# Real-Time Automated donning and doffing detection of PPE based on
Yolov4-tiny ††thanks: 2 These authors contributed equally to this work

1st Anusha Verma  CSE Department
Wright State University
Dayton, United States of America
<EMAIL_ADDRESS>2nd Ghazal Ghajari  CSE Department
Wright State University
Dayton, United States of America
<EMAIL_ADDRESS>3rd K M Tawsik Jawad  4th Dr. Hugh P. Salehi  CSE
Department
Wright State University
Dayton, United States of America
<EMAIL_ADDRESS>BIHE department
Wright State University
Dayton, United States of America
<EMAIL_ADDRESS>5th Dr. Fathi Amsaad  CSE Department
Wright State University
Dayton, United States of America
<EMAIL_ADDRESS>
###### Abstract

Maintaining patient safety and the safety of healthcare workers (HCWs) in
hospitals and clinics highly depends on following the proper protocol for
donning and taking off personal protective equipment (PPE). HCWs can benefit
from a feedback system during the putting on and removal process because the
process is cognitively demanding and errors are common. Centers for Disease
Control and Prevention (CDC) provided guidelines for correct PPE use which
should be followed. A real time object detection along with a unique
sequencing algorithms are used to identify and determine the donning and
doffing process in real time. The purpose of this technical research is two-
fold: The user gets real time alert to the step they missed in the sequence if
they don’t follow the proper procedure during donning or doffing. Secondly,
the use of tiny machine learning (yolov4-tiny) in embedded system architecture
makes it feasible and cost-effective to deploy in different healthcare
settings.

###### Index Terms:

Doffing and Donning, Deep Learning, TinyML, YOLOv4-tiny, Object detection,
Real Time, Darknet, Health Safety, PPE

##  I Introduction

The COVID-19 pandemic and other recent infectious disease outbreaks have
highlighted the vital significance that personal protective equipment (PPE)
plays in preventing cross-contamination and self-contamination among patients
and healthcare personnel[1]. For this Centers for Disease Control and
Prevention (CDC) has provided protocols to control spread of pathogens [2].
Studies on the quality of donning and doffing PPE have shown that mistakes are
common and adherence to CDC protocols is low [3].

[1],[4],[5],[6] Evaluation of PPE adherence in a Polish medical context within
the COVID-19 outbreak: An initial case study by Łukasz Rypicz, Corinne Mowrey,
Izabela Witczak, Sandra Furterer, and Hugh Salehi. Hence, meticulous adherence
to PPE protocols is vital to ensure the safety of healthcare personnel[7][8].

To improve the adherence an automated PPE monitoring systems leveraging real-
time object detection can enhance safety by ensuring proper use of PPE.
Traditional systems often rely on cloud-based solutions where video frames are
sent to a cloud service for analysis. However, these systems face limitations,
including dependence on stable network connections, high bandwidth usage, and
privacy concerns due to external data processing [9] [10]. An edge-computing
approach, where image analysis occurs locally, can mitigate these issues. This
method reduces bandwidth requirements, improves system reliability by
eliminating reliance on internet connectivity, and preserves worker privacy by
processing data locally [11].

TABLE I: Objects Images Distribution Object Name | No of Images
---|---
Coverall | 1157
Face Shield | 429
Gloves | 1657
Goggles | 382
Mask | 1263
Figure 1:  Architecture of the proposed system

In this work, we provide a real-time PPE detection system that makes use of
YOLOv4-tiny deep learning model, specifically designed for healthcare
environments. The system developed ensures correct sequence for wearing and
removing PPE items such as gloves, masks, and gowns, which is crucial for
infection prevention in hospitals.

The following are the primary contributions of this paper:

  1. 1.

Fine-tuning the YOLOv4-tiny model for healthcare settings, evaluating its
performance in detecting various PPE items, and validating its real-time
capabilities.

  2. 2.

Providing real-time feedback on PPE compliance with WHO policy of sequencing
PPE equipment, thereby enhancing safety and reducing the risk of infection.

  3. 3.

Deploying this system on an embedded platform like the Raspberry Pi, we
achieve efficient and low-latency object detection results suitable for real-
time sequencing application.

##  II Related Works

The COVID-19 epidemic has presented the globe with a worldwide health
emergency. The necessity of following regulations for the appropriate use,
care, and training of personal protective equipment (PPE) was brought home by
this situation once more. PPE serves as healthcare workers’ last line of
defense against the transmission of infections. For personal safety as well as
the safety of others, it is crucial to make sure PPE is worn appropriately and
consistently[12]. HCWs, must follow the CDC guidelines for using PPE [13]. Two
strategies, based on gown designs, are used by the CDC for general donning and
doffing PPE, which involve breaking away and unfastening ties.

Current practices do not provide feedback to HCWs and mistakes cannot be
corrected. In a healthcare setting, it is possible for certain PPE to become
improperly worn without having monitoring and feedback.[14] [15].

##  III Architecture

In this paper, we present a model [16] that analyzes the sequence of donning
and doffing of medical PPE Equipment’s. We divided our architecture into three
phases, each contributing to the overall design and implementation of the
architecture.The systems architecture is shown in Fig.1

###  III-A Phase 1: Dataset and Training Object Detection Model

The proposed dataset incorporates samples from the CPPE-5 dataset [17]. Each
image in this dataset is annotated with multiple labels and bounding boxes. To
enhance the effectiveness and robustness of the data, data augmentation
techniques are applied, which also help in preventing model overfitting. The
CPPE-5 dataset consists of 1,029 images and 4,698 object annotations across
five categories: Coverall, Face Shield, Gloves, Goggles, and Mask, as detailed
in Table I. We used Roboflow tool to annotate the images and do data pre
processing and augmentations on the images. The Median height of the images in
our dataset is 696x500. During pre processing we resized all images to
600x600. For augmentation we Flip(Horizontal), Rotation(Between -20° and
+20°), Bounding Box(Shear: ±10° Horizontal, ±10° Vertical). We finally
exported the dataset in YOLO Darknet Format.

###  III-B Phase 2: Object Detection Model for PPE equipment

The proposed model for detection of PPE Equipments listed in Table I is based
on Yolov4-tiny architecture and consists a total of 38 layers. The
architecture incorporates multiple components including convolution layers,
routing layers, pooling layers, upsampling layer and yolo layers. These layers
work together to extract meaningful features from the input images and perform
object detection on the input images. We selected yolov4-tiny so this model
can be easily integrated with Raspberry Pi4 and can be easily deployed in
remote settings with no wifi to make sure medical staff is still following the
doffing and donning process. YOLO divides the input image into S×S grids of
equal sizes where each grid predicts the object located at the center of the
grid. Each grid identiﬁes object bounding boxes with an associated conﬁdence
score, and boxes with the best conﬁdence scores can be used for object
detection. The 4th generation of YOLO (YOLOv4) was released in the early 2020
and is used for PPE gears detection. YOLOv4-Tiny uses CSPDarknet53-Tiny
networks for object detection. When finding the sequence of PPE worn, accuracy
is not a major effecting factor.

Figure 2: Donning(wearing) Sequence Gown, Mask, Googles/Face shield, Gloves

###  III-C Phase 3: Doffing/Donning Sequence Analysis

The risk of contracting respiratory and other healthcare-associated diseases
is considerable for healthcare workers (HCWs),[18] and part of this risk is
due to self-contamination during the removal (or ”doffing”) of contaminated
personal protective equipment (PPE).[19][20][21].Recently we witnessed the
Pandemic Covid-19, in which the concern was for the HCW to not come in contact
with the virus during removing(doffing) the PPE. We developed a checklist
based on hospital protocols for donning and doffing PPE (Appendices 1a and
1b), tailored to the PPE items listed in Table I. This sequencing protocol
complies with the World Health Organization (WHO) [22] regarding PPE use in
the context of COVID-19. Artificial intelligence, particularly computer vision
techniques such as object detection in medical imaging, has seen widespread
adoption [23]. CNN models are commonly used for object detection. There are
different kinds of detectors: one-stage [24] and two-stage detectors[25,
26][27]. When it comes to accuracy of the model, two stage detectors are
better, however if the main objective is faster inference than two-stage
detector is better.

Algorithm 1 Real-time Sequence Detection Algorithm

1: Procedure RealtimeSequenceDetection

2: for $i=1$ to $n$ do

3: if PPE meets thFrequency and thConfidence criteria then

4: Mark the task as done and record the time frame

5: break out of loop

6: else if Mask meets thFrequency and thConfidence criteria then

7: Mark the task as done and record the time frame

8: break out of loop

9: else if Gloves meet thFrequency and thConfidence criteria then

10: Mark the task as done and record the time frame

11: break out of loop

12: else if FaceShield meets thFrequency and thConfidence criteria then

13: Mark the task as done and record the time frame

14: break out of loop

15: else if Glasses meet thFrequency and thConfidence criteria then

16: Mark the task as done and record the time frame

17: break out of loop

18: end if

19: end for

20: Check if donning or doffing sequence is followed

21: return Result

22: End Procedure

Without getting into the intricacies of the PPE donning and doffing procedure,
some study has been done on the use of AI for face mask identification[28] and
other PPE equipment detection[29]. This study aims to develop a model that
verifies the correct donning and doffing procedures. Currently, the process
relies on monitoring by trained educators. This project advances existing
research by creating an innovative algorithm that could (1) ensure healthcare
professionals (HCPs) follow PPE guidelines for donning and doffing, and (2)
provide an innovative tool to support HCP educators in creating simulation
environments that surpass traditional teaching methods. For determining the
sequence of doffing and donning of PPE gears worn from results of YOLOv4-tiny
in real time we have come up with an algorithm. The detection of any object
using the object detection model is highly associated with mAp obtained during
the training of model for each class. We calculate the threshold for each
class separately and once the threshold values are accomplished we mark the
PPE item as worn. The sequence for which we will be checking is shown in Fig.2
and Fig.3.

