A Multi-Wavelength Study of the High Surface Brightness Hotspot in PKS1421-490

0.62 MB·English

by  L. E. H. Godfrey

Draftversion January22,2009
PreprinttypesetusingLATEXstyleemulateapjv.10/09/06
A MULTI-WAVELENGTH STUDY OF THE HIGH SURFACE BRIGHTNESS HOTSPOT IN PKS 1421–490
L.E.H. Godfrey1,2, G.V. Bicknell1, J.E.J. Lovell2,3,4, D.L. Jauncey2, J. Gelbord5,
D. A. Schwartz6, H. L. Marshall7, M. Birkinshaw6,8, M. Georganopoulos9,10, D.W.Murphy11,
E.S. Perlman9, D. M. Worrall6,8
Draft version January 22, 2009
ABSTRACT
9 Long Baseline Array imaging of the z=0.663 broad line radio galaxy PKS 1421–490 reveals a 400
0 pc diameterhighsurfacebrightnesshotspotataprojecteddistance ofapproximately40kpc fromthe
0 active galactic nucleus. The isotropic X-ray luminosity of the hotspot, L2−10keV =3 1044ergss−1,
2 ×
is comparable to the isotropic X-ray luminosity of the entire X-ray jet of PKS 0637–752, and the

n peak radio surface brightness is hundreds of times greater than that of the brightest hotspot in
a Cygnus A. We model the radio to X-ray spectral energy distribution using a one-zone synchrotron
J self Compton model with a near equipartition magnetic field strength of 3 mG. There is a strong

2 brightness asymmetry between the approaching and receding hotspots and the hot spot spectrum
2 remains flat (α 0.5) well beyond the predicted cooling break for a 3 mG magnetic field, indicating
that the hotspot≈emission may be Doppler beamed. A high plasma velocity beyond the terminal jet

] shock could be the result of a dynamically important magnetic field in the jet. There is a change
E
in the slope of the hotspot radio spectrum at GHz frequencies from α 0.5 to α . 0.2, which we
H ∼
model by incorporatinga cut-off in the electronenergy distribution atγ 650,with higher values
min
. implied if the hotspot emission is Doppler beamed. We show that a sharp≈decrease in the electron
h
number density below a Lorentz factor of 650 would arise from the dissipation of bulk kinetic energy
p
- in an electron/protonjet with a Lorentz factor Γjet &5.
o
Subject headings: galaxies:active – galaxies:jets – quasars:individual (PKS 1421–490)
r
t
s
a 1. INTRODUCTION that paper for the details of these observations and im-
[
PKS1421–490wasfirstreportedasabright,flatspec- ages.
1 Figure1 illustrates the arcsecondscaleradiostructure
trum radio source by Ekers (1969). Subsequent VLBI
v of PKS 1421–490; it is annotated to show the naming
imagingrevealed10masscalestructurewithinthebright-
2 convention for different components in the radio image
estcomponentofthissource(Preston et al.1989). Stud-
5 usedbyG05,aswellasthecorrectinterpretationofeach
ies at the Australia Telescope Compact Array (ATCA)
5 of these components brought out in this study. G05 ob-
later revealed significant radio emission on arcsecond
3 tained an optical spectrum of regionB, and suggestedit
scales extending south-west from the brightest compo-
.
1 nent (Lovell 1997). For this reason, PKS 1421–490 was wasnotassociatedwithanactivegalacticnucleus(AGN)
0 included in a Chandra survey of flat spectrum radio in view of the apparent lack of spectral lines (due to
9 poor signal to noise ratio in that spectrum). Region
quasars with arcsecond scale radio jets (Marshall et al.
0 A was known to contain bright VLBI scale radio struc-
2005). Gelbord et al.(2005)(fromhereonG05)reported
: ture (Preston et al. 1989) and had a flat radio spectrum
v onrecentX-ray(Chandra), optical(Magellan)andradio
(α<0.5). Region B was also known to be much weaker
i (ATCA) imaging of this source. We refer the reader to
X thanregionAatradiowavelengths. Consequentlyregion
r Electronicaddress: [email protected] A was thought to be an AGN, while region B was (erro-
a 1Research School of Astronomy and Astrophysics, Australian neously) interpreted by G05 as a jet knot. In this paper
NationalUniversity,Cotter Road,Weston, ACT,2611, Australia we show that in fact region B is the active galactic nu-
2Australia Telescope National Facility, CSIRO, P.O. Box 76,
cleus (see 3), and that regionA contains a high surface
Epping,NSW,2121,Australia §
3CSIRO, Industrial Physics, PO Box218 LindfieldNSW2070, brightness hotspot. The main focus of this paper is the
Australia interpretation and modeling of the exceptional hotspot
4School of Mathematics and Physics, University of Tasmania, in region A which has until now been interpreted as an
Tas7001,Australia
5Department of Physics, Durham University, South Road, AGN.
Durham,DH13LE,UK One of the major results of this paper relates to an
6Harvard-Smithsonian Center for Astrophysics, 60 Garden observed low frequency flattening in the hotspot radio
Street,Cambridge,MA02138,USA
spectrum at GHz frequencies, which indicates that the
7Kavli Institute for Astrophysics and Space Research, Mas-
underlying electron energy distribution flattens towards
sachusetts Institute ofTechnology, USA
8DepartmentofPhysics,UniversityofBristol,TyndallAvenue, lower energies. The low energy electron distribution is
BristolBS81TL,UK not only important for calculating parameters such as
9DepartmentofPhysics,JointCenterforAstrophysics,Univer-
the number density and energy density, it also provides
sityofMaryland-BaltimoreCounty,1000HilltopCircle,Baltimore,
MD21250,USA importantconstraints on the particle accelerationmech-
10NASAGoddard SpaceFlightCenter, MailCode660, Green- anism. Inturn,thiswillhelptoaddressmorefundamen-
belt,MD20771,USA tal issues such as jet composition and speed. We now
11JetPropulsionLaboratory,4800OakGroveDrive,Pasadena,
present a brief overview of the literature relating to the
CA91109, USA
2 Godfrey et al.
they inferred a cut-off Lorentz factor γ 500. All of
min
∼
the above listed γ estimates appear to be distributed
min
-49 13 48 Region A around a value of γmin 600. However, Blundell et al.
∼
(2006) and Erlund et al. (2008) have inferred the exis-
tenceofalowenergycut-offatγ &104inthehotspots
min
50 ofthegiantradiogalaxy6C0905–3955. Theirmethodof
detectingthelowenergycut-offisquitedifferenttothose
00) Hotspot describedabove,andisbasedontheinterpretationofan
20 52 absence of X-ray emission from the eastern hotspot and
J
N ( radio lobe in that source.
ATIO Jet + Lobe disItnri§b8utwioenshaotwγthat a t1u0r0n-ov1e0r0i0n cthane ealreicsteronnateunrearlglyy
N 54 min
CLI Region B fromdissipationofjet∼energy−ifthejethasahighproton
DE (BLRG Core) fraction and a bulk Lorentz factor Γjet & 5. However,
Stawarz et al. (2007) have suggested that the low fre-
56
quency flattening in the radio spectrum of a Cygnus A
hotspotisnotrelatedtothe turn-overinelectronenergy
distribution. Rather,theyargue,itindicatesatransition
58
between two different acceleration mechanisms.
