# Infrared Spectroscopic Survey of the Quiescent Medium of Nearby Clouds: II.
Ice Formation and Grain Growth in Perseus and Serpens

M.C.L. Madden  Department of Astronomy, Columbia University, New York, NY
10027, USA  A.C.A. Boogert  Institute for Astronomy, University of Hawaii,
2680 Woodlawn Drive, Honolulu, HI 96822, USA  Visiting Astronomer at the
InfraRed Telescope Facility, which is operated by the University of Hawaii
under contract 80HQTR19D0030 with the National Aeronautics and Space
Administration.  J.E. Chiar  current address: Diablo Valley College, 321 Golf
Club Road, Pleasant Hill, CA 94523, USA  SETI Institute, 189 Bernardo Av.,
Suite 200, Mountain View, CA 94043, USA  C. Knez  Department of Astronomy,
University of Maryland, College Park, MD 20742, USA  Johns Hopkins University
Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723, USA
Visiting Astronomer at the Infrared Telescope Facility, which is operated by
the University of Hawaii under contract 80HQTR19D0030 with the National
Aeronautics and Space Administration.  Y.J. Pendleton  NASA Ames Research
Center, Moffett Field, CA 94035, USA  A.G.G.M. Tielens  Leiden Observatory,
Leiden University, P.O. Box 9513, 2300 RA Leiden, the Netherlands  A. Yip
Johns Hopkins University, Baltimore, MD 21218, USA

(Accepted 3/24/2022; Published in The Astrophysical Journal, 930, 2)

###### Abstract

The properties of dust change during the transition from diffuse to dense
clouds as a result of ice formation and dust coagulation, but much is still
unclear about this transformation. We present 2-20 $\mu$m spectra of 49 field
stars behind the Perseus and Serpens Molecular Clouds and establish
relationships between the near-infrared continuum extinction ($A_{\rm K}$) and
the depths of the 9.7 $\mu$m silicate ($\tau_{9.7}$) and 3.0 $\mu$m
$\rm{H_{2}O}$ ice ($\tau_{3.0}$) absorption bands. The $\tau_{9.7}$/$A_{\rm
K}$ ratio varies from large, diffuse interstellar medium-like values ($\sim
0.55$), to much lower ratios ($\sim 0.26$). Above extinctions of $A_{\rm
K}\sim 1.2$ ($A_{\rm V}\sim 10$; Perseus, Lupus, dense cores) and $\sim 2.0$
($A_{\rm V}\sim 17$; Serpens), the $\tau_{9.7}$/$A_{\rm K}$ ratio is lowest.
The $\tau_{9.7}$/$A_{\rm K}$ reduction from diffuse to dense clouds is
consistent with a moderate degree of grain growth (sizes up to $\sim 0.5$ $\mu
m$), increasing the near-infrared color excess (and thus $A_{\rm K}$), but not
affecting the ice and silicate band profiles. This grain growth process seems
to be related to the ice column densities and dense core formation thresholds,
highlighting the importance of density. After correction for Serpens
foreground extinction, the H2O ice formation threshold is in the range of
$A_{\rm K}=0.31-0.40$ ($A_{\rm V}=2.6-3.4$) for all clouds, and thus grain
growth takes place after the ices are formed. Finally, abundant
$\rm{CH_{3}OH}$ ice ($\sim$21% relative to $\rm{H_{2}O}$) is reported for
2MASSJ18285266+0028242 (Serpens), a factor of $>$4 larger than for the other
targets.

astrochemistry — infrared astronomy — water ice — silicates — methanol — dust
grains — molecular clouds — Perseus — Serpens

##  1 Introduction

The properties of interstellar grains have long been known to be different in
dense clouds compared to diffuse clouds. The most easily recognizable
differences include the 3.4 $\mu$m aliphatic hydrocarbons absorption feature,
which is only present in diffuse clouds (e.g., Pendleton, 1994; Chiar et al.,
1996), and ice absorption bands, which have only been reported toward dense
clouds (e.g., Boogert et al. 2015). The absence of the 3.4 $\mu$m aliphatic
hydrocarbons absorption feature is still not well understood. The growth of
ice mantles is a consequence of extinction in the ultraviolet (UV), reducing
the effects of photodesorption, and larger densities, increasing gas-grain
interactions (e.g., Hollenbach et al. 2009). Also, the optical and infrared
interstellar extinction curve is flatter in dense clouds, with the ratio of
total to selective extinction $R_{\rm V}=A_{\rm V}/E(B-V)$ increasing from
values of $\sim$3.1 to 5.5 (e.g., Indebetouw et al., 2005; McClure, 2009).
Deeper into the cloud ($A_{\rm V}\sim 20$), increased flattening continues
(Cambrésy et al., 2011). This is consistent with a reduction of the number
density of the smallest grains ($<$0.1 $\mu$m), but does not necessarily trace
growth of the largest grains (Weingartner & Draine, 2001). Very large grains
($>$1 $\mu$m) were found to be associated with dense clouds, however, causing
‘coreshine’ at wavelengths of 3.6 $\mu$m (Pagani et al., 2010). While it is
observationally and theoretically well established that ice mantles are formed
at relatively shallow dense cloud depths ($A_{\rm V}\sim 1.6$, or
observationally at $A_{\rm V}\sim 3.2$ when both the front and the back of the
clouds are traced), the thickness of ice mantles is limited to 5 nm by the
available oxygen budget (e.g., Hollenbach et al., 2009). Therefore,
coagulation of small grains, likely aided by sticky ice coated grains, must
govern the grain growth process (Ormel et al., 2011).

A sensitive indicator of the different dust properties in dense versus diffuse
clouds, is the depth of the 9.7 $\mu$m band of silicates ($\tau_{9.7}$)
relative to the near-infrared continuum extinction ($A_{\rm K}$). A reduction
of $\tau_{9.7}$/$A_{\rm K}$ in dense clouds by up to a factor of 2 was
observed towards a range of sight-lines tracing nearby clouds and cores (Chiar
et al., 2007), isolated dense cores (Boogert et al., 2011), and the Lupus
Cloud (Boogert et al., 2013). Models suggest that this change is likely caused
by grain growth affecting the near-infrared more than the silicate band,
because the 9.7 $\mu$m band profile shows little variation (Van Breemen et
al., 2011). Coagulation models of mixtures of ice coated graphite and silicate
grains confirm this (Ormel et al., 2011).

The $\tau_{9.7}$/$A_{\rm K}$ ratio and the 3.0 $\mu$m ice band optical depth
($\tau_{\rm 3.0}$) are interesting observational probes of the evolution of
dust from diffuse to dense clouds. Following Ormel et al. (2011), it is
expected that ice formation and grain growth are correlated. Observations
generally agree with that expectation, but, perhaps, not in all lines of sight
(Boogert et al., 2013). It is the goal of this paper to further investigate
the origin of the variations of the $\tau_{9.7}$/$A_{\rm K}$ ratio. Following
our papers on isolated dense cores (Boogert et al., 2011), and the Lupus cloud
(Boogert et al., 2013), here we study the $\tau_{9.7}$/$A_{\rm K}$ ratio and
ice abundances towards the Perseus and Serpens Molecular Clouds. These clouds
are well studied, low-mass star- forming regions (Enoch et al., 2006;
Jørgensen et al., 2006; Evans et al., 2009). With the Spitzer Infrared Array
Camera (IRAC), the Legacy Project “From Molecular Clouds to Planet Forming
Disks” (c2d; Evans et al., 2003, 2009) mapped 3.86 deg2 of the Perseus
molecular cloud and 0.89 deg2 of the Serpens molecular cloud (Jørgensen et
al., 2006; Harvey et al., 2006). We present Spitzer InfraRed Spectrograph
(Spitzer/IRS) and NASA InfraRed Telescope Facility SpeX (IRTF/SpeX) and Keck
Near InfraRed SPECtrometer (Keck/NIRSPEC) $K$ and $L$-band spectra of
background stars selected from this survey.

Throughout this paper we will assume Gaia-derived distances (Zucker et al.,
2019) for the relevant clouds: $294\pm 15$ pc for Perseus, $420\pm 15$ pc for
Serpens (Main; see also Ortiz-León et al. 2018), $189\pm 13$ pc for Lupus, and
$141\pm 7$ pc for Taurus.

In §2 and §3, the target selection and observation data are presented,
respectively. In §4, the methods used to fit the spectra are given. §5.1-5.4
show the correlations between the continuum extinction and the 9.7 $\mu$m
silicate and 3.0 $\mu$m ice features. In §5.5, the $\rm{CH_{3}OH}$ abundances
are analyzed. In §5.6, the results are put into a spatial context using maps
of the extinction and the 3.5 $\mu$m broad band emission. In §6.1 and §6.2 the
results are compared to models of grain growth, and implications of the
variations of the observed $\tau_{9.7}/A_{\rm K}$ ratios are discussed. The
results are also combined with those from previous works. The ice formation
thresholds for the sample of clouds are compared in §6.3, and in §6.4 CH3OH
ice abundances are discussed. Finally, a summary including mention of future
work is given in §7.

Figure 1: Perseus target positions labeled by alias and overlaid on extinction
contours (Evans et al., 2009). The contours represent $A_{\rm V}$ extinction
levels of 3, 6, 12, 18, and 24 mag. The target colors refer to the groupings
determined in §5.1. Star symbols represent lines of sight with a 3.0 $\mu$m
ice band optical depth ($\tau_{\rm 3.0}$) larger than 0.5 within the
uncertainties.  Figure 2: Serpens target positions overlaid on extinction
contours (Evans et al., 2009). The contours represent $A_{\rm V}$ extinction
levels of 3, 6, 12, 18, and 24 mag. The target colors refer to the groupings
determined in §5.1. Star symbols represent lines of sight with an ice band
optical depth $\tau_{\rm 3.0}>0.5$ within the uncertainties.

##  2 Source Selection

Background stars were selected from the Perseus and Serpens molecular clouds
which were mapped with Spitzer/IRAC and MIPS by the c2d Legacy team (Evans et
al., 2003, 2009). The maps are complete down to $A_{\rm V}$ = 6 and $A_{\rm
V}$ = 2 for Serpens and Perseus, respectively (Evans et al., 2003). The
selected sources have an overall spectral energy distribution (SED; 2MASS
1.2–2.2 $\mu$m, IRAC 3–8 $\mu$m, MIPS 24 $\mu$m) of a reddened Rayleigh–Jeans
curve. They fall in the “star” category in the c2d catalogs and have MIPS 24
$\mu$m to IRAC 8 $\mu$m flux ratios greater than 4. In addition, fluxes are
high enough ($>$10 mJy at 8.0 $\mu$m) to obtain Spitzer/IRS spectra of high
quality (S/N $>$ 50) within $\sim$20 minutes of observing time per module.
This resulted in a list of roughly 100 stars behind Perseus and 400 stars
behind Serpens. The list was reduced by selecting $\sim$10 sources in each
interval of $A_{\rm V}$ of 2–5, 5–10, and $>$10 mag for Perseus, and 5–10,
10–15, and $>$15 mag for Serpens (taking $A_{\rm V}$ from the c2d catalogs)
and making sure that the physical extent of the clouds are covered. For
Serpens, there are more background stars to choose from and the overall
extinction is higher, reflecting its lower Galactic latitude.

