FLAG Beamformer Project Note 1.4

FLAG Beamformer Specifications

Dunc Lorimer, Maura McLaughlin, DJ Pisano, Richard Prestage, Anish Roshi

25 August 2014

Abstract

This document describes the science case and derived specifications for the FLAG Beamformer.

Contents

1 Scientific Justification 31.1 Pulsars as probes of fundamental physics . . . . . . . . . . . . .. . . . . . . . . . . 31.2 Exploring new phenomena via the transient radio sky . . . .. . . . . . . . . . . . . . 41.3 Studying star formation and the cosmic web via neutral hydrogen . . . . . . . . . . . . 5

2 Scientific Requirements 82.1 Beam Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 82.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 82.3 Frequency and Position Switching . . . . . . . . . . . . . . . . . . .. . . . . . . . . 82.4 Searching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 9

2.4.1 Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4.2 Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10

2.5 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 112.6 Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11

2.6.1 Diffuse HI Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 112.6.2 Extragalactic HI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 112.6.3 Milky Way HI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.7 OH and RRL Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 12

3 FLAG Receiver Parameters 12

4 Derived Backend Requirements and Mode Specification 12

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History

1.0 10 December 2013. Original version from proposal (Richard Prestage).

1.1 January 2014. Various updates (Dunc Lorimer, DJ Pisano)

1.2 04 April 2014. Added Table 2; A summary of beamformer specification (Anish Roshi).

1.3 14 April 2014. Restore lost edits, minor corrections (Richard Prestage)

1.4 25 August 2014. Add FRB requirements, clarify baseline stability specification (Richard Prestage)

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1 Scientific Justification

1.1 Pulsars as probes of fundamental physics

Pulsars, rapidly spinning highly magnetized neutron stars, have long been known as excellent tools tostudy fundamental physics and astronomy. They are used to investigate a wide variety of topics, includ-ing exotic matter physics, low-frequency gravitational waves, fundamental tests of general relativity,interstellar weather, globular cluster astrophysics, extrasolar planets, and planetary physics. Of par-ticular interest are “millisecond pulsars” which rotate with frequencies up to several hundred Hz withclock-like precision. Around 2000 pulsars are currently known. Recent surveys have been extremelysuccessful in revealing the population of millisecond pulsars both in our Galaxy and in its globularcluster system [1–3]. This is still only a small fraction of the total Galactic population (estimated to bearound105 in the Galactic disk [4] and103−4 in globular clusters [5]). It is therefore certain that manyexciting objects remain to be discovered in the coming decade that will provide transformational newscience. The three main science goals outlined below can only be addressed by finding and studyingmore pulsars and, as we demonstrate below, GBT surveys with FLAG would contribute substantially inthis area.

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Figure 1:Left: GBT timing observations of the double pulsar system which constrain the masses of the two pulsars and testthe predictions of General Relativity. The diagonal lines labeled “R” represent the mass ratio based on the semi-major axesof the orbits of A and B. The shaded (orange) region is forbidden from geometrical considerations. The other lines illustratethe relativistic corrections to a Keplerian orbit that are measured. Two lines are plotted for all parameters to illustrate the 1-σerrors. The masses of A and B correspond to the intersection of all lines and are measured to be1.3381 ± 0.0007 M⊙ for Aand1.2489±0.0007 M⊙ for B. Because all lines intersect at a common point, we can say that all measurements of relativisticparameters thus far are consistent with General Relativity. Right: Mass-radius diagram showing constraints on various neutronstar equations-of-state provided by Shapiro time delay measurements of the binary millisecond pulsar J1614−2230 [6]. Thered (upper) horizontal line shows the mass determination ofthe pulsar (the radius of which is currently unknown). The smoothcurves show various mass-radius relations for different equations of state. A number of these models are now excluded bythemass measurement of PSR J1614−2230. The orange and yellow (lower) horizontal lines indicate previous mass constraints.

Goal #1: Make fundamental advances in gravitational physics. Ever since the landmark discovery ofthe first double neutron star system by Hulse & Taylor in 1974 [7], high-precision timing observationsof binary pulsars have enabled a variety of tests of relativistic theories of gravity. The measurementof orbital decay in the Hulse-Taylor binary with Arecibo, for example, provides compelling evidencefor the existence of gravitational waves and timing observations of the ‘double pulsar’ system withthe GBT provide the best-ever test of general relativity in the strong-field regime. While significantprogress in gravitational physics is being made with more refined observations of these and other pulsarbinaries, the discovery of a pulsar–black hole binary system would allow us to test relativistic gravity to

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its limit. Pulsars with stellar-mass black hole companions, and orbiting the supermassive black hole atthe Galactic center (Sgr A*) are expected to be found in the next decade and will significantly advancethis area of fundamental physics via precision measurements of relativistic observables.

