Multi-frequency measurements of the NVSS foreground sources in the Cosmic Background Imager fields. I. Data release
E. Angelakis, A. Kraus, A. C. S. Readhead, J. A. Zensus, R. Bustos, T. P. Krichbaum, A. Witzel, T. J. Pearson
aa r X i v : . [ a s t r o - ph . C O ] M a y Astronomy&Astrophysicsmanuscript no. 1267 c (cid:13)
ESO 2018October 26, 2018
Multi-frequency measurements of the NVSS foreground sources inthe Cosmic Background Imager fields
I. Data release
E. Angelakis , A. Kraus , A. C. S. Readhead , J. A. Zensus , R. Bustos , , T. P. Krichbaum , A. Witzel andT. J. Pearson Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, 53121 Bonn, Germany California Institute of Technology, 1200 East California Boulevard, California 91125, Pasadena, USA Universidad de Concepci´on, Casilla 160-C, Concepci´on, Chile University of Miami, Department of Physics, 1320 Campo Sano Drive, FL 33146, USAReceived -, -; accepted -, -
ABSTRACT
Context.
We present the results of the flux density measurements at 4.85 GHz and 10.45 GHz of a sample of 5 998 NVSS radio sourceswith the E ff elsberg 100 m telescope . Aims.
The initial motivation was the need to identify the NVSS radio sources that could potentially contribute significant contaminat-ing flux in the frequency range at which the Cosmic Background Imager experiment operated.
Methods.
An e ffi cient way to achieve this challenging goal has been to compute the high frequency flux density of those sources byextrapolating their radio spectrum. This is determined by the three-point spectral index measured on the basis of the NVSS entry at1.4 GHz and the measurements at 4.85 GHz and 10.45 GHz carried out with the 100 m E ff elsberg telescope. Results.
These measurements are important since the targeted sample probes the weak part of the flux density distribution, hence thedecision to make the data available.
Conclusions.
We present the table with flux density measurements of 3 434 sources that showed no confusion allowing reliablemeasurements, their detection rates, their spectral index distribution and an interpretation which explains satisfactorily the observeduncertainties.
Key words.
Radio continuum: general – Catalogs – Galaxies: active – cosmic microwave background
1. Introduction
Targeted multi-frequency surveys can be very e ffi cient in serv-ing several fields of astrophysical research such as revealingnew GPS and HFP sources, estimating higher frequency sourcecounts from extrapolating the radio spectra and hence com-puting the confusion limits etc. Consequently, they can be ofessential importance in the study of the Cosmic MicrowaveBackground radiation (CMB) through the characterization ofthe foregrounds. Here, we present the results of the study of asample of 5 998 NRAO VLA Sky Survey (NVSS, Condon et al.1998) sources at three frequencies. 1.4 GHz is provided by theNVSS catalog and 4.85 GHz and 10.45 GHz were observed withthe E ff elsberg 100 m radio telescope. The measurements wereinitially motivated by the need to estimate the emission thatthey could contribute at 31 GHz. This is the band in which theCosmic Background Imager (CBI, Padin et al. 2001) operates,as explained below. In a future publication we plan to use theextrapolated flux densities in order to compute the source countsand the confusion limits at higher frequencies and compare theresults with those from other surveys. Send o ff print requests to : E. Angelakis Having traveled the path between the surface of last scatteringand the observer, the CMB is subject to the influence of numer-ous sources of secondary brightness temperature fluctuations,cumulatively referred to as foregrounds. The reliability of the in-formation extracted from the study of the primordial fluctuationpower spectrum is tightly bound to how carefully such factorshave been accounted for.The potential contaminants can crudely be classified inthose of galactic and those of extragalactic origin (for a re-view, see Refregier 1999; Tegmark et al. 2000). Moreover, de-pending on their character, they influence the power spectrumat di ff erent angular scales. Galactic foregrounds could be thedi ff use synchrotron emission (for a review, see Smoot 1999)attributed to galactic relativistic electrons, the free-free emis-sion originating in H ii regions and the dust emission due todust grains in the interstellar medium that radiate in a blackbody manner. Extragalactic foregrounds could be the thermaland the kinematic Sunyaev-Zel’doviche ff ect in galaxy clusters(Sunyaev & Zeldovich 1970), manifested through the distortionof the black body CMB spectrum induced by either hot ionizedgas in the cluster (in the former case), or matter fluctuations (inthe latter case).In the latter class, radio galaxies and quasars cumulativelyreferred to as point radio sources, populating the entire radio Angelakis et al.: Multi-frequency measurements of the NVSS foreground sources in the CBI fields
Table 1.
The coordinates of the points defining the targetedfields.
Field NE NW SW SE Area(deg )02 h h + d h + d h − d h − d h h + d h + d h − d h − d h h + d h + d h − d h − d h h − d h − d h − d h − d sky, comprise by definition the most severe contaminant a ff ect-ing small angular scales. The sample studied in the current workis exactly the NVSS point radio sources that lie within the fieldstargeted by the CBI experiment. The CBI is a 13-element planar synthesis array operating in 101-GHz channels between 26 and 36 GHz (Padin et al. 2001). It islocated at an altitude of roughly 5 080 m near Cerro Chajnantorin the Atacama desert (northern Chilean Andes). Its task was tostudy the primordial anisotropies at angular scales from 5 ′ to0.5 ◦ (400 < ℓ < S . ≥ . Instead of removing all potentially contaminated pixels from theCMB maps (which would unavoidably cause a significant dataloss), it would su ffi ce to identify the sources that contribute neg-ligible flux density at higher frequencies (below the few-mJythreshold) and ignore them during the CMB data analysis. Onthe basis of the assumptions that:1. the radio spectrum is described by a simple power law of theform S ∼ ν α (with α hereafter being the spectral index)2. the spectrum is not time variablethis identification can in principle be done by the extrapolationof the radio spectrum as obtained at lower frequencies. The ra-dio spectrum consists of the flux density at 1.4 GHz as extractedfrom the NVSS and those at 4.85 and 10.45 GHz as measuredwith the E ff elsberg telescope. The list of targeted sources includes all 5 998 NVSS sourcespresent in the CBI target fields displaying S . ≥ . (mJy)010203040506070 N o r m a li ze d C oun t s ( % ) Fig. 1.
