text: 4 D. Guidetti et al. to the lowest common resolution. This means that we lose resolution in our images, but also that we need to ﬁne-tune the data and/or change the weighting function used in the gridding process as the image frequency increases. Secondly, the cleaning threshold is usually set to some multiple of the expected noise (usually in the range 3 to 5). Using the same criterion for the cleaning in both methods described above means that the individual IF images will have, on average, a noise four times larger than the image produced with the MSMF clean (since 16 individual IFs are summed up). Therefore a large fraction of the sources detected in the sensitive wide-band mosaic obtained by recombining the 16 individual IF mosaics will be sources that were not cleaned, or that were cleaned in some images (some IFs) and not in others. This may aﬀect the source properties by introducing subtle undesirable eﬀects on the ﬁnal mosaic. We imported the combined data-sets (one for each pointing, including all the A- plus B-conﬁguration data) into casa (task importuvfits) and ran the task clean with two Taylor terms in the frequency expansion (mode=mfs, nterms=2). Wide-ﬁeld mode was enabled using gridmode=widefield, wprojplanes=128, facets=1, along with three resolution scales. For each pointing a map with 8192 pixels on-the-side was produced with a pixel size of 0.1 × 0.1 arcsec2. The ﬁelds were cleaned down to about Figure 2. Top: Visibility function of the 5.5GHz mosaic (area versus r.m.s. sensitivity) calculated over the region used to de- 4 times the expected r.m.s. noise of each pointing. The ﬁ- nal restoring beam was set to 0.56 × 0.47 arcsec2 with a rive the source catalogue (see text). Bottom: Observed peak (Sp) ◦ and total ﬂux density (St) distributions of the 5.5GHz sources. position angle of 88 . After the deconvolution, wide-band The dashed red line indicates the peak ﬂux density histogram af- primary beam correction was applied using the casa task ter correcting for the visibility function. A preliminary version of widebandpbcor using a primary beam threshold cut-oﬀ of these plots was shown in Guidetti et al. (2015). 0.15 per cent of the peak. To construct the mosaic, the images of the seven point- ings were transferred back into aips. We re-gridded the im- estimate of the peak brightness and position was obtained ages using the task hgeom to a common centre, and pro- with a simple cubic interpolation around the ﬁtted position duced a noise image for each pointing using the task rmsd. using maxfit in aips. Only the sources for which the ratio of ≥ The re-gridded images were combined, using the noise im- peak brightness and the local noise was 5 (i.e. those with ages as weights, with the task wtsum. Finally, a n(cid:39)oise image SNR≥5) were included in the ﬁnal catalogue. We found a to- of the mosaic was generated. The r.m.s. noise is 1 µJy in tal of 100 components that were visually checked to identify the inner regions, and increases with distance from the cen- possible multiple components of a single radio source. Eight tre of the mosaic. The visibility function (Fig. 2), calculated§ components were converted into 2 single radio sources. In over the region used to extract the source catalogue (see these cases, we “collapsed” all the multiple components in ), shows that about 50 percent of the mapped area is char- the catalogue to a single source entry at the position of the a≤cterized by an r.m.s. noise lower than 3 µJy, and remains brightest component, and we derived the total ﬂux density 10µJy across the whole ﬁeld: this makes our survey the integrating the brightness distribution over the area occu- most sensitive yet at 5.5 GHz. pied by the source. For all the remaining sources we assessed the reliability of the total ﬂux densities derived by sad us- ing simulated sources, added to the uv-dataset of the central 3 SOURCE CATALOGUE pointing. The dataset, including the mock sources, was im- aged and primary beam corrected as the original dataset. Forty mock sources, with total ﬂux density in the range 20- To identify a sample of sources above a given local 200 µJy were inserted for each run of simulation in a re- signal-to-noise ratio (SNR) threshold in the 5.5 GHz mosaic, gion within a radius of 90 arcsec from the pointing centre. we followed the same approach already successfully tested Half of the inserted sources were point-like, while the re- by other radio surveys (e.g. Bondi et al. 2003). We employed maining half had intrinsic sizes between 0.2 and 0.8 arcsec. the aips task sad on both the mosaic image and the noise This procedure was repeated ﬁve times yielding to a sam- image to obtain a catalogue of candidate sources above the ple of 200 mock sources. The total ﬂux density recovered by threshold of 4.5σ. We limited the source extraction and the sad (1-component Gaussian ﬁt) for each mock source was following analysis to a circular region of radius 7 arcmin compared to the intrinsic one injected in the dataset. We around the mosaic centre. For each selected source, sad es- found that the total ﬂux densities derived with this proce- timates the peak and total ﬂuxes, and the position and size dure are systematically higher (on average by 15-20 percent) using a Gaussian ﬁt. Since the Gaussian ﬁt may provide than the true values: the median, mean and standard devi- unreliable and biased results for low SNR sources, a better ation of the ratio between the measured and injected total MNRAS 000, 000–000 (0000)

text: D.

text: Guidetti

text: et

text: al.

text: to

text: the

text: lowest

text: common

text: resolution.

text: This

text: means

text: that

text: we

text: lose

text: resolution

text: in

text: our

text: images,

text: but

text: also

text: that

text: we

text: need

text: to

text: ﬁne-tune

text: the

text: data

text: and/or

text: change

text: the

text: weighting

text: function

text: used

text: in

text: the

text: gridding

text: process

text: as

text: the

text: image

text: frequency

text: increases.

text: Secondly,

text: the

text: cleaning

text: threshold

text: is

text: usually

text: set

text: to

text: some

text: multiple

text: of

text: the

text: expected

text: noise

text: (usually

text: in

text: the

text: range

text: to

text: Using

text: the

text: same

text: criterion

text: for

text: the

text: cleaning

text: in

text: both

text: methods

text: described

text: above

text: means

text: that

text: the

text: individual

text: IF

text: images

text: will

text: have,

text: on

text: average,

text: a

text: noise

text: four

text: times

text: larger

text: than

text: the

text: image

text: produced

text: with

text: the

text: MSMF

text: clean

text: (since

text: individual

text: IFs

text: are

text: summed

text: up).

text: Therefore

text: a

text: large

text: fraction

text: of

text: the

text: sources

text: detected

text: in

text: the

text: sensitive

text: wide-band

text: mosaic

text: obtained

text: by

text: recombining

text: the

text: individual

text: IF

text: mosaics

text: will

text: be

text: sources

text: that

text: were

text: not

text: cleaned,

text: or

text: that

text: were

text: cleaned

text: in

text: some

text: images

text: (some

text: IFs)

text: and

text: not

text: in

text: others.

text: This

text: may

text: aﬀect

text: the

text: source

text: properties

text: by

text: introducing

text: subtle

text: undesirable

text: eﬀects

text: on

text: the

text: ﬁnal

text: mosaic.

text: We

text: imported

text: the

text: combined

text: data-sets

text: (one

text: for

text: each

text: pointing,

text: including

text: all

text: the

text: A-

text: plus

text: B-conﬁguration

text: data)

text: into

text: casa

text: (task

text: importuvfits)

text: and

text: ran

text: the

text: task

text: clean

text: with

text: two

text: Taylor

text: terms

text: in

text: the

text: frequency

text: expansion

text: (mode=mfs,

text: Wide-ﬁeld

text: mode

text: was

text: enabled

text: using

text: gridmode=widefield,

text: along

text: with

text: three

text: resolution

text: scales.

text: For

text: each

text: pointing

text: a

text: map

text: with

text: pixels

text: on-the-side

text: was

text: produced

text: with

text: a

text: pixel

text: size

text: of

text: The

text: ﬁelds

text: were

text: cleaned

text: down

text: to

text: about

text: Figure

text: Top:

text: Visibility

text: function

text: of

text: the

text: mosaic

text: (area

text: versus

text: r.m.s.

text: sensitivity)

text: calculated

text: over

text: the

text: region

text: used

text: to

text: de-

text: times

text: the

text: expected

text: r.m.s.

text: noise

text: of

text: each

text: pointing.

text: The

text: ﬁ-

text: nal

text: restoring

text: beam

text: was

text: set

text: to

text: with

text: a

text: rive

text: the

text: source

text: catalogue

text: (see

text: text).

text: Bottom:

text: Observed

text: peak

text: (Sp)

text: and

text: total

text: ﬂux

text: density

text: (St)

text: distributions

text: of

text: the

text: sources.

text: position

text: angle

text: of

text: After

text: the

text: deconvolution,

text: wide-band

text: The

text: dashed

text: red

text: line

text: indicates

text: the

text: peak

text: ﬂux

text: density

text: histogram

text: af-

text: primary

text: beam

text: correction

text: was

text: applied

text: using

text: the

text: casa

text: task

text: ter

text: correcting

text: for

text: the

text: visibility

text: function.

text: A

text: preliminary

text: version

text: of

text: widebandpbcor

text: using

text: a

text: primary

text: beam

text: threshold

text: cut-oﬀ

text: of

text: these

text: plots

text: was

text: shown

text: in

text: Guidetti

text: et

text: al.

text: per

text: cent

text: of

text: the

text: peak.

text: To

text: construct

text: the

text: mosaic,

text: the

text: images

text: of

text: the

text: seven

text: point-

text: ings

text: were

text: transferred

text: back

text: into

text: aips.

text: We

text: re-gridded

text: the

text: im-

text: estimate

text: of

text: the

text: peak

text: brightness

text: and

text: position

text: was

text: obtained

text: ages

text: using

text: the

text: task

text: hgeom

text: to

text: a

text: common

text: centre,

text: and

text: pro-

text: with

text: a

text: simple

text: cubic

text: interpolation

text: around

text: the

text: ﬁtted

text: position

text: duced

text: a

text: noise

text: image

text: for

text: each

text: pointing

text: using

text: the

text: task

text: rmsd.