Goal #2: Probe the equation of state of matter at high densities.Neutron stars are excellent probesof the physics of matter at the highest densities. High mass and/or extremely rapidly rotating neutronstars have so far allowed us to rule out a number of the many proposed equations of state. Furtherprogress will be made in the future with the discovery of other outlying (in spin or mass) systems or ofa pulsar for which both the mass and radius can be measured. Such a measurement may be possible forthe double pulsar system within five years.

Goal #3: Study the Universe via low-frequency gravitational waves.The direct detection of gravita-tional waves remains one of the greatest challenges confronting modern experimental physics. Currentlya large consortium of astronomers in North America (NANOGrav) is establishing an experiment whichcomplements the search for high-frequency gravitational waves being carried out by LIGO. The novelexperiment monitors a network of pulsars using the GBT and AOto search for gravitational-wave in-duced correlated changes in pulse arrival times. The technique is sensitive to low-frequency (nanohertz)waves produced by coalescing supermassive black holes at the centers of distant galaxies, as well asindividual continuous or transient sources of gravitational waves including known and unknown pop-ulations. The detection of gravitational waves is possiblewithin the next five years. Crucial to thesensitivity of the array is the number of pulsars included. The large number of millisecond pulsars nowbeing discovered is therefore contributing directly to theultimate success of this effort.

Pulsar surveys with FLAG would contribute substantially toall three of the above areas. To quantifythis, we have carried out simulations of the Galactic population of pulsars using thepsrpop softwarepackage1. Our simulations were based on previous works in this area [4, 8] in which optimal mod-els were used which replicate the yield of current surveys with the Parkes telescope. As an example,assuming the nominal parameters of FLAG, a 1200 hr survey of the Galactic plane visible from theGBT (defined by Galactic longitudes in the range−145◦ < l < 60◦ and Galactic latitudes in the range|b| < 3◦) would discover over 600 new normal (i.e. non millisecond) pulsars and 60 millisecond pulsars.A 2000 hr intermediate latitude survey covering the same longitude range, but with5◦ < |b| < 15◦,could discover a further 400 pulsars and 30 millisecond pulsars. As a result of these surveys, it would bepossible to discover over 1000 pulsars in a feasible amount of observing time. Without the survey speedof FLAG, these projects would require over 20,000 hours of GBT time and be completely intractable.

1.2 Exploring new phenomena via the transient radio sky

In addition to the pulsars that are potentially with the reach of GBT surveys using FLAG, the sameobserving time could be used to discover hundreds of non-periodic transient radio sources with a vari-ety of astrophysical origins. Studies of short duration radio transients are poised for a revolution withthe advent of a new generation of large field of view telescopes and flexible, high throughput corre-lators. Discoveries over the past several years show that the radio sky is incredibly dynamic, withknown sources seen to behave in new ways and what may be entirely new classes of sources discov-ered. Fig. 2 illustrates the radio brightnesses of well-known and newly discovered transient sources.Among these sources are the Rotating Radio Transients [9], which manifest themselves in pulsar surveydata as isolated dispersed bursts with no clear periodicity. Rotating Radio Transients may represent an

1http://psrpop.phys.wvu.edu

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Figure 2:Left: A log-log plot of peak fluxS, distanceD, frequencyν, and pulse widthW , with lines of constant brightnesstemperature (in units of Kelvin)T = SD2/2k(νW )2 [17]. Well-known sources include pulsars (PSRs) [18], giant pulses fromthe Crab [19], B1937+21 [20], B1821−24 [21] and B0540−69 [22], Type I and Type II stellar flares [23], active stars like UVCeti [24] and OH masers [25]. Recent discoveries, includingthe rotating radio transients [9], a Galactic center radio transientwith 77-min periodicity [26], radio pulses from anomalous X-ray pulsars [27], a bright possibly extragalactic burst fromJ0118−75 [10], and pulsations from brown dwarf TVLM 513–46546 [28], are shown in red/bold.Right: PeriodP vs periodderivativeP for pulsars (dots [18]), magnetars (cyan squares [27]), thethree isolated neutron stars with measured periods andperiod derivatives (blue diamonds), and the rotating radiotransients (open red stars [9, 29]). Constant characteristic ages andconstant inferred surface dipole magnetic field strengths,derived by assuming spin-down due to magnetic dipole radiation, areindicated by dashed lines.

