D O I: 10.1051/0004-6361/201630008
© E S O 2017
Astronomy
&
Astrophysics
Radiative age mapping of the remnant radio galaxy B2 0924+30:
the LOFAR perspective*
A. Shulevski1,2, R. Morganti1,2, J. J. Harwood1, P. D. Barthel2, M. Jamrozy3, M. Brienza1,2, G. Brunetti4, H. J. A. Rottgering5, M. Murgia6, G. J. W hite7,8, J. H. Croston9, and M. Bruggen10
1 ASTRON, The Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA Dwingeloo, The Netherlands e-mail: s h u le v s k i@ a s tro n .n l
2 University of Groningen, Kapteyn Astronomical Institute, Landleven 12, 9747 AD Groningen, The Netherlands 3 Obserwatorium Astronomiczne, Uniwersytet Jagiellonski, ul Orla 171, 30-244 Kraków, Poland
4 IRA-INAF, via P. Gobetti 101, 40129 Bologna, Italy
5 Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands 6 INAF-Osservatorio Astronomico di Cagliari, via della Scienza 5, 09047 Selargius (CA), Italy
7 Department of Physics and Astronomy, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK 8 RAL Space, The Rutherford Appleton Laboratory, Space Science and Technology Department, Chilton, Didcot,
Oxfordshire OX11 0QX, UK
9 School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK 10 University of Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
Received 3 November 2016 / Accepted 5 January 2017
ABSTRACT
We have observed the steep spectrum radio source B2 0924+30 using the LOw Frequency ARray (LOFAR) telescope. Hosted by a z = 0.026 elliptical galaxy, it has a relatively large angular size of 12' (corresponding to 360 kpc projected linear size) and a morphology reminiscent of a remnant Fanaroff-Riley type II (FRII) radio galaxy. Studying active galactic nuclei (AGN) radio remnants can give us insight into the time-scales involved into the episodic gas accretion by AGNs and their dependence on the AGN host environment. The proximity of the radio galaxy allows us to make detailed studies of its radio structure and map its spectral index and radiative age distribution. We combine LOFAR and archival images to study the spectral properties at a spatial resolution of 1 ' . We derive low frequency spectral index maps and use synchrotron ageing models to infer ages for different regions of the source. Thus, we are able to extend the spectral ageing studies into a hitherto unexplored frequency band, adding more robustness to our results. Our detailed spectral index mapping, while agreeing with earlier lower resolution studies, shows flattening of the spectral index towards the outer edges of the lobes. The spectral index of the lobes is «649 ---1 and gradually steepens to «109---- 1.8 moving towards the inner edges of the lobes. Using radiative ageing model fitting we show that the AGN activity ceased around 50 Myr ago. We note that the outer regions of the lobes are younger than the inner regions which is interpreted as a sign that those regions are remnant hotspots.
We demonstrate the usefulness of maps of AGN radio remnants taken at low frequencies and suggest caution over the interpretation of spectral ages derived from integrated flux density measurements versus age mapping. The spectral index properties as well as the derived ages of B2 0924+30 are consistent with it being an FRII AGN radio remnant. LOFAR data are proving to be instrumental in extending our studies to the lowest radio frequencies and enabling analysis of the oldest source regions.
Key words. galaxies: active - radio continuum: galaxies - galaxies: individual: B2 0924+30
1. Introduction
A lthough active galactic nuclei (AG N ) have been observed to influence their surrounding interstellar and intergalactic m edium (ISM /IG M , M cN am ara & N ulsen 2 0 1 2 ; R andall et al. 2010), the im pact this m ay have depends on a n um ber o f relatively p o orly know n factors, in p articular the duty-cycle o f the activity, i.e. the portion o f tim e the super m assive b lack hole (SM B H ) is active (M endygral et al. 2012) .
T racers o f p a st A G N accretion episodes can b e observed at radio w avelengths. In the case o f rad io -lo u d A GN, their ages (and duty cycle in the case o f restarted sources) can b e d e
rived using th e spectral properties o f the rad io plasm a. O nce the
* The LOFAR and WSRT images used to derive the spectral index and ageing maps are available at the CDS via anonymous ftp to c d s a r c . u - s t r a s b g . f r ( 1 3 8 .7 9 .1 2 8 .5 ) or via
h t t p : / / c d s a r c . u - s t r a s b g . f r / v i z - b i n / q c a t ? J / A + A / 6 8 8 / A 6 5
accretion o f m a tte r onto its S M B H stops, the ejection o f plasm a jets ceases, term inating the supply o f fresh electrons into th e ra dio lobes. T h ese synchrotron radio rem n an t regions then slow ly fade as tim e passes ow ing to p referential cooling o f high energy particles and/or adiabatic expansion. C onsequently, their spectral index steepens ( a < - 1 ) 1, and breaks appear in th e rad io spec
trum (K ardashev 1962; P acholczyk 1970; Jaffe & P e r o la 1973;
K om issarov & G ubanov 1994) . I f the rad io em ission restarts (as observed in a n um ber o f cases) this w ould further m odify the shape o f the so u rce’s radio spectrum (M urgia e t a l. 2011) and m ay influence the so u rce’s m orphology.