text: using

text: maxfit

text: in

text: aips.

text: Only

text: the

text: sources

text: for

text: which

text: the

text: ratio

text: of

text: The

text: re-gridded

text: images

text: were

text: combined,

text: using

text: the

text: noise

text: im-

text: peak

text: brightness

text: and

text: the

text: local

text: noise

text: was

text: (i.e.

text: those

text: with

text: ages

text: as

text: weights,

text: with

text: the

text: task

text: wtsum.

text: Finally,

text: a

text: image

text: were

text: included

text: in

text: the

text: ﬁnal

text: catalogue.

text: We

text: found

text: a

text: to-

text: of

text: the

text: mosaic

text: was

text: generated.

text: The

text: r.m.s.

text: noise

text: is

text: µJy

text: in

text: tal

text: of

text: components

text: that

text: were

text: visually

text: checked

text: to

text: identify

text: the

text: inner

text: regions,

text: and

text: increases

text: with

text: distance

text: from

text: the

text: cen-

text: possible

text: multiple

text: components

text: of

text: a

text: single

text: radio

text: source.

text: Eight

text: tre

text: of

text: the

text: mosaic.

text: The

text: visibility

text: function

text: (Fig.

text: calculated§

text: components

text: were

text: converted

text: into

text: single

text: radio

text: sources.

text: In

text: over

text: the

text: region

text: used

text: to

text: extract

text: the

text: source

text: catalogue

text: (see

text: these

text: cases,

text: we

text: “collapsed”

text: all

text: the

text: multiple

text: components

text: in

text: shows

text: that

text: about

text: percent

text: of

text: the

text: mapped

text: area

text: is

text: char-

text: the

text: catalogue

text: to

text: a

text: single

text: source

text: entry

text: at

text: the

text: position

text: of

text: the

text: a≤cterized

text: by

text: an

text: r.m.s.

text: noise

text: lower

text: than

text: µJy,

text: and

text: remains

text: brightest

text: component,

text: and

text: we

text: derived

text: the

text: total

text: ﬂux

text: density

text: across

text: the

text: whole

text: ﬁeld:

text: this

text: makes

text: our

text: survey

text: the

text: integrating

text: the

text: brightness

text: distribution

text: over

text: the

text: area

text: occu-

text: most

text: sensitive

text: yet

text: at

text: GHz.

text: pied

text: by

text: the

text: source.

text: For

text: all

text: the

text: remaining

text: sources

text: we

text: assessed

text: the

text: reliability

text: of

text: the

text: total

text: ﬂux

text: densities

text: derived

text: by

text: sad

text: us-

text: ing

text: simulated

text: sources,

text: added

text: to

text: the

text: uv-dataset

text: of

text: the

text: central

text: SOURCE

text: CATALOGUE

text: pointing.

text: The

text: dataset,

text: including

text: the

text: mock

text: sources,

text: was

text: im-

text: aged

text: and

text: primary

text: beam

text: corrected

text: as

text: the

text: original

text: dataset.

text: Forty

text: mock

text: sources,

text: with

text: total

text: ﬂux

text: density

text: in

text: the

text: range

text: To

text: identify

text: a

text: sample

text: of

text: sources

text: above

text: a

text: given

text: local

text: µJy

text: were

text: inserted

text: for

text: each

text: run

text: of

text: simulation

text: in

text: a

text: re-

text: signal-to-noise

text: ratio

text: (SNR)

text: threshold

text: in

text: the

text: GHz

text: mosaic,

text: gion

text: within

text: a

text: radius

text: of

text: arcsec

text: from

text: the

text: pointing

text: centre.

text: we

text: followed

text: the

text: same

text: approach

text: already

text: successfully

text: tested

text: Half

text: of

text: the

text: inserted

text: sources

text: were

text: point-like,

text: while

text: the

text: re-

text: by

text: other

text: radio

text: surveys

text: (e.g.

text: Bondi

text: et

text: al.

text: We

text: employed

text: maining

text: half

text: had

text: intrinsic

text: sizes

text: between

text: and

text: arcsec.

text: the

text: aips

text: task

text: sad

text: on

text: both

text: the

text: mosaic

text: image

text: and

text: the

text: noise

text: This

text: procedure

text: was

text: repeated

text: ﬁve

text: times

text: yielding

text: to

text: a

text: sam-

text: image

text: to

text: obtain

text: a

text: catalogue

text: of

text: candidate

text: sources

text: above

text: the

text: ple

text: of

text: mock

text: sources.

text: The

text: total

text: ﬂux

text: density

text: recovered

text: by

text: threshold

text: of

text: We

text: limited

text: the

text: source

text: extraction

text: and

text: the

text: sad

text: Gaussian

text: ﬁt)

text: for

text: each

text: mock

text: source

text: was

text: following

text: analysis

text: to

text: a

text: circular

text: region

text: of

text: radius

text: arcmin

text: compared

text: to

text: the

text: intrinsic

text: one

text: injected

text: in

text: the

text: dataset.

text: We

text: around

text: the

text: mosaic

text: centre.

text: For

text: each

text: selected

text: source,

text: sad

text: es-

text: found

text: that

text: the

text: total

text: ﬂux

text: densities

text: derived

text: with

text: this

text: proce-

text: timates

text: the

text: peak

text: and

text: total

text: ﬂuxes,

text: and

text: the

text: position

text: and

text: size

text: dure

text: are

text: systematically

text: higher

text: (on

text: average

text: by

text: percent)

text: using

text: a

text: Gaussian

text: ﬁt.

text: Since

text: the

text: Gaussian

text: ﬁt

text: may

text: provide

text: than

text: the

text: true

text: values:

text: the

text: median,

text: mean

text: and

text: standard

text: devi-

text: unreliable

text: and

text: biased

text: results

text: for

text: low

text: SNR

text: sources,

text: a

text: better

text: ation

text: of

text: the

text: ratio

text: between

text: the

text: measured

text: and

text: injected

text: total

text: MNRAS


text: 6 D. Guidetti et al. based on the ratio between the total and peak ﬂux densities Table 2. Polarised sources. Col.1: Source name. Col.2: Peak of of the sources (e.g. Prandoni et al. 2000): polarised emission. Col.3: SNR of the polarised emission. Col4: Total polarised emission. Col.5 Average fractional polarisation. S /S = (θ θ )/(b b ) (1) t p min maj min maj Source Name P SNRP Ptot Pol. (µJy) (µJy) (%) where θmin and θmaj are the ﬁtted source FWHM axes J123623+621642 10.4 3.3 10.4 4.9 and bmin and bmaj are the synthesized beam FWHM axes. J123642+621545 6.0 3.3 6.0 10.8 The ﬂux density ratio distribution for all the 94 sources is J123644+621133 20.8 12.6 39.9 4.8 shown in Fig. 3. As expected, at low SNRs we have sources J123646+621629 10.9 5.0 10.9 7.5 with S /S < 1: this is due to the r.m.s. statistical errors J123700+620909 7.3 3.1 7.3 7.2 t p which aﬀect our source size and, in turn, the ﬂux density J123714+620823 19.5 4.8 19.5 1.0 J123721+621129 10.1 4.2 10.1 2.6 estimates. J123726+621128 28.4 9.4 86.8 8.2 To distinguish between unresolved and extended sources, we derived the lower envelope of the ﬂux ratio dis- tribution in Fig. 3 by ﬁtting a curve above which there are at least 90 percent (to discard possible outliers) of the sources with S /S < 1:, and then mirrored it above the S / S =1 T P T P value. The sources located above the upper envelope are con- of 3σ in the polarised intensity image. We then searched for sidered extended, while those below it are considered unre- polarised emission at the positions of the sources in our sam- solved. We stress that the total ﬂux density of the sources is ple. We detected polarised emission in only eight sources. calculated through a 2 component-ﬁt (source + background) These are listed in Table 2. For each source we give the which has proved to be more reliable in measuring the total peak in polarised emission and its SNR, the total polarised ﬂux. ﬂux and the average fractional polarisation (calculated as The upper curve can be de(cid:20)scribed by(cid:21) the equation: the total polarised ﬂux divided by the total ﬂux density of the source from Table 1). Only two sources in Table 2 show extended polarised emission. In particular J123726+621128 a S /S = 1 + (2) has a wide-angle tail (WAT) morphology with polarisation t p (Sp/σ)β detected in the twin jets and in both lobes as shown in Fig. 4. The second extended, polarised source, J123644+621133, where a = 6 and β = 1.5. With this criterion, 56 (38) represents the other galaxy in this ﬁeld showing the clas- sources are considered resolved (unresolved). We considered sical FRI structure (core+jets). as reliable only the deconvolved angular sizes of the resolved We estimated the bandwidth eﬀects on the polarised sources, while those of unresolved sources are set to zero in emission of the sources, assuming a rotation measure (RM) − the catalogue (see Table 1). in the range 10-100 radm 2. These are plausible values for 3.2 Radio sources detected at 5.5 GHz without a the integrated RM of GOODS-N sources: typical intrinsic 1.4 GHz counterpart RM values for extragalactic radio sources are in the range − from a few radm 2 in the poorest environments, through The deepest observations at 1.4 GHz of the GOODS-N − intermediate values of 30-100 radm 2, up to thousands of ﬁeld, published by Morrison et al. (2010), have a circular − ∼ ∼ radm 2 in the centres of cool core clusters (Guidetti et al. beam size of 1.7 arcsec and r.m.s noise level of 3.9 − 2011, 2012). The high Galactic latitude of the GOODS-N µJy beam 1. The 1.4 GHz catalogue lists more than 1200 ∼ − ﬁeld ensures a small contribution from the Galactic fore- radio sources above a 5σ threshold of 20 µJy beam 1 at × ground. For the worst case (i.e. at the lowest frequency of the ﬁeld centre, within a region of 40 40 arcmin2. A sig- our observations, 4.5 GHz), the average rotation across the niﬁcant fraction of the sources detected at 5.5 GHz (17/94, ∼ bandwidth is 10 degrees, resulting in a depolarisation of 18 percent) have no counterpart in the 1.4 GHz catalogue. 0.017 which is negligible compared to the errors due to noise. About half (9/17) of the sources without a 1.4 GHz coun- § Rudnick & Owen (2014) published the results of a po- terpart have SNR> 5.5 or have a NIR identiﬁcation (see ) larisation survey of the GOODS-N ﬁeld at 1.5 GHz. The and these are the most reliable sources. These sources have observations had a detection threshold of 14.5 µJy in po- upper limits in the spectral index ranging from α < 0.66 to − ∝ − larised emission and cover a much larger area than that cov- α < 0.5 (adopting the spectral index deﬁnition S ν α), ered by our 5.5 GHz data. They detected 14 radio sources; and will be discussed in more details in Paper II (Guidetti two are in the ﬁeld of view covered by our observations: et al. in preparation). The number of the remaining sources J123644.3+621132 and J123725.9+621128 (wrongly named (8/17) is consistent with the number of the expected spuri- § as J1237744.1+621128 in Table 1 in Rudnick & Owen ous sources derived in . (2014)) and both show polarised emission at 5.5 GHz. These 4 POLARISATION PROPERTIES are the two extended sources discussed above, and the The mosaics of the Stokes parameters Q and U were sources with the strongest polarised emission at 5.5 GHz. imaged and assembled using the same method applied to Taking into account that the synthesized beam of the × derive the total intensity mosaic. Noise images were also de- 1.5 GHz observations is 1.6 1.6 arcsec2 (compared to × rived. The Stokes Q and U mosaics were combined to derive 0.56 0.47 arcsec2 of our 5.5 GHz observations), the amount the polarised intensity mosaic using the task comb in aips. of polarised ﬂux detected at the two frequencies is consis- The noise images were used to clip signals below a threshold tent. Of the remaining sources we detect at 5.5 GHz, only MNRAS 000, 000–000 (0000) ##LTLine## ##LTLine## ##LTLine## ##LTLine##