enormous population of previously unrecognized neutron stars in the Galaxy. The discovery of a short-duration isolated radio burst [10] resulted in numerous explanations ranging from a binary neutron starmerger [11], a magnetic reconnection event from a neutron stars whose companion has undergone a su-pernova explosion [12], an exploding primordial black hole[13], a cosmic spark on a superconductingstring [14], or a magnetar hyperflare [15]. While short-duration transient phenomena are currently bestexplained by neutron stars, other purported origins remainsuch as evaporating black holes [16].

These searches will focus on radio sources which are transient on very short timescales (<1 sec). Theseare necessarily compact objects undergoing explosive and/or dynamic events which probe exotic physicsin regimes of high acceleration, high magnetic fields, and strong gravitational fields. They are alsoinsightful probes of the interstellar and, potentially, intergalactic medium. Despite these rich scientificreturns, the time domain has remained relatively unexplored at radio wavelengths for many years, as thelarge required data rates and the typically narrow fields of view of radio telescopes make blind searchesfor short-duration transients difficult. The proposed workwould allow wide-field searches for transientswith the GBT and capitalize on its high instantaneous sensitivity.

1.3 Studying star formation and the cosmic web via neutral hydrogen

One of the outstanding questions in astronomy today, as highlighted in the recentAstro2010 decadalsurvey, is how galaxies accrete the gas they need to continueforming stars into the present day. Thecurrent gas content of galaxies is only sufficient to sustaintheir current star formation rates for a fewbillion years, yet the gas content of galaxies has remained roughly constant for the past 11 billion years,despite prolific star formation over that period, implying that galaxies must be accreting gas from theintergalactic medium [30]. Current theory suggests that this accretion occurs in one of two modes: ahot mode where the gas is heated to 106K, or a cold mode where gas remains below 105K [31, 32].The cold mode, in particular, should be the dominant form of accretion for low mass galaxies in low

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density environments. Such accretion should be detectablevia observations of neutral hydrogen at 21-cm (HI) at column densities of NHI ≤ 1018cm−2 [33]. Sensitive observations of discrete HI clouds orHI-rich satellites around nearby galaxies [34–38] find only10% of the needed accretion rate to sustainstar formation at its current levels [37]. These inferred accretion rates are based on numerous surveysprimarily done with interferometers, but these instruments are blind to faint, extended, diffuse HI that isassociated with cold mode accretion. To detect such HI, surveys with single-dish telescopes are requiredto complete the census of gas around galaxies and to determine the origin of this gas.

Goal #1: Completing the census of diffuse HI around galaxies. In order to determine if there isenough gas around galaxies to fuel future star formation, anaccurate census of both clump and diffusegas is required. In addition, it is important to determine how the amount of HI around galaxies dependson their internal and external properties. This strongly motivates a survey of a sample of galaxiesspanning a wide range of masses, environments, and star formation rates. This has already been donefor M 81, NGC 2403, and M 101 [36, 39, 40], while, as part of project GBT11A-055, Pisano et al.have observed the rest of the galaxies in The HI Nearby Galaxies Survey (THINGS, [41]) down toNHI ∼1018cm−2. An example of the type of HI structures being found is shown in Fig. 3.

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Figure 3: Left: A GBT total intensity HI map of NGC 6946 and its nearest companions from project GBT09B-016. Thefilament connecting NGC 6946 with UGC 11583 and L149 was confirmed with a single pointing observation (marked witha circle) to have a NHI ∼2×1018cm−2 and a FWHM of 48 km/s. The lowest contour is at 7×1017cm−2 with subsequentcontours at 2, 5, 10, 20, 40, 100, 200 times higher. Right: The192 hour WSRT map of NGC 6946 and its companionsfrom [35]. Note the inability of the WSRT to detect the extended, low NHI filament, despite the long integration.