The NVSS 1.4 GHz flux density distribution of our sam-ple. Roughly 80% is below 20 mJy. This plot demonstratesclearly the choice made of radio “quiet” sky regions.emission. It has been required that they have IRAS100 µ m emis-sion less than 1 MJy sr − (Pearson et al. 2003), low galactic syn-chrotron emission and no point sources brighter than a few hun-dred mJy at 1.4 GHz. It is clear therefore that the sample of the5 998 sources represents the weak part of the flux density distri-bution. This is the most prominent characteristic of the sample.In fact, it is readily shown in Fig. 1 that roughly 80% of thosesources are of S . ≤
20 mJy. The large galactic latitudes of thetargeted fields indicate that the sample is likely to consist com-pletely of extragalactic discrete radio sources that is, quasars andradio galaxies.In the current work we present the results extracted from asample of 3 434 sources which as it is discussed in Sect. 3.3 and4.2 show no confusion from field sources and hence allow reli-able measurements.
2. Observations
The flux density measurements were conducted with theE ff elsberg telescope between July 2003 and July 2006. Themulti-beam heterodyne receivers at 4.85 GHz and 10.45 GHzwere used. Multi-feed systems use “software beam-switch”for removing mostly linear troposphere e ff ects. Each receiverwas used in two-beam mode (although the 10.45 GHz one isequipped with 4 feeds). In both cases, the beams are separatedin azimuth and each delivers left-handed and right-handed cir-cular polarisation channels (LCP and RCP respectively). Bothsystems are mounted in the secondary focus cabin of the 100 mtelescope. Table 2 gives their characteristics. In order to achieve time e ffi ciency, the observations have beenmade with the “on-on” method. Its essence relies on havingthe source in either of the two beams at each observing phasewhereas the other feed is observing the atmosphere o ff -source(the angular distance of the used feeds is given in table 2). The ngelakis et al.: Multi-frequency measurements of the NVSS foreground sources in the CBI fields 3 subtraction of the two signals removes linear atmospheric ef-fects. For clarity, one complete measurement cycle will hereafterbe termed as one scan. Each scan, in our case, consists of fourstages, or sub-scans.In order to illustrate the exact observing technique used, welabel the feeds of any of the two receivers as referenceand main.Let A be the configuration of having the reference beam on-source while the main beam is o ff -source and B the reciprocalcase. The telescope is then slewed in such a way as to completea sequence of four sub-scans in a A-B-B-A pattern. Assumingthen that the system temperature is the same in both feeds forany given sub-scan the di ff erentiation of the two signals shouldremove any other contribution than that attributed to the sourcepower. The e ffi ciency of the method is demonstrated in Fig. 2.Despite its performance , as it is demonstrated in Fig. 2, thistechnique su ff ers from two major disadvantages: (i) it is sub-ject to pointing errors that may result in power loss. This hasbeen controlled with frequent pointing checks on strong nearbysources. As shown in Sect. 2.3 these errors are negligible; (ii)it is subject to cases of confusion i.e. cases of sources that con-tribute power to o ff -source position causing a false subtractionresult. The solution to that could be either to observe the targetat a di ff erent parallactic angle (at which there would be no con-fusing source in the o ff position), or to correct for it if the powerof the confusing source is known. This approach is discussed inSect. 2.3. Thermal noise:
For both frequencies, the goal of thermal noise( σ rms , see also Sect. 2.4) around 0.2 mJy (1 σ level) has beenset. Had this been the dominant noise factor, setting a 5 σ de-tection threshold would allow the detection of sources as weakas 1 mJy. The total integration time for achieving this thermalnoise level is 1 and 4 minutes at 4.85 GHz and 10.45 GHz, re-spectively. This time is the cumulative integration time for allfour sub-scans making up one observing cycle, that is a scan(see also Sect. 2.2). However, as shown in Sect. 3.2, the domi-nant noise factor is the troposphere rather than thermal noise. Itis shown that the practical limit is of the order of 1.2 mJy whichis judged to be adequate. Field coverage:
A rigid constraint is the minimisation of thetelescope driving time. This was achieved by driving the tele-scope through the field in a “zig-zag” way (travelling salesmanproblem). Each field was organised in stripes parallel to the rightascension axis and roughly 0.5 degrees across in declination.The sources within such a belt have, in turn, been organised indozens in order of monotonous right ascension change. During
Table 2.
Receiver characteristics. ν ∆ ν T sys Γ θ X Pol.(GHz) (MHz) (K) (K / Jy) ( ′′ ) ( ′′ )4.85 500 27 1.5 146 485 LCP, RCP10.45 300 50 1.3 67 182.4 LCP, RCPColumn 1, is the central frequency while Column 2 is the receiverbandwidth. Column 3, gives the system temperature and Column 4the sensitivity. Column 5, shows the full width at half maximum andColumn 6 the angular separation between the two beams. Finally,in Column 7 we give the polarization channels available. Fig. 2.
