AT2018cow: A Luminous Millimeter Transient
Anna Y. Q. Ho
1
, E. Sterl Phinney
2
, Vikram Ravi
1
,
3
, S. R. Kulkarni
1
, Glen Petitpas
3
, Bjorn Emonts
4
, V. Bhalerao
5
,
Ray Blundell
3
, S. Bradley Cenko
6
,
7
, Dougal Dobie
8
,
9
, Ryan Howie
3
, Nikita Kamraj
1
, Mansi M. Kasliwal
1
,
Tara Murphy
8
, Daniel A. Perley
10
, T. K. Sridharan
3
, and Ilsang Yoon
4
1
Cahill Center for Astrophysics, California Institute of Technology, MC 249-17, 1200 E California Boulevard, Pasadena, CA, 91125, USA
2
Theoretical Astrophysics, MC 350-17, California Institute of Technology, Pasadena, CA 91125, USA
3
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
4
National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA
5
Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India
6
Astrophysics Science Division, NASA Goddard Space Flight Center, Mail Code 661, Greenbelt, MD 20771, USA
7
Joint Space-Science Institute, University of Maryland, College Park, MD 20742, USA
8
Sydney Institute for Astronomy, School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia
9
ATNF, CSIRO Astronomy and Space Science, P.O. Box 76, Epping, New South Wales 1710, Australia
10
Astrophysics Research Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
Received 2018 October 31; revised 2018 November 26; accepted 2018 November 26; published 2019 January 23
Abstract
We present detailed submillimeter- through centimeter-wave observations of the extraordinary extragalactic transient
AT2018cow. The apparent characteristics
—
the high radio luminosity, the rise and long-lived emission plateau at
millimeter bands, and the sub-relativistic velocity
—
have no precedent. A basic inte
rpretation of the data suggests
E
410erg
k
48
́
coupled to a fast bu
t sub-relativistic
(
vc
0.13
»
)
shock in a dense
(
n
310cm
e
53
» ́
-
)
medium. We
fi
nd that the X-ray emission is not naturally explained by an extension of the radio-submm synchrotron
spectrum, nor by inverse Compton scattering of the dominant blackbody UV
/
optical
/
IR photons by energetic electrons
within the forward shock. By
t
20 days
D
»
, the X-ray emission shows spectral softening and erratic inter-day
variability. Taken together, we are led to i
nvoke an additional source o
f X-ray emission: the central engine of the event.
Regardless of the nature of this central engine, this source heralds a new class of energetic transients shocking a dense
medium, which at early times are most read
ily observed at millimeter wavelengths.
Key words:
gamma-ray burst: general
–
radio continuum: general
–
submillimeter: general
–
supernovae: general
–
X-rays: general
1. Introduction
1.1. The Transient Millimeter Sky
Although the sky is regularly monitored across many bands of
the electromagnetic spectrum
(
as well as in gravitational waves
and energetic particles
)
the dynamic sky at millimeter to
submillimeter wavelengths
(
0.1
–
10 mm
)
remains poorly explored.
There has only been one blind transient survey speci
fi
ctothe
millimeter band
11
(
Whitehorn et al.
2016
)
; millimeter facilities
are usually only triggered after an initial discovery at another
wavelength. Even when targeting known transients, the success
rate for detection is low, and only a few extragalactic
transients
12
have well-sampled, multifrequency light curves to
date. This sample includes supernovae
(
SNe; Weiler et al.
2007
; Horesh et al.
2013
)
, tidal-disruption events
(
TDEs;
Zauderer et al.
2011
; Yuan et al.
2016
)
, and gamma-ray bursts
(
GRBs; de Ugarte Postigo et al.
2012
; Laskar et al.
2013
;
Perley et al.
2014
; Urata et al.
2014
)
.
The paucity of millimeter transient studies can be attributed
in part to costly receiver and electronics systems and the need
for excellent weather conditions, but it also re
fl
ects challenges
intrinsic to millimeter-wave transients themselves: most known
classes are either too dim
(
SNe, most TDEs
)
to detect unless
they are very nearby, or too short-lived
(
GRBs
)
to detect
without very rapid reaction times
(
<
1 day, and even in these
circumstances the emission may only be apparent from low-
density environments; Laskar et al.
2013
)
.
An evolving technical landscape, together with rapid follow-
up enabled by high-cadence optical surveys, present new
opportunities for millimeter transient astronomy. Lower-noise
receivers and ultra-wide bandwidth capability have greatly
increased the sensitivity of submm facilities
(
e.g., the
Submillimeter Array or SMA; Ho et al.
2004
)
, and the
Atacama Large Millimeter Array
(
ALMA
)
,a
fl
agship facility,
recently began operations. Optical surveys are discovering new
and unexpected classes of transient events whose millimeter
properties are unknown
—
and possibly different from pre-
viously known types
—
motivating renewed follow-up efforts.
1.2. AT2018cow
AT2018cow was discovered on 2018 June 16 UT as an optical
transient
(
Prentice et al.
2018
;Smarttetal.
2018
)
by the Asteroid
Terrestrial-impact
Last Alert System
(
ATLAS; Tonry et al.
2018
)
.
It attracted immediate attention because of its fast rise time
(
t
3
peak
days
)
,whichwasestablishedbye
arlier non-detections
(
Fremling
2018
;Prenticeetal.
2018
)
, together with its high optical
luminosity
(
M
20
peak
~-
)
and its close proximity
(
d
60
=
Mpc
)
.
UV
/
optical
/
IR
(
UVOIR
)
observations
(
Perley et al.
2018
;
Prentice et al.
