Magnetic field near the central region of the Galaxy: Rotation measure of extragalactic sources
aa r X i v : . [ a s t r o - ph ] D ec Astronomy&Astrophysicsmanuscript no. gc.rm.pap c (cid:13)
ESO 2018October 28, 2018
Magnetic field near the central region of the Galaxy: Rotationmeasure of extragalactic sources
Subhashis Roy , , A. Pramesh Rao , and Ravi Subrahmanyan ASTRON, P.O. Box 2, 7990 AA Dwingeloo, The Netherlands. e-mail: [email protected] National Centre for Radio Astrophysics (TIFR), Pune University Campus,Post Bag No.3, Ganeshkhind, Pune 411 007, India. e-mail: [email protected] Raman Research Institute, C. V. Raman Avenue, Sadashivanagar, Bangalore 560 080, India
ABSTRACT
Aims.
We determine the properties of the Faraday screen and the magnetic field near the central region of the Galaxy.
Methods.
We measured the Faraday rotation measure (RM) towards 60 background extragalactic source components through the − ◦ < l < ◦ , − ◦ < b < ◦ region of the Galaxy using the 4.8 and 8.5 GHz bands of the ATCA and VLA. Here we use the measured RMs to estimate thesystematic and the random components of the magnetic fields. Results.
The measured RMs are found to be mostly positive for the sample sources in the region. This is consistent with either a large scalebisymmetric spiral magnetic fields in the Galaxy or with fields oriented along the central bar of the Galaxy. The outer scale of the RM fluctuationis found to be about 40 pc, which is much larger than the observed RM size scales towards the non thermal filaments (NTFs). The RM structurefunction is well-fitted with a power law index of 0.7 ± ∼ ◦ (radius150 pc) from the GC, the strength of the random field in the region is estimated to be ∼ µ G. Conclusions.
Given the highly turbulent magnetoionic ISM in this region, the strength of the systematic component of the magnetic fieldswould most likely be close to that of the random component. This suggests that the earlier estimated milliGauss magnetic field near the NTFsis localised and does not pervade the central 300 pc of the Galaxy.
Key words.
ISM: magnetic fields – Galaxy: center – techniques: polarimetric
1. Introduction:
Magnetic fields are widely recognised as playing an impor-tant role in the evolution of supernova remnants, in star forma-tion, overall structure of ISM, cosmic ray confinement and non-thermal radio emission. This is especially true in central regionof the Galaxy, where magnetic fields could be strong enoughto be significant in the dynamics and evolution of the region(Beck et al. 1996). A relatively high systematic magnetic fieldin the Galactic centre (GC) region was believed to be responsi-ble for the creation and maintenance of the unique non thermalfilaments (NTFs) (Morris et al. 1996, and references therein).Therefore, it is important to measure the magnetic-field geom-etry and strength near the central part of the Galaxy.Other than the central 200 pc of the GC, no systematicstudy has been made in the past to measure the magneticfields in the inner 5 kpc region of the Galaxy (Davidson 1996).Recently, Brown et al. (2007) have surveyed the 4th quadrantof the Galaxy up to l =358 ◦ through Faraday RMs, but theirobservations do not target the central kpc of the Galaxy. Theearlier estimates of magnetic fields within the central 200pc of the Galaxy were based mainly on observations of the non-thermal filaments, and the measured Faraday rotationmeasure (RM) towards these NTFs were found to be ∼ − (Yusef-Zadeh & Morris 1987b; Anantharamaiah et al.1991; Gray et al. 1995; Yusef-Zadeh et al. 1997; Lang et al.1999b). Since magnetic pressure in these NTFs appearsto overcome turbulent ISM pressure (otherwise, the NTFswould have bent due to interaction with molecular clouds),Yusef-Zadeh & Morris (1987a) derived a magnetic-fieldstrength of about 1 milliGauss within these NTFs. Moreover,the high magnetic field in the region is required to be ubiq-uitous. Otherwise, in regions where there is no molecularcloud around NTFs, magnetic pressure within these structureswould be much higher than outside. This will cause the NTFsto expand at Alfven speed and decay at a time scale ( ∼ Subhashis Roy et al.: Magnetic field near the Galactic centre region are oriented almost perpendicular to the Galactic plane, it sug-gests the field lines