# Gain Recovery in Heavily Irradiated Low Gain Avalanche Detectors by High
Temperature Annealing 111The work was partly done in the framework of the RD50
collaboration.

I. Mandić<EMAIL_ADDRESS>V. Cindro  A. Gorišek  B. Hiti  A. Howard  Ž.
Kljun  G. Kramberger  M. Maček Kržmanc  M. Mikuž  B. Novak  Jožef Stefan
Institute, Jamova 39, Ljubljana, Slovenia  University of Ljubljana, Faculty of
Mathematics and Physics, Jadranska 19, Ljubljana, Slovenia

###### Abstract

Studies of annealing at temperatures up to 450∘C with Low Gin Avalnche
Detectors (LGAD) irradiated with neutrons are described. It was found that the
performance of lgads irradiated with 1.5e15 n/cm2 was already improved at 5
minutes of annealing at 250∘C. Isochronal annealing for 30 minutes in 50∘C
steps between 300∘C and 450∘C showed that the largest beneficial effect of
annealing is at around 350∘C. Another set of devices was annealed for 60
minutes at 350∘C and this annealing significantly increased $V_{\mathrm{gl}}$.
The effect is equivalent to reducing the effective acceptor removal constant
by a factor of $\sim$ 4\. Increase of $V_{\mathrm{gl}}$ is the consequence of
increased effective space charge in the gain layer caused by formation of
electrically active defects or re-activation of interstitial boron atoms.

###### keywords:

Particle tracking detectors (Solid-state detectors), Radiation-hard detectors,
Solid state detectors, LGAD, annealing

††journal: Nuclear Instruments and Methods A

##  1 Introduction

In Low Gain Avalanche Detector (LGAD) charge multiplication (gain) is achieved
by introducing a thin highly doped ($\sim 10^{16}$ cm-3) layer of p-type
silicon within high resistivity p-type bulk under the charge collecting n-type
electrode [1]. The doping of the gain layer is tailored so that an electric
field strength of a few 10 V/$\mu$m is established in the layer when it is
depleted. Such a field leads to charge multiplication by impact ionisation of
electrons, with a gain factor of up to 100. At the same time the electric
field strength is too low for significant multiplication of holes which would
lead to breakdown. Moderate gain for electrons enables efficient detection of
MIPs with very thin silicon detectors (50 $\mu$m or less) and provides rapid
signals enabling good signal-to-noise ratio and short dead time. This results
in efficient charged particle detection with good time resolution even in a
high radiation and high rate hadron collider environment. Therefore, LGAD has
been chosen as the technology for timing detectors in both ATLAS and CMS for
the upgrade to HL-LHC [2, 3, 4]. Timing resolution for MIP passage of few tens
of ps can be reached with LGADs. Such an excellent timing resolution can also
be exploited in many other applications.

The main drawback for usage of LGADs in hadron colliders is their sensitivity
to displacement damage caused by energetic hadrons. The problem is the loss of
gain due to radiation induced acceptor removal in the gain layer [5]. The
dominant process leading to gain degradation is interaction of substitutional
boron with an interstitial resulting in electrically inactive interstitial
boron ($I+B_{S}\rightarrow B_{I}$) which can further form different defect
complexes. Smaller space charge concentration leads to smaller electric field
in the gain layer and eventually to loss of gain. This limits the operation of
LGADs in timing detectors at HL-LHC to a maximal fluence of 3$\cdot 10^{15}$
neq/cm2 (1 MeV neutron equivalent) [3].

It is well known that the effects of radiation damage change with time and
that the process is temperature dependent. The effect of annealing at 60∘C on
gain, up to over 20000 minutes, has been studied and only moderate effects on
LGAD performance were observed [6]. However, annealing at higher temperatures
might have more significant effects and in this work we report about
measurements with irradiated LGADs annealed at temperatures up to 450∘C.

Studies of the possibility to recover radiation damage in silicon detectors by
annealing at elevated temperatures have been done before. In [8] authors
discuss the feasibility of Detector Recovery/Improvement Via Elevated-
Temperature-Annealing (DRIVE) approach. It was found that annealing at 450∘C
leads to sign inversion of the effective space charge in p-type silicon and to
lower full depletion voltage. Both effects may result in improved charged
particle detection performance. The effects were explained with introduction
of thermal donors in oxygen-rich MCZ material. Thermal donors compensate
radiation induced negative space charge as well as the negative space charge
introduced by the reverse annealing [9].

It may be expected that high temperature annealing will be beneficial for
performance of LGADs because its degradation is caused by the drop of negative
space charge concentration in the gain layer. This could be compensated by
reverse annealing processes i.e. activation of effective acceptors on the long
time scale. Moreover, it was shown in [5] that higher $N_{\mathrm{eff}}$ in
the bulk of LGAD may also lead to lower operational voltage needed to
establish sufficient gain.

Additional motivation for studies at high temperature was the need of future
measurements with ASIC+LGAD assemblies with irradiated sensors. These are
needed for the development of ATLAS High Granularity Timing Detector (HGTD)
[3]. In the assemblies LGAD is bump bonded to the ASIC and bonds contain
silver (Ag) which forms long lived isotopes after irradiation with neutrons.
Studies would be greatly simplified if LGAD could be irradiated separately and
assembled with the ASIC after irradiation. But the bonding process requires
heating of the assembly to 250∘C for a few minutes which might affect the
performance of irradiated LGAD. To check the effect a study of 5 minutes
annealing at 250∘C was performed and the results are included in this paper.

##  2 Samples, irradiation

Single pad LGADs with a sensitive area of 1.3 $\times$ 1.3 mm2, an active
thickness of 50 $\mu$m and total thickness of the device 200 $\mu$m, produced
by HPK [7] were used for this study. An example is shown in the photo in Fig.
1. Voltages required for depletion of the gain layer $V_{\mathrm{gl}}$ were
between 40 and 55 V before irradiation while full depletion voltages
$V_{\mathrm{fd}}$ were between 45 to 65 V. Samples were irradiated with
neutrons in the TRIGA reactor in Ljubljana [10, 11]. Table 1 summarizes the
properties of the devices and the 1 MeV neutron equivalent fluences to which
they were exposed.

