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Problems and Challenges in the mm/submm. Effect of atmosphere on data: Tsys Mean Refraction Phase fluctuations Correction techniques Other facility considerations UV-coverage / Dynamic range Mosaicing. Column Density as a Function of Altitude. Constituents of Atmospheric Opacity.
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Effect of atmosphere on data: • Tsys • Mean Refraction • Phase fluctuations • Correction techniques • Other facility considerations • UV-coverage / Dynamic range • Mosaicing
Column Density as a Function of Altitude Constituents of Atmospheric Opacity Due to the troposphere (lowest layer of atmosphere): h < 10 km Temperature with altitude: clouds & convection can be significant Dry Constituents of the troposphere:, O2, O3, CO2, Ne, He, Ar, Kr, CH4, N2, H2 H2O: abundance is highly variable but is < 1% in mass, mostly in the form of water vapor “Hydrosols” (i.e. water droplets in the form of clouds and fog) also add a considerable contribution when present Stratosphere Troposphere
At 1.3cm most opacity comes from H2O vapor • At 7mm biggest contribution from dry constituents • At 3mm both components are significant • “hydrosols” i.e. water droplets (not shown) can also add significantly to the opacity total optical depth optical depth due to H2O vapor Optical Depth as a Function of Frequency optical depth due to dry air 43 GHz 7mm Q band 100 GHz 3mm MUSTANG 22 GHz 1.3cm K band ALMA
soTnoise≈Trx +Tatm(1-e-t) Receiver temperature Emission from atmosphere • Consider the signal-to-noise ratio: • S / N = (Tsource e-t) / Tnoise = Tsource / (Tnoise et) • Tsys= Tnoise et ≈Tatm(et -1) + Trxet Tnoise≈ Trx+ Tsky whereTsky =Tatm (1 – e-t)+ Tbge-t Tatm = temperature of the atmosphere ≈ 300 K Tbg = 3 K cosmic background For a perfect antenna, ignoring spillover and efficiencies Sensitivity: System noise temperature Before entering atmosphere the source signalS= Tsource After attenuation by atmosphere the signal becomesS=Tsourcee- In addition to receiver noise, at millimeter wavelengths the atmosphere has a significant brightness temperature (Tsky): • The system sensitivity drops rapidly (exponentially) as opacity increases
Atmospheric opacity, continued Typical optical depth for 230 GHz observing at the CSO: at zenitht225 = 0.15 = 3 mm PWV, at elevation = 30oÞt225 = 0.3 Tsys*(DSB) = et(Tatm(1-e-t) + Trx)= 1.35(77 + 75) ~ 200 K assuming Tatm = 300 K Atmosphere adds considerably to Tsys and since the opacity can change rapidly, Tsys must be measured often Many MM/Submm receivers are double sideband (ALMA Bands 9 and 10 for example) , thus the effective Tsys for spectral lines (which are inherently single sideband) is doubled Tsys*(SSB) = 2 Tsys (DSB) ~ 400 K
Vin =G Tin = G [Trx + Tload] Vout = G Tout = G [Trx +Tatm(1-e-t) +Tbge-t +Tsourcee-t] Load in Load out assume Tatm≈ Tload Vin – Vout Tload VoutTsys Comparing in and out = Tsys = Tload * Tout / (Tin – Tout) Power is really observed but is T in the R-J limit SMA calibration load swings in and out of beam • The “chopper wheel” method: putting an ambient temperature load (Tload) in front of the receiver and measuring the resulting power compared to power when observing sky Tatm (Penzias & Burrus 1973). Interferometric MM Measurement of Tsys How do we measureTsys = Tatm(et -1) + Trxetwithout constantly measuring Trx and the opacity? • IF Tatm≈ Tload, and Tsys is measured often, changes in mean atmospheric absorption are corrected. ALMA will have a two temperature load system which allows independent measure of Trx
Poor Good Medium Note sharp rise in Tsys at low elevations For calibration and imaging Example SMA 345 GHz Tsys Measurements Tsys(8) Tsys(4) Tsys(1) Elevation
S = So * [Tsys(1) * Tsys(2)]0.5 * 130 Jy/K * 5 x 10-6 Jy SMA gain for 6m dish and 75% efficiency Correlator unit conversion factor Corrected data SMA Example of Correcting for Tsys and conversion to a Jy Scale Tsys Raw data
This refraction causes: • - Pointing off-sets, Δθ≈ 2.5x10-4 x tan(i) (radians) • @ elevation 45o typical offset~1’ • - Delay (time of arrival) off-sets • These “mean” errors are generally removed by the online system Mean Effect of Atmosphere on Phase • Since the refractive index of the atmosphere ≠1, an electromagnetic wave propagating through it will experience a phase change (i.e. Snell’s law) • The phase change is related to the refractive index of the air, n, and the distance traveled, D, by • fe = (2p/l) ´n´D • For water vapor nµw • DTatm • so fe»12.6p´wfor Tatm = 270 K • l w=precipitable water vapor (PWV) column Tatm = Temperature of atmosphere
Atmospheric phase fluctuations Variations in the amount of precipitable water vapor (PWV) cause phase fluctuations, which are worse at shorter wavelengths (higher frequencies), and result in Low coherence (loss of sensitivity) Radio “seeing”, typically 1² at 1 mm Anomalous pointing offsets Anomalous delay offsets You can observe in apparently excellent submm weather and still have terrible “seeing” i.e. phase stability Patches of air with different water vapor content (and hence index of refraction) affect the incoming wave front differently.