in the surrounding ISM are also perpen-dicular to the Galactic plane (Morris et al. 1996 and the ref-erences therein). In addition, the NTF Pelican (G358.85+0.47)(Lang et al. 1999a) located about a degree from the GC is foundto be almost parallel to the Galactic plane. This indicates thatthe field lines change their orientation from being perpendic-ular to parallel to the plane beyond a degree from the GC,which is typically observed in the rest of the Galaxy. However,we note that if the NTFs are manifestations of peculiar localenvironments (Shore & Larosa 1999), inferences drawn fromthese observations can be misleading. With the recent discov-ery of many new fainter filamentary structures in the GC regionoriented quite randomly with the Galactic plane (Nord et al.2004), serious doubts are cast on the orientation of the mag-netic field and its ubiquitous nature near the GC.Zeeman splitting of spectral lines can directly yieldthe magnetic field in a region. However, this method isknown to be sensitive to small-scale fields, and there-fore high magnetic field strengths in a small region any-where along the line-of-sight (LOS) can indicate a highmagnetic field, which is not representative of the average.Therefore, past estimates of milliGauss magnetic fields basedon Zeeman splitting (Schwarz & Lasenby 1990; Killeen et al.1992; Yusef-Zadeh et al. 1996, 1999) of HI or OH lines to-wards the GC could have resulted from local enhancement offield ( e.g. , near the cores of high-density molecular clouds).To measure any systematic magnetic field in the region, it isnecessary to use an observational technique that is sensitive tolarge-scale fields. To avoid manifestations of favourable localenvironments, Galactic objects should not be used for this pur-pose.Faraday rotation measure is the integrated LOS magneticfield weighted by the electron density RM = . × Z n e B k dl , (1)where, RM is rotation measure expressed in rad m − , n e isthe electron density expressed in cm − , B k is the LOS com-ponent of the magnetic field in µ G, and the integration is car-ried out along the LOS, with distance expressed in parsec. Ifa model for the electron density is available, observations ofRM towards the extragalactic sources seen through the Galaxycan be used to estimate the average magnetic fields in theISM. A large number of studies of the Galactic magnetic fieldshave already been made using RM towards the extragalac-tic sources Simard-Normandin & Kronberg (1980); Frick et al.(2001); Clegg et al. (1992). Similar studies have also been car-ried out towards pulsars (Rand & Kulkarni 1989; Rand & Lyne1994; Han & Qiao 1994). These studies have shown that thereis one field reversal within and one outside the solar circle,while two more reversals have been suggested by Han et al.(1999). These reversals could be explained by invoking eitherthe bisymmetric spiral model (Simard-Normandin & Kronberg1980; Han et al. 1999) or a ring model, where the direction ofthe field lines reverses in each ring (Rand & Kulkarni 1989).However, there has been no systematic observation of RM to-wards extragalactic sources seen through the GC region. We systematically studied RM properties of 60 extragalac-tic sources seen through the central − ◦ < l < ◦ , − ◦ < b < ◦ region of the Galaxy. The angular scale over which the magne-toionic medium is coherent near the NTFs has been estimatedas ∼ ′′ (Gray et al. 1995, Yusef-Zadeh et al. 1997). Therefore,to avoid any beam depolarisation introduced by the ISM of theGalaxy, our observations were made with the higher resolu-tion configurations of these telescopes, so that the synthesisedbeam sizes are considerably smaller than the coherence scalelength of the Faraday screen near the GC. Preliminary results ofthese observations were published earlier in Roy et al. (2003)and Roy (2004). In Roy et al. (2005) (henceforth Paper I), wedescribed the sample sources, the observations and data analy-sis and then determined their spectral indices, polarisation frac-tion, RM, and the direction of their intrinsic magnetic field. Inthis paper, we interpret the RM observations. In Sect. 2, we pro-vide a graphic representation of the measured RMs (see Paper-I), while interpretation of the results is described in Sect. 3. Theconclusions are presented in Sect. 4.