Figure 1:  Photo of HPK device used in this work. The sensitive area is 1.3 $\times$ 1.3 mm2, active thickness is 50 $\mu$m. Table 1:  Properties of investigated samples. active thickness 50 $\mu$m. Vgl is the depletion voltage of gain layer in LGAD. Device type | Vgl (V) | Gain layer | Vfd (V) |  $\Phi_{\mathrm{eq}}$ (1015 n/cm2)
---|---|---|---|---
|  | depth ($\mu$m) |  |
HPK-P1-T3.1 | 41 | 1.6 | 49 | 0.8, 3, 6
HPK-P1-T3.2 | 55.5 | 2.4 | 64 | 1.5, 4, 6
HPK-P2-W28 | 54.5 | 2.4 | 60 | 1.5

##  3 Experimental techniques

Samples were characterised by capacitance-voltage (CV) and current-voltage
(IV) measurements on the probe station. They were placed on a chuck with
temperature stabilized to (20 $\pm$ 0.2)∘C. Keithley 6517A Electrometer was
used as the high voltage source and the current meter. Capacitances were
measured with HP 4263B LCR meter at 10 kHz.

Timing properties were investigated with signals generated by MIP-like
electrons from a 90Sr source. Samples were wire-bonded to a dedicated
electronics board designed by UCSC [12] and cooled to -30∘C. Signals generated
by passage of electrons were processed with a fast trans-impedance amplifier
followed by a commercial amplifier (Particulars AM-02B, 35 dB, bandwidth $>$ 3
GHz). The signals from the amplification chain were digitised by a 20 GS/s
digitising oscilloscope with 2.5 GHz bandwidth. For measurement of timing
resolution, signals from the investigated sensors were compared with signals
from the reference detector with known timing resolution. Timing resolution
was determined from the spread of the difference in time of arrival between
the investigated and the reference detector. More details about the system and
measurement method can be found in [6].

Heat treatment of samples was made in air or Argon atmosphere, depending on
the equipment used. Heating in air was performed in a laboratory drying oven
(SP-45 C, Kambič, Slovenia). The heat treatments in Argon atmosphere were
performed in the furnace for Simultaneous thermal analysis (STA) Jupiter 449
(Netzsch, Selb, Germany). No study of the effect of different atmospheres was
done in this work.

##  4 Measurements

###  4.1 Annealing for 5 minutes at 250∘C

Figure 2 shows results of CV-IV measurements with HPK-P2-W28 annealed for 5
minutes at 250∘C.

|
---|---
a) | b)
|
c) |
Figure 2:  CV/IV measurements (blue) before and after annealing for 5 minutes at 250∘C (orange) with device irradiated to 1.5$\cdot 10^{15}$ neq/cm2. Figure a) shows C-V measurements and b) shows zoom to low bias voltages. Dashed lines are fits to straight parts of the curve. The intersection of these lines defines the gain layer depletion voltage $V_{\mathrm{gl}}$. Figure c) shows I-V measurements before and after annealing. Measurements were taken at 20∘C.  |
---|---
a) | b)
Figure 3:  Measurements with 90Sr source. Figure a) show collected charge vs.
bias voltage before and after annealing for 5 minutes at 250∘C with device
irradiated to 1.5$\cdot 10^{15}$ neq/cm2. Figure b) timing resolution as a
function of bias voltage and figure c) show leakage current measured on timing
setup at temperature of -30∘C.

Large changes of full depletion and gain layer depletion voltage can be seen:
before annealing full depletion voltage was below 100 V while after annealing
it is above 350 V (see Fig. 2a), the maximum at which measurements were taken.
More important for LGAD is $V_{\mathrm{gl}}$, determined from the location of
the first knee of C-V graph in Fig. 2b), which increases after annealing. This
drop of capacitance is the consequence of gain layer depletion and
$V_{\mathrm{gl}}$ is the bias voltage at which it occurs. $V_{\mathrm{gl}}$ is
defined as the intersection of lines fitted to straight parts on each side of
the knee as shown in Fig. 2b). Figure 2c) shows the comparison of I-V
measurements before and after annealing. It can be seen that the leakage
current is lower by an order of magnitude after annealing.

Figure 3 shows the results of measurements with 90Sr and significant
improvement of charge collection and timing resolution after annealing can be
seen. The voltage at which 10 fC charge is collected V10fC drops from close to
600 V to below 300 V and the same timing resolution is reached at much lower
bias voltage after annealing than before.

The improvement of performance can be explained by the increase of space
charge concentration caused by the annealing. In the depleted gain layer the
increase of space charge concentration increases the electric field which
leads to larger charge multiplication. The increase of space charge
concentration in the gain layer can be attributed to re-activation of boron
dopants by high temperature treatment which causes a change of their state
from interstitial to substitutional (B${}_{I}\rightarrow$ BS). The increase of
space charge concentration in the gain layer needed for the observed change of
$V_{\mathrm{gl}}$ is an order of magnitude higher than the increase of space
charge concentration due to “standard” reverse annealing of deep (radiation
induced) defects [9]. The latter is the dominant process which increases space
charge concentration in the bulk of the device causing increase of full
depletion voltage $V_{\mathrm{fd}}$. It is somewhat less straightforward to
see that increase of $V_{\mathrm{fd}}$ may also lead to better performance at
lower bias voltage. Namely, to establish sufficient electric field strength in
the gain layer, lower bias voltage needs to be applied because voltage drop
over the fully depleted bulk is smaller if space concentration is higher and
so the electric field profile in the bulk is steeper - see [6]. The
improvement of charge collection and timing properties after annealing for 5
minutes at 250∘C is predominantly attributed to this effect because the change
of $V_{\mathrm{gl}}$ is too small.