Demonstration of the e ffi ciency of the observing tech-nique (upper panel) and a prototype detection profile (lowerpanel) in the case of the 10.45 GHz receiver. Each receiver hastwo feeds, each of which delivers two channels (LCP and RCP),giving a total of four channels. Those are shown in the four lowerpanels. The green colour represents the referencehorn signal andthe blue the main horn signal. The left-hand side panels are theLCP and the right-hand side panels are the RCP. The plot at thetop of each panel shows the final profile after subtracting thesignals from each of the two feeds and averaging over LCP andRCP. If MR is the RCP of the main horn and ML the LCP inthe same horn, while RR , RL are for the reference horn, the finalsignal is given by [( ML − RL ) + ( MR − RR )] /
2. It is noteworthythat despite the complete absence of even the hint of a sourcein the individual channels (upper panel), after the subtraction aclear case of a 22-mK signal (roughly 17 mJy) can be seen.an observing session a field would be targeted within hour anglerange from − Pointing o ff set minimisation and calibration: For calibrationpurposes, one of the standard calibrators shown in table 3 wasobserved at the beginning and the end of the observation ofa field, i.e. roughly every six hours. Before the beginning ofthe field, also the focus of the telescope would be optimised.Changes in the focal plane within those six hours were accountedfor by interpolation of the sensitivity factor between the valuesmeasured at the beginning and the end of the run. To main-tain low pointing o ff sets, cross-scans were frequently performedon bright nearby point sources. On average a pointing check Angelakis et al.: Multi-frequency measurements of the NVSS foreground sources in the CBI fields N o r m a li z ed C oun t s ( % ) offset in Azimuthoffset in Elevation Fig. 3.
The distribution of the pointing o ff sets for the case of the10.45 GHz receiver. The dashed line represents the o ff sets in theelevation direction while the solid one gives those in azimuth.The mean o ff set is around 3 ′′ corresponding to roughly 1% powerloss.was done every 30 minutes to 1.5 hours. This sustained averagepointing o ff sets of as low as 3-4 ′′ for the 10.45 GHz and 7-8 ′′ forthe 4.85 GHz measurements. These correspond to 4.5% and 5%of the FWHM at 10.45 GHz and 4.85 GHz respectively and re-sult in a negligible power loss of the order of 1%. As an example,Fig. 3 shows the distribution of pointing o ff sets for the high fre-quency observations. Before any further discussion it must be clarified that despite thefact that the receivers deliver two circular polarization channels(namely LCP and RCP, see Sect. 2.1), the possible circular po-larization has been neglected with the LCP and RCP channelsbeing averaged (see Fig. 2 and appendix B). This is a reason-able assumption provided that the average degree of circular po-larization of these sources is expected to be low ( < . ff et al. 1984).Figure 2 illustrates the “detection pattern”. From that pictureit is clear that a measurement is the di ff erence between the av-erage antenna temperature of the first and the second sub-scans( T left ) as well as that between the third and the fourth ( T right ).These two di ff erences essentially provide two independent mea-surements of the target source. Ideally, the results should beidentical. Di ff erences should be attributed to atmospheric fluc-tuations, given that the overlap of the “o ff ” and the “on” beamis not precisely 100 %, as well as confusion (field sources con-tributing power in the o ff -beam position). This e ff ect however,comprises the most severe uncertainty in the measurement. Adetailed discussion is given in appendix A.Throughout the data reduction process two types of errorsare computed. The first, denoted by σ rms , is the result of the for-mal error propagation (assuming Gaussian statistics) of the datascatter around the average (error in mean), is chiefly a propertyof the detector and is practically computed by the radiometer for-mula. The second is root mean square (rms) in the antenna tem-perature as is measured from the first subtraction (sub-scans 1and 2) and that from the second subtraction (sub-scans 3 and 4). That is, σ ∆ T = | T left − T right | /
2. Subsequently, the max ( σ rms , σ ∆ T )is taken as a first estimate of the error in the measurement. InSect. 3.2, we describe how the final errors reported in table 8have been calculated. Each measurement conducted as described earlier is conse-quently subjected to a number of corrections:
Opacity correction:
This process is meant to correct the atten-uation of the source signal due to the terrestrial atmosphere. Thecomputation of the opacity is done by utilisation of the observedsystem temperatures.
Elevation dependent gain correction:
Small scale diver-gences of the primary reflector’s geometry from the idealparaboloid lower the sensitivity of the antenna. These gravita-tional deformations are a function of elevation with the conse-quence of an elevation-dependent antenna gain. The “elevation-gain” curve is a second order polynomial of the elevation andis constructed experimentally by observing bright point-likesources over the entire elevation range.
Sensitivity correction:
This process is essentially the transla-tion of the antenna temperature to Jy. That is done by observ-ing standard calibrators (table 3). Given a source of known fluxdensity S cal [Jy] and measured antenna temperature T A [K], thesensitivity factor Γ will then be Γ = T A / S cal . However, the sen-sitivity factors obtained this way depend on the quality of axialfocusing. This is optimised at the initialisation of a field observa-tion. Nevertheless, it can change over the span between two suchconsecutive optimisations (of the order of six hours) and partic-ularly when large temperature gradients are present throughoutthe telescope structure. In accounting for that, the sensitivity fac-tors have been measured both after the first focus correction (be-ginning of the observation) and also before the next focus cor-rection (end of the field observation). For an observing instant inbetween, the result of linear interpolation between those two val-ues has been used. The flux densities of the calibrators are takenfrom Ott et al. (1994), Baars et al. (1977) and Kraus priv. comm.It must be noted that apart from NGC 7027 the sources used ascalibrators are point-like for the beamwidth of E ff elsberg tele-scope. NGC 7027 on the other hand, is extended at 10.45 GHz.At this frequency its size is roughly 9.0 × ′′ (the beamwidthat 10.45 GHz is ∼ ′′ ). Nevertheless, the power loss due to thise ff ect is still less than 1 % and therefore, no beam correction isnecessary. Confusion:
A potential limitation for any observation is con-fusion which has been well studied since the early days ofradio surveys (Scheuer 1957). Put simply, it refers to blendsof unresolved sources that build up significant flux densities.Traditionally, confusion has been treated statistically in terms ofexpected flux density per unit area for a given frequency and formodern observing facilities it often constitutes a factor imposingmore severe limits than the thermal noise itself. In the case ofthe currently discussed work, the problem becomes even moresevere because of the beam switch technique used. In this case,any combination of field NVSS sources can be in the vicinity ofthe targeted source within the “on” or any of the “o ff ” positions. ngelakis et al.: Multi-frequency measurements of the NVSS foreground sources in the CBI fields 5 Fig. 4.