2. Results
In Fig. 1, we plot RMs of 60 polarised components (including2 secondary calibrators), which conform to the criteria given inPaper I (i.e., reduced c of the polarisation angle vs. frequencyfit less than or equal to 4.6, depolarisation fraction between4.8 and 8.5 GHz higher than or equal to 0.6 and the sourceis outside the Galaxy). This figure shows our measured RMsdivided into four quadrants according to the signs of Galacticlongitude and latitude. In the rest of this paper, we define quad-rant A when l and b are both positive, quadrant B when l isnegative but b is positive, quadrant C when both l and b arenegative and quadrant D when l is positive but b is negative.The region is dominated by positive RMs, as observed towardsmost of the sources in both positive and negative Galactic lon-gitude. The observed RMs towards sources with | b | ≤ ◦ arequite high ∼ − . Such high RMs have been mea-sured towards extragalactic sources at low Galactic latitudes(45 ◦ < l < ◦ , and | b | < ◦ ) by Clegg et al. (1992) and are dueto passage of radio wave through large path lengths along inter-stellar medium. These results are consistent with positive RMsobserved near l = − ◦ by Brown et al. (2007), which lies nearthe edge of their survey.In general, magnetoionic media responsible for the RMshave structures at different length scales. Reversal of sign of theRM over angular scales of a few degrees shows the existenceof a random component of the magnetic field. We explore thisthrough the structure function analysis of the RMs and thenidentify systematic features in the data. Variations in RM over an angular scale of Dq can be describedby the RM structure function D ( Dq ) = < [ RM ( q ) − RM ( q + Dq )] > . The structure function is measured by computing theexpectation value of the squared differences of the RM among ubhashis Roy et al.: Magnetic field near the Galactic centre region 3 Fig. 1.
Measured Faraday RMs towards the polarised sources in Galactic co-ordinate. The positive values are indicated by ‘cross(X)’ and negative values by ‘circle (O)’. Size of the symbols increase linearly with | RM | . Fig. 2.
The structure function of the measured RMs. See textfor the fit.all pairs of sources within a particular range of angular sepa-ration ( Dq ). We binned the data with Dq from 0.0 ◦ to 0.005 ◦ ,0.005 ◦ to 0.1 ◦ , 0.1 ◦ to 0.33 ◦ , 0.33 ◦ to 0.6 ◦ , and then up to 1.0 ◦ in bin widths of 0.2 ◦ . From 1.0 ◦ to 4.0 ◦ , we binned angular sep-arations with bin widths of 0.5 ◦ , and from 4.0 ◦ to 10 ◦ a singlebin was used. The RM structure function in each bin is plottedat the location of the median angular separation of sources inthat bin in Fig. 2. The errorbars in the plot were estimated bya statistical method called ‘Bootstrap’ (Efron 1976). Figure 2shows that the structure function appears to saturate at beyond ∼ ◦ ; therefore, we fitted a power law f ( Dq ) = A × Dq n for Dq ≤ ◦ , and then f ( Dq ) is held fixed at its value for Dq =0.7 ◦ .The function [ f ( Dq ) ] is well-fitted to the data (reduced c ± × , and the power law index ( n ) is 0.7 ± ◦ or 40 pc for the screen if lo-cated at the distance of GC, 8.0 kpc away. This indicates theRMs of sources lying within an angular distance of < ◦ arelikely to be correlated. Therefore, while determining statisticalquantities in this paper, we ensure independent measurementsby considering the RMs of source components located at leastbeyond 0.2 ◦ from each other. There are a total of 38 sourcecomponents that conforms to this criterion.Given the extreme conditions in the ISM close to the GC,statistical properties of the medium in this region could be dif-ferent from that of its immediate surroundings. To check forany change in outer scale of RM for sources seen within 1.1 ◦ ( ∼
150 pc) of the GC, we carried out the above analysis for6 sources seen through the region. The structure function ofthese sources with angular separations less than 1.1 ◦ is 9.5 ± × rad m − , and is 3.8 ± × rad m − for sources withangular separations between 1.1 ◦ to 2.1 ◦ . This shows the RMschanged by more than 1.7 times the effective error, indicatingthat the structure function of RMs is not saturated for angularseparations of less than a degree ( >
90% confidence). While thesignificance of this result is not very high due to the small num-ber of sources in the sample, we adopt the simplest model andassume the outer scale in the inner 1.1 ◦ region is comparable to40 pc determined from the full sample. In Fig. 1, we notice the dominance of sources with positiveRMs. Following the criteria given above for sources with un-correlated RMs, we find the mean RM from the data to be 413 ±
