Draft version October 30, 2018
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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, PO 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
ABSTRACT
We present detailed submillimeter- through centimeter-wave observations of the ex-
traordinary extragalactic transient AT2018cow. The apparent characteristics — the
high radio luminosity, the long-lived emission plateau at millimeter bands, and the
sub-relativistic velocity — have no precedent. A basic interpretation of the data sug-
gests
E
k
&
4
×
10
48
erg coupled to a fast but sub-relativistic (
v
≈
0
.
13c) shock in a
dense (
n
e
≈
3
×
10
5
cm
−
3
) medium. We find 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 UVOIR photons by energetic elec-
trons within the forward shock. By ∆
t
≈
20 days, the X-ray emission shows spectral
softening and erratic inter-day variability. Taken together, we are led to invoke an
additional source of 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 tran-
arXiv:1810.10880v2 [astro-ph.HE] 28 Oct 2018
2
sients shocking a dense medium, which at early times are most readily observed at
millimeter wavelengths.
3
1.
INTRODUCTION
1.1.
The transient millimeter sky
Although the sky is regularly monitored across many bands of the electromag-
netic spectrum (as well as in gravitational waves and energetic particles) the dy-
namic sky at millimeter to sub-millimeter wavelengths (0.1–10 mm) remains poorly
explored. There has only been one blind transient survey specific to the millimeter
band
1
(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
2
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).
The paucity of millimeter transient studies can be attributed in part to technical
challenges: costly receiver and electronics systems, the need for excellent weather
conditions, and the small fields of view of millimeter interferometers. But it also
reflects 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 correlators have greatly increased
the sensitivity of sub-mm facilities (e.g. the Submillimeter Array or SMA; Ho et al.
2004), and the Atacama Large Millimeter Array (ALMA), a flagship facility, recently
began operations. Optical surveys are discovering new and unexpected classes of
transient events whose millimeter properties are unknown — and possibly different
from previously-known types — motivating renewed follow-up efforts.
1.2.
AT2018cow
AT2018cow was discovered on 2018 June 16 UT as an optical transient (Smartt et
al. 2018; Prentice et al. 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
peak
.
3 days), which was established by earlier non-detections (Fremling
2018; Prentice et al. 2018), together with its high optical luminosity (
M
peak
∼ −
20)
and its close proximity (
d
= 60 Mpc).
1
The authors searched for transient sources at 90 GHz and 150 GHz. They found a single candidate
event, which intriguingly showed linear polarization.
2
Here we use “transient” as distinct from “variable”: millimeter observations are commonly used
to study variability in protostars (e.g. Herczeg et al. 2017) and active galactic nuclei (e.g. Dent et
al. 1983). There have also been millimeter detections of galactic transient sources, primarily stellar
flares (e.g. Bower et al. 2003, Fender et al. 2015).
4
UVOIR observations (Prentice et al. 2018; Perley et al. 2018) revealed unprece-
dented photometric and spectroscopic properties. Long-lived luminous X-ray emis-
sion was detected with
Swift
/XRT (Rivera Sandoval & Maccarone 2018), INTEGRAL
(Ferrigno et al. 2018; Savchenko et al. 2018) and NuSTAR (Margutti et al. 2018;
Grefenstette et al. 2018). Early radio and sub-millimeter detections were reported by
NOEMA (de Ugarte Postigo et al. 2018), JCMT (Smith et al. 2018), AMI (Bright
et al. 2018), and by us using the ATCA (Dobie et al. 2018a,b). The source does not
appear to be a GRB, as no prompt high-energy emission was detected in searches
of
Swift
/BAT (Lien et al. 2018), Fermi/GBM (Dal Canton et al. 2018), Fermi/LAT
(Kocevski & Cheung 2018), and AstroSat CZTI (Sharma et al. 2018).
Perley et al. (2018) suggested that AT2018cow is a new member of the class of
rapidly rising (
t
rise
.
5d) and luminous (
M
peak
<
−
18) blue transients, which have
typically been found in archival searches of optical surveys (Drout et al. 2014; Pur-
siainen et al. 2018; Rest et al. 2018). The leading hypothesis for this class was
circumstellar interaction of a supernova (Ofek et al. 2010), but this was difficult to
test because most of the events were located at cosmological distances, and not dis-
covered in real-time. AT2018cow presented the first 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. Possibilities include failed supernovae and
tidal disruption events, but although AT2018cow shares properties with both of these
classes, it is clearly not a typical member of either (Prentice et al. 2018; Perley et al.