The final target list contains nearly all high $A_{\rm V}$ lines of sight. At
low extinctions, many more sources were available and the brightest were
selected. The observed samples of 28 targets toward Perseus, and 21 toward
Serpens are listed in Tables 1 and 2. The analysis shows that the SEDs of 2
Serpens sources cannot be fitted with stellar models (§5), because they likely
have dust shells (silicate band emission). All other targets were found to be
usable (hyper)giants or in a few cases main sequence stars. One Perseus target
(Per-16) was found to be a foreground, rather than a background star. Reiners
& Zechmeister (2020) measure a distance of 13.7 pc to Per-16, which is the
closest target in our sample size by far. Indeed, we find no evidence for dust
or ice extinction in this line of sight (§5.1).

Figures 1 and 2 plot the location of the observed background stars on
extinction map contours derived from 2MASS and Spitzer photometry (Evans et
al., 2009).

=5in  AliasaaAlias used throughout this paper. Name of Star RegionbbNamed
location within the Perseus cloud, if available. DateccDate of IRTF/SpeX
observations. The instrument mode used is LongXD1.9 (1.95-4.2 $\mu$m), except
for dates labeled with ∗ for which it is LongXD2.1 (2.15-5.0 $\mu$m). AOR key
ModulesddSpitzer/IRS modules used: SL=Short-Low (5-14 $\mu$m, $R\sim 100$),
LL2=Long-Low 2 (14-21.3 $\mu$m, $R\sim 100$), LL=Long-Low 1 and 2 (14-35
$\mu$m, $R\sim 100$) Per- 2MASS Ground-based Spitzer/IRS 1 03245605+3026005
LDN 1455 IRS 1 2008-09-27 23083008 SL, LL2 2 03261355+3029223 IRAS 03222+3034
2008-09-30 23085824 SL, LL2 3 03272467+3022547 2008-09-27 23083008 SL, LL2 4
03275729+3040138 LDN 1455 IRS 1 2008-09-30 23082752 SL, LL2 2010-02-05 5
03281034+3026343 LDN 1455 IRS 1 2008-09-29∗ 23086336 SL, LL2 6
03290508+3022080 LDN 1455 IRS 1 2008-09-30 23087616 SL, LL2 7 03293654+3129465
NGC 1333 2008-09-25∗ 23088128 SL, LL2 8 03295603+3108454 NGC 1333 2008-09-30
23082752 SL, LL2 9 03300474+3023032 IRAS 03271+3013 2008-09-30 23086592 SL 10
03301239+3144408 NGC 1333 2008-09-28∗ 23086848 SL 11 03303022+3027087 IRAS
03271+3013 2008-09-25∗ 23087616 SL, LL2 12 03322030+3050485 IRAS 03292+3039
2008-09-25∗ 23088384 SL, LL2 13 03331023+3050177 IRAS 03292+3039 2008-09-26
23083776 SL, LL2 14 03332416+3117470 2008-09-29∗ 23087360 SL, LL2 15
03334078+3125007 2008-09-27 23083776 SL, LL2 2010-02-05 16 03360868+3118398
2008-09-25∗ 23084800 SL, LL2 17 03384753+3127345 2008-09-26∗ 23084032 SL, LL
18 03384901+3130173 2008-07-08∗ 23085312 SL, LL 19 03420993+3144139 2008-09-30
23086080 SL 20 03431627+3155097 IC 348 2010-02-05∗ 23087872 SL, LL2 21
03432386+3146110 IC 348 2008-09-26∗ 23085568 SL, LL2 22 03434808+3151030 IC
348 2008-09-28∗ 23084544 SL, LL2 2008-09-29∗ 23 03450207+3141196 IC 348
2008-09-27 23084544 SL, LL2 2010-02-05 24 03450796+3204018 IC 348 2008-09-30
23084288 SL, LL2 25 03450839+3234202 2008-09-27 23083264 SL, LL2 2010-02-04 26
03452349+3158573 IC 348 2010-02-04 23083520 SL, LL2 2010-02-05 27
03465115+3238494 2008-09-26 23083264 SL, LL2 2010-02-04 28 03481723+3250595
2008-09-26∗ 23085568 SL, LL2

Table 1: Perseus Target Observations Table 2: Serpens Target Observations AliasaaAlias used throughout this paper. | Name of Star | RegionccNamed location within the Serpens cloud, if available. | Date | InstrumentddWavelength range covered is 2.83-4.15 $\mu$m for Keck/NIRSPEC and 2.15-5.0 $\mu$m for IRTF/SpeX | AOR key | ModuleseeSpitzer/IRS modules used: SL=Short-Low (5-14 $\mu$m, $R\sim 100$), LL2=Long-Low 2 (14-21.3 $\mu$m, $R\sim 100$), LL=Long-Low 1 and 2 (14-35 $\mu$m, $R\sim 100$)
---|---|---|---|---|---|---
Ser- | 2MASS |  | Ground-based | Spitzer/IRS
1 | 18275901+0002337 |  | 2009-10-11 | NIRSPEC | 23073536 | SL, LL2
2 | 18282010+0029141 | Ser/G3-G6 | 2009-10-11 | NIRSPEC | 23073792 | SL, LL2
3 | 18282631+0052133 |  | 2009-10-11 | NIRSPEC | 23072768 | SL, LL
4 | 18284038+0044503 | Ser/G3-G6 | 2009-10-11 | NIRSPEC | 23074816 | SL, LL2
5 | 18284139+0017460 | [EGE2007] Bolo 7 bbEnoch et al. (2007) | 2008-07-09 | SpeX | 23074048 | SL, LL2
6 | 18284797+0037431 | Ser/G3-G6 | 2009-10-11 | NIRSPEC | 23074304 | SL, LL2
7 | 18285266+0028242 | Ser/G3-G6 | 2007-07-05 | NIRSPEC | 13460224 | SL, LL2
|  |  | 2021-07-27 | SpeX |  |
8 | 18290316+0023090 | [EGE2007] Bolo 7 bbEnoch et al. (2007) | 2009-10-11 | NIRSPEC | 23076352 | SL, LL2
9 | 18290436+0116207 | Core | 2009-10-11 | NIRSPEC | 23074304 | SL, LL2
10 | 18290479-0001301 |  | 2008-07-09 | SpeX | 13210112 | SL, LL
11 | 18291546+0016422 | [EGE2007] Bolo 7 bbEnoch et al. (2007) | 2008-07-09 | SpeX | 23075328 | SL, LL
12 | 18291600+0109382 | Core | 2008-07-09 | SpeX | 23073024 | SL, LL
13 | 18291619+0045143 | Ser/G3-G6 | 2009-10-11 | NIRSPEC | 23073024 | SL, LL
14 | 18291699+0037191 |  | 2009-10-11 | NIRSPEC | 23076096 | SL, LL2
15 | 18292528+0003141 |  | 2009-10-11 | NIRSPEC | 23072768 | SL, LL
16 | 18294108+0127449 | Core | 2009-10-11 | NIRSPEC | 23073536 | SL, LL2
17 | 18295604+0104146 | Core | 2008-07-08 | SpeX | 23075328 | SL, LL
18 | 18295940+0041007 |  | 2008-07-08 | SpeX | 23075584 | SL, LL2
|  |  | 2008-07-09 |  |  |
19 | 18300085+0017069 |  | 2009-10-11 | NIRSPEC | 23072768 | SL, LL
20 | 18300896+0114441 | Core | 2009-10-11 | NIRSPEC | 23074816 | SL, LL2
21 | 18301220+0115341 | Core | 2008-07-08 | SpeX | 23075584 | SL, LL2

##  3 Observations

Spitzer/IRS spectra of background stars toward the Perseus and Serpens clouds
were obtained as part of a dedicated Open Time program (PID 40580). Tables 1
and 2 list all sources with their astronomical observation request (AOR) keys
and the IRS modules in which they were observed. The SL module, covering the
5–14 $\mu$m range, includes several ice absorption bands, as well as the 9.7
$\mu$m band of silicates, and has the highest signal-to-noise values
(S/N$>$50). The LL2 module (14–21 $\mu$m) was included in order to trace the
15 $\mu$m band of solid $\rm{CO_{2}}$ and for a better overall continuum
determination, although at a lower S/N of $>$30\. At longer wavelengths, the
background stars are weaker, and the LL1 module ($\sim$20–35 $\mu$m) was used
for only $\sim$30% of the sources. The spectra were extracted and calibrated
from the two-dimensional Basic Calibrated Data produced by the standard
Spitzer pipeline (version S16.1.0), using the same method and routines
discussed in Boogert et al. (2011). Uncertainties (1$\sigma$) for each
spectral point were calculated using the “func” frames provided by the Spitzer
pipeline.

The Spitzer spectra of Perseus and a subset for Serpens were complemented by
ground-based NASA IRTF/SpeX (Rayner et al., 2003) K and L-band spectra. For
the remaining Serpens targets, L-band spectra were obtained with the NIRSPEC
spectrometer (McLean et al., 1998) on Keck II. The SpeX spectra were obtained
in the LongXD1.9 or LongXD2.1 modes, offering wavelength ranges of 1.95-4.2 or
2.15-5.0 $\mu$m, respectively. The M-band portions of these spectra are only
presented if they are of sufficiently high quality. The SpeX observations were
done under observing programs 2008A079, 2008B074, and 2010A107 spread out over
the nights listed in Tables 1 and 2. One target, Ser-7, was observed under
program 2021A092 in the LXD_short mode (1.67-4.2 $\mu$m). For all SpeX
observations, a slit width of 0.3” was used, yielding a resolving power of R
=$\lambda/\Delta\lambda$ = 2500. The spectra were flat fielded, wavelength-
calibrated, and extracted using the Spextool package (Cushing et al., 2004).
The telluric absorption lines were divided out and the spectra were flux
calibrated using the Xtellcor program (Vacca et al., 2003). Standard stars of
spectral type A0V were used for this purpose.

