Heightened Faraday Complexity in the inner 1 kpc of the Galactic Centre
J. D. Livingston, N. M. McClure-Griffiths, B. M. Gaensler, A. Seta, M. J. Alger
MMNRAS , 1–15 (2020) Preprint 3 February 2021 Compiled using MNRAS L A TEX style file v3.0
Heightened Faraday Complexity in the inner 1 kpc of the GalacticCentre
J. D. Livingston, ★ N. M. McClure-Griffiths, B. M. Gaensler, A. Seta and M. J. Alger, , Research School of Astronomy & Astrophysics, The Australian National University, Canberra ACT 2611, Australia Dunlap Institute for Astronomy and Astrophysics, University of Toronto ON M5S 3H4, Canada Data61, CSIRO, Canberra ACT 2601, Australia
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We have measured the Faraday rotation of 62 extra-galactic background sources in 58fields using the CSIRO Australia Telescope Compact Array (ATCA) with a frequency rangeof 1.1 - 3.1 GHz with 2048 channels. Our sources cover a region ∼
12 deg ×
12 deg ( ∼ | 𝑙 | < ◦ exhibitslarge Rotation Measures (RMs) with a maximum |RM| of 1691 . ± . − and a mean | RM | = ±
42 rad m − . The RMs decrease in magnitude with increasing projected distancefrom the Galactic Plane, broadly consistent with previous findings. We find an unusuallyhigh fraction (95%) of the sources show Faraday complexity consistent with multiple Faradaycomponents. We attribute the presences of multiple Faraday rotating screens with widelyseparated Faraday depths to small-scale turbulent RM structure in the Galactic Centre region.The second order structure function of the RM in the Galactic Centre displays a line with agradient of zero for angular separations spanning 0 . ◦ − ◦ ( ∼ − Key words:
ISM: magnetic fields – Galaxy: centre – turbulence
Magnetic fields play a critical role in the dynamics of spiral galaxies,because the energy density of magnetic fields in the InterstellarMedium (ISM) is comparable to the energy densities of the thermalgas and cosmic rays (Heiles & Haverkorn 2012). ISM magneticfields have strengths around a few micro-Gauss and affect starformation (Price & Bate 2008; Birnboim et al. 2015; Krumholz& Federrath 2019) and the spatio-temporal evolution of the ISM(Kobzar et al. 2017).Much is still uncertain about the nature of the magnetic fieldsthat permeate the ISM and in particular those within the centre ofour Galaxy. This is because the measurement and the associatedinterpretation of interstellar magnetic field tracers is difficult (Seta& Beck 2019). The magnetic field of the Galactic Centre has beenstudied in a limited capacity, focusing on filaments and SagittariusA* (Beck & Wielebinski 2013; Roche et al. 2018). ★ E-mail: [email protected]
A few studies have used narrow-bandwidth radio polarisationmeasurements of Faraday rotation to derive the magnetic fieldstrength within 1 kpc (projected distance) of the Galactic Centre,finding large and highly variable amounts of Faraday rotation,but these studies have been limited in their frequency range,accuracy, and resolution (Reich 2003; Roy et al. 2005, 2008; Tayloret al. 2009). Narrow frequency ranges can result in ambiguitiesin the measurements Faraday rotation which can be resolved byobserving over a broad range of frequencies (Farnsworth et al.2011; O’Sullivan et al. 2012; Anderson et al. 2016). The observationof linearly polarised synchrotron radiation using broadband radiointerferometry is one powerful tool for measuring interstellarmagnetic fields. Typically this synchrotron radiation comes frombackground Active Galactic Nuclei (AGN) or foreground objectslike Supernovae remnants. In this paper, we aim to use broadbandpolarimetry from AGN to study turbulence and magnetic fields inthe Galactic Centre.When linearly polarised synchrotron radiation enters amagnetised medium, the polarisation angle, 𝜒 , is rotated based on © a r X i v : . [ a s t r o - ph . GA ] F e b Livingston et al. the wavelength, 𝜆 , of the radiation due to the Faraday effect. Thisrotation is known as Faraday rotation. We define 𝜒 in terms of theStokes parameters Q and U, 𝜒 =
12 tan − (cid:18) UQ (cid:19) . (1)Faraday rotation occurs due to thermal electrons and magnetic fieldsin an ionised plasma and is observed primarily at radio frequencies.The rotation is a function of the initial polarisation angle, 𝜒 , and thewavelength of the observed radiation, 𝜆 obs , 𝜒 ( 𝜆 ) = 𝜒 + RM 𝜆 .Here, RM is the rotation measure of the region.RM describes the magnitude of Faraday rotation of a singleFaraday ‘screen’ along a single line-of-sight, modulated by theline-of-sight thermal electron density, 𝑛 𝑒 (measured in cm − ),RM ≡ 𝐶 ∫ herethere 𝑛 𝑒 B · 𝑑 r [ rad m − ] . (2)Here, B is the magnetic field strength in micro-Gauss, r andd r are the displacement and incremental displacement alongthe line-of-sight measured in pc from the source (there) tothe observer (here), and C is a conversion constant, 𝐶 = .
812 rad m − pc − cm 𝜇 G − .We can interpret a Faraday screen as a region of free electronsand magnetic fields in the ISM. This region is assumed to notbe turbulent or emit polarised synchrotron radiation internally.More complicated Faraday and depolarisation effects can alsooccur along the line-of-sight, such as external and internal Faradaydispersion (Gardner & Whiteoak 1966). These can be caused byturbulent magneto-ionic environments (Sokoloff et al. 1998), andas such the picture becomes more complicated and requires a moresophisticated framework to analyse, which we describe in Section1.1. In reality, regions can have synchrotron-emission or turbulentmagneto-ionic environments; in the case of synchrotron-emissionthis most likely occurs in the AGN source or a foreground object(Anderson et al. 2015). Due to limitations in telescope technology, observations of Faradayrotation only used a few discrete wavelengths and the slope of 𝜒 vs 𝜆 was used to measure the RM of a line-of-sight. When thereare multiple Faraday screens across a single telescope resolvingelement (beam), or external and internal Faraday dispersion, weexpect the linear relationship of 𝑑𝜒 / 𝑑𝜆 to break down (Farnsworthet al. 2011; O’Sullivan et al. 2012). Such sources are known ascomplex Faraday sources. Burn (1966) defined a quantity knownas the Faraday depth, 𝜙 . This quantity indicates the strength andsign of individual Faraday screens within the beam, and is definedsimilarly to that of the RM, 𝜙 ( r ) ≡ 𝐶 ∫ hereX 𝑛 𝑒 B · 𝑑 r [ rad m − ] . (3)Where X is the position in space along the line-of-sight, as 𝜙 isa function of the position along the line-of-sight. The Faradaydepth function, F( 𝜙 ) (Burn 1966; Brentjens & de Bruyn 2005),is the complex polarised flux density per unit Faraday depth. In thecase where there is no external or internal Faraday dispersion frommagnetised regions within the beam, we expect each significantpeak in the F( 𝜙 ) to correspond to the RM of a Faraday screen.RM Synthesis is one of the methods of determining F( 𝜙 ), fromthe complex polarisation vector, P ( 𝜆 ) . This requires polarisationdata over many frequency channels. P is related to Stokes Q and U, the polarisation angle, 𝜒 , the polarisation fraction p , and the totalintensity I as, P = Q + 𝑖 U = 𝑝𝐼𝑒 𝑖𝜒 . (4)This relates to F( 𝜙 ) and a ‘RM spread function’ (RMSF) from thesampling in 𝜆 − space, as,˜F ( 𝜙 ) = F ( 𝜙 ) ∗ RMSF = 𝐾 ∫ ∞−∞ ˜ P ( 𝜆 ) 𝑒 − 𝑖𝜙𝜆 𝑑𝜆 . (5)Here ‘ ∗ ’ represents a convolution. ˜ P ( 𝜆 ) is the observed complexpolarisation vector, ˜ P ( 𝜆 ) = 𝑊 ( 𝜆 )P ( 𝜆 ) . 