2018; Kuin et al. 2018).
Given the unusual nature of the source, we were motivated to undertake high-
frequency observations. We began monitoring AT2018cow with the SMA at 230 GHz
and 340 GHz and carried out supporting observations with the ATCA from 5 GHz to
34 GHz. To our surprise the source was very bright at sub-millimeter wavelengths
and optically thick in the centimeter band, days after the discovery. This finding led
us to seek Director’s discretionary (DD) time with ALMA at even higher frequencies,
which enabled us to resolve the peak of the SED. A technical highlight of the ALMA
observations was the detection of the source at nearly a terahertz frequency (Band 9).
We present the sub-millimeter, 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 (4.1), attribute the high
sub-mm luminosity of AT2018cow to the large density of the surrounding medium
(4.2), and discuss some problems with the synchrotron model parameters (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.
5
2.
OBSERVATIONS
All observations are measured ∆
t
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).
2.1.
Radio and submillimeter observations
2.1.1.
The Submillimeter Array (SMA)
AT2018cow was regularly observed with the SMA over the period of UT 2018 Jun
21–UT 2018 August 3 (∆
t
expl
≈
5–49 days) in the Compact configuration, with an
additional epoch on UT 2018 August 31 (∆
t
expl
≈
76 days). All observations con-
tained 6 to 8 antennas and cover a range of baseline lengths from 16.4 m to 77 m.
These observations 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 two sidebands (32 GHz total) covering a range of frequencies from
188–416 GHz. Each receiver can be tuned independently to provide dual-band obser-
vations. 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
stacking of the lower and upper sidebands to improve 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 flux 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, fluxes were derived directly from the calibrated
visibilities, but the results agree well with flux estimates derived from the CLEANed
images when the data quality and uv-coverage was adequate.
2.1.2.
The Australia Telescope Compact Array (ATCA)
We obtained six epochs of centimeter wavelength observations with the Australia
Telescope Compact Array (ATCA; Frater et al. 1992). During the first three epochs,
the six 22-m dishes were arranged in an east-west 1.5A configuration, with base-
lines ranging from 153 m to 4469 m. During the latter three epochs, five of the six
dishes were moved to a compact H75
3
configuration, occupying a cardinally oriented
‘T’ with baselines ranging from 31 m to 89 m. Full-Stokes data were recorded with
the Compact Array Broadband Backend (Wilson et al. 2011) in a standard contin-
uum
CFB 1M
setup, simultaneously providing two 2.048 GHz bands each with 2048
channels. Observations were obtained with center frequencies of 5.5 GHz & 9 GHz,
16.7 GHz & 21.2 GHz, and 33 GHz & 35 GHz, with data in the latter two bands typi-
3
https://www.narrabri.atnf.csiro.au/operations/array
configurations/configurations.html
6
cally being averaged to form a band centered at 34 GHz. The flux density scale was set
using observations of the ATCA flux standard PKS 1934
−
638. For observations be-
low 33 GHz, PKS 1934
−
638 was also used to calibrate the complex time-independent
bandpasses, and 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
configuration, 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 difficulty 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 multi-frequency synthesis images with uniform weighting.
Single rounds of self-calibration over 5–10 min intervals were found to improve the
image quality in all bands. For data at 5.5 GHz and 9 GHz, point-source models of all
strong unresolved field 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 sufficient signal-to-noise ratio. We report flux densities derived
by fitting point-source models to the final images using the MIRIAD task
imfit
.
2.1.3.
The Atacama Large Millimeter/submillimeter Array (ALMA)
AT2018cow was observed with ALMA as part of DD time during Cycle 5 using
Bands 3, 4, 7, 8, and 9. Observations were performed on 30 June 2018 (∆
t
expl
≈
14 days; Bands 7 and 8), 08 July 2018 (∆
t
expl
≈
22 days; Bands 3 and 4) and on 10
July 2018 (∆
t
expl
≈
23 days; Band 9).