The Keck/NIRSPEC spectra of the Serpens targets were observed in the long-slit
mode with the 0.57” wide slit, resulting in a resolving power of R = 1,500.
Two grating settings were observed, providing a full L-band coverage (2.83-4.2
$\mu$m). The data were reduced from the raw frames in a way standard for
ground-based long-slit spectra with the same IDL routines described in Boogert
et al. (2008). Sky emission lines were used for the wavelength calibration and
bright, nearby main sequence stars were used as telluric and photometric
standards. For the division over the standard star, the S/N was optimized by
carefully matching the wavelength scale to that of the science targets.

In the end, all SpeX, NIRSPEC, and Spitzer spectra were combined with 2MASS
$J$, $H$, and $K_{s}$ broadband photometry (Skrutskie et al., 2006), 3.55,
4.49, 5.73, and 7.87 $\mu$m photometry from c2d Spitzer/IRAC, 24 $\mu$m
photometry from Spitzer/MIPS (Evans et al., 2003), and WISE photometry (Wright
et al., 2010). The 1-5 $\mu$m spectra were matched to the photometry by
convolving them with the $K_{s}$-band filter profile and then multiplying them
along the flux scale. Similarly, the Spitzer/IRS spectra were matched to the
IRAC 7.87 $\mu$m photometric flux. The same photometry was used in the
continuum determination discussed in §4. Catalog flags were taken into
account, such that the photometry of sources listed as being confused within a
2” radius or being located within 2” of a mosaic edge were treated as upper
limits. The c2d catalogs do not include flags for saturation. Therefore,
photometry exceeding the IRAC saturation limit (at the appropriate integration
times) was flagged as a lower limit. In those cases, the nearby WISE
photometric points were used instead. Finally, as the relative photometric
calibration is important for this work, the uncertainties in the Spitzer c2d
and 2MASS photometry were increased with the zero-point magnitude
uncertainties listed in Table 21 of Evans et al. (2009) and further discussed
in Section 3.5.3 of that paper.

##  4 Methods

To determine the interstellar $A_{\rm K}$, $\tau_{3.0}$, and $\tau_{9.7}$
values, contributions from the stellar photosphere to the observed spectra
need to be removed. We did so, following the methods described in Boogert et
al. (2011, 2013), and Chu et al. (2020). The fits to the observed spectra were
significantly more constrained by combining the spectra with broad-band
photometric data (§3).

The fitting process was done in two steps. First, all data available in the
1-5 $\mu$m range were fitted using a large (224) database of template spectra
(Rayner et al., 2009) to derive accurate spectral types, as well as $A_{\rm
K}$ and $\tau_{3.0}$ values. Second, all data in the full 1-20 $\mu$m range
were fitted using a small (13) sample of model spectra (Decin et al., 2004;
Boogert et al., 2011) to provide $\tau_{9.7}$. Throughout this paper, the
$A_{\rm K}$ and $\tau_{3.0}$ values derived from the 1-5 $\mu$m template
fitting process were reported, as they are most accurate considering the much
larger database of template spectra available.

All fit parameters are determined simultaneously, and any dependencies are
taken into account in the uncertainty estimates. For the 1-5 $\mu$m template
fits, this is described in detail in Chu et al. (2020). In short, the key fit
parameters are:

1\. Spectral Type. The CO overtone lines between 2.25-2.60 $\mu$m provide a
sensitive tracer of spectral type. The near-infrared JHK photometry and
absorption features in the 3.8-4.1 $\mu$m spectral range also prove to be
important for this. The JHK photometry depends on the extinction as well,
which is discussed in point 2 below.

2\. Continuum Extinction ($A_{\rm K}$). We adopt the commonly used extinction
curve from Indebetouw et al. (2005). Due to the steepness of the extinction
curve in the 1.0-2.5 $\mu$m region, $A_{\rm K}$ and its uncertainty are
primarily determined by the JHK photometry and the shape of the un-reddened
spectral template spectrum. The dependency on flux values at longer
wavelengths is weak.

3\. $\rm{H_{2}O}$ Absorption Feature ($\tau_{3.0}$). $\rm{H_{2}O}$ ice has a
prominent broad feature at 3.0 $\mu$m. $\tau_{3.0}$ and its uncertainty are
determined by the flux values and the observational noise in the 2.9-3.2
$\mu$m range, including dependencies on the accuracy of the baseline
surrounding the ice feature. For the fitting, an $\rm{H_{2}O}$ ice absorption
spectrum for spherical, pure ice grains using optical constants of amorphous
ice at a temperature of 10 K (Hudgins et al., 1993) is assumed. A grain size
of 0.4 $\mu$m is chosen. This particular ice temperature and grain size have
no significance other than that they match the shape of the 3.0 $\mu$m band
well, providing a tool to derive $\tau_{3.0}$.

Besides the reduced $\chi^{2}$ values derived for the individual wavelength
regions discussed above, a total reduced $\chi^{2}$ ($\chi_{\nu}^{2}$) is
calculated across the wavelength range of 1-4 $\mu$m, using the IRTF template
database. Where this $\chi_{\nu}^{2}$ is lowest, the model template is chosen
as the best fit to the star. The final errors for $A_{\rm K}$ and $\tau_{3.0}$
are increased by including all of the model templates that have
$\chi_{\nu}^{2}$ (1-4 $\mu$m) within a factor of 2 of the best template. This
represents a confidence level of at least 3$\sigma$. In some cases, the
uncertainties on $A_{\rm K}$ and $\tau_{3.0}$ are much smaller than expected
from the $\chi_{\nu}^{2}$ across the full 1-4 $\mu$m wavelength range, because
$A_{\rm K}$ and $\tau_{3.0}$ depend strongly on only a sub-set of this
wavelength range.

For the full 1-21 $\mu$m fits, using a much smaller set of stellar models,
$\tau_{3.0}$ is kept fixed. The strength and shape of the longer wavelength
$\rm{H_{2}O}$ ice bands is set by assuming the $\rm{H_{2}O}$ ice model
discussed above. The 9.7 $\mu$m silicate band is fitted for grains small
compared to the wavelength, having a pyroxene to olivine optical depth ratio
of 0.62 at the 9.7 $\mu$m peak (Boogert et al., 2011). A key factor in the
fitting process is the photospheric SiO band at $\sim$8 $\mu$m, as it overlaps
with the 9.7 $\mu$m band of silicate dust. For some targets, the model
spectral types were optimized to fit that photospheric band best. Also, in
some cases the models were normalized to the data at a wavelength of 8.0
$\mu$m, instead of the default of 5.5 $\mu$m. This provides a better local
baseline for the silicate feature, while reducing the fit quality at other
wavelengths. Accurate $\tau_{9.7}$ values are more important for this work
than a good fit over the larger wavelength range.

##  5 Results

Using the models described in §4, the values for $A_{\rm K}$, $\tau_{3.0}$,
and $\tau_{9.7}$ are derived. The best fitting models are shown in Fig. 15 and
the derived values in Tables 3 and 4.

Table 3: Perseus Target Results

Alias | IRTF Template | Model | $A_{\rm K}$ | $\tau_{3.0}$ | $\tau_{9.7}$ | $\chi_{\nu}^{2}$ | N($\rm{H_{2}O_{ice}}$)aaColumn density upper limits are 3$\sigma$. | Notes
---|---|---|---|---|---|---|---|---
(Per-) | 1-5 $\mu$m | 1-30 $\mu$m | mag |  |  |  | $10^{17}\rm{cm}^{-2}$ |
1 | HD16068 (K3.5II) | K4III | 0.34 $\pm$ 0.07 | 0.0 $\pm$ 0.12 | 0.26 $\pm$ 0.09 | 2.92 |  $<$1.94 |  L-band = 1.15
2 | HD170820 (G9II) | K0III | 0.92 $\pm$ 0.08 | 0.49 $\pm$ 0.17 | 0.23 $\pm$ 0.05 | 0.76 | 7.87 $\pm$ 2.73 |  L-band = 1.15
3 | HD44391 (K0I) | K0IIIbbPoor fit 8 $\mu$m photospheric SiO band. | 0.30 $\pm$ 0.08 | 0.01 $\pm$ 0.05 | 0.24 $\pm$ 0.07 | 0.57 |  $<$0.83 |  …
4 | HD222093 (G9III) | G8III | 0.22 $\pm$ 0.06 | 0.0 $\pm$ 0.05 | 0.22 $\pm$ 0.05 | 2.02 |  $<$0.81 |  L-band = 1.02
5 | HD202314 (G6I) | G8III | 1.27 $\pm$ 0.09 | 0.49 $\pm$ 0.06 | 0.33 $\pm$ 0.05 | 0.51 | 7.91 $\pm$ 0.97 |  L-band = 1.13
6 | HD44391 (K0I) | G8IIIbbPoor fit 8 $\mu$m photospheric SiO band. | 0.75 $\pm$ 0.07 | 0.39 $\pm$ 0.08 | 0.38 $\pm$ 0.05 | 1.70 | 6.29 $\pm$ 1.36 |  L-band = 0.93
7 | HD35620 (K3.5III) | K4III | 1.63 $\pm$ 0.05 | 0.55 $\pm$ 0.05 | 0.35 $\pm$ 0.05 | 0.24 | 8.97 $\pm$ 0.82 |  L-band = 0.97
8 | HD44391 (K0I) | K0IIIbbPoor fit 8 $\mu$m photospheric SiO band. | 0.43 $\pm$ 0.15 | 0.01 $\pm$ 0.11 | 0.26 $\pm$ 0.05 | 0.5 |  $<$1.78 |  L-band = 1.07
9 | HD192713 (G3I) | G8III | 1.41 $\pm$ 0.05 | 0.52 $\pm$ 0.05 | 0.41 $\pm$ 0.05 | 0.67 | 8.47 $\pm$ 0.86 |  L-band = 1.06
10 | HD9852 (K0.5III) | K4III | 1.32 $\pm$ 0.14 | 0.24 $\pm$ 0.08 | 0.57 $\pm$ 0.07 | 1.11 | 3.81 $\pm$ 1.27 |  …
11 | HD132935 (K2III) | K5III | 1.69 $\pm$ 0.07 | 0.84 $\pm$ 0.05 | 0.43 $\pm$ 0.05 | 1.24 | 13.66 $\pm$ 0.82 |  L-band = 1.07
12 | HD182694 (G7III) | G8III | 1.87 $\pm$ 0.12 | 0.92 $\pm$ 0.11 | 0.38 $\pm$ 0.07 | 1.11 | 14.9 $\pm$ 1.79 |  L-band = 0.92
13 | HD9852 (K0.5III) | G8IIIbbPoor fit 8 $\mu$m photospheric SiO band. | 0.21 $\pm$ 0.17 | 0.0 $\pm$ 0.05 | 0.19 $\pm$ 0.05 | 1.08 |  $<$0.81 |  …
14 | HD91810 (K1III) | K3III | 1.43 $\pm$ 0.05 | 0.29 $\pm$ 0.11 | 0.57 $\pm$ 0.09 | 0.81 | 4.76 $\pm$ 1.80 |  …
15 | HD120477 (K5.5III) | K7III | 0.42 $\pm$ 0.11 | 0.0 $\pm$ 0.10 | 0.24 $\pm$ 0.08 | 3.24 |  $<$1.62 |  L-band = 1.03
16 | Gl581 (M2.5V) | G8III | 0.0 $\pm$ 0.05 | 0.09 $\pm$ 0.05 | 0.0 $\pm$ 0.05 | 3.65 | 1.41 $\pm$ 0.78 |  L-band = 0.93
17 | HD35620 (K3.5III) | K7IIIbbPoor fit 8 $\mu$m photospheric SiO band. | 0.67 $\pm$ 0.12 | 0.08 $\pm$ 0.05 | 0.29 $\pm$ 0.07 | 0.59 | 1.32 $\pm$ 0.82 |  L-band = 0.95
18 | HD213893 (M0III) | K4III | 0.58 $\pm$ 0.09 | 0.04 $\pm$ 0.05 | 0.24 $\pm$ 0.06 | 0.71 |  $<$0.84 |  L-band = 0.98
19 | HD108519 (F0V) | G8III | 0.98 $\pm$ 0.05 | 0.18 $\pm$ 0.06 | 0.35 $\pm$ 0.07 | 1.17 | 2.91 $\pm$ 0.97 |  local 9.7 $\mu$m baseline
20 | HD160365 (F6III) | G8III | 1.23 $\pm$ 0.13 | 0.1 $\pm$ 0.06 | 0.54 $\pm$ 0.06 | 4.09 | 1.63 $\pm$ 0.98 |  L-band = 0.95
21 | HD222093 (G9III) | G8IIIbbPoor fit 8 $\mu$m photospheric SiO band. | 0.95 $\pm$ 0.08 | 0.06 $\pm$ 0.05 | 0.34 $\pm$ 0.05 | 0.68 | 0.97 $\pm$ 0.81 |  L-band = 0.98
22 | HD4408 (M4III) | M6III | 0.95 $\pm$ 0.06 | 0.19 $\pm$ 0.05 | 0.33 $\pm$ 0.08 | 2.99 | 3.01 $\pm$ 0.79 |  L-band=0.83, local 9.7 $\mu$m baseline
23 | HD132935 (K2III) | K4III | 0.71 $\pm$ 0.1 | 0.13 $\pm$ 0.08 | 0.37 $\pm$ 0.05 | 0.80 | 2.09 $\pm$ 1.29 |  L-band = 0.90
24 | HD10697 (G3V) | G8III | 0.61 $\pm$ 0.11 | 0.09 $\pm$ 0.09 | 0.27 $\pm$ 0.05 | 1.18 | 1.49 $\pm$ 1.49 |  L-band = 0.95
25 | HD100006 (K0III) | K0III | 0.35 $\pm$ 0.09 | 0.0 $\pm$ 0.06 | 0.12 $\pm$ 0.05 | 1.77 |  $<$0.97 |  …
26 | HD16139 (G8.5III) | G8III | 0.49 $\pm$ 0.09 | 0.04 $\pm$ 0.05 | 0.20 $\pm$ 0.05 | 0.89 |  $<$0.83 |  …
27 | HD132935 (K2III) | K3III | 0.37 $\pm$ 0.05 | 0.05 $\pm$ 0.05 | 0.22 $\pm$ 0.05 | 0.49 | 0.83 $\pm$ 0.83 |  …
28 | HD35620 (K3.5III) | K4IIIbbPoor fit 8 $\mu$m photospheric SiO band. | 0.76 $\pm$ 0.12 | 0.23 $\pm$ 0.11 | 0.26 $\pm$ 0.05 | 0.51 | 3.72 $\pm$ 1.78 |  L-band = 0.95