𝑊 ( 𝜆 ) is called thesampling function which is nonzero at all 𝜆 points that weremeasured. 𝐾 is defined as, 𝐾 = (cid:18)∫ ∞−∞ 𝑊 ( 𝜆 ) 𝑑 ( 𝜆 ) (cid:19) − . (6)The ‘true’ F( 𝜙 ) is convolved with RMSF. This creates the observed˜F ( 𝜙 ) which is highly dependent on the sampling in 𝜆 − space.After deconvolution, the full-width half maximum (FWHM) of theRMSF controls the resolution of the cleaned F( 𝜙 ), 𝛿𝜙 , (Brentjens& de Bruyn 2005; Dickey et al. 2019): 𝛿𝜙 ≈ . Δ 𝜆 . (7)Here Δ 𝜆 = 𝜆 − 𝜆 ; 𝜆 and 𝜆 are the maximumand minimum observed 𝜆 . In this study, we use broadbandpolarisation data, which allow for more complete sampling of theRMSF than previous narrow-band studies, leading to a better F( 𝜙 )resolution, a larger maximum measurable Faraday depth, maximummeasurable- 𝜙 -scale, and sensitivity to faint emission components(Brentjens & de Bruyn 2005; Dickey et al. 2019). Magneto-ionic turbulence is due to the fluid (or hydrodynamic)turbulence within a magnetised plasma. The second order structurefunction (SF) has been used to analytically determine importantscales in fluids (Kolmogorov 1941) and Magneto-Hydrodynamic(MHD) turbulence (Goldreich & Sridhar 1995). A RM structurefunction can be used to find the scales over which the product of themagnetic field ( B ) and electron density ( 𝑛 𝑒 ) varies. The general SFis defined as,SF 𝑓 ( 𝛿𝜃 ) = (cid:104)[ 𝑓 ( 𝜃 ) − 𝑓 ( 𝜃 + 𝛿𝜃 )] (cid:105) 𝜃 . (8)In this notation, 𝜃 is the angular separation, f is the varyingquantity, and (cid:104) ... (cid:105) 𝜃 indicates the average over 𝜃 . The SF RM ( 𝛿𝜃 ) is twice the variance in RM on a scale of 𝛿𝜃 . The 𝛿𝜃 at whichthe structure function changes slope tells us about an importantscale of fluctuations. For example, a break in the slope of the RMstructure function can be related to the outer scale of turbulenceand the slope around this scale indicates how turbulence changeswith angular scales. The outer scale is synonymous with the drivingscale of turbulence.To relate the slope ‘break’ scale of the RM structure functionto the largest scale of magneto-ionic turbulence, we require theassumption that the largest scale of magnetic-ionic variationsis comparable to the outer scale of the fluid turbulence. Thisassumption is motivated by the fact that the correlation scale ofmagnetic fields in numerical simulations of driven turbulence iscomparable to the outer scale of turbulence (Seta et al. 2020). Basedon the fluid and MHD turbulence theories (Kolmogorov 1991; MNRAS , 1–15 (2020) araday Complexity in the Galactic Centre Goldreich & Sridhar 1995), we expect a power law SF where smallerscales contribute less to the turbulent energy within a region thanlarger scales. The physical mechanism causing this is a turbulentcascade, in which energy at larger-scales (maintained due to driving)is transferred to smaller-scales (dissipated due to viscosity).As an example of using the RM structure function to determinethe outer scale of fluid turbulence, Haverkorn et al. (2006a) founda zero gradient with an outer scale on the order of ∼
10 pc for theinner Galactic Plane, indicating that the main source of turbulencehad to be injected on a scale of ∼
10 pc, which they attributed toHii regions.In this paper, we present the calculated peak Faraday depthsof 62 sources close to the Galactic Centre, along with a measureof dispersion between multiple peaks in the F( 𝜙 ) of each source.With these data we construct a RM structure function. The detailsof the observational data are described in Section 2. The data arepresented in Section 3 in Table 1 along with discussion of trendsin the spatial distributions of Faraday depth and comparisons toprevious studies of the Galactic Centre. Section 3 also containsanalysis of the calculated RM structure function. Section 4 containsa discussion of the Faraday complexity of our sources, and thepossible location along the line-of-sight where the Faraday rotationoccurs. Section 5 contains a discussion of the possible causes forthe inferred small scale magneto-ionic turbulence observed withinthe physical distance structure function. Our conclusions are givenin Section 6. The observations for this study were obtained through two separateprojects on the Australia Telescope Compact Array (ATCA). Thefirst set of data were observed for a project to study atomic hydrogenabsorption through a hydrogen cloud in the foreground of theGalactic Centre (Dénes et al. 2018). The observations targeted brightcompact continuum sources over the region | 𝑙 | (cid:47) ◦ , | 𝑏 | (cid:47) ◦ of the Galactic Centre. The target sources were selected from theNVSS catalogue (Condon et al. 1998) and had integrated 1.4 GHzfluxes ≥
200 mJy and were unresolved in NVSS (diameter ≤ ∼
100 minutes betweenMay and June 2015. Observing runs went for 12 hours, the ATCAprimary flux and bandpass calibrator, PKS 1934-638, was observedfor 30 minutes at the start and end of the 12-hr observing session.Fields were observed hourly, which gave sufficient uv coveragefor imaging. Data were obtained for both continuum and atomichydrogen spectral line using the 1M-0.5k correlator configuration onthe Compact Array Broadband Backend (Wilson et al. 2011). Onlythe continuum data covering all four linear polarisation products,XX, YY, XY and YX, were used here. The continuum data coverthe frequency range 1.1 - 3.1 GHz with 2048 channels. Obtained from the Australia Telescope Online Archive
Figure 1.
Example Stokes I image of field 1817-2825 (Named based oncentre of field) reduced using Miriad software package. The image has; aRMS of 0 .
001 Jy/beam, 𝐵 maj = .
6" and 𝐵 min = . Data reduction was carried out with the Miriad softwarepackage (Sault et al. 1995). We used PKS 1934-638 for bandpass,amplitude and leakage calibration assuming that PKS 1934-638is un-polarised (Rayner et al. 2000). The brightest continuumsource observed each day was used for phase calibration(NVSS J172920-234535, J174713-192135, J172836-271236,J175233-223012, J175151-252359, J174713-192135,J175114-323538, J174716-191954). The robust visibilityweighting (Briggs 1995) was set to +1.5 with a mean pixel size of2”, an ideal synthesised beam size of ∼
6” by ∼ × | 𝑙 | (cid:47) ◦ , | 𝑏 | (cid:47) ◦ from the original survey. The telescopeconfiguration and observation strategy were the same as the previousrun of observations. The 6 km baseline available using ATCA wasalso included for these observations. The total observation run wentfor 12 hours, each source was observed for a minimum of 1 minuteper hour, with a total minimum and maximum integration time of11 minutes and 176 minutes, respectively. There was 30 minutes ofcalibration, observing the bandpass calibrator, PKS 1934-638, and30 minutes of overhead time. The phase and polarisation calibratorused was PKS 1827-360, which has a flux density of 3 . ± . uv coverage than the observationstaken in 2015. The field size was of 1000 × 𝜇 Jy/beam. An example Stokes I image of field 1817-2825 isshown in Figure 1.
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Livingston et al.