Confusion examples. The left-hand column shows the de-tection profiles whereas the right-hand one shows the NVSS en-vironment of each target source. There – assuming a Gaussianbeam pattern – the solid line marks the 50% beam gain levelwhile the dashed one denotes the 10% level. The red circles cor-respond to the “on” positions and blue ones to the “o ff ” posi-tions. The target sources are shown in red and the environmentNVSS ones in black. The left-hand side plots show the result ofthe di ff erentiation with respect to the strength of the “confusers”and their position relative to the centre of the beam.That can severely a ff ect the di ff erentiation algorithm by contam-inating the subtracted signal. Some typical confusion cases areshown in Fig. 4. The confusion status has been monitored forevery observed scan on the basis of the NVSS positions andhas been corrected afterwards whenever possible (see descrip-tion appendix B). Table 3.
The flux densities and spectral indices of the standardcalibrators.
Source S . h S . i † S . h S . i † α . . α . . (Jy) (Jy) (Jy) (Jy)3C 48 5.63 5.52 2.68 2.59 − − − − − − + + † The average has been done over data with
S NR ≥ σ .
3. Errors
In general, the requirement of time e ffi ciency can be in conflictwith measurement accuracy by limiting, for instance, the timeinvested in calibration. A careful and realistic quantification ofthe involved uncertainties is therefore essential. The followingdiscussion deals with the system repeatability study which infact sets the pragmatic limit to the reliably detectable flux den-sity. Given the goal of reaching the telescope’s theoretically expectedleast detectable flux density, it is crucial to estimate the repeata-bility of a measurement. Let the term “observing system” collec-tively describe everything but the target source. Hence, it refersto the combination of the telescope, the thermal noise, the at-mosphere, the confusion etc. An ideal observing system shouldoutput exactly the same result for the flux of a source indepen-dently of the number of repetitions of the measurements, as longas the source itself is not variable. If we therefore assume thatthe source is non-variable, the variance of its measured flux den-sity over several repetitions can be perceived as system variabil-ity caused by any combination of the possible factors referredto previously. The estimation of the mean variance of the sys-tem as a whole sets the lower limit in the detectable flux density.Considerable observing time has been spent in monitoring ex-actly this property of the system.A number of sources, hereafter called the “repeaters”, havebeen selected to be observed during every observing run. Theyhave been chosen to satisfy two conditions:1. To be intrinsically non-variable. It is known that sourcesof steep spectrum are unlikely to be intrinsically variable.Therefore, a number of sources with spectral index steeperthan around − . In Sect. 2.4 it was explained that as a first estimate of the error ina measurement, has been taken the maximum between the errorin the mean after the formal error propagation, σ rms and the partinfluenced by the atmospheric fluctuations and confusion, σ ∆ T (i.e. max ( σ rms , σ ∆ T )). The former is a parameter of the detectorand is not expected to vary significantly. The latter on the otherhand can vary even for the same target source as a function of theatmospheric conditions and the geometry of the dual-beam sys-tem with respect to the target source and its NVSS environment(confusion). Angelakis et al.: Multi-frequency measurements of the NVSS foreground sources in the CBI fields
Table 4.
The sources used for pointing correction and the “repeaters”.
Source S . h S . i † rms h S . i † rms α . . α . . (mJy) (mJy) (mJy) (mJy) (mJy)Pointing Sources024104 − ‡
913 1 396 22 1 597 141 + + − − − − − − − − − + − − − − − + − − − − − − − − − − − − − − + − − + − − + − − + − − + − − + ‡
31 35 3 73 19 + + + − + − − + − − + − − + − − − − − − − − − − − − − − − − − − − − − − − − − − − − − + − − + − − + − − + − − + − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − ff elsberg, respectively. Columns 4 and 6 give the rms scatter in those measurements. † The average values are produced by pure detection cases. Only measurements of
S NR ≥ σ are accepted. ‡ Source showing intense variability. Marked with red in the repeatability plots at 10.45 GHz.
A way to statistically quantify the uncertainty in a measure-ment including collectively all possible factors of uncertainty,is to investigate how well the measurement of a target source,assumed intrinsically non-variable, repeats over several obser-vations (see Sect. 3.1). For a given frequency, the measure ofthe system repeatability is the rms in the average flux for everyrepeater as a function of its average flux density, σ rep ( S ). Theassociated plots and are shown in Fig. 5. The rms flux density σ rep ( S ), can be written as a functionof the mean flux density S , being the Pythagorean sum of (i)the flux density independent term, σ and (ii) the flux densitydependent term, m · S . In particular, it is described by: σ rep ( S ) = q σ + ( m · S ) (1)Fitting this function to the 4.85 GHz and 10.45 GHz mea-surements, has resulted in the parameters in table 5. From those ngelakis et al.: Multi-frequency measurements of the NVSS foreground sources in the CBI fields 7 r m s ( m Jy ) r m s ( m Jy ) Fig. 5.