115 rad m − , and the median is 476 rad m − . The mean RMin quadrant A of Fig. 1 is 488 ± ±
294 in quadrant B,354 ±
170 in C and 350 ±
323 in D. To study the systematic
Subhashis Roy et al.: Magnetic field near the Galactic centre region behaviours of this large-scale field, we divided the observedregion in several bins along the Galactic longitude and lati-tude such that a reasonably large number of sources remain ineach bin to yield meaningful statistical properties (mean, rms)of RMs in these bins. Therefore, we selected 5 bins along theGalactic longitude, each 2.4 ◦ wide resulting in ∼ ◦ . Average RMs along Galacticlongitude and latitude are plotted in Fig. 3 (shown with soliderror-bars) and Fig. 4, respectively. Figure 3 shows that the av-erage RM of sources located within | l | < ◦ is significantly lessthan that of sources located beyond | l | > ◦ .To remove possible small-scale variations in RM due toLOS HII regions or supernova remnants (Mitra et al. 2003),thereby getting a clearer picture of the large-scale field in theregion, we used the following method. We estimate the meanand rms RM of sources located in each bin in Table. 1. If mea-sured RM of any source within a bin deviates from the meanin that bin beyond 1.7 times the rms ( ≤
10% probability forGaussian distributed errors), that RM is rejected (flagged) andthe mean and rms RM in that bin is recomputed. This processis repeated till there is no source outside the flag limit. Sincethere are only a few sources per bin, flagging the highly de-viant data points in a bin would reduce the measured rms ascompared to the real rms in the data. However, in a majority ofcases, it results in a drop in measured rms of only ∼ < − ◦ < l < ◦ , where 4 out of 11 sources were flagged, and the rmsRM of sources decreased by almost a factor of 5 after flagging( ∼
5% probability with Gaussian random noise), indicating asignificant small-scale structure (non-Gaussian errors) in theFaraday screen towards this region. The resulting distributionof average RM is plotted in Fig. 3 using dashed errorbars, andto make the symbols visible, the X-axis of this plot is shiftedby − ◦ from what is shown at the bottom. This shows thatthe average RM tends to zero near l =0 ◦ . We applied the sameprocedure for RMs of sources located in each of the bins inTable. 2, and the resulting mean and rms RM values after flag-ging in each bin are tabulated there. No significant change inmean or rms RM is noticed after flagging in this case.
3. Discussion
In the previous section we identified a largely positive RM to-wards background sources, the correlation length of which isabout 40 pc. The RMs averaged in bins along the Galactic lon-gitude was found to decrease near l =0 ◦ . In this section, weidentify the location and properties of the Faraday screen thatis responsible for the above. Then, using a plausible model ofthe electron density distribution near the GC, we investigate -400-200 0 200 400 600 800 1000 1200 -4-2 0 2 4 R o t a t i on m ea s u r e (r ad . m - ) Galactic longitude (deg)
Fig. 3.
Plot of RMs as a function of Galactic longitude.The values shown are averaged over 2.4 degree bins inlongitude. Data points with solid error bars are before flag-ging, and data after flagging are displayed by dashed error-bars with axis shifted by − ◦ to what is displayed alongthe axis at the bottom. Details of flagging are described inthe text. −2.0 −1.5 −1.0 −.5 .0 .5 1.0 1.5 2.0−500050010001500 Galactic latitude (degree) R o t a ti on m ea s u r e (r a d . m − ) −2.0 −1.5 −1.0 −.5 .0 .5 1.0 1.5 2.0−500050010001500 Galactic latitude (degree) R o t a ti on m ea s u r e (r a d . m − ) Fig. 4.
Plot of RMs as a function of Galactic latitude. Thevalues shown are averaged over 0.8 degree bins.the nature of the magnetic fields (comprised of systematic andrandom components) in the region.
Differences in RMs seen along different LOS could occur fromeither (i) a geometrical effect or (ii) change in the property ofthe Faraday screen. The structure function due to a perfectlyuniform Faraday screen will have a measurable geometricalcomponent simply because of the change in the LOS compo-nent of the field with change in the l and b . An observer embed-ded in an extended homogeneous medium with uniform mag-netic field approaching from an arbitrary angle q sees a rota- ubhashis Roy et al.: Magnetic field near the Galactic centre region 5 Table 1.
