Commissioning the HI Observing Mode of the Beamformer for the Cryogenically Cooled Focal L-band Array for the GBT (FLAG)
N. M. Pingel, D. J. Pisano, M. Ruzindana, M. Burnett, K. M. Rajwade, R. Black, B. Jeffs, D. R. Lorimer, D. Anish Roshi, R. Prestage, M. A. McLaughlin, D. Agarwal, T. Chamberlin, L. Hawkins, L. Jensen, P. Marganian, J. D. Nelson, W. Shillue, E. Smith, B. Simon, V. Van Tonder, S. White
DDraft version January 27, 2021
Typeset using L A TEX twocolumn style in AASTeX63
Commissioning the Hi Observing Mode of the Beamformer for the Cryogenically Cooled Focal L-bandArray for the GBT (FLAG)
N. M. Pingel ,
1, 2, 3
D. J. Pisano,
2, 3, 4
M. Ruzindana, M. Burnett, K. M. Rajwade , R. Black, B. Jeffs, K. F. Warnick, D. R. Lorimer,
2, 3
D. Anish Roshi,
7, 8
R. Prestage, † M. A. McLaughlin,
2, 3
D. Agarwal,
2, 3
T. Chamberlin, L. Hawkins, L. Jensen, P. Marganian, J. D. Nelson, W. Shillue, E. Smith,
2, 3
B. Simon, V. Van Tonder, and S. White Research School of Astronomy and AstrophysicsThe Australian National UniversityCanberra, ACT 2611, Australia Department of Physics and AstronomyWest Virginia UniversityWhite Hall, Box 6315, Morgantown, WV 26506 Center for Gravitational Waves and CosmologyWest Virginia UniversityChestnut Ridge Research Building, Morgantown, WV 26505 Adjunct Astronomer at Green Bank Observatory, P.O. Box 2, Green Bank, WV 24944, USA. Brigham Young University (BYU) Provo, UT, 84602, USA Jodrell Bank Centre for AstrophysicsUniversity of ManchesterOxford Road, Manchester M193PL, UK National Radio Astronomy Observatory (NRAO)520 Edgemont Road Charlottesville, VA 22903, USA Arecibo ObservatoryArecibo, Puerto Rico 00612 Green Bank Observatory (GBO)155 Observatory Rd, Green Bank, WV 24944, USA Square Kilometre Array South Africa (SKA SA)Cape Town, South Africa (Received June 18, 2020; Accepted January 20, 2021)
Submitted to AJABSTRACTWe present the results of commissioning observations for a new digital beamforming back end forthe Focal plane L-band Array for the Robert C. Byrd Green Bank Telescope (FLAG), a cryogenicallycooled Phased Array Feed (PAF) with the lowest measured T sys / η of any PAF outfitted on a radiotelescope to date. We describe the custom software used to apply beamforming weights to the rawelement covariances to create research quality spectral line images for the new fine-channel mode, studythe stability of the beam weights over time, characterize FLAG’s sensitivity over a frequency range of150 MHz, and compare the measured noise properties and observed distribution of neutral hydrogenemission from several extragalactic and Galactic sources with data obtained with the current single-pixel L-band receiver. These commissioning runs establish FLAG as the preeminent PAF receivercurrently available for spectral line observations on the world’s major radio telescopes. Corresponding author: Nickolas [email protected] a r X i v : . [ a s t r o - ph . I M ] J a n Pingel et al.
Keywords:
Instrumentation: Phased Array Feeds — Galaxies: general — Galaxies: structure INTRODUCTIONThe increase in survey speed provided by Phased Ar-ray Feed (PAF) receivers embodies the next major ad-vancement in radio astronomy instrumentation. Sucharrays have been used commercially for decades (Mil-ligan 2005), but the unique challenge of operating atextremely low noise levels to detect inherently faint as-trophysical signals has only been overcome within thelast two decades (e.g., Fisher & Bradley 2000). Placingan array of densely packed dipole radiators in the focalplane of a radio telescope allows full sampling of the fo-cal field. Multiplying voltages from the dipoles by differ-ent complex coefficients (i.e., beamformer weights) andsumming them will alter the aperture illumination suchthat the resulting far-field power patterns mimic a multi-beam feed (e.g. Landon et al. 2010), while avoiding thechallenges of positioning physically distinct feeds. Thisis an especially powerful shortcut for L-band observa-tions where relatively large physical feeds are necessaryand only sample a limiting fraction of sky at one instant.Several PAFs have successfully been tested and de-ployed on both large single dishes, such as the 64mParkes telescope, and aperture synthesis arrays. Forinstance, Reynolds et al. (2017) successfully recreateda detailed neutral hydrogen ( Hi ) column density (N HI )map of the Large Magellanic Cloud, originally observedwith the Parkes’ L-band multi-beam receiver, as wellas the direct detection of source from the Hi ParkesAll-Sky Survey (HIPASS; Barnes et al. 2001) and hy-drogen recombination lines. Serra et al. (2015a) utilizedthe PAF-equipped Australian Square Kilometer ArrayPathfinder (ASKAP) to reveal new Hi clouds withinthe IC 1459 galaxy group. More recently, pilot observa-tions of Widefield ASKAP L-band Legacy All-sky BlindSurvey (WALLABY) have expanded the total member-ship of the NGC 7162 galaxy group and provided high-quality Hi data for kinematic modeling (Reynolds et al.2019), identified five new Hi sources in the NGC 7232group (Kleiner et al. 2019), and characterized Hi cloudsthat are likely resolved tidal debris features from theNGC 7232/3 triplet (Lee-Waddell et al. 2019). Addi-tional early science results from WALLABLY are dis-cussed in Elagali et al. (2019) and For et al. (2019).Other recent observations from The Galactic ASKAP(GASKAP; Dickey et al. 2013) survey of the Hi in thenearby Small Magellanic Cloud, where the ∼ × † Deceased extent of the dwarf galaxy was captured in a singlepointing, have demonstrated the clear advantage PAFsprovide in creating wide-field images (McClure-Griffithset al. 2018). Additionally, commissioning observationsfrom the Apertif upgrade to the Westerbork Radio Tele-scope (WSRT; Oosterloo et al. 2009) have shown excel-lent wide-field imaging capabilities.While the increase in the Field-of-View (FoV) will inturn dramatically increase the survey speeds of aperturesynthesis arrays like the Apertif or ASKAP, the smallfilling factors and spacing of the individual antenna ele-ments inherently filter out the largest spatial frequenciesand limit the sensitivity to low surface brightness emis-sion. Complimentary observations from a large singledish provide these vital missing zero spacing measure-ments to ensure angular sensitivity at large scales andhigh surface brightness sensitivity. The decrease in thenecessary telescope time required for deep (N HI ≤ cm − ) on-the-fly (OTF) mapping of extended sources,makes a PAF-equipped GBT the ideal instrument forfuture deep Hi surveys to reach pioneering sensitivitylevels.The Focal L-band Array for the GBT (FLAG) is a19 element, dual-polarization PAF with cryogenicallycooled low noise amplifiers (LNAs) to maximize sensi-tivity over a bandwidth of 150.519 MHz divided up into500 coarse channels. Previous commissioning observa-tions of the front end have shown excellent performancein terms of sensitivity and spectral line imaging capabil-ities (Roshi et al. 2018). In Spring 2018, FLAG recordedthe lowest reported system temperature ( T sys ) normal-ized by aperture efficiency η at 25 ± Hi mapping withthe GBT; the custom software used for post-correlationbeamforming, flux calibration, and imaging are summa- LAG Hi Commissioning Hi properties of several extragalactic andGalactic sources as detected by FLAG and the currentL-band single-pixel receiver, and presents a comparisonbetween the survey speed of FLAG relative to otherPAFs and multi-beam receivers equipped on the world’smajor radio telescopes; finally, our conclusions and in-strument outlook are summarized in Section 7. FLAG SYSTEM ARCHITECTUREThe Focal L-band Array for the Green Bank Telescope(FLAG) was developed in collaboration between theNational Radio Astronomy Observatory (NRAO), theGreen Bank Observatory (GBO), Brigham Young Uni-versity (BYU), and West Virginia University (WVU). Itis a 19 element, dual-polarization, cryogenic PAF withdirect digitization of radio frequency (RF) signals at thefront end, digital signal transport over fiber, and nowpossesses a real-time signal processing back end withup to 150 MHz bandwidth. The front end employs anew digital-down-link (DDL) mechanism that performsall analog-to-digital conversions in a compact assemblythat sits at prime focus (Morgan et al. 2013).Two integral processes in the success of the DDL areachieving bit and byte lock in the back end system.The front end system produces complex sample volt-ages for each dipole element that are serialized into 8-bitreal and 8-bit imaginary components. These are com-bined to form a 16-bit (or 2-byte) word per time sample.These serialized voltages are transmitted over opticalfiber without any sort of encoding such as start/stop bitsto delineate the boundaries between bits. Bit lock refersto the recovery of the most-significant bit by the deseri-alizer in the FLAG back end. This is done by construct-ing a histogram of the arriving samples and comparingto the expected probability density function of a randomGaussian process. Once the sample are correctly alignedin terms of their most-significant bits, the byte-lock pro-cedure ensures that two sequential bytes are correctlyidentified as the real and imaginary components. Dueto the relationship between the magnitudes of complexconjugated signals, if the bytes are incorrectly identified(i.e., there is no byte-lock), a strong test-tone injected ata known positive frequency offset relative to a set centralfrequency will have a symmetric counterpart at the cor-responding negative frequency offset. The bits are thenslipped by eight locations to correctly align the bytes toachieve byte-lock. See Diao (2017) and Burnett (2017)for detailed information on the PAF receiver front endand bit/byte locking procedures, respectively. The FLAG back end consists of five digital opticalreceiver cards, five ROACH II FPGA boards (Parsonset al. 2006), a Mellanox SX 1012 12-port 40 Gbe ethernetswitch, and five Mercury GPU408 4U GPU Server HighPerformance Computers (HPCs). These parts are allconnected in the order listed.The digitized signals from the front end of the systemare serialized and sent over 40 (38 + 2 spare) opticalfibers to the optical receiver cards which are connectedto the ROACH II boards. The boards channelize theapproximately 150 MHz bandwidth into 512 channelseach with a bandwidth of 303.18 kHz.The data is then reduced to 500 frequency channelsand packetized into 10 user-datagram protocol (UDP)packets each containing 50 frequency samples for eightantennas across 20 time samples. These packets arestreamed over 10-Gbe/40-Gbe breakout cables into a12-port 40-Gbe network switch, which redirects packetsinto the HPCs such that each one receives 100 frequencysamples with a width of 303.18 kHz for all 40 antennas.Each HPC then takes these 100 frequency samples anddivides them evenly between two Nvidia GeForce Ti-tan X Graphical Processing Units (GPUs), which con-tain real-time beamformer and coarse/fine channel cor-relator algorithms. Within each HPC is a real-timeoperating system (RTOS) called HASHPIPE used forthread management and pipelining, and a user inter-face called dealer/player. These enable the operation ofthe beamformer and correlator algorithms. Each HPCcan be run in three distinct observing modes: (1) CAL-CORR, which is the mode used to derive the beam-forming weights; (2) PFBCORR, which is used for thespectral line observations and sends a frequency chunkof 100 coarse channels with a total bandwidth of 30.318kHz through a polyphase filterbank implementation toobtain 3200 total fine channels with resolution of 9.47kHz; each GPU in these correlator modes runs a cor-relator thread that processes one-tenth the total band-width; and (3) RTBF mode, which is the mode used forpulsar and transient detection. The properties of theseobserving modes are summarized in Table 1. We referthe reader to Ruzindana (2017) for a detailed descrip-tion on the FLAG back end and Rajwade et al. (2019)for the description and early success of the RTBF mode. MAXIMUM SIGNAL-TO-NOISEBEAMFORMINGThe process of beamforming involves the weightedsum of the individual sensor responses to an incidentastronomical signal. In radio astronomy, where the sig-nals are inherently extremely faint, it is advantageousfor an observer to compute weights that maximize the
Pingel et al.
