1 center for astrophysics, guangzhou university, guangzhou
TRANSCRIPT
Draft version June 17, 2021Typeset using LATEX twocolumn style in AASTeX62
AT 2019avd: A tidal disruption event with a two-phase evolution
Jin-Hong Chen (陈劲鸿),1 Li-Ming Dou (窦立明),2, 3 and Rong-Feng Shen (申荣锋)1
1School of Physics and Astronomy, Sun Yat-Sen University, Zhuhai, 519000, China2Center for Astrophysics, Guangzhou University, Guangzhou, 510006, China
3Astronomy Science and Technology Research Laboratory of Department of Education of Guangdong Province, Guangzhou, 510006, China
(Received xxx; Revised xxx; Accepted xxx)
ABSTRACT
Tidal disruption events (TDEs) can uncover the quiescent super-massive black holes (SMBHs) at
the center of galaxies and also offer a promising method to study them. After the disruption of a star
by a SMBH, the highly elliptical orbit of the debris stream will be gradually circularized due to the
self-crossing, and then the circularized debris will form an accretion disk. The recent TDE candidate
AT 2019avd has double peaks in its optical light curve, and the X-ray emerges near the second peak.
The durations of the peaks are ∼ 400 and 600 days, respectively, and the separation between them is
∼ 700 days. We fit and analyse its spectral energy distribution (SED) in optical/UV, mid-infrared,
and X-ray bands. We find that this source can be interpreted as the circularization process in the first
phase plus the delayed accretion process in the second phase. Under this two-phase scenario, we use the
succession of self-crossing circularization model to fit the first peak, and the delayed accretion model
to fit the second peak. The fitting results are consistent with the partial disruption of a 0.9 M star
by a 7×106 M SMBH with the penetration factor β ' 0.6. Furthermore, we find the large-amplitude
(by factors up to ∼ 5) X-ray variability in AT 2019avd can be interpreted as the rigid-body precession
of the misaligned disk due to the Lense-Thirring effect of a spinning SMBH, with the disk precession
period of 10− 25 days.
Keywords: accretion, accretion disks - black hole physics - galaxies: nuclei
1. INTRODUCTION
Occasionally, a star is disrupted by the SMBH in the
center of galaxy, then its debris will experience a circu-
larization process to form an accretion disk (Rees 1988;
Hayasaki et al. 2013; Dai et al. 2015; Bonnerot et al.
2015, 2017). In such a so-called tidal disruption event
(TDE), the circularization process is mainly driven by
the self-collision of the debris stream near the opocen-
ter. The early optical/UV emission might come form the
circularization process (Jiang et al. 2016b; Lu & Bon-
nerot 2020). During or after the circularization, some
debris should be close to and be accreted by the central
SMBH. Then the accretion process near the SMBH can
emit significant amount of X-ray photons.
The details of the circularization process and the issue
of the disk formation have long been debated. Most of
[email protected], [email protected],[email protected]
the simulations indicate that the circularization process
may be inefficient if the pericenter of the star is not so
close to the SMBH (Hayasaki et al. 2013; Bonnerot et al.
2015, 2017), thus the formation of accretion disk would
be delayed. The inefficient circularization process will
lead to two peaks in the light curve (Chen & Shen 2021),
especially for the partial TDEs in which the pericenter
of the tidally disrupted star is slightly farther away than
the tidal radius. The first and the second peaks corre-
spond to the circularization and the accretion processes,
respectively. Here we call it as the two-phase model.
It is commonly believed that during the circulariza-
tion process the optical/UV emission originates from
the self-collision near the apocenter as the stretched
stream shocks itself near the apocenter due to the apsi-
dal precession (Jiang et al. 2016b; Lu & Bonnerot 2020).
During the accretion process, the optical/UV emission
may come from an outflow when the accretion is super-
Eddington (Strubbe & Quataert 2009; Lodato & Rossi
2011; Metzger & Stone 2016).
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If the early optical/UV emission comes from the cir-
cularization process, the size of the optical/UV emitting
region would be close to the self-collision radius as ex-
pected in the theory (Piran et al. 2015), which is con-
sistent with the observations (Wevers et al. 2019).
A firmer evidence of the two-phase model is from a
study of the late-time UV observations of TDEs by van
Velzen et al. (2019). They found that the late-time emis-
sion which is different from that in the early time, can
be explained by the ongoing disk accretion, which causes
the light curve to show a late-time flattening or peak.
It implies that the optical/UV component of the early
emission is not powered by accretion, instead, it can be
reasonably explained by the circularization model.
A recently reported special TDE candidate AT
2019avd (Malyali et al. 2021), whose optical light curve
has two peaks and the X-ray emerges near the second
peak, is consistent with this two-phase picture. Es-
pecially, the presence of Bowen fluorescence near the
second peak, which is triggered by the high energy pho-
tons (Bowen 1928), is a signature of an activated and
ongoing disk accretion.
In Section 2, we present the observations of AT
2019avd, then fit and analyse its SED in optical/UV,
mid-infrared, and X-ray in Section 3. In Sections 4 -
5, we present the model of circularization and accre-
tion process. In Section 6, we fit the observational data
using the model. In Section 7, we interpret the X-ray
variability as the rigid-disk precession. We summarize
and discuss the results in Section 8.
2. OBSERVATIONS
2.1. Optical and X-ray discoveries
AT 2019avd (ZTF19aaiqmgl) was reported as an
unique TDE candidate by Malyali et al. (2021) based on
its TDE-like X-ray behaviour. However, its double peak
optical light curve is unlike the typical TDEs. In this
paper, we study and show that this transient belongs
to a TDE whose early emission and the re-brightening
comes from the circularization process of the debris and
the delayed accretion process, respectively.
AT 2019avd is a nuclear transient in the inactive
galaxy 2MASX J08233674+0423027 at z = 0.029 (cor-
responds to a luminosity distance of 130 Mpc adopting a
flat ΛCDM cosmology), discovered by Zwicky Transient
Facility (ZTF) on 2019-02-09 (MJD 58523.2) (Nordin
et al. 2019). We downloaded the ZTF optical light curve
of AT 2019avd using the Lasair alert broker (Smith et al.
2019) 1 and show them in the middle panel of Fig. 1.
1 https://lasair.roe.ac.uk/object/ZTF19aaiqmgl/
The first X-ray detection of AT 2019avd on 2020-04-28
(MJD 58967.7) is from a dedicated search for candidate
TDEs in the first eROSITA all-sky survey (Malyali et al.