Electronenergydistributionswithalowenergycut-off
Region C
havealsobeendiscussedinrelationto pc-scalejets. The
14 00 (Counter Lobe)
absenceofsignificantFaradaydepolarizationincompact
sources suggests that the number density of electrons
14 24 32.4 32.2 32.0 31.8 31.6 withLorentzfactorγ &100greatlyexceedsthatoflower
RIGHT ASCENSION (J2000)
energy particles (Wardle 1977; Jones & Odell 1977).
Gopal-Krishna et al. (2004) have argued that some sta-
Fig. 1.— ATCA 20.2GHz imageof PKS 1421–490 with source tistical trends in superluminal pc-scale jets may be un-
components labeled. This image was first presented in G05. To derstood in terms of effects arising from a low energy
avoid confusion, the naming convention used by G05 is also in- cut-offintheelectronenergydistribution. Tsang & Kirk
cluded. Contour levels: 1.5mJy/beam × (1, 2, 4, 8, 16, 32,
(2007) have suggested that a low energy cut-off in the
64, 128, 256, 512, 1024). Peak surface brightness: 2.11Jy/beam.
Beam FWHM: 0.54 × 0.36 arcsec. The scale of the image is 7.0 electron spectrum can alleviate several theoretical diffi-
kpc/arcsecond. culties associatedwith the inverse Comptoncatastrophe
in compact radio sources, including anomalously high
low energy electron distribution in jets and hotspots. brightness temperatures and the apparent lack of clus-
Ina small number ofobjects, flattening ofthe hotspot tering of powerful sources at 1012 K. However, circular
radio spectra towards lower frequencies has been ob- polarization in the pc-scale jet of 3C279 requires a min-
served. In most cases, synchrotron self absorption imum Lorentz factor γmin <20 (Wardle et al. 1998).
and free-free absorption can be ruled out, and the Observational constraints on the low energy electron
observed flattening is interpreted in terms of a turn- distribution in extragalactic jets on kpc-scales are rare.
over in the electron energy distribution (Leahy et al. Alowenergycut-offintheelectronenergydistributionat
1989; Carilli et al. 1988, 1991; Lazio et al. 2006). When γmin 20hasbeenestimatedforthejetofPKS0637–752
∼
modeling hotspot spectra, the turn-over in the elec- (500kpcfromthenucleus)throughmodelingoftheradio
tron energy distribution is usually approximated by to X-ray spectral energy distribution in terms of inverse
setting the electron number density equal to zero be- Comptonscatteringofthecosmicmicrowavebackground
low a cut-off Lorentz factor γ . In each case where (Tavecchio et al. 2000; Uchiyama et al. 2005).
min
flattening of the hotspot radio spectrum has been di- This paper is structured as follows: In 2 we discuss
§
rectly observed, estimates of γ are of the order ourobservationsanddatareduction. In 3wediscussthe
min §
of several hundred: Cygnus A, γ 300 - 400 active galactic nucleus - in particular the optical spec-
min
(Carilli et al.1991;Lazio et al.2006;Hard∼castle 2001b); trumandbroadbandspectralenergydistribution. In 4
§
3C295, γ 800 (Harris et al. 2000; Hardcastle we present the VLBI image of the northern hotspot and
min
2001b); 3C123,∼γ 1000 (Hardcastle et al. 2001a; derive plasma parameters by modeling the broad band
min
Hardcastle 2001b); PK∼S 1421–490, γ 650 (this spectral energy distribution. In 5 we independently es-
work). min ∼ timate the hotspot plasma param§ eters by modeling the
Leahy et al. (1989) presented evidence for a low en- radio spectrum of the entire radio galaxy. In 6 we dis-
§
ergy cut-off in two other hotspots; 3C268.1 and 3C68.1. cuss the incompatibility of the observed spectrum with
In both these ojects, the hotspot radio spectra are sig- the standardcontinuous injectionplus synchrotroncool-
nificantlyflatterbetween150MHzand1.5GHzthanthey ingmodelforhotspots. In 7weconsiderDopplerbeam-
§
areabove1.5GHz,whichsuggestsasimilarvalue ofγ ing as a possible cause of the high radio surface bright-
min
tothoselistedabove,providedthehotspotmagneticfield ness and various other properties of the hotspot. In 8
§
strengths are similar. More recently Hardcastle (2001b) we consider the dissipation of energy associated with a
reported on a possible detection of an optical inverse cold proton/electron jet and present an expression that
Compton hotspot in the quasar 3C196. By modeling relatesthe energyof the peak in the electronenergydis-
the synchrotron self Compton emission and assuming a tribution to the jet bulk Lorentz factor. We then con-
magnetic field strength close to the equipartition value, sidertheimplicationsofthisexpressioninthecaseofthe
The Luminous Hotspot of PKS 1421–490 3
northernhotspotofPKS1421–490andotherobjects. In
§9Twherosuugmhmouatriztehiosuprafipnedrinwges.assume cosmology ΩΛ = yHz] LAiTmCiAts 2 LMimAiStsS H SoEtsDpot
0th.7e3,spΩeMctr=al0i.n2d7e,xH0as=α71=kmlso−g(1FM1/Fp2c)−1s,oatnhdatwtehdeeflfiunxe F [Ji
−log(ν1/ν2) i
density F ν−α.
ν
∝
2. OBSERVATIONSANDDATAREDUCTION Core SED
2.1. Summary z]
H
y
WeobservedPKS1421-490withtheLongBaselineAr- J
ray(LBA)at2.3and8.4GHzandwiththeATCAat2.3, [i
F
4.8, 8.4 and 93.5 GHz. We have also made use of ATCA i
radio data (4.8, 8.6, 17.7 and 20.2 GHz) previously pub-
lishedinGelbord et al.(2005)aswellasarchival1.4GHz
ATCA data. We combined these data with previously
published infra-red, optical and X-ray flux densities to Frequency [Hz]
constructradiotoX-rayspectraforthenorthernhotspot
andthecoreaswellasanaccurateradiospectrumofthe Entire Source
y]
etinotniraenrdadrieofegraelnacxeys.fToraballeld1altisatsutshedeoinbstehrivsasttiuodnyi.nfFoirgmuare- y [J Radio Spectrum
t
2 presents the spectra and indicates the source of each si
n
data point. e
D
Inadditiontothese data,weobtainedanopticalspec- x
u
trum of regionB in order to confirm the classificationof Fl
that region as an active galactic nucleus. The spectro-
scopic observations are described in 2.5.
§
As wellas describingthe observationsanddata reduc-
Frequency [Hz]
tion steps, this section includes a description of some
non-standardproceduresthatwererequiredtoconstruct
the hotspot radio spectrum. Specifically, non-standard Fig. 2.— Spectral energy distribution of the core and North-
procedures were required to determine the hotspot flux ern hotspot of PKS1421-490, as well as the radio spectrum of
the entire radio galaxy. Symbols indicate the source of the data
density from the 8.4GHz LBA data-set due to limited
as follows: Filled squares, ATCA; open squares, LBA; open cir-
(u, v) coverage. These non-standard procedures are de- cles, Magellan (taken from G05); filled triangles, 2MASS (taken
scribed in 2.2.3. Non-standard procedures were also fromG05); opentriangles,MOST(taken fromLargeetal.(1981)
used to obt§ain a lower limit to the hotspot flux density andCampbell-Wilson&Hunstead(1994)),opendiamonds,Parkes
(takenfromWills(1975));filledcircles,Chandra(takenfromG05).
at 93.5GHz. This procedure is described in 2.4.