Rotation measure of sources binned along Galactic longitude
Bin Range No. of Mean Rms on No. of Mean RM Rms on meanNo. in l sources RM mean RM sources after sources RM afterflagged flagged flagging(deg) (rad.m − ) (rad.m − ) (rad.m − ) (rad.m − )1 − − − − − − −
82 524 1.2 to 3.6 5 577 277 0 577 2775 3.6 to 6.0 12 827 193 1 959 154
Table 2.
Rotation measure of sources binned along Galactic latitude
Bin Range No. of Mean Rms on No. of Mean RM Rms on meanNo. in l sources RM mean RM sources after sources RM afterflagged flagged flagging(deg) (rad.m − ) (rad.m − ) (rad.m − ) (rad.m − )1 − − − − − tion measure RM cos ( q − q ) (Clegg et al. 1992), where RM is the RM towards q . However, over the observed longituderange, the contribution from the variation in the ‘cosine’ termis much less than what is observed in Fig. 2. Therefore, we donot consider the geometrical effect any further.The measured RMs towards the sources could have a signif-icant intrinsic contribution from a magnetoionic medium localto the sources. However, in this case, intrinsic RMs towards dif-ferent sources will be uncorrelated. Consequently, differencesin RMs for unrelated sources will persist regardless of their lo-cation on the sky plane, and will not approach zero when theirangular separation tends to zero. However, in Fig. 2, we findthe RM structure function tends to zero at zero angular sepa-ration and increases smoothly with source angular separations.This shows intrinsic RMs can be neglected, and the measuredRMs have an interstellar origin (plasma turbulence) within ourGalaxy. To explain the observed magnetic field orientation inour Galactic disk, two models of magnetic fields, thering (Rand & Kulkarni 1989) and the bisymmetric spi-ral (Simard-Normandin & Kronberg 1980) are widely used.However, both of these models predict that the LOS RM contri-bution from the Galactic disk is quite small when | l | << − ±
46 rad m − . Since the mean RM is quite small,any Faraday screen affecting our sample has to be located atleast beyond the median distance of these pulsars. Moreover,the linear size of an object at this median distance of 3.5 kpcwith angular size of our survey will be ∼
300 pc. Objects knownto produce significant RMs (e.g., HII regions, supernova rem-nants) are typically much smaller than the above size scale.Therefore, no single nearby object has significantly biased theRMs, so we believe the central few kpc region of the Galaxy isresponsible for the observed RMs.
Faraday rotation being the LOS integral of the product of themagnetic field with the electron density, changes in electrondensity or the magnetic field strengths or a change in the direc-tion of the magnetic field vector can contribute variations in theobserved RM. To separate the contribution of these effects, wefirst discuss the available models of the electron density distri-bution and then discuss the large-scale magnetic field near thecentral region of the Galaxy.
The electron density of the ISM is believed to increase to-wards the central region of the Galaxy. Different electron den-sity models are invoked for the inner Galaxy, central kpc, andthe central 100 pc of the Galaxy, which are discussed below.Taylor & Cordes (1993) modelled electron density distri-bution in the Galaxy and included an inner Galactic compo-nent that is considered a ring at a distance of ∼ Subhashis Roy et al.: Magnetic field near the Galactic centre region
Over the central few degrees of the GC, Bower et al. (2001)carried out VLBA observations of 3 extragalactic sources andreport a region of enhanced scattering covering & ◦ in lon-gitude and ≤ ◦ in latitude. The measured scattering diame-ters correspond to about ∼
300 milli-arcsec at 1 GHz, whichis 1.5–6 times the prediction from the Taylor & Cordes (1993)model. Using scatter broadening of OH masers in the vicin-ity of OH/IR stars, van Langevelde et al. (1992) showed thatthere is a region of high scattering within 30 ′ of the GC. Fromfree-free absorption measurements, they suggest the scatteringregion is at a distance of more than 850 pc from the GC. Usinga likelihood analysis, Lazio & Cordes (1998) claim a ‘hyper-strong’ scattering screen ( n e ∼