For each field, multiple sources were identified using the Aegeanv2.1.0 source finding algorithms (Hancock et al. 2012, 2018) oneach total Stokes I intensity Multi Frequency Synthesis (MFS)image. Data extraction was done by collecting the Stokes I, Q,and U values from spectral cubes at a source position as defined bythe generated Aegean catalogue. The RMS of the Stokes I, Q, andU cubes, was found by taking 100 ×
100 pixel boxes correspondingto 2’ ×
2’ away from each source position.If a source had a Signal-to-Noise Ratio (SNR) in Stokes Plower than 3 averaged over all channels, or there were less than50% of the original channels of the source after flagging, the dataremaining was not used in our analysis and the source was discarded.Channels that contained significant Radio Frequency Interference(RFI) were ignored when collecting the Stokes I, Q, and U dataalong with the relevant frequencies. The RFI frequencies flaggedwere broadly consistent for each source and the majority of channelsflagged through data reduction were between 1.5 and 1.7 GHz.Major differences in frequency coverage between sources, due toflagging, were due to the location of sources within the field. Sourcesaway from the centre of the field had higher noise and had a largernumber of flagged frequencies.To test if sources were resolved, we checked the Stokes I profileof each source in R.A. and Decl. against the beam dimensions. Ifthe FWHM of a source in Stokes I was any greater than the beamin either direction with a tolerance of 1” - 2” , that source wasdesignated as resolved. For these sources we re-imaged data cubesusing a common beam resolution set to the largest beam associatedwith the lowest frequency of a cube. Resolved sources are markedwith a † in Table 1.The Faraday dispersion function, F( 𝜙 ), and RMSF for eachsource were computed using the rm synthesis and rm clean(Heald 2017) algorithms from the Canadian Initiative for RadioAstronomy Data Analysis (CIRADA) tool-set RMtools 1D v1.0.1(Purcell et al. 2020). The pipelines find a second order polynomialmodel for the input Stokes I and subsequently use that to findStokes Q/I and U/I, using inverse variance weighting. The RMSFfor each source was determined using the associated 𝜆 coverage,this resulted in each source having a different RMSF. rm cleanused a cleaning cutoff set to three times the noise in Stokes Q/I andU/I. The obtained peak Faraday depths and errors are given in Table1. The RM-synthesis capabilities for this study are shown in Table2. The majority of our sources (89%) appear spatially unresolved onthe scale of the synthesised beam, which on average was ≈
26 by9”. But of these 55 unresolved sources, the majority (77%) showsome sub-structure at our maximum baseline of 6km. In addition,for many sources, the F( 𝜙 ) had two or more strong peaks above aSNR of 7 separated in Faraday depth space. An example is shownin Figure 2.A possible interpretation of these multi-component F( 𝜙 )spectra is that the sources themselves are extended and probe morethan one line-of-sight (Brentjens & de Bruyn 2005), but are notresolved by our angular resolution. These separate Faraday depths This tolerance was set to the limit of our resolution; the size of a pixel indegrees. are most likely to originate in: 1) the AGN themselves or 2) theintervening medium. The other cause of this complexity within aF( 𝜙 ) spectrum may be artefacts from the deconvolution process.Faraday depths that are offset from the RMSF peak by exactlythe width of the first side-lobe would be indicative of incompletedeconvolution. In Figure 3 we show the distribution of Faradaydepth peaks above the noise threshold normalised with respect tothe first RMSF peak (the first side-lobe). As the majority of peakoffsets do not correspond to the position of the first RMSF side-lobewe assert the peaks are not artefacts.We elected to use the second moment, 𝑀 , to assess complexF( 𝜙 ) (e.g. Anderson et al. 2015). The 𝑀 of a source was derivedby masking all peaks in the cleaned F( 𝜙 ) of a source that wereless than 7 times the noise as found through RM Synthesis (e.g.Anderson et al. 2015). This noise level is a standard cutoff to ensurethat the Faraday depths observed are physically real (Hales et al.2012; Macquart et al. 2012). Faraday depth positions, 𝜙 𝑖 , weredetermined using the python scipy.signal package. The first momentwas calculated as, (cid:104) 𝜙 (cid:105) = 𝐽 − 𝑁 ∑︁ 𝑖 = 𝜙 𝑖 | F ( 𝜙 𝑖 )| [ rad m − ] , (9) 𝑁 covers all available Faraday depths. Here J, the normalisationconstant in units of, is given by, 𝐽 = 𝑁 ∑︁ 𝑖 = | F ( 𝜙 𝑖 )| [ Jy / beam ] . (10)The 𝑀 was calculated as, 𝑀 = (cid:118)(cid:117)(cid:116) 𝐽 − 𝑁 ∑︁ 𝑖 = ( 𝜙 𝑖 − (cid:104) 𝜙 (cid:105)) | F ( 𝜙 𝑖 )| [ rad m − ] . (11)The scaling of the separation in Faraday depth from the mean foreach source by F( 𝜙 ) amplitude ensures high signal-to-noise peaksare weighted more heavily than lower signal-to-noise peaks. Theexample spectrum shown in Figure 2 has a large 𝑀 = . ± . − . The error in 𝑀 is calculated as the uncertainty in eachF( 𝜙 ) spectrum and the standard error in the first moment of F( 𝜙 ).Non-zero 𝑀 can derive from: internal Faraday dispersion, 𝛿 RM ; external Faraday dispersion 𝜎 RM , and/or multiple independentFaraday depths, each probing multiple lines-of-sight within thetelescope beam, (cid:104)| RM − RM |(cid:105) , (Ma et al. 2019a). The lattercan be observed where the observed AGN is extended, but only onangular scales smaller than the beam. The calculated values of 𝑀 and the associated errors are found in Table 1; all associated F( 𝜙 )spectra and Stokes information are shown in the supplementarymaterial provided online. We detected 62 polarised sources from the 58 observed fields.Within Table 1, sources were sorted and named based on the closestcorresponding NVSS source from Condon et al. (1998). The meanmagnitude RM and median magnitude RM for the surveyed regionwere 219 ±
42 and 94 ±
52 rad m − , respectively . The standarddeviation of |RM| was 329 rad m − . NVSS J174423-311636 had thegreatest magnitude peak Faraday depth of + . ± . − , Errors on means and medians were calculated as the standard errors for asample of 62 sources. MNRAS , 1–15 (2020) araday Complexity in the Galactic Centre Figure 2.
Example of NVSS J173659-281003 that has two highly separated peaks, giving it a large 𝑀 . In order from left to right, top to bottom; Panel 1:
Thedirty F( 𝜙 ) is shown in orange, the clean F( 𝜙 ) is shown in blue, the RMSF is shown in green, the peak cutoff line (of seven times the noise) is shown in red,and the black crosses indicate peaks within the spectrum, the black dotted line indicates RMs found through QU Fitting. Panel 2:
Stokes I against frequency.
Panel 3:
Stokes q (blue), u (red), and p (black) against 𝜆 along with model stokes (blue), u (red), and p (green) from QU fitting. Panel 4:
Stokes q against u,coloured based on 𝜆 along with model stokes q against u (black) from QU fitting. Panel 5:
Polarisation angle, 𝜒 , against 𝜆 along with model 𝜒 (green) fromQU fitting.MNRAS000
Polarisation angle, 𝜒 , against 𝜆 along with model 𝜒 (green) fromQU fitting.MNRAS000 , 1–15 (2020) Livingston et al.
Figure 3.
Distribution of Faraday depth peaks above the noise thresholdnormalised by the difference in rad m − between the main peak of the RMSFand the peak of its first sidelobe. Peak offsets that are equal to one could beconfused with artefacts from the RMSF. Figure 4.
Plot of the absolute value of RM against 𝑀 . Binned data is inorange and non-binned data is in blue. NVSS J175218-210508 had the smallest magnitude peak Faradaydepth of − . ± . − . For this region, 46% of the observedsources had positive RMs.For any source with a 𝑀 that is consistent with zero withinone standard deviation of its uncertainties, we have assigned 𝑀 = − . Including sources for which 𝑀 =
0, the meanand median 𝑀 were 147 ±
20 rad m − and 103 ±
25 rad m − ,respectively. Anderson et al. (2015) within their sample found amean and median 𝑀 of 5 . ± . − and 0 . ± .
05 rad m − ,respectively. Note that Anderson et al. (2015) used a high frequencycutoff of ∼ 𝑀 with a resolutionof ∼ 𝑀 for all sources found byO’Sullivan et al. (2017) and found that 55% of their sources hadnon-zero 𝑀 . We found a mean and median 𝑀 of 5 . ± . − and 0 . ± − , respectively and a standard deviation of16 . − . Over the 62 sources, 95% had a non-zero 𝑀 ,indicating a high fraction of complex sources in our data comparedto previous studies (Anderson et al. 2015; O’Sullivan et al. 2017).Our mean 𝑀 is 25 times larger than that of the published mean 𝑀 of both Anderson et al. (2015); O’Sullivan et al. (2017).The largest values of 𝑀 did not necessarily correspond tothe largest peak Faraday depths; the largest 𝑀 was for NVSSJ173107-245703 at 856 . ± . − and the smallest non-zero Figure 5.