Thus, rad io studies enable us to identify the presence and the tim escales o f this type o f cycle o f activity. Selecting ra dio sources th at have a steep spectral index over a ran g e o f frequencies is the pred o m in an t w ay o f discovering A G N radio
1 We define the spectral index as: S ~ va .
rem n an ts2, i.e. sources in w hich the radio source has sw itched off. H ow ever, the question rem ains as to w hy there are so few rem nants detected (a few dozen in total) relative to th e entire p opulation o f active rad io galaxies.
B ecause o f the steepness o f the spectrum , the low ra
dio frequency observational w indow is the one w here rem nants can b e m o re easily detected. F or this reason, th e recent availability o f new deep im ages from th e low frequency ar
ray (van H aarlem et al. 2013) has revam ped th e search and the study o f these objects. T he first searches w ith L O FA R have a l
ready provided pro m isin g results w ith th e percentage o f rem nants ranging betw een 10% and 30% (B rienza e t al. 2 0 1 6 a;
H ardcastle e t al. 2016) . T hese observations are starting to p u t constraints on radio galaxy evolution m odels an d are helping us to understand w h at the relevant p hysical processes involved in rem nant evolution are.
A p rerequisite for the com plete characterization o f the A G N duty cycle is the determ ination o f th e active and sw itched off tim es o f individual objects over a statistically significant sam ple. In studies o f several d ouble-double rad io galaxies (D D R G s), K onar e t a l. (2013) and O r r u e t a l. (2015) find th at they have a relatively rap id duty-cycle w ith the tim e elapsed betw een the periods o f activity being a fraction o f the total age o f the source. B o n a fide rem nants can show a total ag e o f over a h u n dred M yr (H arris et al. 1993; V enturi et al. 1998; Jam rozy et al.
2 0 0 4 ; G iacintucci e t al. 2007) . T he duration o f their rem nant p hase in m o st cases appears to b e shorter o r com parable to that o f th e active p hase (P arm a e t a l. 2 0 0 7 ; M u r g ia e ta l. 2 0 1 1 ; D w arakanath & K ale 2 0 0 9 , respectively). C ases w here the re m n an t p hase is (m uch) longer than the active p hase are, so far, rarer (e.g. B rienza e t a l. 2016b) . T he duty cycle likely has a d epen
dence on galaxy m ass and source p ow er during the active phase, as suggested by statistical studies (B est et al. 2 0 0 5 ; S habala et al.
2008) .
D etailed rem nant studies have so far been lim ite d to ju s t a few cases and have often n o t been carried o u t at sufficiently high spatial resolution to enable th e investigation o f the radiative ages across the sources, and o f th eir activity histories.
A n o bject th at offers this p o ssibility is B 2 0924+ 30, the tar
get o f this paper. Its host, IC 2476 (U G C 5043), is the b rig h t
est m em b er o f th e relatively po o r Z w icky cluster 0926.5+ 30.26 (C ordey 1987; E kers et al. 1981; W hite e t al. 1999), w hich is lo cated at a red sh ift o f z = 0.026141. Its S loan D igital Sky S ur
vey (SD SS; A ih a r a e ta l. 2011) spectrum does n o t show em is
sion lines indicative o f an optical AGN. T he radio lum inosity3 o f B 2 0 9 2 4 + 3 0 is L 1400 Mhz ~ 1023 8 W H z -1 . It lacks a d iscernible radio core o r jets/h o tsp o ts and is considered to b e an A G N re m n an t by C ordey ( 1987) . Spectral index studies by Jam rozy et al.
(2 004) show that the spectral index steepens going from the lobes to the inner regions, an d th e overall spectral index distribu
tion is steeper ( a ~ - 1 ) than th at observed in m o st active radio galaxies.
Jam rozy et al. (2004) have also p erfo rm ed a radiative ageing analysis o f B 2 0 9 2 4 + 3 0 and find an overall average source age o f 54+11 Myr.
W-e expand on previous research efforts b y extending the spectral index studies to even lo w er radio frequencies. U sing L O FA R w e have derived the highest spatial resolution spectral 2 To distinguish radio sources produced by past AGN activity, as opposed to steep spectrum sources found in galaxy clusters (relic, phoenix) we name the former AGN remnants.
3 The adopted cosmology in this work is: H0 = 73 k m s-1 Mpc-1,
^ a t t er = 0.27, Ą ,acl,um = 0.73. At the redshift of B2 0924+30, 1" = 0.505 kpc; its luminosity distance is 109.6 Mpc (Wright 2006).
Table 1. LOFAR HBA data properties.
C hannels p er SB (192 kH z) 64
C entral frequency 150 M H z
B andw idth 63.5 M H z
Integration tim e 2 s
O bservation duration 7.5 h
P olarization F ull Stokes
U V coverage 0 .1 - 2 0 k d
index m apping to date extending to 140 M H z, enabling us to characterize in detail the spectral properties o f the rem nant lobes.
O ur aim is also to perfo rm a resolved radiative age m apping o f the source to b etter ascertain its activity history.
T he organization o f this p aper is as follow s. S ection 2 d e
scribes th e data used in this study and outlines the data reduction procedure. S ection 3 outlines ou r results; in Sect. 3.1 w e present the spectral analysis results and w e discuss the derived source ages in Sect. 3 .2 . W e discuss the im plications o f ou r study in Sect. 4 .
