A&A, 690, A74 (2024)
h ps://doi.o g/10.1051/0004-6361/202348524
c
The Au ho s 2024
As onomy
&
As ophysics
The expansion o he GRB 221009A a e glow
S. Gia a ana1,2,?, O. S. Sala ia3,4 , M. Gi ole i2, G. Ghi landa3,4, L. Rhodes5, P. A i6, B. Ma co e7,
J. Yang8, T. An9,10 , G. Ande son11 , J. S. B igh 5, W. Fa ah12,21, R. Fende 5,13, J. K. Leung14,15,16 ,
S. E. Mo a3,5 , M. Pé ez-To es17,18,19 , and A. J. an de Ho s 20
1Dipa imen o di Fisica e As onomia, Uni e si à degli S udi di Bologna, Via Gobe i 93/2, 40129 Bologna, I aly
2INAF Is i u o di Radioas onomia, ia Gobe i 101, 40129 Bologna, I aly
3INAF Osse a o io As onomico di B e a, Via E. Bianchi 46, I-23807 Me a e, I aly
4INFN – sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, (MI), I aly
5As ophysics, Depa men o Physics, Uni e si y o Ox o d, Keble Road, Ox o d OX1 3RH, UK
6ASTRON, Ne he lands Ins i u e o Radio As onomy, Oude Hooge eensedijk 4, 7991 PD Dwingeloo The Ne he lands
7Join Ins i u e o VLBI ERIC, Oude Hooge eensedijk 4, 7991 PD Dwingeloo The Ne he lands
8Depa men o Space, Ea h and En i onmen , Chalme s Uni e si y o Technology, Onsala Space Obse a o y, SE-439 92 Onsala,
Sweden
9Shanghai As onomical Obse a o y, Chinese Academy o Sciences, Nandan Road 80, Shanghai 200030, China
10 Key Labo a o y o Radio As onomy and Technology, Chinese Academy o Sciences, A20 Da un Road, Beijing 100101, PR China
11 In e na ional Cen e o Radio As onomy Resea ch, Cu in Uni e si y, GPO Box U1987, Pe h WA 6845, Aus alia
12 SETI Ins i u e, 339 Be na do A e, Sui e 200, Moun ain View, CA 94043, USA
13 Depa men o As onomy, Uni e si y o Cape Town, P i a e Bag X3, Rondebosch 7701, Sou h A ica
14 Da id A. Dunlap Depa men o As onomy and As ophysics, Uni e si y o To on o, 50 S . Geo ge S ee , To on o, On a io M5S
3H4, Canada
15 Dunlap Ins i u e o As onomy and As ophysics, Uni e si y o To on o, 50 S . Geo ge S ee , To on o, On a io M5S 3H4, Canada
16 Racah Ins i u e o Physics, The Heb ew Uni e si y o Je usalem, Je usalem 91904, Is ael
17 Ins i u o de As o ísica de Andalucía (IAA-CSIC), Glo ie a de la As onomía s/n, E-18008 G anada, Spain
18 Facul ad de Ciencias, Uni e sidad de Za agoza, Ped o Ce buna 12, E-50009 Za agoza, Spain
19 School o Sciences, Eu opean Uni e si y Cyp us, Diogenes s ee , Engomi 1516, Nicosia, Cyp us
20 Depa men o Physics, Geo ge Washing on Uni e si y, 725 21s S NW, Washing on, DC 20052, USA
21 Be keley SETI Resea ch Cen e, Uni e si y o Cali o nia, Be keley, CA 94720, USA
Recei ed 9 No embe 2023 /Accep ed 3 July 2024
ABSTRACT
We obse ed γ- ay bu s (GRB) 221009A using e y long baseline in e e ome y (VLBI) wi h he Eu opean VLBI Ne wo k (EVN)
and he Ve y Long Baseline A ay (VLBA), o e a pe iod spanning om 40 o 262 days a e he ini ial GRB. The high angula
esolu ion (mas) o ou obse a ions allowed us, o he second ime e e , a e GRB 030329, o measu e he p ojec ed size, s, o he
ela i is ic shock caused by he expansion o he GRB ejec a in o he su ounding medium. Ou obse a ions suppo he expansion
o he shock wi h a >4σ-equi alen signi icance, and con i m i s ela i is ic na u e by e ealing an appa en ly supe luminal expansion
a e. Fi ing a powe law expansion model, s∝ a, o he obse ed size e olu ion, we ind a slope a=0.69+0.13
−0.14. Fi ing he da a a each
equency sepa a ely, we ind di e en expansion a es, poin ing o a equency-dependen beha iou . We show ha he obse ed size
e olu ion can be econciled wi h a e e se shock plus o wa d shock, p o ided ha he wo shocks domina e he emission a di e en
equencies and, possibly, a di e en imes.
Key wo ds. echniques: high angula esolu ion – echniques: in e e ome ic – gamma- ay bu s : gene al –
adio con inuum: gene al – gamma- ay bu s : indi idual: GRB 221009A
1. In oduc ion
On he 9 Oc obe 2022, all sa elli es equipped o an-
sien de ec ion we e igge ed by he ex ao dina y γ-
ay bu s (GRB) 221009A (Ve es e al. 2022;Bissaldi e al.
2022;U si e al. 2022;Piano e al. 2022;Go z e al. 2022;
F ede iks e al. 2022;Tan e al. 2022;Mi chell e al. 2022;
Liu e al. 2022;Lapsho e al. 2022;Xiao e al. 2022;Ripa e al.
2022;Dichia a e al. 2022;Kennea e al. 2022). A a edshi
o z=0.151 (de Uga e Pos igo e al. 2022;Malesani e al.
2024), GRB 221009A holds he eco d o he highes e e
measu ed iso opic equi alen ene gy (Eγ,iso &1055 e g –
?Co esponding au ho ; [email p o ec ed]
Lesage e al. 2023). I is he b igh es GRB in he las 50 yea s
and i is es ima ed o be a one in ∼10 000 yea s occu ence
based on he obse ed lux dis ibu ion o o he known long
GRBs (O’Conno e al. 2023;Bu ns e al. 2023;Malesani e al.