Mode Bandwidth [MHz] N chan N chan in Bank ∆ ν [kHz]CALCORR 151.59 500 25 non-contiguous 303.18PFBCORR 30.318 3200 160 contiguous 9.47RTBF 151.59 500 25 non-contiguous 303.18 Table 1.
Properties of Available FLAG Observing Modes signal-to-noise from a given detection. Defining z ( t ) tobe a vector containing the individual responses of eachdipole in an M -dipole PAF measured over a discretetime sample (i.e., integration), a convenient covariancematrix R = z H ( t ) z ( t ) (1)can be constructed such that R is a M × M matrix ofcomplex values that characterizes the correlations be-tween the recorded complex voltages of the individualdipole elements. Note that the H superscript in theabove equation represents the Hermitian (complex con-jugate transpose) form of the vector. Jeffs et al. (2008)goes on to characterize the signal from the array by theequation R = R s + R n , (2)where R s is the signal covariance matrix and R n con-tains the noise covariance from spillover, background,and the mutual coupling of the dipoles. R n can be measured by pointing the telescope to ablank patch of sky so that R ≈ R n . Pointing at a brightpoint source and solving Equation 2 for R s gives thesignal covariance matrix. A steering vector that charac-terizes the response of each dipole in a given directioncan now be computed and is defined by a ( θ ) = R n u max , (3)where u max is the dominant eigenvector of the general-ized eigenvalue equation Ru max = λ max R n u max .Elmer et al. (2012) define the maximum signal-to-noise beamformer by maximizing the following expres-sion w maxSNR = argmax (cid:18) w H R s ww H R n w (cid:19) . (4)The values contained within the weight vector w and itsHermitian form are not yet known. Maximizing Equa-tion 4 by taking the derivative with respect to w andsetting the result equal to zero is equivalent to findingthe dominant eigenvector of the generalized eigenvalueequation R s w maxSNR = λ max R n w maxSNR . (5) A raw power value P in units of counts at a particularfrequency ν and short term integration ( n ) is measuredby calculating P ν, n = w HmaxSNR ,ν, n R s ,ν, n w maxSNR ,ν, n . (6)The max-SNR beamforming algorithm effectively ma-nipulates the individual dipole illumination patternssuch that the aperture is optimally illuminated for eachformed beam in a given direction on the sky. While thisscheme produces the highest gain in a given direction,there is little control over the level of the sidelobes due tothe sharp transition in illumination pattern. High side-lobe levels could introduce stray radiation, where signalis detected in a sidelobe rather than the main formedbeam, affecting the accuracy of flux and mapped struc-ture. For example, stray radiation in the initial datarelease of the Parkes Galactic All-Sky Survey (GASS;McClure-Griffiths et al. (2009)) accounted for upwardsof 35% of the observed emission in some individual spec-tra. Nevertheless, high sensitivity over a large field ofview is particularly advantageous for the detection ofdiffuse (angularly extended and faint) Hi , as evidencedby the abundance of highly detailed and faint structureobserved in the GASS survey even before the applica-tion of corrections for stray radiation. The unique un-blocked aperture design of the GBT ensures inherentlylow sidelobe structure — even in the case of maxSNR —and subsequently high image fidelity. A PAF-equippedGBT will produce high quality maps while also decreas-ing the survey times necessary to pursue — amongstmany applications — the detection of cold gas accre-tion, the study of high velocity clouds (Moss et al. 2013),and the compact clouds being driven from the Galacticcenter (Di Teodoro et al. 2018). OBSERVATIONSThe first step in forming beams is the characteriza-tion of the response of each individual dipole element ina given direction, θ i , in the form of a signal response vec-tor (i.e., Equation 3). For these commissioning observa-tions, we implement a maxSNR beamformer as definedin Equation 4. While a PAF can theoretically form anynumber of beams as long as there exists a sufficient num-ber of steering vectors and recorded covariance matrices, LAG Hi Commissioning Cross-El Offset [deg] E l O ff s e t [ d e g ] Figure 1.
The trajectory from one of our calibration gridscentered on 3C295. The ‘ × ’ symbols denote the mean lo-cation of the reference pointings, and the solid black linesrepresent the trajectory of the grid. we employ two calibration techniques deemed a Calibra-tion Grid and 7-Point Calibration to form seven totalbeams arranged such that the central (i.e., boresight)beam is surrounded by six outer beams in a hexagonalpattern that overlap at approximately the half-powerpoints (see Figure 1 of Rajwade et al. 2019). This par-ticular pattern provides ideal balance between mappingspeed and uniform sensitivity within FLAG’s FoV. Werefer to the boresight beam as ‘Beam 0’; as viewed on thesky, Beam 1 is the upper left beam, and the subsequentbeam numbers increase in a clockwise fashion. Oncea set of w b , is obtained for the b th beam (of B totalbeams) in the direction of θ i , we acquire the raw powervalue at each ν and short term integration n throughEquation 6. Table 2 summarizes all calibration and sci-ence observations discussed in this paper.4.1. Calibration Grid
To obtain measurements of R s , we move the GBTin a grid centered on a strong calibrator spanning 30arcminutes in Cross-elevation (XEL) as set by the hori-zontal celestial coordinate system (i.e. ‘Encoder’ settingwhen using the GBT) for a total of 34 rows spaced 0.91arcminutes (approximately one-tenth the full-width halfmax of the GBT beam at 1.4 GHz) apart in Elevation(EL). We compute R n by tracking two degrees in XELaway from the grid for a duration of ten seconds. Wetrack after every fifth row to attain six total referencepointings with three evenly spaced on each side of thegrid. To ensure adequate spatial sampling, we move thetelescope at a rate of 0.91 arcminutes per second anddump integrations to disk every 0.5 s. The trajectoryof the calibration grid observations performed during session GBT16B 400 12 centered on 3C295 is shown inFigure 1. The total time to complete such a grid is about40 minutes, including scan overhead.The calibration grid provides the necessary covariancematrices with which to characterize the response andquality of the formed beams. A convenient quantity withwhich to compare beam-to-beam sensitivity variations— as it directly measurable — is the system equivalentflux density (SEFD), which is the flux density equivalentof the system temperature, T sys . The SEFD is definedSEFD = S CalSrc (cid:16) (cid:104) P s (cid:105)(cid:104) P n (cid:105) − (cid:17) , (7)where S CalSrc is the known flux density of a calibratorsource in units of Jy and (cid:104) P s (cid:105) and (cid:104) P n (cid:105) are respectivelythe mean on-source and off-source power values. Theseare determined by building distributions of on-sourceand off-source raw beamformed power values containedbetween coarse channels corresponding to 1400.2 MHzto 1416.6 MHz and 1425.1 MHz to 1440.3 MHz to avoidbias from Galactic Hi emission. These distributions arethen fit with separate Gaussian functions to calculate (cid:104) P s (cid:105) and (cid:104) P n (cid:105) . The associated uncertainties are takento be the standard deviations returned by these fits. Incases where the fit does not converge due to complexbandpass shapes, the arithmetic mean and standard de-viations are used. All power values are corrected foratmospheric attenuation. The final uncertainty for theSEFD value is computed by propagating the statisticaluncertainties of (cid:104) P s (cid:105) , (cid:104) P n (cid:105) , and S CalSrc . The flux den-sity of a given calibrator source is taken from Perley &Butler (2017).The SEFD provides a comparison metric between in-dividual beams. If the SEFD is derived for the idealobservation of a blank sky, it can be related to the ratioof T sys and aperture efficiency η through T sys η = 10 − SEFDA g k , (8)where A g is the geometric area of the GBT, and k isthe Boltzmann constant. Substituting the definition forthe SEFD from Equation 7 and putting the power levelsin terms of the product between correlation matricesand beamforming weights from Equation 6 results inthe expression T sys η = 10 − S CalSrc A g k w H R n ww H R s w . (9)This equation is an oft-used metric for comparing andcharacterizing the performance of PAFs (Jeffs et al.2008; Landon et al. 2010; Roshi et al. 2018), since it can Pingel et al.