Comparison between our peak Faraday depths and the RMs ofRoy et al. (2005) and Taylor et al. (2009). 𝑀 was for NVSS J181726-282508-B at 5 . ± . − . We seeno strong correlation between 𝑀 and RM, as shown in Figure 4. We compared our RMs to published values to check for consistency.Roy et al. (2005) and Taylor et al. (2009) both calculated the rotationmeasures of sources close to the Galactic Centre. We have 17sources also in Taylor et al. (2009) which were observed using twofrequencies, 1364.9 MHz and 1435.1 MHz, each with a width of 42MHz, and had a beam radius of 45 arcsec. We have 5 sources alsoobserved by Roy et al. (2005) observed with 16 discrete frequencybands of 128-MHz from 4.80 to 8.68 GHz and a resolution of ≈ × ≈
26 and9”, respectively. Both Roy et al. (2005) and Taylor et al. (2009)treated all sources as simple rotators with a single RM component;extended sources were split into different sub-sources each with aseparate RM measurement. The RMs of the common sources aregiven in Table 1 and a comparison plot is shown in Figure 5.The two sources that showed the largest disagreements withthe Taylor et al. (2009) catalogue were NVSS J180316-274810-Aand NVSS J182057-252813. Our RM for NVSS J180316-274810-Aof − . − is within the n 𝜋 -ambiguity of 652 rad m − discussed by Ma et al. (2019a,b) for the Taylor et al. (2009) RMcatalogue, which could lead to the difference between our RMmeasurement and that of 438.3 rad m − from Taylor et al. (2009).For the source NVSS J182057-252813, it is likely that there is aconfusion between two close objects given that the resolution ofTaylor et al. (2009) is larger than the size of our study, which wouldaccount for the discrepancies between our observed RM of -26.9rad m − and Taylor et al. (2009) observed RM of -273.2 rad m − .Within our analysis of these sources, we expect our observedpeak Faraday depths to be closer to the true peak Faraday depth foreach source than those of Roy et al. (2005) and Taylor et al. (2009)due to our larger frequency coverage of each source. Faraday depthmeasurements do not assume a single thin Faraday screen model foreach source as is assumed in RM measurements and therefore canextract more information about each source. In Figure 6 we show our measured peak Faraday depths plotted overthe S-Band Polarization All Sky Survey (S-PASS) 2.3 GHz (Carrettiet al. 2019). S-PASS 2.3 GHz primarily captures synchrotron
MNRAS , 1–15 (2020) araday Complexity in the Galactic Centre NVSS (1) R.A. (2) Decl. (3) l (4) b (5) Major (6) Minor (7) Beam Major (8) Beam Minor (9) PI (10) 𝜙 (11) (12) RMtay (13) (14)
RMroy (15) (16) 𝑀 (17) (18)Name (J2000) (J2000) (deg) (deg) (arcsec) (arcsec) (arcsec) (arcsec) ( Jy / beam ) ( radm − ) ( ± ) ( radm − ) ( ± ) ( radm − ) ( ± ) ( radm − ) ( ± )NVSS J172829-284610-A † † † † † † † Table 1.
Results for sources found; with the closest NVSS name, location in ra, dec, Galactic longitude and latitude, Aegean modelled major ( 𝑎 ) and minor( 𝑏 ) axes, and average beam major ( 𝑎 b ) and minor ( 𝑏 b ) axes, (columns 1 - 9). The table includes the mean polarised intensity percentage (column 10), Peak 𝜙 ,the RM measurement, of a source (columns 11 - 12), the RM measurement from Taylor et al. (2009) and Roy et al. (2005) catalogues (columns 13 - 16), and 𝑀 (columns 17 - 18) in rad m − . Sources with asterisks are the mean of the same source observed on different dates. Sources with † are resolved or partiallyresolved sources. Range (1) Width (2) Sensitivity (3) Resolution (4) 𝛿𝜙 (5) max-scale (6) 𝜙 max (7)(GHz) (MHz) (mJy/beam) (arcsec) ( rad m − ) ( rad m − ) ( rad m − )1.4 - 3.0 4.4 7 ×
103 317 13796
Table 2.
Table of observational and RM-synthesis capabilities based onfrequency range and channel size. Column 1 and 2 are the mean frequencyrange and channel width of our observations, column 3 is the mean MFSnoise over all fields, column 4 is the mean resolution over all fields inmajor and minor axes. Column 5 is the mean FWHM of RMSF over allsources, column 6 is the mean maximum measurable scale over all sources,and column 7 is the maximum measurable Faraday depth over all sources(Brentjens & de Bruyn 2005; Dickey et al. 2019). radiation and thermal emission. There is a general trend of lowermagnitude peak Faraday depths farther from the Galactic Centre. Wesee larger magnitude peak Faraday depths around the Galactic Planeand large positive values in peak Faraday depths around two regions of high continuum intensity at Galactic latitudes and longitudes ofl = ◦ , b = ◦ and l = ◦ , b = ◦ .In Figure 7 we show our 𝑀 measurements plotted overS-PASS (Carretti et al. 2019) with the area of markers scaled on thesquared value of 𝑀 . There is a weak trend of larger 𝑀 towards theGalactic Plane. We test for Stokes I leakage from Galactic Centrecontinuum emission into the polarised emission of each source. Wecompared the Stokes I at 2 GHz to the 𝑀 for each source shownin Figure 8 and found no correlation between the two. In our ATCAfields the Stokes I emission is almost exclusively from backgroundAGN. The large-scale emission, like that shown in Figures 6 and7, is resolved out by the extended baselines of the interferometer,leaving only the compact sources. This means it is unlikely thatinternal Faraday dispersion plays a large role within our sources.Thus, the connection must be between larger 𝑀 and proximity tothe Galactic Plane. MNRAS000
Table of observational and RM-synthesis capabilities based onfrequency range and channel size. Column 1 and 2 are the mean frequencyrange and channel width of our observations, column 3 is the mean MFSnoise over all fields, column 4 is the mean resolution over all fields inmajor and minor axes. Column 5 is the mean FWHM of RMSF over allsources, column 6 is the mean maximum measurable scale over all sources,and column 7 is the maximum measurable Faraday depth over all sources(Brentjens & de Bruyn 2005; Dickey et al. 2019). radiation and thermal emission. There is a general trend of lowermagnitude peak Faraday depths farther from the Galactic Centre. Wesee larger magnitude peak Faraday depths around the Galactic Planeand large positive values in peak Faraday depths around two regions of high continuum intensity at Galactic latitudes and longitudes ofl = ◦ , b = ◦ and l = ◦ , b = ◦ .In Figure 7 we show our 𝑀 measurements plotted overS-PASS (Carretti et al. 2019) with the area of markers scaled on thesquared value of 𝑀 . There is a weak trend of larger 𝑀 towards theGalactic Plane. We test for Stokes I leakage from Galactic Centrecontinuum emission into the polarised emission of each source. Wecompared the Stokes I at 2 GHz to the 𝑀 for each source shownin Figure 8 and found no correlation between the two. In our ATCAfields the Stokes I emission is almost exclusively from backgroundAGN. The large-scale emission, like that shown in Figures 6 and7, is resolved out by the extended baselines of the interferometer,leaving only the compact sources. This means it is unlikely thatinternal Faraday dispersion plays a large role within our sources.Thus, the connection must be between larger 𝑀 and proximity tothe Galactic Plane. MNRAS000 , 1–15 (2020)
Livingston et al.
Figure 6.
Plot of S-PASS 2.3 GHz (grayscale) with peak Faraday depthmagnitude markers of all sources over-plotted. The area of each markercorresponds to the magnitude of the measured peak Faraday depth. Negativepeak Faraday depths are blue downward triangles, positive peak Faradaydepths are red upward triangles.
Figure 7.