2024). Such a unique e en ini ia ed an unp eceden ed ollow-
up campaign, cha ac e ised by ex ensi e empo al and spec al
co e age. A he highes ene gies, he LHAASO Collabo a-
ion epo ed he de ec ion o sus ained emission well abo e
1 TeV (LHAASO Collabo a ion 2023;Cao e al. 2023). A he
lowe end o he elec omagne ic spec um, adio obse a-
ions o GRB 221009A commenced jus h ee hou s pos -bu s
and de ec ed he b igh es e e adio coun e pa , eaching a
lux densi y o 60 mJy (B igh e al. 2023). Ini ial a emp s
o model he mul i-wa eleng h a e glow emission conside ed
Open Access a icle, published by EDP Sciences, unde he e ms o he C ea i e Commons A ibu ion License (h ps://c ea i ecommons.o g/licenses/by/4.0),
which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed.
This a icle is published in open access unde he Subsc ibe o Open model.Subsc ibe o A&A o suppo open access publica ion.
A74, page 1 o 16
Gia a ana, S. e al.: A&A, 690, A74 (2024)
con ibu ions om bo h he e e se shock (RS) and he o wa d
shock (FS) esul ing om he decele a ion o he ul a- ela i is ic
je by he su ounding ma e ial (Ren e al. 2023;Sa o e al. 2023;
Laska e al. 2023;O’Conno e al. 2023;Gill & G ano 2023;
Zheng e al. 2024). Howe e , unce ain ies pe sis in he inal
in e p e a ion o he da a, despi e inco po a ing mos o he
p esen ly known physical ing edien s go e ning he dynamics
and emission o GRB je s.
Unique measu emen s able o independen ly cons ain he
a e glow e olu ion can be ob ained wi h millia scsecond eso-
lu ion obse a ions. Ve y long baseline in e e ome y (VLBI)
allows o di ec measu emen s o he size o he emis-
sion egion, oge he wi h high-p ecision as ome y. As a
esul , p ope mo ion and sou ce expansion can be measu ed
(Taylo e al. 2004;Mooley e al. 2018;Ghi landa e al. 2019). I
he iewing angle θ be ween he obse e line o sigh and he
GRB je axis is smalle han he je hal -opening angle θj(‘on-
axis’ GRB), he p ojec ed image du ing he a e glow is expec ed
o expand, bu no o show app eciable p ope mo ion. Con-
e sely, i he ou low is obse ed ‘o -axis’ (θ > θj), an appa -
en supe luminal mo ion is expec ed. To da e, measu emen s o
he size and expansion o he emi ing egion ha e only been
possible o GRB 030329 (Taylo e al. 2004,2005), p o iding
he i s di ec e idence o he ela i is ic expansion o GRB
ou lows. O e he las wo decades, nume ous campaigns we e
aimed o epea he success o GRB 030329 (e.g. Nappo e al.
2017;Sala ia e al. 2022;Gia a ana e al. 2022). Howe e , no
e en shone b igh ly and long enough o allow o an expan-
sion measu emen . On he o he hand, o he mul i-messenge
e en GW 170817 (Abbo e al. 2017a,b;Ma gu i & Cho nock
2021), VLBI obse a ions we e undamen al o measu e he
appa en supe luminal mo ion and o cons ain he size o he
emi ing egion o he non- he mal elec omagne ic coun e pa
(Mooley e al. 2018;Ghi landa e al. 2019), p o ing, o he i s
ime e e , ha he me ge s o wo neu on s a s a e able o suc-
cess ully launch ul a- ela i is ic je s.
He e we p esen ou VLBI ollow-up campaign on
GRB 221009A. The da a educ ion is de ailed in Sec. 2. The
me hod implemen ed o measu e he sou ce p ope ies om
adio obse a ions is desc ibed in Sec. 3. In Sec. 4we
p esen he esul s o ou campaign and discuss he physi-
cal implica ions in Sec. 5. Th oughou he wo k, we assume
Planck Collabo a ion VI (2020) cosmological pa ame e s. Wi h
hese pa ame e s, he angula diame e dis ance a z=0.151
is dA=560.3 Mpc. The e o e, 1 mas sepa a ion co esponds o
2.72 pc in p ojec ion a such a dis ance.
2. VLBI obse a ions and da a educ ion
2.1. Eu opean VLBI Ne wo k
We obse ed he ield o GRB 221009A wi h he Eu opean VLBI
Ne wo k (EVN) om 40 o 261 days pos -bu s (PI: Gia a ana,
p ojec code: RG013). Gi en he a ge -o -oppo uni y na u e
o he p oposal, no all an ennas we e a ailable a all epochs.
Table A.1 lis s he an ennas joining each epoch. Table 1p esen s
a summa y o he p ope ies o he obse a ions. The obse a-
ions we e pe o med in wo di e en bands cen ed a 4.9 and
8.3 GHz. The da a we e eco ded a 4 Gbi s s−1. Dual pola i-
sa ion p oduc s (RR, LL) we e co ela ed a he Join Ins i u e
o VLBI in Eu ope (JIVE, Dwingeloo, Ne he lands) using he
Supe FX Co ela o (SFXC; Keimpema e al. 2015) in o six een
sub-bands wi h 32 MHz bandwid h and 64 channels each. Fo
he las epoch, RG013 F, he da a we e co ela ed in o eigh sub-
bands wi h 32 MHz bandwid h and 64 channels each. The i s ,
EVN epoch (RG013 A), ca ied ou 6 days pos bu s a a cen-
al equency o 22.2 GHz, was no usable due o un a ou able
obse ing condi ions.
The obse a ions consis ed o phase- e e encing cycles
wi h 4.5 and 2.5 minu es on he a ge a 4.9 and 8.3 GHz,
espec i ely, and 1.5 minu es on he phase calib a o . Fu -
he scans e e y app oxima ely 30 minu es on some ‘check’
sou ces we e also included. Th oughou he obse a ions,
some scans on a inge inde we e pe o med. The adio
sou ce J190536.4+194308 (J1905+1943 he ea e ) and he
Ve y La ge A ay Sky Su ey (VLASS) compac adio sou ce
J191142.50+195200 (J191142+1952 he ea e ) we e used as
phase calib a o s in he i s wo (RG013 B and C) and in he
las h ee obse a ions (RG013 D, E and F), espec i ely.