2018
)
revealed unprecedented photometric and
spectroscopic properties. Long-lived luminous X-ray emission
was detected with the
Neil Gehrels Swift Observatory
/
X-ray
The Astrophysical Journal,
871:73
(
19pp
)
, 2019 January 20
https:
//
doi.org
/
10.3847
/
1538-4357
/
aaf473
© 2019. The American Astronomical Society. All rights reserved.
11
The authors searched for transient sources at 90 and 150 GHz. They found a
single candidate event, which intriguingly showed linear polarization.
12
Here we use
“
transient
”
as distinct from
“
variable
”
: millimeter observations
are used to study variability in protostars
(
e.g., Herczeg et al.
2017
)
and more
commonly for active galactic nuclei
(
e.g., Dent et al.
1983
)
. There have also
been millimeter detections of galactic transient sources, primarily stellar
fl
ares
(
e.g., Bower et al.
2003
; Fender et al.
2015
)
.
1
Telescope
(
Swift
/
XRT; Rivera Sandoval & Maccarone
2018
)
, International Gamma-Ray Astrophysics Laboratory
(
INTEGRAL
)(
Ferrigno et al.
2018
; Savchenko et al.
2018
)
,
and the
Nuclear Spectroscopic Telescope Array
(
NuSTAR
)
(
Grefenstette et al.
2018
; Margutti et al.
2018a
)
. Early radio and
submillimeter detections were reported by Northern Extended
Millimeter Array
(
NOEMA
)(
de Ugarte Postigo et al.
2018
)
,
JCMT
(
Smith et al.
2018
)
, Arcminute Microkelvin Imager
(
AMI
)(
Bright et al.
2018
)
, and by us using the Australia
Telescope Compact Array
(
ATCA
)(
Dobie et al.
2018a
,
2018b
)
. The source does not appear to be a GRB, as no
prompt high-energy emission was detected in searches of
Swift
/
Burst Alert Telescope
(
BAT
)(
Lien et al.
2018
)
,
Fermi
/
GBM
(
Dal Canton et al.
2018
)
,
Fermi
/
Large Area Telescope
(
LAT
)(
Kocevski & Cheung
2018
)
, and AstroSat Cadmium
Zinc Telluride Imager
(
CZTI
)(
Sharma et al.
2018
)
.
Perley et al.
(
2018
)
suggested that AT2018cow is a new
member of the class of rapidly rising
(
t
5
rise
days
)
and
luminous
(
M
18
peak
<-
)
blue transients, which have typically
been found in archival searches of optical surveys
(
Drout et al.
2014
; Pursiainen et al.
2018
; Rest et al.
2018
)
. The leading
hypothesis for this class was circumstellar interaction of a
supernova
(
SN; Ofek et al.
2010
)
, but this was dif
fi
cult to test
because most of the events were located at cosmological
distances, and not discovered in real time. AT2018cow
presented the
fi
rst opportunity to study a member of this class
up close and in real time, but its origin remains mysterious
despite the intense ensuing observational campaign. Possibi-
lities include failed SNe and TDEs, but although AT2018cow
shares properties with both of these classes, it is clearly not a
typical member of either
(
Kuin et al.
2018
; Perley et al.
2018
;
Prentice et al.
2018
)
.
Given the unusual nature of the source, we were motivated to
undertake high-frequency observations. We began an extensive
monitoring campaign with the SMA at 230 and 340 GHz and
carried out supporting observations with the ATCA from
5
–
34 GHz. To our surprise AT2018cow was very bright and
still rising at submillimeter wavelengths
(
and optically thick in
the centimeter band
)
days after the discovery. Our SMA
observations represent the
fi
rst millimeter observation of a
transient in its rise phase.
This
fi
nding led us to seek Director
’
s Discretionary Time
(
DDT
)
with ALMA at even higher frequencies, which enabled
us to resolve the peak of the spectral energy distribution
(
SED
)
.
A technical highlight of the ALMA observations was the
detection of the source at nearly a terahertz frequency
(
Band 9
)
.
We present the submillimeter, radio, and X-ray observations in
Section
2
, and our modeling of the radio-emitting ejecta in
Section
3
. In Section
4
, we put our velocity and energy
measurements in the context of other transients
(
Section
4.1
)
,
attribute the high submm luminosity of AT2018cow to the
large density of the surrounding medium
(
Section
4.2
)
, and
discuss some problems with the synchrotron model parameters
(
Section
4.3
)
. In Section
5
, we attribute the late-time X-ray
emission to a powerful central engine. We look ahead to the
future in Section
6
.
2. Observations
All observations are measured
t
D
(
observer frame
)
from the
zero-point MJD 58285
(
following Perley et al.
2018
)
, which
lies between the date of discovery
(
MJD 58285.441
)
and the
last non-detection
(
58284.13; Prentice et al.
2018
)
. The full set
of
fl
ux-density measurements at radio and millimeter wave-
lengths is presented in Table
1
.At
t
14 days
D
=
we
fi
nd
excellent agreement between the SMA and the ALMA data,
showing that the
fl
ux scales are consistent.
2.1. Radio and Submillimeter Observations
2.1.1. The SMA
AT2018cow was regularly observed with the SMA under its
DDT
/
Target of opportunity program. Observations took place
over the period of UT 2018 June 21
–
UT 2018 August 3
(
t
5
D
»
–
49 days
)
in the Compact con
fi
guration, with an
additional epoch on UT 2018 August 31
(
t
76
D
»
days
)
. All
observations contained 6
–
8 antennas and covered a range of
baseline lengths from 16.4
–
77 m. A majority of these
observations were short and were repeated almost nightly by
sharing tuning and calibration data with other science tracks.