§ The solid lines through the filled circles indicate the 1σ range of
X-rayspectral index permitted by the Chandra data. Tips of ar-
2.2. VLBI
rowsmarkupperandlowerlimits(seesection2.4fordiscussionof
2.2.1. LBA Observations at 2.3GHz methods used to obtain ATCA limits). Symbol sizes are greater
than or approximately equal to error bars except forthose points
PKS 1421–490 was observed with 6 elements (ATCA, whereerrorbarshavebeenplotted.
Mopra,Parkes,Tidbinbilla 70m,HobartandCeduna)of
atures and antenna gains. We obtained simultaneous
the Australian Long Baseline Array(LBA) on March23
ATCA data during our observation, and this allowed us
2006. A full 12 hour synthesis was obtained, recording
to bootstrap the LBA flux scale to the ATCA flux scale
a single 16MHz bandwidth in both left and right hand
by comparing simultaneous measurements of the point
circular polarization. Regular scans on a nearby phase
like source PKS 1519–273. After scaling the gains us-
calibrator, PKS 1424–418, were scheduled throughout
ing this bootstrappingmethod, andcorrectingthe resid-
the observation, as well as scans on a point like source,
ual delays and rates via fringe fitting, the data-set from
PKS 1519–273 (Linfield et al. 1989), used for gain cal-
the phase reference source was exported to DIFMAP
ibration. Unfortunately, due to hardware issues, we
(Shepherd 1997) where it was edited and imaged. Am-
were only able to process right hand circular polariza-
plitude and phase self calibration corrections obtained
tion. However, this will not affect our results as we do
from imaging the phase reference source were imported
not expect the hotspot emission to be significantly cir- into AIPS using the cordump12 patch kindly supplied to
cularly polarized. Circular polarization in AGN seldom
us by Emil Lenc. These phase and amplitude correc-
exceeds a few tenths of 1% (Rayner et al. 2000). Data
tions were then applied to PKS 1421–490, and the data
were recorded to VHS tapes using the S2 system and
exportedto DIFMAP for deconvolutionandselfcalibra-
correlated using the LBA hardware correlator with 32
tion. The resulting image is shown in figure 3. We mea-
channels and 2 second integration time. The data were
sure a hotspot flux density of 4.25 0.2Jy at 2.3GHz.
correlatedtwice: once with the phase tracking centre lo- ±
Preston et al. (1989) obtained a flux density of 4.1 Jy
cated at the position of the radio peak in region A, and
at 2.3 GHz for the northern hotspot by model fitting
once with the phase tracking centre located 5 arcsec-
∼ SHEVE (Southern Hemisphere VLBI Experiment) data
onds away, at the position of the core (region B).
The initial calibration of the visibility amplitudes was 12 The cordump patch is available for DIFMAP at
performed in AIPS, using the measured system temper- http://astronomy.swin.edu.au/$\sim$elenc/DifmapPatches/
4
TABLE 1
Observation InformationandFlux Densities
FluxDensityof... Instrument Frequency DateObserved Configuration Resolutiona FluxDensity Reference
[Jy]
EntireSource MOST 408MHz 1968-1978 — 2.′8 13.1±0.7 1
EntireSource Parkes 468MHz 1965-1969 — 54′ 11.9±0.1 2
EntireSource Parkes 635MHz 1965-1969 — 30.′5 10.9±0.5 2
EntireSource MOST 843MHz 1990-1993 — 1.′1 9.9±0.5 3
EntireSource ATCA 1.38GHz Feb242000 6Ab 2.′2c 8.5±0.2 4
EntireSource ATCA 2.28GHz Mar232006 6Cb 3′c 7.15±0.15 4
EntireSource ATCA 4.80GHz May192005 H168 3.′5c 5.5±0.1 4
EntireSource ATCA 8.425GHz May192005 H168 2′c 4.25±0.1 4
EntireSource ATCA 8.64GHz Feb42002 6Cb 47′′c 4.1±0.1 4
EntireSource ATCA 17.73GHz May92004 6Cb 30′′c 2.74±0.06 4
EntireSource ATCA 20.16GHz May92004 6Cb 26′′c 2.54±0.05 4
EntireSource ATCA 93.5GHz Aug212005 H214b 10′′c 1.0±0.1 4
NorthernHotspot LBA 2.28GHz Mar232006 Tidbinbilla,ATCA 13.5×11.6mas 4.25±0.2 4
Mopra,Parkes
Hobart,Ceduna
G
NNoorrtthheerrnnHHoottssppoott ALTBCAA 187.4.7235GGHHzz MMaayy19922000045 Parkes,M6oCpra,ATCA 03′.3′5×8×130m′.′a4s3 3.<2+−2.003..23 44 odf
NorthernHotspot ATCA 20.16GHz May92004 6C 0′.′51×0′.′37 <2.1 4 re
NNoorrtthheerrnnHHoottssppoott 2AMTACSAS 1.3983×.51G01H4zHz A19u9g82-122000015 H—214 1∼04′′′c′ 0.8<<F39.37.5×G1H0z−<4 1.1d 45 yet
NNoorrtthheerrnnHHoottssppoott 22MMAASSSS 12..842××11001144HHzz 11999988--22000011 —— ∼∼44′′′′ <<22..71××1100−−44 55 al.
NorthernHotspot Magellan 3.93×1014 Hz Apr262003 MagIC ∼0′.′6 (3.9±0.8)×10−6 5
NorthernHotspot Magellan 4.82×1014 Hz Apr262003 MagIC ∼0′.′6 (3.0±0.9)×10−6 5
NorthernHotspot Magellan 6.29×1014 Hz Apr262003 MagIC ∼0′.′6 (1.9±0.8)×10−6 5
NorthernHotspot Chandra 2.41×1017 Hz Jan162004 ACIS-S 0′.′5 (1.3±0.16)×10−8 5
Core ATCA 4.8GHz Feb42002 6C <7×10−3 5
Core ATCA 8.64GHz Feb42002 6C (9.6±0.6)×10−3 5
Core ATCA 17.73GHz May92004 6C (9.8±0.3)×10−3 5
Core ATCA 20.16GHz May92004 6C (9.2±0.2)×10−3 5
Core 2MASS 1.38×1014 Hz 1998-2001 — ∼4′′ (1.00±0.07)×10−3 5
Core 2MASS 1.82×1014 Hz 1998-2001 — ∼4′′ (8.8±0.6)×10−4 5
Core 2MASS 2.4×1014 Hz 1998-2001 — ∼4′′ (9.1±0.7)×10−4 5
Core Magellan 3.93×1014 Hz Apr262003 MagIC ∼0′.′6 (8±1)×10−4 5
Core Magellan 4.82×1014 Hz Apr262003 MagIC ∼0′.′6 (8±1.5)×10−4 5
Core Magellan 6.29×1014 Hz Apr262003 MagIC ∼0′.′6 (7±2)×10−4 5
Core Chandra 2.41×1017 Hz Jan162004 ACIS-S 0′.′5 (4.9±0.3)×10−8 5
Note. — The uncertaintiesin ATCA flux density are dominated by the uncertainty in the absolute flux calibration, which is estimated to be 2%, except
for 93.5GHz, where the uncertainty is estimated to be 10%. The lower limit on the hotspot flux at 93.5GHz comes from making an assumption about the
non-hotspot spectrumextrapolatedto higher frequenciesfrom 8.4GHz. See section 2.4 for details. References: (1) Largeetal. (1981), (2) Wills (1975), (3)
Campbell-Wilson&Hunstead(1994),(4)Thiswork,(5)Gelbordetal.(2005).
aConverttolinearresolutionusing7.0kpc/arcsecondbOnlyshortbaselinesonwhichtheradiogalaxyisunresolvedwereusedtomeasurethefluxdensity.cRes-
olutionofshortestbaseline.d Seesection2.4.