Plot of S-PASS 2.3 GHz (grayscale) with peak 𝑀 magnitudemarkers of all sources over-plotted. The area of each marker correspondsto the square magnitude of 𝑀 . Pink crosses indicate sources for which 𝑀 = − . The RM structure function, SF RM was calculated by finding thesquare differences in peak Faraday depth of a source and allother sources within some angular separation (Eq. 8). This wasrepeated for each source. The resultant differences were binnedin 11 bins between 0 . ° to 11 ° . Each bin had at least 20 pairs(Stil et al. 2011) and the mean number of pairs per bin was 172. Figure 8.
Plot of Stokes I at 2 GHz against 𝑀 , binned data is in orange andnon-binned data is in blue. The dashed grey line shows the median Stokes I,indicating a lack of correlation between 𝑀 and Stokes I at 2 GHz. We used the python module https://pypi.org/project/bootstrapped/with a confidence level of 66% and 10000 iterations to determinethe spread for each bin to account for the treatment of errors inlog/log plots. This formed the RM structure function for the angularseparation between sources.The structure function is the sum of various sources of variation(Stil et al. 2011),SF RM = 𝜎 + 𝜎 + 𝜎 + 𝜎 , (12)here 𝜎 is the variation of RM generated in the vicinity of the AGN; 𝜎 is the contribution from the intergalactic medium; 𝜎 is thecontribution of the Galactic Centre and ISM, which is ultimately ofthe most interest for this study; and 𝜎 is the noise contributionof the uncertainty in measuring the RM of our sources.To account for 𝜎 , we subtract twice the intrinsicextra-galactic RM scatter of 36 rad − m − found by Schnitzeler(2010). To separate the Galactic Centre and ISM contribution on 𝜎 , we subtract twice the intrinsic Milky Way ISM scatter ofRM found by Schnitzeler (2010) of 64 rad − m − . To subtract thiscontribution we use a stochastic approach choosing a Milky Waycontribution with fluctuations between 0 to 7 𝜎 MW . Anderson et al.(2015) study was centred on a region away from the GalacticPlane with 563 polarised sources. Their sources had a meanand median magnitude RM of 13 ± − and 12 ± − , respectively, with a standard deviation of 33 rad m − . Wesubtract twice the square of standard deviation in RM calculated byAnderson et al. (2015) of 33 rad m − , to account for the intrinsicscatter of background AGN, 𝜎 , as they studied a region of thesky away from the Galactic Plane. We follow the same approach asHaverkorn et al. (2004) when determining and accounting for 𝜎 .This approach separates the RM structure function from a ‘noise’structure function which is calculated as a Gaussian with width of √︁ noise . The resultant structure function is shown in Figure 9.The slope fit of Figure 9 was a zero gradient over the entirescale range. The equation describing the zero gradient model waslog ( SF RM ) = . ± . . (13)This slope was calculated using a log likelihood minimisation RA = 03h29m40s, DEC = -36d16m30s with a grid spanning 7 . ° in RAand 5 . ° in DEC. MNRAS , 1–15 (2020) araday Complexity in the Galactic Centre Figure 9.
Plot of RM structure function as a function of angular separation, 𝜃 . The dashed blue line represents the model calculated using our datawith a log likelihood minimisation method. The size of the horizontal errorbars represent the size in 𝜃 of each bin. The dashed red, grey, brown, andpink lines are the SF models of previous studies of the Galaxy (Haverkornet al. 2008; Mao et al. 2010; Anderson et al. 2015). The vertical errors werecalculated as described in the main text. method which included the error bounds to determine the fit. Azero gradient indicates that the outer scale of turbulence has notbeen reached for angular scales between 0 . ° - 11 ° and must besmaller than 0 . ° . The outer scale is the angular separation atwhich the structure function ‘breaks’ or changes slope (see Section1.2). Typically, the turbulence contribution from smaller scales thanthe outer scale follows a positive power-law slope, as turbulence onsmaller scales decay faster than that at large scales. When comparingour structure function to the structure functions of Haverkorn et al.(2008), Mao et al. (2010), and Anderson et al. (2015), as in Figure9, we see that for the probed ranges of those studies the structurefunction slopes are all steeper than our observed zero gradient. Wealso note that the structure function amplitude of Mao et al. (2010);Anderson et al. (2015) is significantly smaller than the structurefunction in Figure 9. There are several strong indicators of enhanced fluctuations on smallangular-scales of the Faraday rotating medium in the directionof the Galactic Centre. First, 95% of our sources have non-zero 𝑀 measurements, suggesting measurable spatially imposed RMdifferences on the scale of the telescope beam, which is significantwhen compared to other studies of 𝑀 (e.g. Anderson et al. 2015).Second, the amplitude of the structure function in Figure 9 is higherthan found in other parts of the Galaxy (e.g. Mao et al. 2010;Anderson et al. 2015).To understand the large non-zero 𝑀 measurements, we needto understand what causes them and where along the line-of-sightthey originate. We use QU fitting to test if the large 𝑀 are dueto multiple Faraday screens or large 𝜎 RM . QU fitting can recoverproperties of multiple emission components and the quantities arephysically motivated, unlike traditional RM-synthesis (Sun et al.2015). The process of determining the magneto-ionic environment of apolarised signal by modelling the polarised emission is calledQU Fitting. For modelling we only included sources with a peakFaraday depth amplitude above a signal-to-noise ratio of 50. Wehave chosen this cutoff as we are modelling with a large numberof degrees of freedom and we want to ensure every measurementis well determined. In their study, O’Sullivan et al. (2017) foundthat 89% of their sources were modelled with 1 to 2 screens. Theyalso found that 67% of sources had external Faraday dispersion, andonly 9% of their sources required internal Faraday dispersion in thebest-fit model. As discussed in 3.2 internal Faraday dispersion doesnot plays a large role within our sources. So, we have elected touse models with either one or two screens with individual externalFaraday dispersion components; P 𝑗 = 𝑝 𝑗 exp [ 𝑖𝜓 , 𝑗 + RM 𝑗 𝜆 ] exp [− 𝜎 RM , 𝑗 𝜆 ] (14)Where 𝜓 , 𝑗 is the initial polarisation angle of a screen, j . Two screenswere modelled by the addition of two separate P 𝑗 components. Theparameters for the best fit model for each source is found in Table3. We used RMtools 1D v1.0.1 to model each source and usedreduced 𝜒 to determine the best model. For sources in whichthe reduced 𝜒 for 1 and 2 screens models were within 10% ofeach other, we elected to model the source with a single screento avoid over-modelling. The most common model was the twoscreen model making up 95% of our sources. This is a higherproportion than the number of sources modelled with two screen inO’Sullivan et al. (2017) of 52%. The prevalence of sources with twoscreens is interesting and could related to the underlying structure ofbackground radio sources; sources that have two prominent lobesmight typically probe two Faraday screens which could possiblyexplain why in the set from O’Sullivan et al. (2017) 52% of sourceswere best modelled using two Faraday screens.The mean and median difference between RM components, (cid:104)| RM − RM |(cid:105) , for our set was 218 ±