The SMA has two receiver sets each with 8 GHz of bandwidth
in each of two sidebands
(
32 GHz total
)
, covering a range of
frequencies from 188
–
416 GHz. Each receiver can be tuned
independently to provide dual-band observations. Additionally,
the upper and lower sidebands are separated
(
center to center
)
by 16 GHz, allowing up to four simultaneous frequency
measurements. During some observations, the receivers were
tuned to the same local oscillator frequency, allowing the lower
and upper sidebands to be averaged together, improving the
signal-to-noise ratio. For all observations, the quasars 1635
+
381 and 3C 345 were used as primary phase and amplitude
gain calibrators, respectively, with absolute
fl
ux calibration
performed by nightly comparison to Titan, Neptune, or
(
maser-
free
)
continuum observations of the emission-line star
MWC349a. The quasar 3C 279 and
/
or the blazar 3C 454.3
was used for bandpass calibration. Data were calibrated in IDL
using the MIR package. Additional analysis and imaging were
performed using the MIRIAD package. Given that the target
was a point source,
fl
uxes were derived directly from the
calibrated visibilities, but the results agree well with
fl
ux
estimates derived from the CLEANed images when the data
quality and UV coverage was adequate.
2.1.2. The ATCA
We obtained six epochs of centimeter-wavelength observa-
tions with the ATCA
(
Frater et al.
1992
)
. During the
fi
rst three
epochs, the six 22 m dishes were arranged in an east
–
west 1.5A
con
fi
guration, with baselines ranging from 153
–
4469 m.
During the latter three epochs,
fi
ve of the six dishes were
moved to a compact H75
13
con
fi
guration, occupying a
cardinally oriented
“
T
”
with baselines ranging from 31
–
89 m.
Full-Stokes data were recorded with the Compact Array
Broadband Backend
(
Wilson et al.
2011
)
in a standard
continuum CABB Filter Bank
(
CFB
)
1M
setup, simultaneously
providing two 2.048 GHz bands each with 2048 channels.
Observations were obtained with center frequencies of 5.5 and
9 GHz, 16.7 and 21.2 GHz, and 33 and 35 GHz, with data in
the latter two bands typically being averaged to form a band
centered at 34 GHz. The
fl
ux-density scale was set using
observations of the ATCA
fl
ux standard PKS 1934
−
638. For
observations below 33 GHz, PKS 1934
−
638 was also used to
calibrate the complex time-independent bandpasses, and
13
https:
//
www.narrabri.atnf.csiro.au
/
operations
/
array_con
fi
gurations
/
con
fi
gurations.html
2
The Astrophysical Journal,
871:73
(
19pp
)
, 2019 January 20
Ho et al.
regular observations of the compact quasar PKS 1607
+
268
were used to calibrate the time-variable complex gains. For the
higher-frequency observations, a brighter source
(
3C 279
)
was
used for bandpass calibration
(
except for epochs 1 and 4
)
, and
the compact quasar 4C 10.45 was used for gain calibration. In
the H75 con
fi
guration, we only report results from observations
at 34 GHz, from baselines not subject to antenna shadowing.
For all 34 GHz observations, data obtained with the sixth
antenna located 4500 m from the center of the array were
discarded because of the dif
fi
culty of tracking the differential
atmospheric phase over the long baselines to this antenna. The
weather was good for all observations, with negligible wind
and
<
500
μ
m of rms atmospheric path-length variations
(
Middelberg et al.
2006
)
.
The data were reduced and calibrated using standard
techniques implemented in the MIRIAD software
(
Sault
et al.
1995
)
. To search for unresolved emission at the position
of AT2018cow, we made multifrequency synthesis images
with uniform weighting. Single rounds of self-calibration over
5
–
10 minute intervals were found to improve the image
quality in all bands. For data at 5.5 and 9 GHz, point-source
models of all strong unresolved
fi
eld sources were used for
self-calibration. For data at the higher frequencies, self-
calibration was performed using a point-source model for
AT2018cow itself, as no other sources were detected within
the primary beams, and AT2018cow was detected with a
suf
fi
cient signal-to-noi
se ratio. We report
fl
ux densities
derived by
fi
tting point-source models to the
fi
nal images
using the MIRIAD task
im
fi
t
.
2.1.3. ALMA
AT2018cow was observed with ALMA as part of DDT
during Cycle 5 using Bands 3, 4, 7, 8, and 9. Observations were
performed on 2018 June 30
(
t
14 days;
D
»
Bands 7 and 8
)
,
2018 July 08
(
t
22 days;
D
»
Bands 3 and 4
)
, and on 2018 July
10
(
t
23 days;
D
»
Band 9
)
.
14
The ALMA 12 m antenna array was in its most compact
C43-1 con
fi
guration, with 46
–
48 working antennas and
baselines ranging from 12
–
312 m. The on-source integration
time was 6
–
8 minutes for Bands 3
–
8, and 40 minutes for Band
9. The Band 3
–
8 observations used two-sideband
(
2SB
)
receivers with 4 GHz bandwidth each centered on 91.5 and
103.5 GHz
(
Band 3
)
, 138 and 150 GHz
(
Band 4
)
, 337.5 and
349.5 GHz
(
Band 7
)
, and 399 and 411 GHz
(
Band 8
)
. The
Band 9 observations used double-sideband
(
DSB
)
receivers
with 8 GHz bandwidth
(
2 times larger than that for the Band
3
–
8 observation, by using 90
°
Walsh phase switching
)
centered
on 663 and 679 GHz. All calibration and imaging was done
with the Common Astronomical Software Applications
(
CASA; McMullin et al.