2021). And a series of follow-up observations were per-
formed with the Neil Gehrels Swift Observatory.
Between the optical discovery and the eROSITA ob-
servation of AT 2019avd, there is no X-ray observation.
The non-detection of Bowen fluorescence around the
spectroscopic observation of the 2.56 m Nordic Optical
Telescope (NOT) on 2019-03-15 (MJD 58557) implies
that the X-ray flux is low during the first optical peak,
until the appearance of Bowen feature around the ob-
servation of Wide Field Spectrograph (WiFeS) on 2020-
05-29 (MJD 58998) (Malyali et al. 2021). We infer from
this fact that the accretion disk forms near the second
optical peak.
Frederick et al. (2020) estimate the mass of center
SMBH as ∼ 106M and ∼ 107M, which are derived
through the virial method based on the FWHM Hβ
emission and the host-galaxy luminosity, respectively.
2.2. Swift follow-up
We download and reduced the X-ray data (Swift XRT;
Burrows et al. 2005) with the HEASoft V6.26 package
and the latest updated calibration files. We only use the
observations in Photon Counting mode. We extract the
source spectra from the circular region with radius of
47.2′′ and the background spectra from a large source-
free annulus at the same source position center.
In each of the observations, the X-ray spectra show
low count rates in the hard band > 2 keV, thus we only
show the 0.3− 2 keV count rate and present in the bot-
tom panel of Fig. 1. The XRT 0.3 - 2 keV count rate
increases from ∼ 0.03 cts s−1 to ∼ 0.2 cts s−1 in 90 days
and evolves with drastic time variability afterwards (by
factors up to ∼ 5).
The Ultraviolet and Optical Telescope (Swift UVOT;
Roming et al. 2005) observed the source with multi-
wavelength filters (V, B, U, UVM2, UVW1, UVW2)
simultaneously with the XRT observations. The UVOT
flux was extracted with the ’uvotsource’ task from the
circular region with radius of 9′′ and the background
flux from the nearby circular region with 15′′ radius.
The Galactic extinction in optical band is obtained
from NED 2 and extend to the extinction cure model
of Cardelli et al. (1989). After correcting for the Galac-
tic extinction, we subtract the host galaxy contribution
with the same SED model of Malyali et al. (2021).
We present the host-subtracted photometry results in
UVW1, UVW2, UVM2 band in the middle panel of Fig.
2 https://ned.ipac.caltech.edu/forms/calculator.html
AT 2019avd 3
1. Overall, the UV light curve has the same evolution
of the light curve in g, r band, therefore, the optical and
the UV emissions might come from the same process or
location.
2.3. Mid-infrared
In the top panel Fig. 1, we also update and plot
the mid-infrared data of AT 2019avd observed by the
Wide-Field Infrared Survey Explorer mission (WISE,
Wright et al. 2010) and Near-Earth Object WISE
(NEOWISE-R, Mainzer et al. 2014). We extract a
total of fifteen epochs of mid-infrared photometry from
the WISE/NEOWISE archive. There are 10-20 ex-
posures in each epoch. We use only the best-quality
single-frame images by selecting only detections with
data quality flag ”qual frame” > 0. This leaves 9-17
measurements for each epoch. We then average these
fluxes to obtain a mean value at each epoch.
The W1 and W2 band light curves are shown in Fig 1.
The mid-infrared is in the quiescent state before the first
optical outburst, then follows the optical light curve to
rise, and it has a second rise when the optical light curve
reaches its second peak. Therefore, the mid-infrared sig-
nature is associated with AT 2019avd.
3. SPECTRAL ANALYSIS
3.1. UV/optical
We fit the optical/UV SED with the black-body model
by the least square method. We use the nearly simul-
taneous ZTF optical and UVOT ultraviolet observa-
tions from MJD 59123 to MJD 59124 to fit the SED.
The effective temperature and the photospheric radius
given by the fitting are Teff ' 11375 ± 232 K and
Rph ' (7.10 ± 0.34) × 1014 cm, respectively. We plot
the optical/UV SED in Fig. 2.
In order to obtain the luminosity history, we need to
know the evolution of the SED. Unfortunately, we do
not have enough UV observational data to derive the
temperature evolution. Instead, we assume a constant
effective temperature Teff ' 11375 K in the optical/UV
band during the whole evolution. We need to verify the
validity of the constant temperature assumption here.
In Fig. 3, we plot the r − g colour evolution history,
which has only a very slight drop with a average value
r − g ' −0.53. Therefore, it is reasonable to assume a
constant black-body temperature during the outburst.
3.2. Mid-infrared
The mid-infrared brightening after the flare can be
well explained as dust echo from TDE (Dou et al. 2016;
Jiang et al. 2016a; Dou et al. 2017; Jiang et al. 2017).
We apply a black body model to fit the mid-infrared W1
Figure 1. NEOWISE-R (non-host subtracted, top), ZTFand UVOT light curves of AT 2019avd (middle), with theXRT 0.3 - 2 keV count rate history shown in the bottompanel. ZTF and UVOT data are host-subtracted, and theUVOT data is corrected by the Galactic extinction. TheNEOWISE-R observations pre-outburst are observed withmean W1, W2 shown in the top panel by the green and ma-genta dashed lines, respectively. The solid grey vertical lineindicates the MJD of the eRASS1 observation, which is thefirst observation of AT 2019avd in X-ray. The spectroscopicobservations with the NOT on 2019-03-15 (MJD 58557) andWiFeS on 2020-05-29 (MJD 58998) (Malyali et al. 2021) aremarked by the dashed grey vertical lines. The trigger ofBowen fluorescence requires a high flux of FUV or soft X-rayphotons, therefore the appearance of Bowen feature aroundthe WiFeS observation might implicate the formation of ac-cretion disk near the second peak of the light curve. We usethe nearly simultaneous observations shown in the orangeshaded area to fit the optical/UV spectrum, which is shownin Fig. 2. This figure is similar to Figure 5 in Malyali et al.(2021), except that we update the observations of WISE,ZTF and XRT.
and W2 data, in order to obtain the dust temperature
and luminosity (see Fig. 4). The fitting results are listed
in Table 1.
We present the optical/UV luminosity history in Fig.
5 together with the mid-infrared luminosity evolution.
The mid-infrared light curve also has double-peak fea-
ture similar to the optical light curve, and both of the
mid-infrared peaks follow the optical ones, respectively.