39 rad m − and 137 ±
49 rad m − . The mean and median external Faraday dispersion, 𝜎 RM for our set was 29 ± − and 28 ± − . The mean andmedian difference between all Faraday screens, (cid:104)| RM 𝑖 − RM 𝑗 |(cid:105) ,(here i and j are all individual screens) for O’Sullivan et al.(2017) was 52 ± − and 19 ± − . The mean andmedian 𝜎 RM for O’Sullivan et al. (2017) was 13 ± − and9 . ± − . Our mean 𝜎 RM and (cid:104)| RM − RM |(cid:105) are 2 and4 times larger than that of the means of O’Sullivan et al. (2017),respectively. We surmise that we are probing a significantly differentenvironment than that of O’Sullivan et al. (2017) as we expectthe background AGN to be of a similar population. From this weinfer that the enhanced 𝑀 is likely primarily caused by enhanced (cid:104)| RM − RM |(cid:105) and modulated slightly by enhanced 𝜎 RM . Thiswould explain why we don’t see a complete agreement between (cid:104)| RM − RM |(cid:105) and 𝑀 . The question still remains where thiscomplex magneto-ionic environment occurs along the line-of-sight.In the following subsection, we demonstrate that the fluctuationscan reasonably be attributed to the magneto-ionic environment ofthe Galactic Centre. The Galactic Centre is known to exhibit large RMs (Roy et al.2008; Taylor et al. 2009; Law et al. 2011). We compared the RMvalues that we measure in the direction of the Galactic Centre with
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NVSS (1) Pol (2) ± (3) Pol (4) ± (5) RM (6) ± (7) RM (8) ± (9) 𝜎 RM , (10) ± (11) 𝜎 RM , (12) ± (13)Name (%) (%) (rad m − ) (rad m − ) (rad m − ) (rad m − )NVSS J172836-271236 3.2 0.05 2.3 0.22 -63 0.4 -412 23.8 29 0.4 96 3.0NVSS J173133-264015-A 1.7 0.05 7.5 0.07 267 1.6 -52 0.2 9 1.1 1 0.5NVSS J173133-264015-B 8.7 0.02 2.6 0.02 -61 0.2 37 0.7 15 0.1 14 0.4NVSS J173205-242651-A 13.0 0.00 7.4 0.00 -10 0.0 -41 0.0 13 0.0 58 0.0NVSS J173205-242651-B 3.3 0.79 4.7 0.02 -74 19.8 -11 0.2 83 6.2 1 0.5NVSS J173659-281003 6.1 0.01 1.8 0.02 -352 0.1 981 0.9 0 0.1 31 0.4NVSS J173722-223000 6.5 0.00 0.6 0.00 43 0.0 184 0.2 8 0.0 30 0.0NVSS J173806-262443 4.2 0.03 1.9 0.05 49 0.3 -235 1.5 29 0.2 42 0.6NVSS J174202-271311 23.6 0.06 14.3 0.46 -129 0.0 -154 2.7 15 0.0 60 0.6NVSS J174224-203729 3.1 0.00 3.7 0.01 -22 0.0 -74 0.3 14 0.0 67 0.0NVSS J174343-182838 8.1 0.06 1.4 0.01 371 2.2 149 0.1 108 0.1 30 0.0NVSS J174716-191954-A* 2.0 0.24 3.7 0.06 128 0.0 -300 0.1 7 0.1 74 0.2NVSS J174716-191954-B* 17.8 0.03 124 0.1 27 0.1NVSS J174748-312315 2.3 0.01 2.4 0.13 40 0.1 -276 10.5 8 0.1 87 1.1NVSS J174831-324102-A 4.6 0.00 1.9 0.01 -547 0.0 -609 0.2 1 0.0 27 0.1NVSS J174831-324102-B 6.7 0.00 6.2 0.00 -356 0.0 -359 0.1 9 0.0 48 0.0NVSS J174832-225211 7.0 0.00 2.5 0.02 -106 0.0 348 0.3 4 0.0 50 0.1NVSS J174931-210847 2.7 0.02 6.0 0.18 142 0.3 41 5.3 11 0.2 70 0.9NVSS J175114-323538-A 2.2 0.02 11.6 0.00 -206 0.6 -84 0.0 42 0.2 13 0.0NVSS J175114-323538-B 13.1 0.01 5.5 0.16 -27 0.0 -83 2.7 11 0.0 68 0.8NVSS J175233-223012 1.9 0.06 4.2 0.01 542 1.7 -21 0.1 85 0.4 36 0.0NVSS J175526-223211 2.0 0.00 0.6 0.01 -124 0.0 -574 1.1 23 0.0 72 0.3NVSS J175548-233322 5.6 0.00 1.7 0.00 1173 0.0 1270 0.1 16 0.0 27 0.1NVSS J175622-312215 2.8 0.00 5.2 0.00 1 0.0 250 0.0 11 0.0 6 0.0NVSS J180319-265214 7.9 0.00 2.2 0.00 -225 0.0 8 0.1 0 0.0 16 0.1NVSS J180316-274810-A 7.9 0.00 1.4 0.00 -393 0.0 36 0.0 15 0.0 8 0.1NVSS J180316-274810-B 6.0 0.00 5.2 0.00 -7 0.0 -352 0.0 59 0.0 24 0.0NVSS J180356-294716 7.9 0.03 11.0 0.01 47 0.1 -112 0.0 55 0.1 20 0.0NVSS J180542-232244 18.4 0.01 -50 0.0 0 0.0NVSS J180715-230844 1.5 0.08 3.8 0.03 30 2.0 167 0.4 21 1.4 1 0.5NVSS J180953-302521-A 9.7 0.01 13.4 0.02 76 0.0 30 0.2 29 0.0 67 0.1NVSS J180953-302521-B 4.6 0.04 5.9 0.02 127 0.4 1 0.2 29 0.2 13 0.1NVSS J181726-282508-A 4.0 0.04 10.6 0.03 -29 0.6 70 0.0 38 0.3 10 0.2NVSS J181726-282508-B 4.6 0.09 13.6 0.07 -6 1.1 57 0.5 5 0.9 2 0.5NVSS J182057-252813 1.0 0.00 23.5 0.19 -10 0.0 318 0.7 2 0.1 129 0.2NVSS J182040-291005 2.9 0.01 4.6 0.00 36 0.0 -146 0.0 1 0.1 21 0.0NVSS J182319-272627 12.5 0.01 28.9 0.08 81 0.1 -7 1.2 28 0.0 98 0.0 Table 3.
Results for QU fitting; with the closest NVSS name (column 1). The predicted polarisation fraction for screen 1 and 2 (columns 2 - 5). The RM forscreen 1 and 2 (columns 4 - 9). The external Faraday dispersion, 𝜎 RM , i for screen 1 and 2 (columns 10 - 13). Sources with asterisks are the mean of the samesource observed on different dates. other measured values in the Galaxy. To get an indication of typicalRM values, we compare our RM values to those of the Tayloret al. (2009) and Anderson et al. (2015) catalogues. The Andersonet al. (2015) study had a mean and median magnitude RM of 13 ± − and 12 ± − , respectively, with a standarddeviation of 33 rad m − . The Taylor et al. (2009) study was of thewhole northern sky . We take a subsection of the catalogue on theGalactic Plane but away from the Galactic Centre for | 𝑏 | <
40 degand 50 < 𝑙 <
70 deg which contains 5504 polarised sources. Wefound a mean and median |RM| of 33 and 23 rad m − with a standarddeviation of 36 rad m − . The mean and median |RM| of our data aremuch greater at 219 ±
42 and 94 ±
52 rad m − , respectively. Fromthis we can conclude that the process that has caused the RMs forour sources is unusual compared to other regions of the Galaxy. It In the catalogue there is a gap at b ∼ −
30 and l ∼ −
50 of size 50 ° due to skycoverage. The density of sampling was also reduced towards the GalacticPlane (Stil & Taylor 2007). is therefore reasonable to assume that the magnitude of the RMs weobserve originates near or in the Galactic Centre environment.The AGN populations of Anderson et al. (2015) and O’Sullivanet al. (2017) are unlikely to be different to that of our sample. We canuse these studies to understand the contribution of 𝑀 from the AGNthemselves to separate the effects from the intervening medium ofthe Galactic Centre. By comparison to Anderson et al. (2015) andO’Sullivan et al. (2017) with a mean 𝑀 of 5 . − and mediansof 0 .