4
The ALMA 12-m antenna array was in its most compact C43-1 configuration, with
46–48 working antennas and baselines ranging from 12–312 m. The on-source in-
tegration time was 6–8 min for Bands 3–8, and 40 min for Band 9. The Band 3–8
(Band 9) observations used two sidebands with a frequency coverage of 2 GHz (4 GHz)
each, centred on 91.5 and 103.5 GHz (Band 3), 138 and 150 GHz (Band 4), 337.5 and
349.5 GHz (Band 7), 399 and 411 GHz (Band 8), and 663 and 679 GHz (Band 9). All
calibration and imaging was done with the Common Astronomical Software Appli-
cations (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 cal-
ibrate the complex gains, and using J1337
−
1257 (Band 7), J1550+0527 (Band 3/4)
4
Band 9 observations were also performed on 09 July 2018, but these data were of too poor quality
to use as a result of weather conditions.
7
or J1517
−
2422 (Band 8) to calibrate the bandpass response and apply an absolute
flux scale. Band 9 observations were delivered following manual calibration by the
North American ALMA Science Center, using J1540+1447 for gain calibration, and
J1517
−
2422 for bandpass- and flux-calibration. We subsequently applied a phase-only
self-calibration using the target source (for Bands 3–8), performed a deconvolution
(CLEAN), imaged the data, and flux-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
′′
(PA = 29
◦
) in Band 3 to 0
.
50
′′
×
0
.
36
′′
(PA =
−
46
◦
) in Band 9.
The signal-to-noise ratio in the resulting images ranges from
∼
500 in Bands 3 and 4
to
∼
80 in Band 9. Details about the ALMA Band 9 data reduction can be found in
Appendix A.
Table 1
. Flux-density measurements for AT2018cow.
Time of detection used is mean UT of observation. SMA
measurements have formal uncertainties shown, which
are appropriate for in-band measurements 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 measure-
ments have roughly 5% uncertainties in Bands 3 and
4, 10% uncertainties in Bands 7 and 8, and a 20% un-
certainty in Band 9. ATCA measurements have formal
errors listed, but also have systematic uncertainties of
roughly 10%.
∆
t
expl
(d)
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
Table 1 continued on next page
8
Table 1
(continued)
∆
t
expl
(d)
Facility
Frequency (GHz)
Flux Density (mJy)
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
Table 1 continued on next page
9
Table 1
(continued)
∆
t
expl
(d)
Facility
Frequency (GHz)
Flux Density (mJy)
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
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
Table 1 continued on next page
10
Table 1
(continued)
∆
t
expl
(d)
Facility
Frequency (GHz)
Flux Density (mJy)
22.02
ALMA
90.5
91
.
18
±
0
.
46
22.02
ALMA
92.5
92
.
31
±
0
.
46
22.02
ALMA
102.5
93
.
97
±
0
.
47
22.02
ALMA
104.5
93
.
57
±
0
.
47
22.04
ALMA
138.0
85
.
1
±
0
.
43
22.04
ALMA
140.0
84
.
58
±
0
.
42
22.04
ALMA
150.0
80
.
62
±
0
.
4
22.04
ALMA
152.0
79
.
71
±
0
.
4
23.06
ALMA
671.0
31
.
5
±
6
.
3
Note
—
a
Systematic uncertainty 20% due to uncertain flux calibration
2.2.
X-ray observations
2.2.1.
Swift
/XRT
The Neil Gehrels Swift Observatory (
Swift
; Gehrels et al. 2004) has been monitor-
ing AT2018cow since June 19, with both the Ultraviolet-Optical Telescope (UVOT;
Roming et al. 2005) and the X-ray Telescope (XRT; Burrows et al. 2005). The tran-
sient was well-detected in both instruments (e.g. 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
flux, we used the absorbed count-to-flux rate set by the spectrum on the same tool,
4
.
26
×
10
−
11
erg cm
−
2
ct
−
1
. This assumes a photon index of Γ = 1
.
54 and a Galactic
N
H
column of 6
.
57
×
10
20
cm
−
2
(Sandoval et al. 2018).
2.2.2.
NuSTAR
The
Nuclear Spectroscopic Telescope Array
(
NuSTAR
; Harrison et al. 2013) com-
prises 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-fit 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 analysed in XSPEC (v12.10.0c), using
NuSTAR
CALDB files dated
2018 August 14. Rivera Sandoval & Maccarone (2018) report a low absorbing column
density (N
H
= 6
.
8
±
0
.