The calib a ion was pe o med using AIPS1(G eisen 2003),
ollowing he s anda d p ocedu e o EVN phase- e e enced
obse a ions2. The ampli ude calib a ion, which accoun s o
he bandpass esponse, he an enna gain cu es and he sys em
empe a u es, was pe o med by applying he gains de i ed by
he EVN pipeline. We pe o med a co ec ion o he dispe -
si e delay using he IONEX iles om he In e na ional GNSS
Se ice ( lba ec p ocedu e in AIPS), we calcula ed a manual
single band delay on he inge inde ( lbampcl p ocedu e in
AIPS) and we ca ied ou he global inge i ing on he phase
calib a o ( ing ask in AIPS) using a model o he sou ce
de i ed by a conca ena ion (in CASA,McMullin e al. 2007) and
sel -calib a ion (in Di map,Shephe d e al. 1994) o all he is-
ibili ies on he sou ce ob ained ac oss he a ious epochs. Solu-
ions we e in e pola ed (clcal ask in AIPS) and applied o he
phase calib a o i sel , he a ge and some check sou ces (see
Appendix A). Fo he las h ee epochs, we co ec ed he isibil-
i ies o J191142+1952 by ixing he phase cen e in CASA o he
ac ual posi ion o he phase calib a o , as he ini ial posi ion o
his phase calib a o was no cons ained wi h a sub-mas esolu-
ion.
Images o he sou ces we e p oduced using Di map. Fo
he analysis p esen ed in his pape , we selec ed he image wi h
he bes signal- o-noise a io (S/N) among he wo images p o-
duced be o e and a e he sel -calib a ion o he phase calib a o ,
espec i ely. Fo RG013 C, he lux densi y o he GRB enabled
a sel -calib a ion in phase in AIPS (solin =1 min). Fu he in o -
ma ion on he s uc u e and he da a educ ion p ocess can be
ound in Appendix A.
2.2. Ve y Long Baseline A ay
The Ve y Long Baseline A ay (VLBA) da a we e acqui ed
be ween 44 and 262 days pos -bu s (PI: A i, p ojec code:
BA160). The cen al equency was 15.2 GHz, wi h a o al band-
wid h o 512 MHz, di ided in o 4 spec al windows o 128 MHz
and 256 channels each, in ull ci cula pola isa ion (RR, LL, RL,
LR). The numbe o pa icipa ing s a ions con ibu ing use ul
da a was 7, 8, 10 and 10 in expe imen s BA160 B, C, C1 and D
espec i ely (see Table A.1). Each obse a ion included app ox-
ima ely 30-minu e-long geode ic-s yle blocks a he beginning
and a he end o he obse a ion, used o de e mine opo-
sphe e modelling e o s. The cen al pa o he obse a ions
included scans on inge inde b igh calib a o s and epe i ions
1The As onomical Image P ocessing Sys em (AIPS) is a so wa e
package p oduced and main ained by he Na ional Radio As onomy
Obse a o y (NRAO).
2h ps://www.e lbi.o g/e n-da a- educ ion-guide
A74, page 2 o 16
Gia a ana, S. e al.: A&A, 690, A74 (2024)
Table 1. Log able o ou VLBI campaign and summa y esul s o ci cula Gaussian i s o sou ce isibili ies.
Code Da e Time obs − 0A ay νobs bmaj (†)bmin (†)bp.a.(†)Phase Calib a o .m.s. (†)Fν(?)FWHM (?)hβappi(?)
[hh:mm UT] [days] [GHz] [mas] [mas] [deg] [µJy/b] [mJy] [mas] c
RG013 B 2022-11-18 09:30–13:30 40 EVN 8.1–8.6 1.4 0.45 11 J1905+1943 67 1.02+0.05
−0.05 0.12+0.05
−0.07 5.5+2.5
−3.2
RG013 C 2022-11-21 09:30–13:30 43 EVN 4.6–5.1 3.7 0.69 11 J1905+1943 16 1.42+0.03
−0.03 <0.20 <8.7
BA160 B 2022-11-22, 23 19:58–00:58 44 VLBA 14.9–15.3 1.4 0.40 −9 J1905+1943 130 0.80+0.08
−0.07 0.27+0.05
−0.06 11.3+2.1
−2.3
BA160 C 2023-01-31 15:15–20:14 114 VLBA 14.9–15.3 1.4 0.58 3.5 J1905+1943 66 0.27+0.06
−0.05 0.45+0.19
−0.19 7.4+3.1
−3.0
RG013 D 2023-02-03 05:30–11:30 117 EVN 4.6–5.1 7.1 0.9 7.8 J191142+1952 10 0.47+0.03
−0.03 0.35+0.09
−0.12 5.6+1.4
−1.9
RG013 E 2023-02-04 05:30–11:30 118 EVN 8.1–8.6 1.4 0.59 10 J191142+1952 21 0.59+0.07
−0.06 0.39+0.06
−0.07 6.2+0.9
−1.0
BA160 C1 2023-05-02 10:17–15:16 205 VLBA 14.9–15.3 1.5 0.51 −10 J1905+1943 35 0.33+0.09
−0.07 1.39+0.48
−0.42 12.6+4.3
−3.8
RG013 F 2023-06-27, 28 19:30–02:36 261 EVN 4.8–5.1 1.8 1.5 62 J191142+1952 10 0.16+0.01
−0.01 0.42+0.12
−0.17 3.0+0.9
−1.2
BA160 D 2023-06-28 04:08–09:19 262 VLBA 14.9–15.3 1.7 0.57 −3 J1905+1943 37 0.19+0.19
−0.07 <9.3<66
No es. (†)Beam majo axis, mino axis, posi ion angle, .m.s. noise le el wi h na u al weigh s. (?)Median and 68% con idence in e al o he lux
densi y Fνand ull wid h a hal maximum FWHM om i ing a ci cula Gaussian o he sou ce isibili ies; and o he a e age appa en expansion
speed hβappi, assuming ze o size a 0. I he lowe ex emum o he 68% c edible in e al is 0, we epo he 95% uppe limi ins ead.
o a J1905+1943 – J1925+2106 – GRB 221009A sequence,
whe e J1905+1943 and J1925+2106 a e known VLBA calib a-
o s, wi h espec i e du a ions o 30s – 30s – 80s.
The da a we e co ela ed a he NRAO in Soco o using he
Dis ibu ed FX so wa e co ela o (DiFX; Delle e al. 2011).
The da a educ ion was ca ied ou in AIPS, ollowing s anda d
p ocedu es o con inuum phase- e e encing expe imen s. P o-
cedu es lbaeops, lbacco , lbampcl, lbabpss, lbaamp
we e ca ied ou in his o de o he ini ial bandpass and ampli-
ude calib a ion. The ollowing s ep consis ed in he calib a ion
o he oposphe e modeling e o s by unning he ask ing
on he geode ic blocks, ollowed by mbdly and delzn. The inal
phase, a e, and delay inge- i ing was ca ied ou sepa a ely
on J1905+1943 and J1925+2106, yielding high S/N and well-
beha ed solu ions o bo h sou ces. The solu ions om he close
phase calib a o , J1905+1943, we e applied o he a ge ield.