2. Observations and data reduction
T he target w as observed w ith the L O FA R high b an d antennas (HBA ) on the n ig h t o f M arch 13, 2014, fo r a total on source tim e o f 7.5 h. T he observations w ere obtained in th e interleaved m ode, using the full D utch array o f 38 antenna stations. T he tw o H BA antenna fields o f each o f the core stations w ere treated as separate stations and o f the H BA fields o f the rem ote stations only th e inner tiles w ere u sed (this configuration is kno w n as H B A _D U A L _IN N E R ). 3C 196 w as observed as a flux calibrator source for tw o m inutes, follow ed b y a scan o f the target o f 30 m in duration w ith a one m inute gap betw een calibrator and target scans th at allow ed for beam form ing an d target re-acquisition.
W e recorded 325 sub-bands (SB s), over the 63.5 M H z o f b an d w idth betw een 116 M H z and 180 M H z. E ach SB has 64 fre
quency channels and a b andw idth o f 195.3 kH z. T he integration tim e was set to 2 s for both calibrator an d target. F our p o la r
izations w ere recorded. T he H BA station field o f view (FoV, p ri
m ary beam ) covers around 5 degrees full w idth at h a lf m axim um (FW H M ) a t 140 M H z. T he station beam s are com plex valued, tim e, frequency and direction dependent, an d are n o t the sam e for all o f th e stations.
T he data w ere pre-processed b y the observatory pipeline (H e a ld e ta l. 2010) as d escribed below. E ach SB w as au to m at
ically flagged for rad io frequency interference (R FI) using the A O Flagger (O ffringa et al. 2012) , and then averaged in tim e to 10 s p er sam ple and in frequency b y a factor o f 16, m a k ing the frequency resolution o f the o utput data 4 channels/SB . T he calibrator data w ere u sed to derive am plitude solutions for each (D utch) station using the B lackboard se lf calibration (BBS, P andey e t al. 2 0 0 9 ) tool th at takes into account the LO FA R sta
tion beam s variation w ith tim e and frequency. T he flux density scale o f Scaife & H eald (2012) w as u sed in th e calibration m odel for 3C 196 ( S 150 = 83 Jy).
T he am plitudes o f the target visibilities w ere corrected using the derived calibrator solutions. T he target visibilities w ere then ph ase-(self)calibrated increm entally, using progressively longer baselines to obtain the final (highest) im age resolution. The initial p hase calibration m o d el was derived from the V L S S4 4 VLSS is the VLA Low frequency Sky Survey carried out at 74 MHz (Cohen et al. 2007).
Table 2. Image properties.
ID v [MHz] <r [mJy/b] B eam size LO FA R a 113 8.3 | 4.5 5676 X 4 0 79 12072 x 14'/1 LO FA R a 132 4.3 | 3.1 4 8 " x 3574 12 2 " x 1677 LO FA R a 136 4.3 | 3 4 6 79 x 3473 12177 x 17'/1 LO FA R a 160 2.3 | 1.9 5179 x 3776 12 0 " x 1779 LO FA R a 163 2 | 1.8 5676 x 3872 12072 x 1778 LO FA R a 167 1.8 | 1.7 517 1 x 3775 12075 x 1775
L O FA R ac 140 2.5 | 1.2 6 0 " x 43 75 12 2 "
W EN SS 325 3.6 5 4 " x 108"
W S R T b 609 0.77 2 9 " x 56 "
N V SS 1400 0.45 4 5 "
Notes. The image noise and beam size are given for the low and high resolution images respectively. (a) This w o rk ;(b) Jamrozy etal. (2004);
(c) averaged image.
catalogue th at covers th e F oV o u t to th e first null o f the station beam , w hich contains spectral index inform ation for each source in th e m odel. B efore initializing the calibration, w e concatenated the d ata into 4 M H z (20 SB) groups previously averaging each SB to 1 frequency channel to reduce the d ata size. W e chose this set-up to m axim ize the S/N w hile m aintaining frequency- d ependent ionospheric p hase rotation to a m an ageable level. In the calibration, w e neglected direction-dependent effects (iono
sphere and residual clock errors on lo n g e r baselines). However, since ou r target is in th e p hase center o f the FoV, these issues do n o t rep resen t a lim it to ou r science goals (as dem onstrated below ).
T he im aging was p erform ed using the L O FA R AW im ager (T a s s e e ta l. 2013) , w hich incorporates the LO FA R beam and uses the A -projection (C handra et al. 2004) algorithm to im age the entire FoV. W e used B riggs (B riggs 1995) w eights w ith the robustness p aram eter set to 0 , and im aged by selecting b a se lines larger than 0.1 kA. Ten self-calibration steps w ere p er
form ed, each using a sky m o d el g enerated in the previous cy cle and each subsequent one using larger baseline lengths. The self-calibration resulted in im ages th at cover th e H BA band, out o f w hich w e selected a low - an d a high-resolution one (only im ages n o t affected b y calibration errors)5.
W e sm oothed th e high- an d low -resolution L O FA R im age sets to an identical restoring beam size and averaged them to o b tain tw o averaged im ages, each having a b andw idth o f 28 M H z.
W e used these im ages for m o rphological studies o f the target source. T he sm oothed, individual im ages w ere used in our a g e
ing analysis. Table 2 lists the im age properties fo r the LO FA R im age set, as w ell as survey (W E N S S6 and N V S S7) im ages used in o ur subsequent analysis.
To check w hether the station b eam correction applied by th e AW im ager resu lted in correct flux-density scaling across the FoV, w e have the P yB D S M source finder package 5 The selection resulted in six high-resolution and six low-resolution images.
