measuring polariza/on with CARMA (currently possible only in the 1mm band) mode measure benefits correlator LL <LL*> most flexible correlator setup RR <RR*> NONE! (Tsys is slightly higher for RCP rcvrs) DUALPOL <LL*>, <RR*> 2 improvement in spectral line sensi/vity FULLPOL 210 270 GHz: dual circular polariza/on receivers <LL*>, <RR*>, <LR*>, <RL*> measure all 4 Stokes parameters 8 independent windows 8 independent windows 4 independent pairs of windows 4 independent pairs of windows, fewer channels 80 115 GHz: single pol rcvrs; only LL = <YY*> allowed
primary scien/fic mo/va/on: study magne/c fields Zeeman effect splits circular polariza/on of spectral lines measures B parallel linearly polarized thermal emission from magne/cally aligned dust grains measures orienta/on of B perp CN, other molecules with magne/c moments; splihng is << linewidth; a very difficult experiment B to polariza/on direc/on Falgarone+ 2008 Schleuning 1998
the goal of polariza/on observa/ons is to map Stokes parameters east y north x E y cos(ωt + Φ y ) I = <E x2 > + <E y2 > E x cos(ωt + Φ x ) Q = <E x2 > <E y2 > U = 2 <E x E y cos(φ x Φ y )> V = 2 <E x E y sin(φ x Φ y ) > </me average> because E x,e y,φ x,φ y vary randomly with /me units: Jy/beam map Q, U, V just like total intensity I I is always posi/ve, but Q,U,V can be nega/ve if unpolarized Q,U,V = 0 derived quan//es: frac/onal linear pol = (Q 2 + U 2 ) ½ /I posi/on angle = ½ atan2(u,q)
example: DR21OH maps of Stokes parameters and pol vectors I = haluone, Q = red, U = blue contour interval 1σ beginning at ±3σ I = contours orange = polariza/on vectors
interferometer measures Stokes visibili&es (cross correla/on of ant i with ant j) linearly polarized feeds circularly polarized feeds I v = X i X j * Q v = X i X j * + Y i Y j * Y i Y j * I v = R i R * j + L i L * j Q v = j R i L * j j L i R * j U v = X i Y j * + Y i X j * V v = j X i Y j * + j Y i X j * U v = R i L * j + L i R * j V v = R i R * j L i L * j X, Y, R, L are the (complex) voltages at the correlator I v, Q v, U v, V v are complex, but Herme/an ( > maps are real)
why use circularly polarized feeds to measure linear polariza/on? linearly polarized feeds: Q = g xi g xj X i X j * g yi g yj Y i Y j * difference of 2 large numbers, sensi/ve to /ny errors in the receiver gains g x, g y circularly polarized feeds: Q = 1 j g g R L * 2 Ri Lj i j + 1 j g g L R * 2 Li Rj i j <RL> = <LR> = 0 in the absence of linearly polarized emission a null experiment, insensi/ve to fluctua/ons in gains g R, g L
hardware (1 9 GHz) IF amp #1 SIS mixer #1 Orthomode transducer (OMT) separates X, Y linear polariza/ons to outputs #1 and #2 IF #1 to lab IF #2 to lab (1 9 GHz) IF amp #2 SIS mixer #2 Waveguide polarizer converts RCP, LCP to X,Y Horn couples signals from telescope (210 270 GHz, all polariza/ons) into waveguide 1 inch
orthomode transducer separates orthogonal linear polariza/ons Navarrini & Plambeck 2006, IEEE MTT, 54, 272 277
polarizer converts R,L circular to X,Y linear λ/4 retarder slow axis RCP waveguide linear (at 45 ) birefringent dielectric: quartz, sapphire, etc or sloƒed plas/c plate examples of retarders
2 sec/on waveguide circular polarizer λ/2 retarder at 15 λ/4 retarder at 74.5 0.047 diameter facets 0.006 deep Plambeck & Engargiola, CARMA Memo #54
electromagne/c simula/on R Feed horn (sky) OMT X L Y Plambeck & Engargiola, CARMA Memo #54
Polarizer construc/on Aluminum mandrel Copper electroplated onto mandrel Machined Soldered into waveguide flange
polariza/on observa/ons require 2 addi/onal calibra/ons 1. xyphase = phase difference between R and L receivers on each telescope signals travel through different fibers to control bldg R,L cable lengths differ for each correlator sec/on 2 error in xyphase > 1 error in pol PA 2. leakage = cross coupling between R and L receivers on each telescope due mostly to imperfec/ons in the polarizers and orthomode transducers introduces errors in pol intensity and PA
making polariza/on observa/ons observing script: configastroband setup is different there are just 4 bands (1,3,5,7 only 2,4,6,8 are Siamese twins) con/nuum bandwidth is s/ll 4 GHz in each sideband: 4 x 500 MHz x 2pol fewer channels/band; BW500 allows only 2 bit mode data reduc/on: 2 extra steps xyauto computes xyphase correc/on from grid calibra/on data solve for leakages with gpcal, or copy them from a pre exis/ng file mapping map all 4 Stokes parameters (invert stokes=i,q,u,v map=i.mp,q.mp...) measure noise in Q,U,V maps, then compute polarized intensity and posi/on angles with impol
TADPOL key project (Telescope Array Doing POLariza/on) Chat Hull L1157-5 0 5 10 (km/s)
a few other TADPOL results Serpens 8 IRAS2A CB230