###  4.2 Annealing at higher temperatures

For studies at higher temperatures, irradiated LGADs were heated in argon
atmosphere with temperature controlled with accuracy of few degrees. In this
study isochronal steps of 30 minutes were taken at 300∘C, 350∘C, 400∘C and
450∘C with three devices of type HPK-P1-T3.1 irradiated to fluences listed in
table 1. After each annealing step C-V and I-V measurements were performed.
Figures 4a), 4b) and 4c) show C-V curves for the three devices after each
annealing step. Vgl increase with each annealing step can clearly be seen and
the effect is the largest in the LGAD irradiated to the highest fluence.
Measurement at low bias voltages after step 1 for the sample irradiated to
6e15 n/cm2 (Fig. 4c) were too noisy and Vgl could not be extracted but it can
be seen it was not higher than 10 V. After step 4 (450∘C) the aluminium
contact pads were damaged due to the high temperature and good C-V measurement
could only be made with the sample irradiated to 3e15 n/cm2 (Fig. 4b).

|
---|---
a) | b)
|
c) | d)
Figure 4:  Figures a), b) and c) show CV measurements after 30 minute
annealing steps: step 0: before annealing, step 1: 300∘C, step 2: 350∘C, step
3: 400∘C and step 4: 450∘C for LGADs irradiated to different fluences. Figure
d) shows Vgl estimated from CV measurements shown in a), b) and c) as a
function of step number.

Figure 4d) shows the evolution of Vgl estimated from C-V curves. The largest
increase of Vgl is observed after annealing for 30 minutes at 350∘C.

Following these results another experiment was performed in which three LGADs
of type HPK-P1-T3.2 irradiated to different fluences (see table 1) were
annealed in a single annealing step for 60 minutes at 350∘C. Figure 5 shows
C-V and I-V measurements with these three samples. Increase of Vgl can clearly
be seen as well as an almost 2 orders of magnitude large drop of reverse
current. Figure 5c) shows the change of $V_{\mathrm{gl}}$ relative to the pre
irradiation value $V_{\mathrm{gl0}}$ as a function of fluence. Exponential
functions were fitted to annealed and non-annealed points. The value of
$V_{\mathrm{gl}}$ is proportional to the space charge concentration in the
gain layer so the coefficient in the exponent represents an effective acceptor
removal constant. It can be seen that annealing for 60 minutes at 350∘C
reduces this constant by a factor of $\sim$ 4.

|
---|---
a) | b)

---
c)

Figure 5:  a) C-V measurement with three LGADs of type HPK-P1-T3.2 before and
after annealing for 60 minutes at 350∘C. Figure b) shows I-V measurements for
these devices. Figure c) shows $V_{\mathrm{gl}}$ extracted from Fig a)
relative to the pre irradiation value $V_{\mathrm{gl0}}$ as a function of
fluence. Exponential functions are fitted to measured points.

Measurements of these devices were made also with 90Sr source. Collected
charge and time resolution as a function of bias voltage are shown in figure
6. As can be seen, annealing for 60 minutes at 350∘C greatly improves charge
collection and time resolution, and restores the performance of heavily
irradiated LGADs to almost the pre-irradiation level. Before high temperature
annealing, gain operation would not be possible below 350 V after irradiation
to such high fluences [6, 12].

|
---|---
a) | b)
Figure 6:  a) Collected charge vs. bias voltage measured with 90Sr source for
irradiated HPK-P1-T3.2 devices after annealing for 60 minutes at 350∘C. In
figure b) time resolution as a function of bias voltage is shown.

Good results encouraged investigations of performance of LGADs at even higher
fluences. For this purpose the irradiated and annealed HPK-P1-T3.2 devices
were irradiated with additional 4e15 n/cm2 neutrons in the reactor in
Ljubljana and again annealed for 60 minutes at 350∘C. However, this time
annealing was performed with different equipment in standard atmosphere. After
60 minutes at 350∘C the furnace was switched off, however temperature stayed
high (above 200∘C) for another few hours. Therefore, this annealing step is
not directly comparable to previous ones. C-V curves measured after additional
irradiation before and after annealing are shown in Figure 7. Additional
irradiation again reduced Vgl which was subsequently significantly increased
by annealing. In 7c) it can be seen that after annealing $V_{\mathrm{gl}}\sim$
30 V was measured for LGAD irradiated to 1e16 n/cm2. This is a very high value
for such a high fluence and indicates that gain in LGADs might be restored
even after such heavy irradiation. Unfortunately, measurements of timing
performance could not be made because the noise was of too high, with the
origin not clear to us, so further studies are needed to clarify this.

|
---|---
a) | b)
|
c) |
Figure 7:  CV measurements for HPK-P1-3.2 devices measured after two
irradiation and annealing steps. Full lines are measurements after first
irradiation and dashed lines show measurements after another irradiation with
4e15 n/cm2. Figure a) shows 1.5e15 n/cm2 and 5.5e15 n/cm2, figure b) 4e15
n/cm2 and 8e15 n/cm2 and c) 6e15 n/cm2 and 1e16 n/cm2.

##  5 Conclusions

In this work the effect of annealing on irradiated LGADs at very high
temperatures in the range from 250∘C to 450∘C was investigated.

Annealing for 5 minutes at 250∘C slightly increased the gain layer depletion
voltage $V_{\mathrm{gl}}$ and had a large impact on full depletion
$V_{\mathrm{fd}}$. Both can be attributed to the increased space charge
concentration due to reactivation of boron dopants and reverse annealing of
deep defects. Annealing significantly improved performance of devices because
it allowed the operation voltage to stay well below the voltage of single
event burnout and to achieve sufficient gain necessary for good timing
resolution. The improved performance was mainly the consequence of increased
effective space charge concentration in the bulk which reduced voltage drop
over the depleted bulk resulting in lower bias voltage needed for sufficient
electric field strength in the gain layer.

Isochronal annealing study with 30 minutes intervals at temperatures between
300∘C and 450∘C showed that in this temperature range annealing increases
$V_{\mathrm{gl}}$ and that the increase is most significant up to 350∘C.
Following these findings another set of irradiated devices were annealed for
60 minutes at 350∘C which greatly increased $V_{\mathrm{gl}}$. Dependence of
$V_{\mathrm{gl}}$ on fluence (Fig. 5c) can be approximated with an exponential
function and it shows that annealing reduces the effective acceptor removal
constant by a factor of $\sim$ 4.