10 cm − ) of the same angularextent (30 ′ ) towards the GC, but estimated the distance to thisscreen to be 133 + − pc from the GC. This model predicts ascattering diameter for extragalactic sources to be an order ofmagnitude higher than what is observed by Bower et al. (2001).However, the extragalactic source G359.87+0.18 (Lazio et al.1999) is seen through the ‘hyperstrong scattering’ region, butits scattering size is an order of magnitude lower than pre-dicted from the ‘hyperstrong scattering’ model. This indicatesthe screen is patchy Lazio et al. (1999). An improved ver-sion of Taylor & Cordes (1993) model has been published byCordes & Lazio (2002), where contribution from a GC com-ponent corresponding to the contribution from the central 30 ′ region of the Galaxy (Lazio & Cordes 1998) has been added.However, it does not include any contribution from the en-hanced scattering region observed by Bower et al. (2001). Inour observations, all the objects barring one (G359.87+0.18)are seen through the region of enhanced scattering observedby Bower et al. (2001). Therefore, we used their observationsto estimate electron density, which will be used in the rest ofthe paper. If we assume the turbulence scale length of thisscreen to be the same as that of the inner Galaxy componentof Taylor & Cordes (1993), Bower et al. (2001) scattering mea-sure imply an electron density of about 0.4 cm − . This is twiceof what is estimated from the Taylor & Cordes (1993) modelfor the inner Galaxy. The corresponding dispersion measurefrom the inner 2 kpc of the Galaxy is 800 pc cm − . From theCordes & Lazio (2002) model, we also estimate the dispersionmeasure from the rest of the Galaxy along the LOS passingabout a degree away from the GC, which is found to be 800pc cm − . Therefore, the total dispersion measure towards theinner kpc of the Galaxy is ∼ − , and half of the to-tal dispersion measure originates from the inner Galaxy com-ponent. It should be noted that at present the dispersion mea-sure of the inner Galaxy component is uncertain by factor ofa few. Using the above-mentioned dispersion measure of 800pc cm − for the central 2 kpc of the Galaxy and mean RM of413 rad m − (Sect. 2) in Eq. 1, the mean LOS magnetic field isestimated to be 0.6 µ G. As this is an LOS average, it should betreated as a lower limit.
In the presence of various turbulent processes in the GC, anyunravelling of the large-scale field orientation needs to be per-formed statistically, and here we consider possible models toexplain the results (Sect. 2).(i) Magnetohydrodynamic model:Uchida et al. (1985) proposed this model to explain theGalactic Centre Lobes (GCL), which are a pair of limb-brightened radio structures of several hundred parsecs extend-ing from Galactic plane towards positive Galactic latitudes(Sofue & Handa 1984) and seen within the central 1 ◦ of theGalaxy. They carried out non-steady axisymmetric magneto-hydrodynamic simulations in which the magnetic field is as-sumed to be axial at high Galactic latitudes. However, due tothe differential rotation of dense gas near the Galactic plane, thefield acquires a component along this plane. This model pre-dicts an LOS field in quadrants A and C towards the observer(positive RM), and away from the observer in quadrants B andD. Novak et al. (2003) find the signs of the measured RMs to-wards the known NTFs to be consistent with the above predic-tion. From our observations, the estimated mean RM towardssources seen through quadrants A and C is 432 ±
133 rad m − and 379 ±