6 WENSS is the Westerbork Northern Sky Survey carried out at 325 MHz (Rengelink et al. 1997).
7 NVSS stands for the NRAO VLA Sky Survey carried out at a fre
quency of 1400 MHz (Condon et al. 1998).
Fig. 1. Ratio of measured and catalogue extrapolated flux densities for our high- and low-resolution averaged LOFAR images.
(M ohan & R afferty 2015) and have extracted p o in t sources from our averaged im ages. T hen, w e m a tch e d the extracted sources w ith survey catalogs (V LSS, W EN SS and N V SS using a 30 "
m atch radius) an d determ ined the catalogue flux density for each source b y interpolating the flux densities from th e catalogue en tries to th e L O FA R frequency. Finally, w e divided the obtained catalogue flux density a t 140 M H z w ith the m easu red flux d en sity from the L O FA R im age. A ssum ing pow er-law spectra, the ratio should be unity if the station b eam correction gives cor
rect fluxes over the FoV. T he results are given in F ig. 1. W e can see th at for b oth o f the H BA im ages the points cluster around 1, w hich shows that the flux correction over the F oV applied b y the AW im ager gives reasonable flux-density values. T he scatter is around 20% .
O w ing to an in com plete H B A beam m odel, the influence o f the grating side-lobes was n o t properly taken into account during processing, w hich results in a system atic bias in the m easu red source fluxes across the LO FA R band. This show s up
Fig. 2. LOFAR FoV, centred on B2 0924+30, low-resolution image averaged over a band
width of 28 MHz. Beam size: 60" x 43'.'5, a = 2.5 mJy beam-1.
as a system atic steepening o f th e in-band spectral index. W e ap p lied a LO FA R b eam norm alization correction factor to th e m e a
sured flux densities to m itigate th e effect.
3. Results
F igure 2 show s the low -resolution 5° x 5° LO FA R im age o b tained by sm oothing and averaging together six im ages taken across the L O FA R b an d (listed in Table 2) . It has a resolution o f 6 0 " x 4 3 "5 and an rm s n o ise level o f 2.5m Jy b ea m - 1.
F igure 3 show s the L O FA R view o f the target in the-high re s olution (2 2 ") averaged im age (see Table 2 ) . W e no te increased surface brightness regions (> 3 0 m Jy b ea m - 1) w ithin the lobes that are located on opposite sides o f the host galaxy. A lso, there is an enhancem ent o f surface brightness around the position o f th e host galaxy. T he source is enveloped in a low er surface brightness cocoon.
S everal sm aller regions o f increased surface brightness are n o ticeable w ithin the rad io lobes (see Fig. 3b) . Two o f them in th e n orth-east (N E) lobe can b e identified w ith b a c k ground/foreground galaxies.
A p oin t source located off th e outerm ost edge o f th e SW lobe has been identified w ith a q uasar (E kers e t al. 1981) .
T here is n o n o ticeable radio core at the positio n o f the host galaxy as ascertained from our high-resolution im aging and im ages w ith 1" resolution o btained by C ordey ( 1987) at 5000 M H z.
G iovannini et al. ( 1988) place an u pper lim it on the core flux density o f S 49oo MHz < 0.4 m Jy w hich, in relatio n to th e total sur
face brightness, hints a t th e rem nant n ature o f the rad io source.
3.1. Spectral analysis
T he m orphology o f B 2 0 9 2 4 + 3 0 supports its classification as A G N rem nant, fading aw ay after the A G N w hich has created it has shut dow n. H ere, w e elaborate on its spectral properties.
T he shape o f th e integrated flux spectrum encodes th e activity history o f a given radio source and can b e a pow erful tool in understanding th e exact n ature o f the observed radio em ission.
3.1.1. Integrated spectrum
Ja m ro z y et al. (2004) fitted a synchrotron ageing m odel to data collected from th e literature as w ell as their ow n observations.
W e repeated the fitting p rocedure, adding the integrated flux d en sity m easured from ou r averaged LO FA R m ap. A n overview o f the m easurem ents is given in Table 3 .
T he m agnetic field strength w as derived by assum ing an equipartition betw een the energy contained in th e m agnetic field and in relativistic p articles according to M iley ( 1980) . In o u r cal
culations, w e u sed a central frequency o f 609 M H z, w ith a spec
tral index o f a = - 1 .2 (average over the source) and lobe ex ten t o f 4.8. T he cut-off frequency values for the calculation w ere taken to b e 10 M H z and 10 000 M H z, and the electron to p ro ton ratio was set to unity. W e com puted the m agnetic field value for each lobe separately and then averaged the result. O ur e sti
m ate gives a value o f 1.35p G (sim ilar to w hat is found for other rem nant sources; M urgia e t al. 2 0 1 1 ; B rienza et al. 2016b) .
I f w e im pose a low energy cut-off in th e p article spectrum , instead o f a low frequency cut-off in the em itted synchrotron radiation spectrum , for the m agnetic field (B runetti e t al. 1997) w e get
b = 1. 18 rm0n3<3) ( b ') 0-8(3) , (1)
(b) B2 0924+30 LOFAR HBA contours overlaid on an SDSSr image.
Fig. 3. B2 0924+30: LOFAR image obtained by averaging the higher resolution HBA images. Beam size: 22" x 22", t = 2 mJy beam 1. Contour levels: (-3 ,3 , 6,9,12,15) x 2 mJy beam-1.
w here B ' is th e equipartition m agnetic field th at w as calculated previously and Ymin th e low -energy cut-off value. F or y min = 1450, B = B ', w hile for Ymin = 500, B = 1.91 u G (30%
larger). C hoosing an energy cut-off value is som ew hat arbitrary.