Session UT Date UT Start UT End Schedule Block Type Source Mode Integration Length [s] Central Frequency [MHz] Notes
GBT16B 400 03
GBT16B 400 09
GBT16B 400 12 × (cid:3) (cid:48) ‡ N ints = 72; t eff , comb = 60 s2017-08-04 06:12:19 06:14:53 7Pt-Calibration 3C48 CALCORR 0.5 1450.0000 10 s Tracks GBT16B 400 13
GBT16B 400 14
GBT17B 360 01
GBT17B 360 02
GBT17B 360 03 ‡ N ints = 72; t eff , comb = 68 s ‡ N ints = 72; t eff , comb = 68 s ‡ N ints = 72; t eff , comb = 68 s GBT17B 360 04 ‡ N ints = 72; t eff , comb = 68 s; ‡ N ints = 72; t eff , comb = 68 s ‡ N ints = 72; t eff , comb = 68 s ‡ N ints = 72; t eff , comb = 68 s GBT17B 360 05
GBT17B 360 06
GBT17B 360 07
GBT17B 455 01 ‡ N ints = 72; t eff , comb = 60 s2018-02-04 15:09:06 15:18:56 7Pt-Calibration 3C348 CALCORR 0.5 1450.84841 60 s Tracks ‡ N ints = 72; t eff , comb = 60 s Table 2.
Summary of FLAG Observations; ‡ represents mapping scans used to make the science maps; N ints represents thenumber of integration along each row/column; and t eff , map gives the effective integration time of the combined map time inunits of s (see text in Section 4.3). be directly measured. Equation 8 can be rearranged todefine a formed beam sensitivity in units of m K − ateach ν from each direction θS ν ( θ ) = ηA g T sys = 2 k − S CalSrc w H R s ww H R n w . (10)Figure 2 shows the resulting sensitivity map from thecalibration grid in Figure 1 in the XX pol at 1404.74MHz. The inner 0.5 × of the FoV shows uni-form sensitivity, which reflects the aggregate response ofthe individual dipoles on the sky (see Figures 4, 5, and10 from Roshi et al. 2018), before smoothly droppingtowards the edge of the FoV. The excellent uniformityacross the FoV facilitates high-quality beams. The response of the i th formed beam for each ν ateach direction θ is I i ( θ ) = (cid:12)(cid:12) w maxSNR , i H ( θ ) a i ( θ )) (cid:12)(cid:12) . (11)The left panel of Figure 3 shows the formed beam pat-terns for the calibration grid around 3C295 observed forsession GBT17B 360 04. Gaussian fits to cuts in XELand EL at the location of each beam’s peak response(red dashed lines) shown in the right hand panel andsummarized in Table 3 demonstrate that the FWHM ofthe formed beams range between approximately 9 (cid:48) and10.5 (cid:48) , which is comparable with the beam of the cur-rent single-pixel receiver. The offset between the mea-sured location of the peak response of each beam andits indicated position is less than 2% of the measured LAG Hi Commissioning Beam FWHM
XEL [ (cid:48) ] Peak XEL , Intended [ (cid:48) ] Peak XEL , Measured [ (cid:48) ] XEL %-Diff FWHM EL [ (cid:48) ] Peak EL , Intended [ (cid:48) ] Peak EL , Measured [ (cid:48) ] EL %-Diff0 9.14 ± ± − − ± − − ± ± ± ± ± − − ± ± − − ± − − ± − − ± − − ± − − Table 3.
Summary of Gaussian fits to the beam response profiles shown in Figure 3. Column (1): beam number; column(2): FWHM fit along XEL axis at the location of the peak response; column (3) Peak
XEL , Intended is intended location of peakresponse along the XEL axis; column (4) Peak
XEL , Measured is the measured location of peak response along the XEL axis; column(5): XEL %-Offset = | Peak
XEL , Intended − Peak
XEL , Measured | /FWHM XEL × -15 -10 -5 0 5 10 15Cross Elevation [arcmin]-15-10-5051015 E l e v a t i o n [ a r c m i n ] S e n s i t i v i t y [ m K ] Figure 2.
Sensitivity map of the XX polarization at 1404.74MHz derived from the calibration grid shown in Figure 1.The contours levels begin at the − − − FWHM. While the outer beams are more elongated thanthe boresight beam, the fits to the beam profiles showdeviations from a Gaussian approximation at responselevels much below the FWHM. The elongated shape atlevels below 10% of the peak response is largely dueto forming beams near where the sensitivity begins todrop off. For example, the elongation of the low-levelresponse of Beam 3 corresponds to the transition fromthe -1 dB to -3 dB contours in the sensitivity map shownin Figure 2. 4.2.
While it is interesting to obtain detailed spatial infor-mation of the array response provided by a calibrationgrid, the necessary ∼
40 minutes of total observing time(including overhead) is disadvantageous. A 7-Point cal- ibration scan (henceforth 7Pt-Cal) can be performed ininstances where telescope time is a constraint. This pro-cedure will (1) track the area of sky minus two degreesin XEL away from the calibrator source and at the sameEL offset as the center of Beams 4 and 5; (2) directlytrack the source (i.e. the boresight); (3) slew the tele-scope to put calibrator source at desired center of Beams1-6; (4) track the area of sky minus two degrees awayfrom the source and at the same EL offsets as the centersof Beams 1 and 2. The two reference pointings at simi-lar EL offsets as the outer beams allow for constructionof R n and also account for elevation-dependent effects,while the tracks on the desired beam centers collectsthe necessary response data to derive maxSNR weights.The duration of each track ranges between 10 and 30seconds. While more efficient in terms of time than afull calibration grid, the amount of steering vectors a ( θ )obtained during a 7Pt-Cal are only enough to set the lo-cation of the peak response for each beam and derive anSEFD. No additional information concerning the shapeof the formed beams is available. This type of calibra-tion is the primary calibration procedure for pulsar andtransient observations, when detailed knowledge of thebeam shape is not crucial to the science goals as com-pared to e.g., the overall flux sensitivity.4.3. Hi Observations
The spectral line data were collected in the fine chan-nelized PFBCORR mode with an inherent frequencyresolution of 9.47 kHz ( ∼ Hi emission) by steering the telescope along columns ofconstant longitudinal coordinates to make OTF maps.The raw dipole correlation matrices were dumped to diskevery t int = 0.5 s at angular intervals of 1.67 (cid:48) to ensureadequate spatial Nyquist sampling; the columns/rowswere spaced every 3 (cid:48) in each DecLatMap/RaLongMap.The coordinate systems used to make our science mapsinclude horizontal (XEL/EL), J2000, and Galactic. SeeTable 2 and Section 6.3 for a summary of the observa-tional set-up for the Hi sources and Sections 6.3.1, 6.3.2, Pingel et al.
Figure 3. left: The formed beam pattern derived from the calibration grid shown in Figure 1. The red x symbols denotethe intended beam centers. The intersections of the vertical and horizontal dashed red lines denote the location of the peakresponse of each formed beam. The contours represent levels of − − −
10, and −
15 dB. Right: profiles of the normalizedbeam response at the location of the peak response along the XEL (orange) and EL (blue) axes. Gaussian fits are representedby dashed lines, while the intended locations of the peak response in XEL and EL are shown by vertical dotted lines. and 6.3.3 for the results from observations of NGC 6946,NGC 4258, and a field near the Galactic Center.The effective integration time of a map made withFLAG that combines all seven formed beams ( t eff , comb )is derived by first computing the total effective integra-tion time of a map made with a single beam t eff , map , mul-tiplying this by the number of formed beams, N beams ,and dividing by the map area in terms of the total num-ber of beams contained within a map. For example,the 2 × maps of NGC 6946 consists of 41 totalcolumns ( N columns ), each with 72 distinct integrations( N int ). Similar to the calibration procedure outlined inPingel et al. (2018), we obtain a reference spectrum fromthe edges of our science maps by utilizing the first andlast four integrations of a particular map scan. The ef-fective integration time for a single integration in a mapfrom a single formed beam is therefore t eff , int = t int t ref t int + t ref = 0 . · . .