217 rad m − through quadrants B and D . PositiveRMs in all the quadrants are inconsistent with their prediction.However, our sources are observed over a significantly biggerregion around the GC than the NTFs are seen, and the resultsdo not match the prediction of this model.(ii) Ring model:According to this model, magnetic field lines in a galaxy areoriented along circular rings in the galactic plane. As discussedin Rand & Kulkarni (1989), such a geometry arises in galacticdynamo models of the field, in which a symmetric azimuthalmode is dominant (e.g., Krause 1987). Theories involving aprimordial origin of magnetic field also claim to be able toproduce ring fields, but only in the inner regions of galaxies(Sofue et al. 1986). In this model, the LOS magnetic field re-verses with the sign of galactic longitude at a particular galacto-centric radius (r). Reversals of the magnetic field as a functionof galactocentric radius are also predicted by this model. Sinceboth these predictions are inconsistent with the data (Fig. 3),the ring model is not applicable in this region.(iii) Bisymmetric spiral model:Simard-Normandin & Kronberg (1980) proposed this model(see also Han et al. (1999)) to account for the reversals ofmagnetic fields with galactocentric distances in the Galaxy. Aschematic diagram of this model is shown in Fig. 5. It pre-dicts a positive RMs towards l =0 ◦ , which is what is observed.Therefore, the prediction from this model near the GC is con-sistent with our observations.(iv) Another plausible configuration of the magnetic field:Magnetic field lines are typically observed to be aligned withlarge-scale structures in the Galaxy and beyond. In the centralfew kpc region of the Galaxy a bar-like distribution of matterhas been suspected for a long time, and recent Spitzer obser-vations suggest it is oriented at an angle of 44 ◦ with respect toour LOS (Churchwell & Glimpse Team 2005). An impression ubhashis Roy et al.: Magnetic field near the Galactic centre region 7 of this from the top of our Galaxy is shown in Fig. 6 . A barin gas distribution in the central region of the Galaxy has alsobeen claimed (Sawada et al. 2004). If the magnetic field linesare oriented along this bar and have a component towards us,then this could explain the positive RMs observed in all thefour quadrants. We note a decrease in averaged RM near l = ◦ (Fig. 3). Magnetic fields in the GC region are very likely an-chored to the dense molecular clouds, and within ∼ ◦ of theGC, they have large random motions, which reduces the mag-netic field averaged over the 2.4 ◦ bin centred on the GC. In this section, we discuss the power spectrum of the magne-toionic ISM and then estimate the strength of the magnetic fieldresponsible for it. Small-scale variations in a magnetoionicmedium are likely to be related to electron density fluctuationsin ISM, which have been studied through scattering and scin-tillation observations (Rickett 1990). The power spectrum ofelectron density irregularities is expressed by P ( q ) = C n q − a , q < q < q i (2)Where, q is spatial wavenumber, and a is spectral index(Rickett 1977). C n is normalisation constant of the electrondensity power spectrum. The quantities q and q i representwavenumbers corresponding to ‘outer scale’ and ‘inner scale’of the turbulence respectively.Assuming the fluctuations in electron density and magneticfield to be zero mean isotropic Gaussian random processes withthe same outer scale ( l ), Minter & Spangler (1996) derived D RM (cid:181) ( Dq ) a − . For three dimensional Kolmogorov turbulence a = /
3, and D RM (cid:181) ( Dq ) / . However, from Fig. 2, we findthe structure function is well fitted by a power law of index0.7 ± . ◦ and then it gets satu-rated. This is consistent with D RM (cid:181) ( Dq ) / , which would in-dicate a = /
3, expected from two-dimensional Kolmogorovturbulence. Two-dimensional turbulence results if the screenresponsible for it is confined in thin sheets in the sky plane.Minter & Spangler (1996) have found in their data that thestructure function slope changes from about 5/3 to 2/3 at alength scale of about 7 pc. However, in our data we do notobserve any significant deviation from the fit at the smallestangular separation in Fig. 2 near 0.002 ◦ corresponding to a lin-ear scale of 0.3 pc at a distance of the GC. This will indicateif the turbulence is indeed Gaussian in nature, the thickness ofthe screen/screens is ≤ Fig. 5.
A schematic diagram of the bisymmetric spiralstructure of magnetic fields.
Fig. 6.