These features imply that the mid-infrared and the opti-
cal/UV photons are associated with the same event but
come from different processes and locations.
4
Figure 2. SED of AT 2019avd during nearly simultaneousZTF optical and UVOT ultraviolet observations (with thehost galaxy flux removed) from MJD 59123 to MJD 59124.We fit the spectra by a black body. The best-fit parametersare in the lower-left corner of the figure with 1σ error.
58400 58650 58900 59150 59400
-1
-0.8
-0.6
-0.4
-0.2
0
Figure 3. r − g colour evolution history of AT 2019avd.r − g is close to a constant with r − g ' −0.53 during theoutburst. Therefore, it is reasonable to assume a constantblack-body temperature during the outburst.
Table 1. Mid-infrared spectral fitting results with 1σ er-ror. Tdust and Lbb are the black-body temperature and theluminosity of the interstellar dust, respectively.
MJD Tdust[103 K] Lbb[1042 erg/s]
58578 1.560± 0.145 5.70± 3.59
58788 0.975± 0.056 4.55± 1.98
58945 1.052± 0.040 5.99± 1.74
59152 1.099± 0.026 14.82± 2.74
According to the dust echo model, the mid-infrared
emission comes from the interstellar dust that was
heated by the UV and/or X-ray photons of a nuclear
transient event (Lu et al. 2016; Jiang et al. 2017; Dou
et al. 2017; Sun et al. 2020), such as a TDE.
13.6 13.8 14.0 14.2 14.4log10[ /Hz]
14.0
13.5
13.0
12.5
12.0
11.5
11.0
log 1
0[F
/erg
s1
cm2 ]
MJD 58577MJD 58787MJD 58945MJD 59151
Figure 4. Mid-infrared SED of AT 2019avd at differentepochs of WISE observations (with the pre-outburst flux re-moved). We fit the spectrum by the black bodies. The best-fit parameters are shown in the Table 1 with 1σ error.
58400 58600 58800 59000 59200 59400MJD
41.5
42.0
42.5
43.0
43.5
log 1
0[L/
erg
s1 ]
opticla/UVmid-infrared
Figure 5. Optical/UV and mid-infrared bolometric lumi-nosity history of AT 2019avd. The luminosities are obtainedby the spectral fitting which are shown in Fig. 2 and 4. Thedouble-peak feature in the mid-infrared light curve is asso-ciated with the optical/UV light curve. The left red downarrow represents the upper limit on MJD 58421.
We can see from Fig. 5 that the second peak of the
mid-infrared light curve seems to be brighter than the
first one. It implies that the UV and X-ray photons
which trigger the dust echo, are more abundant near
the second peak.
3.3. X-ray
We group the X-ray data to have at least 4 counts in
each bin, and adopt mainly the C-statistic for the Swift
spectral fittings which are performed using XSPEC
(V12.9, Arnaud 1996). We fit the X-ray spectra with
the absorbed black-body model with a column density
AT 2019avd 5
42
43
44lo
g 10[
L x/e
rgs
1 ]
0.51.01.52.0
T bb (
106 K
)
59000 59100 59200 59300MJD
0.0
2.0
4.0
R bb [
R g(1
06M
)]
Figure 6. Bolometric luminosity (top), black-body tem-perature (middle), and photospheric radius (bottom) in X-ray band of AT 2019avd. The luminosity and the tempera-ture which are listed in Table 3 are given by the black-bodyspectral fit. The inferred photospheric radius is almost un-changed with Rbb ∼ Rg(106M), which is indicated by thehorizontal dashed line. It implies that the X-ray photonsemit from the inner part of the accretion disk. The X-rayluminosity evolves with intensive variability that might orig-inate from the disk precession (see the discussion in Section7).
of NH = 2.42×1020 cm−2 in the direction of AT 2019avd
(HI4PI Collaboration et al. 2016, ,HI4PI Map).
The fitting results are given in Table 3. We plot the X-
ray luminosity Lx = Lbb, the effective temperature Tbb,
and the photospheric radius Rbb = [Lx/(2πσT4bb)]1/2 in
Fig. 6. Here σ is the Stefan-Boltzmann constant.
The X-ray luminosity evolves with intensive variabil-
ity (the fluctuation factor up to ∼ 5). We will discuss
the interpretation of the X-ray variability in Section
7. The photospheric radius is almost unchanged with
Rbb ∼ Rg(106M), where Rg = GMh/c2 is the gravi-
tational radius of the SMBH. It implies that the X-ray
photons come from the inner part of the accretion disk.
4. CIRCULARIZATION PROCESS
In this and the next sections, we will demonstrate that
the features of AT 2019avd can be interpreted as a two-
phase evolution model of TDE.
4.1. Stream Crossing
In the central galaxy, the SMBH can tidally disrupt
a approaching star when its pericenter Rp closes to the
tidal radius RT = R∗(Mh/M∗)1/3, i.e., the penetration
factor β ≡ RT/Rp ∼ 1 (Rees 1988; Phinney 1989). In
the unit of BH’s Schwarzschild radius RS = 2GMh/c2,
pericenter radius is
Rp ' 23 β−1M−2/36 r∗m
−1/3∗ RS. (1)
Here R∗ ≡ r∗×R, M∗ ≡ m∗×M are the star’s radius
and mass, respectively.
After the disruption, the stellar debris will fall back
to the pericenter after the time-scale (Guillochon &
Ramirez-Ruiz 2013)
tfb = 2π√a3
0/GMh
' 41 M1/26 r
3/2∗ m−1
∗ day ×
β−3, β . 0.9
1, β > 0.9.
(2)
Here a0 is the semi-major axis of the debris firstly re-
turning to the pericenter, whose specific energy and ec-
centricity are (Lodato et al. 2009)
ε0 'GMh
2a0' GMhR∗
R−2p , β . 0.9
R−2T , β > 0.9
(3)
and e0 = 1−Rp/a0 ' 1, respectively.
Many studies indicate that after the disruption, the
debris stream will collide itself due to the general rel-
ativistic apsidal precession and its orbit will circular-
ize (Rees 1988; Hayasaki et al. 2013; Dai et al. 2015;
Bonnerot et al. 2015, 2017). The self-collision is crucial
for the formation of accretion disk, however, its conse-
quences is complicated.