444 s; (12) t eff , map then follows from N rows × N int × t eff , int =1312 sand increases to t eff , map × N beams = 1312 × (cid:48) , which corre-sponds to an angular area of 1.1331 × (9 . (cid:48) ) ∼ . The area in terms of the number of beams is then4 deg /0.026 deg ∼
153 beams. The final t eff , comb is then just t eff , comb = 9184 s / 153 beams ∼
60 s/beam.These t eff , comb values are listed listed in the Notes col-umn of Table 2 for each science map and can be used inthe ideal radiometer equation to calculate the theoreti-cal noise value in the final images. DATA REDUCTIONThe data reduction and calibration of the Hi datawas performed with a custom Python software packages pyFLAG . This section summarizes the scripts availableto perform the post-correlation beamforming, flux cali-bration, and imaging of FLAG spectral line data.5.1. Post-Correlation Beamforming
A scan performed with FLAG produces several typesof ancillary FITS files that contain important meta-data such as the antenna positions and LO settings.These metadata must be collated and combined withthe raw covariances stored in FITS files to create a sin-gle dish FITS (SDFITS ) file that can be manipulatedin GBTIDL , just as data from the single-pixel receiver. https://github.com/nipingel/pyFLAG https://fits.gsfc.nasa.gov/standard40/fits standard40aa-le.pdf https://safe.nrao.edu/wiki/bin/view/Main/SdfitsDetails http://gbtidl.nrao.edu/ LAG Hi Commissioning pyFLAG software to collate all themetadata and perform the post-correlation beamform-ing (i.e., Equation 6) to generate an SDFITS file for eachformed beam that contains beamformed spectra in unitsof raw counts.This software suite contains all the necessary Pythonand GBTIDL code with which to calibrate and imagespectral line data from FLAG. In both correlator modes(i.e., PFBCORR and CALCORR), each GPU runs twocorrelator threads making use of the xGPU library ,which is optimized to work on FLAG system parame-ters. Each correlator thread handles 1/20th of the totalbandwidth made up of either 25 non-contiguous coarsefrequency channels with 303.18 MHz resolution or 160contiguous fine channels with 9.47 kHz resolution andwrites the raw output to disk in a FITS file format. Thedata acquisition software used to save these data to diskwas borrowed from development code based for the Ver-satile GBT Astronomical Spectrometer (VEGAS) engi-neering FITS format. The output FITS file from eachcorrelator thread is considered a ‘bank’ with a uniqueX-engine ID (XID; i.e., the correlator thread) rangingfrom 0 to 19 that is stored in the primary header of theFITS binary table; there are therefore 20 distinct FITSfiles created for each scan. Reading and sorting the co-variances stored within each bank FITS file — whetherplacing the non-contiguous 25 ×
20 coarse channels inthe correct order or stitching together the the 160 × pyFLAG software.The raw data output for both CALCORR and PF-BCORR correlator modes are the covariance matricescontaining the covariance between individual dipole el-ements. However, due to xGPU limitations, the covari-ance matrices are shaped 64 ×
64 and flattened to a one-dimensional (1D) data vector.An example of how the covariance values are orderedis illustrated in Figure 4. Here, R i , jk corresponds to thecovariance between dipole i and j at frequency channel k . Most of the transpose pairs (e.g., R , ) are shown aszero because they are not included in the 1D data arraythat is saved to disk in order to preserve disk space. Ad-ditionally, since only the covariances between the first 40data streams (19 dipoles × https://github.com/GPU-correlators/xGPU/tree/master/src row-major order, where a block corresponds to a col-ored 2x2 sub-matrix. The reduction scripts treat each4-element contiguous chunk of the 1D data vector as ablock and place it into the larger covariance matrix inrow-major order. Once the first 40 rows have been filledin, a conjugate transpose operation is performed to fillin the missing covariance pairs and the remaining zerosare discarded.When in CALCORR mode, the bank file correspond-ing to XID ID 0 contains covariances matrices for fre-quency channels 0 to 4, 100 to 104, ..., 400 to 404; theXID 1 bank file stores covariance matrices for frequencychannels, 5 to 9, 105 to 109, ..., 405 to 409. Howeverin PFBCORR mode, the covariance matrices for chan-nels 0 to 159 are stored in the bank file correspondingto XID 0 and continue in a contiguous fashion such thatthe bank file corresponding to XID 19 stores data forfrequency channels 3039 to 3199. The logic during datareduction is to process each frequency channel individu-ally, then sort the result into the final bandpass based onthe XID and mode in which the data were taken. Thescripts that drive the creation of an SDFITS file are PAF Filler.py — in essence the ‘main’ function of theprogram — and the two modules metaDataModule .pyand beamformerModule.py .The foremost step in the filling and calibration pro-cess of FLAG data is to solve Equation 5 for the dom-inant eigenvector using the R s and R n covariance ma-trices obtained from calibration scans to determine themaxSNR complex beamforming weights. This is per-formed with the pyFLAG python script, pyWeights.py ,which also generates a series of 20 FITS files (one foreach bank). Each beamformer weight FITS file con-tains a binary table consisting of 14 × × × (64 elements ×
25 frequencychannels × PAF Filler.py can be run. This script reads in andunpacks each bank FITS file to pass the raw data1D covariances to the beamformer object created by beamformingModule.py . Each bank FITS files is pro-cessed in parallel to maximize efficiency.Within this module, the FITS files storing the com-plex beamforming weights are read in and organized intothe form of a 2D numpy array of complex data-type,with the rows representing the 25 coarse frequency chan-nels and columns represent the correlations of the ‘40’dipoles (19 × Pingel et al.
Correlator Output, cont. …
39 40 … 𝑅 𝑘 𝑅 𝑘1,2 … … 𝑅 𝑘2,1 𝑅 𝑘2,2 … … 𝑅 𝑘3,1 𝑅 𝑘3,2 𝑅 𝑘3,3 𝑅 𝑘3,4 … … 𝑅 𝑘4,1 𝑅 𝑘 𝑅 𝑘 𝑅 𝑘4,4 … … … … … … … … … … … … 𝑅 𝑘 𝑅 𝑘 𝑅 𝑘 𝑅 𝑘 … 𝑅 𝑘 𝑅 𝑘 … 𝑅 𝑘40,1 𝑅 𝑘40,2 𝑅 𝑘40,3 𝑅 𝑘40,4 … 𝑅 𝑘40,39 𝑅 𝑘40,40 …
041 0 0 0 0 … … … … … … … … … … … …
64 0 0 0 0 … … 𝑅 𝑘1,1 𝑅 𝑘1,2 𝑅 𝑘2,1 𝑅 𝑘2,2 𝑅 𝑘3,1 𝑅 𝑘3,2 𝑅 𝑘4,1 𝑅 𝑘4,2 𝑅 𝑘3,3 𝑅 𝑘3,4 𝑅 𝑘4,3 𝑅 𝑘4,4 … … 𝑅 𝑘39,3 𝑅 𝑘39,4 𝑅 𝑘40,3 𝑅 𝑘40,4 … 𝑅 𝑘39,39 𝑅 𝑘39,40 𝑅 𝑘 𝑅 𝑘 … Array length = 2112
Complex typedef { float real;float imag;}
Figure 4.
The structure of a covariance matrix used in beamforming. The numbers preceding each row/column correspondto the dipole element. Each element of the matrix stores the covariance between dipole elements i and j for a single frequencychannel, k . The output is ordered in a flattened one-dimensional array that needs to be reshaped into a 40 ×
40 matrix beforebeamforming weights can be applied. Additionally, due to xGPU limitations, the output size is 64 ×
64, which results in manyzeros that need to be thrown away in data processing. format, the raw 1D covariances recorded for each inte-gration are reordered and transposed according to theblock row-major scheme summarized in Figure 4 and re-shaped into a 3D numpy array of complex data-type withrows and columns both representing the correlations be-tween dipoles and the third axis representing a givenfrequency channel. The final returned cube for each in-tegration has dimensions of 40 × × N chan , where N chan is again number of frequency channels per bank file —either 25 or 160, depending on whether FLAG is oper-ating in CALCORR or PFBCORR mode, respectively.Note two important aspects: (1) the irrelevant correla-tions caused by xGPU limitations are thrown away atthis stage; (2) some rows and columns contain zeros asthey correspond to two unused data streams. Equation 6is then applied to each plane of the correlation cubeto construct a beamformed bandpass in units of rawcounts. A 2D array containing the beamformed band-pass for each integration is returned to PAF Filler.py and sorted into global data buffers. The software willrecognize the mode based on the number of channelsstored in a bank FITS file. When in PFBCORR mode,where 100 coarse channels are sent through a PFB im-plementation to obtain a total of 3200 fine channels, thebeamformer weight for an input coarse channel will beapplied across the 32 corresponding output fine chan-nels. After each bank FITS file for a particular scan is pro-cessed, the filled global data buffers are passed to ametadata object created by metaDataModule.py . Thisobject collates all associated metadata, applies the beamoffsets to the recorded antenna positions, and performthe necessary Doppler corrections to the topocentric fre-quencies. Once all corrections to the spatial and spectralcoordinates have been made, the binary FITS tables arecombined and appended to a primary Header Data Unitand returned to
PAF Filler.py where the final SDFITSfile is written to disk. The process then repeats until allbeams for all observed objects are processed. Compre-hensive documentation and usage examples are availableat https://github.com/nipingel/pyFLAG.5.2.
Spectral Line Calibration and Imaging
After post-correlation beamforming to obtain spectrain units of raw system counts, flux calibration of Hi datacan begin. We calculate the SEFD (see Equation 7 anddiscussion in Section 4.1) from the CALCORR calibra-tion scans. The flux measured on the sky is S sky = SEFD (cid:18) P On P Off − (cid:19) . (13)As discussed above, we obtain a reference spectrum touse as P Off from the edges of our science maps by takingthe mean power in each frequency channel for the first LAG Hi Commissioning Session Beam Scan Type SEFD [Jy] Calibration Source Calibration Source Flux [Jy]
GBT16B 400 12 (NGC 6946) ± ± ± ± ± ± ± GBT16B 400 13 (NGC 6946) ± ± ± ± ± ± ± GBT17B 360 03 (NGC 4258 Field) ± ± ± ± ± ± ± GBT17B 360 04 (NGC4258 Field) * 0 Grid 9.3 ± ± ± ± ± ± ± GBT17B 455 01 (G353 − † ± ± ± ± ± ± ± Table 4.
Summary of derived system properties in XX Polarization from calibration scans used to make the science images; † denotes that ν was set to 1450.00000 MHz for Beams 0-6; ‡ denotes that ν was set to 1450.8484 MHz. and last four integrations of a particular map scan. P On in Equation 13 is then the raw power in each integra-tion recorded during the scan. The SEFD values usedto scale the raw power ratios for each beam and eachsession are computed with Equation 7 as discussed inSection 4.1 and summarized in Table 4. The flux cali-bration scripts are written in GBTIDL and driven with apython wrapper, PAF edgeoffkeep parallel.py , in or-der to calibrate each of the seven beams in parallel. Themean SEFD over all beams included in our science maps is 12.3 ± ± η of 0.65 (Boothroyd et al. 2011) for the sake of di-rect comparison with the single-pixel receiver, and usethe more characteristic SEFD value of 10 Jy, Equation 7gives a T sys of 18.5 K. While this assumption of η doesnot consider specific parameters of the FLAG receiver,such as the large spillover from the illumination pattern2 Pingel et al. of individual dipoles and their mutual coupling, this T sys value is consistent with both the existing single-pixel re-ceiver ( ∼
18 K) and the T sys / η measurements of Roshiet al. (2018) at 1.4 GHz ( ∼ T sys / η is directly related to the SEFD(i.e., Equation 8). Consistent SEFD values are criti-cal for accurately reproducing measurements of flux onthe sky between observing sessions and making compar-isons between the data collected by FLAG and otherinstruments. We see that the overall SEFD values pro-gressively converge to the single-pixel value and ob-serve a consistent decrease in the variation betweenbeams and session-to-session with subsequent observ-ing runs. We attribute the steady reduction in bothmeasured SEFD values and associated scatter to consis-tent improvements to the calibration strategies used toobtain and maintain bit and byte-lock — such as theintroduction of scripts to automate this process. Westress that our most accurate flux measurements areobtained from our later observing sessions, specificallyGBT17B 360 04 and beyond. We therefore note thatthe maps presented in Section 6.3 from previous ses-sions are done so with the caveat that the overall fluxscale has high uncertainty relative to later sessions. Fur-thermore, since the overall flux scale of an OTF spectralmap depends on both the area of the assumed telescopebeam and the width of the convolution function usedto interpolate the individual samples to a regular imagegrid (Mangum et al. 2007), we present Hi flux densityprofiles only from sessions where the weights were de-rived from a full calibration grid to ensure the beamresponse is fully characterized over the FoV.5.3. Bandpass Scalloping
An example of a raw and calibrated integration whenthe system is in PFBCORR mode is shown in Figure 5.The nulls, or ‘scalloping’, seen every 303.18 kHz (every32 fine frequency channels) in the top panel is a con-sequence of the two stage PFB architecture approachcurrently implemented in the back end. As the raw com-plex time series data are processed within the ROACHs,a response filter is implemented in the coarse PFB suchthat the adjacent channels overlap at the − Figure 5.
