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(Sub)millimeter Astronomy with Single-Dish Telescopes

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(Sub)millimeter Astronomy with Single-Dish Telescopes Now and in the Future Karl M. Menten (Max-Planck-Institut f r Radioastronomie) The LSST, a telescope ... – PowerPoint PPT presentation

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Title: (Sub)millimeter Astronomy with Single-Dish Telescopes


1
(Sub)millimeter Astronomy with Single-Dish
Telescopes Now and in the Future
Karl M. Menten (Max-Planck-Institut für
Radioastronomie)
2
  • Submillimeter Astronomy Major science drivers
  • The cosmological submm background the star
    formation history of the universe at high z
  • Structure and energetics of molecular clouds
  • Star and planetary system formation
  • Astrochemistry
  • the Solar System

3
  • Single dish vs. interferometer?
  • Basic facts
  • (If you can calibrate your phases) an
    interferometer is much better to detect faint
    (point-like) sources
  • Single dish observations are necessary to
    provide short- spacing information
  • Bolometer arrays will become very large
    (thousands of elements)
  • Many dozen times the collecting area of ALMA
    and, thus, very much faster if noise not
    dominated by systematics (atmosphere) and if
    the confusion limit is not reached
  • Heterodyne arrays will have 100 elements at 3
    and 2 mm and dozens at submm wavelengths

4
  • Advantages of array receivers
  • Mapping speed
  • Mapping homogeneity (map lage areas with similar
    weather conditions/elevation) ? minimize
    calibration uncertainties.

5
Bolometer arrays have completely dominated the
field of submillimeter continuum observations for
20 years now
The power of (bolometer) array science
The Galactic Center Region as seen by SCUBA at
850 ?m
Talks by Borys, Glenn, Greaves, Johnstone,
Kauffmann Posters by Aguirre, Carpenter, Dowell,
Li, Sutzki, et al.
6
The sub-mm Extragalactic Background resolved
Hughes et al. 1998
7
Bolometer arrays are getting ever larger
yesterday very soon
2006?
In addition MAMBO-II, Bolocam, SHARC-II,
8
The HDF-North SCUBA Super-map
850 ?m
  • 12 x 12 (14 FWHM)
  • rms 1 4 mJy
  • 16 sources gt 4 ?
  • 15 sources between 3.5 and ? lt 4
  • at 450 ?m 5 sources gt 4?

Obviously still far from confusion limit
9
Cumulative Number Counts deg-2
Confusion limit ist 0.7 mJy (3?) at 850 ?m. To
cover 1 square degree with 5120 bolometers with
100 mJy s-1/2 takes 40 hours.
10
ALMA will be crucial to get positions accurate
enough for optical spectroscopy (? redshifts),
maybe even determine redshifts on its
own. Accurate position determinations via VLA are
currently a bottleneck, as each source requires
many hours of observing time. and no VLA for
the southern hemisphere. Spitzer positions might
save the day!
11
  • Fundamental innovations in bolometer
    technology/observing
  • Superconducting bolometers
  • Superconducting TES (Transition Edge Sensors)
    thermistors
  • SQUID multiplexer integrated with the bolometers
    on the wafer
  • SQUID readout amplifier
  • Much reduced complexity, greater sensitivity
  • Much larger bolometers possible

12
  • Fundamental innovations in bolometer
    technology/observing
  • Fast scanning ( no chopping)
  • Made possible by changes in read-out electronics
    (DC- biased/AC- coupled ? AC-biased/DC-coupled)
  • DC-coupled electronics allow much faster
    scanning (scanning speed was limited by 2 Hz
    chopper frequency)
  • No chopper means
  • faithful imaging of large structures
  • free choice of scan direction
  • less complexity
  • new observing modes
  • Technique successfully used at SHARC-II/CSO

13
  • Bolometer array sizes will ultimately ( soon) be
    limited by the field of view of the telescope.
  • SCUBAII will completely fill its.
  • Possible solutions
  • Telescopes dedicated to large RX array
    operation?
  • e.g. off-axis antenna/modified Gregorian design
    (South Pole Telescope see http//astro.uchicago
    .edu/cara/research/decadal/decadal-submm.pdf
  • (p. 33 ff)
  • Radically new, different optics designs possible?