The Luminous Hotspot of PKS 1421–490 5
with the simplest model consistent with the data (two 2.3. ATCA Observations
circular Gaussians).
ATCAobservationsofPKS1421–490weremadesimul-
We attempted to detect compact structure within re-
taneously during our LBA observations. We recorded
gionB(thecore)usingthedata-setthathadbeencorre-
a single 64 MHz bandwidth at 8.4 GHz and 128 MHz
lated with the phase centre at that position. The time-
bandwidth at 4.8GHz during our first LBA observation
averaging-andbandwidth-smearedemissionfromregion
in 2005. A single 128MHz bandwidth at 2.3GHz was
A in this dataset was first cleaned to remove the side-
recordedduringoursecondLBAobservationin2006. For
lobes, but we were unable to detect any emission from
each of these observations, the ATCA was in a compact
thelocationofthecoretoalimitofapproximately8mJy
configurationso we couldnot imagethe sourcein detail,
(5 σ). The upper limit to the flux density of regionB at
but we were able to obtain accurate total source flux
4.8GHz is 7mJy (Gelbord et al. 2005)
density measurements (see Table 1). Total source flux
density measurements were also obtained at 1.4GHz us-
2.2.2. LBA Observations at 8.4GHz
ingarchivalATCAdata. Standardcalibrationandimag-
PKS 1421–490 was observed with 5 elements of the ing procedures were used with the MIRIAD processing
LBA (ATCA, Mopra, Parkes, Hobart and Ceduna) in software.
May 2005 at 8.4GHz. A full 12 hour synthesis was ob- In August 2005 we obtained a full 12 hour synthe-
tained,recordingasingle16MHzbandwidthinbothleft sis with the new 3mm receivers. Again, standard cali-
and right hand circular polarization. At this frequency, bration and imaging procedures were used in MIRIAD.
the Northernhotspot of PKS1421–490is completely re- The flux density scale wasdeterminedfromscans onthe
solved on all but the shortest three baselines (baselines planet Uranus and confirmed using the point-like source
between Parkes, the ATCA and Mopra). We fringe fit- PKS 1921–293,the flux density of which had been mea-
ted our target source data using a point source model sured 4 days prior to our observing run as 8.8 0.9Jy
in AIPS, before performing model-fitting and phase self at 93.5GHz. We detected a single point like com±ponent
calibration iterations in DIFMAP. in the 93.5GHz image of PKS 1421–490 coincident with
region A, the flux density of which we regard as being
2.2.3. Determination of Hotspot Flux Density from the the total source flux density at this frequency, since the
8.4GHz LBA Data Set resolutionoftheshortestbaselinelargerthanthesource.
Due to the small number of baselines, we use model- The upper limit onflux densityat93.5GHz forregionB
fitting in the (u, v)-plane rather than CLEAN deconvo- and C is 5mJy (5 σ).
lution to measure the hotspot flux density at 8.4GHz. Errors in the flux densities reported in Table 1 are
Model-fitting involves specifying a starting model in the dominated by uncertainties in the primary flux calibra-
imageplane,consistingofanumberofellipticalGaussian tionwhichareestimatedtobeoforder 2%atcmwave-
∼
components,eachwithaparticularfluxdensity,position, lengths, and of order 10% at 3mm.
∼
size and position angle, then allowing the model fitting
algorithmtolocateachi-squaredminimumbyfittingthe 2.4. Constraints on the Hotspot Radio Spectrum from
Fourier transform of the model to the (u, v)-data. ATCA Images
Care is necessary when comparing the LBA flux den- Thehotspotis unresolvedinthe ATCAimages,andis
sity measurements at the two different frequencies, due blendedwithemissionfromthesurroundingregions. We
to the limited (u, v) coverage. At 2.3 GHz, the data are therefore unable to directly measure the flux density
cover (u, v) spacings between 0.5 and 13 Mλ, while at of the hotspot from the ATCA data. However, we are
8.4GHz the data cover (u, v) spacings between 2 and 9 able to constrainthe flux density of the hotspot, and we
Mλ. Therefore,providedthe sourcestructurecanbe de- nowdiscussthemethods usedtoobtainupperandlower
scribedbyasimplemodelconsistingofasetofGaussian limits.
components, the comparison of model flux densities will Using radio data that was first presented in
be valid. Gelbord et al.(2005),wefindupperlimitsonthehotspot
Inordertodeterminetherangeofallowablefluxdensi- flux density at 17.7GHz and 20.2GHz by summing the
tiesinthe8.4GHz data-set,wespecifiedawiderangeof CLEANcomponentsatthepositionofthehotspot. Simi-
differentmodelsconsistingof3,4or5ellipticalGaussian larly,weobtainanupperlimittothehotspotfluxdensity
components,broadlyconsistentwiththe 2.3GHzimage, at 93.5GHz from the measurement of total source flux
then let the model-fitting algorithm adjust the model to densityatthatfrequency. Weobtainalowerlimitonthe
fit the 8.4 GHz data. While it is not possible to pre- hotspotflux density at93.5 GHz via the followingsteps:
ciselyconstrainthe flux density ofthe hotspotwith only
three baselines, we found that the total flux density of 1. We subtract the LBA-measured hotspot flux den-
all acceptable models (using between three and five el- sity from the total source flux density at 2.3GHz
liptical Gaussiancomponents and a wide range of initial and 8.4GHz to obtain two estimates of the non-
model parameters) was never less than 2.9Jy, and the hotspot flux density, from which we calculate a
flux density of the best-fitting model was 3.2Jy. The non-hotspot spectral index (α8.4GHz(non-hotspot)
2.3GHz
8.6GHz ATCA image contains an unresolved source of = 0.78).
3.3 Jy at the position of the hotspot, and this provides
an upper limit to the hotspot flux density at 8.6GHz. 2. We extrapolate the non-hotspot power law to
We therefore adopt a hotspot flux density at 8.4 GHz of 93.5GHz.
F =3.2+0.2Jy.
8.4GHz −0.3 3. We reasonably assume that the non-hotspot spec-
trum becomes steeper towards higher frequencies.
6 Godfrey et al.
arcseconds -11-050500000 Flux Density (Normalized) Flux Density (Normalized)
milli-150 Wavelength (Angstroms) Wavelength (Angstroms)
-200 Fig. 4.—ThenormalizedopticalspectrumofregionB.Thisspec-
trum clearly shows that region B is a broad lineAGN at redshift
-250 0.6628. Increasinginwavelength,thearrowsindicatethepositions
100 0 -100 -200 -300 -400 -500 -600
milliarcseconds of the following emission lines: Mg II 2799, [Ne V] 3426, [O II]
3726/3729, [NeIII]3869,Hβ,[OIII]4959, [OIII]5007.