03 rad m − and 0 . − , respectively, our measured meanand median 𝑀 were much larger at 147 ±
20 rad m − and 103 ±
25 rad m − . For our sources we found 95% of sources had a non-zero 𝑀 measurement, which is much higher than found by Andersonet al. (2015) and O’Sullivan et al. (2017). This is not an issue ofdiffering signal-to-noise cutoffs as both our 𝑀 measurement andour calculations of O’Sullivan et al. (2017) used a cutoff of 7 timesthe noise of F( 𝜙 ), they also had a similar frequency range and assuch a similar max-scale in F( 𝜙 ). Anderson et al. (2015) used aminimum single-to-noise ratio cutoff of 6 times the noise of F( 𝜙 ).When comparing the results of QU fitting against those ofO’Sullivan et al. (2017), we found that for our set the mean 𝜎 RM was MNRAS , 1–15 (2020) araday Complexity in the Galactic Centre double and the mean difference between the RMs of Faraday screens( (cid:104)| RM − RM |(cid:105) ) was 4 times larger than that of O’Sullivan et al.(2017). The scale of the RM variations within a resolution elementfor our measurements, as characterised by (cid:104)| RM − RM |(cid:105) , is largewhen compared to that expected from the RM variations for otherregions in the Galaxy (away from the Galactic Centre on the Planeand away from the Galactic Plane) indicating that the variation likelyoriginates in the Galactic Centre.Another way of comparing the magnitude of our observed RMvariations with other areas is with a structure function. We created astructure function of the Galactic Plane from the catalogue of Tayloret al. (2009) and a structure function for the set from O’Sullivanet al. (2017) to determine if our results shown in Figure 9 areunusual, compared with other RM catalogues. This was calculatedusing the same method as described in Section 3.3. We used asubsection of the Taylor et al. (2009) catalogue as shown in thetop-left of Figure 10 to compute a Galactic Plane RM structurefunction (Stil et al. 2011). The region selected was a 20 ° × ° boxcentred on 𝑙 = ° , 𝑏 = ° . The distribution of angular separationsfor our structure function, the Galactic Plane structure function andthe structure function calculated from O’Sullivan et al. (2017) areshown in the top-right of Figure 10; the structure functions arepresented in the bottom of Figure 10.The approximate slope of the Galactic Plane region SF is,log ( SF Plane ) ∼ / ∗ log ( 𝛿𝜃 ) + . . (15)The approximate slope of the O’Sullivan et al. (2017) SF is,log ( SF Plane ) ∼ . ∗ log ( 𝛿𝜃 ) + . . (16)The value of the Plane region structure function is 1 order ofmagnitude lower than the height of the structure function shownin Figure 9. The height slope of the O’Sullivan et al. (2017) SF is 3orders of magnitude lower than the height of our structure function.This significant difference suggests that the amplitude of the flatstructure function found in Figure 9 would not be expected if oursurveyed region was away from the Galactic Centre.Based on the magnitude of RM fluctuations in the direction ofthe Galactic Centre and the knowledge that only the Galactic Centreregion itself is capable of producing such large RMs, we concludethat the Galactic Centre region is likely responsible for the large (cid:104)| RM − RM |(cid:105) we observe. If the bulk of the Faraday rotationoccurs at the Galactic Centre then these multiple lines-of-sightwithin a beam are probing the magneto-ionic environment at thedistance of the Galactic Centre. To include small angular scales in the structure function, we use ourmodelled values of (cid:104)| RM − RM | (cid:105) (see Section 4.1 and Table 3).We note that the RM structure function is defined as the mean squaredifference of RM across varying angular size scales (shown in Eq.8). Measuring (cid:104)| RM − RM | (cid:105) provides an equivalent extensionto scales below the synthesised beam-width. For these scales, weaccount for the intrinsic RM scatter of multiple screens along theline-of-sight by subtracting the mean squared, (cid:104)| RM 𝑖 − RM 𝑗 | (cid:105) ,from O’Sullivan et al. (2017) of 2700 ±
700 rad m − (see Section4.1). As for the RM structure function (see Section 3.3) we subtractthe intrinsic scatter of RM for the Milky Way ISM and extra-galacticcontribution found by Schnitzeler (2010) of 64 rad − m − and36 rad − m − , respectively.For unresolved sources, the angular separation we use theaverage width of our beams of 17”, which serves as an upper limit. For resolved sources, we use the angular diameter of the source. Theangular separation for the mean (cid:104)| RM − RM | (cid:105) bin was taken asthe mean of these sizes, or ∼ ∼ (cid:104)| RM − RM | (cid:105) bin. Thestructure function that includes both the peak Faraday depth and (cid:104)| RM − RM | (cid:105) points is shown in Figure 11.We can see from Figure 11, the (cid:104)| RM − RM | (cid:105) point is lowerthan that of the rest of the structure function. Typically, from themechanism of a turbulent cascade, we expect smaller angular scalesto contribute less to the turbulent energy of a structure functionthan larger scales. This drop in the turbulent energy contributionat smaller angular scales suggests a possible break in the structurefunction.For sub-sonic (almost incompressible) turbulence we expectturbulent cascade to follow a power-law slope of 2/3 (Kolmogorov1991) below the outer scale. For super sonic (compressible)turbulence we expect a steeper slope of 11/10 (Federrath 2013).We have plotted both slopes, such that they intersect the height ofthe SF RM and the mean (cid:104)| RM − RM | (cid:105) bin in Figure 11. The gasspeed for the ISM over kpc scales is typically trans sonic (Gaensleret al. 2011). As such, we take the mean between the assumptions ofsub and super sonic cascade (slopes of 2/3 and 11/10). As we areonly fitting a single point this provides us with an upper limit forthe mean outer angular scale. This upper limit is 66 + − ".The mean outer scale of the slopes of Haverkorn et al. (2008)was 0 . ◦ and for Anderson et al. (2015) the outer scale was 1 . ◦ .These angular outer scales are significantly larger than our estimateof 66 + − ". Haverkorn et al. (2008) covers an area close to the innerGalactic Plane and the structure function of Anderson et al. (2015)covers a high latitude area of the Galaxy and had a significantlysmaller amplitude, further indicating we are probing a differentmagneto-ionic environment.By assuming the magneto-ionic environment is atapproximately the distance of the Galactic Centre (see Section4.2) we can make the important conversion between the angularseparations of sources and the angular scale of the telescoperesolution, and a physical scale. We use the distance to the GalacticCentre of 8.122 ± sky ∼ tan ( 𝜃 ) × .
122 kpc. With thisconversion we construct a structure function for physical distancesshown in Figure 11. The impact parameters at which our sight-linesintersect the Faraday rotating material near the Galactic Centre areat projected galactocentric separations ranging from 269 pc (NVSSJ174202-271311) to 1505 pc (NVSS J174712-190550). Convertingfrom our previous upper limit of 66 + − ", this suggests an upperlimit for the outer scale of turbulence of 3 + − pc. We aim to find a possible cause for the implied outer scale upperlimit of turbulence for our studied region of the Galactic Centre of3 pc. Outer scales of 10s of parsecs have been observed at highGalactic latitudes (Simonetti & Cordes 1986) and low Galacticlatitudes (Simonetti & Cordes 1986; Clegg et al. 1992), in the spiralarm regions of the Milky Way (Haverkorn et al. 2006b, 2008), as
MNRAS , 1–15 (2020) Livingston et al.
Figure 10.
Plot of Oppermann et al. (2015) RM map with the selected region from the Taylor et al. (2009) catalogue and our surveyed region (top-left). Plotof the angular separation distribution of the Galactic Plane region, the structure function from O’Sullivan et al. (2017), and our structure function (top-right),and the resultant structure functions for the region, from O’Sullivan et al. (2017), and the structure function from Figure 9 (bottom). The colour map for theOppermann et al. (2015) RM map (top-left) indicates the size and sign of Faraday depth where reds correspond to large positive Faraday depths and blues withlarge negative Faraday depths; the scale ranges between -500 and 500 rad m − . Figure 11.