1
×
10
20
cm
−
2
), hence we ignore this component in fitting. We
opt for a simple phenomenological model to describe the spectrum. We do not fit for a
11
Table 2.
NuSTAR
flux measurements for AT2018cow, and the spectral model parameters
Epoch
OBSID
Exp. time
∆
t
expl
Flux (10
−
12
erg cm
−
2
s
−
1
)
Photon Index
χ
2
/DOF
ks
d
3–10 keV
10–20 keV
20–40 keV
40–80 keV
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
1
90401327002
a
32.4
7.9
4.94
±
0.04
4.41
±
0.10
12.21
±
0.39
21.46
±
4.29
···
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
···
1
.
51
±
0
.
04
174/169
4
90401327008
33.0
36.8
1.10
±
0.02
0.92
±
0.05
1.02
±
0.20
···
1
.
59
±
0
.
05
134/135
Note
—Fluxes were measured with a model-independent method.
a
OBSID 90401327002 is best described by a
bkn2pow
model with parameters Γ
1
= 1
.
24
±
0
.
05,
E
1
= 9
.
0
±
0
.
3 keV, Γ
2
= 3
.
6
±
0
.
7,
E
2
= 11
.
1
±
0
.
3 keV, Γ
3
= 0
.
50
±
0
.
05. All reported values are for this model.
cross-normalisation 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 fit it with the
bkn2pow
model (obtaining spectral breaks at 9
±
0
.
3 keV
and 11
±
0
.
3 keV). Spectra of the remaining three epochs are well-fit by a simple,
unabsorbed power law.
We calculate the flux directly from energies of individual source and background
photons detected, converted into flux using the Ancillary Response Files (ARF) gen-
erated 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 flux
from this random sample. By repeating this process 10000 times for each OBSID and
each energy range, we calculate the 1-sigma error bars on the fluxes. This method
gives answers consistent with
xspec
flux and
cflux
measurements for bright sources
(see for instance Kaspi et al. 2014), but has the advantage of giving flux measure-
ments without the need to assume a spectral model for the source. We find that the
source 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
shows significant variability, presumably from inhomogeneities in the surrounding
medium. By ∆
t
= 50 days, the radio luminosity
νf
ν
has diminished both due to
the peak frequency shifting to lower frequencies,
and
to a decay in the peak flux.
Specifically, the peak of the 15 GHz light curve is 19 mJy around 47 days (A. Horesh,
personal communication), substantially less luminous than the peak of the 230 GHz
or the 34 GHz light curve.
The X-ray light curve seems to have two distinct phases. We call the first phase
(∆
t
.
20 days) the
plateau
phase because the X-ray emission is relatively flat. The
12
second phase, which we call the
decline
phase, begins around ∆
t
≈
20 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 Sandoval et
al. 2018; Kuin et al. 2018; Perley et al. 2018).
Figure 1.
Radio (top panel) and X-ray (bottom panel) 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
ν
∝
ν
−
1
. We scaled
all SMA fluxes so that the reference quasar 1635+381 would have the value of its mean
flux 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 crosses on the top demarcate the epochs
with spectra shown in Figure 3. The last two
NuSTAR
epochs have a non-detection in the
highest-frequency band (40–80 keV).
13
We use the shortest timescale of variability in the 230 GHz light curve to infer the
size of the radio-emitting region, and do the same for the X-ray emission in Section
5. On Days 5–6, the 230 GHz flux changed by order unity in one day, setting a length
scale for the source size of ∆
R
=
c
∆
t
= 2
.
6
×
10
15
cm (170 AU). We find no evidence
for shorter-timescale variability in our long SMA tracks from the first few days of
observations (Figure 2).
Together with the 230 GHz flux density (
S
ν
≈
30 mJy) and the distance (
d
=
60 Mpc) we infer an angular size of
θ
= 2
.
8
μ
as and a brightness temperature of
T
B
=
S
ν
c
2
2
kν
2
∆Ω
&
3
×
10
10
K
(1)
where ∆Ω =
πθ
2
. This brightness temperature is close to the typical rest-frame
equipartition brightness temperatures of the most compact radio sources,
T
B
∼
5
×
10
10
K (Readhead 1994).
Figure 2.
Zoomed-in light curves for the first five days of SMA observations. These were
the only tracks long enough for binning in time.
14
3.2.