2007
)
. The data in Bands 3
–
8 were
calibrated with the standard ALMA pipeline, using J1540
+
1447, J1606
+
1814, or J1619
+
2247 to calibrate the complex
gains, and using J1337
−
1257
(
Band 7
)
, J1550
+
0527
(
Band 3
/
4
)
,
or J1517
−
2422
(
Band 8
)
to calibrate the bandpass response and
apply an absolute
fl
ux scale. Band 9 observations were delivered
followingmanualcalibrationbytheNorthAmericanALMA
Science Center, using J1540
+
1447 for gain calibration, and
J1517
−
2422 for bandpass- and
fl
ux calibration. We subsequently
applied a phase-only self-calibration using the target source
Table 1
Flux-density Measurements for AT2018cow
t
D
(
days
)
Facility
Frequency
(
GHz
)
Flux Density
(
mJy
)
5.39
SMA
215.5
15.14
±
0.56
5.39
SMA
231.5
16.19
±
0.65
6.31
SMA
215.5
31.17
±
0.87
6.31
SMA
231.5
31.36
±
0.97
7.37
SMA
215.5
40.19
±
0.56
7.37
SMA
231.5
41.92
±
0.66
7.41
SMA
330.8
36.39
±
2.25
7.41
SMA
346.8
30.7
±
1.99
8.37
SMA
215.5
41.19
±
0.47
8.37
SMA
231.5
41.44
±
0.56
8.38
SMA
344.8
26.74
±
1.42
8.38
SMA
360.8
22.79
±
1.63
9.26
SMA
243.3
35.21
±
0.75
9.26
SMA
259.3
36.1
±
1.0
9.28
SMA
341.5
22.85
±
1.53
9.28
SMA
357.5
25.84
±
2.5
10.26
SMA
243.3
36.6
±
0.81
10.26
SMA
259.3
31.21
±
0.92
10.26
SMA
341.5
19.49
±
1.47
10.26
SMA
357.5
17.42
±
2.8
11.26
SMA
243.3
22.14
±
1.05
11.26
SMA
259.3
20.02
±
1.28
13.3
SMA
215.5
35.67
±
0.81
13.3
SMA
231.5
32.94
±
1.01
14.36
SMA
344.8
26.85
±
2.22
14.36
SMA
360.8
26.13
±
2.77
14.37
SMA
215.5
42.05
±
0.5
14.37
SMA
231.5
38.71
±
0.58
15.23
SMA
225.0
30.82
±
2.41
15.23
SMA
233.0
28.64
±
4.0
15.23
SMA
241.0
27.41
±
3.21
15.23
SMA
249.0
15.4
±
4.74
17.29
SMA
234.6
36.57
±
1.55
17.29
SMA
250.6
34.04
±
1.81
18.4
SMA
217.5
52.52
±
0.55
18.4
SMA
233.5
49.32
±
0.65
19.25
SMA
193.5
59.27
±
1.49
19.25
SMA
202.0
56.03
±
1.5
19.25
SMA
209.5
55.09
±
1.39
19.25
SMA
218.0
54.54
±
1.33
20.28
SMA
215.5
50.6
±
1.69
20.28
SMA
231.5
49.16
±
1.84
20.28
SMA
267.0
41.69
±
1.62
20.28
SMA
283.0
37.84
±
1.63
24.39
SMA
215.5
55.57
±
0.53
24.39
SMA
231.5
53.2
±
0.6
24.4
SMA
333.0
23.98
±
1.39
24.4
SMA
349.0
28.46
±
1.37
26.26
SMA
215.6
38.83
±
1.2
26.26
SMA
231.6
34.1
±
1.33
31.2
SMA
230.6
36.76
±
1.12
a
31.2
SMA
246.6
31.41
±
1.42
a
35.34
SMA
215.5
21.59
±
0.89
35.34
SMA
231.5
20.63
±
1.04
36.34
SMA
215.5
24.32
±
1.19
36.34
SMA
231.5
20.79
±
1.42
39.25
SMA
217.0
18.34
±
1.65
39.25
SMA
233.0
19.74
±
1.76
39.26
SMA
264.0
17.61
±
2.79
39.26
SMA
280.0
8.27
±
2.93
41.24
SMA
217.0
12.58
±
1.5
41.24
SMA
225.0
8.91
±
1.9
41.24
SMA
233.0
15.08
±
1.73
41.24
SMA
241.0
9.64
±
2.13
44.24
SMA
230.6
9.42
±
1.61
14
Band 9 observations were also performed on 2018 July 09, but these data
were of too poor quality to use as a result of weather conditions.
3
The Astrophysical Journal,
871:73
(
19pp
)
, 2019 January 20
Ho et al.
(
for Bands 3
–
8
)
, performed a deconvolution, imaged the data, and
fl
ux-corrected for the response of the primary beam. AT2018cow
is unresolved in our ALMA data, with a synthesized beam
that ranges from
3
. 3 2. 5
́
(
P
A29
=
)
in Band 3 to
0
.50 0.36
́
(
P
A46
=-
)
in Band 9. The signal-to-noise
ratio in the resulting images ranges from
∼
500inBands3and4
to
∼
80 in Band 9. Details about the ALMA Band 9 data
reduction can be found in Appendix
A
.
2.2. X-Ray Observations
2.2.1.
Swift
/
XRT
Swift
(
Gehrels et al.
2004
)
has been monitoring AT2018cow
since June 19, with both the Ultraviolet-Optical Telescope
(
Roming et al.
2005
)
and the XRT
(
Burrows et al.
2005
)
. The
transient was well detected in both instruments
(
e.g., Rivera
Sandoval et al.
2018
)
.
We downloaded the
Swift
/
XRT data products
(
light curves
and spectra
)
using the web-based tools developed by the
Swift
-
XRT team
(
Evans et al.
2009
)
. We used the default values, but
binned the data by observation. To convert from count rate to
fl
ux, we used the absorbed count-to-
fl
ux rate set by the
spectrum on the same tool,
4
.26 10 erg cm ct
11
2 1
́
---
. This
assumes a photon index of
1.54
G
=
and a Galactic
N
H
column
of
6.57 10 cm
20
2
́
-
.