The repeatability plots. The upper plot corresponds to4.85 GHz and the lower one to 10.45 GHz. The parameters of thefitted curves are given in table 5. In the lower panel (10.45 GHz)the red points correspond to sources that are known to exhibitvariability characteristics and have been excluded during the fit-ting procedure (namely, 025515 + σ , thesmallest detectable flux density is roughly 6 mJy. In appendix Awe discuss the comparison of the fitted values of σ with theerror of an individual measurement and give a quasi-empiricalinterpretation of the measured parameters. From the discussionpreviously and in Sect. 2.4 the most reasonable (and rather con-servative) estimate of the errors, would be: err = max (cid:16) σ rms , σ ∆ T , σ rep (cid:17) (2)This definition is used to derive the final errors reported in ta-ble 8. Table 5.
The fitted parameters for the repeatability curves.
Frequency σ Error m Error(GHz) (mJy) (mJy) (%) (%)4.85 1.2 0.2 1.3 0.0210.45 1.3 0.1 1.6 0.04The σ parameter is the one determining the least detectable flux. Depending on the configuration of the dual-beam system in thesky relative to the target source and the instantaneous spatial dis-tribution of NVSS field sources, a given scan can show di ff erentconfusion “flavors”. On this basis, there can be three scan classesdiscriminated by their confusion status at a given observing fre-quency:1. Cleanscans. Those are the measurements during which therewere no contaminating sources within any of the beam posi-tions (see top panel in Fig. 6). For these cases, further actionneed not be taken.2. Clustered scans. These are scans on sources that are accom-panied by neighboring sources within a radius smaller thanthe associated beam-width (hence the term cluster). Thesesources cannot be discriminated (see middle panel in Fig. 6)and reliable measurement is impossible. For a given fre-quency only an instrument of larger aperture could resolvethem (e.g. interferometer). For this reason, these scans areabsent from the discussions in the current paper.3. Confused scans. This refers to the case of having any com-bination of field sources within any beam (see lower panelin Fig. 6). For these cases one must either conduct a mea-surement at di ff erent parallactic angle such that the confus-ing source will not coincide with an “o ff ” position, or recon-struct their flux from the exact knowledge of the flux of the“confusers” (see appendix B).It is important to underline that this e ff ect refers to confusionfrom field NVSS sources alone and not to blends of unresolvedbackground radio sources which may contribute significant flux.In table 6 we show the detected confusion flavors for eachfield and frequency. From this table it is readily noticeablethat the confusion becomes less important with increasing fre-quency. For instance, the fraction of sources that su ff er neitherfrom clustering nor from confusion e ff ects increases from 59%at 4.85 GHz to 92% at 10.45 GHz. This is easily interpretablein terms of smaller beam-width (67 ′′ as opposed to 146 ′′ at4.85 GHz). In fact, considering that the majority of sources showsteep radio spectra (see Sect. 4.3), it is expected that in practicesignificantly fewer sources will su ff er from confusion simply be-cause their field sources are too weak already at 4.85 GHz and10.45 GHz. It is important to state that in the following studieswe consider only a sub-sample of 3 434 sources which are eitherclean or have been de-confused.
4. Results
The essence of our task is identifying the detection rates at eachobserving frequency. Assuming that the detectability of a tar-get source is solely due to its spectral behavior, the detectionrates can reveal the subset of sources that exhibit flat or invertedspectra which can adversely a ff ect CBI data (i.e. α ≥ − . S ∝ ν α ). The current sub-section deals with this problem. Thatis, essentially counting the sources that have been detected ateach frequency. For both frequencies the detection threshold hasbeen set to 5 σ , with σ being the error in the individual measure-ment as defined by Eq. 2.A supervisory way to describe the detection rates is using the2-bitbinary detectiondescriptor as in table 7. That is, a two-bitbinary in which the left-hand side bit describes the detection at Angelakis et al.: Multi-frequency measurements of the NVSS foreground sources in the CBI fields
Fig. 6.
Confusion flavors. From top to bottom: a clean, a clusterand a confusioncase. The notation is identical to that in Fig. 4.the low frequency and the one on the right-hand side that at thehigh frequency with “0” denoting a non-detection and “1” de-noting a detection. From all the sources in the sample we haveselected only those that are either cleanat 4.85 GHz or have beende-confused as described in appendix B. Those sources mustthen also be cleanat 10.45 where the beam-width is significantlysmaller.
In table 8, available at the CDS, we summarise the acquiredE ff elsberg measurements along with the computed spectral in- Table 6.
The frequencies of confusion flavors of the observedscans (measurements) for each field and observing frequency.
Field Clean Cluster ⋆ Confused de-confused(%) (%) (%) (%)4.85 GHz (
FWHM ≈ ′′ )02 h
59 18 23 4 (17)08 h
57 18 25 9 (36)14 h
60 20 20 4 (20)20 h
59 19 22 6 (27)Average 59 19 22 6 (27)10.45 GHz (
FWHM ≈ ′′ )02 h
92 1 7 0 (0)08 h
93 2 5 0 (0)14 h
90 1 9 2 (22)20 h
92 2 6 1 (17)Average 92 ∼ ∼ ∼ ⋆ Here the term cluster is meant to represent both, the cases of pureclustering flavour and those that are clustered and confused simul-taneously.
Table 7.
The detection rates.