The THINGS sample lacks extremely deep HI observations withan interferometer to detect clumpy HI,nor does it span as wide a range of galaxy properties as would be desired. To rectify this, there arecurrently plans to observe the diffuse HI around galaxies from the Westerbork HALOGAS sample [42]and MHONGOOSE sample. The MHONGOOSE survey is a 6000 hour project to map HI in and around30 nearby galaxies down to NHI ∼5×1017cm−2 with the MeerKAT interferometer. The single-dish datais necessary for both these surveys to provide information on the diffuse HI. Currently, with the GBT,we could survey four square degrees around this sample of 50 galaxies down to NHI ∼1018cm−2 in 500hours. With FLAG we could complete the survey in about 125 hours. Alternatively, we could observedown to NHI ∼5×1017cm−2, in 500 hours providing a more complete census of diffuse HI.Similarstudies are currently ongoing with the GBT around other galaxies as well [?, 43,44].

Goal #2: Determining the origin of diffuse HI around galaxies. There are two approaches to deter-mine the origin of diffuse HI around galaxies. The first approach is to compare the results of the surveysdescribed above to the predictions from theoretical models[31, 32]. Specifically, cold mode accretionis predicted to be dominant around low mass galaxies in low density environments. A large, diversesample of galaxies with deep HI observations is essential for this approach to work.

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The second approach is to study individual systems to very low column density, NHI ∼1017cm−2 to de-termine if the gas is consistent with a tidal origin or predictions from simulations of cold mode accretion.Currently, there is only one viable option for such a study: the HI bridge between M 31 and M 33 [45].This bridge, shown in Figure 4, appears to be composed of diffuse HI down to NHI ∼1017cm−2 with awidth of ∼10 kpc and covering an area of∼80 square degrees. As part of project GBT11B-051, a 12square degree portion of this bridge was mapped [46] (see Fig. 4) down to NHI ∼1017cm−2, but withan angular resolution of 9’ instead of 49’ and a velocity resolution of 5.2 km s−1 instead of 16 km s−1.This project required the GBT to reach a sensitivity of∼2 mK with excellent baseline stability, some-thing it is easily capable of achieving. The improved resolution and matching sensitivity show that thisdiffuse filament is actually composed of discrete clouds. The higher column densities of these clouds,combined with their internal kinematics, appear to be consistent with this filament being a tidal featureinstead of a cold flow [46]. To be certain of the origin, we mustmap a larger area of this HI bridge. Thiswould require many thousands of hours with the current GBT receiver. FLAG will make this a feasiblesurvey and will provide unmatched view of a cold flow or tidal debris around a nearby galaxy.

Figure 4:Left: The WSRT map of the HI bridge connecting M 31 and M 33 in units of NHI that may be part of the cosmicweb or may be tidal in origin [45]. The solid box is the region which we have mapped with the GBT. If this HI filament ispart of the cosmic web, then both regions should have similarproperties. If it is tidal, however, then they should be moreanalogous to the Magellanic Stream and the Leading Arm, or Magellanic Bridge regions. Right, our GBT HI observationsof the region in the small box in units of NHI demonstrating that this filament is actually composed of small clouds withpeak NHI

<∼ 1019cm−2. Contours are at log NHI=17.5, 17.8, 18.1, 18.4, 18.7. The clumpy nature of this filament and the

distribution and kinematics of these clouds is more consistent with a tidal origin [46].

In addition to studying diffuse HI, FLAG will enable significant new spectral line surveys of galacticand interstellar gas. The instrument will be capable of mapping the EVLA primary beam out to the halfpower beam width (HPBW), which will facilitate total power mapping for extragalactic HI in galaxies.Such information is critical when studying the relationship between star formation and gas content[47, 48]. FLAG will also permit very sensitive, large area studies of the high velocity gas around theMilky Way and associated with the Magellanic Stream [49–53]. Recent work has shown that there aresignificant amounts of molecular gas in the diffuse interstellar medium, so much so that half of the high-latitude sky is covered by molecular clouds. Emission from OH at 18cm is an excellent probe of theseobjects, as this molecule is formed at early times in chemical evolution models—earlier than CO—andis more widely distributed. FLAG would be of immediate use inmapping these clouds to analyze theircomplex interstellar chemistry and their relationship to dust evolution and the neutral ISM [54–57].

The Green Bank Telescope (GBT) is the ideal telescope for such surveys due to its low system tem-perature, high gain, clean primary beam, stable baselines,and relatively high angular resolution; acombination unmatched by any other existing or planned single-dish radio telescope. While such sur-veys are possible with the GBT today, they require exceedingly large amounts of observing time due

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to its single pixel receiver. With FLAG, the GBT will be able to survey diffuse HI over large areas ata speed unmatched by any other existing or planned telescope. For HI surveys such as those describedabove, only modest bandwidths (∼10 MHz) are required, making these surveys feasible starting in thefirst year of this proposal.