Figure 3: Doffing(removing) Sequence Gloves, Googles/Face shield, Gown, Mask-
Unfastening Ties Strategy

The Real-time Sequence Detection algorithm presented in this study serves as a
pivotal component in our research endeavor, aimed at enhancing the efficiency
and accuracy of personal protective equipment (PPE) monitoring systems. The
algorithm below shows the pseudo code for the sequencing algorithm.
thFrequency is the Threshold Frequency and thConfidence is the Threshold
Confidence value calculated from the mAP value for each class. The correct
calculation of threshold values is very important to successfully determine if
the correct sequence or pattern is followed or not. Overall, the Real-time
Sequence Detection algorithm represents a significant advancement in
monitoring PPE usage patterns, with implications for improving safety
protocols, enhancing data-driven decision-making, and ultimately mitigating
risks associated with infectious diseases or workplace hazards.

##  IV Experimental Results

We have utilized a open-source CNN framework written in C and CUDA, Darknet
[30] We imported pre-trained weights from AlexeyAB’s Darknet for the purpose
of training the model. More specifically, the yolov4.conv.137 weights were
used to train the YOLOv4-tiny model. The filter size for the yolov4-tiny model
was calculated using the equation $(\text{class}+5)\times 3$. This
implementation was done using an online NVIDIA Tesla A100 GPU that is
accessible through Google Colab.

Figure 4: Loss Graph for the Yolov4-tiny model

After training for 45 minutes, the Tiny YOLOv4 models attained 10,000
iterations. Analysing the graph in Fig.4, we can conclude the loss factor for
Tiny YOLOv4 was 0.1798 at the training step 7000. A YouTube video with the
proper donning sequence was chosen to validate the trained Tiny YOLOv4 model’s
prediction results and check for our sequencing algorithm. The results in
Fig.5 shows the snapshots taken after detection was performed on the video. we
have set confidence threshold for each class. In Fig.5(b) PPE shows less
confidence than the threshold confidence.

(b)

(c)

Figure 5: output video snapshots.

##  V Conclusion

In this study, a PPE wearing automated real time detection and task sequencing
model based on YOLOv4-tiny is proposed for medical professionals. This model
uses deep learning techniques to intelligently identify between various PPE
products. Our study’s findings suggest that this model can be utilized to
consistently and effectively track medical staff members’ PPE donning and
doffing situations, lessen the possibility of injury from human subjectivity
throughout the management process, and conserve medical resources.

Moreover, Our research demonstrates the feasibility of integrating our object
detection model with a Raspberry Pi 4 for real-time action in remote areas. We
have demonstrated that it is feasible to create autonomous and responsive
systems in resource-constrained contexts by utilizing the Raspberry Pi’s low
power consumption, small form factor, and processing capacity in conjunction
with our optimized custom model.

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# Dust changes in Sakurai’s Object: new PAHs and SiC with coagulation of
submicron-sized silicate dust into 10$\mu$m-sized melilite grains

Janet E. Bowey1
1 School of Physics and Astronomy, Cardiff University, Queens Buildings, The
Parade, Cardiff CF24 3AA, UK E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

6–14 µm Spitzer spectra obtained at 6 epochs between April 2005 and October
2008 are used to determine temporal changes in dust features associated with
Sakurai’s Object (V4334 Sgr), a low mass post-AGB star that has been forming
dust in an eruptive event since 1996\. The obscured carbon-rich photosphere is
surrounded by a 40-milliarcsec torus and 32 arcsec PN. An initially rapid mid-
infrared flux decrease stalled after 21 April 2008. Optically-thin emission
due to nanometre-sized SiC grains reached a minimum in October 2007, increased
rapidly between 21–30 April 2008 and more slowly to October 2008\. 6.3-µm
absorption due to PAHs increased throughout. 20 µm-sized SiC grains might have
contributed to the 6–7 µm absorption after May 2007. Mass estimates based on
the optically-thick emission agree with those in the absorption features if
the large SiC grains formed before May 1999 and PAHs formed in April–June
1999. Estimated masses of PAH and large-SiC grains in October 2008, were
$3\times 10^{-9}$ M☉ and $10^{-8}$ M☉, respectively. Some of the submicron-
sized silicates responsible for a weak 10 µm absorption feature are probably
located within the PN because the optical depth decreased between October 2007
and October 2008. 6.9 µm absorption assigned to $\sim$10 µm-sized crystalline
melilite silicates increased between April 2005 and October 2008. Abundance
and spectroscopic constraints are satisfied if $\la$2.8 per cent of the
submicron-sized silicates coagulated to form melilites. This figure is similar
to the abundance of melilite-bearing calcium-aluminium-rich inclusions in
chondritic meteorites.

###### keywords:

stars: AGB and post-AGB < Stars, (stars:) circumstellar matter < Stars, stars:
carbon < Stars, (ISM:) dust, extinction < Interstellar Medium (ISM), Nebulae,
stars: individual:… < Stars, stars: evolution < Stars

††pubyear: 2020††pagerange: Dust changes in Sakurai’s Object: new PAHs and SiC
with coagulation of submicron-sized silicate dust into 10$\mu$m-sized melilite
grains–Dust changes in Sakurai’s Object: new PAHs and SiC with coagulation of
submicron-sized silicate dust into 10$\mu$m-sized melilite grains

##  1 Introduction

Sakurai’s Object (V4334 Sgr) is a low mass post-AGB star that is undergoing a
very late thermal pulse caused by the ignition of a residual helium shell. It
has formed substantial quantities of dust during the 25 years since its
discovery by Yukio Sakurai in 1996 (Nakano et al., 1996). The source was later
identified (V$\sim$ 12.5 mag) in pre-discovery optical images from January
1995; it brightened to 11.4 mag in the first 12 months and showed no nova-like
emission lines. In March 1996 the photosphere was hydrogen-poor with over
abundances of carbon and oxygen and centred in a 32 ″circular planetary nebula
(Duerbeck & Benetti, 1996). Once the photosphere was obscured CN, C2 and CO
were detected in its atmosphere (Eyres et al., 1998). Later infrared
observations revealed HCN and C2H2 with 12C to 13C isotope ratios which are
consistently lower than the Solar System values;(see Evans et al., 2020,
hereinafter Ev2020, for a detailed history). Like other ‘Born Again Giants’ it
lies at the centre of an older faint planetary nebula (PN) (Pollacco, 1999).
Chesneau et al. (2009) obtained high spatial-resolution 7.5–13.5 µm
observations in June 2007 and deduced that the star was surrounded by a
$30\times 40$ milliarcsec opaque dusty disc or torus inclined at 75 $\deg$ to
the plane of the sky and aligned with a low level of asymmetry seen in the old
PN. The source continues to evolve and the 2015–2019 expansion of the bipolar
nebula has recently been mapped in the near-infrared by Hinkle et al. (2020)
and images show the existence of 760 K dust which are likely to be a
consequence of a near-IR brightening event observed in 2008 (e.g. Hinkle &
Joyce, 2014).

Figure 1: 5.2–7.5µm spectra of Sakurai’s object (grey error bars) with
features fitted with a black body obscured by PAHs, melilite and bSiC (dotted;
equation 1) and derived continua (dashed).

To date the dust mineralogy has not been studied in much detail; this work is
focussed on Ev2020’s reporting of a weak, but consistent, absorption feature
with minima at 6.3 µm and 6.9 µm (Figure 1) in their low-resolution Spitzer
spectra of the source which they tentatively attributed to hydrogenated
amorphous carbon (HAC) formed in an early mass ejection phase prior to 1997.
These features resemble part of similar absorption bands in dense cold ($\la
100$ K) lines of sight through young stellar objects (YSOs) and molecular
clouds (e.g. Keane et al., 2001; Boogert et al., 2011) which are normally
associated with a combination of ices, carbonaceous material, carbonates, or
occasionally with overtone bands of a crystalline silicate called melilite
(Bowey & Hofmeister, 2005). Overtone bands are 1/100th the strength of
fundamental bands like the 10 µm Si-O stretch and are therefore seen only in
samples where the fundamental bands are opaque due to larger grain sizes or in
micron to 100 µm-thick films of finely-ground powders. Since the grain density
in YSO discs is extremely high (Bowey & Hofmeister, 2005) did not make the
connection with large grain sizes or coagulated grains producing the features.
In Sakurai’s Object the absence of evidence for H2O ice at 3.0 µm and 6.0 µm
in the currently oxygen-poor environment means that H2O and other ices and
carbonates (which are not known to form in the absence of water) can be ruled
out as carriers of the 6.3 µm and 6.9 µm bands. However, its complex history
of mass-loss and planetary nebula would suggest that carbonaceous materials,
silicates and other refractory components could contribute to the absorption
features.

The Spitzer observations used in this analysis are described in Section 2.
Models of the 5.9–7.5 µm and 8.3–13.3 µm spectra are developed and the choice
of laboratory data explained in Sections 3 and 5. The fits to each range are
described in Sections 4 and 6 and the observational results summarised in
Section 7. A time-averaged dust profile for the 6–7.5 µm-range is produced in
Section 4.2. Dust column mass and number densities are quoted in Section 8
together with estimates of the masses of carbonaceous dust formed. The
evolution of the dust during the Spitzer observations is discussed in Section
9. Conclusions are in Section 10.