If the photons can diffuse away efficiently induced by
the self-collision, the intersection is inelastic collision as
in Dai et al. (2015); Bonnerot et al. (2017). The stream
thus undergoes a succession of self crossing, which dis-
sipates an amount of the specific energy to circularize.
Eventually, the stream will settle into the circularization
radius Rc ' 2Rp, if the stream’s angular momentum is
almost unchanged during the circularization process.
In the following, we will consider the succession of
self crossing by analytic method, and in Section 8 we
will discuss other possible models of the circularization
process.
4.2. Succession of Self Crossing
In the “succession of self crossing” model (named
SSC hereafter), the stream precesses by a small angle
φ ∼ RS/Rp upon each passage of the pericenter, thus
undergoes a succession of self crossings, which dissipates
an amount of the specific energy. Consequently, the
apocenter of the stream’s new orbit moves closer to the
BH, and its eccentricity decreases. Finally, the stream
is fully circularized and settles into the circularization
radius Rc with the orbital energy εc = GMh/(2Rc).
We adopt the differential equation (see the Eq. (9) in
Chen & Shen (2021))
ε =∆ε0tfb
1
e20
(1− ε
εc
)(ε
ε0
)3/2
(4)
6
0 200 400 600 800day since disruption
41
42
43
44
45lo
g 10[
L/er
gs
1 ]LsLtLcir = Ls + Lt
Figure 7. Bolometric luminosity history during the circu-larization process for the disruption of a star (m∗ = r∗ = 1)by a 106 M SMBH. The penetration factor is β = 1. Thedashed line and the dot dashed line represent the luminos-ity of the self-collision and the tail shock, respectively. Thecircularization luminosity consists of both contributions.
to calculate the energy dissipation rate history.
Letting u = (ε/ε0)−1/2, we can rewrite the above equa-
tion as
u =1
tcir(ε0εcu−2 − 1). (5)
Here
tcir =2ε0tfbe
20
∆ε0
' 328 M−7/66 m
−4/3∗ r
7/2∗ day ×
β−4, β . 0.9
β−3, β > 0.9
(6)
is the time-scale of circularization similar to the defini-
tion in Bonnerot et al. (2017). Using the solution of Eq.
(5), i.e.,
t− 1.5tfbtcir
= 1−√ε0ε
+
√ε0εc
log
√1 + (ε/εc)1/2
1− (ε/εc)1/2, (7)
we can solve Eq. (4) by the Newton’s iteration. Here
t = 0 is the disruption time, and the self-crossing occurs
at t = 1.5 tfb.
Using the differential Eq. (4), we can write the lumi-
nosity of self-collision as
Ls(t) 'Ms(t)ε(t), (8)
where
Ms(t) =
∫ t
tfb
Mfb dt (9)
is the mass of the “main stream” consisting of the total
fallback mass from the beginning to now. In this paper,
we adopt the following fallback rate
Mfb = Mp
(t
tfb
)−n. (10)
It satisfies∫∞tfbMfb dt = ∆Mfb, wherer ∆Mfb is the to-
tal fallback mass. So the peak fallback rate is Mp '(n − 1)∆Mfb/tfb. For full and partial TDEs, we let
n = 5/3 and 9/4, respectively (Coughlin & Nixon 2019;
Ryu et al. 2020).
The total fallback mass depends on the stellar poly-
tropic index γ and the penetration factor β (Guillochon
& Ramirez-Ruiz 2013). In this paper, we adopt the fit-
ting formulae of the simulation results in Guillochon &
Ramirez-Ruiz (2013) to calculate the β-∆Mfb relation
and assume γ = 5/3. For β = 0.6 and 0.7, the total
fallback mass are ∆Mfb ' 0.0254 and 0.1222 M∗, re-
spectively.
In fact the fallback rate is not in a single power law
decay, it rises and decays, then to a asymptotic power
law at the late times. Recent hydrodynamic simulations
found that the shape of fallback rate depends on the
stellar properties, penetration factor β, and the BH’s
spin (Evans & Kochanek 1989; Lodato et al. 2009; Guil-
lochon & Ramirez-Ruiz 2013; Gafton & Rosswog 2019;
Golightly et al. 2019).
However, in the beginning of the self-crossing, the
“main stream” already has most of the mass of the fall-
back debris, i.e., Ms(1.5tfb) ∼ ∆Mfb. Thus the specific
shape of the fallback rate is unimportant in our calcu-
lation, and its power law only affect little the late time
behaviour. In this paper, we set the power law decay
of fallback rate as n = 5/3 and 9/4 for β & 0.9 and
β < 0.9, respectively, which correspond to the full TDE
and the partial TDE regimes, respectively (Lodato et al.
2009; Golightly et al. 2019).
Besides the self-collision of the main stream, the tail of
returning stream will join into the “main stream” during
the circularization process. The luminosity of this tail
shock is
Lt ' Mfb(t)[ε(t)− εt(t)]. (11)
Here εt(t) is the specific energy of the tail of returning
stream, it is given by the energy-period relation, i.e.,
εt '1
2
(2πGMh
t− 0.5tfb
)2/3
, (12)
where the factor 0.5 tfb is given by the fact that Lt = 0
at the beginning of the self-crossing.
We plot the circularization luminosity Lcir = Ls + Lt
as a function of time in Figure 7.
AT 2019avd 7
5. DELAYED ACCRETION PROCESS
After the circularization process, the gas will settle to
the vicinity of the BH and form an accretion disk. In
the accretion stage, the inflow gas and the tail of the
fallback gas will supply to the accreton disk.
Such accretion process can be considered to be a de-
layed accretion. The mean accretion rate is Macc 'Md/tacc, which Md and tacc are the disk mass and the
accretion time-scale, respectively. The change rate of
the disk mass is dMd/dt = Msup − Macc, which Msup
is the mass supply rate onto the disk. The solution of
this equation can be written as (Kumar et al. 2008; Lin
et al. 2017; Chen & Shen 2018; Mockler et al. 2019)
Macc(t) =1
tacc
(e−t/tacc
∫ t
td0
et′/taccMsup(t′) dt′
),
(13)
where td0 is the starting time of the mass supply.
The supplied mass includes the bound debris which
flows to the vicinity of the SMBH and the tail of the
fallback stream. The process of supply is complicated,
so we simply write the mass supply rate as a constant,
i.e.,
Msup '
∆Msup/tsup, td0 . t . td0 + tsup
0, otherwise.(14)
Here ∆Msup and tsup are the total supplied mass and
supply time-scale, respectively. The supply time-scale
tsup is about the time-scale of mass supplying to the
accretion disk. Because the accretion process is delayed,
the fallback rate of the stream’s tail is flattened when the
accretion starts. We expect that the supple time-scale
is longer than the fallback time-scale, i.e., tsup > tfb.