An example of an uncalibrated, beamformedspectrum taken from the 35th integration of the 19th col-umn of a DecLatMap scan of NGC6946. The − Bottom : The cal-ibrated version of the above spectrum. While the scallopingbehavior appears to be mitigated, the signal aliasing at theedge of a coarse channel is still present. sition bands of the coarse-channel bandpass filter resultin residual structure. Additionally, this scheme leadsto signal aliasing stemming from the overlap in coarsechannels. Such near-coarse-channel-band-edge aliasingartifacts are present in a number of other existing astro-nomical two-stage zoom spectrometers. These artifactsdo not hinder the performance of FLAG in terms of sen-sitivity, but a fix for the signal aliasing is a priority goingforward. A provisional fix with the capability to provideboth coarse and narrowband spectra is realized by a two-stage channelizer architecture. The first implemented inthe ROACH and the second as part of PFBCORR modein the GPU. Both stages of processing use PFBs for com-putationally efficient channelization. In our case we areimplementing critically sampled PFBs at both stages.To remove spectral artifacts (aliasing, scalloping) thefirst stage channelizer must be an oversampled PFB toallow adjacent channels to overlap. In the output of the
LAG Hi Commissioning chanBlank parallel.py script before imagingto ensure no signal is aliased in the final maps. Theseblanked calibrated spectra are smoothed with a Gaus-sian kernel to a final resolution of 5.2 km s − and imagedwith the gbtgridder tool, utilizing a Gaussian-taperedcircular Bessel gridding function. Note that we presentimages of only the XX linear polarization due to com-plications with the YY polarization signal chain duringour two observing runs that has since been rectified.We account for the use of a single polarization in ourcalculations of sensitivity and comparison to equivalentsingle-pixel data. RESULTS6.1.
Beamformer Weights
The calibration procedure described in Section 4.1contributes to ∼
40 minutes of overhead and, in prin-ciple, can remain valid for several weeks if bit/byte lockis not lost. However, since lock is currently lost withevery change in the local oscillator setting, it is rec-ommended that an observer derive fresh beam weightsat the beginning of each observing session. Other rea-sons re-calibration may be necessary include: large vari-ations in the contribution of spillover and sky noise tothe signal model and the relative electronic gain driftbetween dipoles (Jeffs et al. 2008). Important factorsthat impact the quality of the weights are robust bitand byte locks, constraining the desired steering vec-tor for a formed beam, and utilizing a sufficiently brightcalibration source to adequately characterize the systemresponse when on and off source.While the current state of the FLAG system effec-tively requires new beamforming weights every session, https://github.com/GreenBankObservatory/gbtgridder Days N o r m a li z e d d Figure 6.
Variation of the phase distance metric betweensubsequent beamforming weights for the boresight beam asa function of time. The d values are corrected for the bulkphase offset according to Equation 15 and normalized by thefirst d value from each observing epoch for clarity. it is still interesting to explore how the complex weightvectors derived from a given calibration observation varywith time. Studying the variations will help reveal char-acteristic properties and behavior of the weights thatdemonstrate the stability of the system with time.Recall that a given element in the weight vector is acomplex number that contains the amplitude and phaseinformation to be applied to the output of a given dipolein order to steer a beam in the desired direction. Beamsteering is primarily influenced by varying the ampli-tude of the weights applied to each dipole. Given thereliable placement of our formed beams demonstrated inFigure 3, we wish to investigate how the formed beamresponses are influenced by the second-order effect ofphase variations. To measure the difference in phase, adistance metric can be defined d = || a − ˜a || , (14)where a and a are the vector norms (i.e., the squareroot of the sum of each element’s squared complex mod-ulus) of the weight vectors, or w / || w || and w / || w || ,respectively. The vector ˜a represents the subsequentweight vector that has been corrected for the bulk phaseoffset between the two vectors. This bulk phase off-set arises from the steering vectors, which are found bysolving for the dominant eigenvector in the generalizedeigenvalue problem in Equation 5. Since eigenvectors4 Pingel et al. are basis vectors that have arbitrary scaling, it is theunknown scaling of the phase between calibration datasets that contributes to the bulk phase offset. A subse-quent weight vector can be phase aligned to some initialweight vector by first making the first element of a realand then computing ˆ φ = ∠ (cid:0) a H2 a (cid:1) , (15)where ˆ φ is the angle of the product of a H2 a . The cor-rection for the bulk phase offset is therefore a complexscaling factor applied to all phases in the latter weightvector to ensure the phase differences in the remainingdipoles arise strictly from the systematic (e.g., bit/bytelock) and instrumental effects between different weightcalibrations. The phase aligned weight vector is there-fore ˜a = e i ˆ φ a .Because the distance metric d is the overall magni-tude of an element-wise difference between two M el-ement vectors, it encapsulates all the phase differencesbetween respective dipoles into a single quantity. Smallvariations in d over time indicate similar phases (savefor the bulk phase offset due, in part, to new bit/bytelock) between the derived weight vectors, meaning thedirectional response of the array is stable over the timespan of a typical observing run; thus, the beam patternshape remains relatively unchanged.Figure 6 shows the variation of the normalized d distance metric as a function of time for the boresightbeam. We see similar trends for each of the outer beamsand no discernible difference between types of calibra-tion scans performed. The initial set of beamformerweights (i.e., a ) is taken to be the first set of weightsderived for that particular observing run. We compareall subsequent weights from a given observing run withthis first set. The time values are taken to be the dif-ference between the mean Modified Julian Date (MJD)values associated with a given calibration scan, with theinitial MJD taken to be from the first calibration scanin a given observing run. The scatter in the phase vari-ations is well below the 1% level, indicating that the di-rectional response to identical coincident signals is verysimilar over time, which ensures the peak response isreliably located in the desired direction on the sky andsimilar beam structure between sessions.Figure 7 demonstrates the effect of varying beamform-ing weights on the measured beam shapes. Weightsderived from the calibration grids performed duringthe GBT17B 360 04 observing sessions were applied tosteering vectors from the GBT17B 360 07 calibrationgrid. Weights derived during an earlier session appliedto steering vectors from a subsequent session are con-sidered to be stale, since the sample delays required to achieve a previous bit/byte lock will produce a differentphase response. By examining the changes in overallbeam shape, the locations of the peak response of eachformed beam relative to the desired pointing center, andchange in sensitivity (i.e., Equation 10), we are able toinvestigate the stability of these beam weights betweenobserving sessions.The beams formed with stale weights retain their over-all Gaussian shape. While the peak response of the staleboresight beam is close to the desired pointing center,the peak responses of some of the outer beams, specifi-cally Beam 3, shifts significantly. The difference map inthe bottom left panel reveals that the relative phase off-set in the stale weights degrades the sidelobe structure,shifting the low-level beam response towards the edgeof the FoV. The change in the low-level beam responseis further illustrated in the partial histograms shown inthe bottom left panel. The peaks in the histograms thatrepresent the sidelobe structure shift to higher valuesand become broader, indicating a change in the overallbeam shape below the 10% level. The change in shapeof each distribution is due to the relative phase offsetpresent in the stale weights.We compute a measure of sensitivity for each formedbeam using Equation 10. The value of w H R s w is takento be the maximum power value at 1420 MHz in a 7-Pt calibration scan when the calibrator is centered ina given beam, and the w H R n w value is the averagepower value in the nearest reference pointing at thatsame frequency. Taking the ratio of the sensitivity val-ues between beams formed from stale weights to thoseformed with the correct weights reveals an average dropof 56% between all formed beams. Overall, the beamsformed with stale weights are stable above the 50% levelof the peak response. However, the application of staleweights results in beam patterns that are, on average,half as sensitive and possess altered directional responsesto the same incident signal at the levels of the first side-lobes. An observer should account for the overhead toperform at least a 7Pt-Cal to derive contemporaneousweights.A calibration strategy deemed ‘word lock’ that, inprinciple, will allow observers to reuse previously derivedweights is nearing deployment. This procedure accountsfor the variable amount of sample delays between eachbit/byte lock cycle by utilizing the time-shift propertyof the Fourier Transform to insert shifts in the full 16-bit/2-byte word. By inserting the optimal amount ofshifts that minimizes the variation in phase across fre-quency relative to a reference dipole (Burnett 2017), thephase response of the previous set of weights will nowapply to the current state of the system. LAG Hi Commissioning -10 0 10-10010 Beam 0 -10 0 10-10010
Beam 1 -10 0 10-10010
Beam 2 -10 0 10-10010
Beam 3 -10 0 10-10010
Beam 4 -10 0 10-10010
Beam 5 -10 0 10-10010
Beam 6 [ d B ] XEL Offset [arcmin] E L O ff s e t [ a r c m i n ] -10 0 10-10010 Beam 0 -10 0 10-10010
Beam 1 -10 0 10-10010
Beam 2 -10 0 10-10010
Beam 3 -10 0 10-10010
Beam 4 -10 0 10-10010
Beam 5 -10 0 10-10010
Beam 6 [ d B ] XEL Offset [arcmin] E L O ff s e t [ a r c m i n ] -10 0 10-10010 Beam 0 -10 0 10-10010
Beam 1 -10 0 10-10010
Beam 2 -10 0 10-10010
Beam 3 -10 0 10-10010
Beam 4 -10 0 10-10010
Beam 5 -10 0 10-10010
Beam 6 [ R e l a t i v e D i ff e r e n c e ] XEL Offset [arcmin] E L O ff s e t [ a r c m i n ] Beam 0
Correct WeightsStale Weights0.00 0.05 0.10 0.15 0.200255075100125150175
Beam 1
Beam 2
Beam 3
Beam 4
Beam 5
Beam 6
Normalized Beam Response Values I n c i d e n c e Figure 7.