##  2 Observations

Figure 2: Merged Spitzer SL2 (5–7.5 µm), SL3 (7.5–8.5 µm) and SL1 (7.6–14.0
µm)–spectra of Sakurai’s Object for Epochs 2–5. SL2 only for Epoch 1; SL1 data
were saturated. Table 1: Spitzer LRS Observations (Ev2020)

Epoch | MJD111Modified Julian Date (MJD) is used to identify the time of the observations. MJD is related to Julian Date (JD) by MJD = JD – 2400000.5 | Date | AOR | T/K |  $F_{5.6}$/Jy222Weighted mean of 5.25–6.00 µm flux.
---|---|---|---|---|---
1 | 53475 | 2005-04-15 | 10840320 | 284 | $3.54\pm 0.01$
2 | 54225 | 2007-05-04 | 17740544 | 226 | $0.921\pm 0.003$
3 | 54388 | 2007-10-15 | 17742336 | 217 | $0.734\pm 0.003$
4A | 54577 | 2008-04-21 | 17742592 | – | $0.591\pm 0.003$
4B | 54586 | 2008-04-30 | 22273280 | – | $0.604\pm 0.002$
5 | 54757 | 2008-10-18 | 22272768 | 207 | $0.571\pm 0.002$

Sakurai’s Object was observed with the Low-Resolution Spectrometer (LRS)
(Houck et al., 2004) on the Spitzer Space Telescope (Werner et al., 2004) on
six occasions between 15 April 2005 and 18 October 2008 at intervals of 750,
163, 189, 9, and 171 days, respectively designated Epochs 1, 2, 3, 4A , 4B and
5 in Table 1 and Figure 2. The PI was A. Evans and the programmes were 3362,
30077 and 40061. The 5.6 µm flux fell by a factor of 4 in the between April
2005 and April 2007 (Epochs 1–2) and stabilised at 1/6th of the original flux
between April and October 2008 (Epochs 4–5).

The Spitzer observing modes and results from both high (HR) and low resolution
(LR) observations are described by (Evans et al., 2006, AOR 10840320) and
Ev2020. Pipeline-reduced and optimally-extracted spectra covering orders SL 1,
2 and 3 used in this paper were obtained from the Combined Atlas of Sources
with Spitzer/IRS Spectra (CASSIS) (Lebouteiller et al., 2011) in 2020; CASSIS
used data reduction pipeline S18.18.0. Fits were constrained with the combined
systematic and RMS errors (the most pessimistic uncertainties); AOR 17742592
SL 1 observations were constrained only with RMS errors because this part of
the CASSIS spectrum did not include systematic errors. The observations are
shown with the fitted models in Figures 1 and 6(a).

Due to the disjointed nature of both the laboratory and observational data, I
initially fitted 5.3-7.5 µm SL 2 spectra and then extended the analysis to the
SL 1 (7.6–14.0µm) and SL 3 (7.5–8.5 µm) bands in a piecemeal fashion. SL 1 and
SL 3 spectral segments were scaled by up to $\pm 5$ percent to match the SL 2
fluxes and the weighted means of interleaved regions obtained before fitting
them. SL 1 data were trimmed at 13.5 µm before analysis to exclude a spectral
artefact known as the 14-µm teardrop (see IRS, 2011). HR spectra cover the the
10 µm to 37 µm range which excludes the PAH bands and half the 10 µm
astronomical silicate feature modelled here. Slopes of scaled 9.9–13.5 µm HR
spectra match those of the LL spectra, but the HR data are otherwise beyond
the scope of this work.

##  3 Model for 5.9 to 7.5 µm SL 2 Spectra

In order to determine the absorption optical depth profile, the likely dust
components, and a continuum, the Spitzer SL 2 flux spectra were fitted with an
obscured black body model with up to three foreground absorption components,
where the flux, $F_{\nu}$ is given by:

$F_{\nu}=c_{0}B_{\nu}(T)\exp{(-\sum^{3}_{i=1}c_{i}\uptau_{i}(\lambda))},$ (1)

where $B_{\nu}(T)$ is the Planck function, and $\uptau_{i}$ is the shape of
the $i^{th}$ absorption feature, normalised to unity at the tallest peak in
the wavelength range of interest, and $c_{0}$ and $c_{1}$ to $c_{3}$ are the
fitted scale factors. $c_{0}$, was determined so that the continuum was
matched to the feature at 6.0µm, i.e. the foreground absorption was assumed
zero at this wavelength. Absorption components were selected on the basis of
their ability to the peak and width of observed absorption bands with a
preference for fewer components and an improvement in $\chi^{2}$ values if
more components were added. Absorption components were fitted simultaneously
using the down-hill simplex method of $\chi^{2}$-minimization. Laboratory data
used in fitting are listed in Table 2, described in Appendices A.2, and A.3,
and the preferred candidates are discussed below. Optical depth profiles were
obtained for each epoch by deriving a source continuum with the foreground
absorption set to zero, i.e. $\uptau=\ln{(F_{o}/c_{0}B_{\nu}(T))}$, where
$F_{o}$ is the observed spectrum.

Due to the narrow wavelength ranges involved in fitting in comparison to the
breadth of the peak of the Planck function, the black body temperature will
drift to unrealistic values and other parameters will not settle if it is
unconstrained. Therefore temperature was selected by trial and error to
provide the lowest $\chi^{2}$. Values used were consistent with those obtained
by Ev2020; where they differ significantly (Epoch 5), this is likely to be due
to the $<8\mu$m spectra being insensitive to the cooler dust components. The
current model does not include a term for the interstellar reddening (powerlaw
extinction) because, the visual extinction is low (A${}_{V}\sim 2$; Evans et
al., 2002), the photosphere obscured and the temperature relatively
unconstrained. Fits to the flux spectra and continua are in Figure 1. The
derived optical depth profiles of dust towards Sakurai’s Object for the
different Epochs and the laboratory spectra used in fitting are compared in
Figure 3.

Table 2: Laboratory data and band asignments of the C-rich (PAH, bSiC and nSiC) and O-rich (melilite and astrosilicate) dust components used in the models; mass absorption coefficients are given at the peak wavelengths marked in bold type; see the appendices for further information Sample | Bands | Approximate | Size333Representative grain length assuming approximately cubic geometry. | $\rho$ | $\kappa_{pk}$ |  $m_{g}$444Representative mass of single grain, assuming volume=(size)3 | Ref555Reference for spectrum (also see appendices): 1–Carpentier et al. 2012; 2–Hofmeister et al. 2009; 3–Bowey & Hofmeister 2005; 4–Speck, Thompson, & Hofmeister 2005;5–Bowey & Adamson 2002
---|---|---|---|---|---|---|---
|  | Assignment |  | gcm-3 |  $10^{2}$cm2g-1 | g |
PAH |  6.3, 6.9 | Arom. C=C | 53${}_{30}^{70}$ nm | $0.39^{0.2}_{1.8}$ |  $600_{130}^{1200}$666Best estimates. The superscripts and subscripts indicate the range depending on the effective mass density of the soot sample, the value of 1200 pertains to a grain of 30nm and bulk mass density; see Appendix A.2 | $5.8\times 10^{-17}$ | 1
| 7.3 | stretch |  |  |  |  |
| 8.0 | C–C defect |  |  |  |  |
| 11.3, 11.9 | Arom. CH bend |  |  |  |  |
bSiC | 6.2, 6.6 | Overtones | 25 µm | 3.2 | 2.4 | 5.0$\times 10^{-8}$ | 2
| 7.1, 7.6 |  |  |  |  |  |
nSiC | 12.3 | Si–C stretch | 3 nm | 3.2 | $15000$ | $8.6\times 10^{-20}$ | 2, 4
melilite777The formula of this melilite sample is (Ca1.7Na0.3)(Fe0.2Mg0.4Al0.4)(Al0.1Si1.9)O7); it is an Si-rich intermediate member of the åkermanite (Ca2MgSiO7) to gehlenite (Ca2Al(AlSi)O7) solid-solution series in which one of the Si atoms is replaced by Al. | 6.1, 6.9 | Overtones | 12 µm | 3.0 | 2.2 | $5.2\times 10^{-9}$ | 3
astrosilicate888Represented by the line of sight to Cyg OB2 no.12; $\rho$ is an estimate given by the mean of forsterite and enstatite mass densities; $\kappa_{pk}$ from Bowey & Adamson (2002). | 9.8 | Si–O stretch | 0.3 µm | 3.3 | 26 | $8.9\times 10^{-14}$ |

###  3.1 6.3µm: Polycyclic Aromatic Hydrocarbons (PAHs)

Figure 3: 6–7.5 µm optical depth profiles of Sakurai’s Object (error bars)
with fits (solid); fitted PAH (dotted -top), bSiC (dotted) and melilite
(dashed) components. Dot-dash curves indicate the effect of removing the bSiC
component from the fits.

The Hydrogenated Amorphous Carbon (HAC) compounds suggested by Ev2020, were
not a good match to the features since the proposed spectra (Grishko & Duley,
2002) are dominated by a broad merged 5.8 µm (attributed to carbonyl C$=$O)
and 6.2 µm peak which is not observed in Sakurai’s Object (see Appendix A.1).
Good eye-ball single-component matches to the $\sim$6.3 µm absorption peak and
the position of the $\sim 6.9$-µm peak were obtained with the spectrum of a
PAH-dominated soot sample created and characterised by Carpentier et al.
(2012) (see Figure 3). However, these PAH bands are too structured to match
the strength and breadth of 6.9 µm absorption band without an additional
component. I have not found a carbonaceous material with a sufficiently broad
absoption feature at this wavelength (e.g. Gavilan et al., 2017, presented 56
spectra of PAHs in this wavelength range) and but given the complexity of dust
formation this possibility cannot be completely ruled out.