14
The LSST, a telescope designed for a 3 field
8.4 m diameter f/1.25
Cryostat window diameter 1.28 m
Not feasible for radio astronomy ? huge sidelobes
cryostat
http//www.lsst.org/lsst_home.shtml
15
APEX Cassegrain optics
?N. Halverson/E. Kreysa
16
Heterodyne arrays are becoming available just now
HERA HEterodyne Receiver Array
17
Common sense requirements
Schuster et al. 2004 http//iram.fr/IRAMES/telesco
pe/HERA/
  • Important
  • Uniform beams
  • Uniform TRX
  • and
  • TRX not much worse than TRX of
    state-of-the-art single pixel RX

18
Factor 160 in resolution!
Ungerechts Thaddeus 1987
Schuster et al. 2004
19
  • 16 elements
  • 325 375 GHz
  • 14" FWHM

http//www.mrao.cam.ac.uk/projects/harp/
20
CHAMP Carbon Heterodyne Array of the MPIfR
  • 7 pixels
  • frequency range 602 720 and
    790 950
    simultaneously
  • beamsize 9" 7" and 7" 6"
  • IF band 4 8 GHz

http//www.mpifr-bonn.mpg.de/div/mm/tech/het.html
champ http//www.strw.leidenuniv.nl/champ/
21
Common sense requirements for any array RX
  • Important
  • Uniform beams
  • Uniform TRX
  • and
  • TRX not much worse than TRX of
    state-of-the-art single pixel RX

All of the above superbly met by MMIC array
spectrographs!
22
  • focal plane array 44 pattern.
  • currently mounted on the FCRAO
    14m telescope
  • Will be moved to the LMT
  • fixed tuning gt best performance at all
    frequencies
  • being expanded to 32 elements
  • InP MMIC pre-amplifiers 35-40 dB gain band
  • (Tsys50 80 K)
  • instantaneous bandwidth 15 GHz (85 115.6 GHz
    with only two local oscillator
    settings)

http//www.astro.umass.edu/fcrao/instrumentation/
sequoia/seq.html
23
W-band (80 116 GHz) Science with MMIC Array
Spectrographs (MASs) Apart from CO J1-0 lines
there are ground- or near-ground-state
transitions of HCN, HNC, CN, N2H, HCO, CH3OH,
SiO all between 80 and 115 GHz Because of their
high dipole moments, these species trace high
density gas, n gt 104 cm-3 (? CO n gt 102
cm-3) Large-scale distribution of these molecules
on larger GMC scales poorly known Strong emission
in these lines, as well as in rare C18O isotope,
traces high column densities (? star
formation) These lines are very widespread (
everywhere) over the whole Galactic center region
(-0.50 lt l lt 20)
24
Other most interesting projects include complete
(mostly) 12CO and 13CO mapping of nearby
galaxies. These are HUGE (many square arc
minutes)! Such maps would be interesting in
their own right and are absolutely necessary as
zero spacing information for CARMA, the PdBI, and
ALMA. REALLY FANTASTIC would be MASs on CARMA
and the PdBI!!! and they would make these
facilities highly competitive in the ALMA era, as
ALMA will (probably) not have MASs for a very
long time.
25
Sensitivity
const ?1 for 8/10 bit sampling
? FFT spectrometers!
With the IRAM 30m telescope at 90 GHz it would
take 25/N hours to produce a Nyquist-sampled map
of area one square degree with an N element MAS
at an rms noise level of 0.2 K and a velocity
resolution of 1 km/s.
26
  • New Backend Option
  • Fast Fourier-Transform (FFT)-Spectrometers
  • Principle
  • Direct sampling of RX IF with
    8/10 bit resolution
  • Continuous FFT calculation with
    given window function
    (to suppress side
    lobes)
  • Calculation of power spectrum
  • Power spectrum averaging

27
  • Overwhelming advantages of FFT Spectrometers
  • ???? FPGAs Field-Programmable Gate Arrays
  • ADC with 8 or 10 bit sampling (ACs 2bit)
  • higher sensitivity, no need for total power
    detectors
  • Much higher dynamic range ? Leveling much
    simpler ? simplification of IF module
  • 100 mass production chips ? no custom made
    chips ? much better reacion to markets ? take
    full advantage of Moores law
  • very high channel numbers
  • Today 1 GHz/32768 channels
  • Soon (1 2 yrs) 2 GHz/65536 channels
  • Very high degree of integration Integration of
    a complete spectrometer(digital filters,
    windows, FFT, power builder and accumulator) of
    one chip (ACs use cascaded chips ?
  • can be re-programmed
  • much lower power consumption (more reliable)