2 Scientific Requirements

2.1 Beam Quality

For spectral line work, particularly HI, we want to preservethe high quality GBT beam as much aspossible. The current GBT beam has its first sidelobes at the -30 dB level. For comparison, the 20cmmultibeam on Parkes has its first sidelobe level at the -15 dB level. Just as important as maintaining theclean GBT beam, however, is keeping the beam shape stable andknown over long periods of time. Ata minimum, it should be stable over a typical mapping observing run, about 8-10 hours. The individualbeams formed by the PAF will certainly be different, and thatis okay, provided that they are stable.While the quality and stability of the beam shape are important for all mapping observations, it isparticularly the case for HI observations where emission can be spread across a large region of the sky(in the case of the Milky Way) or when we are searching for faint HI emission close to a bright source(such as in the case of mapping the cosmic web). If the beams and their sidelobes are fixed with respectto the sky, that would be ideal, but it is not a requirement. Observations of other spectral lines, suchas radio recombination lines (RRLs) or OH, are less affectedby the sidelobes either because all of theemission is faint, in the former case, or sources are relatively small, in the latter case.

2.2 Calibration

With the current GBT L-band system, the system temperature is measured by injecting a noise diodesignal before the first amplifier and blinking it while observing. Using this approach, it is currentlypossible to do absolute flux calibration to within 5-10%. If Tcal values are measured by on-sky ob-servations of a flux calibrator, the fluxes should be accurateto within 1-5%. Using a blinking noisediode also allows for changes in Tsys or the gain to be tracked on short timescales (during the scan).Unfortunately, this approach is not feasible with FLAG because it is not possible to inject a noise diodesignal into the signal path before the first amplifier. As a result, we can only do absolute flux calibrationvia on-sky measurements of a source with known flux. The system must remain stable to within a fewpercent over the course of an observing run in order to achieve flux calibration good to within 5%. Ifit varies on shorter timescales, then more frequent observations of the flux calibrator will be needed,hence increasing observing overheads.

2.3 Frequency and Position Switching

When mapping spectral lines with the current GBT L-band system, both frequency-switching andposition-switching techniques are used. Typically, position-switching, where the edge of the map ora more distant reference position is used as the “off” position, yields flatter baselines. However, whenmapping Galactic HI or any field where the emission fills the field of view, frequency-switching is used.Unfortunately, since there is no front-end local oscillator in the signal path of FLAG and the entire fre-quency band is sent to the backend, frequency-switching is not feasible. As a result, when observing

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sources that fill the region being mapped, the baseline region must remain stable over longer timescalesand a template bandpass shape will have to be subtracted. We should be able to test the feasibilty of thisapproach using current GBT data.

2.4 Searching

In this section, we review the main considerations necessary when considering FLAG’s potential as asearch instrument for new pulsars and short-duration radiotransients. The main conclusion from thestudies described below is that, to optimize the science return, a 150 MHz bandwidth system is neces-sary; a 300-MHz upgrade would be highly desirable. There is some flexibility in the time and frequencyresolution. The calculations below assume 300MHZ bandwidth, 0.1 MHz frequency resolution and100µs dump times. An acceptable reduction in this data rate wouldbe a channelization of 150 MHzinto 1024 spectral channels dumped every 100µs.

2.4.1 Pulsars

Pulsars are weak radio sources. As we dig deeper into the population, typical flux densities of newlydiscovered pulsars are well below a mJy. We have used thePsrPopPy simulation package [58] topredict the likely yields of pulsar searches with FLAG. We consider “normal” and “millisecond” pulsarpopulations separately. In addition to taking into accountmodels for pulsar evolution,PsrPopPycan synthesize the Parkes multibeam and High Time Resolution Universe surveys to determine thenumber of normal and millisecond pulsar detections and discoveries by surveys with the GBT andFLAG. For both populations, we find that the survey yields aresubstantially greater if the bandwidthcan be maximized. Since pulsar science is driven by the discovery of rare and exotic systems, wetherefore strongly encourage the goal to realize a 300 MHz bandwidth system.

