

~/K2/c12/short-cadence-concat $ ../../software/model_planets/model_planets.py ./all.csv 
Number of samples: 95518
Duration: 74.1635742188 days

 

The results gave generally smaller sizes for the planets than before. Without understanding the consequences, I found one reference to cadence length in one of the scripts and replaced a value (0.0188) with 0.000244 and re-ran.

Below the results are from the following runs:

• A - raw long cadence data
• B - Vanderburg's long cadence data
• C - short cadence data
• D - short cadence data w/ 0.000244

 

Assuming false results, I imagine that by splitting the TPF and processing in chunks as I did (to work around the script crashing), I may have compressed the dynamic range or something of that nature such that the transit dips are less deep which I expect would then result in smaller sizes as seen here.

 

... by chunking the file into 10000-sample files instead of 1000 and recombining, the planet sizes are moving back in the right direction, so I suspect the full file does need to be processed in one go for best results... but for the crash.

[furrysocks2]

Quote

Make a Kepler orrery gif or movie of all the Kepler multi-planet systems

Source: https://github.com/ethankruse/kepler_orrery

I went to http://exoplanetarchive.ipac.caltech.edu/cgi-bin/TblView/nph-tblView?app=ExoTbls&config=planets and handcrafted a table for the TRAPPIST-1 planets as input to Ethan's script, as they don't appear in the file provided and I wanted to generate an animation of TRAPPIST-1, only. I then realised that only six of the columns are read in, and of those, five I could have populated myself.

I fiddled with the script to remove planet and temperature scale, limit number of frames, change resolution, date, duration, etc... just a bit of fun.

Edit: updated animation based on confirmed orbital period of planet h

[furrysocks2]

On 07/03/2017 at 20:24, furrysocks2 said:

[Kepler] now operates only in the ecliptic plane which minimises the effect of the solar wind to work around the hardware failures.

 

It's actually rather clever, using the pressure of the solar wind to stabilise the craft in one axis...

Quote

Using the sun and the two remaining reaction wheels, engineers have devised an innovative technique to stabilize and control the spacecraft in all three directions of motion.

To achieve the necessary stability, the orientation of the spacecraft must be nearly parallel to its orbital path around the sun, which is slightly offset from the ecliptic, the orbital plane of Earth.

Source: https://www.nasa.gov/kepler/keplers-second-light-how-k2-will-work

[furrysocks2]

Confirmation of planet h:

Quote

We conduct three separate transit searches on the long cadence light curve, aiming to constrain the period of planet h, which had only been observed to transit once. ...

A dynamical analysis made by our team prior to the release of the K2 data suggested that certain discrete values of the period could be expected if h were in a three-body Laplace resonance with planets f and g. ...

... a single value of the period (18.765 d) corresponds to additional transit times in windows that were missed by all previous observational campaigns.

...

To test this hypothesis, in our first transit search we simply fold the long cadence light curve at the four expected times of transit given this 3 period and the single Spitzer transit time, finding evidence for a transiting planet at that period. Follow-up with detrended short cadence data confirms the transit-like shape of each of the four events and a depth consistent with that of h.

Source: https://arxiv.org/abs/1703.04166