Note. — Perseus targets observed by alias along with the fitted IRTF
templates, full spectra templates assuming spectral types, extinctions, water
ice optical depths, silicate optical depths, $\chi_{\nu}^{2}$ values for the
IRTF template database fits, water ice column densities, and extra notes.

Table 4: Serpens Target Results

Alias | IRTF Template | Model | $A_{\rm K}$ | $\tau_{3.0}$ | $\tau_{9.7}$ | $\chi_{\nu}^{2}$ | N($\rm{H_{2}O_{ice}}$)aaColumn density upper limits are 3$\sigma$. | Notes
---|---|---|---|---|---|---|---|---
(Ser-) | 1-5 $\mu$m | 1-30 $\mu$m | mag |  |  |  | $10^{17}\rm{cm}^{-2}$ |
1 | HD204724 (M1III) | M1IIIccPoor fit 8 $\mu$m photospheric SiO band. | 0.73 $\pm$ 0.23 | 0.10 $\pm$ 0.10 | 0.24 $\pm$ 0.05 | 0.86 | 1.64 $\pm$ 1.64 |  …
2 | HD196610 (M6III) | M7III | 0.87 $\pm$ 0.16 | 0.10 $\pm$ 0.18 | — bbPoor full spectrum fit, resulting in discarded $\tau_{9.7}$ value. | 1.25 |  $<$2.93 |  …
3 | HD179870 (K0II) | K3IIIccPoor fit 8 $\mu$m photospheric SiO band. | 0.75 $\pm$ 0.19 | 0.03 $\pm$ 0.06 | 0.31 $\pm$ 0.05 | 1.91 |  $<$0.97 |  L-band = 0.95
4 | HD28487 (M3.5III) | M3III | 1.12 $\pm$ 0.17 | 0.24 $\pm$ 0.12 | 0.38 $\pm$ 0.08 | 1.18 | 3.81 $\pm$ 1.91 |  …
5 | HD64332 (S4.5) | M1III | 1.09 $\pm$ 0.07 | 0.22 $\pm$ 0.08 | 0.36 $\pm$ 0.05 | 0.24 | 3.62 $\pm$ 1.32 |  L-band = 1.10
6 | HD4408 (M4III) | M1III | 1.01 $\pm$ 0.05 | 0.21 $\pm$ 0.09 | 0.44 $\pm$ 0.07 | 0.64 | 3.32 $\pm$ 1.42 |  local 9.7 $\mu$m baseline
7 | HD18191 (M6III) | M6III | 4.75 $\pm$ 0.44 | 1.63 $\pm$ 0.06 | 1.18 $\pm$ 0.06 | 0.87 | 26.33 $\pm$ 0.97 |  L-band = 1.10, local 9.7 $\mu$m baseline
8 | HD4408 (M4III) | M6III | 0.73 $\pm$ 0.05 | 0.09 $\pm$ 0.05 | 0.42 $\pm$ 0.05 | 0.64 | 1.52 $\pm$ 0.85 |  …
9 | HD201065 (K4I) | M0III | 0.92 $\pm$ 0.40 | 0.08 $\pm$ 0.07 | 0.37 $\pm$ 0.05 | 1.01 | 1.38 $\pm$ 1.20 |  …
10 | HD39045 (M3III) | M1III | 0.73 $\pm$ 0.08 | 0.13 $\pm$ 0.13 | 0.31 $\pm$ 0.05 | 0.26 | 2.18 $\pm$ 2.18 |  L-band = 0.95
11 | HD204724 (M1III) | M6III | 1.44 $\pm$ 0.12 | 0.47 $\pm$ 0.13 | 0.54 $\pm$ 0.05 | 0.48 | 7.66 $\pm$ 2.12 |  …
12 | HD204724 (M1III) | M0III | 0.71 $\pm$ 0.13 | 0.03 $\pm$ 0.11 | 0.19 $\pm$ 0.06 | 3.03 |  $<$1.81 |  L-band = 1.10
13 | HD194193 (K7III) | M1III | 0.78 $\pm$ 0.15 | 0.05 $\pm$ 0.12 | — bbPoor full spectrum fit, resulting in discarded $\tau_{9.7}$ value. | 0.94 |  $<$2.02 |  L-band = 1.15
14 | HD4408 (M4III) | M6III | 2.03 $\pm$ 0.09 | 0.63 $\pm$ 0.20 | 0.61 $\pm$ 0.09 | 0.89 | 10.16 $\pm$ 3.22 |  local 9.7 $\mu$m baseline
15 | HD201065 (K4I) | K7IIIccPoor fit 8 $\mu$m photospheric SiO band. | 0.69 $\pm$ 0.33 | 0.03 $\pm$ 0.05 | 0.29 $\pm$ 0.08 | 0.81 |  $<$0.82 |  …
16 | HD201065 (K4I) | M1III | 0.83 $\pm$ 0.24 | 0.06 $\pm$ 0.07 | 0.28 $\pm$ 0.08 | 1.13 |  $<$1.15 |  …
17 | HD94705 (M5.5III) | M6III | 1.40 $\pm$ 0.05 | 0.08 $\pm$ 0.18 | 0.54 $\pm$ 0.13 | 0.39 |  $<$2.88 |  …
18 | HD108477 (G4III) | G8III | 1.91 $\pm$ 0.20 | 0.50 $\pm$ 0.05 | 0.74 $\pm$ 0.06 | 0.54 | 8.13 $\pm$ 0.81 |  L-band = 1.08
19 | HD11443 (F6IV) | G8III | 0.98 $\pm$ 0.24 | 0.0 $\pm$ 0.05 | 0.43 $\pm$ 0.06 | 3.50 |  $<$0.81 |  …
20 | HD28487 (M3.5III) | M6III | 1.19 $\pm$ 0.15 | 0.24 $\pm$ 0.12 | 0.43 $\pm$ 0.05 | 0.93 | 3.87 $\pm$ 1.94 |  …
21 | HD44391 (K0I) | G8III | 1.61 $\pm$ 0.10 | 0.29 $\pm$ 0.05 | 0.57 $\pm$ 0.05 | 0.48 | 4.63 $\pm$ 0.80 |  L-band = 1.07

Note. — Serpens targets observed by alias along with the fitted IRTF
templates, full spectra templates assuming spectral types, extinctions, water
ice optical depths, silicate optical depths, the total reduced
$\chi_{\nu}^{2}$ values for the IRTF template database fits, water ice column
densities, and extra notes.