After annealing the timing properties of the devices were characterized with
90Sr and a timing resolution close to 30 ps could be achieved at bias of 300 V
with LGAD irradiated with 6e15 n/cm2. This is very good performance,
comparable to that before irradiation. Initial results of high temperature
annealing at fluences up to 1e16 n/cm2 are also encouraging and it can be
hoped that their operating range can be extended up to such high radiation
levels.

Annealing of irradiated silicon detectors at elevated temperatures to deal
with radiation damage was proposed a long time ago in [8]. Positive effects on
full depletion voltage were seen after annealing at 450∘C and the effect was
attributed to generation of thermal donors which compensated radiation induced
negative space charge. Heating silicon detectors to such high temperatures in
real experiment is a difficult technical problem but several possibilities
were proposed in [8] such as localised laser heating or a pre-built-in
external heating circuit.

It should be noted that LGADs are better suited for application of annealing
because lower temperatures are needed to improve their performance. The reason
is that unlike in standard detectors, in LGADs the increase of negative space
charge concentration (i.e. by reverse annealing) in the gain layer and in the
bulk are beneficial. Another important aspect of LGADs is that improvement
might be achieved by heating only the very thin gain layer while keeping other
sensitive parts of the detector system at lower temperatures. An example of
such approach can be found in [13] where radiation damage in temperature
sensing diodes was mitigated by heating with tungsten heater integrated in the
device.

##  6 Acknowledgments

The authors would like to thank the crew at the TRIGA reactor in Ljubljana for
help with irradiation of detectors. Part of this work was performed in the
framework of the CERN-RD50 collaboration. The authors acknowledge the
financial support from the Slovenian Research Agency (research core funding
No. P1-0135 and project No. J1-1699).

## References

  * [1] G. Pellegrini et al., Technology developments and first measurements of Low Gain Avalanche Detectors (LGAD) for high energy physics applications, Nucl. Instr. and Meth. A 765 (2014) 12.
  * [2] H.F-W. Sadrozinski, A. Seiden and N. Cartiglia, 4D tracking with ultra-fast silicon detectors, Rep. Prog. Phys. 81 (2018) 026101.
  * [3] ATLAS collaboration, Title Technical Design Report: A High-Granularity Timing Detector for the ATLAS Phase-II Upgrade, CERN-LHCC-2020-007.
  * [4] ATLAS collaboration, Title Technical Design Report: A MIP Timing Detector for the CMS Phase-2 Upgrade, CERN-LHCC-2019-003.
  * [5] G. Kramberger et al., Radiation effects in Low Gain Avalanche Detectors after hadron irradiations, 2015 JINST 10 P07006.
  * [6] G. Kramberger et al., Annealing effects on operation of thin Low Gain Avalanche Detectors, 2020 JINST 15 P08017
  * [7] Hamamatsu photonics
  * [8] Zheng Li, E. Verbitskaya, V. Eremin, A. Ivanov, J. Härkönen, E. Tuovinen, and P. Luukka, Detector Recovery/Improvement Via Elevated-Temperature-Annealing (DRIVE)—A New Approach for Si Detector Applications in High Radiation Environment in SLHC IEEE Trans. Nucl. Sci., Vol. 53 (2006) p 1551-1556.
  * [9] ROSE collaboration, G. Lindström et al., Radiation hard silicon detectors developments by the RD48 (ROSE) collaboration, Nucl. Instrum. Meth. A 466 (2001) 308.
  * [10] L. Snoj, G. Žerovnik and A. Trkov, Computational analysis of irradiation facilities at the JSI TRIGA reactor, Appl. Radiat. Isot. 70 (2012) 483.
  * [11] K. Ambrožič, G. Žerovnik and A. Trkov, Computational analysis of dose rates at the JSI TRIGA reactor irradiation facilities, Appl. Radiat. Isot. 130 (2017) 140.
  * [12] Z. Galloway et al., Properties of HPK UFSD after neutron irradiation up to 6e15 n/cm2, Nucl. Instr. Meth. A 940 (2019) 19
  * [13] L. A. Francis, N. André, P. Gérard, S. Z. Ali, F. Udrea, and D. Flandre, A Low-Power and In Situ Annealing Mitigation Technique for Fast Neutrons Irradiation of Integrated Temperature Sensing Diodes, 2015 4th International Conference on Advancements in Nuclear Instrumentation Measurement Methods and their Applications (ANIMMA), 2015, pp. 1-6, doi: 10.1109/ANIMMA.2015.7465594.


# Effective Temperature and the Light Curve Solution of Contact Binary Systems

##  1 Introduction

00footnotetext: © 2023 The Author(s). Published by Astronomical Observatory of
Belgrade and Faculty of Mathematics, University of Belgrade. This open access
article is distributed under CC BY-NC-ND 4.0 International licence.

Numerous all sky surveys have resulted in a massive proliferation in the
identification of contact binary systems with approximately half a million
catalogued in the International Variable Star Index (VSX) (Watson et al.
2006). With such proliferation there has been a corresponding increase in
published analysis of contact binary light curves. It is known that the shape
of contact binary light curves, particularly those exhibiting total eclipses,
are almost entirely dependent on three main geometric parameters namely the
inclination ($i$), the mass ratio ($q$) and degree of contact or fill-out
($f$) (Rucinski 1993, 2001, Wadhwa et al. 2022). There is strong correlation
between these parameters and successful light curve analysis in the absence of
radial velocity measurements can only be achieved if some constraints can be
placed due to the shape of the light curve itself. The presence of total
eclipses provides the morphological features that place a strong constrain on
the [$q,i$] domain. In the presence of total eclipses one can systematically
search the [$q,i$] domain to find a set of geometric parameters that yield the
best fit between observed and modelled light curves (Terrell and Wilson 2005).

