11institutetext:  ELTE Eötvös Loránd University, Gothard Astrophysical
Observatory, 9700 Szombathely, Szent Imre H. st. 112, Hungary 22institutetext:
MTA-ELTE Lendület ”Momentum” Milky Way Research Group, Szent Imre h. u. 112.,
Szombathely H-9700, Hungary 33institutetext: Space Telescope Science
Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA 44institutetext:
Instituto de Astrofísica de Canarias (IAC), E-38200 La Laguna, Tenerife, Spain
55institutetext: Departamento de Astrofísica, Universidad de La Laguna (ULL),
E-38206 la Laguna, Tenerife, Spain 66institutetext: Konkoly Observatory, HUN-
REN Research Centre for Astronomy and Earth Sciences (CSFK), Konkoly Thege M.
út 15-17, 1121, Budapest, Hungary 77institutetext: CSFK, MTA Centre of
Excellence, Budapest, Konkoly Thege Miklós út 15-17., H-1121, Hungary
88institutetext: HUN-REN–ELTE Exoplanet Systems Research Group, Szent Imre h.
u. 112., Szombathely H-9700, Hungary 99institutetext: Sensor Science Division,
National Institute of Standards and Technology, Gaithersburg, MD 20899-8441,
USA 1010institutetext: The University of Arizona, Steward Observatory, 933
North Cherry Avenue, Tucson, AZ 85719, USA 1111institutetext: Department of
Experimental Physics, Institute of Physics, University of Szeged, Dóm tér 9,
6720, Szeged, Hungary

# The updated BOSZ synthetic stellar spectral library

Szabolcs Mészáros 1122 Ralph Bohlin 33 Carlos Allende Prieto 4455 Borbála Cseh
226677 József Kovács 112288 Scott W. Fleming 33 Zoltán Dencs 1122 Susana
Deustua 3399 Karl D. Gordon 33 Ivan Hubeny 1010 György Mező 6677 Márton
Truszek 1111

###### Abstract

Context. The modeling of stellar spectra of flux standards observed by the
Hubble and James Webb space telescopes requires a large synthetic spectral
library that covers a wide atmospheric parameter range.

Aims. The aim of this paper is to present and describe the calculation methods
behind the updated version of the BOSZ synthetic spectral database, which was
originally designed to fit the CALSPEC flux standards. These new local
thermodynamic equilibrium (LTE) models incorporate both MARCS and ATLAS9 model
atmospheres, updated continuous opacities, and 23 new molecular line lists.

Methods. The new grid was calculated with Synspec using the LTE approximation
and covers metallicities [M/H] from $-$2.5 to 0.75 dex, [$\alpha$/M] from
$-$0.25 to 0.5 dex, and [C/M] from $-$0.75 to 0.5 dex, providing spectra for
336 unique compositions. Calculations for stars between 2800 and 8000 K use
MARCS model atmospheres, and ATLAS9 is used between 7500 and 16,000 K.

Results. The new BOSZ grid includes 628,620 synthetic spectra from 50 nm to 32
$\mu$m with models for 495 $T_{\rm eff}$ – log $g$ parameter pairs per
composition and per microturbulent velocity. Each spectrum has eight different
resolutions spanning a range from R = 500 to 50,000 as well as the original
resolution of the synthesis. The microturbulent velocities are 0, 1, 2, and 4
km s-1.

Conclusions. The new BOSZ grid extends the temperature range to cooler
temperatures compared to the original grid because the updated molecular line
lists make modeling possible for cooler stars. A publicly available and
consistently calculated database of model spectra is important for many
astrophysical analyses, for example spectroscopic surveys and the
determination of stellar elemental compositions.

###### Key Words.:

techniques: spectroscopic – Galaxy: abundances – Galaxy: evolution – Galaxy:
fundamental parameters

##  1 Introduction

The design of the James Webb Space Telescope (JWST) absolute flux calibration
program follows the absolute calibration methods used for the Hubble Space
Telescope (HST) and directly ties measured fluxes to laboratory standards
(Gordon et al. 2022). Nonlocal thermodynamic equilibrium (NLTE) models of
three primary hot white dwarfs define the flux calibrations for HST. These
theoretical spectral energy distributions (SEDs) provide the relative flux
versus wavelength, and only the absolute flux level must be reconciled between
the measured absolute flux of Vega in the visible and the Midcourse Space
Experiment values for Sirius in the mid-IR (Bohlin et al. 2014, 2020). Fitting
of NLTE models to Balmer line profiles determines the $T_{\rm eff}$ and log
$g$ of the three primary white dwarfs. To produce secondary flux standards for
calibrating JWST, model spectra with IR coverage to 32 $\mu$m are then fit to
HST observations shortward of 2.5 $\mu$m.