Modeling the broad-band SED
The shape of the broad-band SED (Figure 3), together with the high brightness
temperature implied by the luminosity and variability timescale (Section 3.1), can
only be explained by non-thermal emission (Readhead 1994). The observed spec-
trum is assumed to arise from a population of electrons with a power-law number
distribution in Lorentz factor
γ
e
, with some minimum Lorentz factor
γ
m
:
dN
(
γ
e
)
dγ
e
∝
γ
−
p
e
, γ
e
≥
γ
m
.
(2)
We expect an adiabatic strong shock moving into a weakly magnetized, ionized media
at a non-relativistic speed. First-order Fermi acceleration gives
p
= (
r
+ 2)
/
(
r
−
1),
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 flow, weakening the gas dynamic subshock
and reducing the compression ratio from the strong shock
r
= 3, so typical 2
.
5
< p <
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 field lines after their first shock crossing, but the limiting
value is
s
∼
2
.
3 (Pelletier et al. 2017).
Equation 3 provides an expression for
γ
m
. Behind the shock (velocity
v
) some
fraction
e
of the total energy density goes into accelerating electrons. Conserving
shock energy flux gives,
γ
m
−
1
≈
e
m
p
m
e
v
2
c
2
.
(3)
The value of
γ
m
is large for relativistic shocks, e.g. in GRBs. But we will see that for
this source (
v/c
∼
0
.
1,
e
∼
0
.
1), the bulk of the electrons are just mildly relativistic
(
γ
m
∼
2
−
3). For ordinary supernova shocks
γ
m
is always non-relativistic (
γ
m
−
1
<
1).
Thus in the parameter estimations below, we follow supernova convention and assume
that the relativistic electrons follow a power-law distribution down to a fixed
γ
m
∼
2
and apply
e
only
to this relativistic power-law, not to the nonrelativistic thermal
distribution of shock-heated particles at lower energy.
We now describe each of the break frequencies that characterize the observed spec-
trum. First, the characteristic synchrotron frequency
ν
m
emitted by the minimum
energy electrons is:
ν
m
=
γ
2
m
ν
g
(4)
where
ν
g
is the gyrofrequency,
ν
g
=
q
e
B
2
πm
e
c
(5)
15
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 and interpolate the SMA data between Day 20 and Day 24 at 215.5 GHz
and 231.5 GHz. We also show the Band 9 measurement from Day 24 as a star. We also
interpolate the ATCA data at 34 GHz, since it varies smoothly (see Fig 1). Uncertainties
are smaller than the size of the points. The ATCA data is consistent with a self-absorbed
spectral index (
F
ν
∝
ν
5
/
2
) 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 fit 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).
and
q
e
is the unit charge,
B
is the magnetic field strength,
m
e
is the electron mass,
and
c
is the speed of light.
Next, there is the cooling frequency
ν
c
≡
ν
(
γ
c
), the frequency below which electrons
have lost the equivalent of their total energies to radiation via cooling. At ∆
t >
16
10 days, electrons with
γ
e
> γ
c
cool principally by synchrotron radiation to
γ
c
in a
time
t
, where
γ
c
=
6
πm
e
c
σ
T
B
2
t
.
(6)
For
t <
10 days, Compton cooling on the UVOIR flux exceeds the synchrotron
cooling rate by a factor
∼
(
t/
10 days)
−
5
/
2
, and
γ
c
is correspondingly lowered. The
cooled electrons emit around the characteristic synchrotron frequency
ν
c
=
γ
2
c
ν
g
.
(7)
In general, the timescale for synchrotron cooling depends on the Lorentz factor as
t
∝
γ
−
1
e
. 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) scattering. Below, as well as in Section
5, we find that IC scattering dominates at early times and that synchrotron losses
dominate at later times.