The fits to the 1-5 $\mu$m wavelength region, using the IRTF template
database, are generally good. In a fair number of cases, however, we did
notice deficiencies in fitting the continuum region near 4.0 $\mu$m, even
though the data at shorter wavelengths were fitted well. This could be due to
calibration errors in the slope of the 2-4 $\mu$m SpeX spectra or in the
Spitzer or WISE photometry used to calibrate the NIRSPEC spectra (for which no
$K-$band portion is available). It could also reflect an uncertainty in the
extinction curve or incompleteness of the spectral database. Regardless of the
origin, we reduced the effect on the derived $\tau_{3.0}$ by scaling the
L-band spectrum to match the best-fitting model. The scaling factors are
provided in Tables 3 and 4. In five cases, this correction factor is less than
5%, and in twenty-three cases 5-17%. We are confident in the derived values of
$\tau_{3.0}$, as the absorption band can be distinguished by the shape to the
$L-$band spectrum, and the adjustments are essentially local baseline
corrections.

Of all 49 targets, 7 have deviating slopes in the 8-12 $\mu$m region, even
though the IRTF template fits in the 1-5 $\mu$m range are good. This may
reflect the small number of 1-20 $\mu$m photospheric models available. In
order to improve the fit of the 9.7 $\mu$m silicate feature, a local baseline
correction was applied by changing the wavelength range for which the model is
normalized to the observations from the default of 5.34-5.50 $\mu$m to 7.3-7.5
$\mu$m. However, for two of these targets (Ser-2 and Ser-13), this approach
was insufficient. The deviations from the model are very large, and there is a
hint of silicate emission affecting the shape of the 9.7 $\mu$m absorption
feature. For these, probably more evolved, mass losing stars, we discarded the
derived $\tau_{9.7}$ values. For another 10 targets, while the 8-12 $\mu$m
slopes are in good agreement with the spectral types derived from the 1-5
$\mu$m range, the 8 $\mu$m SiO photospheric absorption band suggests later
spectral types. Such inconsistency was also noted for several Lupus background
stars (Boogert et al., 2013). The affected targets are indicated in Tables 3
and 4, and the effect on the reported $\tau_{9.7}$ values was taken into
account.

###  5.1 $\tau_{9.7}$ and $A_{\rm K}$ Correlation

Analogous to earlier work (Chiar et al., 2007; Boogert et al., 2013), we plot
the derived values for $\tau_{9.7}$ against $A_{\rm K}$ (Fig. 3). The rising
trend is fitted with:

$\tau_{9.7}=m\times A_{\rm K}$ (1)

We find that for Perseus, $m=0.416\pm 0.026$, and for Serpens, $m=0.406\pm
0.041$. A significant amount of scatter is visible in these plots, especially
for Perseus. In order to investigate the origin of these variations, we
separate the target into different groups. Throughout this work, we will refer
to these as Groups A to E.

The targets that fall at least $6\sigma$ below the linear fit are referred to
as “Group A.” Those that are at least $6\sigma$ above this relation will be
referred to as “Group B.” As can be seen in Fig. 3, Group A targets follow the
Lupus IV dense cloud relation ($m=0.26$; Boogert et al., 2013), and Group B
targets follow the diffuse ISM relation ($m=0.554$; Whittet, 2003). Based on
this, targets that fall within $6\sigma$ of more than one of these three
relations are assigned to “Group C,” and targets that exclusively follow the
fits over all targets are in “Group D.” Only Serpens exhibits this latter
Group. For Perseus, several Group C targets follow the overall fit, but the
uncertainties are too large to assign them to Group D. Finally, targets for
which no reliable $\tau_{9.7}$ values could be derived, but that do have
$A_{\rm K}$ and $\tau_{3.0}$ measurements, are in “Group E.” Also, note that
one target (Per-16) has $A_{\rm K}=0.0\pm 0.05$ (Table 3), which is consistent
with its distance of 13.7 pc (Reiners & Zechmeister, 2020), indicating this
target is actually a Perseus foreground, rather than background, star.

Figure 3: Silicate band optical depth and extinction correlation for Perseus
(a) and Serpens (b and c) targets. The error bars are of 3$\sigma$
significance. The solid black line is a least square fit to all targets in the
cloud. The dashed yellow line is the Lupus IV correlation from Boogert et al.
(2013). The dashed green line is the Diffuse ISM correlation from Whittet
(2003). Panel c zooms in on the lower extinction Serpens targets. The colors
of the bullets represent the groups defined in §5.1, and are indicated in
panel c. They apply to panels a and b as well as to the other Figures in this
paper. Figure 4: Water ice band optical depth and extinction correlations for
Perseus (a) and Serpens (b and c) targets. The error bars are of 3$\sigma$
significance. The solid black line is a least square fit to all targets in the
cloud. The dashed purple line is the Taurus molecular cloud correlation from
Whittet et al. (2001). The colors of the data points correspond to the
groupings defined in §5.1 and Fig. 3. Panel c zooms in on the lower extinction
Serpens targets. Figure 5: Water ice and silicate band optical depth
correlations for Perseus (a) and Serpens (b and c) targets. The error bars are
of 3$\sigma$ significance. The solid black line is a least square fit to all
targets in the cloud. The dashed blue line is the correlation derived from
dense cores in Boogert et al. (2011). The colors of the data points correspond
to the groupings defined in §5.1 and Fig. 3. Panel c zooms in on the lower
extinction Serpens targets.

Figure 6: Relation between the $\tau_{9.7}$/$A_{\rm K}$ ratio and $\tau_{3.0}$
for Perseus (a), Serpens (b), and Lupus (c) clouds, as well as isolated dense
cores (d). The error bars are of 3$\sigma$ significance. The colors of the
data points in panels a and b correspond to the groupings in Fig. 3.

###  5.2 $\tau_{3.0}$ and $A_{\rm K}$ Correlation

The relation between $\tau_{3.0}$ and $A_{\rm K}$ can be used to determine the
ice formation threshold (e.g., Whittet et al., 2001) and to determine the
abundance of ices relative to dust. This relation is plotted for Perseus and
Serpens in Fig. 4. Generally, $\tau_{3.0}$ increases as a function of $A_{\rm
K}$, and the relation does not go through the origin. The data points are
therefore fitted with the function:

$\tau_{3.0}=a\times A_{\rm K}+b$ (2)

We find that for Perseus, $a=0.430\pm 0.054$ and $b=-0.136\pm 0.052$, and for
Serpens, $a=0.391\pm 0.021$ and $b=-0.241\pm 0.032$. The abscissa of this
relation gives the ice formation threshold. For Perseus this is $A_{\rm
K}=0.315\pm 0.127$, and for Serpens $A_{\rm K}=0.616\pm 0.087$. The Perseus
values are comparable to those for Lupus IV: $a=0.44\pm 0.03$ and $b=-0.11\pm
0.03$, and an ice formation threshold of $A_{\rm K}=0.25\pm 0.07$ (Boogert et
al., 2013). The Serpens ice formation threshold is almost twice that of the
other clouds, which may relate to unrelated foreground extinction at the
larger distance of Serpens (§6.3; Zucker et al. 2019).

For Perseus, $\tau_{3.0}$ shows a significant scatter as a function of $A_{\rm
K}$ (Fig. 4a). By indicating the different groups identified in the
$\tau_{9.7}$ versus $A_{\rm K}$ correlation (§5.1), it is evident that the
Group A targets, i.e., those with the most suppressed, “dense core-like”
silicate bands, have deeper water ice bands at a given $A_{\rm K}$ than the
Group C targets. These Group A targets closely follow the Taurus ice
correlation, within $3\sigma$ ($a=0.60\pm 0.02$, $b=-0.23\pm 0.01$; Whittet et
al. 2001).

For Serpens (Fig. 4b and c), all targets have $\tau_{3.0}$ values that fall
significantly below the Taurus correlation. This is not only reflected in the
higher extinction threshold derived above, but also in the shallower slope of
the correlation. The latter might indicate lower $\rm{H_{2}O}$ ice abundances
in Serpens compared to Taurus. It might also be a reflection of smaller grain
sizes in Serpens, enhancing $A_{\rm K}$ relative to $\tau_{3.0}$ (§6.1). Here
again, the different groups, distinguished in the $\tau_{9.7}$ versus $A_{\rm
K}$ correlation, are indicated. All groups follow the same correlation, but
Group A targets are higher on the correlation than Group C and D targets,
respectively. It is also worth noting that all targets, with the exception of
Ser-19 (Group C), have $\rm{H_{2}O}$ ice detections, including the Group B
“diffuse ISM” target Ser-8.

###  5.3 $\tau_{3.0}$ and $\tau_{9.7}$ Correlation

The relations between $\tau_{3.0}$ and $\tau_{9.7}$ (Fig. 5) are linear,
although they are distincly different for Serpens and Perseus. Least square
fits yield for Perseus

$\tau_{9.7}=(0.21\pm 0.09)\times\tau_{3.0}+(0.26\pm 0.03)$ (3)

and for Serpens

$\tau_{9.7}=(0.55\pm 0.06)\times\tau_{3.0}+(0.31\pm 0.03)$ (4)

For comparison, the relation in a sample of isolated dense cores (Boogert et
al., 2011) is

$\tau_{9.7}=(0.36\pm 0.06)\times\tau_{3.0}+(0.36\pm 0.09)$ (5)

The relation is significantly steeper in Serpens compared to Perseus. In fact,
for $\tau_{3.0}>0.15$ the Perseus relation is almost flat, i.e., while
$\tau_{3.0}$ increases with a factor of 5, $\tau_{9.7}$ increases by at most a
factor of 1.5. Also, compared to the dense cores, the Perseus $\tau_{9.7}$
values are systematically a factor of 2 lower. The Serpens relation is in
better agreement with that of dense cores (Boogert et al., 2011), although the
slope in Serpens is steeper.

###  5.4 $\tau_{9.7}$/$A_{\rm K}$ and $\tau_{3.0}$ Correlation

The Group A targets are well separated from the other groups along the
$\tau_{3.0}$ axis in Fig. 5. This is confirmed in the relations between
$\tau_{9.7}$/$A_{\rm K}$ and $\tau_{3.0}$ (Fig. 6), where the Group A targets
have the lowest $\tau_{9.7}$/$A_{\rm K}$ ratios and the largest $\tau_{3.0}$
values. Such trend is also visible for Lupus. The isolated dense cores are
biased to the highest $A_{\rm K}$ and $\tau_{3.0}$ values. The group of points
with the higher $\tau_{9.7}$/$A_{\rm K}$ ratios are from the core L328, which
has a known diffuse dust foreground component.

###  5.5 $\rm{CH_{3}OH}$ Ice

A number of targets show ice absorption features in the 5-20 $\mu$m wavelength
range, most commonly the 6 $\mu$m O-H bending mode of $\rm{H_{2}O}$. Three of
them, two behind Perseus and one behind Serpens, show particularly deep ice
absorption features (Fig. 7). The 9.7 $\mu$m CO stretch mode arising from
$\rm{CH_{3}OH}$ is only detected in Ser-7. Despite the good S/N of the spectra
for the other two ice targets, Per-6 and Per-11, there is no significant
detection of $\rm{CH_{3}OH}$ (Fig. 8). This also shows that the 6.85 $\mu$m
absorption feature, which is detected in all three targets, is for at most a
small fraction due to the C-H deformation mode of CH3OH. The most promising
candidate is solid NH${}_{4}^{+}$ (Schutte & Khanna, 2003; Raunier et al.,
2003; Gibb et al., 2004; Boogert et al., 2008). For other potential
contributors, we refer to Keane et al. (2001).