While many high-resolution theoretical spectral libraries (Gustafsson et al.
2008; Zwitter et al. 2004; Coelho 2014) based on either ATLAS9 (Kurucz 1979)
or MARCS (Gustafsson et al. 2008) model atmospheres already existed, the flux
calibration of JWST required a grid that extended to 30 $\mu$m. Our previous
work, the BOSZ (named using letters from the names of the first two authors)
synthetic spectral grid (Bohlin et al. 2017), was created to fit the secondary
flux standards from the CALSPEC
database111http://www.stsci.edu/hst/instrumentation/reference-data-for-
calibration-and-tools/astronomical-catalogs/calspec.

This grid utilized the APOGEE-ATLAS model atmosphere database (Mészáros et al.
2012) of ATLAS9 models (Kurucz 1979) that was originally calculated for the
SDSS-III APOGEE survey (Majewski et al. 2017). The high-resolution spectra
were synthesized with SYNTHE (Kurucz & Avrett 1981) using the Linux-ported
version (Sbordone et al. 2004) and the Asplund et al. (2005) solar reference
abundances. With a total of 336 different compositions, as well as 14 [M/H], 4
[$\alpha$/M], and 6 [C/M] values that cover the majority of observed stellar
atmospheric parameters, this grid was the largest such theoretical spectrum
database available online. The spectra spanned the wavelength range of 100 nm
– 32 $\mu$m with vacuum wavelengths using an atomic line list compiled by
Robert Kurucz in 2016, and with line lists of 12 molecules from Kurucz’s
website222http://kurucz.harvard.edu/. Each composition had 415 models for a
total of 139,440 theoretical spectra in the final grid.

Allende Prieto et al. (2018) used more recent line and continuum opacities
than those available for Kurucz’s SYNTHE code and synthesized a large spectral
grid with ASS$\epsilon$T (Koesterke et al. 2008; Koesterke 2009) between 120
and 6500 nm using the APOGEE-ATLAS model atmospheres (Mészáros et al. 2012).
While their spectral library does not cover the entire JWST wavelength range,
important updates were made in the treatment of radiative transfer and
continuous opacities. Both Bohlin et al. (2017) and Allende Prieto et al.
(2018) used older molecular line lists compiled by Robert Kurucz; but
recently, the ExoMol project (Barton et al. 2017a, b) published new molecular
line lists that enabled further refinements to the online spectral databases.

The goal of this paper is to present the updated BOSZ grid, in which the
temperature range is extended down to 2800 K, continuum opacities are updated
from Allende Prieto et al. (2018), and an extended molecular line list for the
atmospheres of cool stars is included. The paper is structured as follows:
Section 2 details the model atmosphere database behind the new grid, in
Section 3 the atmospheric parameters of the new spectral library and the
synthesis are described, and in Section 4 the old and new BOSZ grids are
compared for three CALSPEC stars.

##  2 Model atmosphere assumptions

###  2.1 MARCS and ATLAS9

One of the most significant updates in the new calculations is the replacement
of ATLAS9 (Kurucz 1979) model atmospheres with MARCS (Gustafsson et al. 2008)
for stars below 8000 K, while above 8000 K ATLAS9 models from Mészáros et al.
(2012) using Asplund et al. (2005) as solar reference remain the
same333https://www.iac.es/proyecto/ATLAS-APOGEE/. The cool end of the BOSZ
grid now extends down to 2800 K. The MARCS grid used here was originally
computed for the derivation of atmospheric parameters and abundances released
by APOGEE in the 16th data release of SDSS (Ahumada et al. 2020). The
description of these models is explained by Jönsson et al. (2020), and the
grid is on the SDSS
website444https://data.sdss.org/sas/dr17/apogee/spectro/speclib/atmos/marcs/.
The solar reference abundances are from Grevesse et al. (2007), and the
$\alpha$ elements are defined as O, Ne, Mg, Si, S, Ar, Ca, and Ti. An
important upgrade is the inclusion of C2H2 and C3 line opacities in the MARCS
models, which make their atmospheric structure more realistic. A detailed
analysis of the effect of these molecules on the atmospheres is presented by
Gustafsson et al. (2008).