###  3.2 Melilite as the carrier of the broad $6.9\mu$m band

####  3.2.1 Absence of ice and carbonate towards Sakurai’s Object

The similar YSO and molecular-cloud 6.9-µm feature is frequently associated
with methanol ice or carbonates, but neither produce an ideal match (e.g.
Keane et al., 2001; Boogert et al., 2011; Bowey & Hofmeister, 2005). Of these
candidates methanol is preferred because its abundance in molecular clouds and
YSOs is 3–30% of H2O ice (e.g. Whittet, 2003). However, the low visual
extinction and absence of a H2O-ice detection towards Sakurai’s Object makes
this identification implausible in this environment. In addition methanol ice
has a narrower band, more similar to the similar to the PAH 6.9-µm band, than
to the missing absorption component. The absence of water in the environment
would also preclude the existence of carbonates which form in the presence of
liquid water within asteroid bodies or terrestrial environments (e.g. Abreu &
Brearley, 2005).

####  3.2.2 Oxygen-rich candidates: melilite and hibonite

Even though Sakurai is currently C-rich the presence of the old PN indicates
that this may not always have been the case. Dual dust chemistries have been
observed in PNe associated with Wolf-Rayet stars with PAH emission below $\sim
15\mu$m and crystalline silicates at longer wavelengths (Cohen et al., 2002);
features from both C-rich and O-rich materials are also seen in the oxygen-
rich PN of NGC 6302 which displays prominent PAH emission as well as emission
from crystalline silicates (Molster et al., 2001) and (Hofmeister et al.,
2004) associated far-infrared emission bands with melilite and hibonite. In
the near-infrared, Bowey & Hofmeister (2005) presented overtone spectra of
$\sim 30$ refractory minerals present in meteorites and showed that the broad
6.9 µm bands in YSOs are matched reasonably well by an overtone feature seen
in 12 µm-thick samples of compressed crystalline melilite powder, i.e. with an
effective grain size of $\sim 12\mu$m, or possibly $\sim~{}60~{}\mu$m-sized
grains of disordered (metamict) hibonite ($\sim$CaAl12O19) (see Appendix A.3).
These large grains have opaque fundamental bands (e.g. Si–O stretches in
melilite) and therefore indetectable at the wavelengths where astronomical
mineral searches are normally conducted. Only the melilite feature is observed
because melilites have particularly strong overtone features which are three
times as strong those of other anhydrous crystalline silicates (e.g.
forsterite, pyroxenes, felspars) and ten times those of forsterite and
diopside glass (see Bowey & Hofmeister, 2005).

Melilites are an important component of calcium-aluminium-rich inclusions
(CAIs) in primitive meteorites. CAIs are early high-temperature condensates in
solar nebular theories (e.g. review by Rubin & Ma, 2017). CAI abundance in the
most primitive (CO3) chondrites is $\sim 1.5$ area per cent999i.e. on average
1.5 per cent of the surface area of the sampled meteorite slices were
comprised of CAIs; this number is very similar to the volume per cent. Some
other chondrite types, especially CVs have more, with $\sim$ 3 area per cent
on average (e.g. Hezel et al., 2008). with an average CAI size of $98.4\pm
54.4$ µm (Zhang et al., 2020). Melilite-rich inclusions and spinel-pyroxene
CAIs comprise 80-100 percent of the total CAIs for each chondrite; Zhang et
al. argued that the spinel-pyroxene CAIs in these and more processed
meteorites are alteration products derived from melilites and found that a
subset of fluffy melilites were composed of loosely aggregated $<15$µm-sized
melilite grains.

Hibonite is less plausible because the fits are poorer, fewer than 4.8 per
cent of CAIs in meteorites are hibonite (and grossite; $\sim$CaAl4O7)-bearing
(Zhang et al., 2020), with the metamict form being relatively rare and other
hibonites have weaker overtones which do not occur at 6.9 $\mu$m, and hibonite
bands are bands are 5-30 times weaker than the melilite feature (see Appendix
A.3 and Bowey & Hofmeister, 2005).

Since Sakurai’s Object has had a complicated history of mass-loss and is
surrounded by a PN and an interstellar silicate absorption feature was
detected by Evans et al. (2002) and no other candidate has been found I
modelled the data with a melilite component (Figure 3). Statistics of two
component fits ($\chi^{2}_{\nu 2}$) are given in Table 3 and the sum of the
PAH and melilite components of the fit to Epoch 5 indicated by the dashed
curve in Figure 3.

###  3.3 A component due to 25µm -sized Carbide Grains?

Isotope measurements exist for thousands of 0.1–20 µm-sized meteoritic grains
with non-solar isotope ratios of pre-solar origin (e.g. Hoppe et al., 1994;
Speck, Thompson, & Hofmeister, 2005) suggesting that they somehow travelled
from C-stars to the Solar Nebula. However, SiC has not been detected in the
interstellar medium (e.g Whittet, Duley, & Martin, 1990). This is probably a
consequence of its high opacity, since grains have to be nanometre-sized to
produce reliable unsaturated bands (see Hofmeister et al., 2009). However,
$\la 25~{}\mu$m SiC grains, hereinafter denoted bSiC (for “big” SiC grains),
produce small peaks at 6.2 and 6.6 µm, whilst being opaque in their
fundamental Si-C stretch at 12.3 µm (Hofmeister et al., 2009, see Appendix A.3
for its derivation), so I included them in three-component models. Due to
slight rounding of the 6.6 µm peak, 25 µm is likely to be an upper size limit
(see Appendix A.3).

##  4 5.9 – 7.5µm Fits

Table 3: Fits to 5.9–7.5 µm spectra of Sakurai’s object: black body absorbed by PAHs, melilite, and bSiC. The 1 sigma confidence intervals $\sigma$, for $c_{pah}$ are 1–2 per cent; for $c_{mel}$ they are normally 4–5 per cent and 7 per cent in Epoch 1. $\uptau_{6.3}$ and $\uptau_{6.9}$ are the measured optical depths of the 6.3 and 6.9µm peaks, respectively. $\chi^{2}_{\nu}$ and $\chi^{2}_{\nu 2}$ denote three-component and two-component (PAH and melilite only) fits, respectively. Ep. | T/K | $c_{pah}$ | ${c_{mel}}$ | $c_{SiC}$ | $\sigma$ | $\chi^{2}_{\nu}$ | $\chi^{2}_{\nu 2}$ | $\uptau_{6.3}$ | $\uptau_{6.9}$
---|---|---|---|---|---|---|---|---|---
1 | 275 | 0.085 | 0.031 |  $<$0.007 | 59 | 0.90 | 0.91 | 0.10 | 0.11
2 | 226 | 0.13 | 0.058 | 0.011 | 28 | 0.96 | 1.1 | 0.15 | 0.17
3 | 224 | 0.16 | 0.067 |  $<$0.010 | 50 | 0.99 | 1.0 | 0.19 | 0.20
4A | 222 | 0.20 | 0.067 | 0.020 | 26 | 0.77 | 0.91 | 0.23 | 0.24
4B | 227 | 0.21 | 0.067 | 0.026 | 15 | 0.52 | 0.85 | 0.24 | 0.26
5 | 227 | 0.23 | 0.081 | 0.027 | 20 | 0.70 | 1.0 | 0.26 | 0.28
WM |  | 0.80 | 0.29 | 0.098 |  | 4.3 |  | 0.90 | 1.0

The best three-component fits to each Epoch are listed in Table 3 and plotted
with the observations and continua in Figure 1. Derived optical depth profiles
are plotted with the modelled laboratory components in Figure 3. The increases
in $c_{pah}$, $c_{mel}$ and $c_{SiC}$ with time will be discussed in Section
4.1.

At Epochs 1 and 3 the observational uncertainties are too large giving
confidence intervals $>50$ percent and little improvement in $\chi^{2}_{\nu}$
with three components and the SiC contribution is quoted as an upper limit.
Fits to Epochs 2, 4A, 4B and 5 were slightly better with a bSiC component
(improvement in $\chi^{2}_{\nu}$ 0.05–0.33) and the 1-sigma confidence
intervals for bSiC were $\sigma_{bSiC}<30$ per cent, with little change in
$c_{pah}$ (0-10 per cent lower) and $c_{mel}$ (increased by 7–10 per cent) for
all but Epoch 5, where $c_{pah}$ and $c_{mel}$ decreased by 50 per cent and 4
per cent, respectively. The improvement in fit quality was due to the 6.2 and
6.6 µm bands combining with the 6.3-µm PAH band to broaden it and flatten the
interval between it and the 6.9 µm band (compare solid and dot-dash curves in
Figure 3). The modelled bSiC components will be extrapolated in Section 6.4 to
show the influence of weaker 7.1 and 7.6 µm overtones.

Figure 4: Increases in dust mass during the Spitzer observing period. Values
obtained by Ev2020 are from the flux method. $c_{pah}$, $c_{mel}$ and
$c_{SiC}$ are the fitted optical depths of the small PAH and melilite and bSiC
overtones, respectively. Each indicator, except $c_{SiC}$, is ratioed to the
value at Epoch 1 (2005-04); $c_{SiC}$ is ratioed its value at Epoch 2
(2007-05). Offsets are indicated by dotted lines. Slopes in the figure are in
optical depth per day, Uncertainties in the fitted slopes are 0.0005 (Ev2020),
0.00004 ($c_{pah}$), 0.0001 ($c_{mel}$) per day.