A e p epa ing a model o he phase calib a o using Di map, a
cycle o ampli ude and phase solu ions we e de e mined o he
calib a o i sel and applied o he a ge o u he e ine he cal-
ib a ion. Finally, we p oduced single-sou ce equency-a e aged
da ase s o he a ge , which we e imaged in AIPS wi h a na u al
weigh ing scheme.
Ou VLBA campaign included one mo e epoch, BA160 A,
a app oxima ely 14 days pos -bu s . Howe e , as he an ennas
we e poin ed a an inco ec posi ion in he sky, he GRB ell
ou side he p ima y beam o he VLBA, which is app oxima ely
3 a cmin a 15 GHz. While he educed sensi i i y (app oxi-
ma ely 25% o nominal) s ill allowed o he de ec ion o he
bu s , a sa is ac o y calib a ion o he complex isibili ies was
hampe ed. The e o e, we did no include his expe imen in ou
analysis.
3. Me hods
3.1. Sou ce lux densi y, size and a e age appa en
expansion eloci y es ima e
In o de o ex ac in o ma ion abou he o al lux densi y, size
and posi ion o he sou ce om each o ou epochs, we i ed a
ci cula Gaussian sou ce model o he calib a ed isibili y da a
adop ing a Ma ko Chain Mon e Ca lo (MCMC) app oach. The
me hod, which is an ex ension o ha adop ed in Sala ia e al.
(2022), is desc ibed in Appendix B. The p ojec ed angula diam-
e e o he sou ce image is p opo ional o he ull wid h a hal
maximum (FWHM) o he i ed ci cula Gaussian, wi h a p o-
po ionali y cons an o o de uni y ha depends on he de ailed
su ace b igh ness p o ile (G ano e al. 1999,2005;Taylo e al.
2004;Pihls öm e al. 2007;G ano 2008;Sala ia e al. 2022). In
wha ollows, we se he p opo ionali y cons an equal o 1, and
discuss i whene e ele an . Once his diame e is measu ed, he
a e age appa en expansion eloci y can be calcula ed (assuming
he size o be ze o a he ime 0o he explosion) as
hβappi=(1 +z)dAs
2( obs − 0)c,(1)
whe e sis he FWHM, obs is he ime o he obse a ion, and c
is he speed o ligh .
Table 1summa ises he esul o he ci cula Gaussian i -
ing, along wi h he de i ed a e age appa en expansion eloc-
i y. In Appendix Bwe p o ide mo e de ailed in o ma ion in he
o m o co ne plo s ha illus a e he pos e io p obabili y den-
si y o he lux densi y and sou ce size om he ci cula Gaussian
i ing. Figu e 1addi ionally shows ‘ iolin plo s’ ha illus a e a
ke nel densi y es ima e o he pos e io p obabili y densi y o he
FWHM o each epoch.
3.2. Sou ce size e olu ion model i ing
In o de o i a size e olu ion model sm( obs,θ) o he obse -
a ions, whe e θis a ec o o ee pa ame e s, we adop ed a
Bayesian app oach. By Bayes’ heo em, and gi en he ac ha
he size es ima es om di e en obse a ions a e independen ,
he pos e io p obabili y on θis p opo ional o he p io π(θ)
imes he p oduc o he likelihoods. This can be w i en as
Pθ|{di}M
i=1∝π(θ)
M
Y
i=1
Psm( obs,i)|di
π(s),(2)
whe e M is he numbe o epochs included in he i , diis he da a
(i.e. he isibili ies) o he i- h epoch, obs,iis he ime o he i- h
obse a ion, π(s)= Θ(s) (whe e Θis he Hea iside s ep unc-
ion) is he p io on he size adop ed in he ci cula Gaussian i s,
P(s|di) is he pos e io om such i s (Eq. B.3) ma ginalised on
all pa ame e s excep s. In o de o e alua e Eq. (2), we app ox-
ima ed he ma ginalised pos e io on he size P(s|di) wi h a
Gaussian ke nel densi y es ima e based on he pos e io samples
de i ed om he MCMC desc ibed in Sec . 3.1. This allowed us
o sample he pos e io on θagain h ough an MCMC app oach.
A74, page 3 o 16
Gia a ana, S. e al.: A&A, 690, A74 (2024)
101102103
Time a e explosion [days]
10 2
10 1
100
101
P ojec ed FWHM [mas]
EVN (8.3 GHz)
EVN (4.9 GHz)
VLBA (15 GHz)
0.0 0.5 1.0 1.5
slope
Fig. 1. Sou ce size as a unc ion o ime. The sou ce size cons ain s ob ained as desc ibed in Sec ion 3.1 a e shown in he o m o iolin plo s
o di e en colou s, cen ed a he obse ing ime o each epoch and o p opo ional wid h o he pos e io p obabili y densi y o he FWHM. In
addi ion, we show he median and 68% c edible in e al wi h an e o ba o he same colo , o he 95% c edible uppe limi wi h a iangle i he
o me in e al ex ends o 0. The black dashed line and he wo g ey shaded a eas show espec i ely he median, 68% c edible in e al and 95%
c edible in e al o he pos e io p edic i e dis ibu ion o he sou ce size e olu ion ob ained om i ing a powe law model s∝ a
obs o he sizes
om all he epochs. The inse shows he pos e io p obabili y densi y o he slope a om such i .
3.3. Fo wa d and e e se shock size e olu ion and p ope
mo ion model
In o de o in e p e ou obse a ions in he con ex o he s an-
da d a e glow scena io, we de i ed a simple physical model o
he size e olu ion and, in he case o a je no aligned wi h he
obse e ’s line o sigh , he p ope mo ion o he sou ce expec ed
i he emission is domina ed by ei he he FS o he RS p o-
duced as a ela i is ic je expands in o an ex e nal medium wi h
a powe law numbe densi y p o ile n(R)=A(R/R?)−k, whe e
Ris he dis ance om he explosion si e (i.e. he p ogeni o
es ige) and R?=5.5×1017 cm is a e e ence adius3. We
assumed a uni o m je angula ene gy p o ile o simplici y, wi h
an iso opic-equi alen kine ic ene gy E, a hal -opening angle
θj, an ini ial Lo en z ac o Γ0and a du a ion T(which se s he
je adial wid h ∆R∼cT). The iewing angle is assumed o
be ei he θ =0 (on-axis, o he calcula ion o he p ojec ed
size) o θ > θj(o -axis, o he calcula ion o he appa en
p ope mo ion). The model is based on he s anda d ela i is ic-
hyd odynamical heo y o a ela i is ic shock ha a ises om a
ela i is ic explosion in o a s a ic, cold ex e nal medium (e.g.