Even though the shape of the light curve, especially when total eclipses are
not present, may be influenced by the absolute value of the component
temperatures (Wilson 2020), the presence of complete eclipses and the
associated constraints on the geometric parameters greatly overshadows these
variations such that temperature variations of a few hundred degrees are
thought not to influence the light curve modelled geometric parameters. During
analysis of contact binary light curves the temperature of the secondary
($T_{2}$), $f$, $i$ and the dimensionless luminosity of the primary ($L_{1}$)
are regarded as the adjustable parameters while the temperature of the primary
component ($\rm T_{1}$) is fixed. There is no standard method for the
assigning of $\rm T_{1}$ and wide variations in the effective temperature can
be found depending on the colour or spectral classification used. In a recent
study reporting photometric analysis of twelve extreme low mass ratio contact
binaries, the authors reported wide variations in effective temperature of the
primary based on various catalogued colour and spectral calibrations (Wadhwa
et al. 2023b).

Given the wide variations in effective temperature, particularly with colour
based estimates, many investigators are increasingly using low resolution
spectral classification as a guide to assigning $\rm T_{1}$. Unfortunately,
even for bright examples, spectral observations still require access to mid-
level equipment which may not be readily available. As noted above, numerous
all sky surveys have been undertaken recently covering a wide range of the
electromagnetic spectrum from ultraviolet to infrared. As described by
(Robitaille et al. 2007, Bayo et al. 2008) it is possible to collectively
examine the multi-band photometry as a single Spectral Energy Distribution
(SED) which can then be fitted to modelled synthetic spectra to estimate the
effective temperature. Using isolated examples few investigators have shown
good correlation between spectral class and SED determined effective
temperature (Panchal et al. 2022, Wadhwa et al. 2023a).

Although theoretical framework Kallrath and Milone (2009) suggests that the
geometric light curve solution will not differ with absolute temperature
values we can find no formal published study that demonstrates this
practically. Also, as noted above, only isolated examples exist demonstrating
the utility of SED in assigning effective temperature. In this study we
explore both of these issues. Firstly, we compare the spectral class
determined temperature of the primary with the SED determined temperature for
contact binaries from spectral class F3 to K4. Secondly, we undertake detailed
modelling, of the V and R band light curves, of two totally eclipsing contact
binary with temperature of the primary fixed using either spectral class or
SED $\pm$ 100, 300 and 500K to confirm that geometric solutions do not change
significantly with changing absolute temperature values.

##  2 Spectral Class and SED

We selected 12 bright contact binaries with determined spectral class from The
Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) survey (Luo
et al. 2018). We chose relatively bright examples as these were more likely to
have been included in many of the photometric surveys. We determined the
spectral class based effective temperature using the April 2022 update of
Pecaut and Mamajek (2013) calibration tables of spectral class and temperature
for main sequence stars. We constructed collective photometric SEDs for each
star as described by Bayo et al. (2008). All SEDs were then fitted to modelled
synthetic spectra which incorporated Kurucz atmospheres using ${\chi}^{2}$
minimisation as a goodness of fit parameter. Comparison of spectral class and
SED determined effective temperature is summarised in Table 1 and
representative SED and fitted modelled spectra are illustrated in Figure 1. As
can be seen from Table 1 there is good agreement between SED and spectral
class determined effective temperature and we consider SED as a more robust
alternative to single colour calibration for assigning $\rm T_{1}$ when
spectral observations are lacking.