###  4.1 Increases in PAH, melilite and bSiC with time

The fitted PAH, melilite and bSiC optical depths at each Epoch are listed in
Table 3 and plotted against their modified julian dates (MJD; Table 1) Figure
4. In the Figure each parameter has been ratioed to its value at the earliest
Epoch, MJD0, with a proper detection (not an upper limit). Hence, $c_{pah}$
and $c_{mel}$ are ratioed to values at Epoch 1, whilst $c_{SiC}$ is ratioed at
Epoch 2.

Slopes of linear fits to $c_{pah}$ and $c_{mel}$ indicate increase rates of
$0.44\pm 0.01$ yr-1 and $0.40\pm 0.04$ yr-1. These rates are consistent with
Ev2020’s $0.6\pm 0.2$ yr-1 estimate of the rate of increase in dust mass from
the emitted flux ($\lambda F_{\lambda}$) within the uncertainties, even though
the absorbing grains may have been formed at an earlier time. Within the
1-sigma confidence intervals, the slope of $c_{pah}$ appears to increase to
$0.99\pm 0.06$ yr-1 during Epochs 2–4B before readopting the slower rate of
increase between Epochs 4B and 5. $c_{mel}$ increases between Epochs 1 and 5.
There is an apparent increase in bSiC with a jump between 4A and 4B but the
uncertainty in this is large.

###  4.2 Weighted mean optical depth profile

Figure 5: Weighted mean of normalised optical depths (grey) with 3 component
fit (black) and components below.

Since variation in the relative proportions of the dust components is small it
is possible to obtain a higher signal-to-noise time-averaged 6–7 µm dust
profile for comparison with dust features other environments such as molecular
clouds and YSOs. The profile was obtained after normalising the profiles from
Epochs 1 to 5 at 6.9 µm. The weighted mean dust profile, together with fits of
the PAH, melilite and bSiC components, is presented in Figure 5. As expected,
fits to the PAH, melilite and bSiC features resemble those of the strongest
features observed in Epoch 5; when scaled to $\uptau_{6.9}$ they are, 0.22,
0.81, 0.027, respectively: only $c_{pah}$ is slightly lower, reflecting its
faster growth rate.

##  5 Fitting 8.4–13.3 µm spectra

Figure 6: Fits between 8.3 and 13.3 µm. (a) 8.3 and 13.3µm fits (solid curves)
to the SL1 flux spectra (grey error bars) using the PAH fit to the SL 2 data;
dotted curves – effect of removing foreground silicate absorption; dashed
curves - modelled continua when the foreground absorption is zero. Y-axis
offsets (bottom to top) are 0.0, 15, 25, 35 and 45 Jy.

Figure 7:  Changes in the 10-µm astrosilicate absorption compared with Cyg OB2
no. 12 after subtraction of the PAH component. Noisy points (uncertainty >
0.04 ) have been removed for clarity. Bars indicate the centres of PAH bands,
which may be too deep.

.

Figure 8: Modelled nSiC emission: when the 11.3-µm PAH absorption band matches
the observations (solid), dashed when it does not. Grey and black curves
indicate falling and rising optically-thin fractions, respectively. The
laboratory profile of nSiC is shown below (arbitrary normalisation; offset
-0.05 in the Y-axis).

Longer-wavelength observations at Epochs 3 and 4A appeared to have a narrow
absorption feature at 11.3 µm (Figure 6(a)) so a single-component PAH model
was extended to derive a continuum for it. Melilite and bSiC components were
not included because these grains are opaque in this wavelength range.
However, fits with Equation 1 did not match the overall shape of the flux
spectrum until a foreground ’interstellar’ 10 µm silicate absorption feature
was added, represented by the diffuse-medium dust profile towards Cyg OB2 no.
12, hereinafter called astrosilicate; the feature shape, shown in Figure 9(b)
$\uptau_{sil}(\lambda)$ is derived in Appendix A.4.

Fits were further improved when a single-temperature optically-thin emission
component due to nanometer-sized SiC grains, called nSiC (see Figure 8), was
added so that the source flux, $F_{\nu*}$ is given by,

$F_{\nu*}\propto B_{\nu}(T_{1})+B_{\nu}(T_{2})c_{nSiC}\uptau_{nSiC}(\lambda)$
(2)

where T1 and T2 are the temperatures of the optically-thick and optically-thin
emission components and $c_{nSiC}$ is a scaling constant for normalised nSiC
emission, $\uptau_{nSiC}(\lambda)$. This emitted continuum was then
extinguished by foreground astrosilicate dust to give the observed flux, Fν,

$F_{\nu}=c^{\prime}_{0}F_{\nu*}\exp{(-c_{pah}\uptau_{pah}(\lambda)-c_{sil}\uptau_{sil}(\lambda))}$
(3)

where, scaling constant $c^{\prime}_{0}$, T2 and $c_{sil}$ were fitted by
$\chi^{2}$-minimization and $c_{pah}$ was fixed to the value obtained from the
5.9–7.5 µm fits. Continua for merged SL 1–SL 3 5–13.5 µm spectra were derived
by setting $c_{pah}$ and $c_{sil}$, to zero and extending the wavelength
range.

###  5.1 Constraints and exclusions

No attempt was made to model the 7.5–8.3 µm-range for several reasons: (i)
there are inherent incertainties in the LRS observations because of merging
between orders, (ii) laboratory spectra of PAHs show a great deal of
variability in the shape of the defect band, (iii) silicate overtones merge
with Si–O bands making results highly dependent on the baseline subtraction in
the laboratory data (see Bowey & Hofmeister, 2005), (iv) the bSiC and melilite
grains responsible for overtone features are a separate population to the
submicron-sized and nanometer-sized grains responsible for features between
8–13 µm and it is not clear how to merge the data in these simple models.

Since the PAH bands surround the 10-µm silicate absorption band (Figure 9(b))
$c_{pah}$ was set to zero to explore the interplay between them. In these
cases statistically better fits were obtained, the temperature was $\sim 20$-K
cooler, optically-thin emission negligible and the foreground silicate
absorption very weak. These fits were disregarded because the fluxes of these
continua fell well-below the fluxes of the merged 5–8 µm spectra which is
inconsistent with a central stellar energy source.

##  6 8.3–13.3 µm Fits

Table 4: Fits to 8–13 µm SL 1 spectra of Sakurai’s Object, $T_{1}$ (pre-set) and $T_{2}$ (fitted) are the temperatures of the optically-thick and optically-thin components, respectively. Sakurai was not observed at 8–13 µm during Epoch 1. Epoch | T1 | T2 | $\epsilon_{12.5}$ |  $F_{12.5}$101010Weighted mean flux between 12.0 and 13.0 µm; $\pm$0.1 Jy plus order match uncertainty |  $c_{sil}$($\sigma$1111111 sigma confidence interval per cent.) | $\chi^{2}_{\nu}$ | PAH?
---|---|---|---|---|---|---|---
| K | K |  | Jy |  |  | 11.3
2 | 237 | 119 | 0.123 | 40.3 | 0.071 (3) | 3.5 | –
3 | 225 | 137 | 0.057 | 33.8 | 0.15 (2) | 0.77 | Y
4A | 225 | 81 | 0.059 | 28.7 | 0.14 (0.7) | 8.4121212Reflects only RMS errors; CASSIS did not output systematic errors for SL 1 | Y
4B | 228 | 100 | 0.132 | 28.5 | 0.12 (2) | 1.8 | –
5 | 228 | 75 | 0.191 | 28.0 | 0.11 (2) | 1.2 | –

The observations (grey error bars), fits (solid curves) and continua (dashed
curves) are displayed in Figure 6. If the silicate absorption component is
excluded the fits do not match the curvature of the observations between 11
and 12 µm (dotted curves). Fitted parameters are listed in Table 4. 11.3 µm
absorption bands in Epochs 3 and 4A are well-matched by the modelled SL 1 PAH
strengths, but the absorption bands are not observed at other Epochs. Epoch 2
might have a narrow PAH emission band at 11.3 µm, but this may be coincidental
with the noise.

Fits to all Epochs required both optically-thick and optically-thin emission
components and the proportion of optically-thin nSiC emission varied with
time. The temperature of the optically-thick component was usually 1–3-K
warmer than the 6–7 $\mu$m continuum, but Epoch 2 required a 11 K higher
blackbody temperature and weaker foreground silicate absorption ($\uptau\sim
0.07$); the difference is caused by narrow-band structures in the spectrum of
unknown origin at 9.7 and 10.5µm – either unidentified gas-phase absorption or
noise since the error bars are large. The temperature of the optically-thin
component, $T_{2}$, settled on values 50–155 K cooler than the optically-thick
emission but the absence of an identifiable trend indicates it is not well-
constrained.