A schematic view of the Galaxy from the top of theGalactic plane. Notice the kpc scale bar within the central4 kpc from the GC.turbulence to be two-dimensional if Gaussian random processis assumed.To estimate the strength of the random magnetic fields, weassume the RMs to be correlated within the outer scale of theRM structure function (40 pc) (henceforth called cells). It is
Subhashis Roy et al.: Magnetic field near the Galactic centre region quite easy to show that along our LOS D RM = { . × ( D n e × < B k > + n e × D B k ) × l × √ n } where D n e and D B k correspond to the fluctuating componentof the electron density and magnetic fields along our LOS re-spectively. In the above equation, l is the size of each cell and‘n’ the number of such cells along each LOS. As discussedin Sect. 3.2.1, n e is estimated to be about 0.4 cm −
3, and D n e is also believed to be about the same. In Sect. 3.2.1, < B k > is estimated to be 0.6 µ G. If the central 2 kpc region is be-lieved to be responsible for the observed RMs, then there willbe about 50 cells along each LOS. The estimated random mag-netic fields at length scales of 40 pc corresponding to the RMstructure function of 3.7 × rad m − (Fig. 2) is 6 µ G. Wenote that electron density distribution is quite clumpy in the in-ner Galaxy (Cordes et al. 1985). Therefore, the number of suchcells could be much less, such that the total dispersion measureremains almost the same. In that case, D B k would be given by ∼ × p ( n / ) µ G. In previous sections we have estimated an average LOS sys-tematic magnetic field of ∼ µ G and a random field of 6 µ G.However, this does not address the overall magnetic field in thecentral one degree from the GC, which is described below.The observed magnetic fields in galaxies are rarely system-atic. This is due to turbulence, and the random component has afield strength that is about the same in magnitude as the system-atic field (Zweibel & Heiles 1997). In the GC region, a highlyturbulent magnetoionic media causes high scatter broadeningof extragalactic sources. Here we estimate the strength of thisrandom component in this region from our data, which willprovide an estimate of the strength of the systematic field. Asshown in Sect. 2.1.1, the outer scale of RM of sources in thisregion is about 40 pc, and we follow the same approach as inthe previous section for calculating the random magnetic fields.There are about 7 cells within a region of angular radius 1 ◦ cor-responding to a linear size of about 300 pc at a distance of 8.0kpc. With an electron density of 0.4 cm − in the region, if thereis a net LOS magnetic field of 1 milliGauss over a size scaleequivalent to the size of these cells, this region would intro-duce a RM of ∼ − . As the magnetic fields in thesecells are uncorrelated, the mean value of RMs towards sourcescould be small, but the rms value of RMs along different LOSswould be ∼ − . There are 6 source components inour sample seen through the central 1.1 ◦ from the GC, but wedo not find any of their absolute RMs to be significantly higherthan the mean RM from the whole sample. The estimated rmsRM from our sample is consistent with a random field of ∼ µ G in this central 300 pc region of the Galaxy. This suggeststhat the strong magnetic fields near the NTFs could only be alocal enhancement to the GC magnetic fields and does not fillthe entire 300 pc region.This outer scale is much larger than the measured sizescale of the Faraday screen of ∼ ′′ (0.4 pc) towardsthe GC NTFs G359.54+0.18 (Yusef-Zadeh et al. 1997) and Snake (G359.1 −
4. Conclusions
To study the properties of the Faraday screen near the GC, wemeasured RMs towards 60 background extragalactic sourcesthrough the − ◦ < l < ◦ , − ◦ < b < ◦ region of the Galaxy.To our knowledge, this provides the first direct determinationof large-scale magnetoionic properties of the central 1 kpc re-gion of the Galaxy not biased by NTF environments. We finda large-scale LOS magnetic fields that point towards us. Eitherthe bisymmetric spiral model of magnetic field in the Galaxy orthe magnetic-field lines that are mostly aligned with the centralbar of the Galaxy could explain a largely positive RM in thecentral 1 kpc of the Galaxy. This large-scale magnetic field hasa lower limit of 0.6 µ G along the LOS. The outer scale of theRM structure function is about 40 pc. The RM structure func-tion is well-fitted with a power law index of 0.7 ± ∼ µ G along with electron den-sity fluctuation could explain the observed RM structure func-tion in the central 1 kpc of the Galaxy. However, in the inner300 pc, the maximum random component of the magnetic fieldis estimated to be ∼ µ G. Since GC region has a highly turbu-lent ISM, this random magnetic field is very likely have a sim-ilar strength to the systematic field. The observed outer scaleof the magnetoionic medium in this region also does not ap-pear to be less than what is determined from the whole sample( ∼
40 pc). This is much larger than the scale size of the RMstructure function ∼ ′′ (0.4 pc) observed near the NTFs inthe GC. This indicates that properties of the Faraday screen inthe GC is very different from what is found close to the NTFs.The milliGauss magnetic fields estimated near the NTFs arelocalised and do not pervade the central 300 pc of the Galaxy.A more detailed investigation of the magnetic field involvingbackground sources several times more than the present studywould, however, be required to make a model of the magneticfield configuration in the region. Acknowledgements.
We thank Rajaram Nityananda for introducingthe Bootstrap technique to us. We also thank the anonymous refereewhose comments helped to improve the quality of the paper.ubhashis Roy et al.: Magnetic field near the Galactic centre region 9
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