?B. Klein
28
http//www.acquiris.com/
http//www.drao-ofr.hia-iha.nrc-cnrc.gc.ca/science
/jcmt_correlator/
FFTS
40 x 1 GHz (40 x 32768 channels) ?? 30 kHz ? ?v
0.03km/s_at_300 GHz
32 x 0.8 GHz (32 x 1024 channels) ?? 1 MHz ? ?v
1km/s_at_300 GHz
29
  • SEQUOIA is just the beginning
  • MMIC Array Spectrographs (MASs) will
  • soon (within a few years) have 100 elements
    and
  • somewhat later have many 100s of elements
  • Large MMIC FPAs currently being developed at JPL
    (PI Todd Gaier) driven by cosmology (T.
    Readhead)/space
  • (FFTS) backends will be available
  • With LOs integrated, MASs will revolutionize
    large areas of molecular line astronomy
  • Question Will HEMTs become competitive at
    shorter ???

30
  • Mapping speed and sensitivity estimates indicate
    that very large sections (if not all) of the
    Galactic plane can be imaged
  • HUGE advantage over SiS arrays Many lines in
    HEMT band can be imaged simultaneously
  • Necessary Spectrometer capability
  • Example W-Band
  • Want to do 20 lines simultaneously
  • need 300 km/s ( 100 MHz) each
  • Need N ? 20 ? 100 MHz N ? 2 GHz
  • 2 GHz FFTS bandwidth cost 40 kEU today/MUCH
    less next year
  • At todays prizes, an FFTS for a 100 element
    array would cost 4 MEU
  • HOWEVER Above is the de luxe correlator. To save
    money, could do fewer lines, use narrower
    bandwidths

Also Remember Moores Law!!!
Actually, FFTS prizes are falling hyper-Moore
these days Expect 3 kEU/GHz very soon
31
The same spectrometer serving a multi-element MAS
would also allow very wide band spectral line
surveys toward single positions
32
(Belloche, Comito, Hieret, Leurini, Menten,
Müller, Schilke)
3 mm region (70 116 GHz) in 500 MHz chunks 4000
5000 lines!!!!
With a HEMT RX this would have taken 2 LO
settings ? Factor 100 savings in observing time
33
  • FFT-Spectrometers
    Timeline and Perspectives
  • 2005/MPIfR Development of an FFT Spectrometer
    with
  • 16384 channels
  • 500 MHz bandwidth
  • SUCCESS Brought into operation at the 100m
    telescope (April 2005) and (1GHz/32768channels)
    at APEX (June 2005)!
  • ? FFTS Technology available today!

34
  • FFT Timeline Perspectives (cont'd)
  • 2005 2009
  • Doable today(!)
  • 3 GHz BW using three cascaded ADCs _at_ 2GS/s
    (10- bit) and
  • analog input BW of 3.3 GHz
  • FFT-Processing continuous 4 GS/s with 64.000
    channels in one high-end Xilinx-Chip
    (XILINX VII Pro70) (Study by
    RF-Engines).
  • Cost kEU 15 20 for 1 GHz BW (Hardware)
  • ca. 90 kEUR (one time only) for
    Xilinx-programming
  • Firm RF-Engines http//www.rfel.com/Newsev
    entsdetail.asp?ID68

35
  • Timeline Perspectives (cont'd)
  • gt 2009
  • Complexity of Xilinx chips doubles every 14 18
    months
  • ? Costs
  • Grow linearly with each RX element
  • Minimal serial production costs by simple
    reproduction of system

36
  • FFTSs and MASs
  • Synergy Pooling resources
  • FFTSs
  • Bernd Klein, MPIfR, bklein_at_mpifr-bonn.mpg.de
  • Collaboration with Arnold Benz (ETH
    Zürich/Acqiris)
  • Potential users for FFTSs and MASs
  • ( possible co-financers)
  • IRAM
  • APEX
  • LMT
  • Effelsberg 100m telescope
  • GBT
  • Madrid 40m telescope, Sardinia Telescope
  • ...