###  6.1 Temporal variation in the 10 µm astrosilicate absorption

Fitted optical depths of the foreground silicate absorption, $c_{sil}$, are
within $\pm 0.04$ of the $0.105\pm 0.005$ value deduced by Evans et al. (2002)
and modelled values increase between Epochs 2 and 3 before decreasing between
Epochs 3 and 5 (Figure 4 and Table 4). The silicate absorption profiles are
shown in Figure 7 after subtraction of the modelled PAH absorption: the
feature in Epoch 2 is not really detected above the noise but changes in the
features between Epochs 3 and 5 are significant and inconsistent with a
homogeneous distribution of _interstellar_ silicate along the line of sight
which is unrelated to Sakurai’s Object. It is plausible that some of the
astrosilicate absorption is due to dust distributed within the ancient PN and
that disturbances associated with the eruptive dust-formation event are
causing silicates to coagulate into larger grains. The interstellar feature
towards Cyg OB2 no. 12 dust can still be used for modelling because the
profile is similar in shape to the emission from new dust surrounding the
O-rich AGB star $\mu$ Cephei (e.g Bowey, Rawlings, & Adamson, 2004). The
relationship between the decrease in astrosilicate and possible increase in
melilite in Epoch 5 will be explored in Section 9.2

###  6.2 Temporal variation of optically-thin nSiC emission

The ratios of the optically-thin emission to the optically-thick emission at
each Epoch are compared in Figure 8. The optically-thin component is smallest
at Epochs 3 and 4A, in which the 11.3-µm absorption feature matches the 6–7-µm
fits. The fraction of optically-thin emission is largest when the fitted
silicate absorption is weakest indicating that during fitting the two
parameters work together to increase the curvature of the flux spectrum to
make it rise at longer wavelengths.

Both the the total flux and the proportion of optically-thin emission
decreased between Epochs 2 and 3. Between Epochs 3 and 4A the flux decreased
more slowly and the optically-thin component did not change significantly
(though it might have cooled). The flux did not change between Epochs 4A and
5, but became significantly more optically-thin, changing rapidly in the in
the 9 days between Epochs 4A and 4B (April 2008). Unfortunately it is
impossible to know if the apparent increase in the optically-thin component in
the 171 days between Epochs 4B and 5 occurred as rapidly as the change in the
days preceeding it.

###  6.3 5.9–13.3 µm Absorption Components

Figure 9: (a) Optical depth profiles (grey error bars) obtained with modelled
8.3–13.3 µm continua; offsets in the Y-axis are 0.0, 0.3, 0.6, 0.9 and 1.2;
8–13 µm black solid curves are the fitted absorption features, 6-7.5 µm are
the fitted features from the SL 2 offset in the Y-axis to match the level of
the longer-wavelength fits (additional offsets are indicated); dotted curves
between 7.5 and 8.0 µm indicate the contribution from bSiC extrapolated from
the SL 2 fits. (b) Absorption profiles used to model 8.3–13.3 µm spectra: PAH
spectrum (solid) and silicate absorption (dashed) modelled with the profile of
interstellar dust towards Cyg OB2 no. 12. Profiles are normalised at 6.3 and
9.75 µm, respectively.

Optical depth profiles for Epochs 2–5 are compared with absorption profiles
fitted to the 8.3–13.3 µm and 6–7.5 µm data (solid curves) in Figure 9(a);
short dotted curves show an extrapolation of the bSiC contribution (Section
3.3). Offsets are added to the 6–7.5 µm fits to allow for the difference in
scaling constants $c_{0}$ and $c^{\prime}_{0}$. The discrepancy between the
slopes of the 6–7.5 µm fit and the profile for Epoch 2 is caused by the 11 K
difference in the temperature of the optically-thick emission.

###  6.4 PAH and bSiC

The 11.3-µm PAH absorption features in Epochs 3 and 4A match the band
strengths implied by 6–7.5 µm values of $c_{pah}$. However, the observed 11.3
µm PAH absorption is negligible in Epochs 4B and 5. The feature might occur in
emission at Epoch 2. It is conceivable that the observed changes are
consistent with the trend in nSiC emission because as time progresses the PAH
feature moves from emission, to absorption followed by the emission feature
filling in the absorption feature - but there is insufficient data to prove
this.

There is also some correlation between the shape of excess absorption near 8.0
µm and the shape and position of the C=C defect band (Figure 9(b)) even though
this is probably suppressed by unconsidered emission or absorption components
in the line of sight. Surprisingly, the extrapolated weak bSiC features
identified in the 6–7.5µm data resemble the shape of weak structure in the
merged spectra between 7.2 and 8.0 µm but the uncertainties are large. If the
features are real, the 6.0– 8.0-µm spectral region is the place to reconcile
astronomical and meteoritic studies of SiC grains. The existence of warmer
nSiC grains and cool bSiC grains is consistent with Speck, Thompson, &
Hofmeister (2005)’s hypothesis that SiC grains become smaller as the star
evolves.

##  7 Summary of observational results

During the period of the Spitzer observations:

  1. 1.

The mid-infrared flux decreased. The 5.6 and 12.5 µm fluxes decreased rapidly
between Epochs 1 and 2, but the rate of change slowed between Epochs 2-4A and
stopped between Epochs 4A and 5.

  2. 2.

The proportion of optically-thin emission decreased between Epochs 2 and 3,
did not vary between Epochs 3 and 4A (though it might have become cooler)
before increasing rapidly in the 9 days between Epochs 4A and 4B and
increasing more slowly into Epoch 5.

  3. 3.

The mass of cold carbonaceous dust increased. PAH absorption increased
throughout the observations, possibly with the rate accelerating during Epochs
2–4B, and then slowing between Epochs 4B and 5. Concurrent increases in bSiC
abundance might be significant, but are particularly affected by the low
sensitivity to the overtone features at Epochs 1–3.

  4. 4.

The apparent composition of the cold oxygen-rich dust changed with more
melilite and less astrosilicate. The melilite absorption increased between
Epochs 1 and 5. The astrosilicate abundance decreased between Epochs 3 and 5.

Some of the spectral changes are subtle and their significance affected by
observational sensitivities. I believe changes in the features to be real
because they progressed between multiple observations and some features were
modelled independently in different spectral ranges.

##  8 Estimates of mass column density, number density and dust mass

###  8.1 Mass Column Density and Number Density

Table 5: Column Mass Density and Number Density for Carbonaceous and Oxygen-rich dust Components | Carbonaceous Dust | Oxygen-rich Dust
---|---|---
Grain | Mass Density | Number Density | Mass Density | Number Density
Size |  |  |  | 53 nm | 25 µm | 3 nm |  |  | 12 µm |  $<0.3$ µm
Dust | PAH | bSiC | nSiC | PAH | bSiC | nSiC | melilite | astrosilicate | melilite | astrosilicate
|  $10^{-6}$ gcm-2 | cm-2 |  $\times 10^{-6}$ gcm-2 | cm-2
Epoch |  |  |  |  |  |  |  |  |  |
1 | $1.4_{0.71}^{6.5}$ |  | – | 2.4$\times 10^{10}$ |  | – | 140 | – | 27000 | –
2 | $2.2_{1.1}^{10}$ | 46 | 0.082 | 3.8$\times 10^{10}$ | 920 | 9.5$\times 10^{11}$ | 260 | 27 | 50000 | 3.0$\times 10^{8}$
3 | $2.7_{1.3}^{12}$ |  | 0.038 | 4.7$\times 10^{10}$ |  | 4.4$\times 10^{11}$ | 310 | 58 | 60000 | 6.5$\times 10^{8}$
4A | $3.3_{1.7}^{15}$ | 83 | 0.039 | 5.7$\times 10^{10}$ | 1660 | 4.5$\times 10^{11}$ | 310 | 54 | 60000 | 6.1$\times 10^{8}$
4B | $3.5_{1.7}^{16}$ | 110 | 0.088 | 6.0$\times 10^{10}$ | 2200 | 10$\times 10^{11}$ | 310 | 46 | 60000 | 5.2$\times 10^{8}$
5 | $3.7_{1.8}^{17}$ | 113 | 0.13 | 6.4$\times 10^{10}$ | 2300 | 15$\times 10^{11}$ | 370 | 42 | 71000 | 4.7$\times 10^{8}$
WM131313PAH, bSiC and melilite -from fits to weighted mean spectrum scaled to mean of Epochs 3–5 ($\uptau_{6.9}=0.25$); nSiC and astrosilicate from mean of Epochs 3–5. | $3.3_{1.7}^{15}$ | 100 | 0.073 | 5.7$\times 10^{10}$ | 2000 | 8.4$\times 10^{11}$ | 330 | 50 | 68000 | 5.6$\times 10^{8}$

An estimate of the mass column density of dust surrounding the region of
optically-thick emission can be obtained because the peak optical depth,
$\uptau_{pk}$, of an absorber is related to the mass absorption coefficient,
$\kappa_{pk}$:

$\uptau_{pk}=\rho\kappa_{pk}L,$ (4)

where $\rho$ is the effective mass density of the absorber and $L$ is the
path-length of the light through the dust so that the mass column density of
absorbers, $\Sigma=$ along the line of sight is given by:

$\Sigma=\rho L=\uptau_{pk}/\kappa_{pk}.$ (5)

The column number density of grains is obtained by dividing $\Sigma$, by the
single-grain masses, $m_{g}$, in Table 2. The mass and grain column densities
are listed in Table 5.

###  8.2 Rates of increase in Mass Density and Number Density

Equation 5 and the rates of change of PAH and melilite optical-depths obtained
in Section 4.1 can be used to deduce the rate of increase in mass and number
density: the average rate of increase in PAH density between Epochs 1–5 is
$d\Sigma_{pah}/dt=7.3\times 10^{-6}$ gcm-2yr-1 ($1.3\times 10^{11}$ grains
cm-2yr-1) and the enhanced rate between Epochs 2 and 4B is
$d\Sigma_{pah}/dt=17\times 10^{-6}$ ($2.8\times 10^{11}$ grains cm-2yr-1) For
melilite, the mean rate of mass density increase, $d\Sigma_{mel}/dt=1.8\times
10^{-3}$gcm-2yr-1 or $0.35\times 10^{6}$ grains cm-2yr-1.

