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

chenjh258@mail2.sysu.edu.cn, doulm@gzhu.edu.cn,shenrf3@mail.sysu.edu.cn

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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58988 0.49 36.59± 8.62 104.0+70.7−30.8 1.71± 0.4 3.4± 0.8 5.45± 1.28

58994 1.73 33.69± 4.57 122.0+18.7−15.6 1.19± 0.16 2.34± 0.32 3.24± 0.44

59003 1.98 33.61± 4.26 106.0+16.3−14.5 1.28± 0.16 2.53± 0.32 3.92± 0.5

59011 1.96 37.7± 4.5 93.7+12.5−11.3 1.58± 0.19 3.15± 0.38 5.59± 0.67

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

59259 1.19 61.49± 7.27 107.0+12.9−11.3 2.63± 0.31 5.2± 0.61 8.01± 0.95

59261 1.35 182.5± 11.7 112.0+7.5−6.9 6.66± 0.43 13.18± 0.84 19.52± 1.25

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59285 1.53 207.8± 11.8 111.0+7.6−7.0 7.44± 0.42 14.72± 0.84 21.96± 1.25

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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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