This new MARCS grid is substantially larger than the MARCS models described in
Mészáros et al. (2012). This paper includes only the subset of the chemical
element perturbations that are relevant for most of the stars observed by the
large high-resolution spectroscopic sky surveys. The chemical composition of
the new BOSZ grid is listed in Table 1 and shown in the bottom two panels of
Figure 1. Metallicity is varied between $-$2.5 and 0.75 dex, the [$\alpha$/M]
between $-$0.25 and 0.5 dex, and [C/M] between $-$0.75 and 0.5 dex with 0.25
dex steps for all three parameters. These chemical variations are the same for
all $T_{\rm eff}$, log $g$ pairs in the entire grid.

Within each composition, seven different mini-grids are defined based on the
$T_{\rm eff}$ and log $g$ listed in Table 2. Below 4000 K, the step size is
100 K, between 4250 and 12000 K steps are 250 K, and above 12000 K 500 K.
Unlike the old BOSZ database, models with temperature higher than 16000 K are
not included due to the lack of the necessary NLTE effects in ATLAS9. For this
reason, Bohlin et al. (2022) recently replaced the BOSZ models with NLTE ones.
The step size of log $g$ is 0.5 dex everywhere, but the minimum value of
surface gravity increases with increasing temperature to roughly follow the
Eddington-limit. In the MARCS model atmospheres, spherical geometry is used
between log $g$ = $-$1 and 3 with $v_{\rm micro}$ = 2 km s-1; and plane-
parallel geometry is assumed between log $g$= 3.5 and 5.5 dex with $v_{\rm
micro}$ = 1 km s-1. All ATLAS9 models are plane-parallel model atmospheres
with $v_{\rm micro}$ = 2 km s-1. The $T_{\rm eff}$$-$log $g$ diagram of our
selected parameters appears in the top panel of Figure 1. Spectra are
synthesized from both ATLAS9 and MARCS model atmospheres between 7500 and 8000
K.

Table 1: Chemical composition of all MARCS and ATLAS9 spectra.

Par. |  Min. |  Max. |  Step
---|---|---|---
[M/H] |  $-$2.5 |  0.75 |  0.25
[$\alpha$/M] |  $-$0.25 |  0.5 |  0.25
[C/M] |  $-$0.75 |  0.5 |  0.25

Table 2: Temperature and surface gravity range of the BOSZ grid.

Teff Min. |  Teff Max. |  Teff Step |  $\log$ g Min. |  $\log$ g Max. |  $\log$ g Step | n |
---|---|---|---|---|---|---|---
MARCS |  |  |  |  |  |  |
2800 |  4000 |  100 |  -0.5 |  5.5 |  0.5 | 203 928 |
4250 |  4750 |  250 |  -0.5 |  5 |  0.5 | 43 456 |
5000 |  5750 |  250 |  0 |  5 |  0.5 | 54 484 |
6000 |  7000 |  250 |  1 |  5 |  0.5 | 57 712 |
7250 |  8000 |  250 |  2 |  5 |  0.5 | 36 528 |
ATLAS9 |  |  |  |  |  |  |
7500 |  12000 |  250 |  2 |  5 |  0.5 | 178 752 |
12500 |  16000 |  500 |  3 |  5 |  0.5 | 53 760 |

  * •

All models are calculated with four microturbulent velocity values: $v_{\rm
micro}$= 0, 1, 2, 4 km s-1; and 8 resolutions: original, 500, 1000, 2000,
5000, 10 000, 20 000, and 50 000.

Table 3: Parameters of the missing MARCS models.

$T_{\rm eff}$ |  log $g$ |  [M/H] |  [$\alpha$/M] |  [C/M]
---|---|---|---|---
2800 |  +0.0 |  +0.00 |  +0.00 |  +0.50
2800 |  +0.0 |  +0.00 |  +0.25 |  -0.25
2800 |  +0.0 |  +0.00 |  -0.25 |  +0.25
2800 |  +0.0 |  +0.00 |  +0.25 |  -0.75
2800 |  +0.0 |  +0.00 |  +0.50 |  -0.25

  * •

The full version of the table is available at the CDS.