label: paragraph

text: D.

text: Guidetti

text: et

text: al.

text: based

text: on

text: the

text: ratio

text: between

text: the

text: total

text: and

text: peak

text: ﬂux

text: densities

text: Table

text: Polarised

label: caption

text: sources.

text: Source

text: name.

text: Peak

text: of

text: of

text: the

text: sources

text: (e.g.

text: Prandoni

text: et

text: al.

text: polarised

text: emission.

text: SNR

text: of

text: the

text: polarised

text: emission.

text: Total

text: polarised

text: emission.

text: Average

text: fractional

text: polarisation.

text: S

label: equation

text: /S

text: (θ

text: θ

text: )/(b

text: b

text: t

text: p

text: min

text: maj

text: min

text: maj

text: Source

label: table

text: Name

text: P

text: SNRP

text: Ptot

text: Pol.

text: (µJy)

text: (µJy)

text: where

text: θmin

text: and

text: θmaj

text: are

text: the

text: ﬁtted

text: source

text: FWHM

text: axes

text: and

text: bmin

text: and

text: bmaj

text: are

text: the

text: synthesized

text: beam

text: FWHM

text: axes.

text: The

text: ﬂux

text: density

text: ratio

text: distribution

text: for

text: all

text: the

text: sources

text: is

text: shown

text: in

text: Fig.

text: As

text: expected,

text: at

text: low

text: SNRs

text: we

text: have

text: sources

text: with

text: S

text: /S

text: this

text: is

text: due

text: to

text: the

text: r.m.s.

text: statistical

text: errors

text: t

text: p

text: which

text: aﬀect

text: our

text: source

text: size

text: and,

text: in

text: turn,

text: the

text: ﬂux

text: density

text: estimates.

text: To

text: distinguish

text: between

text: unresolved

text: and

text: extended

text: sources,

text: we

text: derived

text: the

text: lower

text: envelope

text: of

text: the

text: ﬂux

text: ratio

text: dis-

text: tribution

text: in

text: Fig.

text: by

text: ﬁtting

text: a

text: curve

text: above

text: which

text: there

text: are

text: at

text: least

text: percent

text: (to

text: discard

text: possible

text: outliers)

text: of

text: the

text: sources

text: with

text: S

text: /S

text: and

text: then

text: mirrored

text: it

text: above

text: the

text: S

text: S

text: T

text: P

text: T

text: P

text: value.

text: The

text: sources

text: located

text: above

text: the

text: upper

text: envelope

text: are

text: con-

text: of

text: 3σ

text: in

text: the

text: polarised

text: intensity

text: image.

text: We

text: then

text: searched

text: for

text: sidered

text: extended,

text: while

text: those

text: below

text: it

text: are

text: considered

text: unre-

text: polarised

text: emission

text: at

text: the

text: positions

text: of

text: the

text: sources

text: in

text: our

text: sam-

text: solved.

text: We

text: stress

text: that

text: the

text: total

text: ﬂux

text: density

text: of

text: the

text: sources

text: is

text: ple.

text: We

text: detected

text: polarised

text: emission

text: in

text: only

text: eight

text: sources.

text: calculated

text: through

text: a

text: component-ﬁt

text: (source

text: background)

text: These

text: are

text: listed

text: in

text: Table

text: For

text: each

text: source

text: we

text: give

text: the

text: which

text: has

text: proved

text: to

text: be

text: more

text: reliable

text: in

text: measuring

text: the

text: total

text: peak

text: in

text: polarised

text: emission

text: and

text: its

text: SNR,

text: the

text: total

text: polarised

text: ﬂux.

text: ﬂux

text: and

text: the

text: average

text: fractional

text: polarisation

text: (calculated

text: as

text: The

text: upper

text: curve

text: can

text: be

text: the

text: equation:

text: the

text: total

text: polarised

text: ﬂux

text: divided

text: by

text: the

text: total

text: ﬂux

text: density

text: of

text: the

text: source

text: from

text: Table

text: Only

text: two

text: sources

text: in

text: Table

text: show

text: extended

text: polarised

text: emission.

text: In

text: particular

text: a

text: S

text: /S

text: has

text: a

text: wide-angle

text: tail

text: (WAT)

text: morphology

text: with

text: polarisation

text: t

text: p

text: (Sp/σ)β

text: detected

text: in

text: the

text: twin

text: jets

text: and

text: in

text: both

text: lobes

text: as

text: shown

text: in

text: Fig.

text: The

text: second

text: extended,

text: polarised

text: source,

text: where

text: a

text: and

text: β

text: With

text: this

text: criterion,

text: represents

text: the

text: other

text: galaxy

text: in

text: this

text: ﬁeld

text: showing

text: the

text: clas-

text: sources

text: are

text: considered

text: resolved

text: (unresolved).

text: We

text: considered

text: sical

text: FRI

text: structure

text: (core+jets).

text: as

text: reliable

text: only

text: the

text: deconvolved

text: angular

text: sizes

text: of

text: the

text: resolved

text: We

text: estimated

text: the

text: bandwidth

text: eﬀects

text: on

text: the

text: polarised

text: sources,

text: while

text: those

text: of

text: unresolved

text: sources

text: are

text: set

text: to

text: zero

text: in

text: emission

text: of

text: the

text: sources,

text: assuming

text: a

text: rotation

text: measure

text: (RM)

text: the

text: catalogue

text: (see

text: Table

text: in

text: the

text: range

text: radm

text: These

text: are

text: plausible

text: values

text: for

text: Radio

text: sources

text: detected

text: at

text: GHz

text: without

text: a

text: the

text: integrated

text: RM

text: of

text: GOODS-N

text: sources:

text: typical

text: intrinsic

text: GHz

text: counterpart

text: RM

text: values

text: for

text: extragalactic

text: radio

text: sources

text: are

text: in

text: the

text: range

text: from

text: a

text: few

text: radm

text: in

text: the

text: poorest

text: environments,

text: through

text: The

text: deepest

text: observations

text: at

text: GHz

text: of

text: the

text: GOODS-N

text: intermediate

text: values

text: of

text: radm

text: up

text: to

text: thousands

text: of

text: ﬁeld,

text: published

text: by

text: Morrison

text: et

text: al.

text: have

text: a

text: circular

text: radm

text: in

text: the

text: centres

text: of

text: cool

text: core

text: clusters

text: (Guidetti

text: et

text: al.

text: beam

text: size

text: of

text: arcsec

text: and

text: r.m.s

text: noise

text: level

text: of

text: The

text: high

text: Galactic

text: latitude

text: of

text: the

text: GOODS-N

text: µJy

text: beam

text: The

text: GHz

text: catalogue

text: lists

text: more

text: than

text: ﬁeld

text: ensures

text: a

text: small

text: contribution

text: from

text: the

text: Galactic

text: fore-

text: radio

text: sources

text: above

text: a

text: 5σ

text: threshold

text: of

text: µJy

text: beam

text: at

text: ground.

text: For

text: the

text: worst

text: case

text: (i.e.

text: at

text: the

text: lowest

text: frequency

text: of

text: the

text: ﬁeld

text: centre,

text: within

text: a

text: region

text: of

text: A

text: sig-

text: our

text: observations,

text: GHz),

text: the

text: average

text: rotation

text: across

text: the

text: niﬁcant

text: fraction

text: of

text: the

text: sources

text: detected

text: at

text: GHz

text: bandwidth

text: is

text: degrees,

text: resulting

text: in

text: a

text: depolarisation

text: of

text: percent)

text: have

text: no

text: counterpart

text: in

text: the

text: GHz

text: catalogue.

text: which

text: is

text: negligible

text: compared

text: to

text: the

text: errors

text: due

text: to

text: noise.