Mesza os & Rees 1993;Pi an e al. 1993;Sa i & Pi an 1995;
Kobayashi e al. 1999;Kobayashi & Zhang 2003;Yi e al. 2013)
and is desc ibed in de ail in Appendix D. We no e ha he model
does no include he possible sideways expansion o he shock.
The ee pa ame e s o he model a e he ene gy- o-densi y
a io E/A, he du a ion T, he ini ial Lo en z ac o Γ0, he je
3Wi h his de ini ion, Ahas he same meaning as he usual A?=
1 ( ˙
Mw/10−5My −1)( w/1000 km s−1) cm−3pa ame e in he wind-like
ex e nal medium case (k=2), whe e ˙
Mwand wa e he mass
loss a e and he eloci y o he p ogeni o wind, assumed cons an
(Panai escu & Kuma 2000). In he k=0 case, i is simply equal o
he homogeneous ex e nal numbe densi y, A=n.
hal -opening angle θj, he ex e nal medium densi y p o ile slope
kand he iewing angle θ . He ea e we ix T=T90/(1 +z)=
251 s, whe e T90 e e s o he ime encompassing he 5% o 95%
pe cen ile o he o al pho on coun s as seen in he obse e ’s e -
e ence ame, and we assume Γ0=103based on he lowe limi s
om Lesage e al. (2023). Mo eo e , we conside only wo al-
ues o he ex e nal medium densi y p o ile slope, which a e k=0
(homogeneous ex e nal medium) and k=2 (wind-like ex e nal
medium).
The model p edic s he ime e olu ion o he p ojec ed angu-
la diame e o he o wa d and e e se shock images (Eq. D.7).
On he o he hand, ou es ima ed sou ce sizes a e ob ained by
i ing a ci cula Gaussian model o he isibili y da a. The a io
o he wo sizes ξ=sm/s(whe e smis he angula diame e
p edic ed by he model, and sis he FWHM o he ci cula
Gaussian) depends on he lowes -o de e ms o he MacLau-
in expansion in UV adius o he Fou ie ans o m o he
su ace b igh ness dis ibu ion o he sou ce (Thompson e al.
2017). Taking he su ace b igh ness om Bland o d & McKee
(1976) as compu ed in G ano (2008) as e e ence, we expec
1.2.ξ.1.8. This ange accommoda es alues p e iously
conside ed in he li e a u e, such as he alue ξ=1.4 used in
Pihls öm e al. (2007) and ξ=1.3 used in Sala ia e al. (2022).
Since ou model does no p edic he su ace b igh ness dis ibu-
ion, we include ξin ou model as a nuisance pa ame e , wi h a
uni o m p io in he ange [1.2,1.8].
4. Resul s
4.1. Sou ce size expansion
Figu e 1shows he sou ce size cons ain s om Table 1in he
o m o a ‘ iolin plo ’, wi h he wid h o each shaded egion
being p opo ional o he pos e io p obabili y densi y o he
A74, page 4 o 16
Gia a ana, S. e al.: A&A, 690, A74 (2024)
FWHM, ho izon ally cen ed a he ime o he obse a ion.
Addi ionally, we show he median and 68% symme ic c edi-
ble in e al on he FWHM by means o an e o ba o each
obse a ion, excep o cases whe e he pos e io p obabili y
densi y does no show a clea peak, o which we show ins ead
he 3σuppe limi wi h a downwa d-poin ing iangle. In o de
o quan i y he sou ce size e olu ion om hese obse a ions,
we i a simple phenomenological powe law e olu ion model,
sm( obs)∝ a
obs, o hese size measu emen s, h ough he me hod
ou lined in Sec . 3.2. The esul ing pos e io p obabili y densi y
o he powe law slope is shown in he inse o Figu e 1. The
median and symme ic 68% c edible in e al is a=0.69+0.13
−0.14.
We ound ha mo e han 99.99% o he pos e io p obabili y
(>4σ-equi alen ) is loca ed a a>0. The e o e, ou obse a-
ions s ongly suppo he expansion o he sou ce. In he main
panel o Figu e 1, we show wi h a black dashed line he median
o he pos e io p edic i e dis ibu ion, ha is, he p obabili y
dis ibu ion o sm( obs) a each ixed obs, as de i ed om he i .
The do ed lines encompass he 68% symme ic c edible in e al
o he same dis ibu ion, illed wi h a g ey shade. A ligh e g ey
shading shows he 95% symme ic c edible in e al. We no e ha
he size measu emen s in ou 15 GHz VLBA epochs a 44 and
205 days a e in mild ension wi h he EVN measu emen s a sim-
ila imes. To explo e he possibili y o a equency-dependen
size, we epea ed he powe law size e olu ion model i con-
side ing only obse a ions pe o med wi h he EVN o VLBA.
Fig. 2shows he esul ing size e olu ion as i ed o EVN obse -
a ions a 4.9 GHz and 8.3 GHz (uppe panel) o VLBA obse -
a ions a 15 GHz (lowe panel). The plo s a e simila o Figu e
1, excep ha he epochs no conside ed in he i a e shown wi h
a ligh g ey shading. The cons ain on a om hese i s esul s
in medians and symme ic c edible in e als o a=0.79+0.19
−0.23
(4.9–8.3 GHz) and a=0.98+0.36
−0.38 (15 GHz), in ag eemen wi h
each o he . On he o he hand, he no malisa ions o he EVN and
VLBA powe laws di e a he ∼2σle el, as can be e inced om
he wo-dimensional pos e io p obabili ies shown in Fig. 3.
In o de o exclude he possibili y ha ou esul s wi h he
EVN a e d i en by sys ema ic e ec s, we ca ied ou a se ies
o es s including he check sou ce J1905+1943. We p esen he
esul s o ou es s in Appendix C. The esul s o hese es s indi-
ca e ha he obse ed e olu ion is no d i en by sys ema ic e o s
in he calib a ions.