2.2.2.
NuSTAR
NuSTAR
(
Harrison et al.
2013
)
comprises two co-aligned
telescopes, Focal Plane Module A
(
FPMA
)
and FPMB. Each is
sensitive to X-rays in the 3
–
79 keV range, with slightly
different response functions.
NuSTAR
observed AT2018cow on
four epochs, and a log of these observations as well as the best-
fi
t spectral model parameters is presented in Table
2
.
NuSTAR
data were extracted using
nustardas
_
06Jul17
_
v1
from HEASOFT
6.24. Source photons were
extracted from a circle of 60
′′
radius, visually centered on the
object. We note that such a large region, appropriate for
NuSTAR
data, includes the transient as well as the host galaxy.
Background photons were extracted from a non-overlapping
circular region with 120
′′
radius on the same chip. Spectra were
grouped to 20 source photons per bin, ignoring energies below
3
keV and above 80
keV.
Spectra were analyzed in XSPEC
(
v12.10.0c
)
, using
NuSTAR
CALDB
fi
les dated 2018 August 14. Rivera Sandoval
et al.
(
2018
)
report a low absorbing column density
(
N
7.0 10 cm
H
20
2
= ́
-
)
, hence we ignore this component in
fi
tting. We opt for a simple phenomenological model to
describe the spectrum. We do not
fi
t for a cross-normalization
constant between
NuSTAR
FPMA and FPMB. Epoch 1
(
OBSID 90401327002
)
spectra are not consistent with a
simple power law or a broken power law, hence we
fi
t it with
the
bkn2pow
model
(
obtaining spectral breaks at
9.0
±
0.3 keV and
11.1 0.3 keV
)
. Spectra of the remaining
three epochs are well
fi
t by a simple, unabsorbed power law.
We calculate the
fl
ux directly from energies of individual
source and background photons detected, converted into
fl
ux
using the Ancillary Response Files generated by the
NuSTAR
pipeline. We use a bootstrap method to estimate the error bars:
we draw photons from the data with replacement, and calculate
the source
fl
ux from this random sample. By repeating this
process 10,000 times for each OBSID and each energy range,
we calculate the 1
σ
error bars on the
fl
uxes. This method gives
answers consistent with
xspec
fl
ux and
c
fl
ux
measurements
for bright sources
(
see for instance Kaspi et al.
2014
)
, but has
the advantage of giving
fl
ux measurements without the need to
assume a spectral model for the source. We
fi
nd that the source
Table 1
(
Continued
)
t
D
(
days
)
Facility
Frequency
(
GHz
)
Flux Density
(
mJy
)
44.24
SMA
234.6
8.04
±
2.51
44.24
SMA
246.3
10.43
±
2.13
44.24
SMA
250.6
10.06
±
3.24
45.23
SMA
217.0
8.28
±
2.24
45.23
SMA
233.0
10.55
±
2.39
45.23
SMA
264.0
8.35
±
3.27
45.23
SMA
280.0
5.7
±
3.49
47.24
SMA
230.6
11.47
±
2.81
47.24
SMA
234.6
10.81
±
4.39
47.24
SMA
246.6
11.65
±
3.76
47.24
SMA
250.6
5.6
±
5.37
48.31
SMA
217.5
7.63
±
1.11
48.31
SMA
233.5
5.73
±
1.32
76.27
SMA
215.5
1.33
±
0.55
76.27
SMA
231.5
0.61
±
0.63
76.27
SMA
335.0
−
2.27
±
1.87
76.27
SMA
351.0
−
0.32
±
1.76
10.48
ATCA
5.5
<
0.15
10.48
ATCA
9.0
0.27
±
0.06
10.48
ATCA
34.0
5.6
±
0.16
13.47
ATCA
5.5
0.22
±
0.05
13.47
ATCA
9.0
0.52
±
0.04
13.47
ATCA
16.7
1.5
±
0.1
13.47
ATCA
21.2
2.3
±
0.3
13.47
ATCA
34.0
7.6
±
0.5
17.47
ATCA
5.5
0.41
±
0.04
17.47
ATCA
9.0
0.99
±
0.03
19.615
ATCA
34.0
14.26
±
0.21
28.44
ATCA
34.0
30.59
±
0.2
34.43
ATCA
34.0
42.68
±
0.19
81.37
ATCA
34.0
6.97
±
0.09
14.03
ALMA
336.5
29.4
±
2.94
14.03
ALMA
338.5
29.1
±
2.91
14.03
ALMA
348.5
28.49
±
2.85
14.03
ALMA
350.5
28.29
±
2.83
14.14
ALMA
398.0
26.46
±
2.65
14.14
ALMA
400.0
26.21
±
2.62
14.14
ALMA
410.0
25.69
±
2.57
14.14
ALMA
412.0
25.95
±
2.6
22.02
ALMA
90.5
91.18
±
4.6
22.02
ALMA
92.5
92.31
±
4.6
22.02
ALMA
102.5
93.97
±
4.7
22.02
ALMA
104.5
93.57
±
4.7
22.04
ALMA
138.0
85.1
±
4.3
22.04
ALMA
140.0
84.58
±
4.2
22.04
ALMA
150.0
80.62
±
4.0
22.04
ALMA
152.0
79.71
±
4.0
23.06
ALMA
671.0
31.5
±
6.3
Notes.
Time of detection used is mean UT of observation. SMA measurements
have formal uncertainties shown, which are appropriate for in-band measure-
ments on a given night. However, for night-to-night comparisons, true errors
are dominated by systematics and are roughly 10%
–
15% unless indicated
otherwise. ALMA measurements have roughly 5% uncertainties in Bands 3
and 4, 10% uncertainties in Bands 7 and 8, and a 20% uncertainty in Band 9.