text: About

text: half

text: of

text: the

text: sources

text: without

text: a

text: GHz

text: coun-

text: Rudnick

text: Owen

text: published

text: the

text: results

text: of

text: a

text: po-

text: terpart

text: have

text: SNR>

text: or

text: have

text: a

text: NIR

text: identiﬁcation

text: (see

text: larisation

text: survey

text: of

text: the

text: GOODS-N

text: ﬁeld

text: at

text: GHz.

text: The

text: and

text: these

text: are

text: the

text: most

text: reliable

text: sources.

text: These

text: sources

text: have

text: observations

text: had

text: a

text: detection

text: threshold

text: of

text: µJy

text: in

text: po-

text: upper

text: limits

text: in

text: the

text: spectral

text: index

text: ranging

text: from

text: α

text: to

text: larised

text: emission

text: and

text: cover

text: a

text: much

text: larger

text: area

text: than

text: that

text: cov-

text: α

text: (adopting

text: the

text: spectral

text: index

text: deﬁnition

text: S

text: ν

text: α),

text: ered

text: by

text: our

text: GHz

text: data.

text: They

text: detected

text: radio

text: sources;

text: and

text: will

text: be

text: discussed

text: in

text: more

text: details

text: in

text: Paper

text: II

text: (Guidetti

text: two

text: are

text: in

text: the

text: ﬁeld

text: of

text: view

text: covered

text: by

text: our

text: observations:

text: et

text: al.

text: in

text: preparation).

text: The

text: number

text: of

text: the

text: remaining

text: sources

text: and

text: (wrongly

text: named

text: is

text: consistent

text: with

text: the

text: number

text: of

text: the

text: expected

text: spuri-

text: as

text: in

text: Table

text: in

text: Rudnick

text: Owen

text: ous

text: sources

text: derived

text: in

text: and

text: both

text: show

text: polarised

text: emission

text: at

text: GHz.

text: These

text: POLARISATION

text: PROPERTIES

text: are

text: the

text: two

text: extended

text: sources

text: discussed

text: above,

text: and

text: the

text: The

text: mosaics

text: of

text: the

text: Stokes

text: parameters

text: Q

text: and

text: U

text: were

text: sources

text: with

text: the

text: strongest

text: polarised

text: emission

text: at

text: GHz.

text: imaged

text: and

text: assembled

text: using

text: the

text: same

text: method

text: applied

text: to

text: Taking

text: into

text: account

text: that

text: the

text: synthesized

text: beam

text: of

text: the

text: derive

text: the

text: total

text: intensity

text: mosaic.

text: Noise

text: images

text: were

text: also

text: de-

text: GHz

text: observations

text: is

text: (compared

text: to

text: rived.

text: The

text: Stokes

text: Q

text: and

text: U

text: mosaics

text: were

text: combined

text: to

text: derive

text: of

text: our

text: GHz

text: observations),

text: the

text: amount

text: the

text: polarised

text: intensity

text: mosaic

text: using

text: the

text: task

text: comb

text: in

text: aips.

text: of

text: polarised

text: ﬂux

text: detected

text: at

text: the

text: two

text: frequencies

text: is

text: consis-

text: The

text: noise

text: images

text: were

text: used

text: to

text: clip

text: signals

text: below

text: a

text: threshold

text: tent.

text: Of

text: the

text: remaining

text: sources

text: we

text: detect

text: at

text: GHz,

text: only

text: MNRAS

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: 8 D. Guidetti et al. 24 µm MIPS counterparts. One source is identiﬁed in both the IRAC and MIPS catalogues, for two radio sources an as- sociation is found in the IRAC catalogue and, ﬁnally, for one source a counterpart is found in the 24 µm MIPS catalogue only. In summary, we found four possible MIR counterparts among the eleven source without NIR identiﬁcations. One of the remaining sources is actually a famous galaxy, being associated to HDF 850.1, the brightest submillimiter source in the ﬁeld (Walter et al. 2012, and references within). These radio sources, without a deep NIR identiﬁcation but with a MIR or sub-mm counterpart, are potentially very interesting objects and we will investigate their properties in a later publication, but since they do not possess detec- tions in other bands we cannot include them in the analysis § described in , which is limited to the NIR-identiﬁed sample. 5.2 Spectroscopic & photometric redshifts Many papers presents spectroscopic and/or photomet- ric redshifts obtained in the GOODS-N ﬁeld (e.g. Cowie et al. 2001; Wirth et al. 2004; Barger et al. 2008; Kajisawa et al. 2011; Skelton et al. 2014; Momcheva et al. 2016). In order to obtain a homogeneous and updated set of Figure 6. Ks magnitude distribution for the radio source coun- terparts (solid line) and for the NIR-selected sample (Wang et redshifts we adopt, when available, the redshifts from the al. 2010) limited to sources within the same area covered by the 3D-HST Treasury survey catalogues (Skelton et al. 2014; radio mosaic (dashed line). Momcheva et al. 2016). GOODS-N is one of the ﬁve CAN- DELS ﬁelds for which WFC3 G141 spectroscopic data are available. Spectroscopic redshifts are either measured with space-based dispersion grisms (Momcheva et al. 2016) or ob- 0.5 arcsec. The level of random coincidences with these fur- ther NIR catalogues is still <∼ 3 percent. tained from ground-based slit spectroscopy from the litera- ture (Skelton et al. 2014). Photometric redshifts are deter- In summary, we have a secure identiﬁcations for 83 ra- mined with the EAZY code (Brammer et al. 2008) and listed dio sources (88 percent of the whole radio catalogue). In in Skelton et al. (2014). The normalized median absolute de- the following discussion we will refer to these 83 sources as viation (MAD) scatter between the photometric and spec- the NIR-identiﬁed sample. If we restrict the radio sample to × × ≥ troscopic redshifts is σ = 1.48 MAD < 0.027 (1+z) sources with SNR 5.5, then we have 79 radio sources, 76 NMAD (Skelton et al. 2014). For ﬁve sources, not included in the of which have a secure NIR counterpart (96 percent of the ∼ 3D-HST photometric catalogue of GOODS-N we searched radio sample). The high fraction ( 90 percent) of reliable the literature for an appropriate redshift. identiﬁcations is a natural consequence of the depth of the Spectroscopic redshifts are available for 51 NIR coun- NIR catalogues used to cross identify the radio sources, and terparts and photometric redshifts for 28 sources yielding is consistent with that found in other studies (e.g. Simpson to 95 percent (79/83) the fraction of NIR identiﬁed sources et al. 2006; Smolˇci´c et al. 2017a). with a redshift. There are 4/83 NIR identiﬁed radio sources The distribution of the K magnitude for the NIR- s with no redshift measurement. These are all located at the identiﬁed sample is shown in Fig. 6, together with that of the edges of the GOODS-N radio ﬁeld in a region not covered Wang et al. (2010) K selected sample, restricted to sources s by the IRAC observations. in the area of our radio observations (dotted histogram). The Hereafter we use spectroscopic redshifts where avail- K magnitude histogram of radio sources displays a much s able, and photometric redshifts otherwise. The redshift dis- ﬂatter distribution than the overall NIR sample, this should tribution is shown in Fig. 7. It appears to follow a bi- be due to our radio/NIR selection function and demonstrat- modal distribution which shows a correspondence to the ing that we are probing a diﬀerent source population than (less prominent) peaks noted in the K magnitude distribu- purely NIR-selected samples. (cid:39) s tion. There is a peak around z 0.5 with a tail extending 5.1 Sources without near-IR counterparts (cid:39) to z 1 populated by the brighter sources (17 < K < 21) (cid:39) s Eleven sources are still unidentiﬁed at a limiting K and a secondary peak around z 2. One radio source is s magnitude of 24.5-25.0. All of them are low SNR radio identiﬁed with a local galaxy at z < 0.1. sources (SNR < 5.8) and eight of them have SNR < 5.5. The z-ﬁtting procedure used in Momcheva et al. (2016), Moreover, none of the 11 unidentiﬁed sources has a coun- based on combining grism and multi-band photometric terpart at 1.4 GHz in Morrison et al. (2010). We searched datasets, provides photometric redshifts for some low red- for possible Infrared Array Camera (IRAC) and Multi-band shift (z <∼ 0.7), and often red and/or faint galaxies, although Imaging Photometer for Spitzer (MIPS) counterparts of the they might have a spectroscopic redshift in the literature. NIR unidentiﬁed radio sources in the S-CANDELS cata- For these objects, the photometric ﬁt alone provides a more logue (Ashby et al. 2015) and GOODS-N Legacy Survey accurate redshift, and the contribution of the grism spec- 24 µm catalogue (Magnelli et al. 2011). We used a matching trum to the combined ﬁt is negligible. This explains the pho- radius of 2 and 4 arcsec for searching, respectively, IRAC and tometric redshifts assigned to some low redshift (z <∼ 0.7) MNRAS 000, 000–000 (0000)

text: D.

text: Guidetti

text: et

text: al.

text: µm

text: MIPS

text: counterparts.

text: One

text: source

text: is

text: identiﬁed

text: in

text: both

text: the

text: IRAC

text: and

text: MIPS

text: catalogues,

text: for

text: two

text: radio

text: sources

text: an

text: as-

text: sociation

text: is

text: found

text: in

text: the

text: IRAC

text: catalogue

text: and,

text: ﬁnally,

text: for

text: one

text: source

text: a

text: counterpart

text: is

text: found

text: in

text: the

text: µm

text: MIPS

text: catalogue

text: only.

text: In

text: summary,

text: we

text: found

text: four

text: possible

text: MIR

text: counterparts

text: among

text: the

text: eleven

text: source

text: without

text: NIR

text: identiﬁcations.

text: One

text: of

text: the

text: remaining

text: sources

text: is

text: actually

text: a

text: famous

text: galaxy,

text: being

text: associated

text: to

text: HDF

text: the

text: brightest

text: submillimiter

text: source

text: in

text: the

text: ﬁeld

text: (Walter

text: et

text: al.