“Root phase structure function” (Butler & Desai 1999) • RMS phase fluctuations grow as a function of increasing baseline length until break when baseline length ≈ thickness of turbulent layer • The position of the break and the maximum noise are weather and wavelength dependent Atmospheric phase fluctuations, continued… log (RMS Phase Variations) Break Phase noise as function of baseline length log (Baseline Length) • RMS phase of fluctuations given by Kolmogorov turbulence theory • frms = K ba / l [deg] • b = baseline length (km) • = 1/3 to 5/6 • = wavelength (mm) K = constant (~100 for ALMA, 300 for VLA)
Residual Phase and Decorrelation Q-band (7mm) VLA C-config. data from “good” day An average phase has been removed from absolute flux calibrator 3C286 Coherence = (vector average/true visibility amplitude) = áVñ/ V0 Where, V = V0eif The effect of phase noise, frms, on the measured visibility amplitude : áVñ = V0´áeifñ = V0´e-f2rms/2(Gaussian phase fluctuations) Example: if frms = 1 radian (~60 deg), coherence = áVñ = 0.60V0 Short baselines For these data, the residual rms phase (5-20 degrees) from applying an average phase solution produces a 7% error in the flux scale (minutes) Long baselines • Residual phase on long baselines have larger amplitude, than short baselines
self-cal with t = 30min: self-cal with t = 30sec: All data: Reduction in peak flux (decorrelation) and smearing due to phase fluctuations over 60 min No sign of phase fluctuations with timescale ~ 30 s one-minute snapshots at t = 0 and t = 59 min with 30min self-cal applied Sidelobe pattern shows signature of antenna based phase errors small scale variations that are uncorrelated Position offsets due to large scale structures that are correlated phase gradient across array VLA observations of the calibrator 2007+404 at 22 GHz (13 mm) with a resolution of 0.1² (Max baseline 30 km) • Uncorrelated phase variations degrades and decorrelates image Correlated phase offsets = position shift
ÞPhase fluctuations severe at mm/submm wavelengths, correction methods are needed Self-calibration:OK for bright sources that can be detected in a few seconds. Fast switching:used at the EVLA for high frequencies and will be used at ALMA. Choose fast switching cycle time, tcyc, short enough to reduce frmsto an acceptable level. Calibrate in the normal way. Phase transfer: simultaneously observe low and high frequencies, and transfer scaled phase solutions from low to high frequency. Can be tricky, requires well characterized system due to differing electronics at the frequencies of interest. Paired array calibration:divide array into two separate arrays, one for observing the source, and another for observing a nearby calibrator. Will not remove fluctuations caused by electronic phase noise Only works for arrays with large numbers of antennas (e.g., CARMA, EVLA, ALMA)
183 GHz Phase correction methods (continued): w=precipitable water vapor (PWV) column 22 GHz Radiometry: measure fluctuations in TBatm with a radiometer, use these to derive changes in water vapor column (w) and convert this into a phase correction using fe»12.6p´w l Monitor: 22 GHz H2O line (CARMA, VLA) 183 GHz H2O line (CSO-JCMT, SMA, ALMA) total power (IRAM, BIMA) (Bremer et al. 1997)
Testing of ALMA WVR Correction Two different baselines Jan 4, 2010 Data WVR Residual • There are 4 “channels” flanking the peak of the 183 GHz line • Matching data from opposite sides are averaged • Data taken every second • The four channels allow flexibility for avoiding saturation • Next challenges are to perfect models for relating the WVR data to the correction for the data to reduce residual WVR correction will have the largest impact for targets that cannot be self-calibrated and for baselines > 1 km
Test Data from Two weeks Ago Raw WVR Corrected
ΔSn= 10 Jy Absolute gain calibration • Instead, planets and moons are typically used:roughly black bodies of known size and temperature: • Uranus @ 230 GHz: Sn ~ 37 Jy, θ ~ 4² • Callisto @ 230 GHz: Sn ~ 7.2 Jy, θ ~ 1.4² • Sn is derived from models, and can be uncertain by ~ 10% • If the planet is resolved, you need to use visibility model for each baseline • If larger than primary beam it shouldn’t be used at all Flux (Jy) MJD There are no non-variable quasars in the mm/sub-mm for setting the absolute flux scale ΔSn= 35 Jy Flux (Jy) MJD