Field sample ⋆
00 10 11 01(%) (%) (%) (%)02 h
914 70.5 16.0 12.7 0.808 h
692 66.8 19.2 12.4 1.614 h
923 70.7 18.2 10.6 0.520 h
905 67.8 19.6 11.3 1.3Total 3434 69.0 18.3 11.7 1.0The detection threshold for either frequency has been set to 5 σ with sigma being the error in the individual measurement as givenby Eq. 2. ⋆ The sample includes measurements that are clean or de-confused.The de-confusion includes also the rare cases of having the sourceobserved at di ff erent parallactic angle. dices for each source. For the construction of this table, onlyclean or de-confused cases have been considered. In that table,Column 1 lists the name of the source, Columns 2 and 3 givethe NVSS flux density and its error respectively, Columns 4 and5 give the flux density at 4.85 GHz and its error respectively.Columns 6 and 7 list the flux density at 10.45 GHz and its error.The 4.85 GHz and 10.45 GHz have been measured with 100 mradio telescope in E ff elsberg. Columns 8 and 9 give the lowfrequency spectral index α . . between 1.4 GHz and 4.85 GHzand its error. Similarly, Columns 10 and 11 give the high fre-quency spectral index α . . between 4.85 GHz and 10.45 GHzand its error. Finally, Columns 12 and 13, give the least-squarefit spectral index α , from the 1.4 GHz (NVSS), 4.85 GHz and10.45 GHz data points and its error.As mentioned earlier, a measurement is regarded to be a de-tection only if it is characterized by S NR ≥
5. Whenever thisis not the case an upper limit of 5 σ is put, with sigma being ngelakis et al.: Multi-frequency measurements of the NVSS foreground sources in the CBI fields 9 the error computed as described in Sect. 2.4. In such cases, theassociated spectral indices are not quoted in the table.According to our discussion in Sect. 3.2, the errors quotedin table 8 can not be < . < . ff ering from confusion are not included. Itmust be noted that concerning the CMB experiments these casesstill provide useful information. Typically, they are characterizedby lower angular resolutions and hence clustered sources can betreated as individual objects. All in all, the sources included thereamount to about 57% of the whole sample amounting to 3 434entries. The motivation for the current program has been, as discussedearlier, the estimation of the extrapolated flux to be expected athigher frequency bands performed on the basis of the three-pointspectral index. Here we summarize the findings of the spectralindices study. Hereafter, it is assumed that S ∝ ν α .To begin with, Fig. 7 shows the spectral index distributionsfor the spectral indices in table 8. In particular, the distributionsof α . . , α . . and least-squares fit three-point α are shown.All three of those are constructed only with 5 σ data. For com-puting the three-point spectral index, an implementation of thenonlinear least-squares (NLS) Marquardt-Levenberg algorithm(Marquardt 1963) was used. That imposes natural weighting (i.e.1 /σ ).The median spectral index α is around − .
71 whereas theaverage value is roughly − .
59 indicating the skewness of thedistribution. On the other hand, α . . shows a median value ofroughly − .
69 whereas α . . has also a median of − .
75. Of the402 sources detected at both frequencies, 136 (34%) appear witha spectral index α ≥ − . α ≤ − . ≈
87% with2-bit binary detection descriptor of 00 or 10. What is importantabout this population is that these are the sources that need notbe “vetoed out” during the CMB data analysis since they arenot bright enough to contribute detectable flux at the frequenciesnear 30 GHz at which experiments like CBI operate.All the measurements have been conducted in an approxi-mately quasi-simultaneous way. The coherence time varies be-tween hours to days. It is therefore important to contemplate onhow the lack of simultaneity influences the results. Provided thatmost of the sources follow a steep spectrum trend and steep spec-trum sources are not expected to vary significantly, it is reason-able to assume that statistically it will be insignificant.
5. Conclusions
1. The applied observing technique has been chosen to be ef-ficient in terms of time. Its combination with the beam-switch allows a remarkably e ffi cient removal of linear at-mospheric e ff ects. However, it su ff ers from “analytic” con-fusion (caused by sources of positions known from other -3 -2 -1 0 1 2Spectral Index010203040 N o r m a li ze d C oun t s ( % ) least-squares fit αα α Fig. 7.
The normalized spectral index distributions. The greyarea histogram shows the distribution of the three-point least-square-fit spectral index, α , for sources that have been detected atboth frequencies with sigma-to-noise of at least 5 (402 sources,table 7). The same sub-sample is used for the blue line distribu-tion which denotes that of the ”high” frequency spectral index, α . . . Finally, the red line shows the distribution of the ”low”frequency index, α . . , for a number of 1104 sources detected at4.85 GHz (see table 7). The mean values of α , α . . and α . . are − . − .
54 and − .
69, respectively.surveys) as expected. Nevertheless, the confusion e ff ect de-creases fast with frequency (from ∼
22% to ∼ ≥
5) detectable flux density has been the troposphericturbulence. In Appendix A we show that the troposphericfactor is of the order of 0.9 mJy and 1.3 mJy for the 4.85 GHzand the 10.45 GHz observations, respectively. On the otherhand, while the second most important factor for the lowfrequency is the confusion caused by blends of unresolvedsources (see Section 3.2 and Table 5), for the higher fre-quency thermal “receiver” noise dominates. The confusionin the latter case drops dramatically by an order of magni-tude to 0.08 mJy due to the smaller beamwidth and the pre-sumed spectral behaviour of radio sources. From this dis-cussion it is clear that the major limiting factor has been thetroposphere itself setting a physical limitation in the least de-tectable flux density. That appears to be between 5 × . = × . = . / formulation of theerrors described in Appendix A and the observed ones fromthe study of the “repeaters” is noteworthy.4. In Appendix B an algorithm for achieving “de-confusion”is presented. That is, reconstructing a source antenna tem-perature on the basis of some elementary presumptions. Thealgorithm has been successfully used in 6 % of the cases in Table 8.