text: and

text: references

text: within).

text: These

text: radio

text: sources,

text: without

text: a

text: deep

text: NIR

text: identiﬁcation

text: but

text: with

text: a

text: MIR

text: or

text: sub-mm

text: counterpart,

text: are

text: potentially

text: very

text: interesting

text: objects

text: and

text: we

text: will

text: investigate

text: their

text: properties

text: in

text: a

text: later

text: publication,

text: but

text: since

text: they

text: do

text: not

text: possess

text: detec-

text: tions

text: in

text: other

text: bands

text: we

text: cannot

text: include

text: them

text: in

text: the

text: analysis

text: described

text: in

text: which

text: is

text: limited

text: to

text: the

text: NIR-identiﬁed

text: sample.

text: Spectroscopic

text: photometric

text: redshifts

text: Many

text: papers

text: presents

text: spectroscopic

text: and/or

text: photomet-

text: ric

text: redshifts

text: obtained

text: in

text: the

text: GOODS-N

text: ﬁeld

text: (e.g.

text: Cowie

text: et

text: al.

text: Wirth

text: et

text: al.

text: Barger

text: et

text: al.

text: Kajisawa

text: et

text: al.

text: Skelton

text: et

text: al.

text: Momcheva

text: et

text: al.

text: In

text: order

text: to

text: obtain

text: a

text: homogeneous

text: and

text: updated

text: set

text: of

text: Figure

text: Ks

text: magnitude

text: distribution

text: for

text: the

text: radio

text: source

text: coun-

text: terparts

text: (solid

text: line)

text: and

text: for

text: the

text: NIR-selected

text: sample

text: (Wang

text: et

text: redshifts

text: we

text: adopt,

text: when

text: available,

text: the

text: redshifts

text: from

text: the

text: al.

text: limited

text: to

text: sources

text: within

text: the

text: same

text: area

text: covered

text: by

text: the

text: Treasury

text: survey

text: catalogues

text: (Skelton

text: et

text: al.

text: radio

text: mosaic

text: (dashed

text: line).

text: Momcheva

text: et

text: al.

text: GOODS-N

text: is

text: one

text: of

text: the

text: ﬁve

text: CAN-

text: DELS

text: ﬁelds

text: for

text: which

text: spectroscopic

text: data

text: are

text: available.

text: Spectroscopic

text: redshifts

text: are

text: either

text: measured

text: with

text: space-based

text: dispersion

text: grisms

text: (Momcheva

text: et

text: al.

text: or

text: ob-

text: arcsec.

text: The

text: level

text: of

text: random

text: coincidences

text: with

text: these

text: fur-

text: ther

text: NIR

text: catalogues

text: is

text: still

text: percent.

text: tained

text: from

text: ground-based

text: slit

text: spectroscopy

text: from

text: the

text: litera-

text: ture

text: (Skelton

text: et

text: al.

text: Photometric

text: redshifts

text: are

text: deter-

text: In

text: summary,

text: we

text: have

text: a

text: secure

text: identiﬁcations

text: for

text: ra-

text: mined

text: with

text: the

text: EAZY

text: code

text: (Brammer

text: et

text: al.

text: and

text: listed

text: dio

text: sources

text: percent

text: of

text: the

text: whole

text: radio

text: catalogue).

text: In

text: in

text: Skelton

text: et

text: al.

text: The

text: normalized

text: median

text: absolute

text: de-

text: the

text: following

text: discussion

text: we

text: will

text: refer

text: to

text: these

text: sources

text: as

text: viation

text: (MAD)

text: scatter

text: between

text: the

text: photometric

text: and

text: spec-

text: the

text: NIR-identiﬁed

text: sample.

text: If

text: we

text: restrict

text: the

text: radio

text: sample

text: to

text: troscopic

text: redshifts

text: is

text: σ

text: MAD

text: sources

text: with

text: SNR

text: then

text: we

text: have

text: radio

text: sources,

text: NMAD

text: (Skelton

text: et

text: al.

text: For

text: ﬁve

text: sources,

text: not

text: included

text: in

text: the

text: of

text: which

text: have

text: a

text: secure

text: NIR

text: counterpart

text: percent

text: of

text: the

text: photometric

text: catalogue

text: of

text: GOODS-N

text: we

text: searched

text: radio

text: sample).

text: The

text: high

text: fraction

text: percent)

text: of

text: reliable

text: the

text: literature

text: for

text: an

text: appropriate

text: redshift.

text: identiﬁcations

text: is

text: a

text: natural

text: consequence

text: of

text: the

text: depth

text: of

text: the

text: Spectroscopic

text: redshifts

text: are

text: available

text: for

text: NIR

text: coun-

text: NIR

text: catalogues

text: used

text: to

text: cross

text: identify

text: the

text: radio

text: sources,

text: and

text: terparts

text: and

text: photometric

text: redshifts

text: for

text: sources

text: yielding

text: is

text: consistent

text: with

text: that

text: found

text: in

text: other

text: studies

text: (e.g.

text: Simpson

text: to

text: percent

text: the

text: fraction

text: of

text: NIR

text: identiﬁed

text: sources

text: et

text: al.

text: Smolˇci´c

text: et

text: al.

text: with

text: a

text: redshift.

text: There

text: are

text: NIR

text: identiﬁed

text: radio

text: sources

text: The

text: distribution

text: of

text: the

text: K

text: magnitude

text: for

text: the

text: NIR-

text: s

text: with

text: no

text: redshift

text: measurement.

text: These

text: are

text: all

text: located

text: at

text: the

text: identiﬁed

text: sample

text: is

text: shown

text: in

text: Fig.

text: together

text: with

text: that

text: of

text: the

text: edges

text: of

text: the

text: GOODS-N

text: radio

text: ﬁeld

text: in

text: a

text: region

text: not

text: covered

text: Wang

text: et

text: al.

text: K

text: selected

text: sample,

text: restricted

text: to

text: sources

text: s

text: by

text: the

text: IRAC

text: observations.

text: in

text: the

text: area

text: of

text: our

text: radio

text: observations

text: (dotted

text: histogram).

text: The

text: Hereafter

text: we

text: use

text: spectroscopic

text: redshifts

text: where

text: avail-

text: K

text: magnitude

text: histogram

text: of

text: radio

text: sources

text: displays

text: a

text: much

text: s

text: able,

text: and

text: photometric

text: redshifts

text: otherwise.

text: The

text: redshift

text: dis-

text: ﬂatter

text: distribution

text: than

text: the

text: overall

text: NIR

text: sample,

text: this

text: should

text: tribution

text: is

text: shown

text: in

text: Fig.

text: It

text: appears

text: to

text: follow

text: a

text: bi-

text: be

text: due

text: to

text: our

text: radio/NIR

text: selection

text: function

text: and

text: demonstrat-

text: modal

text: distribution

text: which

text: shows

text: a

text: correspondence

text: to

text: the

text: ing

text: that

text: we

text: are

text: probing

text: a

text: diﬀerent

text: source

text: population

text: than

text: (less

text: prominent)

text: peaks

text: noted

text: in

text: the

text: K

text: magnitude

text: distribu-

text: purely

text: NIR-selected

text: samples.

text: s

text: tion.

text: There

text: is

text: a

text: peak

text: around

text: z

text: with

text: a

text: tail

text: extending

text: Sources

text: without

text: near-IR

text: counterparts

text: to

text: z

text: populated

text: by

text: the

text: brighter

text: sources

text: K

text: s

text: Eleven

text: sources

text: are

text: still

text: unidentiﬁed

text: at

text: a

text: limiting

text: K

text: and

text: a

text: secondary

text: peak

text: around

text: z

text: One

text: radio

text: source

text: is

text: s

text: magnitude

text: of

text: All

text: of

text: them

text: are

text: low

text: SNR

text: radio

text: identiﬁed

text: with

text: a

text: local

text: galaxy

text: at

text: z

text: sources

text: (SNR

text: and

text: eight

text: of

text: them

text: have

text: SNR

text: The

text: z-ﬁtting

text: procedure

text: used

text: in

text: Momcheva

text: et

text: al.

text: Moreover,

text: of

text: the

text: unidentiﬁed

text: sources

text: has

text: a

text: coun-

text: based

text: on

text: combining

text: grism

text: and

text: multi-band

text: photometric

text: terpart

text: at

text: GHz

text: in

text: Morrison

text: et

text: al.

text: We

text: searched

text: datasets,

text: provides

text: photometric

text: redshifts

text: for

text: some

text: low

text: red-

text: for

text: possible

text: Infrared

text: Array

text: Camera

text: (IRAC)

text: and

text: Multi-band

text: shift

text: (z

text: and

text: often

text: red

text: and/or

text: faint

text: galaxies,

text: although

text: Imaging

text: Photometer

text: for

text: Spitzer

text: (MIPS)

text: counterparts

text: of

text: the

text: they

text: might

text: have

text: a

text: spectroscopic

text: redshift

text: in

text: the

text: literature.

text: NIR

text: unidentiﬁed

text: radio

text: sources

text: in

text: the

text: S-CANDELS

text: cata-

text: For

text: these

text: objects,

text: the

text: photometric

text: ﬁt

text: alone

text: provides

text: a

text: more

text: logue

text: (Ashby

text: et

text: al.

text: and

text: GOODS-N

text: Legacy

text: Survey

text: accurate

text: redshift,

text: and

text: the

text: contribution

text: of

text: the

text: grism

text: spec-

text: µm

text: catalogue

text: (Magnelli

text: et

text: al.

text: We

text: used

text: a

text: matching

text: trum

text: to

text: the

text: combined

text: ﬁt

text: is

text: negligible.