ATCA measurements have formal errors listed, but also have systematic
uncertainties of roughly 10%.
a
Systematic uncertainty 20% due to uncertain
fl
ux calibration.
4
The Astrophysical Journal,
871:73
(
19pp
)
, 2019 January 20
Ho et al.
is not well detected in the 40
–
80 keV band at the third and
fourth epochs.
3. Basic Properties of the Shock
3.1. Light Curve
The radio and X-ray light curves are shown in Figure
1
.
The 230 GHz light curve rises
(
the
fi
rst observation of a
millimeter transient in its rise phase
)
andthenshows
signi
fi
cant variability, presumably from inhomogeneities in
the surrounding medium. We have tentative evidence that the
rise is at least in part due to a d
ecreasing peak frequency: at
t
5
D
=
–
6days, the
fl
ux is marginally higher at 231.5 GHz
than at 215.5 GHz, and at
t
7
D
=
–
8days, it seems that the
peak may have been within the SMA observing bands.
However, the position of the pe
ak is ill-constrained; future
early observations would bene
fi
t from observations at more
frequencies.
Table 2
NuSTAR
Flux Measurements for AT2018cow and the Spectral Model Parameters
Epoch
OBSID
Exp. Time
(
ks
)
t
D
(
days
)
Flux
(
1
0ergcms
12
2 1
---
)
Photon Index
2
c
/
DOF
3
–
10
keV
10
–
20
keV
20
–
40
keV
40
–
80
keV
1
90401327002
a
32.4
7.9
4.94
±
0.04 4.41
±
0.10 12.21
±
0.39 21.46
±
4.29
L
421
/
443
2
90401327004
30.0
16.8
5.21
±
0.04 4.99
±
0.10
7.70
±
0.33
12.80
±
4.79
1.39
±
0.02
424
/
412
3
90401327006
31.2
28.5
1.58
±
0.03 1.45
±
0.06
1.74
±
0.21
L
1.51
±
0.04
174
/
169
4
90401327008
33.0
36.8
1.10
±
0.02 0.92
±
0.05
1.02
±
0.20
L
1.59
±
0.05
134
/
135
Notes.
Fluxes were measured with a model-independent method.
a
OBSID 90401327002 is best described by a
bkn2pow
model with parameters
1.24 0.05
1
G
=
,
E
9.0 0.3 keV
1
=
,
3.6 0.7
2
G
=
,
E
11.1 0.3 ke
V
2
=
,
0.50 0.05
3
G
=
. All reported values are for this model.
Figure 1.
(
Top panel
)
Submillimeter
(
SMA
)
through radio
(
ATCA
)
light curves of AT2018cow, with a timeline of the evolution of the UVOIR spectra
(
based on
Perley et al.
2018
)
shown above. There were four SMA observations with no frequency tunings in the ranges shown. For these, we took the closest value to 231.5 GHz
(
243.3 GHz for Days 9, 10, and 11; 218 GHz for Day 19
)
and scaled them to 231.5 GHz assuming a spectral index
F
1
n
μ
n
-
. We scaled all SMA
fl
uxes so that the
reference quasar 1635
+
381 would have the value of its mean
fl
ux at that frequency. The uncertainties shown on the SMA data represent a combination of formal
uncertainties and 15% systematic uncertainties, which is a conservative estimate. Non-detections are represented as a 3
σ
upper limit
(
horizontal bar
)
and a vertical
arrow down to the measurement. The upper limit measurement at 350.1 GHz is
−
0.32, below the limit of the panel. The error bars shown on the ATCA data are a
combination of formal uncertainties and an estimated 10% systematic uncertainty. The ATCA 34 GHz measurements rise as
t
2
, shown as a dotted line. The full set of
SMA light curves for all frequency tunings are shown in Appendix
B
. The letters
“
S
”
on the top demarcate the epochs with spectra shown in Figure
3
.
(
Bottom panel
)
X-ray light curve from
Swift
/
XRT together with four epochs of
NuSTAR
observations. The last two
NuSTAR
epochs have a non-detection in the highest-frequency
band
(
40
–
80 keV
)
. We denote two distinct phases of the X-ray light curve, the plateau phase, and the decline phase, discussed in detail in Section
3
.
5
The Astrophysical Journal,
871:73
(
19pp
)
, 2019 January 20
Ho et al.
By
t
50 days
D
=
, the radio
fl
ux has diminished both due to
the peak frequency shifting to lower frequencies,
and
to a
decay in the peak
fl
ux. Speci
fi
cally, the peak of the 15 GHz
light curve is 19 mJy around 47 days
(
A. Horesh 2018, personal
communication
)
, substantially less luminous than the peak of
the 230 GHz or the 34 GHz light curve. As we discuss in
Section
4.2
, this diminishing peak
fl
ux suggests that the
interaction itself is diminishing, and enables us to constrain the
size of the
“
circum-bubble
”
of material.
The X-ray light curve seems to have two distinct phases. We
call the
fi
rst phase
(
t
20
D
days
)
the
plateau
phase because
the X-ray emission is relatively
fl
at. The second phase, which
we call the
decline
phase, begins around
t
20
D
»
days. During
this period, the X-ray emission exhibits an overall steep
decline, but also exhibits strong variation
(
by factors of up to
10
)
on shorter timescales
(
see also Kuin et al.
2018
; Perley
et al.
2018
; Rivera Sandoval et al.
2018
)
.
We use the shortest timescale of variability in the 230 GHz light
curve to infer the size of the radi
o-emitting region, and do the same
for the X-ray emission in Section
5
.OnDays5
–
6, the 230 GHz
fl
ux changed by order unity in one d
ay, setting a length scale for
the source size of
Rct
2.6 10 c
m
15
D
=D= ́
(
170 au
)
.We
fi
nd no evidence for shorter-times
cale variability in our long SMA
tracks from the
fi
rst few days of observations
(
Figure
2
)
.