The E ff elsberg measured flux densities along with the NVSS ones and the computed spectral indices (it is assumed that S ∼ ν α ). Source S . err S . err S . err α . . err α . . err α err(mJy) (mJy) (mJy) (mJy) (mJy) (mJy)023958 + < < + < < + < < + < < + < < + < + + < − + − − − + < < + < < < σ . The source name is marked with ⋆ or † in case de-confusioncorrection has been applied at 4.85 or 10.45 GHz, respectively. The complete table is available in electronic form at the CDS via anonymousftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http: // cdsweb.u-strasbg.fr / cgi-bin / qcat?J / A + A / the current study and can be easily generalised in projectsdemanding automation.5. In Appendix C we present an algorithm that is responsi-ble for the “quality check” of every observation (a “scan”).Incorporating a number of tests can be used for automaticallydetecting cases of bad quality data and can be generalised tobe used in a “blind” mode. Acknowledgements.
The authors would like to thank the anonymous refereefor the comments that significantly improved the content of the manuscript.Furthermore, we want to thank the internal referee Dr D. Graham also for hiscomments and suggestions. We would like to acknowledge the help of Dr I.Agudo, Mrs S. Bernhart, Dr V. M. C. Impellizzeri and Dr R. Reeves and allthe operators at the 100 m telescope for their help with the observations. Theauthor was mostly financed by EC funding under the contract HPRN-CT-2002-00321 (ENIGMA) and completed this work as member of the International MaxPlanck Research School (IMPRS) for Radio and Infrared Astronomy. All the re-sults presented here have been based on observations with the 100 m telescopeof the MPIfR (Max-Planck-Institut f¨ur Radioastronomie).
References
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Appendix A: Expected versus observeduncertainties
Here we investigate how the fitted values of σ and m comparewith those semi-empirically known. To begin with, the constantterm σ in Eq. 1 can be decomposed in three constituents asfollows: σ = σ + σ + σ (A.1) σ rms the thermal noise, computable from the radiometerformula σ conf the confusion error, known semi-empirically(Condon et al. 1989) σ atm variable atmospheric emission error, computablefrom the atmospheric opacity change.Separately for each frequency these quantities give: Frequency σ rms σ conf σ atm σ Fitted σ (GHz) (mJy) (mJy) (mJy) (mJy) (mJy)4.85 0.16 0.80 0.92 1.23 1.210.45 0.22 0.08 1.30 1.32 1.3 being satisfactorily close to the expected values. Similarly, theflux dependent part of Eq. 1 can be understood as a multi-factore ff ect. Specifically, it can be written that: m = m + m + m (A.2) m poi pointing o ff set error, easily calculable on the basisof a Gaussian-like beam pattern and from the mea-sured average pointing o ff sets ( ≈ ′′ ) m cal instability of noise diode estimated from Intra-dayVariability experiments (Kraus priv. comm.) m atm variable atmospheric absorption error, estimatedfrom the Water Vapor Radiometer data (Roy 2006).The expected factor m ′ as compared to the fitted one m , will be: ngelakis et al.: Multi-frequency measurements of the NVSS foreground sources in the CBI fields 11Frequency m poi m cal m atm m Fitted m (GHz) (%) (%) (%) (%) (%)4.85 0.21 1.3 0.004 1.32 1.310.45 1.01 1.3 0.005 1.64 1.6 Fig. B.1.
The horn arrangement as a function of time during theexecution of an observation. In blue is the horn that is pointingo ff -source each time and in red the one on-source. Within eachhorn there might be a population of confusing sources the fluxof which is represented by S i , S i ′ or S i ′′ , with i =
1, 2, 3, 4 ... S in yellow is the target source. The two blue circles on the left aremisplaced because the sky rotates within a scan.The term determining the detection threshold is clearly theterm σ in Eq. A.1. From the above discussion, it is clear thatfor the low frequency observations both the atmospheric andthe confusion terms are significant. However, For the higher fre-quency there appears a decrease in the confusion term (due tothe smaller beam size) and the dominant remaining factor is theatmospheric itself. Appendix B: Resolving the confusion
Here we present a method to partially resolve the confusioncaused by known field sources. The goal is to reconstruct theflux density of a target source whenever possible from know-ing the parameters of the ones causing the confusion. These pa-rameters are known from the observations described here sincethey also belong to the same source sample and hence are ob-served. Note that in the majority of the cases ( ∼ FWHM ) about the target source ( S i in Fig. B.1)and each contributes antenna temperature T i . Hence, cumula-tively this group will contribute a brightness temperature: T ON = X i T i (B.1) The “SUB-1,4” population, which are the sources S ′ i locatedwithin a circle of 1 FWHM of the horn position during sub-scan 1 or 4. This is the position of the main horn during the 1 st and 4 th sub-scan. This population will contribute a brightnesstemperature: T , = X i T ′ i (B.2)The “SUB-2 and 3” population of the sources occupying thebeam position during sub-scans 2 and 3. This is the positionof the reference horn during those sub-scans. Their contributionwill then be: T − = X i T ′′ i (B.3)In Eq. B.1, B.2 and B.3 T i , T ′ i or T ′′ i , is the brightness temper-ature contribution of a source at the frequency of interest afteraccounting for the distance from the center of the beam. Hence,a source of intrinsic brightness temperature T src that lies x ′′ fromthe center of the beam of the 4.85 GHz system, will contribute: T = T src · e − x FWHM (B.4)From the above it is clear that T ON , T − and T − will be addedto the system temperature T sys altering the result of the di ff eren-tiation method.Preserving the notation used in Sect. 2.4, it can be shown thatthe “real” source brightness temperature, T real can be recoveredfrom observable T left and T right , by: T left = T real + T ON − T − − T T right = T real + T ON − T − − T T real and T ON in practice cannot be resolved(clustercases, angular resolution limitation), it is meaningless torefer to them separately. This is why we refer to the clustercasesseparately throughout the text and why we do not include themin table 8. For the sake of the following discussion we refer tothem cumulatively as T obs = T real + T ON .This simple method has some weaknesses:1. Clustered “confusers”:
In the above discussion it is pre-sumed that the flux densities of the members of a population(e.g. S ′ i ), are known from the measurement of which targetwas themselves (all the sources we discuss are from of thesame sample after all and hence have been targeted). This istrue only if the distance of a pair of sources of the same pop-ulation is ≥ FWHM /