[.5]() Star | Sp Class | Sp $T_{eff}$ (K) | SED $T_{eff}$ (K)
---|---|---|---
[.5]0 CRTS J090136.9+443723 | F3 | 6750 | 6500
[.5]0 PQ Leo | F4 | 6670 | 6750
[.5]0 NU Boo | F5 | 6550 | 6250
[.5]0 V356 Dor | F6 | 6350 | 6250
[.5]0 NN Lyn | F7 | 6280 | 6000
[.5]0 EI CMi | F8 | 6180 | 6000
[.5]0 OR Leo | G0 | 5930 | 6000
[.5]0 KR Lyn | G2 | 5770 | 5750
[.5]0 GSC 02992-01147 | G4 | 5680 | 5500
[.5]0 OV Leo | G7 | 5550 | 5250
[.5]0 HZ CVn | G9 | 5380 | 5250
[.5]0 V625 And | K1 | 5170 | 5000
[.5]0 ASAS J020753+2034.1 | K4 | 4600 | 4750
Table 1: Comparison of effective temperatures of contact binaries based on spectral class and spectral energy distribution from F3 to K4. Figure 1: Observed and fitted SEDs for contact binaries ranging from spectral class F4 to K1. The observed photometry is indicated in purple and the fitted model in green. The flux on the vertical axes is in erg/cm2/s/Å. The wavelength is in Angstroms (Å). Both axes are in log scale. Figure 2: Spectra, SEDs and fitted light curves for A1801 and A1906. SED flux on the vertical axes is in erg/cm2/s/Å. The wavelength is in Angstroms (Å). Both axes are in log scale. LC $\rm T_{1}$ | 5750K | 5950K | 6150K | 6250K | 6350K | 6550K | 6750K
---|---|---|---|---|---|---|---
[.5]() $T_{2}$(K) | $5554\pm 10$ | $5729\pm 10$ | $5933\pm 10$ | $\mathbf{6024\pm 10}$ | $6127\pm 12$ | $6310\pm 11$ | $6510\pm 10$
[.5]0 $T_{2}/T_{1}$ | 0.97 | 0.96 | 0.96 | 0.96 | 0.96 | 0.96 | 0.96
[.5]0 Incl.(∘) | $76.5\pm 0.3$ | $76.2\pm 0.3$ | $76.0\pm 0.3$ | $\mathbf{77.0\pm 0.5}$ | $77.2\pm 0.4$ | $77.3\pm 0.4$ | $77.4\pm 0.5$
[.5]0 Fillout (%) | $34\pm 5$ | $34\pm 5$ | $35\pm 4$ | $\mathbf{34\pm 4}$ | $35\pm 5$ | $34\pm 4$ | $33\pm 4$
[.5]0 Mass Ratio ($q$) | $0.151$ | $0.153$ | $0.151$ | $\mathbf{0.151}$ | $0.150$ | $0.151$ | $0.151$
[.5]0 $r_{1}$ (mean) | 0.559 | 0.558 | 0.559 | 0.559 | 0.560 | 0.559 | 0.559
[.5]0 $r_{2}$(mean) | 0.245 | 0.246 | 0.245 | 0.245 | 0.245 | 0.245 | 0.244
Table 2: A1801 Light curve (LC) solution for different values of $\rm T_{1}$ from 5750K to 6750K. $T_{2}/T_{1}$ represents the component temperature ratio and $r_{1,2}$ are the geometric mean of the fractional radii. The error for the mass ratio was $\pm 0.002$ in all cases. The central highlighted solution corresponds to SED modelled value of $\rm T_{1}$. LC $\rm T_{1}$ | 5220K | 5420K | 5620K | 5720K | 5820K | 6020K | 6220K
---|---|---|---|---|---|---|---
[.5]() $T_{2}$(K) | $5105\pm 20$ | $5293\pm 18$ | $5481\pm 15$ | $\mathbf{5578\pm 15}$ | $5681\pm 16$ | $5867\pm 16$ | $062\pm 20$
[.5]0 $T_{2}/T_{1}$ | 0.98 | 0.98 | 0.98 | 0.98 | 0.98 | 0.97 | 0.97
[.5]0 Incl.(∘) | $89.90^{+0.1}_{-2.2}$ | $90.00^{+0.0}_{-1.8}$ | $89.9^{+0.1}_{-1.4}$ | $\mathbf{89.8^{+0.2}_{-1.5}}$ | $89.8^{+0.2}_{-1.5}$ | $89.9^{+0.2}_{-1.3}$ | $89.7^{+0.3}_{-2.0}$
[.5]0 Fillout (%) | $46\pm 7$ | $45\pm 8$ | $50\pm 6$ | $\mathbf{50\pm 5}$ | $49\pm 5$ | $52\pm 5$ | $53\pm 5$
[.5]0 Mass Ratio ($q$) | $0.188$ | $0.191$ | $0.190$ | $\mathbf{0.191}$ | $0.191$ | $0.192$ | $0.191$
[.5]0 $r_{1}$ (mean) | 0.547 | 0.545 | 0.548 | 0.548 | 0.547 | 0.548 | 0.549
[.5]0 $r_{2}$(mean) | 0.267 | 0.2680 | 0.271 | 0.271 | 0.271 | 0.273 | 0.273
Table 3: A1916 Light curve (LC) solution for different values of $\rm T_{1}$
from 5220K to 6220K. $T_{2}/T_{1}$ represents the component temperature ratio
and $r_{1,2}$ are the geometric mean of the fractional radii. Due to increased
scatter the fit for A1916 was not as clean as for A1801 and the error for the
mass ratio was $\pm 0.004$ in all cases. The central highlighted solution
corresponds to spectra modelled value of $\rm T_{1}$.

##  3 Light Curve Solution and $\rm T_{1}$

ASAS J180157-7228.1 (A1801) ($\alpha_{2000.0}=18\ 01\ 56.66$,
$\delta_{2000.0}=-72\ 28\ 07.0$) was recognised a contact binary by the All
Aky Automated Survey (ASAS) (Pojmanski 2002) with a period of 0.355909 days
and an amplitude of 0.35 magnitude. The system was observed over 4 night in
August 2023 with the Western Sydney University 0.6m telescope equipped with
standard Johnson V and R filters and a cooled SBIG 8300T CCD camera. Images
were obtained using both V and R filters. All images were calibrated using
multiple dark, flat and bias frames. Differential photometry was performed
using the AstroImageJ (Collins et al. 2017) package. TYC 9298-140-1 was used
as the comparison star and 2MASS 18023134-7230047 as the check star. The V
band amplitude of the system was estimated to be 0.35 mag with brightest
magnitude of 10.36 and mid eclipse magnitude of 10.66. Using all available
observed and survey V band data we refine the orbital elements as follows:

$HJD_{min}=2460150.9825208(406)+0.3559121(30)E$

ASAS J191621-6802.3 (A1916) ($\alpha_{2000.0}=19\ 16\ 21.01$,
$\delta_{2000.0}=-68\ 02\ 19.2$) another ASAS discovery with an amplitude of
0.46 magnitude and period 0.364588 days. The system was observed over 5 nights
between July and August 2023 with the Western Sydney University 0.6m
telescope. Again V and R band images were acquired, calibrated and photometry
performed using the AstroImageJ package. TYC 110-123-59 was the comparison
star and 2MASS 19155297-6758004 was the check star. The V band amplitude of
the system was estimated to be 0.46 mag (12.03 - 12.49) and mid eclipse
magnitude of 12.43. Using all available observed and survey V band data we
refine the orbital elements as follows:

$HJD_{min}=2460155.1296218(753)+0.36459189(25)E$

Low resolution spectra for each system was obtained using the 2 meter
telescopes of the Las Cumbres Observatory (LCO) network over two nights in
August 2023. The LCO is a fully automated network and provides fully
calibrated spectra without user input. We compared the LCO spectra against
standard library spectra (Jacoby et al. 1984, Pickles 1998) to assign the
spectral class as F9 for A1801 and G3 for A1916. The corresponding
temperatures (6050K and 5720K) were interpolated from the April 2022 updated
tables from (Pecaut and Mamajek 2013). We constructed and fitted SEDs for each
system as described above. The SED determined temperatures for A1801 was 6250K
and 6000K for A1916. The observed and modelled spectra and SEDs are
illustrated in Figure 2.