Fig. 3.— VLBI image of the Northern Hotspot of PKS 1421–
490 at 2.3GHz. Contour levels: 3.5mJy/beam × (1, 2, 4, 8, 3. REGIONB:THEACTIVEGALACTICNUCLEUS
16, 32, 64, 128). Peak surface brightness: 0.47Jy/beam. Beam
FWHM:13.5mas×11.6mas. Thescaleofthisimageis7.0pc/milli- 3.1. Optical Spectrum of Region B
arcsecond.
The normalized optical spectrum of region B is dis-
played in Figure 4. We detect several broad and nar-
row emission lines: Mg II 2799, [Ne V] 3346 and 3426,
Therefore the extrapolated flux density from step
the blended [O II] 3726,3729 doublet, [Ne III] 3869 and
2 is anupper limit to the non-hotspotflux density.
3967, Hδ (marginal), Hγ, [O III] 4363, Hβ, and [O III]
4959 and 5007. Hβ has both a broad and narrow com-
4. We subtract the non-hotspot upper limit from the
ponent; their measured FWHM values (uncorrected for
observedentiresourcefluxdensitytoobtainalower
instrumentalresolution)are6500km/sand516km/sre-
limit on the hotspot flux density at 93.5GHz.
spectively. The narrow Hβ line width is consistent with
that of the OIII lines (510 km/s). From these features
Theassumptioninstep3isbasedontheobservationthat
we measure the redshift z =0.6628 0.0001.
thenon-hotspotemissionarisesinthelobes,jetsandthe ±
southern hotspot (the core is negligible). Jet and lobe 3.2. Spectral Energy Distribution of the Core
spectraareoftenobservedtosteepentowardshigherfre-
quency. Indeed, the 17.7GHz and 20.2GHz ATCA im- We did not detect the active galactic nucleus with the
agesindicatethatthespectralindexofthenorthernlobe LBA, but obtain an upper limit on the flux density of
region steepens significantly at higher frequency. The approximately8mJyat2.3GHz. This is consistentwith
limits on hotspot flux density obtained from the ATCA theATCAcorefluxdensitymeasurements(seeTable1).
imagesarerepresentedbythetipsofthearrowsinFigure The core is completely dominated by its optical emis-
sion. In fact, the optical flux density is so great relative
2, and are listed in Table 1.
to the radio (α662.4nm = 0.23 0.02), the core would
8.6GHz ±
2.5. Optical Spectroscopy be classified as radio quiet in the strictest sense. The
radio to optical spectral index cannot be explained in
Optical spectra were taken with the Magellan IMACS
termsofstandardsynchrotronselfabsorptionmodelsfor
camera on 14 May 2005 in service mode. Three ten
flat radio spectra (eg. Marscher 1988), since this would
′′
minute exposures were obtained using a long slit (0.9
requireatleastpartofthejettobeselfabsorbedatopti-
width) alignedwith regionsA and B. The 300lines/mm
cal wavelengths and would imply an unrealistically high
grismwasused,toyieldaspectralresolutionofR 1000
magnetic fieldstrength. This regionhas anopticalspec-
spanning roughly 4000–10000 ˚A. The spectra w∼ere re-
tral index α =0.2 0.1, in the range typical of quasars
o
duced with IRAF. No standard stars were observed, so ±
(Francis et al. 1991), suggesting that the strong optical
no effort was made to flux calibrate the spectra or to
emission may be due to an unusually large contribution
remove telluric absorption features.
from the accretion disk thermal component. The radio
No significant spectral features were detected in the toX-rayspectralindex(α1keV =0.710 0.005)istyp-
spectrum of regionA, consistent with synchrotronemis- 8.6GHz ±
icalofradiogalaxiesatsimilarredshift(eg.Belsole et al.
sion from a hotspot. However, only a very high equiva-
2006). The optical to X-ray spectral index is α =1.62
ox
lentwidthemissionline couldhavebeen detecteddue to
(G05). There is clearly an excess of optical flux relative
the low signal to noise ratio of these data.
totheradioandX-rayfluxwhencomparedtosamplesof
The spectrum of region B contains several broad and
other radio galaxies (eg. Gambill et al. 2003). Note that
narrow emission lines, which allowed a precise determi-
measurements of the B-band magnitude have shown no
nation of the redshift (see 3.1). This is not the first
variability, to within 0.6 magnitudes, over the past 35
§
spectrum of the nucleus to be published — a spectrum
years (GO5).
of region B was presented in G05. However, the spec-
trumpresentedinG05didnotallowidentificationofany 4. THENORTHERNHOTSPOT
spectral lines because the strongest spectral features fell
4.1. Morphology
beyond the wavelength coverage, and the spectrum was
takenas a single shortexposure with a high background Figure3showstheLBAimageoftheNorthernhotspot
due to the pre-dawn sky. at2.3GHz. Lessthan0.2Jy(5%ofthehotspotfluxden-
sity)remainsonthelongestbaseline( 12.9Mλ),imply-
∼
ing that there is little structure on scales smaller than
15 mas (100 pc). This limit on substructure within the
The Luminous Hotspot of PKS 1421–490 7
hotspot is relevant to possible synchrotron self absorp- _
tion models for the hotspot spectrum, which we discuss ] ( R G ) 44 0.8 8G MH H z z= 0.34
y
further in 4.2. J
The flux§ density of the hotspot in our LBA image y [ _
t (R G ) 9 3 .5 G H z = 0.58
is 60 % of the total source flux density at 2.3 GHz, si 8.4GHz
n
and 75 % at 8 GHz. The peak surface brightness is
e
Isu2p.me3aGkinHgzI=ν 26ν0−00J.2y/(tahrcessepce2c.trEaxltirnadpeoxlaotfiαng to0.82GbeHtwzeaesn- ux D _ ( H S ) 28 ..34 GG H H zz = 0.22
these frequ∝encies is calculated in 4.2) an∼d accounting Fl
§
for cosmological dimming and redshifting, we find that
the peak surface brightness of the northern hotspot of
PKS 1421-490 would be more than 1000 times brighter
Frequency [Hz]
than the brightest hotspot of Cygnus A if they were at
the same redshift (Carilli et al. 1999). The monochro-
matic hotspot luminosity is L =8 1027 WHz−1.
2.3GHz Fig. 5.— Radio spectrum of the entire radio galaxy (filled
×
A protrusion on the Eastern edge of the hotspot re- squares)andhotspot(filledcirclesandtipsofarrows). Thisfigure
sembles the “compact protrusions” seen in numerical servestoillustratethelowfrequencyflatteninginthehotspotradio
simulations (eg. Norman 1996). According to Norman spectrum referredtointhetext (§4.2.1 and§8). Thedotted lines
illustratepowerlawfitstospecificsectionsofthedata.