Thus we obtain the accretion rate
Macc '
∆Msup
tsup
(1− e−
t−td0tacc
), td0 . t . td0 + tsup
∆Msup
tsup
(1− e−
tsuptacc
)e−
t−td0−tsuptacc , t & td0 + tsup.
(15)
And the accretion luminosity is Lacc ' ηMaccc2, where
the efficiency η = 1/12 for a Schwarzschild BH.
6. MODEL FITTING TO THE OPTICAL/UV
LUMINOSITY HISTORY
In most of the TDE theories, the optical/UV radiation
comes from the shocks in the circularization process, and
in the accretion process it comes from the reprocessing
process and/or from the outer regions of the accretion
disk (Loeb & Ulmer 1997; Strubbe & Quataert 2009;
Metzger & Stone 2016; Dai et al. 2018).
Here we fit the overall optical/UV luminosity history
of AT 2019avd with our two-phase evolution model.
Note that here we do not attempt to investigate the
detailed mechanism/origin of the optical/UV emission
during the accretion phase, for instances, whether an
outflow exists and how its reprocessing produces the sec-
ond peak, or how large is the disk’s radial extension.
We fit the first peak of the light curve (MJD . 58840)
by the SSC model, and the second peak of the light curve
(MJD & 58840) by the delayed accretion model. In the
fitting procedure, we use the mass-radius relation of a
main sequence star (Kippenhahn & Weigert 1994)
r∗ =
m0.8∗ , 0.08 < m∗ < 1
m0.6∗ , 1 < m∗ < 10.
(16)
The variant of the emcee ensemble-based Markov
chain Monte Carlo (MCMC) routine (Goodman &
Weare 2010; Foreman-Mackey et al. 2013) is employed.
We use 40000 steps with 30 walkers and 5000 steps
with 30 walkers to fit the circularization and accretion
phase, respectively. The posterior distribution of model
parameters in the fits are shown in Fig. 8. The opti-
cal/UV luminosity history and the fitting light curves
are shown in Fig. 9. The fitting results are listed in
Table 2.
The fit results imply that AT 2019avd is a TDE can-
didate that is a partial disruption of a ∼ 0.87M star
by a ∼ 6.6 × 106M SMBH with β ' 0.56. The BH
mass is consistent with the estimation derived through
the Hβ emission and the host-galaxy luminosity in Fred-
erick et al. (2020) and Malyali et al. (2021).
β determines the pericenter radius of the star. The
self-collision is stronger for larger β, causing faster cir-
cularization and higher luminosity. For β < 0.9, the
total fallback mass is sensitive to β. Our fitting results
of SSC (Table 2) indicate that AT 2019avd is a partial
disruption with β ' 0.56 whose total fallback mass is
∆Mfb ' 0.02 M.
For the delayed accretion model, we have four free pa-
rameters: total supplied mass ∆Msup, suply time-scale
tsup, accretion time-scale tacc and the start time of ac-
cretion td0. The accretion time-scale and the supply
time-scale determine the slope and the rise time of the
luminosity history, respectively. The total supplied mass
determines the total radiative energy by accretion.
The supply time-scale tsup ' 373 days, and the ac-
cretion phase start time td0 ' 58839 MJD imply that
the process of the mass supply to the disk is long, and
the time of accretion is delayed. After the disruption,
the debris should experience a long-term circularization
process if the general relativity effect is weak. For the
partial disruption of a star by a modest SMBH, the gen-
eral relativity effect might not be strong for the rapid
8
0.270
0.255
0.240
0.225
0.210
log 1
0()
6.3
6.6
6.9
7.2
log 1
0(M
h)
0.6 0.3 0.0 0.3 0.6
log10(m * )
1.95
2.10
2.25
2.40
log 1
0[(5
8432
t 0)/d
ay]
0.270
0.255
0.240
0.225
0.210
log10( )
6.3 6.6 6.9 7.2
log10(Mh)
1.95
2.10
2.25
2.40
log10[(58432 t0)/day]
0.50
0.75
1.00
1.25
1.50
log 1
0[(5
8849
t d0)
/day
]
1.9
2.0
2.1
2.2
log 1
0[t a
cc/d
ay]
2.950
2.925
2.900
2.875
2.850
log10[Msup/M ]
2.525
2.550
2.575
2.600
log 1
0[t s
up/d
ay]
0.50
0.75
1.00
1.25
1.50
log10[(58849 td0)/day]
1.9 2.0 2.1 2.2
log10[tacc/day]2.5
252.5
502.5
752.6
00
log10[tsup/day]
Figure 8. Posterior distribution of model parameters in the fits of AT 2019avd for the circularization phase (left) and thedelayed accretion phase (right). The fitting results with 1σ error are shown in Table 2. And we plot the corresponding lightcurves in Fig. 9.
Table 2. Model fitting results. The fitting parameters on the columns 2 - 9 are stellar mass, penetration factor, BH mass, starttime of self-crossing, total supplied mass in the accretion phase, start time of accretion, accretion time-scale, and mass supplytime-scale, respectively.
Model M∗ β Mh t0 ∆Msup td0 tacc tsup
(M) (106 M) (MJD) (10−3 M) (MJD) (day) (day)
SSC 0.87+0.57−0.36 0.56+0.01
−0.02 6.61+3.91−3.65 58278+27
−30
Delay accretion 1.28+0.05−0.05 58839+3
−4 105+13−13 373+10
−12
58250 58500 58750 59000 59250MJD
40.5
41.0
41.5
42.0
42.5
43.0
43.5
log 1
0[L/
erg
s1 ]
Figure 9. Optical/UV bolometric luminosity history of AT2019avd and the fitting light curves. We fit the two peaks bythe SSC model (left) and the delayed accretion model (right).The best-fit light curves are represented by the black dottedlines with the distributions shown by the shaded areas.
formation of accretion disk. Therefore, most of the de-
bris will not necessarily flow into the last stable circular
orbit of the SMBH at the early time, and the accre-
tion process is delayed. The supplied mass includes the
bound debris which flows to the vicinity of the SMBH
and the tail of the fallback stream. However, the de-
tails about how the mass supply to the accretion disk
is an open question, and it needs future simulation to
elucidate.