For the normal pulsar population, we followed the standard evolutionary model that is described indetail elsewhere [59] to reproduce the results of the Parkesmultibeam survey of the Galactic plane [1].This process models the spindown and kinematic evolution ofthe pulsars and is normalized to matchthe yields of the Parkes surveys. Using this model, we find that for a 100 MHz bandwidth survey withFLAG using 5-min pointings to cover the Galactic plane visible within |b| < 5◦ from Green Bank woulddetect over 1100 pulsars. Taking into account the surveys previously carried out, we predict around 50normal pulsars would be new discoveries. The power of the simulations allows us to easily model theimpact of a larger bandwdith on the survey yields. For the normal pulsars, we find that the number ofdiscoveries scales linearly with bandwidth. A 300 MHz system could, therefore, discover around 150pulsars in the same integration time.

For the millisecond pulsar population, we also use the Parkes multibeam survey to normalize the yield.However, given the greater uncertainties in modeling the spin-down of the population, we adopt a “snap-shot” approach whereby the millisecond pulsars are distributed according to pre-determined functionsacross a synthetic galaxy. For a 100 MHz system with 5-min integrations, the number of millisecondpulsars scales again approximately linearly with bandwidth. In the Galactic plane (|b| < 5◦), only about4 millisecond pulsars are expected to be discovered with 100MHz and 5 min pointings. A similar resultis found at intermediate latitudes (5◦ < |b| < 15◦. By far the best prospects are found when searchingfor millisecond pulsars at high latitudes (|b| > 15◦). There, the expected number of discoveries for 100MHz is 15. This number approximately doubles if we triple thebandwidth.

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2.4.2 Transients

The Rotating Radio Transients [9] are not specifically modeled here. However, based on previoussurveys the number of such sources discovered could be an additional 50% of the normal pulsar yield.Although further modeling could be done to address this question, since the distribution of RotatingRadio Transients in the Galaxy is likely very similar to thatof the normal pulsars, we expect that surveyswith 300 MHz bandwidth will provide substantially larger yields of sources compared to 100 MHzbandwidth surveys.

Fast Radio Bursts (FRBs) — highly dispersed short-durationbroadband radio pulsars of unknown origin— represent a very exciting emerging source population [10,60]. The pulsar surveys described abovewould be routinely searched for bright transients. To get some idea of the expected event rate, we havetaken the predictions from a recent population model of FRBs[61] and computed the expected eventrates as seen by FLAG assuming a 300 MHz bandwidth system.

Figure 5:Left: Flux density — redshift relationship for FRBs assuming a simlple cosmological model in which the sourcesare standard candles uniformly distributed in comoving volume. Center: Differential event rate as a function of redshift.Right: Cumulative event rate as a function of redshift.

As can be seen, under the assumption that FRBs are cosmological sources, the expected event rate issignificant — of order one FRB per day of observing time. As further surveys are carried out over thenext year, these estimates will be refined further. At the present time, however, the prospects for FRBdiscovery science with FLAG are very promising.

The requirements for FRB searching are ideally to collect data commensally with any other FLAGproject using the same filterbank parameters as would be collected for pulsar search observations. Toreduce complexities in calibration, we recommend not trying to capture full Stokes information and onlyconsidering total power spectra. For 150 MHz bandwidth observing, the recommended pulsar searchsample time for each beam is 100 us with 0.1 MHz frequency resolution. As is the case for pulsarsearching, the FRB science is maximized by having as many beams as possible. An excellent system tocapture FRBs would consist of 13 beams with the above spectral parameters which are fed to a rack ofGPUs for real-time analysis. The logical architecture to adopt would either be the systems at Arecibo(ALFABURST; PI: Lorimer) or on the Green Bank 20-m (PI: Ellingson) to carry out the dedispersionand detection.

Should trade-offs need to be made, we would prefer these to bein the frequency resolution capabilities,rather than the number of available beams. For example, 0.3 MHz frequency resolution and 300µssampling would reduce the data rate by close to an order of magnitude. Such a system would still havegood sensitivity to FRBs and may be a more realistic first steptowards a fully autonomous FRB pipeline.

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2.5 Timing

FLAG will not be used for pulsar timing, and so this observingmode does not drive the beamformerperformance specification.

2.6 Mapping

In the following sections, we will consider the necessary bandwidth, spectral resolution, and mappingmodes that are needed for particular spectral line science projects.