Together with the 230 GHz
fl
ux density
(
S
30 mJy
»
n
)
and
the distance
(
d
60 Mpc
=
)
we infer an angular size of
2.8 as
q
m
=
and a brightness temperature of
T
Sc
k
2
310K
1
B
2
2
10
n
=
DW
́
n
()
where
2
pq
D
W=
. This brightness temperature is close to the
typical rest-frame equipartition brightness temperatures of the
most compact radio sources,
T
510
B
10
~ ́
K
(
Readhead
1994
)
.
Figure 2.
Zoomed-in light curves for the
fi
rst
fi
ve days of SMA observations. These were the only tracks long enough for binning in time.
6
The Astrophysical Journal,
871:73
(
19pp
)
, 2019 January 20
Ho et al.
3.2. Modeling the Radio to Submillimeter SED
The shape of the radio to submillimeter SED
(
Figure
3
)
,
together with the high brightness temperature implied by the
luminosity and variability timescale
(
Section
3.1
)
, can only be
explained by nonthermal emission
(
Readhead
1994
)
. The
observed spectrum is assumed to arise from a population of
electrons with a power-law number distribution in Lorentz
factor
e
g
, with some minimum Lorentz factor
m
g
and electron
energy power index
p
:
dN
d
,. 2
e
e
e
p
em
g
g
ggg
μ
-
()
()
As argued below, we expect an adiabatic strong shock
moving into a weakly magnetized, ionized medium at a
nonrelativistic speed. First-order Fermi acceleration gives
pr
r
21
=+ -
()()
, where
r
is the compression ratio of the
shock. A strong matter-dominated shock has
r
=
4, hence
p
=
2
(
Blandford & Eichler
1987
)
. However the back-reaction
of the accelerated particles decelerates the gas
fl
ow, weakening
the gas dynamic subshock and reducing the compression ratio
from the strong shock
r
=
3, so typical
p
2
.5
3
<<
are
obtained in both simulations and astrophysical data
(
Jones &
Ellison
1991
)
. Quasi-perpendicular magnetized and relativistic
shocks are more subtle, since some particles cannot return
along
fi
eld lines after their
fi
rst shock crossing, but the limiting
value is
p
2.
3
~
(
Pelletier et al.
2017
)
.
Equation
(
3
)
provides an expression for
m
g
. Behind the shock
(
velocity
v
)
some fraction
e
of the total energy density goes
into accelerating electrons. Conserving shock energy
fl
ux gives
m
m
v
c
1.
3
me
p
e
2
2
g
-»
()
The value of
m
g
is large for relativistic shocks, e.g., in GRBs.
But we will see that for this source
(
vc
0.
1
~
,
0.1
e
~
)
, the bulk
of the electrons are just mildly relativistic
(
2
3
m
g
~
–
)
.For
ordinary SN shocks
m
g
is always nonrelativistic
(
11
m
g
-<
)
.
Thus, in the parameter estim
ations below, we follow SN
convention and assume that the r
elativistic electrons follow a
power-law distribution down to a
fi
xed
m
g
(
Chevalier
1982
,
1998
;
Kulkarni et al.
1998
;Frailetal.
2000
; Soderberg et al.
2005
)
.We
apply
e
only
to this relativistic power law, not to the nonrelativistic
thermal distribution of shock-h
eated particles at lower energy.
Figure 3.
Spectrum of AT2018cow at three epochs. In the top panel, we plot the Day 10 data as presented in Table
1
. In the middle panel, we plot the ATCA data from
Day 13 and the SMA and ALMA data from Day 14. In the bottom panel, we plot the ALMA data from Day 22, interpolate the SMA data between Day 20 and Day 24
at 215.5 and 231.5 GHz, and interpolate the ATCA data at 34 GHz
(
since it varies smoothly; Figure
1
)
. We also show the Band 9 measurement from Day 24 as a star.
The ATCA data is consistent with a self-absorbed spectral index
(
F
52
n
μ
n
)
with an excess at lower frequencies. The peak frequency is resolved on Day 22 with
ALMA observations at Band 3
(
see inset
)
. To measure the optically thin spectral index, we performed a least squares
fi
t in log space. To estimate the uncertainty on the
spectral index, we performed a Monte Carlo analysis, sampling 10
4
times to measure the standard deviation of the resulting spectral index. On Day 10, we used an
uncertainty of 15% for each SMA measurement. On Days 14 and 22, we used 10% uncertainty for each ALMA measurement and 20% for each SMA measurement
(
to
take into account the much longer length of the SMA tracks
)
. Uncertainties are too small to be visible on this plot, except for the inset panel, where we do not
display them.
7
The Astrophysical Journal,
871:73
(
19pp
)
, 2019 January 20
Ho et al.
We now describe each of the break frequencies that
characterize the observed spectrum. First, the characteristic
synchrotron frequency
m
n
emitted by the minimum energy
electrons is:
4
m
m
g
2
ngn
=
()
where
g
n
is the gyrofrequency,
qB
mc
2
5
g
e
e
n
p
=
()
and
q
e
is the unit charge,
B
is the magnetic
fi
eld strength,
m
e
is
the electron mass, and
c
is the speed of light.
Next, there is the cooling frequency
c
c
n
ng
º
()
, the
frequency below which electrons have lost the equivalent of
their total energies to radiation via cooling. In general, the
timescale for synchrotron cooling depends on the Lorentz
factor as
t
e
1
g
μ
-
. Thus, electrons radiating at higher
frequencies cool more quickly. Separately, electrons could
also lose energy by Compton upscattering of ambient
(
low
energy
)
photons
—
the so-called Inverse Compton
(
IC
)
scatter-
ing. In Section
5
,we
fi
nd that IC scattering dominates at early
times and that synchrotron losses dominate at later times, and
that the transition is at
t
13 days
»
.