text: This

text: explains

text: the

text: pho-

text: radius

text: of

text: and

text: arcsec

text: for

text: searching,

text: respectively,

text: IRAC

text: and

text: tometric

text: redshifts

text: assigned

text: to

text: some

text: low

text: redshift

text: (z

text: MNRAS


text: 2 propose next steps forward. Table I The paper is structured around these contributions. Section EXPLANATION OF TERMS USED IN THIS PAPER introduces key concepts such as abstraction, representation Term Explanation and instantiation, which are prerequisite to virtualization and The act of ignoring details to consider general important for the rest of the paper. Section introduces the Abstraction characteristics theory on which the paper is grounded. In Section we Existing as a thought, idea, or concept, but without Abstract examine the constituent components of networks, and how physical existence these components can be virtualized. We give an overview The act of symbolising or portraying something in a Representation particular way of network and wireless network virtualization in Section , Instantiation Creating a concrete realization of a concept or idea to introduce the survey. Since the main focus of this paper is on wireless link virtualization, in Section we perform a survey of existing literature on wireless link virtualization. logical domain), and the relationship between these domains. This survey allows us to identify open research directions in The physical domain, P, is deﬁned as consisting of all physical Section , before concluding in Section . ∈ objects, p P. The abstract domain, M, consists of all abstract ∈ objects, m M. For instance, a computer is an object in the II. PREREQUISITES TO VIRTUALIZATION physical domain, which can be in different physical states, There are a number of concepts, which are key to developing while a computation is a set of objects and relations in the a formal theory of virtualization and in the opening section of abstract domain. Bold font is used to indicate an object in the paper we carefully deﬁne these concepts. The ﬁrst two of the physical domain; italic font for an object in the abstract these are the concepts of abstraction and representation. Table domain. I shows an explanation of these and other terms used in this A physical object can be represented in the abstract domain, paper. through a representational relationship, R. For example, a In this paper, the term ‘abstraction’ means the act of physical on-off switch can be represented in the abstract ignoring or hiding details to consider general characteristics, domain by a binary digit, shown in Figure 1. The general rather than concrete realities. Thus abstraction manages the representation relation between a physical object, p, and an way in which systems interact, and the complexity of the → abstract object, mp, is through a directed map R : p mp. interaction, by hiding details that are not relevant to the inter- The abstract object, mp is said to be an abstract representation action. Increased abstraction allows systems to be used more of the physical object p. It it very important to keep in mind easily for speciﬁc applications, but this comes at the cost of that the representation relation is not a mathematical function decreased ﬂexibility and customization. Although abstraction or a logical relation, but rather a modelling relation that bridges is an important concept in computing, as it governs the inter- the divide between the physical and the abstract spaces. action between humans and computers, it is not necessarily of importance to virtualization. However, it is important to note In the abstract domain, there can be an evolution or process, the difference between abstraction and the adjective ‘abstract’. → (cid:48) The term ‘abstract’ refers to ideas and concepts that do not C : mp mp, that c(cid:48)hanges an abstract object mp to have physical existence. another abstract object mp. Simila→rly (cid:48)in the physical domain, a corresponding evolution H : p p , changes the physical The term ‘representation’ means to describe or symbolize (cid:48) (cid:48) state p to physical state p . This physical state, p can then something in a particular way. The term ‘instantiation’ means the implementation or realization of a concept or idea. Repres- be represented as mp(cid:48), th(cid:12)rough the (cid:12)representation relation, R. These concepts are show(cid:12)n in Figure(cid:12) 2 (a). entation and instantiation are very important to computing as (cid:48) they describe the relationship between abstract entities and the The two abstract objects, m−p(cid:48) (cid:48)an≤d mp, lead us to a key physical world. As this paper will show later, representation concep||t in AR theory. If mp(cid:48) mp (cid:15), for some error (cid:15) and norm , then we can say that the abstract evolution, C, and and instantiation are of great importance to virtualization, since the corresponding physical evolution, H, commute. Under the virtualization can only be done in the abstract domain, while → above condition, the two representation relationships, R: p network resources exist in the physical domain. (cid:48) → We now turn to the recently developed Abstrac- mp and R: p m→p(cid:48), (cid:48)and the pair→of (cid:48)abstract and physical tion/Representation (AR) theory, to provide us with a formal evolutions C : mp mp and H : p p , can be said to form a commuting diagram. When a set of abstract and physical framework of abstraction and representation [12], [13]. Be- objects form a commuting diagram using the representation, cause this theory is very new, we explain the most important aspects here, borrowed from [12], before we go on to extend R, then mp is a faithful abstract representation of physical the ideas for the purposes of this paper. system p for the evolutions C(mp) and H(p). This means we can be conﬁdent that the evolution C in the abstract domain A. Abstraction/Representation Theory 1 corresponds to the evolution H in the physical domain. Abstraction/Representation theory 2 is concerned with the The implication of commuting diagrams is that the ab- physical domain and the abstract domain (also known as the stract representation of the ﬁnal state of a physical object (cid:48) 1Based on [12] (i.e. mp/mp(cid:48)) can be found either by following the physical evolution and then representing the output abstractly, or by 2AR Theory might be better named as Representation Theory, since it deals mostly with representation, but that name has already been taken. theoretically evolving the representation of the physical state. ##LTLine## ##LTLine## ##LTLine##

text: propose

label: list

text: next

text: steps

text: forward.

text: Table

text: I

text: The

text: paper

text: is

text: structured

text: around

text: these

text: contributions.

text: Section

text: EXPLANATION

text: OF

text: TERMS

text: USED

text: IN

text: THIS

text: PAPER

text: introduces

text: key

text: concepts

text: such

text: as

text: abstraction,

text: representation

text: Term

text: Explanation

text: and

text: instantiation,

text: which

text: are

text: prerequisite

text: to

text: virtualization

text: and

text: The

text: act

text: of

text: ignoring

text: details

text: to

text: consider

text: general

text: important

text: for

text: the

text: rest

text: of

text: the

text: paper.

text: Section

text: introduces

text: the

text: Abstraction

text: characteristics

text: theory

text: on

text: which

text: the

text: paper

text: is

text: grounded.

text: In

text: Section

text: we

text: Existing

text: as

text: a

text: thought,

text: idea,

text: or

text: concept,

text: but

text: without

text: Abstract

text: examine

text: the

text: constituent

text: components

text: of

text: networks,

text: and

text: how

text: physical

text: existence

text: these

text: components

text: can

text: be

text: virtualized.

text: We

text: give

text: an

text: overview

text: The

text: act

text: of

text: symbolising

text: or

text: portraying

text: something

text: in

text: a

text: Representation

text: particular

text: way

text: of

text: network

text: and

text: wireless

text: network

text: virtualization

text: in

text: Section

text: Instantiation

text: Creating

text: a

text: concrete

text: realization

text: of

text: a

text: concept

text: or

text: idea

text: to

text: introduce

text: the

text: survey.

text: Since

text: the

text: main

text: focus

text: of

text: this

text: paper

text: is

text: on

text: wireless

text: link

text: virtualization,

text: in

text: Section

text: we

text: perform

text: a

text: survey

text: of

text: existing

text: literature

text: on

text: wireless

text: link

text: virtualization.

text: logical

text: domain),

text: and

text: the

text: relationship

text: between

text: these

text: domains.

text: This

text: survey

text: allows

text: us

text: to

text: identify

text: open

text: research

text: directions

text: in

text: The

text: physical

text: domain,

text: P,

text: is

text: deﬁned

text: as

text: consisting

text: of

text: all

text: physical

text: Section

text: before

text: concluding

text: in

text: Section

text: objects,

text: p

text: P.

text: The

text: abstract

text: domain,

text: M,

text: consists

text: of

text: all

text: abstract

text: objects,

text: m

text: M.

text: For

text: instance,

text: a

text: computer

text: is

text: an

text: object

text: in

text: the

text: II.

text: PREREQUISITES

text: TO

text: VIRTUALIZATION

text: physical

text: domain,

text: which

text: can

text: be

text: in

text: different

text: physical

text: states,

text: There

text: are

text: a

text: number

text: of

text: concepts,

text: which

text: are

text: key

text: to

text: developing

text: while

text: a

text: computation

text: is

text: a

text: set

text: of

text: objects

text: and

text: relations

text: in

text: the

text: a

text: formal

text: theory

text: of

text: virtualization

text: and

text: in

text: the

text: opening

text: section

text: of

text: abstract

text: domain.

text: Bold

text: font

text: is

text: used

text: to

text: indicate

text: an

text: object

text: in

text: the

text: paper

text: we

text: carefully

text: deﬁne

text: these

text: concepts.

text: The

text: ﬁrst

text: two

text: of

text: the

text: physical

text: domain;

text: italic

text: font

text: for

text: an

text: object

text: in

text: the

text: abstract

text: these

text: are

text: the

text: concepts

text: of

text: abstraction

text: and

text: representation.

text: Table

text: domain.

text: I

text: shows

text: an

text: explanation

text: of

text: these

text: and

text: other

text: terms

text: used

text: in

text: this

text: A

text: physical

text: object

text: can

text: be

text: represented

text: in

text: the

text: abstract

text: domain,

text: paper.

text: through

text: a

text: representational

text: relationship,

text: R.

text: For

text: example,

text: a

text: In

text: this

text: paper,

text: the

text: term

text: ‘abstraction’

text: means

text: the

text: act

text: of

text: physical

text: on-off

text: switch

text: can

text: be

text: represented

text: in

text: the

text: abstract

text: ignoring

text: or

text: hiding

text: details

text: to

text: consider

text: general

text: characteristics,

text: domain

text: by

text: a

text: binary

text: digit,

text: shown

text: in

text: Figure

text: The

text: general

text: rather

text: than

text: concrete

text: realities.