B ased on equipartition argum ents, Jam rozy et al. (2 0 0 4 ) d erive a value o f B = 1.6 u G . W e therefore d ecide to adopt th e equipar
titio n value that w e initially derived and assum e a m agnetic field strength o f B = 1.35u G for all subsequent analysis.
W e fitted a continuous-injection m odel w ith an off phase (KGJP, K om issarov & G ubanov 1994) to th e integrated flux den sity m easurem ents. B ased on a m odification o f th e expression found in Shulevski et al. (20 1 5 ) , th e p article distribution fu n c
tio n is
Table 3. B2 0924+30 flux density.
v [MHz] S v [mJy] Ref.
140 6306 ± 1261 1
151 46 0 0 ± 360 2
325 2425 ± 124 1 ,5
609 1094 ± 56 1 ,3
1400 4 2 0 ± 43 3
4750 60 ± 7 3
1 0 5 5 0 10 ± 4 4
N (toff, ton, b,Y, E ) =
£ - ( Y + 1 )
References. (1) this work; (2) Cordey ( 1987); (3) Jamrozy et al. (2004);
(4) Gregorini et al. ( 1992); (5) Rengelink et al. ( 1997).
* (r-1 )((1 -* E « off )Y-1- ( 1 -b E ( f0n +toff ))Y-1) E“(Y+1)
b(y-1)(1-bEtoS )Y-1
for
for
for
E < 1
1
b ( t o n + t o f f ) b ( t on + t o ff )
T h e observed flux density is given b y:
btoff
S (v) = S 0 E > b7 - ,b toff ’VV/ '
F (x) x -15 N (x)dx, (4)(2) w here, to n and toff are th e active phase d uration and th e tim e elapsed since source shut-dow n, b is a te rm describing th e en ergy losses o f th e particles, and E ~ y fv jx is th e energy o f the particles. x = v /vb represents th e so-called scaled frequency. W e assum e a ran g e o f scaled frequencies, i.e. w e do n ot fit for the break frequency explicitly. T he energy-loss te rm w as ta k en to be th e one described by Jaffe & P erola ( 1973) ; h ence th e JP suffix in th e m odel label
b ~ B 2 ( Big \
3 + ( B ) (3)
w here Big = ^ |b gmb is th e effective inverse C om pton m ag n etic field, and Bgmb = 3.25(1 + z)2 is the equivalent cosm ic m icrow ave b ackground (C M B ) m agnetic field.
w here S 0 represents a scaling factor, F (x ) = x K5j3(z)dz is defined by P acholczyk ( 1970) an d K5/3 is the m odified B essel function.
T he K G JP m odel is w arranted since th e integrated flux d en sity includes contribution from form erly active source regions w here particle acceleration w as ongoing.
T he best-fit values for th e tim e during w hich th e source was active and th e tim e elapsed since th e p article in jection has ceased (tim e since shut-dow n) w ere found to be: ton = 55.65 ± 2.25 M yr and toff = 32.04 ± 1.57 M yr respectively. W e assum ed th at the m agnetic field is constant in tim e an d over th e source extent and w e neglect adiabatic losses. T he best-fit value for th e injection spectral index (the spectral index o f th e particles im m ediately after they w ere accelerated/energized) w as found to b e a ^ j = -0 .8 5 + 0 1 W e u se d th e K apteyn p ackage (Terlouw & Vogelaar 2012) for th e m odel-fitting. T he m odel acceptance criteria are identical to th o se presen ted in S hulevski et al. (2015). O ur best fit-value for th e total source age is ts = ton + toff ~ 88 Myr.
0
(a) B2 0924+30 LOFAR HBA
Fig. 4. Best fit Komissarov-Gubanov JP (KGJP) model to the integrated flux density measurements. The red triangle represents the LOFAR data point.
O ur derived ages differ from those reported by Jam rozy et al.
(2004) o f 54-12 M y r (they also assum e a constant m agnetic field strength and neg lect adiabatic losses). W e are, however, in agreem ent w ith th eir derived value for the injection spec
tral index ( a inj = - 0 .8 7 ± 0.09). T he values w e derive for the epochs o f source activity are n o t directly com parable to those o f Jam rozy et al. (2004) since they u sed an ageing-only (JP) m odel in their integrated flux density spectral analysis. T he b e st m odel fit is show n in Fig. 4 . W hile the spectral curvature is expected for a rem n an t radio source, the steepness o f the injection spec
tral index (confirm ed by ou r L O FA R m easurem ents) is puzzling.
3.1.2. S pectral index and c u rva tu re m aps
To study the p lasm a properties in the rem nant lobes, w e have pro d u ced the highest resolution spectral index m ap o f B 2 0 9 2 4 + 3 0 at low frequencies to date. W e averaged together the low er resolution H BA im ages to a single low frequency im age (140 M H z) an d used the 609 M H z W S R T im age from Jam rozy et al. (2004) . T he d ata sets have a closely m atching U V coverage. T he spectral analysis input im ages w ere sm oothed to a resolution o f 6 0 " and registered to the sam e pixel size. W e d e
rived the spectral index in th e standard m anner, an d p ropagated the errors o f th e flux-density to g e t an estim ate o f the error in d e
term ining the spectral index. W e assum ed th at the flux-density errors in both m aps are uncorrelated. W e d id this for each pixel above a !<r level in the inp u t im ages.