Next, the self-absorption frequency
ν
a
is the frequency at which the optical depth
to synchrotron self-absorption is unity. The rise at 34 GHz obeys a
f
ν
∝
t
2
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 (
ν
a
>
34 GHz). Figure 3 also shows that the emission in the SMA
bands is optically thin at ∆
t
&
10 days, constraining the self-absorption frequency to
be
ν
a
<
230 GHz.
On Day 22, we resolve the peak of the SED with our ALMA data (
ν
p
≈
100 GHz and
F
p
≈
94 GHz). Motivated by the observation of optically thick emission at
ν < ν
p
, we
assume that
ν
p
=
ν
a
, 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 equation (11) and equation (12) in C98, the outer shock radius
R
p
can
be estimated as
R
p
=
[
6
c
p
+5
6
F
p
+6
p
D
2
p
+12
(
e
/
B
)
f
(
p
−
2)
π
p
+5
c
p
+6
5
E
p
−
2
l
]
1
/
(2
p
+13)
(
ν
p
2
c
1
)
−
1
(8)
and the magnetic field can be estimated as
B
p
=
[
36
π
3
c
5
(
e
/
B
)
2
f
2
(
p
−
2)
2
c
3
6
E
2(
p
−
2)
l
F
p
D
2
]
2
/
(2
p
+13)
(
ν
p
2
c
1
)
(9)
where
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
1
= 6
.
27
×
10
18
in
cgs units, and the constants
c
5
and
c
6
are tabulated as a function of
p
on page 232 of
17
Pacholczyk (1970).
D
is the distance to the source,
E
l
= 0
.
51 MeV is the electron rest
mass energy, and
e
/
B
is the ratio of energy density in electrons to energy density in
magnetic fields (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 filling factor: the emitting
region is approximated as a planar region with thickness
s
and area in the sky
πR
2
,
and thus a volume
πR
2
s
, which can be characterized as a spherical emitting volume
V
= 4
πfR
3
/
3 =
πR
2
s
.
On Day 22, we measure
α
=
−
1
.
1 where
F
ν
∝
ν
α
, which corresponds to
p
= 3
.
2.
Later in this section we show that our sub-millimeter 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, equation 8 and equation 9 reduce
to equation (13) and equation (14) in C98, respectively, reproduced here:
R
p
= 8
.
8
×
10
15
(
e
B
)
−
1
/
19
(
f
0
.
5
)
−
1
/
19
(
F
p
Jy
)
9
/
19
(
D
Mpc
)
18
/
19
(
ν
p
5 GHz
)
−
1
cm
,
(10)
B
p
= 0
.
58
(
e
B
)
−
4
/
19
(
f
0
.
5
)
−
4
/
19
(
F
p
Jy
)
−
2
/
19
(
D
Mpc
)
−
4
/
19
(
ν
p
5 GHz
)
G
.
(11)
Next we estimate the energy. For
p
= 3, equation 10 and equation 11 can be
combined into the following expression for
U
=
U
B
/
B
,
U
=
1
B
4
π
3
fR
3
(
B
2
8
π
)
= (1
.
9
×
10
46
erg)
1
B
(
e
B
)
−
11
/
19
(
f
0
.
5
)
8
/
19
(
F
p
Jy
)
23
/
19
(
D
Mpc
)
46
/
19
(
ν
p
5 GHz
)
−
1
.
(12)
Following C98 we take
f
= 0
.
5, but the dependence on this parameter is weak.
In choosing
B
and
e
there are several normalizations (or assumptions) used in the
literature. As a result the inferred energy can vary enormously (see Section 4.1 for
further details). For now, we follow Soderberg et al. (2010) in setting
e
=
B
= 1
/
3
(in other words, that energy is equally partitioned between electrons, protons, and
magnetic fields). With all of these choices, we find that at ∆
t
≈
22 days,
R
p
≈
7
×
10
15
cm and
B
p
≈
6 G. We find that the total energy
U
≈
4
×
10
48
erg. Assuming
10% uncertainties in
F
p
and
ν
p
and a 50% uncertainty in
p
, a Monte Carlo with 10,000
18
samples gives uncertainties of 0.15–0.3 dex in these derived parameters. Our results
are robust to departures from equipartition given the large penalty in the required
energy (Readhead 1994).
The mean velocity up to ∆
t
≈
22 days is
v
=
R
p
/t
p
= 0
.
13c. We can write a
general expression for
v/c
(taking
L
p
= 4
πF
p
D
2
, noting that 4
π
Jy Mpc
2
= 1
.
2
×
10
27
erg s
−
1
Hz
−
1
):
v/c
≈
(
e
B
)
−
1
/
19
(
f
0
.
5
)
−
1
/
19
(
L
p
10
26
erg s
−
1
Hz
−
1
)
9
/
19
(
ν
p
5 GHz
)
−
1
(
t
p
1 days
)
−
1
.