Formed beam patterns and resulting histograms wherein beamforming weights derived from the calibration gridsperformed during the GBT17B 360 04 and GBT17B 360 07 observing sessions were applied to steering vectors from theGBT17B 360 04 calibration grid. The contours, red dash lines, and × symbols are the same as in Figure 3. The whitevertical and horizontal dashed lines correspond to the red lines from the upper right panel as a reference to the shift in peakresponse caused by the application of stale weights. Top left : beam pattern derived using the correct weights.
Top right : beampattern derived using stale (i.e., from GBT17B 360 07) weights.
Bottom left : the difference of the top left and right panels. Thesolid (dashed) contours denote the 90%, 50%, and 25% level of the maximum relative difference between each formed beam.
Bottom right : Partial histograms of the beam response values shown in the upper panels. The range of response values is chosento highlight the difference at the levels of the sidelobes. Pingel et al.
Sensitivity as a Function of Frequency
Figure 8 shows the result of Equation 9 derived fromfrequency sweep observations performed as engineeringtests for several of the commissioning runs. The goalof this test is to characterize the sensitivity over a widerange of frequencies and identify frequencies most af-fected by narrowband RFI features. We performed aseries of 7Pt-Cal scans with the LO set to 50 MHz incre-ments beginning at 1100 MHz and continuing up to 1700MHz. For each calibration scan, we calculate T sys / η asa function of the 150 MHz bandpass for each formedbeam at the coarse channel resolution of 0.30318 MHzand merge the results.As can be expected with significant improvementsto the system made between subsequent commissioningruns, T sys / η decreases as a function of epoch for bothpolarizations with the February 2018 calibration datashowing the lowest observed T sys / η . Since T sys / η andSEFD depend on one another, we also attribute thistrend to improvements made to the signal processing al-gorithms of the back end and calibration strategies toobtain bit/byte lock. Specifically, a correction to in-crease the digital gain to avoid a bit underflow whenthe data in the ROACH is reduced to 8-bit/8-bit realand imaginary values just before packetization was im-plemented for the February 2018 observing runs.The measured T sys / η are compared to several PAFsystem models (see Figure 8). In general, these modelsare produced by first obtaining the modified full po-larization response pattern of the individual dipole ele-ments embedded in the array. Finite element solutionsof electromagnetic equations were used to obtain theseresponse patterns. The patterns along with a model ofthe GBT optics were used to predict the full polarizedelectromagnetic field pattern in the antenna apertureand to characterize ground spillover. These results wereused to compute the signal covariance and the noisecovariance due to the ground spillover and sky back-ground. A noise model for the cryogenic LNAs is uti-lized to pre dict the receiver contribution to the noisecovariances. The maxSNR beamforming algorithm isthen applied to the signal and noise covariances to pre-dict the final T sys / η at a given frequency. See Roshiet al. (2019b) (hereafter RSF19) for further details onmodeling.The measured T sys / η for the February observing runare largely consistent with the models at a frequencyof 1.4 GHz. Overall, the measured sensitivity acrossfunctional frequency range of the receiver are consistentwith expectations models with only moderate narrow-band RFI near the Hi transition. The discrepancy be-tween the models and measurements at lower frequencies may be due to differences between the modeled and ac-tual roll-off of the analog filter. Obvious RFI artifactspresent between 1000 MHz and 1100 MHz and near 1625MHz need to be considered when planning potential ob-servations of radio recombination lines and the OH 1665MHz and 1667 MHz transitions. While we only show re-sults for the boresight beam, the trends are similar forall outer beams. 6.3. Hi Results
NGC 6946
The external galaxy, NGC 6946, was chosen as thefirst science target for Hi on the basis of ample GBTsingle-pixel data available for comparison (e.g., Pisano2014). The presence of high-velocity gas from galacticfountain activity (Boomsma et al. 2008) and an Hi fila-ment, possibly related to recent accretion (Pisano 2014),and several smaller nearby companions are also ideal fea-tures to test the sensitivity of this new receiver.This source was observed in the horizontal celestial co-ordinate system to ensure beam offsets, which are deter-mined in the same coordinate frame by definition, werecorrect. The images presented here are 2 ◦ × ◦ large andhad the central frequency ( ν ) set to 1450.0000 MHz inthe topocentric Doppler reference frame. For a directcomparison with previous single-pixel data and a sin-gle FLAG beam, we show channel maps from the bore-sight beam in Figure 9 to demonstrate that FLAG ef-fectively reproduces single-pixel observations. Overall,the FLAG and single-pixel contours agree well with theslight offsets in the lowest level contours are attributedto the fact that the FLAG data are a factor of almost10 times less sensitive than the single-pixel data. Thedifference in sensitivity between these two maps also ex-plains the non-detection of the two unresolved compan-ions, UGC11583 and L149, in the channel maps from asingle beam. Figure 10 reveals the presence of the twocompanions once data from all seven FLAG beams arecombined in a single map. Here, the slight differencesat the lowest contour levels likely arise from the compli-cated beamshape and sidelobe structure resulting fromaveraging the seven distinct formed beams.6.3.2. NGC 4258 Field
NGC 4258 resides in the Canes Venatici II Group (deVaucouleurs 1975), which is comprised of several com-panions including the late-type galaxies NGC 4288 andUGC 7408 to the southwest and J121811.04+465501.1— a low surface brightness dwarf galaxy (Liang et al.2007) — slightly to the southeast. The most appealingtarget in the field is a prominent Hi filament extendingfrom NGC 4288 that points towards NGC 4258. This LAG Hi Commissioning T s y s / η Aug 2017 (YY)Aug 2017 (XX)Feb 2018 (YY)Feb 2018 (XX)RSF19XX ModelRSF19YY Model
Figure 8. T sys / η (see Equation 9) as a function of frequency derived for a set of 7Pt-Cal scans in which the LO wassequentially shifted by 50 MHz. The PAF model results form Roshi et al. (2019b) corresponding tot he two polarizations aremarked RSF19XX and RSF19YY. These model results correspond to a thermal transition length of 9.1 cm and its loss of 1 K.See Roshi et al. (2019b) for further details. filament was seen previously with the 76.2m Lovell tele-scope at the Jodrell Bank Observatory (UK) as partof the Hi Jodrell All Sky Survey (HIJASS); (Wolfin-ger et al. 2013). It is classified as an ‘ Hi cloud’ withthe designation HIJASS J1219+46; no known opticalcounterparts are observed over the spatial extent of the Hi emission. The single-pixel data used as a compari-son, which was collected during a GBT survey to pro-vide the single-dish counterpart to the high-resolutionWestorbork Radio Synthesis Telescope (WSRT) Hydro-gen Accretion in LOcal GAlaxieS (HALOGAS) Survey(Heald et al. 2011; Pingel et al. 2018), shows a peak fluxof ∼ ∼
80 kpc,assuming the same distance as to NGC 4258.A total of six 1.5 ◦ × ◦ maps evenly split over two sep-arate observing sessions were performed. Improvementsto how the beam offsets were applied in the custom re- duction software enabled mapping in equatorial coordi-nates. The first session the ν set to 1450.0000 MHzand 1449.84841 MHz, respectively, to circumvent thefrequency scallopping (see Figure 5 and discussion inSection 5.2). The relative weak flux, extended nature,and complex kinematics originating from a possible tidalinteraction between HIJASS J1219+46 and other groupmembers provide an excellent benchmark for the map-ping capabilities of FLAG.The channel maps of the NGC 4258 Field in Fig-ure 11 contain data from all seven beams from sessions17B 360 03 and 17B 360 04, with data from the formersession being scaled by the factor listed in Table 5 toensure a consistent flux scale. While there is not a spe-cific cause for the relatively large scale factor of ∼ Pingel et al. +59°48'+60°00'12'24'36' D e c ( J ) [ J y / B e a m ] +59°48'+60°00'12'24'36' D e c ( J ) RA (J2000) +59°48'+60°00'12'24'36' D e c ( J ) RA (J2000)
RA (J2000)
Figure 9.