In F igs. 5a and b, w e can see th at th e spectral index in the lobes varies from a ~ - 1 .4 at th eir inner edges, to a < - 0 .7 5 at th e outer edges. T he average value for the integrated spectral index o f the source is relatively steep at low frequencies, around a ~ - 1 , in agreem ent w ith previous studies (Jam rozy et al.
2004), as w ell as w ith the injection spectral index w e obtained previously from fitting the integrated spectrum in Sect. 3.1 .1 .
W e observe th at the lobes have steep spectral index values that flatten o u t going tow ards the outerm ost lobe edges; this is especially p rom inent in the N E lobe.
W e also derived a spectral curvature m ap (SPC = a <109-a(1400) in an analogous fashion to the spectral index m ap,
using an N V SS survey 8 im age o f the target as the highest fre
quency d ata point. W e derived the spectral curvature for pixels above a 3 ^ level in all o f the inp u t im ages, to be able to m ap the regions around th e host galaxy. T he results are show n in F igs. 5c and d.
In lin e w ith o ur previous discussion, the curvature m ap provides interesting insights into th e spectral properties o f the source. T he rem n a n t lobes reveal m ore structure, w ith som e ar
eas show ing large curvature up to SPC = 1. This suggests that different regions have spectral breaks at different frequencies, w hich indicates different radiative ages. F o r exam ple, the lateral lo b e edges show pron o u n ced spectral steepening at higher fre
quencies.
3.2. Radiative ages
To gain a b etter insight into the activity history o f the rad io source, w e took o ur averaged L O FA R im age, together w ith an 609 M H z W S R T im age and an N V SS survey m ap (Table 2 ), and fitted a JP ageing-only m odel w ith a p article distribution function:
N (toff, b, y, E ) =
( E -Y(1 - bEtoff)Y-2 for E < b ff
i 0 for E > btff,
to p roduce an age m ap fo r the source, show n in F ig. 6 . T he in je c
tion index w as n o t fitted for; its value w as fixed to th e one found ( a inj = - 0 .8 5 ) during the integrated flux density spectrum - fitting in Sect. 4 . T he m agnetic field strength used w as also the sam e as w e u sed earlier, B = 1.35 uG .
A g e m apping provides m ore inform ation com pared to age- m odel fitting to integrated flux-density m easurem ents fo r a given source. In the case o f B 2 0924+ 30, for the y o ungest regions at the edges o f th e lobes w e determ ined an age o f around 50 M yr;
the source age increases as w e lo o k tow ard th e h o st galaxy; the lo b e inner edges show ages o f up to 120 M yr, and the center r e gions around 150 M yr. T hese findings are in agreem ent w ith the ageing profile rep o rted by Jam rozy et al. (2004) . S ince w e fit
ted an ageing-only m o d el (JP), w e have an estim ate fo r the tim e elapsed since th e p lasm a was la st energized across the source.
C onsequently, for resolved sources, w e can estim ate th e d u ratio n o f their active p h ase as the difference betw een th e o ld est and y o ungest ag e read -o ff from the m a p : ton = tmax - tmin.
F or B 2 0924+ 30, w e find an active p hase duration o f around 100 M yr. F urtherm ore, th e elapsed tim e since th e shut-dow n is given by th e youngest age found (toff = tmin) and, in the case o f B 2 0924+ 30, this is found to be around 50 Myr.
T he age m apping w as done w ith a m o re lim ited spectral cov
erage than the integrated spectral index fit w hich w e perform ed in Sect. 3.1 .1 . T he reason is th at the available m aps at freq u en cies h igher than 1400 M H z w ere o f low er resolution (> 1 ') and less sensitive to extended em ission. E ven so, the m apping shows th at (as expected) the source ag e derived from a (K G JP) m odel fit to the integrated spectrum is only an estim ate for the total source age.
8 The NVSS image (Table 2) is missing flux on large angular scales.
The integrated flux-density value at 1400 MHz that we use (Table 3) is taken from Jamrozy et al. (2004), who used single dish Effelsberg tele
scope measurements to correct for the loss. Based on inspection of the corrected image (Fig. 5a in Jamrozy et al. 2004), we conclude that our spectral curvature and ageing derivation (for the lobe and core regions) is not affected by us using the uncorrected NVSS map.
(5)
Fig. 5. Spectral index and spectral curvature maps for pixels with surface brightness greater than 7 a and 3 a , respectively, in all of the input maps.
We used the averaged low-resolution LOFAR image (Table 2). Overlaid are LOFAR contour levels spanning the interval between - 1 0 a and 60a, with a step of 10a, where a = 4 mJy beam-1. The black cross indicates the position of the host galaxy.
Fig. 6. Radiative ages and age errors derived from fitting an ageing-only model using a JP-loss term to the data for a inj = -0.85. Contours are the same as in Fig. 5.
Fig. 7. X values of the model fit (measuring the goodness of the fit for one degree of freedom), as defined in Shulevski et al. (2015). Contours are the same as in Fig. 5 .
T he source age w e derived using age m apping is around tw o tim es h igher than th e age obtained b y m o d el fitting to the in te grated flux-density m easurem ents rep o rted in Sect. 3.1 .1 .