The $\rm{CH_{3}OH}$ ice column density is calculated using an integrated band
strength of $A=1.6\times 10^{-17}$ cm $\cdot$ molecule-1 (Kerkhof et al.,
1999). This $A$-value is an average across different mixtures with a variation
of $\sim$20%. The abundance relative to $\rm{H_{2}O}$ is 21$\pm$2% for Ser-7
(Table 5). The uncertainty reflects baseline fluctuations, and does not take
into account the uncertainty in the $A$-value. Ser-7 has the highest
$\rm{CH_{3}OH}$ abundance measured toward a background star of a dense cloud
or core to date (Boogert et al., 2011; Chu et al., 2020). It is also
significantly higher (factors of 2-6) than the upper limits derived for the
other two ice targets (Table 5).

Figure 7: 5-20 $\mu$m optical depth spectra of the targets with the strongest
ice absorption features: Per-6, Per-11, and Ser-7, from top to bottom,
respectively. A model for the 9.7 $\mu$m and 18 $\mu$m silicate bands has been
subtracted. Ice absorption feature identifications are indicated. The 6 $\mu$m
and 6.85 $\mu$m absorption features consist of overlapping ice bands, and not
all components have been securely identified. The structure between 8-9 $\mu$m
toward Per-6 is likely due to insufficiently corrected photospheric
absorption. Offsets of 0.5 along the y-axis were applied for clarity.

Figure 8: Comparison of the deep $\rm{CH_{3}OH}$ feature in Ser-7 (green) to a
selection of other targets with deep 3.0 $\mu$m $\rm{H_{2}O}$ ice bands, Per-6
(left) and Per-11 (right) in black. A model for the 9.7 $\mu$m silicate
feature has been subtracted. Ser-7 has an extinction of $A_{\rm K}=4.75\pm
0.44$, Per-6 of $A_{\rm K}=0.75\pm 0.07$, and Per-11 of $A_{\rm K}=1.69\pm
0.07$. Gaussians (red) demonstrate the expected peak depths if the CH3OH
abundance relative to $\rm{H_{2}O}$ were the same in these targets as in
Ser-7. CH3OH is clearly absent, and upper limits are listed in Table 5. Table
5: CH3OH Ice Abundances

Alias | $A_{\rm K}$ | N($\rm{H_{2}O}$) | N($\rm{CH_{3}OH}$) | $\frac{N(CH_{3}OH)}{N(H_{2}O)}$
---|---|---|---|---
| mag | $(10^{17}cm^{-2})$ | $(10^{17}cm^{-2})$ |
Ser-7 | 4.75$\pm$0.44 | 26.33$\pm$0.97 | 5.4$\pm$0.5 | 0.21$\pm$0.02
Per-6 | 0.75$\pm$0.07 | 6.29$\pm$1.36 |  $<$0.64 |  $<$0.10
Per-11 | 1.69$\pm$0.07 | 13.66$\pm$0.82 |  $<$0.39 |  $<$0.03

Note. — The three targets with deep ice bands, as in Fig. 7, including their
aliases, extinctions, water ice column densities, methanol column densities,
and their methanol to water ice ratios.

###  5.6 Spatial Context

In order to put the variations in the dust and ice properties observed toward
the Perseus and Serpens background stars in a spatial context, we compare them
to infrared images, extinction maps, and the YSO population.

We use Spitzer extinction maps and infrared images that were produced by the
c2d Legacy project (Evans et al., 2003, 2009). The Perseus extinction map,
derived from near-infrared colors, has a resolution of 180” and has a minimum
of $A_{\rm V}=2$ mag. For Serpens, the resolution is 90” and starts at the
$A_{\rm V}=5$ mag cloud boundary. For the infrared images, we chose the IRAC1
filter at 3.6 $\mu$m, as this is more sensitive to dust scattering than the
longer wavelengths. To select the protostellar population, we used the Spitzer
c2d catalogs (Evans et al., 2009) available through the InfraRed Sky Archive
(IRSA) interface. All Perseus and Serpens targets with infrared spectral
indices $\alpha>-0.3$ were selected, where $\alpha$ follows the definition of
Lada (1987). These represent the most embedded population of stars. We then
designated targets with $-0.3\leq\alpha<0.3$ as “flat spectrum” YSOs, and
targets with $\alpha\geq 0.3$ as Class I targets. We also added the more
embedded Class 0 sources, that are harder to identify using Spitzer photometry
alone due to their weakness. Thirteen Class 0 targets in Perseus were obtained
from Jørgensen et al. (2006), and four in Serpens from Hogerheijde et al.
(1999). The YSO populations and the background star groups defined by the
$\tau_{9.7}$ versus $A_{\rm K}$ correlation (§5.1) are indicated on the IRAC
images and extinction maps in Figures 9 and 10 for Perseus and Serpens,
respectively.

Figure 9: Top panel: Location of the background stars (yellow, green, and red
circles and star symbols, as defined in Fig. 3) compared to Class 0 (black)
and Class I and “flat spectrum” (white) YSOs observed toward Perseus overlaid
the IRAC1 map (3.6 $\mu$m). The colorbar is in units of MJy/sr. The contours
represent the extinction map of $A_{\rm V}$ levels of 3, 6, 12, 18, and 24
mag. The star symbols represent the targets that exhibit strong ice features,
at $\tau_{3.0}>0.5$ within the uncertainties. Bottom panels: Zoomed in regions
of top panel, The red star symbol in the left panel represents Per-6, and the
yellow star symbol to the far left Per-11, both of which have particularly
deep ice absorption bands.

Figure 10: Top panel: Location of the background stars (colored bullets and
star symbols, as defined in Fig. 3) compared to Class 0 (black) and Class I
and “flat spectrum” (white) YSOs observed toward Serpens overlaid the IRAC1
map (3.6 $\mu$m). The colorbar is in units of MJy/sr. The contours represent
the extinction map of $A_{\rm V}$ levels of 3, 6, 12, 18, and 24 mag. The star
symbols represent the targets that exhibit strong ice features, at
$\tau_{3.0}>0.5$ within the uncertainties Bottom panels: Zoomed in regions for
known clusters in Serpens, the “core” (left) and “Ser/G3-G6” (right). The
yellow asterisk near the center represents Ser-7, which exhibits particularly
strong ice features.

For Perseus, the majority of the Group A (“dense” cloud-type) targets are
located in the Western portion of the cloud (Fig. 9). This is also where the
five Class 0 YSOs are all located. Class 0 envelopes extend to typically 1
arcmin in Perseus (Enoch et al., 2006). Group A target Per-9 is located 143”
(35,631 AU) from the Class I YSO IRAS 03271+3013. Another Group A target,
Per-12, is located 67” (16,819 AU) from the Class 0 YSO IRAS 03292+3039. The
smallest distance is 53” between the background star Per-11 and the Class 0
target [DCE2008] 081, and, therefore, it appears that none of the background
stars significantly trace Class 0 envelopes.

It is noteworthy that the two Group B (“diffuse ISM-like”) targets are located
in the Western part of Perseus as well. They are located at the edges of
extinction enhancements, and somewhat further away from YSOs compared to
several Group A targets. The number of targets is small, however, and these
trends are not statistically significant. The median distance between the six
Group A targets and nearest YSOs is 176” with a standard deviation of 240”;
the distances of the two Group B targets and their nearest YSOs are 657” and
671”.

The Perseus targets with the deepest ice bands, Per-6 (Group C) and Per-11
(Group A), are also located in the Western region of Perseus. Per-11 is
located among a small cluster of Class I and “flat spectrum” YSOs, but Per-6
is also located near such YSOs. Overall, these results indicate a significant
variety of dust properties within Perseus. Dense-cloud like dust is found
within the vicinity ($\sim$15,000 AU) of YSOs but also in regions without
YSOs. Diffuse ISM-like dust may have strong ice absorption, and is also found
in the denser regions.

In Serpens, most of the Class I and “flat spectrum” YSOs are concentrated in
two clusters, one located in the upper half of Serpens, and the other,
“Ser/G3-G6,” located around the middle of the molecular cloud (Zhang et al.,
1988). The four Class 0 YSOs are toward the center of the upper cluster (Fig.
10). The Group A target Ser-7 is located at the edge of Ser/G3-G6, but within
an arcminute of the YSO cluster. Ser-7 has very deep ice bands, and a very
large $\rm{CH_{3}OH}$ ice abundance. This likely reflects a high density
associated with the star formation in this cluster. The single Group B target
is located in a local extinction minimum. Group D targets (intermediate
between “diffuse ISM-like” and “dense-like” dust) are spread out along the
molecular cloud, in some cases located near the edges of local cores or near
YSOs, but certainly not in all cases.

Overall, as for Perseus, no clear correlations stand out for Serpens, and the
dust properties are governed by local physical conditions not evident in these
tracers. The distances between the two Group A targets and their nearest YSOs
are 180” (standard deviation 23”); for the one Group B target, there is a
distance of 285”; and for the six Group D targets, there is a median distance
of 118” with a standard deviation of 105”.

##  6 Discussion

###  6.1 The $A_{\rm K}$/$\tau_{9.7}$ Ratio in Grain Growth Models

Grain growth, starting when most grains are much smaller than the near-
infrared wavelength, i.e., in the Rayleigh limit, will increase $A_{\rm K}$
initially. But when the grain sizes become comparable to or larger than $\sim
0.4$ $\mu$m ($\lambda/2\pi$), gray extinction becomes important, and $A_{\rm
K}$ (per dust mass), derived from the near-IR color excess, will decrease.
This implies that the observed $A_{\rm K}$/$\tau_{9.7}$ reduction in dense
clouds (Fig. 3) could trace a moderate amount of grain growth. This is also
concluded by Ormel et al. (2011) based on grain growth models. These models
further infer that the grain growth is in the form of aggregates of ice coated
silicate and ice coated carbonaceous grains. The increased stickiness of ice
coated grains is key in the coagulation process. The observed relation between
$A_{\rm K}$/$\tau_{9.7}$ and the ices ($\tau_{3.0}$) will be discussed in
§6.2.