4.2. Appa en p ope mo ion
VLBI obse a ions can cons ain he appa en p ope mo ion
o he cen oid o he emission and, he e o e, he je iewing
angle. The sou ce posi ion a each VLBA epoch is displayed in
Fig. 4: ou esul s do no show any signi ican appa en p ope
mo ion be ween 44 and 262 days pos -bu s , bu ou s a is ical
e o s can accommoda e a displacemen o up o abou 0.6 mas
(a he one-σle el) o e ha pe iod. As shown in Appendix
D.2, such an uppe limi does no cons ain s ongly θ , which
can s ill be se e al deg ees o he edge o he je , unless he
ene gy- o-densi y a io o he explosion is e y la ge. S ill, a
numbe o s udies including LHAASO Collabo a ion (2023) and
O’Conno e al. (2023) ha e used hei da a o jus i y a e y
small θ o GRB 221009A, indica ing ha we a e iewing he je
close o on-axis. The lack o signi ican p ope mo ion obse ed
du ing ou VLBI campaign is ully consis en wi h such on-axis
scena io.
We no e ha he EVN campaign was no used o such s udy
because o he change in phase e e ence sou ce be ween he sec-
ond and hi d epoch. While his change was mo i a ed by he
101102103
Time a e explosion [days]
10 2
10 1
100
101
P ojec ed FWHM [mas]
EVN (8.3 GHz)
EVN (4.9 GHz)
012
slope
101102103
Time a e explosion [days]
10 2
10 1
100
101
P ojec ed FWHM [mas]
VLBA (15 GHz)
012
slope
Fig. 2. Size e olu ion conside ing only obse a ions om a single a ay
(uppe panel: EVN; lowe panel: VLBA). Each panel is simila o
Figu e 1, excep ha he epochs no conside ed in he i a e shown
wi h ligh g ey shading o cla i y.
disco e y o a close phase calib a o (and hence a mo e e i-
cien obse ing s a egy), he di e en sys ema ics and he lack
o a eliable a p io i posi ion o he new calib a o p e en a eli-
able as ome ic cha ac e isa ion.
5. Discussion
5.1. Slope o he size e olu ion wi h ime
The size e olu ion powe law slope a=0.69+0.13
−0.14 we
de i ed is compa ible wi h he expec ed slopes o a sphe ical
Bland o d & McKee (1976) blas wa e expanding in o a homo-
geneous medium, α=5/8=0.625, o a wind-like medium,
α=3/4=0.75. Mo eo e , he e olu ion o he p ojec ed phys-
ical size is qui e simila o ha o GRB 030329, he only o he
bu s o da e wi h a measu ed expansion a e (Taylo e al. 2004,
Fig. 5).
A74, page 5 o 16

Gia a ana, S. e al.: A&A, 690, A74 (2024)
0.0 0.2 0.4 0.6 0.8
Size a 100 days [mas]
0.5
0.0
0.5
1.0
1.5
2.0
2.5
Slope
EVN (4.9-8.3 GHz)
VLBA (15 GHz)
Fig. 3. Compa ison o he slope and no malisa ion o he size e olu ion
as p obed by he EVN and he VLBA. The con ou s in he plo con ain
68% (da ke con ou s) and 95% (ligh e con ou s) o he pos e io p ob-
abili y on he wo pa ame e s (slope and size a a e e ence ime o 100
days) o a single powe law i ed o he EVN (blue) o VLBA (o ange)
size e olu ion.
0.40.20.00.20.4
RA [mas]
0.4
0.2
0.0
0.2
Dec [mas]
Rela i e o 19h13m3.50116s +19d46m24.22970s
BA160 B (44 d)
BA160 C (114 d)
BA160 C1 (205 d)
BA160 D (262 d)
Fig. 4. Sou ce posi ion in ou VLBA obse a ions. Fo each epoch, we
show he s a is ical e o ba cen e ed on he median posi ion om he
ci cula Gaussian sou ce i , wi h ba s spanning he symme ic 68%
c edible in e al on he sou ce posi ion in each di ec ion.
On he o he hand, a he ime o ou obse a ions, he
aniso opy o he shock due o he ini e opening angle o he
je should be obse able, bo h in e ms o a s eepening (a ‘je
b eak’, Rhoads 1997) in he ligh cu es, and in e ms o a
la ening in he e olu ion o he p ojec ed size (G ano e al.
2005). The p esence o a je b eak in he e y high ene gy
a e glow ligh cu e a <1000 seconds pos - igge has been
discussed by LHAASO Collabo a ion (2023). A je -b eak was
also sugges ed by Le an e al. (2023) a .2600 seconds pos -
igge , using op ical o mid-IR da a. The expec ed pos -je -
b eak size e olu ion slope in he case o a homogeneous ex e -
nal medium is a=1/4, in absence o an e icien sideways
expansion o he shock (G ano e al. 2005). Such a shallow
101102
Time - T0/(1 +
z
) [days]
1018
1019
1020
P ojec ed size [cm]
GRB 030329
GRB 221009A
Fig. 5. Compa ison o size measu emen s om VLBI obse a ions o
GRB 030329 ( ed ci cles; Taylo e al. 2004;Pihls öm e al. 2007) and
GRB 221009A (da k blue squa es, his wo k). T iangles ep esen uppe
limi s.
slope is in ension wi h he obse ed one a he ∼3σle el. Con-
e sely, he expec ed a e age slope is s eepe and lies in he
ange hai ∼ 0.6−0.8 i he shock expands sideways (G ano e al.
2005), which is compa ible wi h he obse ed one. The e o e,
in he homogeneous ex e nal medium scena io, ou obse a-
ions indica e ha ei he he je b eak has no happened ye ,
o ha he shock is expanding sideways. Gi en he e y la ge
iso opic equi alen ene gy in he gamma- ays, he ‘la e je
b eak’ scena io would pose e y demanding equi emen s on
he o al ene gy (see e.g. O’Conno e al. 2023). On he o he
hand, nume ical simula ions o ex e nal shocks a ising om
ela i is ic je s and analy ical a gumen s seem o indica e ha
he sideways expansion is ine icien , unless he ini ial open-
ing angle is e y na ow ( an Ee en e al. 2010;De Colle e al.
2012;G ano & Pi an 2012). These di icul ies could be alle i-
a ed i he je ea u es a s uc u e consis ing o a na ow ‘co e’
su ounded by ‘wings’ whe e he kine ic ene gy pe uni solid
angle dec eases slowly, as sugges ed by O’Conno e al. (2023)
and Gill & G ano (2023). This p o ile would s eepen he e olu-
ion o he obse ed size, making i mo e simila o he sphe ical
case, bu wi h a educed ene gy equi emen wi h espec o a
wide je wi h a uni o m angula ene gy p o ile.