37
  • Submillimeter Facilities in the high Atacama
    desert
  • ASTE The Atacama Submillimeter Telescope
    Experiment
  • 10m
  • NAO Japan, Tokyo U., Osaka Prefecture U., U.
    Chile
  • http//www.alma.nrao.edu/library/alma99/abstra
    cts/sekimoto/sekimoto.pdf
  • ? Talk by H. Ezawa (next)
  • Nanten-2
  • 4m
  • Nagoya U., Osaka Prefecture U., Seoul National
    U., Cologne U., Bonn U., U. Chile
  • http//scorpius.phys.nagoya-u.ac.jp/workshop/kaw
    ai/NANTEN-2.html
  • http//www.ph1.uni-koeln.de/workgroups/astro_inst
    rumentation/nanten2/
  • APEX The Atacama Pathfinder Experiment

38
The APEX telescope
  • Built and operated by
  • Max-Planck-Institut fur Radioastronomie
  • Onsala Space Observatory
  • European Southern Observatory
  • on
  • Llano de Chajnantor (Chile)
  • Longitude 67 45 33.2 W
  • Latitude 23 00 20.7 S
  • Altitude 5098.0 m
  • ?12 m
  • ? 200 ?m 2 mm
  • 15 ?m rms surface accuracy
  • currently (June 2005) in final testing phase
  • First facility instruments
  • 345 GHz heterodyne RX
  • 295 element 870 ?m Large Apex Bolo- meter Camera
    (LABOCA)
  • http//www.mpifr-bonn.mpg.de/div/mm/apex/

39
Instrumentation
  • Bolometers
  • LABOCA-1 295-channel at 870 µm (MPIfR, Bochum
    U., IPHT Jena)
  • FOV 11', beam 18 (same as MSX and Herschel
    250µm)
  • 37-channel at 350 µm (MPIfR)
  • 324-channel at 1.4/2 mm for Sunyaev-Zel'dovich
    survey (UCB, MPIfR)
  • new software BoA (Python/F95) www.openboa.de
  • Heterodyne
  • 183 GHz water vapour radiometer
  • 210-270 GHz (OSO)
  • 270-375 GHz (OSO)
  • 375-500 GHz (OSO)
  • 460/810 GHz dual channel First Light Apex
    Submillimeter Heterdyne Rx (FLASH)
  • 800-900 GHz (MPIfR/SRON, PI)
  • CHAMP 600-720/790-920 GHz, 27-elements
    (MPIfR, PI)
  • FIR receivers up to 1.5 THz 200 micron (OSO,
    Köln)

40
  • Two Major Apex projects
  • APEX-SZ
  • A 870 ?m Survey of the Galactic plane

Concrete projects (Start Late 2005)
Concept
41
The Sunyaev-Zel'dovich Effect
today
Big Bang
0
379,000 yr z1089
14 Gyr
time
Zhang, Pen, Wang 2002
42
SZ differential surface brightness is independent
of redshift.
SZ
X
Carlstrom et al.
APEX beam at 2mm (40") BIMA beam at 1 cm
43
UCB/APEX SZ Array
http//bolo.berkeley.edu/apexsz/
14 cm
  • 1.4f? horns coupled array
  • 330 bolos in 6 wedges
  • Each TES bolometer coupled through resonant
    circuit to SQUID readout
  • direct path to Multiplexing
  • 150 GHz and 217 GHz by swapping horns filters

44
Simulations by M. White
45
The APEX Sunyaev-Zel'dovich Galaxy Cluster Survey
Basu Beelen Bertoldi/Co-PI Kreysa Menten Muders Sc
hilke Cho Dobbs Halverson Holzapfel Kermish Kneiss
l Lanting Lee/Co-PI Lueker Mehl Plagge Richards Sc
hwan Spieler White Sunyaev Böhringer Horellou
a collaboration between MPIfR and U.C. Berkeley
in association with RAIUB, MPE, MPA, OSO,
  • Discover and catalog several 1000 galaxy clusters
    in a mass limited survey map 200 deg2 to 10
    mK rms per 60" pixel.
  • Constrain cosmological parameters and dark energy
    equation of state, w.
  • SZ contribution of zgt10 Supernova-remnants.
  • Observe evolution of structure, and test theories
    of structure formation.
  • Study clusters in detail structure, evolution,
    galaxy populations.
  • Study CMB secondary anisotropies, weak lensing,
    Ostriker-Vishniac effect, quadratic Doppler
    effect, etc.