If we assume the mass is supplied to the disk at the
circularization radiusRc, then the accretion time-scale is
approximate to the viscous time-scale at Rc, i.e., tacc 'tν ' [αΩk(Rc)]−1(H/R)−2. Here we let the viscosity
parameter α ' 0.1 and the height to radius ratio H/R '0.1 (Kato et al. 1998). Substituting the fitting results of
SSC model into the angular velocity Ωk(Rc), we obtain
tν ∼ 156 day. Therefore, the accretion time-scale tacc ∼100 day from of the fitting is reasonable.
For the SSC model, the total fallback mass is larger
than the total supplied mass (∆Msup/∆Mfb ∼ 0.1). It
AT 2019avd 9
implies that the SMBH can only accrete one tenth of
the debris. Most of the debris might become unbound
during the circularization process as outflow and/or dur-
ing the accretion process as disk wind. These unbound
debris can reprocess some portion of the X-ray photons
into the optical/UV emission.
7. INTERPRETATION TO THE X-RAY
VARIABILITY
Large-amplitude variabilities in accreting-BH related
X-ray transients, such as seen in AT 2019avd (Section
3.3) might originate from a precessing relativistic jet (Lei
et al. 2013; Wang et al. 2014) , a precessing accretion
disk (Stone & Loeb 2012; Shen & Matzner 2014), or
the disk instability (Lightman & Eardley 1974; Janiuk
& Czerny 2011). The lack of hard X-ray photons de-
tected in AT 2019avd makes it unlikely that variability
is induced by jet precession, a scenario similar to the jet-
TDE Swift J1644+57 (Burrows et al. 2011). The ther-
mal instability or the viscous instability in accretion disk
can cause a limit-cycle behavior of the light curve (Ja-
niuk et al. 2004; Merloni & Nayakshin 2006; Grzdzielski
et al. 2017). However, such instability-induced variabil-
ity often has a duty cycle 1 that is not observed in
AT 2019avd.
We consider that the X-ray variability of AT 2019avd
is caused by the disk precession. It is very likely that the
accretion disk is misaligned with the equatorial plane of
the spinning BH, the accretion disk will be subject to
Lense-Thirring effect (Lense & Thirring 1918).
The Lense-Thirring torque has strong radial depen-
dence, i.e., ∝ R−3, thus frame dragging acts most
rapidly on the inner regions of the disk. The outcome
of the torque depends on the structure of the accretion
disk. If the disk is thin (H/R 1), in the inner region,
the warp of the disk propagates in a diffusive way and
would lead to rapid alignment by the Bardeen-Petterson
effect (Bardeen & Petterson 1975). However, if the disk
is thick which is expected in TDE (Strubbe & Quataert
2009), the disk will precess as a solid body rotator as
shown in the simulations (Nelson & Papaloizou 2000;
Fragile & Anninos 2005; Fragile et al. 2007; Dexter &
Fragile 2011).
The disk surface density is usually proportional to
some power law of radius, i.e., Σ(R) ∝ R−ζ , thus the pe-
riod of the rigid disk precession within the outer radius
Rout is given by (Stone & Loeb 2012; Shen & Matzner
2014)
Pd =πc3
2aG2M2h
∫ Rout
RinR′3/2Σ(R′) dR′∫ Rout
RinR′−3/2Σ(R′) dR′
= PLTf(rout, ζ).
(17)
Here
PLT =πc3
aG2M2h
R3in (18)
is the Lense-Thirring precession period for a gas particle
located at the innermost circular orbit Rin and
f(rout, ζ) =
∫ rout1
r′3/2Σ(r′) dr′∫ rout1
r′−3/2Σ(r′) dr′
'
2ζ+12ζ−5r
3out, ζ . −1/2
2ζ+12ζ−5r
5/2−ζout , −1/2 < ζ < 5/2
2ζ+12ζ−5 , ζ & 5/2,
(19)
is a function of the ratio rout ≡ Rout/Rin and the power
law index of the surface density ζ. Here the normalized
variable r ≡ R/Rin & 1. The second equation is ob-
tained by letting rout 1. The above equation implies
that if ζ . 5/2, f ∝ r3out or r
5/2−ζout , the outer regions of
the disk contribute most of the Lense-Thirring torque,
otherwise if ζ 5/2, f ' 1, the precession is dominated
by the inner regions of the disk.
Shen & Matzner (2014) studied the disk evolution of
TDE. They found that the power law is −1/2 . ζ . 1/2
for the advective index regime, and −3/2 . ζ . −1/2
for the radiative regime of the disk. The disk in either
of the two regimes can always precess as solid bodies.
Therefore, we consider the range of ζ as−3/2 . ζ . 1/2.
The inner radius of the disk depends on the spin of
the SMBH, and is approximated the innermost stable
circular orbit (negative/positive sign below corresponds
to the prograde/retrograde orbit) (Bardeen et al. 1972)
Rin '(
3 + Z2 ±√
(3− Z1)(3 + Z1 + 2Z2))Rg
' g(a)Rg,(20)
where Z1 = 1 + (1− a2)1/3((1 + a)1/3 + (1− a)1/3) and
Z2 = (3a2 + Z21 )1/2. For the prograde and retrograde
orbit with maximum spin a = 1, we have g(a) = 1 and
g(a) = 9, respectively.
Substituting Eq. (19) and (20) into Eq. (17), one can
rewrite the period of the disk precession as
Pd ' 1.8 M6g(a)3
a
f(rout, ζ)
104day. (21)
Here Mh ≡M6×106 M is the BH’s mass. We plot the
period of the disk precession Pd in Fig. 10 with respect
to the power law index ζ and the ratio rout.
The period of the disk precession in AT 2019avd is
∼ 10− 25 day. We cannot obtain the precise period due
to long gaps in the X-ray data for frequency analysis.
We can infer from Fig. 10 that the outer radius of the
10
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0log[Rout/Rin]
1.5
1.0
0.5
0.0
0.5
1.0 10
.0
20.0
30.0
40.0
Figure 10. Period of the disk precession as a solid bodywith respect to the power law ζ of the disk surface densityand the ratio Rout/Rin of the precessing disk. We use thelines with different color to represent the period, with thevalues Pd shown along the lines. The solid and the dashedlines represent BH’s spins a = 0.5 and a = 1, respectively.The period is given by Eq. (21) with BH’s mass 106M.
precessing disk is Rout ∼ few × 10 Rin, if the BH mass
is 106 M with moderate spin a = 0.5. This ratio of the
radius Rout/Rin is consistent with the size of accretion
disk expected in TDE (Strubbe & Quataert 2009; Shen
& Matzner 2014).