###  8.3 Dust Mass estimates and their rate of increase

Since mass column density is related to the effective mass density of a dust
grain, Equation 4 can be used to estimate the total dust mass of each
component at each Epoch with the caveats that neither the distance to
Sakurai’s object, nor the geometry of the dusty region associated with it, nor
the mass absorption coefficent of PAHs are well-defined (see Appendix A.2 for
my derivation of $\kappa_{pk}$). Estimates of the distance to Sakarai’s Object
vary considerably (reviewed by Hinkle & Joyce, 2014). I adopt a distance of
3.5kpc which is the maximum used by Chesneau et al. (2009) in models of their
mid-infrared observations and consistent with Ev2020’s preferred value of
$3.8\pm 0.6$kpc. Chesneau et al. (2009) obtained mid-infrared interferometer
observations of Sakurai’s object on 2007 June 29–30 (MJD 54280–54281; 55 days
after Epoch 2) and deduced that the source is surrounded by an opaque dusty
torus or thick disk of $105\times 140$AU and a scale height of $47\pm 7$AU.

Assuming that the cold PAHs and bSiC grains are located in the torus I use a
cylindrical geometry to give a volume of $\pi R^{3}$, where R is 50 AU and the
optical path length from the optically-thick shell $L=R$ so that the mass,
$M$, of dust in the torus due to an absorber is approximated by

$M=\Sigma\pi R^{2}$ (6)

$M_{50AU}\approx 8.8\times 10^{-4}\Sigma\ M_{\sun}$ (7)

and the rate of mass increase can be deduced by replacing $\Sigma$ with
$d\Sigma/dt$. An inferred mass of nSiC is not given because the optically-thin
emission probably derives from a region closer to the optically-thick
‘photosphere’ of unknown volume.

For the 50AU torus, $d\Sigma_{pah}/dt$ equate to an average mass increase of
6.4$\times 10^{-9}$ M☉ yr-1 and an accelerated rate between Epochs 2 and 4B of
16$\times 10^{-9}$ M☉ yr-1; the faster rate is similar to Evans et al. (2020)
estimate in May 1999, which was 11$\times 10^{-9}$ M☉ yr-1, when scaled to the
PAH density, but lower than the rate of 40$\times 10^{-9}$ M☉ yr-1 in Sept
2001.

##  9 Evolution of the dust

###  9.1 PAH, bSiC and nSiC

Table 6: Estimated masses of carbonaceous dust (PAH and bSiC) in the 50 AU torus compared with Ev2020 estimates by the peak flux ($\lambda F_{\lambda}$) method after conversion to PAH or SiC mass densities instead of amorphous carbon ($\rho=1.5$gcm-3) and scaled by 0.85 to reflect the choice of D=3.5 kpc. |  | 6–7µm mass |  $\lambda$Fλ |  $\lambda$Fλ mass similar to 6–7µm mass
---|---|---|---|---
|  | PAH | bSiC | PAH |  | PAH | SiC | T
Ep. | Date141414day-month-year |  $10^{-9}$ M☉ | Date |  $10^{-9}$ M☉ | K
1 | 15-04-2005 | 1.2 |  | 1100 | 18-08-1998 |  | 0.92 | 1210
2 | 04-05-2007 | 1.9 | 41 | 2400 | 21-04-1999 | 3.9 | 32 | 841
3 | 15-10-2007 | 2.4 |  | 2900 |  |  |  |
4A | 21-04-2008 | 2.9 | 74 | 3400151515Measured on MJD 54564, 8 April 2008 |  |  |  |
4B | 30-04-2008 | 3.1 | 96 | – | 03-05-1999 | 14 | 120 | 723
5 | 18-10-2008 | 3.3 | 99 | 3400 | 08-06-1999 | 16 | 130 | 717
|  |  |  |  | 14-06-1999 | 16 | 130 | 717
|  |  |  |  | 06-09-1999 | 24 | 200 | 661

My dust mass estimates are compared with Ev2020 masses deduced from optically-
thick emission in Table 6. Ev2020 estimates have been scaled to PAH and SiC
mass densities, as appropriate, and a distance of 3.5 kpc. Since it is
impossible to distinguish between dust types in their data, I have converted
their values for amorphous carbon to PAH and SiC masses and quoted both for
blackbody temperatures between the PAH condensation temperature of 850 K
(Helling et al., 1996) and 650 K. I assume that the bulk of their 200–300 K
dust is formed of PAHs. The black-body temperature of 1210 K on 18 August 1998
(MJD 51043; Geballe et al. (2002)) was low enough for SiC condensation, but
too hot for PAH formation so I assume that this is SiC dust. It is plausible
that the inferred absorbing 20 µm bSiC grains were formed at this stage
followed by the nanometre-sized grains in the modelled optically-thin
emission. This interpretation is consistent with Speck, Thompson, &
Hofmeister’s observational and laboratory-based hypothesis that SiC grains in
AGB stars grow to large sizes in early condensation phases when the mass-loss
rate is low but that they become nm-sized when the stellar mass-loss rate
increases.

My inferred masses of bSiC and PAHs for Epochs 1–5 are, respectively, 2 and 3
orders of magnitude lower than Ev2020 estimates from the optically-thick
emission on the same dates but our methods measure different grain
populations: Ev2020 measurement of optically-thick emission infers the dust
mass of the coolest external edge of the expanding shell161616The mass
estimate is sensitive to increases in surface area, but insensitive to warmer
conditions inside the shell where most of the condensation occurs. Therefore
foreground cool dust includes SiC dust condensed at an early time, but this
contributes a decreasing fraction of the total mass. Due to the increasing
surface area of the expanding dust shell and the low temperature of the
optically thick leading edge inferred dust masses at the 200–300 K
temperatures will probably reflect some geometric effects but an effect of 2–3
magnitudes seems unfeasibly large.. My method estimates the mass of absorbing
dust in front of the optically-thick region. This dust is not emitting at 6–7
µm so it must be cooler; I agree, with Ev2020, that this cooler dust must be
older than dust in the optically-thick shell.

PAH formation probably occurred from around 21 April 1999 (MJD 51289) when the
temperature was 841 K and the SiC dust mass was 32$\times 10^{-9}$ M☉), a
value similar to the 41$\times 10^{-9}$ M☉ estimate of mass in large SiC
grains in Spitzer Epoch 2 (4 May 2007). The effect of this rapid condensation
is seen in Ev2020’s third measurement on 3 May 1999 (MJD 51301) in which there
is a nearly four-fold increase in mass and the temperature has dropped by 100
K in the 12 days following the previous measurement followed by little change
both values in measurements 36 and 42 days later (08 and 14 June 1999).

The increases in the 6–7 µm PAH absorption seem to record this condensation
event in the enhanced rate of change in the 6.3 µm PAH absorption between
Epochs 2 and 4B and the reduced rate to Epoch 5. The cold dust masses observed
in the Spitzer data during Epochs 2 and 4B (04 May 2007 and 30 April 2008)
correspond to the warm dust masses inferred by Ev2020 on 21 April to 03 May
1999. The slight change between Epochs 4B and 5 might match the small increase
between 03 May and 08 June 1999. By September 1999 Ev2020 dust mass is 50%
higher than the June values, but there are no more Spitzer observations with
which to compare it. If the PAH absorption continued to grow at the rate of
0.44 yr-1 the 6.3µm PAH absorption feature would have been opaque
($\uptau_{6.3}\approx 4$) by July 2016 when Evans et al. (2020) Sofia data
were obtained and its non-detection is a consequence of high opacity, rather
than noisier data.

###  9.2 Silicate coagulation in Epochs 3 to 5

The decreases in the astrosilicate absorption and consequent increases in the
large grains of melilite might be a consequence of the coagulation of smaller
astrosilicate dust into larger grains within the torus or PN. However,
astrosilicate is assumed to be glassy whilst the large melilites are
crystalline and a mechanism would be required to introduce crystallinity on a
short timescale unless the astrosilicate already included a varied mixture of
crystalline silicates with narrow bands that merge to form the assumed smooth
10 µm absorption feauture (see Bowey & Adamson, 2002). This form of silicate
dust is far more consistent with meteoritic and terrestrial materials than
entirely amorphous dust.

Classic astrosilicates are also Mg-rich with between olivine and pyroxene
stoichiometry $\sim$Mg1.5SiO3.5 (e.g. Fogerty et al., 2016) with 1.5 Mg atoms
per Si atom, whilst the approximate stoichiometry of Si-rich melilite is
Ca1.5Mg0.5SiO3.5, i.e. 1.5 Ca atoms per Si atom and 3 Ca atoms for every Mg
atom. In the diffuse medium the ratio of Ca to Mg atoms depleted from the gas
into the dust is 8.4 per cent (Snow & Witt, 1996). Hence, if the available Ca
were entirely located in melilites up to 2.8 per cent of the silicate
molecules or 2.5 per cent of the astrosilicate mass could have had melilite
stoichiometry. This upper limit is similar to the 1.5–3 area per cent
abundance of CAIs in chondritic meteorites and more than 80 per cent of the
CAIs are formed of melilite or its alteration products (Section 3.2.2). It is
also plausible that the melilites are the only coagulated components observed
due to the strength of its overtone band which is 3 times that of other
anhydrous crystalline silicates. I conclude that the astrosilicates may have
clumped together to form the inferred melilites observed in the overtone
features and that it is plausible that grains like these were precursors to
the melilite in the CAIs in meteorites.