Both light curves demonstrate complete eclipses and hence are suitable for
light curve analysis. The light curves were analysed using the 2013 version of
the Wilson-Devenney code (Kallrath et al. 1998, Wilson 1990). To fully
illustrate the flexibility of assigning the temperature of the primary we
fixed the temperature of the primary as 6250K for A1801 (SED based) and 5720K
for A1916 (spectral based). We utilised the mass ratio search grid method for
fixed value of $q$ from 0.05 to 1.0 in increments of 0.01 to $q=0.1$ and then
in increments of 0.02 to $q=1.0$. The adjustable parameters were $T_{2}$,
$L_{1}$, $f$ and $i$. As the estimated temperature is less than 7200K the
gravity darkening coefficients were fixed as ($g_{1,2}=0.32$), bolometric
albedoes were fixed as ($A_{1,2}=0.5$) and simple reflection treatment was
applied. Limb darkening coefficients were interpolated from (van Hamme 1993).
Iterations were carried out until the suggested corrections was less than the
reported standard deviation for each adjustable parameter. Once the
approximate solution was obtained the $q$ search was further narrowed to 0.001
increments to find the best fit solution.

The above analysis was repeated for various fixed values of $\rm T_{1}$ at
$T_{1},T_{1}\pm 100\rm K,T_{1}\pm 300\rm K$, and $T_{1}\pm 500\rm K$ for both
systems. In total each system was modelled for 7 different values of $\rm
T_{1}$ in the range $T_{1}\pm 500\rm K$. The geometric elements for each
solution are summarised in Tables 2 and 3 and the observed and fitted light
curves both systems are illustrated in Figure 2.

##  4 Absolute Parameters

In the absence of high resolution radial velocity measurements one is reliant
of various astrophysical correlations to estimate the absolute parameters of
contact binaries. The black body approximation $L=4\sigma R^{2}T^{4}$ is often
used to estimate the radius of the primary ($R_{1}$) from the assigned value
of $T_{1}$ and the observed luminosity (absolute magnitude) of the system. The
mass-radius relation for main sequence stars is then used to estimate the mass
of the primary and from the light curve solution the mass of the secondary and
then Kepler’s third law to estimate the separation of the components. Such an
approach, although valid for single stars, likely only represents a rough
estimate in the case of contact binary systems as it is highly dependent on
the assigned temperature. As noted above there can be wide variation in the
estimated temperature of the primary and as noted by Wadhwa et al. (2023c), a
200K variation in the assigned value of $T_{1}$ can lead to a greater than 10%
change in the estimated value of $M_{1}$ for low mass stars. Additionally, a
number of steps are required to determine luminosity, radius and then mass,
each associated with its own error which would require propagation leading to
a larger overall error in the estimate. Lastly, the black body and main
sequence approximations are based on a spherical configuration, it is well
known that binary star components are extended, distorted and fill their Roche
lobes such that the mean radius of both the primary and secondary are
considerably larger than their main sequence counterparts (Wadhwa et al.
2022).

| $M_{V1}$ | $M_{1}/M_{\odot}$ | $M_{2}/M_{\odot}$ | $R_{1}/R_{\odot}$ | $R_{2}/R_{\odot}$ | $A/R_{\odot}$
---|---|---|---|---|---|---
A1801 | $4.05\pm 0.08$ | $1.11\pm 0.02$ | $0.17\pm 0.01$ | $1.28\pm 0.02$ | $0.56\pm 0.01$ | $2.29\pm 0.02$
A1916 | $4.39\pm 0.06$ | $1.04\pm 0.02$ | $0.20\pm 0.01$ | $1.26\pm 0.02$ | $0.63\pm 0.02$ | $2.30\pm 0.02$
Table 4: Absolute parameters for A1801 and A1916.

We favour an observational approach for estimating the mass of the primary.
The Two Micron All Sky Survey (2MASS) acquired high precision simultaneous
photometry in multiple infrared bands (Skrutskie et al. 2006) and the GAIA -
EDR3 provides high precision distance estimates, particularly for nearby
systems (Anders et al. 2022, Gaia Collaboration et al. 2023). We have
previously described Wadhwa et al. (2023b) methodology to estimate the mass of
the primary as a mean of the 2MASS $J-H$ colour - mass of low mass main
sequence stars calibration and the absolute magnitude - main sequence
calibration. The apparent magnitude of the secondary eclipse, being total,
represents the apparent magnitude of the primary and can be used to estimate
its absolute magnitude. As extinction maps estimate extinction to infinity we
distance scale the extinction based on GAIA distance to determine absolute
magnitude for the primary as described in (Wadhwa et al. 2023b). The mass of
the secondary can be determined from the mass ratio and separation ($A$) using
Kepler’s third law. As the systems are in a contact configuration the radii of
the components can be estimated as $R_{1,2}=A(r_{1,2})$ where $r_{1,2}$ are
the geometric means of the fractional radii from three different orientations
provided by the light curve solution. The absolute parameters determined using
this methodology are summarised in Table 4. Our preference for the methodology
are obvious. We estimate absolute parameters adopting observations and
geometric elements of the light curve solution. As we have shown in this
report the estimation of absolute parameters are essentially independent of
the assigned value of $T_{1}$ unlike the black body approximations often used.
In presence of total eclipses the Roche geometry places tight constrains on
the ($q,i$) and ($q,f$) domains such that the light curve solution is
essentially the same regardless of the assigned temperature, at least within
500K as demonstrated here.

##  5 Discussion and Conclusion

Since the confirmation that luminous red novae are the result of merger of
contact binary components (Tylenda et al. 2011) combined with ever increasing
number of catalogued contact binary systems there has been a proliferation
contact binary curve solutions appearing in the literature. The hallmark of
achieving a successful light curve solution is the presence of a complete
eclipse. During such analysis various, mainly geometric, parameters are
adjusted to achieve a good fit between observed and modelled light curves.
Absolute value of the component temperatures, at least theoretically, are not
thought to have a significant influence on the determination of geometric
parameters such as the mass ratio, fractional radii, fill-out and inclination.
Theory suggests that where completely eclipsing light curves are present there
is tight constrain on the $T_{2}/T_{1}$ ratio but not the absolute
temperatures (Rucinski 1993, 2001). This is the first study, that we are aware
of, that tests theory through a practical example. We performed detailed
modelling of two low amplitude contact binary system with total eclipses. We
carried out modelling at various temperatures above a below an estimate of the
temperature of the primary. As can be seen from Tables 2 and 3 there is very
little difference in the modelled geometric parameters regardless of the fixed
temperature assigned to the primary component. As expected there is tight
constrain on the $T_{2}/T_{1}$ ratio which remained essentially fixed
regardless of the assigned value of $\rm T_{1}$.