Channel maps of NGC 6946 and nearby companions. Hi emission detected by the FLAG boresight beam isrepresented by the color scale and white contours, while emission detected by the single-pixel receiver is denoted by orangecontours. Both sets of contours begin at the 130 mJy/Beam level ( ∼ σ meas in Table 5) and continue at 10 and 25 times thatlevel. for the first time before the latter session, which hasshown to significantly increase the stability of the sys-tem over the course of multiple observing sessions thatuse the same LO configuration. These channel mapsdemonstrate that FLAG can reproduce the features ofdiffuse structures detected by the single-pixel receiverwhen mapping at similar sensitivities. The contourstracing the filament, HIJASS J1219+46, extending fromNGC 4288 between the velocities of 378 km s − and 409km s − are in agreement, albeit for the lowest level con-tours that are affected by the unconstrained sidelobe levels. The Hi column density image in Figure 12, inwhich a mask was applied such that only pixels with aS/N > Hi cloud.Figures 13 and 14 present Hi flux density profiles com-paring FLAG and single-pixel data, with the formercomparing measurements from individual beams and thelatter showing profiles taken from the rectangular re-gions in the combined map as denoted in Figure 12; the LAG Hi Commissioning RA (J2000) +59°48'+60°00'12'24'36' D e c ( J ) N H I [ c m ] × Figure 10. Hi column density map of NGC 6946. FLAGdata is represented by the color scale and white contours,while the single-pixel equivalent column density levels areoverlaid in orange. The outer contour is at a level of 1 × cm − , which represents a 3 σ detection over the integrated11.4 km s − to 181.4 km s − velocity range, while the in-ner contours go as 5, 10, and 25 times that level. We haveassumed the emission is optically thin and a similar gain of1.86 K/Jy to convert the FLAG data to units of brightnesstemperature. measured fluxes and associated Hi masses are summa-rized in the row denoted S meas under 17B 360 04 in Ta-ble 5. Since the intensity units of Hi maps are presentedin terms of surface brightness, it is vital to have knowl-edge of the beam area. Unfortunately, as demonstratedin the beam patterns shown in Figure 3, each formedbeam has a unique area. For each beam, we take thederived beam pattern and fit two Gaussians along twoorthogonal cuts along the central horizontal and verticalaxes. The beam area is then calculated from the aver-age of these two Gaussians. The final beam area of thecombined map is taken to be the mean of these indi-vidual beam areas; see again Table 5 for a summary ofthese areas. Given the variation in early SEFD values,relative uncertainty with the final beam areas, possibleerrors in bandpass calibration, the presence of interfer-ence, and modeling for atmospheric effects, we adopt anoverall 10% flux uncertainty.The profiles and total flux measurements of Beams 0-3 and Beam 6 agree very well with the flux values fromthe equivalent single-pixel map. The offset in Beam4 and Beam 5, while still within the 10% flux uncer- tainty, is likely influenced by the deviations from Gaus-sianity in the main lobe of these formed beams and rela-tively high sidelobes. The combined maps and profiles ofboth NGC4258 and HIJASS J1219+46 agree very wellwith their single-pixel counterparts. The overall con-sistency between the FLAG and single-pixel data of theNGC 4258 Field and detection of a very diffuse Hi clouddemonstrate the capability of FLAG to provide equiva-lent and accurate spectral line maps relative to the cur-rent single-pixel receiver on the GBT.6.3.3. Galactic Center
A recent single-pixel survey of Hi above and below theGalactic Center undertaken by Di Teodoro et al. (2018)revealed a population of anomalous velocity clouds ex-panding out in a biconic shape, which likely arises fromnuclear wind driven by the star formation activity in theinner regions of the Milky Way. As a demonstration ofFLAG’s capability to map extended Galactic emissionand characterize gas moving at anomalous velocities, wemapped a 2 ◦ × ◦ region centered on l = 353 ◦ and b = − ◦ in the Galactic coordinate system with ν set to1449.84841 MHz.Figure 15 presents Hi column density of structures to-wards the Milky Way center that are moving at anoma-lous approaching and receding velocities. Once more,the spatial distribution of the emission detected byFLAG is sufficiently consistent with the single-pixel con-tours. The comparisons of Hi spatial extent clearly high-light FLAG’s ability to characterize both the diffuse Hi associated with extragalactic sources and the complexkinematic properties of anomalous velocity clouds in andaround the Milky Way.6.3.4. Discrepancies and Improvements
Figures 9-15 demonstrate broad agreement with pre-vious single-pixel observations. However, there are no-table discrepancies between FLAG and single-pixel con-tours that are at the same absolute flux density and col-umn density levels. There are several possible sourcesfor such discrepancies including stray radiation from thecomplex beam shapes, differences in sensitivity betweenmaps, and a flux offset between FLAG and single-pixeldata.Figure 16 shows the beam patterns for the boresight(Beam 0) and Beam 2 derived from the calibration gridfrom session GBT17B 360 04 with overlaid contoursfrom a model of the GBT single-pixel L-Band beamshown in Figure 1 of Pingel et al. (2018). There is excel-lent agreement between the single-pixel beam model andBeam 0 from the FWHM response level extending downto the level of the first sidelobe at the 0.1%. The side-lobes is highly asymmetric in both FLAG beams, with0
Pingel et al. +46°00'30'+47°00'30' D e c ( J ) [ J y / B e a m ] +46°00'30'+47°00'30' D e c ( J ) RA (J2000) +46°00'30'+47°00'30' D e c ( J ) RA (J2000)
RA (J2000)
Figure 11.
Channel maps of the NGC 4258 Field. Hi emission detected by FLAG is represented by the color scale and whitecontours, while emission detected by the single-pixel receiver is denoted by orange contours. Both sets of contours begin at the27 mJy/Beam level ( ∼ σ meas in Table 5) and continue at 5 and 10 times that level. the peak sidelobe in the outer Beam 2 peaking an orderof magnitude higher than that of the boresight beam;also, note that this sidelobe overlaps almost directlywith the peak of the boresight response. Given thatthat dynamic range of the our observations is typicallyon the order of several hundred, it is feasible that suchcomplex beam shapes — especially in the final combinedFLAG maps, where the beam responses are effectively averaged together – will affect the observed morphologyof diffuse structures.To test the degree to which the complex sidelobesstructure in the formed FLAG beams affect the dis-crepancies in the flux density contours, we convolve theFLAG map made with the boresight beam of NGC 6946with a single-pixel beam model re-gridded to a com-mon pixel grid. Likewise, the single-pixel map is con- LAG Hi Commissioning RA (J2000) +46°00'20'40'+47°00'20'40' D e c ( J ) N H I [ c m ] × Figure 12. Hi column density map of the NGC4258 Fieldobserved by FLAG (color scale and white contours) withequivalent single-pixel data (orange contours) overlaid. Thecontour levels beginning at 2 × cm − , which representsa 5 σ detection over a 20 km s − line, and continuing at 15,100, and 500 and 1000 times that level. The dashed anddot-dashed rectangles denote the angular areas over whichthe flux profiles shown in Figure were integrated. volved with the FLAG boresight beam pattern; the re-sulting column density map shown in Figure 17 nowshows the same sky brightness distribution convolvedwith the same response. The apparent bridge of mate-rial that now connects NGC 6946 with its companionsis due to the degraded angular resolution from convolu-tion with both beams. The contours to the south are inbetter agreement with deviations on the scale of a singlepixel, confirming that the asymmetric sidelobe patternsof the formed FLAG beams indeed influence the mor-phology of diffuse emission by a non-negligible amount.The larger discrepancies towards the north and aroundthe unresolved companions can be attributed to the or-der of magnitude difference in sensitivity between theFLAG and single-pixel map, which detects an apprecia-ble amount of diffuse Hi below a column density level of1 × cm − — including a conspicuous Hi plume —that likely influences these northern contours (Pisano2014). Differences between the overall flux scale, whichhas since been addressed with improvements to the over-all stability of the system, can also cause such discrep-ancies.There are several possible avenues to mitigate effectsfrom the complex sidelobe patterns, including utiliz- ing alternative beamforming algorithms. However, at-tempts to constrain the sidelobe levels of formed beamson other radio telescopes sacrifice sensitivity at unac-ceptable levels. Fortunately, the raw covariance dataobtained from FLAG can be used to aid development ofnew algorithms. A more traditional approach would beto apply a stray radiation correction first developed byvan Woerden (1962), demonstrated for single dish tele-scopes e.g., Kalberla et al. (1980), Winkel et al. (2016),and applied to multibeam systems in Kalberla et al.(2010). Such a correction requires detailed knowledgeof the sidelobes, which can easily be obtained using asufficiently large calibration grid. The correction canalso be considerably simplified by having a known all-sky brightness temperature distribution. Ample archivaldata from the single-pixel exists to attempt such correc-tions for future FLAG data.6.4. Survey Speed Comparison
We now aim to quantify the performance of FLAGrelative to the single-pixel receiver and the PAFs andmulti-beam receivers available on other prominent radiotelescopes. We do this through the survey speed (SS)metric.To obtain an expression for SS , we first define a givensurface brightness sensitivity (in units of K) to be σ = T sys (cid:112) ∆ νN p t , (16)where ∆ ν is the width of a frequency bin, N p is thenumber of polarizations, and t is the integration timenecessary to reach a given surface brightness sensitiv-ity. Putting T sys in terms of SEFD (Equation 8) andabsorbing the antenna gain factors gives an equivalentexpression for point source sensitivity ( σ s in units of Jy)that can be rearranged to give the time necessary toreach a given point source sensitivity t = 1∆ νN p (cid:16) σ s SEFD (cid:17) (17)Following Johnston & Gray (2006), the speed at whicha single dish can survey an area of sky to the necessarysensitivity limit is the ratio of its inherent FoV to t or SS = FoV∆ νN p (cid:16) σ s SEFD (cid:17) (18)where the FoV is measured in square degrees. In thecase of FLAG, we define the FoV to be the area of skyover which the sensitivity map (see again Figure 2) re-mains above a − .2 Pingel et al.
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Beam 6 Velocity [km s ] F l u x D e n s i t y [ J y ] Figure 13. Hi flux density profiles of NGC 4258 from each FLAG beam (blue) with equivalent single-pixel profile (orange)overlaid. These profiles were measured by integrating over the dashed rectangular region overlaided in Figure 12. We employ the Source Finding Application (SoFiA;Serra et al. 2015b) software package to measure thenoise in the FLAG cubes and compare with similar datafrom the single-pixel receiver. We utilize the featurein which the rms is estimated from a Gaussian fit tothe negative half of the histogram of pixel values. Thehistogram is constructed using only emission-free chan-nels to avoid spectral channels whose reference spectra have been contaminated by Milky Way emission duringcalibration. Table 5 lists the measured noise returnedby SoFiA for the cubes produced for each individuallyformed beam, the combined beam cube, and the single-pixel cube. The measured noise in the combined beamcubes generally scale by the reciprocal of the square rootnumber of beams, as expected from pure Gaussian noise.The beam-to-beam variation in SEFD values also influ-
LAG Hi Commissioning
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Figure 14.
Left: Hi flux density profiles of NGC 4258 from the combined FLAG map (blue) with equivalent single-pixelprofile (orange) overlaid. Right: Hi flux density profiles from the same maps of the faint Hi cloud, HIJASS J1219+46. Theseprofiles were measured by integrating over the dashed and dot-dashed rectangular regions overlaid in Figure 12. G a l a c t i c L a t i t u d e N H I [ c m ] × G a l a c t i c L a t i t u d e N H I [ c m ] × Figure 15. Hi column density maps of the FLAG (color scale and white contours) with equivalent single-pixel data (orangecontours) overlaid for the Galactic Center observations; left : Hi map derived by integrating over approaching LSR velocities(see text). The contours begin at a level of 6 × cm − and continue at 5 and 10 times that level; right : Hi map derived byintegrating over receding LSR velocities with the same contour levels. Pingel et al.
Figure 16.
The beam patterns from the boresight FLAGbeam (left) and outer Beam 2 (right). The white contoursdenote the response from a model of the singel-pixel beam.Contours begin at a level of 0.001, 0.01, 0.1 and 0.5 timesthe peak response. The outer beam is shown to highlightthe highly peaked sidelobe that overlaps near the peak ofthe boresight.