Zhang, Pen, Wang 2002
46
A Galactic Plane surveywith APEX
F. Schuller, K. M. Menten, P. Schilke, F.
Wyrowski Max Planck Institut für Radioastronomie
47
The APEX GalacticPlane surveySurvey definition
Sensitivity reach 1 Msun in nearby regions, and
a few 10 Msun in Galactic Center Gas mass in
cores using Hildebrand (1983) and standard
physical parameters, b2, Td50 K
Fn(870 mm) d200 pc d1 kpc d3 kpc d8.5 kpc
10 mJy 0.0033 0.083 0.75 6.0
30 mJy 0.010 0.25 2.25 18.0
50 mJy 0.017 0.42 3.75 30.1
100 mJy 0.033 0.83 7.5 60.2
48
The APEX GalacticPlane survey
  • Main goals
  • To have a complete census of high mass star
    formation in the Galaxy
  • To derive the protostellar IMF down to below 1
    Msol in a number of nearby regions
  • Proposed area to observe at 870 mm
  • -80 lt l lt 20 b lt 1
  • Northern part of the plane complementarity with
    SCUBA-2

49
The APEX GalacticPlane survey
  • Sensitivity one-s 10 mJy
  • 0.4 Msun detected at 5s at 1 kpc
  • 30 Msun detected at 5s in the Gal. Center
  • Some limited areas in a few southern star
    forming regions with higher sensitivity (well
    below 1 Msol)
  • Total observing time about 1000 hours

50
The APEX GalacticPlane survey
  • Instrumentation LABOCA (Large APEX BOlometer
    CAmera) 295 bolometers for observing at 870 mm
  • APEX beam at 870 mm
  • 18" MSX pixels Herschel at 250 mm

51
The APEX GalacticPlane surveyPossible extensions
  • Additional observations at shorter wavelengths
    a 37- channel array operating at 350 ?m will be
    available soon
  • complementary observations in selected regions
  • Polarimetry at all wavelengths
  • Additional observations at longer wavelengths
    use of the UC Berkeley SZ camera (1.4 and 2 mm)
    as a backup project well-suited for poor weather
    conditions ? dust emissivities (?s)
  • Great complementarity with Herschel GP surveys

52
APEX Timeline
Telescope ready 11 / 2003 Holography 5
/ 2004 1.2 mm Bolometer 5 / 2004 - first
light May 29 460/810 GHz Rx 6 /
2004 Holography 5 / 2005 Regular
operation 8? / 2005 LABOCA-1 12?
/ 2005 ASZCa ? / late 2005 CHAMP
? / fall 2005 350 micron bolometer ? /
2006 LABOCA-2 (TES technology) ?
15 ?m rms
53
Cornell Caltech Atacama Telescope
  • Joint project of Cornell and Caltech/JPL
  • New telescope for submillimeter astronomy
  • 25 m diameter not confusion limited in
    reasonable exposure
  • High aperture efficiency up to 200 µm wavelength
  • High, dry, low latitude site northern Chile (gt
    5000 m)
  • Field of view (gt 15') for large format bolometer
    arrays
  • 12 µm surface quality, closed loop active control
  • Feasibility study underway
  • Construction 2008 2012

CCAT Slides courtesy of S. Radford ? Poster
http//www.astro.cornell.edu/research/projects/ata
cama/
54
CCATDesign Concept
  • 25 m dia., 12 µm surf
  • RC optics, 20' FOV
  • Active primary surface
  • Panels large, stiff, kinematic mounts
  • Steel mirror truss
  • Nasmyth foci
  • Az Hydrostatic bearings
  • El Rolling elem. bearings
  • Calotte dome