Unless the estimated value of $\rm T_{1}$ is to be used in further analysis
such as luminosity and radius estimations, although these are probably better
estimated using distance, absolute magnitude and colour calibrations, a
reasonable estimation should suffice to get accurate estimation of geometric
parameters which are more important in determining potential orbital
stability. Unfortunately even a reasonable estimation of $\rm T_{1}$ can prove
problematic given the very wide variation between different colour and
spectral calibrations. Spectra based estimations probably represent a good
standard method however obtaining, even low resolution spectra, requires
access to modest equipment levels. A possible solution is to use a collective
photometric SED which incorporates most available photometric data and model
the SED to theoretical spectra. We show in this study that such an approach
for low mass (spectral class F to K) is sufficiently accurate and results
compare favourably to spectral class estimation of the effective temperature.

In conclusion, we feel that rigorous estimation for the effective temperature
of the primary component which is normally fixed during light curve analysis
is not required in the case of totally eclipsing systems and where only
geometric parameters determined through light curve analysis are required for
further analysis. The classical case is the determination of orbital
stability. Using the detailed observational methodology described in Wadhwa et
al. (2023b) we estimate the mass of the primary of A1801 as $1.11\pm
0.02M_{\odot}$ and of A1901 as $1.04\pm 0.02M_{\odot}$. Using the simplified
quadratic relations from Wadhwa et al. (2021) the orbital instability mass
ratio range for A1801 is 0.085 - 0.097 and for A1901 0.095 - 0.110. The
modelled mass ratios for both systems are higher than the upper limit of the
instability mass ratio and as such both systems would be considered stable.
This conclusion does not change regardless of the assigned temperature of the
primary as the modelled geometric parameters are not influenced by absolute
value of the assigned temperature.

Acknowledgements – Based on data acquired on the Western Sydney University,
Penrith Observatory Telescope. We acknowledge the traditional custodians of
the land on which the Observatory stands, the Dharug people, and pay our
respects to elders past and present.

This publication makes use of VOSA, developed under the Spanish Virtual
Observatory (https://svo.cab.inta-csic.es) project funded by
MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00. VOSA has
been partially updated by using funding from the European Union’s Horizon 2020
Research and Innovation Programme, under Grant Agreement number 776403.

## References

  * Anders et al. (2022) Anders, F., Khalatyan, A., Queiroz, A. B. A., et al. 2022, A&A, 658, A91
  * Bayo et al. (2008) Bayo, A., Rodrigo, C., Barrado Y Navascués, D., et al. 2008, A&A, 492, 277
  * Collins et al. (2017) Collins, K. A., Kielkopf, J. F., Stassun, K. G., and Hessman, F. V. 2017, AJ, 153, 77
  * Gaia Collaboration et al. (2023) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1
  * Jacoby et al. (1984) Jacoby, G. H., Hunter, D. A., and Christian, C. A. 1984, ApJS, 56, 257
  * Kallrath and Milone (2009) Kallrath, J. and Milone, E. F. 2009, Eclipsing Binary Stars: Modeling and Analysis (Springer New York, NY)
  * Kallrath et al. (1998) Kallrath, J., Milone, E. F., Terrell, D., and Young, A. T. 1998, ApJ, 508, 308
  * Luo et al. (2018) Luo, A. L., Zhao, Y. H., Zhao, G., and et al. 2018, VizieR Online Data Catalog, in press (DOI: ), V/153
  * Panchal et al. (2022) Panchal, A., Joshi, Y. C., De Cat, P., and Tiwari, S. N. 2022, ApJ, 927, 12
  * Pecaut and Mamajek (2013) Pecaut, M. J. and Mamajek, E. E. 2013, ApJS, 208, 9
  * Pickles (1998) Pickles, A. J. 1998, PASP, 110, 863
  * Pojmanski (2002) Pojmanski, G. 2002, AcA, 52, 397
  * Robitaille et al. (2007) Robitaille, T. P., Whitney, B. A., Indebetouw, R., and Wood, K. 2007, ApJS, 169, 328
  * Rucinski (1993) Rucinski, S. M. 1993, PASP, 105, 1433
  * Rucinski (2001) Rucinski, S. M. 2001, AJ, 122, 1007
  * Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163
  * Terrell and Wilson (2005) Terrell, D. and Wilson, R. E. 2005, Ap&SS, 296, 221
  * Tylenda et al. (2011) Tylenda, R., Hajduk, M., Kamiński, T., et al. 2011, A&A, 528, A114
  * van Hamme (1993) van Hamme, W. 1993, AJ, 106, 2096
  * Wadhwa et al. (2023a) Wadhwa, S. S., Arbutina, B., Petrovic, J., et al. 2023a, arXiv e-prints, in press (DOI: 10.48550/arXiv.2308.09998), arXiv:2308.09998
  * Wadhwa et al. (2023b) Wadhwa, S. S., Arbutina, B., Tothill, N. F. H., et al. 2023b, PASP, 135, 074202
  * Wadhwa et al. (2021) Wadhwa, S. S., De Horta, A., Filipović, M. D., et al. 2021, MNRAS, 501, 229
  * Wadhwa et al. (2022) Wadhwa, S. S., De Horta, A. Y., Filipović, M. D., et al. 2022, Journal of Astrophysics and Astronomy, 43, 94
  * Wadhwa et al. (2023c) Wadhwa, S. S., Petrovic, J., Tothill, N. F. H., et al. 2023c, arXiv e-prints, in press (DOI: 10.48550/arXiv.2308.11906), arXiv:2308.11906
  * Watson et al. (2006) Watson, C. L., Henden, A. A., and Price, A. 2006, Society for Astronomical Sciences Annual Symposium, 25, 47
  * Wilson (1990) Wilson, R. E. 1990, ApJ, 356, 613
  * Wilson (2020) Wilson, R. E. 2020, Galaxies, 8, 57