Plot of RM structure function with the mean of (cid:104)| RM − RM | (cid:105) as a function of angular separation (bottom axis) and physical distance (topaxis). The dashed green and purple lines are the Kolmogorov and Burgersturbulent cascade slopes of 2/3 and 11/10 that intersect with the height ofthe RM structure function and the mean (cid:104)| RM − RM | (cid:105) bin. well as in the Large Magellanic Cloud where outer scales of 90 pcwere observed (Gaensler et al. 2005).Structure functions above the Galactic plane have hadshallower slopes, whereas structure functions below the Galactic plane have shown steeper slopes (Simonetti & Cordes 1986; Clegget al. 1992). Structure functions closer to the Galactic Plane(Uyaniker et al. 2004; Haverkorn et al. 2003, 2008) show shallowslopes as well as structure functions of the Fornax region (Andersonet al. 2015). A comparison between our structure function and thestructure functions of Haverkorn et al. (2008) and Anderson et al.(2015), as well as the aforementioned structure functions aroundthe Galaxy, highlights the flatness of the slope and the particularlysmall upper limit on the outer scale shown in Figure 11, especiallyconsidering the large range of angular and physical scales we areprobing. Given the smaller than usual upper limit on the outerscale, we consider astrophysical effects that are unique to the regionbetween 𝑅 𝑔 ∼
270 pc and 𝑅 𝑔 ∼ ∼ MNRAS , 1–15 (2020) araday Complexity in the Galactic Centre We first consider whether stellar feedback may set the outer scalein our data. Stellar feedback, both in the form of stellar winds,Hii regions, and Supernovae (SNe), is commonly assumed to be themain source of turbulent energy injection in the Galaxy. Supernovaeand super-bubbles are the most powerful interactions, with withtheoretical characteristic size scales of ∼
70 and ∼ ∼ ∼
100 pc scale of SNe is muchlarger than an outer scale inferred from our work, and is thereforean unlikely cause.The theoretical size scale of Hii regions can be found as(Norman & Ferrara 1996),L H II = (cid:18) 𝑐 𝑠, II 𝑐 𝑠, I (cid:19) / 𝑅 𝑠 . (17)Where 𝑐 𝑠, I and 𝑐 𝑠, II are the sound speeds of the neutral and ionisedmedia respectively, and 𝑅 𝑠 is the Strömgren radius of the Hiiregion (Strömgren 1939). At a Galactic Centre Hi gas density of10 cm − (Kauffmann et al. 2017), 𝑅 𝑠 will be between 0.1 - 1 pc.This means that the size scale for the Hii regions of the GalacticCentre will be on the order of 10s of parsecs. In their work on RMstructure in the Galactic Plane, Haverkorn et al. (2006b) found H iiregions to be the most likely cause of the ∼
17 pc outer scale ininter-arm regions, although they also concluded that it is unlikelya wide-spread phenomenon due to the importance supernovae havein turbulence injection. From the observation and theoretical limitsof 𝐿 H II , we can rule H II regions out as the likely cause our upperlimit on the outer scale of 3 pc.Another source of stellar feedback may be outflows and bubblesaround young stars. Although the size scale for outflows and smallbubbles is closer to our 3 pc outer scale, they generally lack power.The expected kinetic energy for these objects is ∼ − and ∼ ergs (Lada 1985; Bachiller 1996), respectively, which issignificantly lower than the average kinetic energy of supernovaeof 10 ergs (Blondin et al. 1998). For the turbulence driven by aspherical explosion with energy 𝐸 sph , the driving scale of turbulence 𝑙 sph is proportional to 𝐸 / (Eq. 5.2 of Seta 2019). If 𝐸 sph is afactor of 10 smaller for small bubbles as compared to supernovaexplosions, 𝑙 sph should be smaller by a factor of 10 . This theorysuggests that if SNe inject turbulence on scales of 100 pc, the drivingscale of turbulence due to small bubbles will roughly be of the orderof 1 pc, which is similar to our observed upper limit for the outerscale.Observations on the isolated Taurus molecular cloud by Liet al. (2015) showed that the turbulence could not be explained withoutflows alone. However, the star formation rate within the CentralMolecular Zone of the Galactic Centre (Morris & Serabyn 1996;Longmore et al. 2013) is much higher than in Taurus, and thereforethe density of objects may be enough to boost the importanceof outflows and small bubbles as a source of turbulent energyinjection. We tentatively suggest that stellar outflows and bubblesare a likely candidate, given that only they have enough power inthe Galactic Centre, explaining why they are not the main candidatefor magneto-ionic turbulence in other galactic regions. An alternative turbulence injection mechanism may be the uniqueand powerful dynamics of the Galactic Centre. Within the Galactic Centre’s bar exists a resonance between the driving torque of thebar and the gases within. This leads to strong shocks within thegas and deviations from circular motion (Morris & Serabyn 1996).This resonance forms in two regions of the Galactic Centre knownas the Inner and Outer Lindblad Resonances. The Inner LindbladResonance (ILR) extends out to 1 kpc from the Galactic Centre andis formed due to the orbits effectively overtaking the bar periodicallyon their journey around the Galactic Centre. The region of sky weare observing sits mostly within the ILR, although we have severallines-of-sight that sit towards the edge of this region. Portail et al.(2017) find that this radius ( ∼ 𝐿 ins ) found by Krumholz &Kruijssen (2015) increases outwards from the Galactic Centre, fromscales of 𝐿 ins ∼ − pc at ∼
100 pc from the Galactic Centre to 𝐿 ins ∼ − pc at ∼
400 pc from the Galactic Centre. We expectthis relationship between radius and 𝐿 ins to continue out until theILR at ∼ We collected broadband polarisation data over 1 - 3 GHz of 58 fieldswithin ∼ ° of the Galactic Centre using the ATCA. The peakFaraday depth (RM) and F( 𝜙 ) for the 62 detected polarised sourceswere calculated using RM Synthesis. The RM measurements werefound to be in good agreement with previous observations. We usedF( 𝜙 ) for our sources to find the second moment, 𝑀 , of Faradaydepth and thereby determine the Faraday complexity of each source.The majority (95%) of our sources had non-zero 𝑀 , indicatingthey have complex RM structure on the scale of the beam. This issignificantly higher than the findings of previous studies of Faradaycomplexity (Anderson et al. 2015; O’Sullivan et al. 2017). Wemodelled our sources using QU fitting and found that 95% of sources MNRAS000
400 pc from the Galactic Centre. We expectthis relationship between radius and 𝐿 ins to continue out until theILR at ∼ We collected broadband polarisation data over 1 - 3 GHz of 58 fieldswithin ∼ ° of the Galactic Centre using the ATCA. The peakFaraday depth (RM) and F( 𝜙 ) for the 62 detected polarised sourceswere calculated using RM Synthesis. The RM measurements werefound to be in good agreement with previous observations. We usedF( 𝜙 ) for our sources to find the second moment, 𝑀 , of Faradaydepth and thereby determine the Faraday complexity of each source.The majority (95%) of our sources had non-zero 𝑀 , indicatingthey have complex RM structure on the scale of the beam. This issignificantly higher than the findings of previous studies of Faradaycomplexity (Anderson et al. 2015; O’Sullivan et al. 2017). Wemodelled our sources using QU fitting and found that 95% of sources MNRAS000 , 1–15 (2020) Livingston et al. were well modelled with two Faraday screens and external Faradaydispersion.We combined the peak Faraday depth data and the meandifference between the RMs for each source, (cid:104)| RM − RM | (cid:105) , toform a second order RM structure function, which covered angularseparations between 17” and 11 ° . Using an assumption of thelocation of the surveyed magneto-ionic environment, this resulted ina structure function covering physical distance separations between0 . ∼ ∼ ACKNOWLEDGEMENTS
The Australia Telescope Compact Array is part of the AustraliaTelescope National Facility which is funded by the AustralianGovernment for operation as a National Facility managed by CSIRO.We acknowledge the Gomeroi people as the traditional owners of theObservatory site. We also acknowledge the Ngunnawal and Ngambripeople as the traditional owners and ongoing custodians of the landon which the Research School of Astronomy & Astrophysics is sitedat Mt Stromlo. First Nations people were the first astronomers of thisland and make up both an important part of the history of astronomyand an integral part of astronomy going forward.We thank the anonymous referee for a thorough review of thework. We thank Craig Anderson and Alec Thomson for helpfuldiscussions related to the paper. This research was supported by theAustralian Research Council (ARC) through grant DP160100723.J.D.L and M.J.A were supported by the Australian GovernmentResearch Training Program. N.M.G. acknowledges the support ofthe ARC through Future Fellowship FT150100024. The DunlapInstitute is funded through an endowment established by the DavidDunlap family and the University of Toronto. B.M.G. acknowledgesthe support of the Natural Sciences and Engineering ResearchCouncil of Canada (NSERC) through grant RGPIN-2015-05948,and of the Canada Research Chairs program.
DATA AVAILABILITY
The data underlying this article were accessed from theCSIRO Australia Telescope National Facility online archive athttps://atoa.atnf.csiro.au, under the project codes C3020 and C3259.The derived data generated in this research will be shared onreasonable request to the corresponding author.
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