55
(No Transcript)
56
http//safir.jpl.nasa.gov/
? Gary Melnicks talk
57
Dome C Concordia Station Altitude 3250 m
South pole 2300 m Dome A gt 4000 m
Could build large single dish plus interferometer
of arbitrary baseline length
http//www.concordiastation.org/
58
Thank You
59
Bonus Material
60
Lots of new entries for Glen Petitpas Dumb Or
Overly Forced Astronomical Acronyms Site (or
DOOFAAS) http//www.astro.umd.edu/petitpas/Links/
Astroacro.html
61
AC-coupling/DC-bias (old ) vs. DC-coupling vs.
AC-bias (new)
  • DC-bias (old)
  • simpler to implement
  • Amplifier have extra noise that rises with
    falling frequency (1/f). With a wobbler this is
    not a problem, because we have amplifiers with
    which 1/f noise only appears below the wobbler
    frequency (2Hz)
  • Downside is By wobbling, we do not modulate
    the total power at the input, therefore the
    total power is still affected by 1/f-noise.
  • Block DC part and let only AC part through
    (capacitor between bolo and preamp input ?
    throw away total power)
  • AC-bias (LABOCA)
  • get rid of 1/f noise
  • need phase sensitive detection at the bias
    frequency ? more complex to implement
  • Big advantage Retain total power ? maps
    contain all the structure
  • Other additional complexity Need to compensate
    any change of voltage at the input of the
    amplifier (atmospheric variations) by an
    opposing voltage between scans AND keep track
    of that voltage.
  • ? Solved at SHARC II/CSO

62
  • Solar system objects
  • size scales lt1 (moons, KBOs) to 1 (Jupiter)
  • best done with ALMA (except for nearby comets)
  • no array detector advantage

Matthews/Senay/Jewitt (JCMT)
63
3 mm region (70 116 GHz) in 500 MHz chunks 4000
5000 lines!!!!
With ALMA it will be possible to observe that
whole spectral range within 10 minutes to
confusion limit
64
  • To make any believable identification of a new
    species (e.g., glycine) in this jungle you need
    an interferometer.
  • Show that many lines from candidate species all
    arise from the same position with the correct
    relative intensities.
  • Usefulness of this approach was demonstrated by
    L. Snyder and collaborators using BIMA.

65
Spectral line emission in Orion-KL
? Henrik Beuthers talk
  • Toward source I mainly SiO
  • Sulphur-bearing species toward
  • Hot Core and Compact Ridge
  • Sulphur- and oxygen-bearing
  • species toward IRc6

Confusing picture Effects of chemistry and
excitation
  • Imaging helps to identify lines

Imaging helps!
  • Oxygen-bearing molecules
  • weaker toward Hot Core and
  • strong toward Compact Ridge
  • Nitrogen-bearing molecules
  • strong toward Hot Core

66
Above all You need to use an interferometer
  • To do science with (3D) line surveys one needs
    very advanced data analysis tools
  • Automatic line identification and information
    extraction (fluxes, velocities)
  • requires up-tp-date living molecular
    spectroscopy database
  • LTE analysis
  • ? maps of N(X), Trot
  • non-LTE analysis (LVG/Monte Carlo least sqares
    method see Leurini et al. 2004 for CH3OH)
  • ? maps of n, Tkin, X/H2
  • Fit dynamical models

67
  • K-band-Science (18 26 GHz)
  • For temperature and column density determinations
    ideal Ammonia (NH3)
  • Multiple K-band lines (23.6 25 GHz) that can
    be done simultaneously
  • and
  • simultaneously with 22.2 GHz H2O maser line
  • and
  • simultaneously with 25 GHz series of CH3OH lines
    (maser and thermal)
  • K-band RX array would be VERY interesting!

68
Mapping speed (1 square degree)
  • rms(1 sec) 0.2 K at 90 GHz
  • IRAM 30m
  • 24 FWHM_at_90 GHz
  • Positions to observe for a Nyquist-sampled map of
    1 square degree
  • 90000
  • Time needed for a map with an N pixel array
  • 25/N hours

69
Current and future SZ surveys
name type beam telescope clusters
when arcmin m ACBAR Bolo 4
few ? Bolocam Bolo 151 1 10 10s
? SuZIE Bolo 1 10 ?
1997 BIMA HEMT few
2001 CBI HEMT 13 4 0.9 ? ? SZA HEMT 8 0.1
3.5 ? 2005? AMiBA HEMT 19 2 1.2
100s 2006 AMI HEMT 10 1 3.7 100s
2006 APEX Bolo 325 0.75 12 1,000s
2006 ACT Bolo 1000 1 6 1,000s
2007 Bolocam-2 Bolo 0.2 40 ?
2007? SPT Bolo 1000 1 8 20,000
2007 Planck Bolo 5 2 10,000 2008
Compilation F. Bertoldi
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