text: Thus

text: abstraction

text: manages

text: the

text: representation

text: relation

text: between

text: a

text: physical

text: object,

text: p,

text: and

text: an

text: way

text: in

text: which

text: systems

text: interact,

text: and

text: the

text: complexity

text: of

text: the

text: abstract

text: object,

text: mp,

text: is

text: through

text: a

text: directed

text: map

text: R

text: p

text: mp.

text: interaction,

text: by

text: hiding

text: details

text: that

text: are

text: not

text: relevant

text: to

text: the

text: inter-

text: The

text: abstract

text: object,

text: mp

text: is

text: said

text: to

text: be

text: an

text: abstract

text: representation

text: action.

text: Increased

text: abstraction

text: allows

text: systems

text: to

text: be

text: used

text: more

text: of

text: the

text: physical

text: object

text: p.

text: It

text: it

text: very

text: important

text: to

text: keep

text: in

text: mind

text: easily

text: for

text: speciﬁc

text: applications,

text: but

text: this

text: comes

text: at

text: the

text: cost

text: of

text: that

text: the

text: representation

text: relation

text: is

text: not

text: a

text: mathematical

text: function

text: decreased

text: ﬂexibility

text: and

text: customization.

text: Although

text: abstraction

text: or

text: a

text: logical

text: relation,

text: but

text: rather

text: a

text: modelling

text: relation

text: that

text: bridges

text: is

text: an

text: important

text: concept

text: in

text: computing,

text: as

text: it

text: governs

text: the

text: inter-

text: the

text: divide

text: between

text: the

text: physical

text: and

text: the

text: abstract

text: spaces.

text: action

text: between

text: humans

text: and

text: computers,

text: it

text: is

text: not

text: necessarily

text: of

text: importance

text: to

text: virtualization.

text: However,

text: it

text: is

text: important

text: to

text: note

text: In

text: the

text: abstract

text: domain,

text: there

text: can

text: be

text: an

text: evolution

text: or

text: process,

text: the

text: difference

text: between

text: abstraction

text: and

text: the

text: adjective

text: ‘abstract’.

text: The

text: term

text: ‘abstract’

text: refers

text: to

text: ideas

text: and

text: concepts

text: that

text: do

text: not

text: C

text: mp

text: mp,

text: that

text: an

text: abstract

text: object

text: mp

text: to

text: have

text: physical

text: existence.

text: another

text: abstract

text: object

text: mp.

text: Simila→rly

text: the

text: physical

text: domain,

text: a

text: corresponding

text: evolution

text: H

text: p

text: p

text: changes

text: the

text: physical

text: The

text: term

text: ‘representation’

text: means

text: to

text: describe

text: or

text: symbolize

text: state

text: p

text: to

text: physical

text: state

text: p

text: This

text: physical

text: state,

text: p

text: can

text: then

text: something

text: in

text: a

text: particular

text: way.

text: The

text: term

text: ‘instantiation’

text: means

text: the

text: implementation

text: or

text: realization

text: of

text: a

text: concept

text: or

text: idea.

text: Repres-

text: be

text: represented

text: as

text: the

text: relation,

text: R.

text: These

text: concepts

text: are

text: in

text: (a).

text: entation

text: and

text: instantiation

text: are

text: very

text: important

text: to

text: computing

text: as

text: they

text: describe

text: the

text: relationship

text: between

text: abstract

text: entities

text: and

text: the

text: The

text: two

text: abstract

text: objects,

text: mp,

text: lead

text: us

text: to

text: a

text: key

text: physical

text: world.

text: As

text: this

text: paper

text: will

text: show

text: later,

text: representation

text: concep||t

text: in

text: AR

text: theory.

text: If

text: mp

text: for

text: some

text: error

text: and

text: norm

text: then

text: we

text: can

text: say

text: that

text: the

text: abstract

text: evolution,

text: C,

text: and

text: and

text: instantiation

text: are

text: of

text: great

text: importance

text: to

text: virtualization,

text: since

text: the

text: corresponding

text: physical

text: evolution,

text: H,

text: commute.

text: Under

text: the

text: virtualization

text: can

text: only

text: be

text: done

text: in

text: the

text: abstract

text: domain,

text: while

text: above

text: condition,

text: the

text: two

text: representation

text: relationships,

text: R:

text: p

text: network

text: resources

text: exist

text: in

text: the

text: physical

text: domain.

text: We

text: now

text: turn

text: to

text: the

text: recently

text: developed

text: Abstrac-

text: mp

text: and

text: R:

text: p

text: the

text: pair→of

text: and

text: physical

text: tion/Representation

text: (AR)

text: theory,

text: to

text: provide

text: us

text: with

text: a

text: formal

text: evolutions

text: C

text: mp

text: mp

text: and

text: H

text: p

text: p

text: can

text: be

text: said

text: to

text: form

text: a

text: commuting

text: diagram.

text: When

text: a

text: set

text: of

text: abstract

text: and

text: physical

text: framework

text: of

text: abstraction

text: and

text: representation

text: Be-

text: objects

text: form

text: a

text: commuting

text: diagram

text: using

text: the

text: representation,

text: cause

text: this

text: theory

text: is

text: very

text: new,

text: we

text: explain

text: the

text: most

text: important

text: aspects

text: here,

text: borrowed

text: from

text: before

text: we

text: go

text: on

text: to

text: extend

text: R,

text: then

text: mp

text: is

text: a

text: faithful

text: abstract

text: representation

text: of

text: physical

text: the

text: ideas

text: for

text: the

text: purposes

text: of

text: this

text: paper.

text: system

text: p

text: for

text: the

text: evolutions

text: C(mp)

text: and

text: H(p).

text: This

text: means

text: we

text: can

text: be

text: conﬁdent

text: that

text: the

text: evolution

text: C

text: in

text: the

text: abstract

text: domain

text: A.

text: Abstraction/Representation

text: Theory

text: corresponds

text: to

text: the

text: evolution

text: H

text: in

text: the

text: physical

text: domain.

text: Abstraction/Representation

text: theory

text: is

text: concerned

text: with

text: the

text: The

text: implication

text: of

text: commuting

text: diagrams

text: is

text: that

text: the

text: ab-

text: physical

text: domain

text: and

text: the

text: abstract

text: domain

text: (also

text: known

text: as

text: the

text: stract

text: representation

text: of

text: the

text: ﬁnal

text: state

text: of

text: a

text: physical

text: object

text: on

text: (i.e.

text: can

text: be

text: found

text: either

text: by

text: following

text: the

text: physical

text: evolution

text: and

text: then

text: representing

text: the

text: output

text: abstractly,

text: or

text: by

text: Theory

text: might

text: be

text: better

text: named

text: as

text: Representation

text: Theory,

text: since

text: it

text: deals

text: mostly

text: with

text: representation,

text: but

text: that

text: name

text: has

text: already

text: been

text: taken.

text: theoretically

text: evolving

text: the

text: representation

text: of

text: the

text: physical

text: state.

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: MNRAS 000, 1–15 (2017) Preprint 30 May 2020 Compiled using MNRAS LATEX style ﬁle v3.0 The redshift evolution of major merger triggering of luminous AGN: ∼ a slight enhancement at z 2 Timothy Hewlett,1 Carolin Villforth,1 2 Vivienne Wild,1 Jairo Mendez-Abreu,1 3 4 (cid:63) , , , Milena Pawlik1 and Kate Rowlands1 5 , 1Department of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, KY16 9SS, Scotland 2University of Bath, Department of Physics, Claverton Down, Bath BA2 7AY, United Kingdom 3Instituto de Astrofca de Canarias, Calle Vea s/n, E-38205 La Laguna, Tenerife, Spain 4Departamento de Astrofca, Universidad de La Laguna, E-38200 La Laguna, Tenerife, Spain 5Department of Physics & Astronomy, Johns Hopkins University, Bloomberg Center, 3400 N. Charles St., Baltimore, MD 21218, USA Accepted 2017 April 24. Received 2017 April 21; in original form 2016 October 06 ABSTRACT Active galactic nuclei (AGN), particularly the most luminous AGN, are commonly as- sumed to be triggered through major mergers, however observational evidence for this scenario is mixed. To investigate any inﬂuence of galaxy mergers on AGN triggering and luminosities through cosmic time, we present a sample of 106 luminous X-ray selected type 1 AGN from the COSMOS survey. These AGN occupy a large redshift range (0.5 < z < 2.2) and two orders of magnitude in X-ray luminosity (∼1043 - 1045 erg s-1). AGN hosts are carefully mass and redshift matched to 486 control galaxies. A novel technique for identifying and quantifying merger features in galaxies is developed, subtracting galfit galaxy models and quantifying the residuals. Comparison to visual classiﬁcation conﬁrms this measure reliably picks out disturbance features in galaxies. No enhancement of merger features with increasing AGN luminosity is found with this metric, or by visual inspection. We analyse the redshift evolution of AGN associated with galaxy mergers and ﬁnd no merger enhancement in lower redshift bins. Contrarily, in the highest redshift bin (z∼2) AGN are ∼4 times more likely to be in galaxies exhibiting evidence of morphological disturbance compared to control galaxies, at 99% conﬁdence level (∼2.4 ) from visual inspection. Since only ∼15% of these AGN are σ found to be in morphologically disturbed galaxies, it is implied that major mergers at high redshift make a noticeable but subdominant contribution to AGN fuelling. At low redshifts other processes dominate and mergers become a less signiﬁcant triggering mechanism. Key words: AGN – galaxies – mergers 1 INTRODUCTION momentum of the gas, allowing for the highest accretion rates onto the central black hole whilst transforming the galaxy morphology Supermassive black holes (SMBHs) are believed to exist in (Toomre & Toomre 1972; Barnes 1988, 1991; Di Matteo et al. 2005; the centres of all massive galaxies (Kormendy & Richstone 1995). (cid:199) Cox et al. 2008). Gas rich mergers may trigger nuclear and global A small proportion of these are growing, with gas accretion rates starbursts (Mihos & Hernquist 1994, 1996; Hopkins et al. 2006) and ranging from ∼10-4 - 10 M year-1 and a proportionately wide major mergers disrupt the morphologies of the colliding galaxies, range of bolometric luminosities (∼1042 - 1047 erg s-1). These are often exhibiting long tidal tails or shells of expelled gas and stars Active Galactic Nuclei (AGN) and may accrete large fractions of soon after the merger has begun. Detecting this can be challeng- their mass in bursts of rapid accretion (Croton et al. 2006), requir- ing however, since the single new galaxy has a relaxation timescale ing rapid inﬂow of gas from galaxy length-scales. Stripping the gas after which morphological features of mergers fade (Tinsley 1978; of enough angular momentum to allow for such rapid accretion, Kennicutt et al. 1987; Ellison et al. 2013). Observational evidence thereby powering the most luminous AGN, proves extremely chal- suggesting a link between major mergers and SMBH accretion has lenging. Theoretical work suggests major mergers can provide the been mixed (e.g. Gabor et al. 2009; Cisternas et al. 2011; Schawin- torque to displace such an overwhelming fraction of the angular ski et al. 2011; Kocevski et al. 2012; Treister et al. 2012; Villforth et al. 2013; Ellison et al. 2013; Villforth et al. 2014; Kocevski et al. 2015; Villforth et al. 2017). Alternatively, AGN may be triggered E-mail: th51@st-andrews.ac.uk (TH) (cid:63) © 2017 The Authors