(1996), a compact protrusion is produced in their 3-
D non-relativistic hydrodynamic simulations when the diameter of region HS1 (400pc). The surface brightness
light, supersonic jet reaches the leading contact discon- of regionHS2 is more than a factor of 10 times the peak
tinuity. At this point, the jet is generally flattened to a surface brightness of the brightest hotspot of Cygnus A.
width substantially less than the inlet jet diameter, and In addition, the flux density from region HS2 alone (
the compact protrusionarises where the jet impinges on 0.6 Jy at 2.3GHz) is more than 4 times the total flu∼x
the contact discontinuity surface. density of the whole counter lobe and hotspot. There
The width of the hotspot at the peak (region HS1) is are two possible interpretations for region HS2, and the
400pc measured perpendicular to the inferred jet direc- interpretation of this region has implications for the in-
tion. The lower surface brightness emission behind the terpretation of region HS1.
hotspot peak (region HS2) is 700pc measured perpen- The first interpretation is in terms of emission from
dicular to the jet direction. The length of the hotspot turbulent back-flow in the cocoon. If this interpretation
(regions HS1 and HS2) is approximately 1kpc. The geo- is correct, we cannot appeal to Doppler beaming to ac-
metricmeanofthemajorandminoraxes(forcomparison count for the high surface brightness of region HS2 rela-
with Hardcastle et al. (1998) and Jeyakumar & Saikia tive to other hotspots, and the high flux density relative
(2000))is0.63kpc. Thisisafactorof4belowthemedian to the counter hotspot and lobe. If we cannot appeal
value(2.4kpc)ofhotspotsizesgiveninHardcastle et al. to Doppler beaming for region HS2, it would seem un-
(1998). However, the size of the hotspot relative to the reasonable to appeal to Doppler beaming to explain the
linear size of the source is consistent with the correla- high surface brightness of region HS1. The arm length
tion between these parametersgiven in Hardcastle et al. symmetry places a tight upper limit on the expansion
(1998) and Jeyakumar & Saikia (2000). velocity of the lobes at v <0.1c, indicating that
expansion
The jet exhibits a bend of almost 60 degrees (pro- the whole complex (region HS1 and HS2) cannot be ad-
jected)approximately5arcseconds(35kpc)fromthecore vancing relativistically.
atthewesternendoftheridgeofemissionextendingwest The second possible interpretation for region HS2 is
fromthehotspotinFigure1. Bridle et al.(1994)showed thattheemissionisassociatedwithobliqueshocksinthe
that hotspot brightness is anti-correlated with apparent jet as it approaches the hotspot. In this case, we may
jet deflection angle. They found that, for the twelve appeal to Doppler beaming to explain the high surface
quasars in their sample, the ratio of hotspot flux den- brightness of both regions HS1 and HS2. However, this
sitytolobefluxdensitydecreaseswithlargerjetbending interpretationwould imply that the jet diameter at HS2
angles, particularly when the deflection occurs abruptly. ( 700pc)issignificantlygreaterthanthediameterofthe
PKS 1421–490does not follow this trend. h∼otspot at HS1 ( 400pc) and also greater than the jet
We detect what appears to be a jet knot (region J1) diameter at J1 ( ∼400 600pc). It should be noted that
512mas ( 3.5kpc projected)atpositionangle-107de- the width of regi∼onJ1,−presumably associatedwith a jet
∼
grees (North through East) from the hotspot peak. The knot,ispoorlyconstraineddue tothelowsignaltonoise
knot is extended along a position angle almost perpen- of this component. Future LBA observations at 1.4GHz
dicular to the apparent jet direction. The major axis of may provide better constraints on the size of regions J1
the knot is poorly constrained due to the low signal to and HS2.
noise of this component, but the data suggests a width
of approximately 400 - 600pc. 4.2. Modeling the Hotspot Spectral Energy Distribution
4.2.1. Low Frequency Flattening
4.1.1. Interpretation of Region HS2
Figure 5 illustrates that the hotspot radio spectrum
Wenowconsidertheinterpretationofthelowersurface changes slope at GHz frequencies, becoming flatter to-
brightness region HS2 just behind the hotspot peak. As wards lower frequency. We now discuss this feature in
mentionedabove,the diameterofregionHS2 perpendic- more detail and consider the possible causes.
ular to the jet direction (700pc) is much larger than the The hotspot spectral index calculated from our LBA
8 Godfrey et al.
flux density measurements is relatively flat at GHz fre- that an instantaneous cut-off in number density is not
quencies (α8.4GHz = 0.22+0.08). The hotspot spec- physical- itis merelyanapproximationto a sharpturn-
2.3GHz −0.05
trumcannotcontinuewiththisslopetomillimeterwave- over in the electron energy distribution. In 8 we show
§
lengths, since it would substantially over-predictthe ob- that interpreting the observed flattening in terms of a
served 93.5GHz flux density. We therefore require that turn-over in the electron energy distribution has consid-
the hotspot spectrum be steeper at frequencies above erable implications.
8GHz , with spectral index α&αATCA93.5GHz =0.48. Low frequency flattening in hotspot spectra has been
LBA8.4GHz
Our conclusion of a flat spectral index at GHz fre- observed in a small number of other objects (see 1).
§
quenciesbasedontheLBAfluxdensitymeasurementsis
4.2.2. The High Frequency Synchrotron Spectrum
strengthenedbyinspectionofthewholesourcespectrum
(seeFigure5). Thefluxdensityoftheentireradiogalaxy The hotspot spectrum remains relatively flat between
has a spectral index of 0.58 above 8.4GHz, but flattens 8GHz and 93.5GHz,havingspectralindex 0.4<α<0.6
to a spectral index of 0.34 below 4.8GHz. The northern (based on the two point spectral index from the 8.4GHz
hotspot is the dominant component at GHz frequencies, LBA data point to the ATCA upper and lower limits at
hence,theflatteningofthetotalsourcespectrumimplies 93.5GHz). The synchrotron spectrum above 93 GHz is
there is flattening in the hotspot spectrum. There are a poorly constrained, but the simplest model — a power
number of possible causes of this GHz frequency flatten- law spectrum with spectral index 0.4 < α < 0.6 and an
ing, but most of them are implausible. We now consider exponential cut-off at high frequency (i.e. a synchrotron
a number of such explanations. spectrum from a power law electron energy distribution
If synchrotron self absorption were responsible for the withnumberdensitysettozeroaboveγ ),isunableto
max
flattening, the required magnetic field strength is B satisfy the optical data and the 2MASS infra-red upper
G
10−5ν5θ4F−2(1+z)−1 where B is the magnetic fiel∼d limits simultaneously. Either a break to a steeper spec-
p p G
strength in Gauss, F is the peak flux density in Jy, ν trum somewhere between 1011 1013 Hz is required,
p p ∼ −
is the frequency inGHz atthe peak andθ is the angular or a gradual cut-off at high electron energy, rather than
size in milliarcseconds (de Young 2002, pg. 325). In the anabruptcut-offatγmax,mustexist. Giventhehighra-
case of the Northern hotspot of PKS 1421–490 we esti- dio luminosity, hence high magnetic field strength, syn-
mate(conservatively)ν 1GHz,θ 100mas,F 5Jy chrotron losses are likely to be important. We there-
p p
and z = 0.663. Therefor∼e, a magne∼tic field streng∼th of foreallowforasynchrotroncoolingbreakatanarbitrary
B 20G is required to produce the observed flattening break frequency in order to fit the radio through optical
—∼four orders of magnitude greater than the equipar- spectrum. Different choices of model spectrum are pos-
tition magnetic field strength. Less than 0.2Jy (5% of sible, but they would not significantly affect our major
the hotspot flux density) remains on the longest base- results. We discuss the model electron energy distribu-
lines (12.9 Mλ 15 mas resolution), implying that the tion in 4.2.4, and further discuss the self-consistency of
hotspotcannot⇒becomposedofmanysmallself-absorbed this mo§del in 6.