8. CONCLUSIONS AND DISCUSSION
The TDE candidate AT 2019avd has double peaks
in its optical light curve, and the Bowen fluorescence
lines and the X-rays emerge near its second peak. These
features raise a question – whether its two peaks belong
to different processes. We fit the SEDs of AT 2019avd
in optical/UV, mid-infrared, and X-ray bands, then plot
their corresponding luminosity histories. We find that
the mid-infrared luminosity have double peaks similar to
the optical/UV light curve, and its second peak seems
to be brighter than the first one.
The presence of Bowen fluorescence lines, the detec-
tion of the X-ray, and the renewed and enhanced second
mid-infrared rise, all the three features happen near the
second optical peak. This implies a delayed formation of
accretion disk around that time. We consider that the
first and the second peaks come from the circularization
and the delayed accretion process, respectively.
We use the circularization process plus the delayed ac-
cretion to interpret the double-peak feature in the light
curve of AT 2019avd. The fitting results are consis-
tent with the partial disruption of a 0.87M star by a
7×106M SMBH with β ' 0.56. Therefore, AT 2019avd
can be interpreted as a the partial TDE.
If the general relativity effect is weak, the debris can-
not rapidly form an accretion disk, instead, the debris
will experience a long-term circularization process until
the debris have lost enough energy and angular momen-
tum for accretion (Hayasaki et al. 2013; Bonnerot et al.
2015, 2017). In this case, i.e., partial TDE, the pericen-
ter of the star is far from the SMBH, that weakens the
self-collision and causes delay formation of the accretion
disk.
We analyse the X-ray properties, and find that the X-
ray photons come from the inner part of the accretion
disk and the luminosity evolves with intensive variabil-
ity (fluctuation factors up to ∼ 5). This variability can
be explained by the rigid disk precession, whose period
is ∼ 10 − 25 days (see the discussion in Section 7). To
our knowledge, it is the first ever non-jetted TDE can-
didate that has show putative sign of disk rigid-body
precession.
The disk precession might diminish due to the align-
ment process. Franchini et al. (2016) consider that the
time-scale of the alignment depends on the viscosity pa-
rameter, BH’s mass and spin. If the X-ray variability
originates form the disc precession, we expect that the
X-ray variability will diminish within 103 days, with the
BH’s mass ∼ 106M and moderate spin a . 0.5.
The SSC circularization model we use to fit the data,
is based on the assumption that the photons induced
by the self-collision can diffuse away efficiently. In par-
tial TDE, the radiative diffusion is efficient due to little
amount of the debris stream (Chen & Shen 2021), thus
this assumption is acceptable.
However, if the photon cannot diffuse efficiently, the
post-shock gas will be pushed away by the radiation
pressure. In this case, the consequences are more com-
plicated. In the simulation of Lu & Bonnerot (2020)
and Bonnerot & Lu (2020), they consider that if the
self-collision is intensive due to the strong general rela-
tivity effect, some of the post-shock gas will be unbound
which is the so called collision induced outflow (CIO).
And some of the bound gas will flow into the vicinity of
the BH and produce the second shock. The second shock
which occur near the BH, is crucial for the formation of
accretion disk and also the main source of radiation. As
the mass inflow rate follows the mass fallback rate, the
luminosity should follow the fallback rate to decay as a
power-law in the late time.
In Fig. 9, the SSC model can fit well the light curve
except for the late time of the circularization phase. The
decay after the first peak looks like a power-law decay
which is similar to the scenario discussed above. Thus
we use a power-law decay (t/tp)−n to fit the decay part
of the light curve during the circularization phase, as
AT 2019avd 11
58500 58600 58700 58800MJD
41.5
42.0
42.5
43.0
43.5lo
g 10[
L/er
gs
1 ]n = 5/3n = 9/4
Figure 11. Power-law fit of the decay of the first peak in theoptical/UV bolometric luminosity. The decay can fit well bythe power-law decays.
shown in Fig. 11. For full and partial TDEs with n =
5/3 and 9/4, the decay time-scales are tp ' 53 and 102
day, respectively. The decay time-scales are consistent
with the typical TDE fallback time-scale (see Eq. (2)).
The circularization process of TDEs is still a unsolved
problem which is about how and when the formation of
accretion disk in TDE. We can use the observations to
check the theory of the circularization process and the
disk formation of TDE in the future.
There are other reported TDEs that have double-
peaks light curves, e.g., ASASSN-15lh and PS1-10adi.
ASASSN-15lh was first reported as a hydrogen-poor
superluminous supernova (Dong et al. 2016). Further
monitoring indicates that ASASSN-15lh is more consis-
tent with a TDE with a rapidly spinning and heavy
SMBH (& 108M) than with a superluminous super-
nova (Leloudas et al. 2016; Krühler et al. 2018). How-
ever, the likelihood of a TDE with such a high-mass
SMBH is very low. PS1-10adi was reported as a TDE or
a supernova occurring at the center of an active galaxy
(Kankare et al. 2017). The rebrightening of PS1-10adi in
the optical/UV is very late, about 1500 days after the
main peak, with a short duration (∼ 250 days). And
the infrared luminosity near the rebrightening is dim-
mer than that near the main peak. These features are
different from AT 2019avd. It is considered that the
rebrightening of PS1-10adi is powered by shock interac-
tion between an outflow and a surrounding torus (Jiang
et al. 2019; Zhuang & Shen 2021).
9. ACKNOWLEDGMENTS
RFS benefited tremendously from the discussion with
Dr. Yanan Wang about AT 2019avd. This work is sup-
ported by the National Natural Science Foundation of
China (12073091), Guangdong Basic and Applied Basic
Research Foundation (2019A1515011119) and Guang-
dong Major Project of Basic and Applied Basic Research
(2019B030302001).
Software: emcee(Foreman-Mackeyetal.2013),HEA-
soft (https://heasarc.gsfc.nasa.gov/lheasoft/) XSPEC
(V12.9, Arnaud 1996)
APPENDIX
A. SWIFT FOLLOW-UP AND X-RAY SPECTRAL FIT RESULTS
All Swift XRT and UVOT follow-up observations are presented in Table 3 and Table 4 below, respectively.