text: MNRAS

font: ITVAOD+TeXGyreTermes-Regular

font: CZQLYC+TeXGyreTermes-Bold

text: Preprint

text: May

text: Compiled

text: using

text: MNRAS

text: LATEX

text: style

text: ﬁle

text: The

label: title

text: redshift

text: evolution

text: of

text: major

text: merger

text: triggering

text: of

text: luminous

text: AGN:

font: IFMCGE+txsys

text: a

text: slight

text: enhancement

text: at

text: z

text: Timothy

label: author

text: Carolin

text: Vivienne

text: Jairo

font: WAJXUN+rtxmi

text: Milena

text: and

text: Kate

text: of

text: Physics

text: and

text: Astronomy,

text: University

text: of

text: St

text: Andrews,

text: North

text: Haugh,

text: St

text: Andrews,

text: Scotland

text: of

text: Bath,

text: Department

text: of

text: Physics,

text: Claverton

text: Down,

text: Bath

text: United

text: Kingdom

text: de

text: Astrofca

text: de

text: Canarias,

text: Calle

text: Vea

text: s/n,

text: La

text: Laguna,

text: Tenerife,

text: Spain

text: de

text: Astrofca,

text: Universidad

text: de

text: La

text: Laguna,

text: La

text: Laguna,

text: Tenerife,

text: Spain

text: of

text: Physics

text: Astronomy,

text: Johns

text: Hopkins

text: University,

text: Bloomberg

text: Center,

text: N.

text: Charles

text: St.,

text: Baltimore,

text: MD

text: USA

text: Accepted

text: April

text: Received

text: April

text: in

text: original

text: form

text: October

text: ABSTRACT

text: Active

text: galactic

text: nuclei

text: (AGN),

text: particularly

text: the

text: most

text: luminous

text: AGN,

text: are

text: commonly

text: as-

text: sumed

text: to

text: be

text: triggered

text: through

text: major

text: mergers,

text: however

text: observational

text: evidence

text: for

text: this

text: scenario

text: is

text: mixed.

text: To

text: investigate

text: any

text: inﬂuence

text: of

text: galaxy

text: mergers

text: on

text: AGN

text: triggering

text: and

text: luminosities

text: through

text: cosmic

text: time,

text: we

text: present

text: a

text: sample

text: of

text: luminous

text: X-ray

text: selected

text: type

text: AGN

text: from

text: the

text: COSMOS

text: survey.

text: These

text: AGN

text: occupy

text: a

text: large

text: redshift

text: range

text: z

text: and

text: two

text: orders

text: of

text: magnitude

text: in

text: X-ray

text: luminosity

text: erg

text: AGN

text: hosts

text: are

text: carefully

text: mass

text: and

text: redshift

text: matched

text: to

text: control

text: galaxies.

text: A

text: novel

text: technique

text: for

text: identifying

text: and

text: quantifying

text: merger

text: features

text: in

text: galaxies

text: is

text: developed,

text: subtracting

text: galfit

text: galaxy

text: models

text: and

text: quantifying

text: the

text: residuals.

text: Comparison

text: to

text: visual

text: classiﬁcation

text: conﬁrms

text: this

text: measure

text: reliably

text: picks

text: out

text: disturbance

text: features

text: in

text: galaxies.

text: No

text: enhancement

text: of

text: merger

text: features

text: with

text: increasing

text: AGN

text: luminosity

text: is

text: found

text: with

text: this

text: metric,

text: or

text: by

text: visual

text: inspection.

text: We

text: analyse

text: the

text: redshift

text: evolution

text: of

text: AGN

text: associated

text: with

text: galaxy

text: mergers

text: and

text: ﬁnd

text: no

text: merger

text: enhancement

text: in

text: lower

text: redshift

text: bins.

text: Contrarily,

text: in

text: the

text: highest

text: redshift

text: bin

text: AGN

text: are

text: ∼4

text: times

text: more

text: likely

text: to

text: be

text: in

text: galaxies

text: exhibiting

text: evidence

text: of

text: morphological

text: disturbance

text: compared

text: to

text: control

text: galaxies,

text: at

text: conﬁdence

text: level

text: from

text: visual

text: inspection.

text: Since

text: only

text: of

text: these

text: AGN

text: are

text: σ

text: found

text: to

text: be

text: in

text: morphologically

text: disturbed

text: galaxies,

text: it

text: is

text: implied

text: that

text: major

text: mergers

text: at

text: high

text: redshift

text: make

text: a

text: noticeable

text: but

text: subdominant

text: contribution

text: to

text: AGN

text: fuelling.

text: At

text: low

text: redshifts

text: other

text: processes

text: dominate

text: and

text: mergers

text: become

text: a

text: less

text: signiﬁcant

text: triggering

text: mechanism.

text: Key

text: words:

text: AGN

text: galaxies

text: mergers

text: INTRODUCTION

text: momentum

text: of

text: the

text: gas,

text: allowing

text: for

text: the

text: highest

text: accretion

text: rates

text: onto

text: the

text: central

text: black

text: hole

text: whilst

text: transforming

text: the

text: galaxy

text: morphology

text: Supermassive

text: black

text: holes

text: (SMBHs)

text: are

text: believed

text: to

text: exist

text: in

text: (Toomre

text: Toomre

text: Barnes

text: Di

text: Matteo

text: et

text: al.

text: the

text: centres

text: of

text: all

text: massive

text: galaxies

text: (Kormendy

text: Richstone

text: Cox

text: et

text: al.

text: Gas

text: rich

text: mergers

text: may

text: trigger

text: nuclear

text: and

text: global

text: A

text: small

text: proportion

text: of

text: these

text: are

text: growing,

text: with

text: gas

text: accretion

text: rates

text: starbursts

text: (Mihos

text: Hernquist

text: Hopkins

text: et

text: al.

text: and

text: ranging

text: from

text: M

text: and

text: a

text: proportionately

text: wide

text: major

text: mergers

text: disrupt

text: the

text: morphologies

text: of

text: the

text: colliding

text: galaxies,

text: range

text: of

text: bolometric

text: luminosities

text: erg

text: These

text: are

text: often

text: exhibiting

text: long

text: tidal

text: tails

text: or

text: shells

text: of

text: expelled

text: gas

text: and

text: stars

text: Active

text: Galactic

text: Nuclei

text: (AGN)

text: and

text: may

text: accrete

text: large

text: fractions

text: of

text: soon

text: after

text: the

text: merger

text: has

text: begun.

text: Detecting

text: this

text: can

text: be

text: challeng-

text: their

text: mass

text: in

text: bursts

text: of

text: rapid

text: accretion

text: (Croton

text: et

text: al.

text: requir-

text: ing

text: however,

text: since

text: the

text: single

text: new

text: galaxy

text: has

text: a

text: relaxation

text: timescale

text: ing

text: rapid

text: inﬂow

text: of

text: gas

text: from

text: galaxy

text: length-scales.

text: Stripping

text: the

text: gas

text: after

text: which

text: morphological

text: features

text: of

text: mergers

text: fade

text: (Tinsley

text: of

text: enough

text: angular

text: momentum

text: to

text: allow

text: for

text: such

text: rapid

text: accretion,

text: Kennicutt

text: et

text: al.

text: Ellison

text: et

text: al.

text: Observational

text: evidence

text: thereby

text: powering

text: the

text: most

text: luminous

text: AGN,

text: proves

text: extremely

text: chal-

text: suggesting

text: a

text: link

text: between

text: major

text: mergers

text: and

text: SMBH

text: accretion

text: has

text: lenging.

text: Theoretical

text: work

text: suggests

text: major

text: mergers

text: can

text: provide

text: the

text: been

text: mixed

text: (e.g.

text: Gabor

text: et

text: al.

text: Cisternas

text: et

text: al.

text: Schawin-

text: torque

text: to

text: displace

text: such

text: an

text: overwhelming

text: fraction

text: of

text: the

text: angular

text: ski

text: et

text: al.

text: Kocevski

text: et

text: al.

text: Treister

text: et

text: al.

text: Villforth

text: et

text: al.

text: Ellison

text: et

text: al.

text: Villforth

text: et

text: al.

text: Kocevski

text: et

text: al.

text: Villforth

text: et

text: al.

text: Alternatively,

text: AGN

text: may

text: be

text: triggered

text: E-mail:

text: (TH)

text: The

text: Authors