§
sub-components. Therefore, we do not consider syn-
4.2.3. Hotspot X-ray Emission
chrotron self absorption to be a viable explanation for
the flattening. Figure 6 shows the spectral energydistribution (SED)
We next consider free-free absorption by interstellar of the northern hotspot. The level of X-ray flux density
clouds in the hotspot environment as a possible mech- relative to the optical flux density indicates the pres-
anism for the observed flattening of the radio spec- ence of two distinct spectral components: synchrotron
trum. Consider a cloud of size L kpc, temperature emission from radio to optical frequencies, and inverse
kpc
T 104 K, electron number density n cm−3 and pres- Compton emission at X-ray frequencies and above.
4 e
sure×p−12 10−12dyn/cm2. The opticaldepth τ to free- The energy density of the locally generated syn-
free absor×ptionat a frequency ν GHz is givenby (eg. chrotron emission within the hotspot (assuming no
GHz Dopplerbeaming)ismorethan104timestheenergyden-
de Young 2002, pg.326)
sity of the cosmic microwave background(CMB) at this
τ=3.3 10−4n2L ν−2.1T−1.35 (1) redshift. If the hotspot plasma is moving relativistically
× e kpc GHz 4 withvelocityv =βcatanangleθtothelineofsight,the
n 2
=2 10−4L ν−2.1 p2 e T−3.35 (2) ratio of synchrotron to CMB energy density is reduced
× kpc GHz −12 n 4 by a factor of Γ−2δ−3 where δ = [Γ(1 βcosθ)]−1
Assuming a characteristic pressure(cid:16)in th(cid:17)e outer regions is the Doppler∼factor and Γ = (1 β2−)−1/2 is the
of an elliptical galaxy p 10−12dyn/cm2, a character- bulk Lorentz factor, and we have assu−med the hotspot
istic temperature for an∼ionized cloud T 104 K and is associated with plasma moving through a station-
∼
a reasonable cloud size L . 1kpc, the optical depth to ary volume/pattern rather than a moving blob, so that
free-free absorption above 1GHz is less than 5 10−5. I =δ2I′ (Lind & Blandford 1985). Therefore, if δ .6
× ν ν′
We therefore interpret the change of slope in the (assuming Γ δ), inverse Compton scattering of locally
hotspot radio spectrum in terms of a change in the un- generated syn∼chrotron photons is the dominant source
derlyingelectronenergydistribution. In 4.2.4wemodel of inverse Compton X-ray emission. While a Lorentz
§
theSEDbyincorporatingalowenergycut-offintheelec- factor of Γ 6 is not ruled out, such a high Lorentz
tron energy distribution. A low-energy cut-off at some factor is not∼required by the data, and we consider only
minimum Lorentz factor γmin produces a spectrum with Lorentz factors Γ . 3. We therefore ignore the inverse
F ν1/3 at frequencies below the characteristic emis- Compton scattering of CMB photons in the following
ν
∝
sion frequency of electrons with Lorentz factor γ (see treatment. We also ignore any contribution to the X-
min
eg. Worrall & Birkinshaw 2006). We must emphasize ray flux density from “upstream Compton” scattering
The Luminous Hotspot of PKS 1421–490 9
and spectral index, the synchrotron plus self Comp-
ton spectrum is characterized by the five parameters
K ,B,γ ,γ ,γ . Incalculatingthemodelspectrum,
e min b max
these parameters appear in the following combinations
(see appendix A):
A =K Ωα+1 (5)
syn e 0
A =K γ (6)
ssc e b
δ 3
ν = Ω γ2 (7)
1 (1+z)4π 0 min
δ 3
ν = Ω γ2 (8)
Fig. 6.—HotspotSpectralEnergyDistributionwithSSCmodel b (1+z)4π 0 b
overlaid. The“bow-tie”aroundtheX-raydatapointindicatesthe δ 3
1σrangeofX-rayslopes. Thesolidlineisthebestfitsynchrotron ν = Ω γ2 (9)
plus self Compton model spectrum with the Doppler factor fixed 2 (1+z)4π 0 max
at δ = 1. The dashed line is the best fit SSC component with
theDopplerfactorfixedatδ=3. Themodelsynchrotronspectra where α=(a 1)/2 is the radio spectral index between
for δ = 3 and δ = 1 are exactly the same, and so do not appear frequencies ν−and ν , Ω is the non-relativistic gyro-
1 b 0
as separate curves in the plot. The LBA data points (plotted as
frequency. The parameters ν , ν and ν correspond to
filledcircles)haveerrorbarssmallerthanthesymbolsize. Tipsof 1 b 2
arrowsmarkthepositionofupperandlowerlimits. X-ray,optical the characteristic frequency emitted by electrons with
andinfra-redpointsaretakenfromGelbordetal.(2005). Lorentz factor γ , γ and γ in a magnetic field of
min b max
flux density B, and are therefore identified with the low
(Georganopoulos & Kazanas2003),wherebyelectronsin frequencyturn-over,synchrotroncooling breakandhigh
thejetupstreamfromthehotspotinverseComptonscat- frequencycut-offrespectively. Theadvantageofthisfor-
ter synchrotron photons produced within the hotspot. mulation, described in Appendix A, is that it allows the
We note that if the upstream Compton process makes a model to be specified in terms of the observed values of
significant contribution to the observed X-ray flux den- ν ,ν and ν . The parameters A and A are nor-
1 b 2 syn ssc
sity,theSSC fluxdensitymustbe lessthanthe observed malization factors for the synchrotron and SSC spectral
flux density, in which case the magnetic field strengthin components respectively.
thehotspotwouldbegreaterthanthatreportedinTable WeestimatebestfitvaluesforB,K ,γ ,γ andγ
e min b max
2, and therefore greater than the equipartition value. using chi-squared minimization with the following three
constraints: (1) We fix the electron energy index at a=
4.2.4. Synchrotron Self Compton Modeling
2.06 so that the spectral index α = 0.53 for frequencies
To model the radio to X-ray spectral energy distribu- ν <<ν <<ν (that is, between about 10 GHz and 100
1 b
tion we use the standard one-zone SSC model: a spheri- GHz). Thisistheelectronenergyindexdeterminedfrom
cal region of plasma with uniform density and magnetic modeling the hotspot radio spectrum as described in 5.
§
fieldstrength. Weassumethatthemagneticfieldis“tan- The spectralindex α=0.53alsoagreeswith the ratioof
gled”withanisotropicdistributionoffielddirection. We peaksurfacebrightness(atthelocationofthehotspot)in
further assume that the number density of electrons per the17.7GHzand20.2GHzATCAimages. (2)Wefixthe
unit Lorentz factor is described by radiusatR=320pc. Theradiohotspotiselongatedinan
approximately cylindrical shape of volume V 4 1057
m3. A radius of 320pc gives a spherical mod≈el of×equal
0 γ <γ , γ >γ
N¯(γ)=( (Ka−eγ1b)γ−(a+1)g γγb γmin <miγn <γmax max vTohliusmise.cl(o3s)eWtoethfiexltohweebstrebarkeafrkefqrueeqnuceyncaytaνlblo=we5d00bGyHthze.
(cid:16) (cid:17) (3) data. Higher break frequencies are permitted but cause
where a worse fit to the optical data. The break frequency is
a−1 not well constrained by the data, but the results are not
γ 1 1 γ γ <γ sensitive to the assumed value of the break frequency.
g(cid:18)γb(cid:19)=(1−(cid:16) − γb(cid:17) γ >γbb (4) (4)Wefixtheuppercut-offfrequencyatνmax =1014 Hz
to fit the optical flux densities.