In he wind medium case, he expec ed pos -je -b eak size
e olu ion slope is a=1/2 in absence o sideways expansion.
The e o e, in such a scena io, he obse ed e olu ion does no
indica e he need o sideways expansion no o a non-uni o m
s uc u e wi hin he opening angle.
5.2. Possible equency-dependen size
As discussed in sec ion 4.1, ou da a sugges he p esence o a
equency-dependen size e olu ion. We explo e he e a possi-
ble a enue o in e p e his beha iou . The adio a e glow o
his GRB canno be explained by a simple FS p opaga ing ei he
in o a wind-like o a homogeneous en i onmen (Ren e al. 2023;
A74, page 6 o 16
Gia a ana, S. e al.: A&A, 690, A74 (2024)
101102
Time a e explosion [days]
10 2
10 1
100
101
P ojec ed FWHM [mas]
k
= 0
15 GHz: FS-domina ed
4.9-8.3 GHz: RS-domina ed
RS
FS
101102
Time a e explosion [days]
10 2
10 1
100
101
P ojec ed FWHM [mas]
k
= 2
15 GHz: FS-domina ed
4.9-8.3 GHz: RS-domina ed
RS
FS
Fig. 6. Model size e olu ion in a FS plus RS scena io. The iolins and
he e o ba s show he sou ce size e olu ion as in e ed by ou obse -
a ions, in he same way as in Figu e 1. The g ay do ed line and o ange
dashed lines show he medians o he pos e io p edic i e dis ibu ions
o he FS and RS size, espec i ely, as ob ained by i ing he physi-
cal model desc ibed in Appendix D o he sizes shown in he igu e,
assuming a homogeneous ( op panel) o wind-like (bo om panel) ex e -
nal medium, and assuming he FS o domina e a 15 GHz and he RS o
domina e a 4.9 and 8.3 GHz. The shaded bands a ound hese lines show
he 68% c edible in e al o he pos e io p edic i e dis ibu ion.
Sa o e al. 2023;Ren e al. 2024;Zheng e al. 2024). Using a
da a se encompassing obse a ions om he GeV o he adio
domain, Laska e al. (2023) showed ha he s anda d a e glow
model s uggles a explaining he adio emission bo h wi h a
FS and a RS o a conical je p opaga ing h ough a wind-like
en i onmen , leading hem o in oke an addi ional componen
whose empo al e olu ion does no ollow he s anda d p esc ip-
ions. Such a componen could be a RS, domina ing he emission
a he lowe equencies (.10 GHz) up o obs .100 d (see he
modelling o O’Conno e al. 2023;Gill & G ano 2023).
S imula ed by hese s udies, we explo ed a scena io whe e
he emission we obse ed is a supe posi ion o a FS and a RS. We
i ed he model desc ibed in Sec . 3.3 o he obse ed size e olu-
ion, lea ing E/Aand θjas ou ee pa ame e s, and addi ionally
including he ξnuisance pa ame e (see sec ion 3.3). The ex e -
nal medium powe law index was ixed o k=0 o k=2. Based
56.90+1.02
0.84
54
55
56
57
58
log((
E
/
A
)/e gcm3)
8
16
24
je
[deg]
54.0
54.5
55.0
55.5
56.0
56.5
57.0
6
12
18
24
30
je
[deg]
21.18+8.82
8.23
(95%)
54.98+0.48
0.45
54.0
54.5
55.0
55.5
56.0
log((
E
/
A
)/e gcm3)
6
12
18
24
30
je
[deg]
53.0
53.5
54.0
54.5
55.0
6
12
18
24
30
je
[deg]
23.14+6.86
7.12
(95%)
Fig. 7. Co ne plo o he pos e io p obabili y densi y o he physical
model pa ame e s in he homogeneous ( op panel) o wind-like (bo -
om panel) ex e nal medium case and assuming he FS o domina e
a 15 GHz and he RS o domina e a 4.9–8.3 GHz. In each panel, he
ed his og ams show he ma ginalised pos e io p obabili y densi ies,
wi h black solid e ical lines showing he median and dashed lines
showing he 68% c edible in e al o , i he la e ex ends o he lowe
(uppe ) ex emum o he p io ange, he 95% uppe (lowe ) limi ( al-
ues epo ed on op o he panels). The illed con ou s show he small-
es egions con aining 68% and 95% o he wo-dimensional pos e io
p obabili y, wi h he black squa es showing he posi ion o he median.
The g ey lines show con ou s o cons an o al je ene gy assuming
A=1 cm−3. Each con ou is labeled wi h he base-10 loga i hm o he
co esponding o al je ene gy.
on he appa en possible equency-dependen beha iou , we
assumed he highe - equency obse a ions (15 GHz) o be dom-
ina ed by he FS, while he lowe - equency ones (4.9–8.3 GHz)
o be domina ed by he RS. Fo each ex e nal densi y p o ile, he
pos e io p obabili y densi y o (E/A, θj, ξ) was de i ed h ough
he Bayesian app oach desc ibed in Sec . 3.2, wi h uni o m-
in-log p io s on E/Ain he ange [1052,1058] e g cm3and on
θjin he ange [0.5,30] deg, and a uni o m p io on ξin he
ange [1.2,1.8], as explained in sec ion 3.3. Figu e 6shows
he FS and RS model size e olu ion i ed o he obse a ions.
Figu e 7shows co ne plo s o he pos e io p obabili y densi-
ies, ma ginalized o e ξ.
The model can easonably ep oduce he da a in bo h he
homogeneous (k=0) and wind-like (k=2) ex e nal medium
A74, page 7 o 16
Gia a ana, S. e al.: A&A, 690, A74 (2024)
cases. Due o he ela i ely s eep obse ed size e olu ion, and
gi en ha ou model does no include sideways expansion, he
equi ed je hal -opening angle is la ge (θj>13 deg a he 95%
c edible le el o k=0; θj>16 deg o k=2). Assuming
he s anda d e e ence ex e nal densi y A=1 cm−3, his in u n
pushes he o al je ene gy Eje =E(1 −cos θj) o e y la ge al-
ues, as demons a ed by he g ey con ou s in Fig. 7. The ene gy
equi emen can be educed i he ex e nal densi y is much lowe
han he e e ence alue, A1 cm−3, o i he je ea u es
an angula s uc u e such ha he ene gy pe uni solid angle
dec eases away om he je axis, as discussed in he p e ious
sec ion. In his case, he dec ease mus be shallow (E∝θ−awi h
a<2, whe e θis he angle om he je axis), o he wise bo h
he emission and he size e olu ion would simply e lec hose o
a uni o m je (O’Conno e al. 2023), leading again o he same
di icul ies wi h he je opening angle and o al ene gy.