Such moderate grain growth is consistent with the invariant profiles of the
9.7 $\mu$m absorption bands. This was also the primary conclusion of the
extensive study by Van Breemen et al. (2011). The coagulated grains are too
small to affect the profile of the 3.0 $\mu$m ice band as well, as little
variation is observed as a function of extinction (Fig. 11). The long-
wavelength wing, which is thought to be affected by large grain scattering,
limits the grains to sizes of $\frac{3}{2\pi}\approx$ 0.5 $\mu$m and less.
Some variation is observed on the short wavelength wing, which might be a
result of NH3 abundance variations due to the N-H stretching mode at 2.9
$\mu$m. Indeed, the target with the strongest short-wavelength wing also shows
a more pronounced 3.47 $\mu$m feature, which results from ammonia hydrates
(Dartois & d’Hendecourt, 2001).

Figure 11: Profile of the 3 $\mu$m water ice bands observed toward four
targets tracing a range of extinctions ($A_{K}=0.75-4.75$). Per-6 is Group C,
Per-11 is Group A, Ser-7 is Group A, and Ser-18 is Group D. The spectra have
been normalized and smoothed to a resolving power of 100. Little variation is
evident in the long-wavelength wing, indicating insignificant growth of the
relative population of grains larger than $\sim$0.5.

A different scenario was discussed in Chiar et al. (2007) and Ormel et al.
(2011). Considering that the $K-$band extinction is primarily caused by
carbonaceous grains, the reduction of the $\tau_{9.7}$/$A_{\rm K}$ ratio (Fig.
3) is possible if growth is limited to silicate grains in the inner cloud
regions. These grains would need to be much larger than 1 $\mu$m so that they
do not contribute to the $\tau_{9.7}$ absorption feature (and also not to
$A_{\rm K}$), and not change its profile. In the models of Ormel et al.
(2011), the silicate absorption feature disappears for time scales longer than
1 Myr at a density of 105 cm-3, or at shorter time scales at higher densities.
Thus, in this scenario, large ice-rich silicate grains reside in the inner,
dense regions of the clouds, while the small silicate grains in the outer
regions are responsible for the 9.7 $\mu$m absorption feature. Carbonaceous
grains would not form such large grains, perhaps due to not acquiring ice
mantles. It is unclear why this would be the case. In fact, the increase of
$\tau_{3.0}$ as a function of $A_{\rm K}$, as observed in both Perseus and
Serpens (Fig. 4), is difficult to explain with ice-less carbonaceous grains.
If only silicate grains, tracing the outer cloud layers, are covered with ice
mantles, the $\tau_{3.0}$ as a function of $A_{\rm K}$ would flatten, which is
clearly not the case. Thus, overall, this scenario seems less likely.

###  6.2 $A_{\rm K}$/$\tau_{9.7}$ Variations and Relations with Ices and Dense
Core Formation

Striking variations in the relation between $A_{\rm K}$ and $\tau_{9.7}$ are
observed (Fig. 3). At the highest extinctions, the targets are trending to lie
systematically below the linear fit, i.e., $\tau_{9.7}$ is suppressed relative
to $A_{\rm K}$. For Perseus, this inflection occurs at $A_{\rm K}\sim 1.2$
($A_{\rm V}\sim 10$, assuming $A_{\rm V}$/$A_{\rm K}$ = 8.4), while for
Serpens, it is near $A_{\rm K}\sim 2$ ($A_{\rm V}\sim 17$). Below this
inflection point, the data points are located between the diffuse and dense
cloud relations. Above this inflection point, the data points tend to follow
the dense cloud relation. The same is observed for the third cloud in our
survey, Lupus, which shows an inflection point similar to Perseus (Boogert et
al., 2013).

In Fig. 12, we accumulate all $\tau_{9.7}$ and $A_{\rm K}$ data of other
clouds and cores known to us (Chiar et al., 2007; Boogert et al., 2011, 2013).
In addition to Perseus, Serpens, and Lupus (I and IV), this includes targets
tracing Taurus, IC 5146, Barnard 68, Chameleon I, and a range of isolated
dense cores. The isolated dense cores extend the $A_{\rm K}$ range to much
higher values. An overall correlation is visible, but the scatter is large.
The fitted line to all the data lies between the diffuse ISM and dense core
correlations, just as for our individual cloud fits. An overall inflection
point, after which the targets center around the dense cloud correlation, is
also visible, near $A_{\rm K}\sim 1.5$ ($A_{\rm V}\sim 13$). Thus, overall,
assuming that the $\tau_{9.7}/A_{\rm K}$ ratio is a measure of grain sizes
(§6.1), Fig. 12 shows that the dust coagulation process follows a smilar
pattern across different clouds.

Figure 12: Silicate ice and extinction correlation for the Perseus, Serpens,
Lupus, Taurus, and Chameleon I molecular clouds, as well as several dense
cores, taken from Chiar et al. (2007), and Boogert et al. (2011, 2013). The
bottom panel zooms in on the lower extinctions. The data points are color-
coordinated by cloud, as indicated. The black line is the linear fit to all
targets. The green dotted line is the diffuse ISM correlation (Whittet, 2003),
and the yellow dotted line is the Lupus IV correlation (Boogert et al., 2011).
The error bars, when available, are 3$\sigma$. Four Lupus IV sources have
upper limits that are consistent with the general correlation but are not
included in this graph. The isolated dense core targets near the diffuse ISM
relation trace L328, which is thought to be strongly contaminated by
foreground dust absorption.

It does appear that these $\tau_{9.7}$/$A_{\rm K}$ variations relate to the
ice band optical depths. For Perseus, the $\tau_{3.0}$ values for Group A
targets (lowest $\tau_{9.7}$/$A_{\rm K}$) are significantly higher compared to
all other targets, even those at similar $A_{\rm K}$ (Fig. 4). Indeed, the
Group A targets are well separated in the $\tau_{9.7}$/$A_{\rm K}$ versus
$\tau_{3.0}$ correlation plots (Fig. 6). The Lupus cloud shows a similar
behavior. For Serpens, targets with the largest $\tau_{9.7}$/$A_{\rm K}$
ratios, have the largest $\tau_{3.0}$ values, although very few lines of sight
with deep 3.0 $\mu$m ice bands are available.

The threshold for ice formation is similarly low for all clouds ($A_{\rm
V}\sim 2.6-3.4$; §6.3), and thus it appears that not only the mere presence of
ice on the grains, but also the ice column density (traced by $\tau_{3.0}$) is
an important factor in the grain growth process. This, in turn, relates to the
cloud density, as lines of sight with deeper ice bands, likely trace higher
densities deeper into the cloud.

Indeed, for both scenarios discussed in §6.1, the $\tau_{9.7}$ versus $A_{\rm
K}$ relation is a measure of the density structure of the clouds. The
inflection point in this relation reflects a transition to higher density
inner cloud regions where grain growth accelerates. This implies that the
density structure for Serpens is shallower than for Perseus, Lupus, and other
dense cores, although the density at the cloud edge is similar for all these
clouds, as evidenced by their similar ice formation thresholds (§6.3). Within
Perseus, however, coagulation is strongest for the targets with the largest
ice column densities.

In addition to the overall trends described above, there are deviations,
indicating that local conditions, such as density fluctuations, across the
cloud also matter. Such local scatter in the $\tau_{9.7}$ versus $A_{\rm K}$
plots was also noted for Lupus (Boogert et al., 2013). Fig. 13 compares the
optical depth spectra of Per-19 (Group C) and Per-2 (Group A), which have
similar $A_{\rm K}$ values, but Per-19 has a 50% deeper 9.7 $\mu$m silicate
band. Conforming with its diffuse ISM nature, Per-19 has a factor of $\sim$2.5
less water ice than Per-2. Thus, Per-19 appears to trace lower density cloud
material. In contrast, Ser-19 and Ser-6 have similar $\tau_{9.7}$ and $A_{\rm
K}$ at very different $\tau_{3.0}$ (Fig. 14). Ser-19 is in fact the only
Serpens target without ice. It is relatively isolated on the edge of the
cloud, but it is unclear if this plays a role. Unfortunately, Ser-19 and Ser-6
have uncertainn $\tau_{9.7}/A_{\rm K}$ ratios (Group C), precluding a
distinction between dense-like (Group A) or diffuse-like (Group B) dust.

It is worthwhile to note that the inflection points in the $A_{\rm K}$ versus
$\tau_{9.7}$ relation of $A_{\rm V}\sim 10$ and $A_{\rm V}\sim 17$ for Perseus
and Serpens, respectively, are comparable to the dense core formation
thresholds in these clouds. Enoch et al. (2007) derive dense core formation
thresholds of $A_{\rm V}\sim 8$ and $A_{\rm V}\sim 15$ from comprehensive
infrared and sub-millimeter surveys. This reinforces the idea that the dust
coagulation process is enhanced at higher densities.

Figure 13: Comparison of the 3.0 and 9.7 $\mu$m ice and silicate bands of the
targets Per-19 and Per-2. Both targets have similar $A_{\rm K}$ values, but
Per-19 has a much deeper 9.7 $\mu$m silicate band (and thus belongs to
“diffuse ISM” Group B). Conforming with its diffuse ISM nature, Per-19 has a
factor of $\sim$2.5 less water ice than Per-2, as seen by the shallower 3.0
$\mu$m $\rm{H_{2}O}$ feature. Such variations might point to a relation
between ice formation and grain coagulation. The negative optical depth values
between 5-8 $\mu$m for Per-19 are due to the choise of a local baseline for
the 9.7 $\mu$m absorption feature, as noted in Table 3.

Figure 14: The targets Ser-19 and Ser-6 have similar $A_{\rm K}$ values and
9.7 $\mu$m silicate band depths, but only Ser-6 displays the 3.0 $\mu$m
$\rm{H_{2}O}$ feature. The $L$-band portions have been smoothed to a resolving
power of 25. This comparison indicates that ice formation is not the only
factor that affects coagulation as traced by the $A_{\rm K}$/$\tau_{9.7}$
ratio.

###  6.3 Ice Formation Threshold

The relation between $A_{\rm K}$ and $\tau_{3.0}$ (§5.2, Fig. 4) for Serpens
shows a cut-off along the $A_{\rm K}$ axis of $0.616\pm 0.087$ ($A_{V}=5.17\pm
0.06$), which is approximately twice that of Perseus ($A_{V}=2.65\pm 0.25$),
Lupus IV ($A_{V}=2.10\pm 0.59$; Boogert et al. 2011), and Taurus
($A_{V}=3.2\pm 0.1$; Whittet et al. 2001). This might be attributed to
extinction by unrelated foreground dust. Serpens is located at a larger
distance ($420\pm 15$ pc) than all these other clouds: $294\pm 15$ pc for
Perseus, $141\pm 7$ pc for Taurus, and $189\pm 13$ pc for Lupus (Ortiz-León et
al., 2018; Zucker et al., 2019). To the first order, the foreground extinction
due to diffuse dust in the Galactic Plane may be estimated by scaling to the
extinction of $A_{\rm V}\sim 30$ towards the Galactic Center (Rieke et al.
1989 and references therein) at $\sim 8$ kpc. This results in foreground
contributions of $A_{\rm V}\sim 1.6$, 1.1, 0.7, and 0.5 mag for Serpens,
Perseus, Lupus IV, and Taurus, respectively. Models using Gaia-derived
distances (Zucker et al., 2019), however, point to a larger foreground
contribution ($A_{\rm V}=3.0$) for Serpens than for all the other clouds
($A_{\rm V}=1.0)$. This could be related to its location closer to the
Galactic Plane ($b\sim+4^{\circ}$), more directed to the Galactic Center
($l\sim 30^{\circ}$) than the other clouds.