N¯(γ) is the volume averaged energy distribution pro- We determined best fit parameter values while fixing
ducedbycontinuousinjectionofapower-lawenergydis- the Doppler factor at δ =1,2 and 3. The derived model
tribution N(γ) = K γ−a at a shock with synchrotron parameters are presented in Table 2. The uncertainties
e
cooling in a uniform magnetic field downstream. It de- in Table 2 are determined from the range of parameter
scribes a broken power-law spectrum with the electron valuesinthesetofmodelshavingχ2 <χ2 +2.71. The
min
spectral index smoothly changing from -a to -(a+1) at observed X-ray spectral index was not included in the
γ γ . The break in the electron spectrum at γ chi-squared calculations, but the model X-ray spectral
b b
≈
corresponds to the electron energy at which the syn- index is consistent with the observed value within the
chrotron cooling timescale is comparable to the dynam- uncertainties.
ical timescale for electrons to escape from the hotspot. In Figure 6 we plot the observed hotspot flux densi-
Thesynchrotroncoolingbreakisdiscussedfurtherin 6. ties with the best fit model spectra (for Doppler factors
FortheelectronenergydistributiondescribedbyN¯(γ§), fixed at δ =1 and δ =3) overlaid. The simple one-zone
and given a particular radius, redshift, Doppler factor model with a near equipartition magnetic field strength
10 Godfrey et al.
TABLE 2
SynchrotronSelfCompton Model ParametersforNorthernHotspot
FixedParameters DerivedParameters
δ [pRc] α [Hνbz] ν[Hmazx] [mBG] B/Beq [×10−n5ecm−3] γmin [×γ1b04] [×γm1a0x5] α70..05kkeeVV
1.0 320 0.53 5×1011 1014 3.2±0.5 1.5+−00..32 2.7±0.4 650±80 & 0.8 1.1±0.1 0.5±0.1
2.0 320 0.53 5×1011 1014 1.0±0.2 0.75±0.15 2.2±0.3 800±100 & 1 1.4±0.2 0.45±0.1
3.0 320 0.53 5×1011 1014 0.5±0.1 0.5±0.1 1.9±0.3 950±100 & 1.1 1.6±0.2 0.45±0.1
Note. — The quoted uncertainties on model parameters are an estimate of the level of uncertainty from model fitting, and
correspondtotherangeofparametervaluesinthesetofmodelshavingχ2<χ2min+2.71.
provides a good description of the available data. Hard-
Parkes Flux Densities (Whole Source)
castle et al. (2002) used more complicated spectral and MOST Flux Densities (Whole Source)
ATCA Flux Densities (Whole Source)
spatialmodels for three sources,and found that this did LBA Flux Densities (Hotspot Only)
Component 1 (Hotspot Model)
not have a significant effect on the derived plasma pa- Component 2 (Rest of Source Model)
Sum of Model Components 1 and 2
rameters. We are therefore confident in our parameter y]
estimates using this “first-order” one-zone model. [Ji
F
5. MODELINGTHERADIOSPECTRUMOFTHEENTIRE
RADIOGALAXY
We now describe a consistency check for the model of
the hotspot radio spectrum in terms of a cut-off in the
electronenergydistribution atγ . This check is based
min
on the observed flattening in the spectrum of the entire
i(cid:3)[Hz]
radio galaxy (Figure 7). In order to test whether the
observed flattening is consistent with the inferred low Fig. 7.— Radio spectrum of the radio galaxy PKS 1421–490.
Open diamonds represent flux densities of the entire radio galaxy
energy cut-off in the electron distribution, we fit a sim-
fromtheMolongloSynthesisRadioTelescope(MOST).Filleddia-
ple two-component model to the radio galaxy spectrum
monds representflux densities of the entireradiogalaxy fromthe
between408MHzand93.5GHz. The modelcomponents Parkestelescope. Filledcirclesrepresentfluxdensitiesoftheentire
are: (1)Thesynchrotronspectrumproducedbytheelec- radiogalaxyfromtheATCA.Opensquaresrepresentfluxdensities
ofthe Northernhotspot fromthe LBA (seeTable 1). Alsoshown
tronenergydistributionofequation(3). Thiscomponent
is the spectral decomposition described in section 5. Component
describes emission from the hotspot. (2) A pure power- 1(curveddashedline)istheangle-averagedsynchrotronspectrum
law approximating emission from the rest of the source. fromapower-lawelectrondistributionoftheformN(γ)∝γ−2.06
Note that the core flux density is negligible compared with a low energy cut-off at a Lorentz factor corresponding to
withthatofthejets,lobesandhotspots,sothatnocom- ν1 =2.6GHz (see equation (7)). This component describes emis-
sionfromthehotspot,andisconsistentwiththeLBAfluxdensities
ponent is included to represent emission from the AGN.
plotted as open squares. Component 2 (straight dotted line) is a
The synchrotron spectrum of component 1 is calcu- pure power-law with spectral index 0.64. This component is an
lated using equation (A8). We assume the same source approximation to the emission from the rest of the source. The
solidlineisthesumofcomponents1and2. Modelparametersare
volume as in 4.2.4, fix the lab frame break frequency at
§ giveninTable3.
ν =500GHzandthelabframehighfrequencycut-offat
b .
ν =1.1 1014Hz,consistentwiththevaluesdetermined
2
from mo×deling the hotspot spectrum in 4.2.4. With werenotincludedinthe fittingprocess,butareincluded
these assumed values, the parameters ν a§nd ν do not in Figure 7 for comparisonwith the spectrum of compo-
b 2
affect the shape of the spectrum below about 100GHz, nent 1.
but they weakly affect the calculation of equipartition Again,wepointoutthatthecut-offinnumberdensity
magnetic field strength. The spectrum of component 1 per unit Lorentz factor below γmin used in our modeling
is therefore determined by the spectral index α , the is not physically realistic, it is merely an approximation
1
turn-over frequency ν and the synchrotron amplitude toanelectronenergydistributionwithasharpturn-over.
1
A =K Ωα1+1. Theflux densityofthe secondcompo- The success of this simple model in simultaneously ac-
syn e 0
nent is of the form countingfor the flattening in boththe hotspotspectrum
and the radio galaxy spectrum supports an interpreta-
ν −α2
F =F (10) tionoftheflatteningintermsofasharpturn-overinthe
ν,2 2.3GHz,2
2.3GHz hotspot electron energy distribution at a Lorentz factor
(cid:16) (cid:17)
Chi-squaredminimizationwasusedtodeterminethebest of order γ 600.
∼
fit values for the parameters α , A , ν , F
and α . The resulting model is1showsynnin mFiingure2.73.GTHhz,i2s 6. SYNCHROTRONCOOLINGBREAK
2
simple two-componentmodel providesanexcellentfit to The magnetic field strength inferred from spectral
the radio galaxy spectrum. Component 1 (describing modeling in section 4.2.4 implies that there should be a
emissionfromthehotspot)isingoodagreementwiththe synchrotroncoolingbreakinthehotspotradiospectrum
LBAfluxdensitymeasurementsat2.3GHzand8.4GHz. at 1GHziftheelectronenergydistributioninjectedat
∼
We emphasize that the LBA flux density measurements the shock is a pure power law. This is inconsistent with