T he ages derived for the inner lobe regions o f B 2 0 9 24+ 30 are com parable to the oldest sources in, for exam ple, the sam ple of M u rg ia e t al. (2011) .
3.3. Spectral shifts
Investigating the source energetics can b e done in an an alo gous m anner to the spectral curvature m ap (Fig. 5 c) b y plotting the low - an d high-frequency spectra in a “c o lo u r-c o lo u r” plot (K atz-S tone e t al. 1993) . This approach enables us to visualize the spectral shapes o f different source regions an d com pare them w ith (spectral) ageing m odels.
To this end, w e p erform ed the analysis on the sam e data set w e used in the ageing m o delling, described above. F orty-one m easurem ent regions w ere u sed (show n in F ig. 8, top left panel);
their spectra w ere p lotted on the a 10o - a 6o9° colour-colour plane.
In the sam e plot, w e show the loci o f points occupied by d ifferent ageing m odels, as w ell as a sim ple pow er law. T he distribution o f points that rep resen t th e regions shows th at the spectral shape, for m o st o f them , is b e st fitted b y synchrotron radiation from an aged p lasm a (Fig. 8, top rig h t panel).
W e can reco n stru ct the global spectrum o f the source by shifting the spectra (in th e lo g (S ) - log(v) plane) o f each region so that, finally, all o f the spectra line up. W e p erform th e shifting by choosing a reference region and aligning the spectral breaks o f the rem aining regions w ith the b reak o f the chosen region.
T he spectral breaks w ere com puted b y follow ing the expression given b y K ardashev ( 1962) :
Vb * 3.4 x 105B -3 t f f (6 )
w here v is expressed in G H z, B in u G , an d t in M yr. This tech nique has been im plem ented in a n um ber o f cases, for exam ple van W eeren et al. (2012), and it has the advantage o f extending the spectral analysis over a w ider ran g e in frequency. I f there is a g lobal electron energy distribution across the source, the spec
tra o f the individual regions trace it, and the differences betw een
them are due to energy losses (radiative, adiabatic), m agnetic field variations, and variations in electron density. B y shifting the spectra, w e account for these effects. T he shift results are given in F ig. 8 (bottom right panel).
T he am ount o f shift n eed ed in the flux density-frequency plane p e r region is show n in Fig. 8 (bottom left panel). W e see th at the shift values lie on a straight line; this is a strong indicator th at the spectral shape o f the regions is d o m inated by radiative losses. I f w e sam ple regions w ith sim ilar p hysical conditions, the slope o f th e fit represents th e injection spectral index. In our case, th e slope value is - 0 .85, w hich is in line w ith the best-fit injection spectral index th at w e arrived a t in Sect. 3.1.1, w hich provides inner consistency to ou r analysis.
4. Discussion
B 2 0 9 2 4 + 3 0 is an A G N rad io rem nant, a leftover from the tim e w hen it was an active radio galaxy. T he rem nant rad io lobes are very w ell outlined, w hich m ay indicate confinem ent by the IGM . O ur analysis shows that th e y o ungest p lasm a is located at the outer lobe edges. R egions closer to the host galaxy are p ro g re s
sively older, an d the diffuse rad io em ission at th e position o f the host galaxy (noticeable in the L O FA R im age) is the o ldest region o f the source. T here is n o sign o f restarted A G N activity.
In Sect. 3 w e p erform ed a d etailed spectral index, curvature, and ageing analysis, m apping these quantities w ith th e h ig h est spatial resolution to date (extending to low frequencies) and com paring our results to previous studies. W e found th at the values derived for the spectral age using integrated flux density m easurem ents are higher than values obtained in previous stud
ies. T he injection spectral-index values are in agreem ent w ith the literature and p o in t to a steeper ( a inj 0.85) injection index than is usually assum ed.
C om paring o ur low frequency spectral index m ap (Fig. 5a) w ith studies p erform ed using higher frequency data (Jam rozy et al. 2004) , w e in fer th at the lobe spectral index is som ew hat flatter; this is m o st p ronounced a t the o uter edges o f the lobes.
A t the frequencies w e study w ith LO FA R, w e w ould expect that the spectrum is a pow er law th at is representative o f the in je c
tion spectral index. R ecent studies (H arw ood 2017b) have show n th at integrated flux-density m odels (incorporating a continuous injection phase) are unreliable in the recovery o f param eters.
T hey tend to depend on the frequency coverage and m ay p ro vide system atically higher values for th e injection spectral in dex. Further, determ ining the injection spectral index from the low -frequency spectrum alone is problem atic. H arw ood (2017a) show th at the h o tspot spectrum in m aps o f active sources is affected b y stochastic acceleration and/or absorption processes th at flatten the spectrum a t low frequencies. A t present, it is n o t know n how (or w hether) these processes reflect on rem nant hotspot regions in inactive radio galaxies. H ence, it is uncer
tain how accurately w e can determ ine the injection spectral in dex. In any case, w ithin the stated errors, the injection index is in approxim ate agreem ent w ith studies o f active radio galaxies (H arw ood et al. 2 0 1 5 , 2016) . F urtherm ore, sim ulations suggest (K apinska et al. 2015) th at th e observed integrated spectrum can steepen ow ing to m ixing o f electron populations.