Overall, when correcting for the larger foreground extinction towards Serpens,
it thus seems that H2O ice is formed at similar depths for all studied clouds.
This would be at $A_{\rm V}\sim 2.6-3.4$, or $\sim 1.6-2.4$ when subtracting
the 1.0 mag foreground for all (Zucker et al., 2019). If we further correct
for the fact that the observations trace both the front and back of the
clouds, the cloud depth at which H2O ice is abundantly formed is $A_{Vf}\sim
0.8-1.2$ mag. Following Hollenbach et al. (2009), this could indicate that the
cloud edges have similar densities ($n$), provided that they experience
similar interstellar radiation fields $F_{0}G_{0}$

$A_{Vf}=0.56\times ln\left(\frac{G_{0}F_{0}Y}{n(O)\nu_{0}}\right)$ (6)

where Y is the total yield of photodesorbing $\rm{H_{2}O}$ ice, and $\nu_{O}$
is the vibrational frequency of O atoms bound to a grain surface related to
dust temperature. For typical conditions (Hollenbach et al., 2009), this
corresponds to $n\sim 3\times 10^{4}$ at $A_{Vf}\sim 0.8-1.2$ mag

A higher threshold was observed toward the Ophiuchus cloud (Tanaka et al.,
1990) and is usually ascribed to the presence of a nearby O and B-stars,
increasing $F_{0}$, photodesorbing the ices. No such sources for a high UV
radiation field near the other clouds are known. Note that if the larger cut-
off in the relation between $A_{\rm K}$ and $\tau_{3.0}$ is not caused by
foreground dust, Eq. 6 would imply a lower Serpens cloud edge density compared
to the other clouds by a factor of $\sim$7.

###  6.4 $\rm{CH_{3}OH}$

One of our targets, Ser-7, shows a very high $\rm{CH_{3}OH}$ abundance of
$\sim$21% relative to $\rm{H_{2}O}$, surpassing previous records for
background stars of L694 ($\sim$14%; Chu et al., 2020) and L429-C ($\sim$12%;
Boogert et al., 2011). This target was also noted as containing high
abundances of other organic molecules, such as methane ($\rm{CH_{4}}$), and,
tentatively, solid acetylene ($\rm{C_{2}H_{2}}$) at 13.5 $\mu$m (Knez et al.,
2008, 2012).

The $\rm{CH_{3}OH}$ abundance toward Ser-7 is significantly larger than the
upper limits derived for other Serpens and Perseus background stars (Fig. 8).
It approaches the largest CH3OH ice abundances observed toward YSOs in Serpens
(28%; Pontoppidan et al. 2004; Perotti et al. 2020). Of all background stars
in our sample, Ser-7 is closest to a YSO (2MASSJ18285277+0028463), which is a
member of the Ser/G3-G6 cluster of Class I and “flat spectrum” YSOs. At an
angular distance of 23” (5,725 AU), the large CH3OH abundance might trace the
very outer edges of the envelope of this flat spectrum YSO, or the high
density core material within which the cluster formed. While $\rm{CH_{3}OH}$
is also expected to form at low densities (e.g., Qasim et al. 2018), its
formation is strongly enhanced at high densities ($10^{5}$ cm-3) when CO
rapidly freezes out (Cuppen et al., 2009). Indeed, so far all CH3OH ice
detections toward background stars trace sightlines with very high extinction,
above a threshold of $A_{\rm V}\sim 18$ ($A_{\rm K}\sim 2$; Boogert et al.
2015; Chu et al. 2020). Ser-7 is the only target in our Serpens and Perseus
sample with an extinction ($A_{\rm K}=4.75\pm 0.44$) above this threshold.

##  7 Summary and Future Work

We present 2-4 and 5-20 $\mu$m spectra of a sample of 28 stars behind the
Perseus and 21 stars behind the Serpens molecular clouds. We fitted the target
spectra using a combination of template spectra from the IRTF spectral
database and photospheric model spectra, combined with extinction curves,
laboratory $\rm{H_{2}O}$ ice spectra, and silicate absorption spectra to
derive $A_{\rm K}$, $\tau_{3.0}$, and $\tau_{9.7}$ values. Correlation plots
of $\tau_{9.7}$ versus$A_{\rm K}$ show a variation of a factor of $\sim$2 for
both clouds. Combining our $\tau_{9.7}$ and $A_{\rm K}$ values with those
available in the literature indicates that such scatter is common.

In general, the $\tau_{9.7}$/$A_{\rm K}$ ratios are reduced relative to the
diffuse ISM. The largest reductions, up to a factor of 2, are visible above
$A_{K}\sim$1.2 for Perseus and Lupus, and above $A_{K}\sim 2.0$ for Serpens. A
picture emerges that grains, after acquiring ice mantles (at
$A_{K}\sim$0.2-0.4), grow to moderate sizes due to higher densities deeper in
the cloud, especially above $A_{K}\sim$1.2-2. A significant population of
grains larger than $\sim 0.5$ $\mu$m is unlikely, however, as this would
increase the $\tau_{9.7}$/$A_{\rm K}$ ratio, and would also change the
profiles of the 3.0 and 9.7 $\mu$m absorption profiles, which is not observed.

The regions with the lowest $\tau_{9.7}$/$A_{\rm K}$ ratios are also the
regions where dense core (and thus star) formation will take place,
considering similar dense core formation extinction thresholds. Indeed,
Serpens stands out by having a factor of $\sim$2 higher inflection in the
$\tau_{9.7}$ versus $A_{\rm K}$ relation, and also a factor of 2 larger dense
core formation threshold. These aspects may indicate that Serpens has an
overall shallower density profile than the other clouds.

We derived H2O ice formation thresholds of $A_{\rm V}\sim 2.6-3.4$ for all
studied clouds, after correction for a 2 mag larger foreground extinction
towards Serpens. This threshold is well below the extinctions where the lowest
$\tau_{9.7}$/$A_{\rm K}$ ratios are observed. Thus we conclude that, in
agreement with the grain growth models by Ormel et al. (2011), grain
coagulation is facilitated by ice mantles, and enhanced at higher densities.
Targets tracing the highest ice column densities (proportional to
$\tau_{3.0}$), and thus likely densities, have the lowest $\tau_{9.7}/A_{\rm
K}$ ratios.

Besides the overall trends, we also found a large scatter in the
$\tau_{9.7}$/$A_{\rm K}$ ratio across small $A_{\rm K}$ intervals. Using
extinction maps, infrared images, YSO and molecular outflow locations, we did
not find strong correlations of these variations with cloud location. Finally,
we found three targets (Per-6, Per-11, Ser-7) with particularly deep ice
bands, of which Ser-7 has an especially high $\rm{CH_{3}OH}$ ice abundance of
21% relative to $\rm{H_{2}O}$. This is significantly higher than the upper
limits in the other sources, which is attributed to high densities in a local
star formation region.

A larger sample of sight-lines, fully covering a wide range of $A_{\rm K}$
values and molecular cloud conditions is needed to further constrain the
relation between ice formation, the silicate band, and continuum extinction. A
confirmation of the inflection in the $A_{\rm K}$ versus $\tau_{9.7}$ relation
is needed, as well as studies of the origin of the scatter in the
$\tau_{9.7}/A_{K}$ ratio, in particular the relation with local density.
Future work will rely heavily on observations with the James Webb Space
Telescope (JWST), enabling the construction of detailed maps of $A_{\rm K}$,
$\tau_{3.0}$, and $\tau_{9.7}$, facilitating an assessment of the relation
between grain coagulation and other cloud properties.

##  8 Acknowledgments

We thank Lee Mundy and Ewine van Dishoeck for their help with the early stages
of this project. We thank Megan Kiminki who worked on this project while an
REU student at the SETI Institute, supported by NSF grant AST-1359346. MCLM
thanks the Institute for Astronomy at UH Manoa for their hospitalty, and
Columbia University in the City of New York and the I.I. Rabi Scholars Program
for their generous financial support. We thank the referee for insightful
comments, in particular on the cloud distances and foreground extinction
correction, that helped improve this paper. This work is based on observations
made at the IRTF and Keck telescopes. We wish to extend our special thanks to
those of Hawaiian ancestry on whose sacred mountain of Maunakea we are
privileged to be guests. The observations presented herein would not have been
possible without their generosity. The authors recognize that the summit of
Maunakea has always held a very significant cultural role for the indigenous
Hawaiian community. We are thankful to have the opportunity to use
observations from this mountain.

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##  9 Appendix

Figure 15: The model fits and optical depth plots of the 28 Perseus and 21
Serpens targets. Each target has a 2x6 format of its plots: short wavelength
IRTF model (top left), full wavelength IRTF and Spitzer model (top middle),
5-8 $\mu$m (top right), 2-4 $\mu$m (bottom left), 8-12 $\mu$m (bottom middle),
and optical depth (bottom right). Black indicates the observed data, and red
the model data. The 2-4 $\mu$m plot indicates any presence of the 3 $\mu$m OH
stretch mode, which is made more prominent by the blue model flux which has
the $\rm{H_{2}O}$ ice contribution omitted; the models do not include
parameters to fit the wings around 3.4 $\mu$m. The 8-12 $\mu$m plot indicates
any presence of the 9.7 $\mu$m silicates, which is made more prominent by the
blue model flux which has the silicates contribution omitted. The 5-8 $\mu$m
plot indicates any presence of the 6 $\mu$m OH stretch mode and the 6.85
$\mu$m absorption feature due to, tentatively, NH${}_{4}^{+}$.  Figure 15:
(Continuation) Figure 15: (Continuation) Figure 15: (Continuation) Figure 15:
(Continuation) Figure 15: (Continuation) Figure 15: (Continuation) Figure 15:
(Continuation) Figure 15: (Continuation) Figure 15: (Continuation) Figure 15:
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(Continuation) Figure 15: (Continuation) Figure 15: (Continuation) Figure 15:
(Continuation)