##  10 Conclusions

The mid-infrared flux decreased during the period of the Spitzer observations.
The 5.6 and 12.5 µm fluxes decreased rapidly between April 2005 and May 2007,
but the rate of change slowed between May 2007 and April 2008 and stopped
between April and October 2008.

The proportion of optically-thin emission due to nanometre-sized SiC grains
decreased between May 2007 and an apparent minumum in October 2007 which
continued until 21 April 2008. The optically-thin proportion then increased
rapidly in the 9 days to 30 April 2008 and then more slowly in the six months
to October 2008.

The mass of cold carbonaceous dust increased. PAH absorption increased
throughout the observations, with the rate accelerating between May 2007 and
May 2008 and slowing down in the six months to October 2008. Increases in the
abundance of $\la 25$µm-sized SiC grains in April 2008 might be significant
but the data are not very sensitive to the overtone features before this time.

SiC formation mainly occurred before May 1999, followed by PAH formation in
April–June 1999 once the dust was sufficiently cool. These grains are likely
to be responsible for the growth in absorption due to PAH and $\la 25$ µm-
sized SiC dust between May 2007 and April 2008. The formation of large grains
during the earlier period of mass loss and later optically-thin emission from
3nm-sized SiC is consistent with the hypothesis of Speck, Thompson, &
Hofmeister (2005) that SiC grains are large in early phases when the mass-loss
rate is low but that they become nm-sized when the infrared emission is
optically thick and the stellar mass-loss rate is high.

Much of the dust responsible for the weak 10 µm silicate absorption towards
Sakarai’s Object is likely to be associated with Sakurai’s PN rather than
interstellar in origin, because the optical-depth of the feature decreased
between October 2007 and October 2008. Decreases in the astrosilicate
absorption and increases in the large grains of melilite might be a
consequence of the coagulation of smaller astrosilicate dust into larger
grains within the torus or PN. Spectroscopic and Ca-abundance requirements are
satisfied if up to 3 per cent of astrosilicate is converted to grains which
produce melilite overtone features. It is plausible that grains like these
were the precursors to the melilite in the CAIs in meteorites because more
than 80 per cent of the CAIs are formed of melilite or its alteration products
and the area per cent abundance of CAIs in chondritic meteorites is 1.5–3 per
cent.

This study illustrates the importance of continued monitoring of mass-losing
objects similar to Sakurai’s Object in the mid-infrared. Intriguing results
from this study are the appearance, growth and possible and disappearance of
the 6–7 µm absorption features and their use for the detection of PAHs and
inference of 10 to 20 micron-sized melilite and SiC grains which are otherwise
indetectable due to their high opacity in the 10 µm Si–O and Si-C stretching
bands. The detection of melilite overtone absorption bands in circumstellar
dust around oxygen-rich stars in the absence of H2O ice and carbonaceous dust
would be a priority, but it may be that the grains in these environments are
too small and the grain-density too low to produce overtone features.

## Acknowledgements

The author would like to thank the anonymous referee for insightful and
careful reviews which have improved this paper. The author is supported by a
2-year _Science and Technology Research Council_ Ernest Rutherford Returner
Fellowship (ST/S004106/1). Spectra of SiC were supplied by A. M. Hofmeister.
LR Spitzer spectra were obtained from the Combined Atlas of Sources with
Spitzer/IRS Spectra (CASSIS), a product of the Infrared Science Center at
Cornell University, supported by NASA and JPL. This work is based on
observations made with the Spitzer Space Telescope, which is operated by the
Jet Propulsion Laboratory, California Institute of Technology under a contract
with NASA.

## Data Statement

Data generated in this article will be shared on reasonable request to the
corresponding author.

##  Appendix A Laboratory and astronomical absorption profiles

###  A.1 Hydrogenated Amorphous Carbon (HAC)

The mean optical depth profile of Sakurai’s Object calculated in Section 4.2
is compared with various HAC samples synthesized by Grishko & Duley (2002) in
Figure 10. HAC fails to match the 6.3 µm peak of Sakurai’s Object due to
excess absorption at 5.8 to 6.0 µm.

Figure 10: Comparison between digitized spectra of HAC samples (grey,
arbitrary normalisation) synthesized by from graphite in various gas mixtures
Grishko & Duley (2002) and the mean profile of Sakurai’s Object (black)
calculated in Section 4.2. The ratios of mixed gases during formation were
9:1. Fine structure below the resolution of the Spitzer spectra has been
excluded.

###  A.2 Polycyclic Aromatic Hydrocarbons (PAHs)

Three spectra of well-characterised soot samples obtained by Carpentier et al.
(2012) were compared with data for Sakurai’s Object. Soot sample 3 (which is
dominated by PAH units with many defects and twisted rings) provided the best
match to observed 6–7 µm bands171717Carpentier et al. found that the positions
of these peaks matched the positions of class C aromatic infrared bands (AIBs)
defined by by Peeters et al. 2002 from emission bands observed in post-AGB
objects (IRAS 13416 and CRL 2688), better than their other samples which had
fewer defects.. The laboratory sample consisted of agglomerated particles with
diameters of $\sim 30$ nm. I removed narrow bands in the 5–8-µm region due to
H2O vapour contamination in the spectrometer and a broader carbonyl -C=O band
at 5.821 µm due to the use of oxygen in during sample preparation to produce
the spectrum presented here.

Due to the inhomogeneous nature and undetermined particle thickness of the
samples used for spectroscopy, Carpentier et al. wisely presented spectra with
arbitrary optical depth scales. However, astrophysical studies require a an
estimate of the band strength using equation 4, $\kappa_{pk}=\uptau_{pk}\rho
L$, where $\rho$ is the effective mass-density and $L$ is the optical path
length. Gavilan et al. (2017) used the same sooting apparatus to produce films
with peaks near 6.3 µm with an optical depths $\uptau\sim 0.07$ so I shall
adopt this value. In a compressed sample $\rho$ will be close to the density
of the bulk solid. However, the soot particles are uncompressed and the
effective mass is highly dependent on the degree of agglomeration and likely
to be far less than that for a ‘solid lump’ of PAH ($\sim$ 1.8 gcm-3).
(Rissler et al., 2013) ascertained effective mass densities of soot of
geometric diameters of 53-70 nm produced by a propane flame of 0.39–0.20 gcm-3
based on a primary particle density of 1.8 gcm-3. Hence, the value of
$\kappa_{pk}$ could be $1.3\times 10^{4}$ cm2g-1($\rho\approx 1.8$gcm-3),
$6\times 10^{4}$ cm2g-1 ($\rho\approx 0.39$ gcm-3) or $12\times 10^{4}$ cm2g-1
($\rho\approx 0.2$ gcm-3). I adopt the primary particle size of 0.53 nm and
density of 0.39 gcm-3 preferred by Rissler et al. (2013) giving
$\kappa_{pk}$=$6\times 10^{4}$ cm2g-1.

###  A.3 Melilite, Hibonite and SiC

Figure 11: Comparison between melilite(grey), metamict hibonite (black) and
$\beta$ SiC overtones (dotted). Each spectrum is normalised to its largest
peak.

.

Normalised overtone spectra of compressed crystalline melilite and metamict
hibonite powders (Bowey & Hofmeister, 2005) are compared with the normalised
spectrum of a $\sim 25$ µm-thick wafer of $\beta$ SiC (Hofmeister et al.,
2009) in Figure 11.

The spectrum of a compressed powder is representative of the feature provided
by a crystal of similar size because there are virtually no spaces between the
grains, but orientational effects are lost; this is probably near to a lower
limit for the melilite grain size because powder was added until the overtone
was observed. The metamict hibonite overtone is broader than the melilite
overtone due to a subpeak at 6.3µm. The band strength, $\kappa_{pk}(6.9)$ of
metamict hibonite is $0.48\times 10^{2}$cm2g-1. Other hibonite overtones peak
at 7.3 µm and have even weaker $\kappa_{pk}$ of 0.08–0.14 $\times
10^{2}$cm2g-1 and do not have any peaks at 6.9 µm.

The 25µm thickness of the SiC wafer is likely to be an upper size limit
because larger grains are opaque, even in the overtones; see Hofmeister et al.
(2009) for the spectrum of a 308 µm sample. Ideally a 20µm wafer would have
been measured because the 6.6 µm peak is slightly rounded, but this risked
destruction of the specimen (Hofmeister, personal communication). Rounding of
the peak and other artefacts occur in specimens which are opaque at the peak
wavelength (see Hofmeister, Keppel, & Speck, 2003). The nano-$\beta$ SiC
spectrum (Speck, Thompson, & Hofmeister, 2005) is of a thin film of 97% purity
consisting of 3 nm particles181818This is their tabulated value; in the text
it says the grains were 20 nm; values can be scaled accordingly, of thickness
0.34µm (Hofmeister et al., 2009).

###  A.4 Cyg OB2 no. 12

The shape of the interstellar silicate absorption feature in Figure 9(b) was
derived from a CASSIS Spitzer LRS spectrum (AOR 27570176) calibrated by the
method described in Section 2. Since the 8–13-µm spectrum was very similar to
ground-based observations obtained by Bowey, Adamson, & Whittet (1998) and
Bowey, Rawlings, & Adamson (2004), the continuum was estimated by scaling and
extrapolating a continuum derived by Bowey, Rawlings, & Adamson (2004) to the
wavelength-range of the Spitzer SL 1 spectrum. The resulting absorption
profile was then normalised to unity at the peak wavelength (9.75 µm) and
narrow lines (probably due to hydrogen emission local to the star) removed
before comparison with Sakurai data. A detailed and different analysis of
silicate dust in this line of sight has been published by Fogerty et al.
(2016).

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