Figure 17. Hi column density map of NGC 6946 after con-volving the FLAG data with a model of the GBT L-Bandsingle-pixel beam (color scale and white contours) with con-tours from the data single-pixel overlaid after a similar con-volution with the FLAG boresight beam pattern. The convo-lution ensures the both maps have effectively equal responsesto the observed sky brightness distribution. The contours areat the same levels listed in the caption from Figure 10. ences the final noise floor in the combined cubes. Be-cause the available single-pixel cubes are generally moresensitive than the FLAG commissioning maps, a straightcalculation of the SS metric using the measured noiseproperties will give a convoluted comparison. To ensurea normalized comparison, we use the measured single-pixel noise while taking the FLAG SEFD values avail-able in Table 4 to compute Equation 18. The quoteduncertainties are propagated from the SEFD uncertain-ties. For all observing sessions, FLAG possesses a higher SS in the final combined maps, largely aided by the in-crease in FoV.As broader comparison, we assume a desired pointsource sensitivity level of 5 mJy and plot the SS ofFLAG, the single-pixel receiver, and several other multi-pixel receivers and PAFs already available or planned forother major radio telescopes as function of angular reso-lution in Figure 18. When comparing different receivers,we must make a consistent definition of the FoV, sincesensitivity maps for the other receivers are not readilyavailable. In these cases, we consider the field of viewto be FoV eff = N b Ω b , (19)where N b is the number of beams and Ω b is the beamsolid angle in square degrees as measured at the FWHM.Table 6 summarizes the parameters used in the calcula-tion of Equation 18.ASKAP and Apertif, being PAF-equipped interfero-metric telescopes, possess a distinct advantage in termsof angular resolution due to their capability to samplelarge spatial frequencies. However, even when consider-ing point-source sensitivity, they are ultimately limitedin their SS by their relatively large SEFDs. On theother hand, the SEFDs of single dish telescopes benefitfrom their large and continuous apertures but suffer interms of angular resolution. The SS of FLAG relativeto the GBT single-pixel reciever is about an order ofmagnitude higher, and the cryogenically cooled LNAsin its front end enhance its performance to exceed allother existing PAFs, while providing comparable reso-lution. Relative to multiple horn receivers, FLAG beatsthe 13 beam multibeam receiver on Parkes in terms ofangular resolution and SS and also produces compara-ble SS metrics to the 7-beam ALFA receiver on the nowdefunct 300m Arecibo telescope. In fact, the survey ca-pabilities of the GBT when equipped with FLAG areonly exceeded by the multibeam receiver on FAST, theworld’s largest primary reflector telescope that cannotbe fully steered. CONCLUSIONS AND OUTLOOKThis work summarized the commissioning of the cal-ibration and spectral-line observing modes for a newbeamforming back end for FLAG, a cryogenically cooledPAF L-band receiver for the GBT. These observationsrepresent the culmination of several commissioning runsfrom 2016 to 2018 wherein the system was incrementallytested on a diverse range of extragalactic and Galactic Hi science targets and known calibrator sources. Themain results from these commissioning runs are: • The beamforming weights derived from Calibra-tion Grids and 7Pt-Cal scans produce seven si-
LAG Hi Commissioning Session Property Beam 0 Beam 1 Beam 2 Beam 3 Beam 4 Beam 5 Beam 6 Combined single-pixel
16B 400 12 σ meas [mJy Beam − ] 43 45 46 46 49 49 49 19 4SS [deg hr − ] 0.38 ± ± ± ± ± ± ± ± ±
16B 400 13 σ meas [mJy/Beam − ] 44 49 46 51 53 57 51 20 4SS [deg hr − ] 0.37 ± ± ± ± ± ± ± ± ±
17B 360 03
Scaling Factor † σ meas [mJy/Beam − ] 30 31 29 30 33 33 33 16 8SS [deg hr − ] 1.09 ± ± ± ± ± ± ± ± ±
17B 360 04
Ω [arcmin ] 95 100 101 105 110 122 114 107 94 S meas [Jy km s − ] 410 ±
40 400 ±
40 420 ±
40 370 ±
40 350 ±
40 340 ±
30 390 ±
40 380 ±
40 410 ± σ meas [mJy/Beam − ] 15 15 15 15 16 15 15 8 8SS [deg hr − ] 3.38 ± ± ± ± ± ± ± ± ± Table 5.
Measured noise ( σ meas ), survey speeds ( SS ), beam area (Ω), and measured flux ( S meas ); † represents the scaling factorapplied before combination with an associated frequency-dithered session. Receiver N b FWHM [arcmin] Resolution [arcmin] FoV eff [deg ] SEFD [Jy] SS [deg hr − ] ReferenceFLAG 7 9.1 9.1 0.144 10 6.3 × − This workGBT single-pixel 1 9.1 9.1 0.018 9.7 8.4 × − This workApertif 37 30.0 0.3 10.500 330 4.2 × − Oosterloo et al. 2009ASKAP 36 60.0 0.2 46.200 1700 7.0 × − David McConnell (2020; private communication)ALFA 7 3.5 3.5 0.027 3 1.3 × − Peek et al. 2011; http://outreach.naci.edu/ao/scientist-user-portal/astronomy/recieversALPACA 40 3.3 3.3 0.137 3 6.7 × − Roshi et al. 2019aEffelsberg PAF 36 7.6 7.6 0.650 130 1.7 × − Rajwade et al. 2019FAST Mutli-Beam 19 2.9 2.9 0.014 0.4 3.8 × − Jiang et al. 2020Parkes Multi-Beam 13 14.5 14.5 0.86 25 6.0 × − Staveley-Smith et al. 1996; McClure-Griffiths et al. 2009Parkes PAF 17 13.0 13.0 0.900 65 9.4 × − Reynolds et al. 2017
Table 6.
Survey Speed Parameters. Note that the FWHM for ASKAP and Apertif refer to the size of a single formed primarybeam, while resolution refers to the size of a typical synthesized beam. log (Resolution [arcmin]) l o g ( S u r v e y Sp ee d [ d e g h r ]) FLAGGBT (single-pixel)ALFAALPACAParkes multi-BeamParkes PAFEffelsberg PAFFAST multi-beamASKAPAptertif
Figure 18.
Comparison of various receiver survey speeds.The dotted lines denote different PAF recievers, while thesolid lines represent traditional multi-beam and single-pixelreceivers. multaneously formed beams optimally spaced toachieve uniform sensitivity across the FoV. The measured beam shapes are sufficiently Gaussiandown to the 3% level of the peak response withFWHM’s ranging from 8.7 (cid:48) to 9.5 (cid:48) . The locationsof the peak response for each beam beam are reli-ably located within 5% of the their intended point-ing centers. • The custom python package, pyFLAG , is used to ap-ply the beamforming weights to the raw covariancematrices to create SDFITS files that contain un-calibrated beamformed spectra. Through severalGBTIDL and GBO tools, these spectra are fluxcalibrated and imaged to create SDFITS cubes foreach formed beam. A beam combined cube is pro-duced by averaging all spectra from these individ-ual cubes. • The overall phase of the derived complex beam-forming weights varies less than 1% over timescalesof ∼ Pingel et al. structure, sensitivity, and shifts the peak responseaway from the intended pointing center. An ob-server should at least perform a 7Pt-Cal scan toderive contemporaneous weights. In the future,the word lock calibration procedure will ensure thephase response of a previous set of weights appliesto the current state of the system. Weights canthen be reused without deterioration of sensitivityor overall beam shape. • The measures of sensitivity across the entire 150MHz bandpass show steady improvement overour commissioning runs. Likewise, the measuredSEFDs used to scale spectra to the correct fluxscale converged towards the single-pixel value inlater sessions. These improvements are the re-sult of improvements in our calibration strate-gies to obtain and maintain bit and byte-lock,which ensure the serialized complex voltages sam-ples streaming from the front end over optical fiberare correctly decoded for downstream processingin the back end. • The observed Hi science targets were chosen toincrementally test the spectral line mapping capa-bilities of FLAG. The map of NGC 6946 compareswell with equivalent single-pixel data. The Hi fluxdensity profiles of sources within the NGC 4258field are also well-matched to equivalent single-pixel data and demonstrate accurate measure-ments of the shape of the FLAG beams. The de-tection of the diffuse Hi cloud, HIJASS J1219+46,and emission at anomalous velocities towards theGalactic Center shows that FLAG is able to repro-duce a wide-range of Hi properties observed in andaround extragalactic sources and Galactic regions. • The relatively high sidelobes inherent to maxSNRbeamforming do affect the overall morphology oflow-level emission. Correcting for stray radiationusing proven techniques can mitigate these effectsin future observations. • The compromise between survey speed and an-gular resolution when compared between FLAG,the current GBT single-pixel receiver, and othermulti-beam and PAF receivers available orplanned for the world’s major radio telescopes isonly matched by those with much larger aperturesthat are not fully steerable. Overall, the new beamforming back end for FLAGperformed exceptionally well in terms of the derivationof stable beamforming weights and generally reproducesequivalent observations from the current single-pixel re-ceiver. There are several possible avenues of improve-ment including the correcting for stray radiation. Theincrease in survey speed provided by FLAG and its up-graded backend, coupled with the sky coverage availableonly from a fully steerable dish, will ensure the GBT re-mains a premiere instrument for radio astrophysics.ACKNOWLEDGMENTSThe authors wish to thank Richard Prestage for lead-ing the organizational efforts during these commission-ing observations and for significant contributions to thefield of radio astronomy. We also thank the anonymousreferee whose comments greatly improved the quality ofthis work. We acknowledge the significant funding forthe FLAG receiver provided by GBO and NRAO. TheGreen Bank Observatory is a major facility supportedby the National Science Foundation and operated un-der cooperative agreement by Associated Universities,Inc. The National Radio Astronomy Observatory is afacility of the National Science Foundation operated un-der cooperative agreement by Associated Universities,Inc. NMP, KMR, DRL, DA, DJP, and MAM acknowl-edge partial support from National Science Foundationgrant AST-1309815. KMR acknowledges funding fromthe European Research Council (ERC) under the Eu-ropean Union’s Horizon 2020 research and innovationprogramme (grant agreement No 694745). This materialis based upon the work supported by National ScienceFoundation Grant No. 1309832.
Software:
This research made use of Astropy, acommunity-developed core Python package for Astron-omy (Astropy Collaboration et al. 2013, 2018). LAG Hi Commissioning