Antenna requirements • Aperture efficiency, h: Ruze formula gives • h = exp(-[4psrms/l]2) • for h = 80% at 350 GHz, need a surface accuracy, srms, of 30mm • ALMA surface accuracy goal of 25 µm Pointing: 10 m antenna operating at 350 GHz the primary beam is ~ 20² a 3² error Þ D(Gain) at pointing center = 5% D(Gain) at half power point = 22% need pointing accurate to ~1² ALMA pointing accuracy goal 0.6² • Baseline determination: phase errors due to errors in the positions of the telescopes are given by • Df = 2p ´Db ´ Dq • l • Þto keep Df < Dq need Db < l/2p • e.g., for l = 1.3 mm need Db < 0.2 mm Dq = angular separation between source & calibrator, can be large in mm/sub-mm Db = baseline error
Summary Atmospheric emission can dominate the system temperature Calibration of Tsys is different from that at cm wavelengths Tropospheric water vapor causes significant phase fluctuations Need to calibrate more often than at cm wavelengths Phase correction techniques are under development at all mm/sub-mm observatories around the world Observing strategies should include measurements to quantify the effect of the phase fluctuations Instrumentation is more difficult at mm/sub-mm wavelengths Observing strategies must include pointing measurements to avoid loss of sensitivity Need to calibrate instrumental effects on timescales of 10s of mins, or more often when the temperature is changing rapidly
Challenges • Image sources larger than the primary beam (PB) • at 1mm a 12m dish has PB~21” • Mosaic • Image sources with structure larger than the largest angular scale • For shortest baseline of 15m (1.25*diameter) ~14” at 1mm • Add total power from single dish • Accurate continuum images in presence of copious line emission and accurate delay calibration (bandpass) • Spectral line mode all the time • Sensitive linearly polarized feeds • Many quasars are linearly polarized • Full polarization calibration always
Image Quality M17 VLA 21cm • Image quality depends on: • U-V coverage • Density of U-V samples • Image fidelity is improved when high density regions are well matched to source brightness distribution • U-V coverage isn’t enough • DYNAMIC RANGE can be more important than sensitivity 3’ = 1.2 kl
Heterogeneous Arrays • eSMA • 6m • 1 15m (JCMT) + 1 10.4m (CSO) CARMA 6 10.4m 10 6.1m 8 3.5m 1 10.4m for total power ALMA 50-60 12m antennas in main array (two designs) 12 7m antennas in ACA (Atacama Compact Array) 4 12m with nutators for total power
Large Nearby Galaxies • SMA ~1.3 mm observations • Primary beam ~1’ • Resolution ~3” 3.0’ ALMA 1.3mm PB ALMA 0.85mm PB CFHT 1.5’ Petitpas et al. 2006, in prep.
Galactic Star Formation BIMA 46 pointing mosaic covering 10’ x 15’ CO(1-0) at ~115 GHz ~10” resolution ALMA 0.85mm PB Williams et al. (2003)
Mosaicing Considerations • Each pointing ideally should have similar U-V coverage and hence synthesized beams – similar S/N is more important • Nyquist sampling of pointings • On-the-fly mosaicing can be more efficient at lower frequencies • Small beams imply many pointings • At higher frequencies weather conditions can change rapidly • Push to have very good instantaneous snapshot U-V coverage • Polarimetry even more demanding for control of systematics due to rotation of polarization beam on sky • Accurate primary beam characterization • Account for heterogeneous array properties < 3 minutes!
Total Power Considerations • Adding Single Dish (SD) zero-spacing tricky because it requires • Large degree of overlap between SD size and shortest interferometer baseline in order to accurately cross-calibrate • Excellent pointing accuracy which is more difficult with increasing dish size • *Comparable* sensitivity to interferometric data • On-the-fly mapping requires rapid (but stable, i.e. short settle time) telescope movement • SD Continuum calibration – stable, accurate, large throws (i.e. nutators)
Model Image Spitzer GLIMPSE 5.8 mm image • CASA simulation of ALMA with 50 antennas in the compact configuration (< 100 m) • 100 GHz 7 x 7 pointing mosaic • +/- 2hrs
50 antenna + SD ALMA Clean results Model Clean Mosaic + 12m SD + 24m SD