(13)
Furthermore, from the
t
2
rise at 34 GHz (Figure 1) we can infer that the radius
increases as
R
∝
t
and therefore that the velocity
v
=
dR/dt
is constant. We put this
derived energy and velocity into the context of other energetic transients in Section
4.1.
Next, we estimate the density of the medium into which the forward shock is propa-
gating. The ejecta expands into the medium with velocity
v
1
, producing a shock front
(a discontinuity in pressure, density, and temperature) with shock-heated ejecta im-
mediately behind this front. Conservation of momentum across this (forward) shock
front requires that
p
1
+
ρ
1
v
2
1
=
p
2
+
ρ
2
v
2
2
(14)
where the subscript 1 refers to the upstream medium (the ambient CSM) and the
subscript 2 refers to the downstream medium (the shocked ejecta). Far upstream,
the pressure can be taken to be 0, and in the limit of strong shocks (for a monatomic
gas)
ρ
2
/ρ
1
=
v
1
/v
2
= 4. Thus this can be simplified to
3
ρ
1
v
2
1
4
=
p
2
.
(15)
If the medium is composed of fully ionized hydrogen,
μ
p
= 1 and the number densi-
ties of protons and electrons are equal (
n
p
=
n
e
). Using equation 15 together with
equation 11,
n
e
≈
(79 cm
−
3
)
(
e
B
)
−
6
/
19
(
f
0
.
5
)(
L
p
10
26
erg s
−
1
Hz
−
1
)
−
22
/
19
(
ν
p
5 GHz
)
4
(
t
p
1 days
)
2
.
(16)
We find that the number density of electrons at ∆
t
≈
22 days is
n
e
≈
3
×
10
5
cm
−
3
.
At such a high density, the optical depth to free-free absorption
τ
ff
might be expected
to have a significant effect on the shape of the spectrum at low radio frequencies.
From Lang (1999), we have
τ
ff
= 8
.
235
×
10
−
2
(
T
e
K
)
−
1
.
35
(
ν
GHz
)
−
2
.
1
∫
(
N
e
cm
−
3
)
2
(
dl
pc
)
(17)
19
Table 3.
Quantities derived from Day 22 measurements,
using different equipartition assumptions. In the text un-
less otherwise stated we use
e
=
B
= 1
/
3
Parameter
e
=
B
= 1
/
3
e
= 0
.
1
,
B
= 0
.
01
ν
a
=
ν
p
(GHz)
100
100
F
ν,p
(mJy)
94
94
r
(10
15
cm)
7
6
v/c
0.13
0.11
B
(G)
6
4
U
(10
48
erg)
4
35
n
e
(10
5
cm
−
3
)
3
41
ν
c
(GHz)
2
8
which, with our measured values of
n
e
and
R
on Day 22, gives the characteristic value
̃
τ
ff
= 68
(
T
e
8000K
)
−
1
.
35
(
ν
GHz
)
−
2
.
1
.
(18)
However, in AT2018cow the gas through which the shock is propagating is
not
at
normal HII-region temperatures of
∼
10
4
K, but Compton heated to much higher
temperature: the huge UV-X-ray flux through the gas yields to an ioniziation param-
eter many orders of magnitude larger even than quasar broad-line regions, and the
duration is so short that thermal and ionization equilibrium are not attained. The
UV and X-ray photons emitted at early times will completely ionize and Compton
heat any surrounding gas: for gas at the density and radius given in Table 3, the
lifetime to photoionization of a neutral hydrogen atom is less than 0.01 s, while the
recombination time is years
5
. Compton heating of the electrons (which at these den-
sities and temperatures turn out to be poorly coupled by Coulomb collisions to the
protons) increases their temperature at the rate
d
(3
/
2)
kT
e
dt
=
H
=
σ
T
m
e
c
2
∫
∞
0
hνL
ν
f
KN
(
hν/m
e
c
2
)
4
πR
2
dν
(19)
5
For much lower temperatures
T
∼
10
4
K, the Case B (high-density limit) recombination coeffi-
cient is
α
B
(
T
= 10
4
K) = 2
.
6
×
10
−
13
cm
3
s
−
1
(Draine 2011), and the timescale is
t
recomb
= 1
/
(
α
B
n
e
).
For
n
e
= 3
×
10
5
cm
−
3
,
t
recomb
≈
250 days. This timescale becomes even longer for the expected
higher temperatures.