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Table 3. Log of Swift/XRT observations, and X-ray spectral fit results from the extracted XRT spectra. Lbb is the singleblack-body luminosity, and kT is the corresponding temperature of black body. We set the equivalent Galactic neutral hydrogencolumn density in the direction of AT 2019avd to be NH = 2.42× 1020 cm−2 (see Section 3.3).
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59108 2.95 245.5± 9.22 115.0+4.2−4.0 11.5± 0.43 22.72± 0.85 32.89± 1.24
59109 0.28 313.8± 33.9 101.0+11.8−10.3 11.99± 1.3 23.84± 2.58 38.71± 4.18
59117 1.03 97.35± 9.81 106.0+11.0−9.9 3.58± 0.36 7.09± 0.71 11.0± 1.11
59117 0.88 178.3± 14.3 90.4+9.3−8.2 7.53± 0.6 15.08± 1.21 28.02± 2.25
59118 0.35 80.66± 15.6 101.0+24.9−18.8 3.22± 0.62 6.4± 1.24 10.44± 2.02
59120 0.85 229.3± 16.5 114.0+8.4−7.6 12.47± 0.9 24.65± 1.77 35.89± 2.58
59120 0.63 241.8± 19.7 109.0+10.4−9.1 9.14± 0.74 18.11± 1.48 27.38± 2.23
59121 0.47 107.1± 15.1 109.0+20.1−15.5 7.27± 1.02 14.39± 2.03 21.75± 3.07
59123 0.82 129.6± 12.6 103.0+10.2−9.2 5.89± 0.57 11.71± 1.14 18.77± 1.82
59187 0.95 63.23± 8.24 103.0+17.2−14.6 2.39± 0.31 4.75± 0.62 7.56± 0.99
59191 0.52 191.9± 19.4 110.0+11.4−10.2 7.1± 0.72 14.06± 1.42 21.04± 2.13
59195 0.27 110.0± 20.5 102.0+26.6−18.8 4.63± 0.86 9.2± 1.71 14.8± 2.76
59205 0.75 64.17± 9.29 85.6+14.5−12.0 2.84± 0.41 5.7± 0.83 11.41± 1.65
59207 0.94 51.33± 7.56 99.0+18.0−14.3 2.12± 0.31 4.23± 0.62 7.04± 1.04
59209 1.02 124.1± 11.1 96.5+9.1−8.3 6.33± 0.57 12.62± 1.13 21.63± 1.93
59211 0.97 95.49± 9.97 97.3+11.2−10.1 3.76± 0.39 7.49± 0.78 12.71± 1.33
59213 0.92 248.9± 16.6 110.0+7.3−6.7 9.63± 0.64 19.07± 1.27 28.51± 1.9
59217 0.56 55.64± 10.0 123.0+23.9−19.2 2.0± 0.36 3.94± 0.71 5.41± 0.97
59256 1.42 89.4± 8.07 102.0+9.9−10.9 4.24± 0.38 8.43± 0.76 13.64± 1.23
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AT 2019avd 13
Table 4. Swift/UVOT photometry. The corrected magnitudes are shown in the parenthesis (see Section 2.2).
MJD UVW1 MJD UVM2 MJD UVW2
58983 18.29± 0.05(18.79) 58988 18.55± 0.11(18.88) 58988 18.53± 0.1(18.8)
58988 18.52± 0.17(19.29) 58994 18.52± 0.07(18.82) 58994 18.57± 0.06(18.87)
58994 18.11± 0.07(18.47) 59117 18.64± 0.09(19.04) 59117 18.59± 0.07(18.89)
59004 18.14± 0.04(18.52) 59117 18.54± 0.09(18.85) 59117 18.54± 0.08(18.82)
59011 18.05± 0.04(18.36) 59120 18.48± 0.09(18.76) 59118 18.46± 0.07(18.68)
59117 18.06± 0.07(18.38) 59120 18.5± 0.09(18.8) 59120 18.53± 0.08(18.79)
59117 17.98± 0.07(18.26) 59121 18.55± 0.12(18.88) 59120 18.61± 0.09(18.93)
59120 18.06± 0.07(18.38) 59123 18.52± 0.09(18.82) 59121 18.58± 0.1(18.88)
59120 18.07± 0.09(18.4) 59187 18.53± 0.08(18.84) 59123 18.64± 0.08(18.99)
59121 18.17± 0.1(18.57) 59191 18.63± 0.11(19.02) 59187 18.68± 0.07(19.05)
59123 18.06± 0.07(18.39) 59195 18.52± 0.15(18.83) 59191 18.59± 0.07(18.9)
59187 18.05± 0.06(18.37) 59205 18.68± 0.1(19.13) 59195 18.52± 0.13(18.78)
59195 17.96± 0.11(18.23) 59207 18.48± 0.08(18.76) 59205 18.77± 0.09(19.22)
59205 18.12± 0.07(18.49) 59211 18.44± 0.08(18.7) 59207 18.65± 0.07(19.0)
59207 18.06± 0.07(18.39) 59213 18.52± 0.08(18.82) 59211 18.61± 0.07(18.93)
59211 17.98± 0.06(18.26) 59217 18.56± 0.1(18.89) 59213 18.48± 0.07(18.72)
59213 18.02± 0.06(18.32) 59256 18.62± 0.07(19.01) 59217 18.59± 0.07(18.89)
59256 18.23± 0.08(18.68) 59259 18.59± 0.07(18.96) 59256 18.69± 0.07(19.08)
59259 18.19± 0.09(18.61) 59261 18.7± 0.07(19.16) 59259 18.65± 0.07(18.99)
59261 18.18± 0.08(18.6) 59262 18.88± 0.07(19.55) 59261 18.78± 0.07(19.25)
59262 18.32± 0.08(18.85) 59266 18.66± 0.07(19.07) 59262 18.98± 0.08(19.69)
59266 18.38± 0.09(18.97) 59273 18.77± 0.08(19.31) 59266 18.73± 0.08(19.14)
59269 18.25± 0.09(18.72) 59282 18.87± 0.12(19.54) 59272 18.83± 0.07(19.34)
59272 18.28± 0.07(18.77) 59285 18.74± 0.07(19.25) 59281 18.93± 0.17(19.57)
59281 18.42± 0.12(19.05) 59282 18.68± 0.11(19.05)
59282 18.35± 0.1(18.92) 59285 18.77± 0.07(19.22)
59285 18.38± 0.08(18.98)
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