2.6.1 Diffuse HI Mapping

The goal of mapping diffuse HI around individual galaxies isto identify low column density HI thatmay be associated with accretion by the galaxy from the cosmic web. Such projects require mappinga moderate area (under 10 square degrees) around an individual galaxy or a group of galaxies. Currentprojects use either 12.5 MHz or 50 MHz bandwidth. If frequency-switching is used during observations,a larger bandwidth is preferred to assure that switching does not bring Galactic HI on top of the extra-galactic HI signal. For position-switched observations, 12.5 MHz is sufficient to detect all HI associatedwith an individual system. A larger bandwidth allows simultaneous observations of HI and RRLs. Thespectral resolution for these observations is also relatively modest, 24.4 kHz (5.2 km s−1) is typical for afinal data cube, although higher resolution is often used initially to assure narrow RFI can be effectivelyflagged with minimal effect on the final data cube.

With the current single-pixel L-band feed, mapping is done by making an on-the-fly map of a regionalong lines of constant Right Ascension and Declination. The mapping rates are relatively slow, lessthan 1 degree per minute, with integration times (5 seconds)assuring better than Nyquist samplingalong the scan direction. Individual rows of the map are offset by 3′ to assure Nyquist sampling in bothdirections. Despite the fact that with FLAG the individual formed beams have approximately Nyquistspacing, for improved calibration and image fidelity, it would be best to Nyquist sample each individualbeam in both directions when mapping. One reason this shouldbe done is that the parallactic angle ofthe receiver on the sky will change with time. By assuring that each individual beam is Nyquist sampled,there will be no gaps in the final map. If FLAG is capable of tracking in parallactic angle, this techniqueis still beneficial, but less necessary. As a result, we wouldstill use the same mapping routines as atpresent, but would require less time to reach the same sensitivity. The stable, clean beam produced byFLAG (as discussed above) would assure that we are able to detect faint, extended HI close to the galaxycontaining a bright HI signal.

2.6.2 Extragalactic HI

When measuring the total HI signal from a galaxy, current observational techniques assume that thesignal is entirely contained within a single GBT beam (9.1′) and the telescope is position-switched forcalibration. With FLAG it will be possible to make small mapsof larger galaxies in order to bettermeasure their total HI content. To do this, one would use aDaisy mapping technique repeatedly slewingthe telescope over the galaxy position with the edges of the map being used for an “off” position. In thiscase, the map would only extend 3-4× the field of view of FLAG. Bandwidth and spectral resolutionrequirements would be the same as above. For this type of observation, we would only require thatthe FLAG field of view is Nyquist sampled, not each beam. This would still require shorter integration

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times than in the above case. If the field of view is about 23′ (2.5 HPBW), then we would want tomove no more than∼9′ per integration. At the maximum slew rate of the GBT, this would require anintegration time of 0.5 seconds. Since we would not be movingthe telescope this fast, an integrationtime of 1 second should be sufficient. Since the map must be bigenough to get off the galaxy, a typicalDaisy map would have a radius of about 2 degrees.

2.6.3 Milky Way HI

For mapping Milky Way HI, we would use the same mapping modes as for diffuse HI. There are onlythree differences in requirements. First, frequency-switching must be used since HI will fill the fieldof view of any observation. Second, the total bandwidth neednot be larger than 12.5 MHz, since allGalactic HI is easily contained in this range even when frequency-switching. Finally, when observingGalactic HI, we can detect both the warm and cold components of the HI. This means that higher spectralresolution is required; typically 1.5 kHz (0.3 km s−1) to assure narrow lines are resolved.

2.7 OH and RRL Surveys

While HI observations will be the primary spectral line observations conducted with FLAG, mappingobservations of OH and RRLs are also likely to take place. Therequirements for these surveys aresecondary to HI, but are desirable to achieve if the resources required are not prohibitive.

For RRL surveys, the larger the bandwidth, the more RRL linescan be observed simultaneously im-proving the sensitivity of the final map when the lines are stacked. Spectral resolution requirements aremodest, 24.414 kHz is sufficient to resolve the lines. There is roughly one RRL line every 20 MHz inL-band. So if this resolution can be achieved across the fullinstantaneous bandwidth of FLAG, 300MHz, then about 15 RRLs could be simultaneous observed.

For OH surveys, higher spectral resolution is required, 1.5kHz would be the worst acceptable resolution;higher resolution would be needed if OH masers were being surveyed. In addition, it would be beneficialto observe all four lines of OH (1612, 1665, 1667, and 1720 MHz) simultaneously to probe the physicalconditions. If needed, the 1612 MHz line could be ignored, since RFI is particularly bad in this region.

For either type of survey, the mapping modes would be the sameas for HI.

3 FLAG Receiver Parameters

The capabilities of the FLAG receiver are specified in Table 1. These are not derived from the beam-former scientific requirements, but are properties of the FLAG frontend.