6. Conclusions
In his pape , we p esen ed VLBI obse a ions o he b igh es γ-
ay bu s e e obse ed, GRB 221009A. The high angula esolu-
ion p o ided by he EVN and he VLBA allowed us o cons ain
he size and he expansion o he blas wa e p oduced by he
GRB ejec a o he second ime e e . The expansion a e is con-
sis en wi h he expec a ion o a sphe ical Bland o d & McKee
(1976) blas wa e (i.e., an ul a- ela i is ic FS) p opaga ing in o
a homogeneous o wind-like medium. This could be aken as an
indica ion ha he shock is aniso opic only on angula scales
la ge han hose p obed by ou obse a ions (i.e. he je b eak
has no happened ye ). This in u n poin s o an ex emely la ge
o al (collima ion-co ec ed) ene gy in he je , especially i he
ex e nal medium ea u es a homogeneous densi y. The demand-
ing ene gy equi emen could be alle ia ed i he ex e nal den-
si y we e much lowe han usually assumed, o i he je ene gy
pe uni solid angle dec eased slowly wi h he angle om he je
axis, as p oposed by O’Conno e al. (2023) and Gill & G ano
(2023). Al e na i ely, he shock could be unde going sideways
expansion du ing he ime co e ed by ou obse a ions.
Addi ionally, ou obse a ions sugges a equency-
dependen size e olu ion, wi h he VLBA obse a ions a
15 GHz showing a somewha la ge size a 40 days a e he
explosion, and a as e inc ease a e wa ds, wi h espec o he
EVN obse a ions a 5 and 8 GHz. This could be due o he
emission being domina ed by he e e se shock a he lowe
equencies, and by he o wa d shock a he highe equencies.
Ou wo k highligh s he c ucial ole played by mul i-wa eleng h
VLBI moni o ing o ansien e en s bo h a ea ly and la e imes,
and in p o iding a i al insigh in o he physics o such e en s.
Da a a ailabili y
A copy o he educed isibili ies is a ailable a he CDS ia
anonymous p o cdsa c.cds.unis a. (130.79.128.5)
o ia h ps://cdsa c.cds.unis a. / iz-bin/ca /J/
A+A/690/A74
Acknowledgemen s. The Eu opean VLBI Ne wo k is a join acili y o indepen-
den Eu opean, A ican, Asian, and No h Ame ican adio as onomy ins i u es.
Scien i ic esul s om da a p esen ed in his publica ion a e de i ed om he
ollowing EVN p ojec code: RG013. The Na ional Radio As onomy Obse a-
o y is a acili y o he Na ional Science Founda ion ope a ed unde coope a i e
ag eemen by Associa ed Uni e si ies, Inc. This wo k made use o he Swin-
bu ne Uni e si y o Technology so wa e co ela o , de eloped as pa o he
Aus alian Majo Na ional Resea ch Facili ies P og amme and ope a ed unde
licence. SG would like o hank Z. Pa agi and he s a o JIVE o hei help
and suppo du ing his isi ing pe iod in Dwingeloo. We would like o hank
he di ec o s and s a o all he EVN elescopes o app o ing, execu ing, and
p ocessing ou ou -o -session ToO obse a ions. The esea ch leading o hese
esul s has ecei ed unding om he Eu opean Union’s Ho izon 2020 Resea ch
and Inno a ion P og amme unde g an ag eemen No. 101004719 (OPTICON
RadioNe Pilo ). The esea ch leading o hese esul s has ecei ed unding om
he Eu opean Union’s Ho izon 2020 P og amme unde he AHEAD2020 p ojec
(g an ag eemen n. 871158). This wo k has been unded by he Eu opean Union-
Nex Gene a ion EU, PRIN 2022 RFF M4C21.1 (202298J7KT – PEACE). OS
acknowledges unding om he Is i u o Nazionale di As o isica, p ojec num-
be 1.05.23.04.04. BM acknowledges inancial suppo om he S a e Agency
o Resea ch o he Spanish Minis y o Science and Inno a ion unde g an
PID2019-105510GB-C31/AEI/10.13039/501100011033 and h ough he Uni o
Excellence Ma ía de Maez u 2020–2023 awa d o he Ins i u e o Cosmos Sci-
ences (CEX2019- 000918-M). MPT acknowledges inancial suppo h ough
g an s CEX2021-001131-S and PID2020-117404GB-C21 unded by he Spanish
MCIN/AEI/10.13039/501100011033.
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Gia a ana, S. e al.: A&A, 690, A74 (2024)
54 55 56 57
log(
E
/
A
)
[e g cm
3
]
1
2
3
4
5
6
7
8
9
10
11
12
13
j
[deg]
j= 0.5
deg
54 55 56 57
log(
E
/
A
)
[e g cm
3
]
j= 1.0
deg
54 55 56 57
log(
E
/
A
)
[e g cm
3
]
j= 2.0
deg
54 55 56 57
log(
E
/
A
)
[e g cm
3
]
Wind ex . medium (
k
= 2
)
j= 4.0
deg
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
(262d) (44d)
[mas]
56 57 58 59
log(
E
/
A
)
[e g cm
3
]
1
2
3
4
5
6
7
8
9
10
11
12
13
j
[deg]
56 57 58 59
log(
E
/
A
)
[e g cm
3
]
56 57 58 59
log(
E
/
A
)
[e g cm
3
]
56 57 58 59
log(
E
/
A
)
[e g cm
3
]
Homog. ex . medium (
k
= 0
)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(262d) (44d)
[mas]
Fig. D1. Cons ain on he iewing angle om he absence o an obse ed sou ce appa en displacemen in ou VLBA obse a ions. In each panel,
illed con ou s show he displacemen o he cen e o he i ed Gaussian expec ed be ween 44 d and 262 d, colo coded as shown in he colo ba
on he igh , as a unc ion o he E/A a io and o he o -edge iewing angle θ −θj. The ed con ou shows ∆(262 d) −∆(44 d) =0.6 mas, which
ep esen s he la ges displacemen compa ible a 1 σwi h ou obse a ions. The ed con ou hence con ains he excluded pa ame e egion. The
uppe panel ow e e s o a wind-like ex e nal medium, while he lowe ow e e s o a homogeneous ex e nal medium. Each column assumes a
di e en je hal -opening angle, gi en a he op o he column.
A74, page 16 o 16