T he appearance o f the core regions w ith their steepest spec
tral index, as w ell as the spectral index and age gradient, suggest th at B 2 0 9 2 4 + 3 0 is a fading F R II source; the y o ungest regions are found tow ards th e outer edges o f th e lobes, and the oldest are the regions tow ards the h o st galaxy. Taken together, these in ferences p o in t to the fact th at w e are observing source regions
Fig. 8. Top left: measurement regions overlaid on a LOFAR gray-scale map of the source. Top right: colour-colour plot. The colour of the plotted points indicates their high spectral index value, while their size is proportional to their low spectral index value. Here, a low = a ® and a high = a^400.
Bottom left: shift plot. The slope of the fit is -0.87 ± 0.01. Bottom right: total set of shifted data and a (JP) model fit for all of the regions. Data points belonging to a given region share the same colour.
w ith particles th at w ere last energized ju s t befo re source shut
dow n. O ur m apping suggests th at w e are seeing the rem nants o f hotspots w hich are p rom inent features in active F R II radio galaxies.
W e w ere able to estim ate a lim it to the duty cycle for B 2 0 9 2 4 + 3 0 using the duration o f the active and d orm ant p e riods th at w ere rea d off the derived age m aps. T he tim e elapsed since it has shut dow n is estim ated to b e h a lf o f that spent in an active phase. This is in line w ith the D D R G sources studied by K onar et al. (2013) th at w e m entioned earlier (w hich, m o r
phologically, appear to b e restarted F R II sources) and different from the case p resented in B rienza e t al. (2016b), w hich shows
a significantly shorter active com pared to dorm ant p hase and seem s to have F R I m orphology (L 1400 MHz = 1 .5 x 1 0 24 W H z -1 ).
T he spectral index and spectral ageing m aps w e produced n o t only support the claim th at this is an F R II A G N rem nant; the m odel fitting produces p lasm a ages th at are h igher than those derived using integrated flux density data.
T he discrepancies betw een the ages derived from the in te
grated flux density analysis an d resolved studies are m odel dependent. T he integrated flux density analysis averages over source regions w ith different physical properties and co n se
quently p article activity histories. Thus, the ages derived from
the integrated flux density analysis m a y b e different to th at found using age m apping.
In Sect. 3.3, w e show that the dom inant energy-loss m e ch anism s are inverse C om pton and synchrotron radiation, sug
gesting th at adiabatic expansion energy losses are negligible.
This hints at the p o ssibility that th e rad io p lasm a is som ew hat confined. T he presence o f a low significance, possibly extended ROSAT X -ray em ission detection that is associated w ith th e h ost galaxy (C anosa et al. 1999) m ay b e relevant in this regard.
T he fact th at w e can detect rem nant hotspots suggests that relatively short tim e has elapsed since source shut-dow n (esti
m ated a t 50 M yr).
T he paucity o f A G N radio rem nants m ay b e due to long A G N duty cycles (the tim e elapsed betw een active phases b eing longer than the rad io p lasm a lifetim e) and/or the rad io p la sm a ageing m ore rapidly ow ing to expansion losses.
A larger sam ple o f A G N rad io rem nants is n eed ed to put firm er constraints on these assum ptions.
5. Conclusions
We have used LO FA R to obtain im ages o f B 2 0 9 24+ 39 a t low frequencies w ith the highest spatial resolution yet obtained for this source. This has enabled us to pro d u ce detailed spectral in dex m aps and derive radiative ages over the extent o f th e source.
We confirm ed p revious inferences (Jam rozy et al. 2004) th at are consistent w ith this source being a F R II rem nant. W e have also show n th at there is a continuum o f ages th at increase from the outer lobes to the regions at th e p osition o f the host galaxy.
In addition, w e have dem onstrated the detection o f re m nan t h otspot regions a t th e o uter lo b e edges, further support
ing the F R II n ature o f this source. This resu lt highlights the value o f high-resolution, high surface-brightness sensitivity L O - FA R m aps obtained at low frequencies in studying rem nant radio galaxies, disentangling their n ature and activity history.
W e have show n th at age estim ates obtained from integrated flux density m easurem ents differ from those obtained using r e solved studies. This finding indicates caution; ages obtained by fitting m odels to integrated flux-density m easurem ents tend to be affected b y the activity history o f those sources, o r only provide lim its to the ages obtained b y m apping.
D etailed studies o f larg er sam ples o f A G N rem nants are n eeded to answ er the question as to w hether th e derived tim escales are typical an d co nsistent for this source type, and infer th e details o f their duty cycles.
Acknowledgements. The authors thank the anonymous referee for the use
ful comments and suggestions that helped improve this paper. LOFAR, the Low Frequency Array designed and constructed by ASTRON, has facili
ties in several countries that are owned by various parties (each with their own funding sources), and that are collectively operated by the Interna
tional LOFAR Telescope (ILT) foundation under a joint scientific policy.
R.M. gratefully acknowledges support from the European Research Coun
cil under the European Union’s Seventh Framework Programme (FP/2007- 2013)/ERC Advanced Grant RADIOLIFE-320745. G.J.W. gratefully acknowl
edges support from The Leverhulme Trust. This work has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propul
sion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This work has made use of python (w w w .python.org), including the packages numpy (www.numpy.org), scipy (van der Walt et al. 2011, w w w .scip y .o rg ) and IPython (Perez & Granger 2007). Plots have been produced with matplotlib (Hunter 2007). This research made use of Astropy, a community-developed core Python package for Astron
omy (Astropy Collaboration et al. 2013) This research made use of APLpy, an open-source plotting package for Python (Robitaille & Bressert 2012).
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