2. Hence, the above method has beenapplied only in those cases.2.
Missing “confusers”:
The confusing sources are searchedamong the the NVSS ones. Hence, sources that are not de-tected by the NVSS survey which may become detectable athigher frequencies are neglected.3.
Upper limits:
As seen in table 8, often the upper limits in theflux density are significant. However, they are not accountedfor during the de-confusion algorithm.4.
No corrections applied:
The correction discussed inSect. 2.4.1 are not applied for the confusing sources duringthe resolving algorithm.5.
Inaccurate positions of beams and non-Gaussian beams:
In all the above it has been assumed that the positions ofthe beams are precisely known and that there are no point-ing o ff sets. Furthermore, the beam pattern is supposed to bedescribed by a simple circular Gaussian. Appendix C: Data reduction “pipeline”
The data volume acquired during the course of the currentproject has been reduced in a pipeline manner. E ff ort has beenput into developing software beyond the standard data reductionpackages used in E ff elsberg that could assist the observer to re-duce the data as automatically as possible at all stages. Here weattempt a rough and very brief description of only some of thesteps followed. Throughout the pipeline, every system parame-ter is monitored and recorded. Some details are omitted in thisdescription. The front-end:
The front-end of the pipeline is the point atwhich “counts” (power) from the telescope are piped in the datareduction code. The input consists of four power data channelstwo (LCP and RCP) for each horn along with the signal froma noise diode of known temperature, for each one of them, i.e.eight channels in total.
RFI mitigation:
Before any operation is applied to the signal,Radio Frequency Interference (RFI) mitigation takes place. InFig. C.1 an example is shown. Here, black represents the signalbefore and red the signal after RFI mitigation. In the top panel allfour channels of the sky signal are shown in terms of “counts”.A short-lived spike of extremely intense radiation, characteristicof RFI, is clearly seen. A routine iteratively measures the RMSin that sub-scan and removes the points above a pre-set thresh-old. The resulting signal is shown in red. The same procedureis followed for the noise diode signal. Finally, the bottom panelshows the final detection pattern free of RFI.
The signal pre-calibration:
After the signals have been“cleaned” comes the stage of the comparison of each data pointwith the noise diode signal, both being measured in counts. Thedemand for achieving flux densities as low as theoretically pre-dicted for the 100 m telescope imposes the necessity of having anoise diode signal that ideally should be constant with an RMSof no more than a fraction of a percentile. However, often occur-ring cross-talk between di ff erent channels or other e ff ects, mayresult in intra-scan instabilities (as shown in Fig. C.2) that maydistort the detection pattern. The way around this problem hasbeen the idea to normalize (”calibrate”) the data to the average,over the whole scan, diode signal. The default would be a point-by-point calibration that may on the other hand significantly dis-tort the detection pattern. System temperature measurement:
Having the data pre-calibrated (meaning in terms of antenna temperature), allowssystem temperature measurements. That in turn, allows measur-ing the atmospheric opacity for each particular observing ses-sion by using the system temperature of each scan. Later in thepipeline, this information is used for correcting for the opacity.
The corrections:
Following the previous stage is that of sub-tracting the signal of two feeds and the calculation of the antennatemperature. Afterwards,the opacity, gain curve and sensitivitycorrections are applied as described in Sect. 2.4.1.
The quality check:
The conceptual end of the pipeline is thequality check subject to which has been every single scan. The
Fig. C.1.
Demonstration of the e ffi ciency of the RFI mitigationalgorithm. Top panel: the sky signal before (black) and after(red) RFI mitigation. Lower panel: the final detection profile freeof RFI. Fig. C.2.
Characteristic cases of intra-scan instabilities of thenoise diode signal. Each column corresponds to a di ff erent scanand each row to a di ff erent channel. The signal is in terms ofcounts.term “quality check” wraps up a number of tests imposed oneach scan. Some of them are:1. The system temperature of each channel is compared to theempirically expected one. Flags are raised at excess of 10, 20and 30 %. This test serves as an excellent tracer of weathere ff ects, system defects etc.2. A second test is the RMS and the peak-to-peak variation ofthe data in each sub-scan for each channel separately as wellas for the final profile. An increase can be caused by ex- ngelakis et al.: Multi-frequency measurements of the NVSS foreground sources in the CBI fields 13 treme non-linear atmospheric e ff ects as well as linear slopespresent in the data. The latter is most often the result of in-creasing atmospheric opacity as the source is tracked at lowelevations.3. In order to trace cases that show a clear linear drift as aresult of increasing opacity, each scan has been sliced intofour segments. A straight line has consecutively been fittedto each segment. A flag is raised when the slope of a segmentis above some preset value.4. It is examined whether the final measurement profile is in-verted and if so whether the absolute source flux density sat-isfies the detection threshold being set. It is possible in casesof confusion that a source in the o ff position may result in aninverted profile.5. It is checked whether sensitivity factor (K //