At
t
13 days
D
>
, electrons with
ec
g
g
>
cool principally by
synchrotron radiation to
c
g
in a time
t
, where
mc
Bt
6
.6
c
e
T
2
g
p
s
=
()
For
t
13 days
<
, Compton cooling on the UVOIR
fl
ux
exceeds the synchrotron cooling rate by a factor
t
10 days
52
~
-
()
,and
c
g
is correspondingly lowered. The cooled
electrons emit around the characteristic synchrotron frequency
.7
c
c
g
2
ngn
=
()
Next, the self-absorption frequency
a
n
is the frequency at
which the optical depth to synchrotron self-absorption is unity.
The rise at 34 GHz obeys a
ft
2
μ
n
power law
(
as shown in
Figure
1
)
, consistent with the optically thick spectral index we
measure
(
Figure
3
)
. This indicates that the self-absorption
frequency is above the ATCA bands
(
34 GH
z
a
n
>
)
. Figure
3
also shows that the emission in the SMA bands is optically thin
at
t
10 days
D
, constraining the self-absorption frequency to
be
230 GH
z
a
n
<
.
On Day 22, we resolve the peak of the SED with our ALMA
data. We denote the peak frequency
p
n
and the
fl
ux at the peak
frequency
F
p
, and
fi
nd
100 GHz
p
n
»
and
F
94 mJy
p
»
.
Motivated by the observation of optically thick emission at
p
n
n
<
, we assume that
pa
n
n
=
, and adopt the framework in
Chevalier
(
1998
)(
hereafter referred to as
C98
)
to estimate
properties of the shock at this epoch. These properties are
summarized in Table
3
, and outlined in detail below.
Following Equations
(
11
)
and
(
12
)
in
C98
, the outer shock
radius
R
p
can be estimated as
R
cFD
fp
c E
c
6
2
2
8
p
p
p
p
p
eB
p
p
l
p
p
p
6
5
6
212
5
5
62
12 13
1
1
p
n
=
-
+
+
+
+
+-
+
-
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
⎛
⎝
⎜
⎞
⎠
⎟
()( )
()
()
and the magnetic
fi
eld can be estimated as
B
c
fp
cE
FD
c
36
2
2
9
p
eB
l
p
p
p
p
3
5
22
2
6
3
22
2
22 13
1
p
n
=
-
-
+
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
⎛
⎝
⎜
⎞
⎠
⎟
()( )
()
()
()
where, as in Equation
(
2
)
,
p
is the electron energy index. Note
that
C98
use
γ
for the electron energy power index. We use
p
instead and
γ
for the Lorentz factor. The constant
c
6.27 10
1
18
= ́
in cgs units, and the constants
c
5
and
c
6
are
tabulated as a function of
p
on page 232 of Pacholczyk
(
1970
)
.
D
is the distance to the source,
E
0.51
l
=
MeV is the electron
rest mass energy, and
eB
is the ratio of energy density in
electrons to energy density in magnetic
fi
elds
(
in
C98
this ratio
is parameterized as
α
, but we use
α
as the optically thin
spectral index of the radio SED.
)
Finally,
f
is the
fi
lling factor:
the emitting region is approximated as a planar region with
thickness
s
and area in the sky
R
2
p
, and thus a volume
Rs
2
p
,
which can be characterized as a spherical emitting
volume
V
fR
R s
43
32
pp
==
.
On Day 22, we measure
1.
1
a
=-
where
F
n
μ
n
a
, which
corresponds to
p
=
3.2. Later in this section we show that our
submillimeter observations lie above the cooling frequency,
and therefore that the index of the
source
function of electrons
is
p
s
=
2.2. However, the
C98
prescription considers a
distribution as it exists when the electrons are observed, from
a combination of the initial acceleration and the energy losses
(
to cooling
)
. So, we proceed with
p
=
3.2, and discuss this
unusual regime in Section
4.3
. The closest value of
p
in the
table in Pacholczyk
(
1970
)
is
p
=
3, so we use this value to
select the constants
(
and note that, as stated in
C98
, the results
do not depend strongly on the value of
p
.
)
With this,
Equations
(
8
)
and
(
9
)
reduce to Equations
(
13
)
and
(
14
)
in
C98
, respectively, reproduced here:
R
f
F
D
8.8 10
0.5
Jy
Mpc
5 GHz
cm,
10
p
e
B
pp
15
119
119
919
1819
1
n
= ́
́
-
-
-
⎜⎟
⎜⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
()
B
f
F
D
0.58
0.5
Jy
Mpc
5 GHz
G.
11
p
e
B
pp
419
419
219
419
n
=
́
-
-
--
⎜⎟
⎜⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
()
Next we estimate the total energy
U
. For
p
=
3,
Equations
(
10
)
and
(
11
)
can be combined into the following
Table 3
Quantities Derived from Day 22 Measurements, Using Different Equipartition
Assumptions
Parameter
13
eB
==
0.1,
0.01
eB
==
ap
nn
=
(
GHz
)
100
100
F
p
,
n
(
mJy
)
94
94
r
(
10
15
cm
)
76
v
/
c
0.13
0.11
B
(
G
)
64
U
10
4
8
(
erg
)
435
n
e
(
1
0
5
cm
−
3
)
341
c
n
(
GHz
)
28
Note.
In the text unless otherwise stated we use
13
eB
==
.
8
The Astrophysical Journal,
871:73
(
19pp
)
, 2019 January 20
Ho et al.