4 Derived Backend Requirements and Mode Specification

The above sections result in the derived specifications listed in table 2. Given these specifications, wepropose the different observing modes listed in table 3.

FBPN 1.4 13

Quantity Target Goal NotesFrontend ArrayElements

19 x 2 po-larizations

same

Number ofsimultaneous formedbeams

7 same

Bandwidth 1300 - 180MHz

sameMHz

May depend on RFIEnvironment

System noisetemperature

35K 25K To date has only beenmeasured at a single frequency

Inverse sensitivity 50K 35KField of View 1.25

HPBW2.5HPBW

After future upgrade

Table 1: Targets and Goals for the FLAG receiver

Quantity TargetFirst Sidelobe Level -15 dBSidelobe Stability less than 2% variation over eight hoursBeam Uniformity Not a driver as long as beams are stableBeam Orientation Preference but not requirement for fixed onskyGain Stability 2% over eight hoursBaseline Stability ∆(T)/TSY S < 0.011.Searching Target 0.3 MHz resolution, 100µs dump timeSearching Goal 0.1 MHz resolution, 50µs dump timeMapping bandwidth 10 MHz bandwidth with 10 and 1.5 kHz resolution

50 MHz bandwidth with 10 kHz resolutionMapping Dump Time 0.5 seconds

Table 2: Derived Specifications for the FLAG Backend

(1) After calibration of the spectrum, and removal of a low-order (< 4) polynomial over 10 MHz bandwidth, the residual rmsin the spectrum should be equal∆(T)/TSY S < 0.011. This stability must be maintained for periods of up to 30 minutes

FBPN 1.4 14

Table 3: Summary of beamformer specification1

Number Proc. Coarse Subband Number Frequency Min Priority2 Noteof beams bwidth Channel bwidth of res. per integ.or elements -ization subbands subband time

(MHz) (MHz) (KHz) (msec)Voltage Beamforming2,3 + XX∗, YY∗, XY∗ spectra

7 Beams 150 1024 150 1 500 0.1 2 a7 Beams 150 1024 10 1 10 500 1 b7 Beams 150 1024 10 1 1.5 500 3 c7 Beams 150 1024 50 1 10 500 4 d7 Beams 150 1024 10 8 10 500 5 e

Commensal FRB Transient Searching4 (XX∗, YY∗, XY∗ spectra)13 beams 150 512 150 1 300 0.3

Cross correlation spectra (XiX∗

j , YiY∗

j , XiY∗

j )19 Elements 150 1024 300/150 1 1000 1000 1 f19 Elements 150 1024 10 1 10 500 2 b

(1) Full cross correlation spectra (full covariance matrix) will be output in all modes of operation except those with 0.3 msand 0.1ms integration times (i.e. voltage beamforming withnote (a) and commensal FRB transient searching). In the coarsefilterbank mode (i.e. pulsar or FRB seach modes) only 10% of the frequency channels will have corss correlation spectra(covarieance matrix) data stored. All channels wiull have integrated (0.3ms or 0.1ms) beamformed data stored. This limitationis due to I/O bandwidth constraints of the GPUs.(2) For HI observations, the 10 MHz subband bandwidth, priority 1, formed beam configuration is needed. The 10 MHzsubband bandwidth, priority 2 configuration will be useful for commissioning. All other configurations with priority≥ 3 areoptional; these configurations are useful to do a variety of science projects if they can be made available during the projecttime scale.(3) Beams for polarizations X and Y are formed first and spectra are measured at the output of the formed beam.(4) IF we end up implementing Simplified Version 1 of the XB-engine block diagram, there will be no commensal FRBTransient searching while operating in HI mapping mode. It would operate as a separate stand-alone mode. Commensaloperation is the desired design, but development constraints may restrict it to stand-alone operation only.(a) This configuration is for pulsar search with bandwidth 150 MHz. Spectral resolution between 1 and 0.5 MHz will beadequate for this work.(b) These configurations are for Extragalactic HI observations in position switched mode. The observations can be done eitherin beam forming mode (priority 1) or by measuring the cross correlation (priority 2). Subband bandwidths between 8 and15 MHz and spectral resolution of about 1/1000 of the subbandbandwidth will be adequate for the observations. The crosscorrelation configuration will be needed during commissioning work to study the beam properties.(c) For galactic HI/OH observations.(d) For Extragalactic HI observations.(e) For Recombination line observations.

FBPN 1.4 15

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