Figure 1: The parameter space covered by the new BOSZ grid. Top panel: $T_{\rm
eff}$ $-$ log $g$ diagram of the new BOSZ grid. Middle panel: [$\alpha$/M] as
a function of [M/H]. Bottom panel: [C/M] as a function of [M/H]. There are 336
different chemical compositions included in the database, and each composition
has 322 MARCS and 173 ATLAS9 model atmospheres. The star density from APOGEE
DR17 (Abdurro’uf et al. 2022) is the colored background and shows that the
selected parameters cover most of the stars that are observed in the Milky
Way.

###  2.2 Missing models

While both model atmosphere calculation methods can suffer from convergence
problems, the ATLAS9 grid is complete between 8000 and 16000 K. Unfortunately,
the MARCS model atmospheres do not always fully converge at low temperatures
and low or very high surface gravities, or for unconventional chemical
compositions. This issue is most apparent at the edges of the parameter space.
Out of the 108 192 MARCS files, 9165 did not converge (8.5%), and their
parameters are listed in Table 3. Most of the un-converged models (i.e.,
holes) are near the top of the red giant branch as only 24% of the log $g$ =
$-$0.5 cases could be computed.

Table 4: Molecular line lists.

Molecule |  File Path |  Reference
---|---|---
AlH |  molecules/alh/alhax.asc, molecules/alh/alhxx.asc |  Yurchenko et al. (2018b)
AlO |  molecules/alo/alopatrascu.asc |  Patrascu et al. (2015)
C2 |  molecules/c2/c2dabrookek.asc, linelists/linesmol/c2ax.asc |  Brooke et al. (2013)
|  linelists/linesmol/c2ba.asc, linelists/linesmol/c2ea.asc |
CaH |  molecules/cah/cah.asc |  Weck et al. (2003); Yadin et al. (2012); Li et al. (2012); Shayesteh et al. (2013)
CaO |  molecules/cao/caoyurchenko.asc |  Yurchenko et al. (2016)
CH |  molecules/ch/chmasseron.asc |  Masseron et al. (2014)
CN |  molecules/cn/cnaxbrookek.asc, molecules/cn/cnbxbrookek.asc |  Brooke et al. (2014)
|  molecules/cn/cnxx12brooke.asc |
CO |  molecules/co/coax.asc, linelists/linesmol/coxx.asc |  http://kurucz.harvard.edu/
CrH |  molecules/crh/crhaxbernath.asc |  Bauschlicher et al. (2001); Burrows et al. (2002)
FeH |  molecules/feh/fehfx.asc |  Dulick et al. (2003)
H2 |  linelists/linesmol/h2.asc, linelists/linesmol/h2bx.asc |  http://kurucz.harvard.edu/
|  linelists/linesmol/h2cx.asc, linelists/linesmol/h2xx.asc |
H2O |  Synspec addition |  Barton et al. (2017a, b); Hubeny et al. (2021)
MgH |  molecules/mgh/mgh.asc |  Shayesteh et al. (2007); Yadin et al. (2012); GharibNezhad et al. (2013); Hinkle et al. (2013)
MgO |  molecules/mgo/mgodaily.asc |  Daily et al. (2002)
NaH |  molecules/nah/nahrivlin.asc |  Rivlin et al. (2015)
NH |  linelists/linesmol/nh.asc |  http://kurucz.harvard.edu/
OH |  molecules/oh/ohupdate.asc |  http://kurucz.harvard.edu/
OH+ |  molecules/ohplus/ohplusax.asc, molecules/ohplus/ohplusxx.asc |  Hodges et al. (2018)
SiH |  molecules/sih/sihaxsightly.asc, molecules/sih/sihxxsightly.asc |  Yurchenko et al. (2018a)
SiO |  linelists/linesmol/sioax.asc, linelists/linesmol/sioex.asc |  http://kurucz.harvard.edu/
|  linelists/linesmol/sioxx.asc |
TiH |  molecules/tih/tih.asc |  Burrows et al. (2005)
TiO |  Synspec addition |  McKemmish et al. (2019); Hubeny et al. (2021)
VO |  molecules/vo/vomyt.asc |  McKemmish et al. (2016)

  * •

The file path comes after http://kurucz.harvard.edu/. H2O and TiO line lists
were formatted for Synspec by Hubeny et al. (2021).

To make a complete grid, these holes were filled by copying other model
atmospheres similar in chemical composition to the missing models by Jönsson
et al. (2020). While this would make it possible to have a complete BOSZ grid,
we chose not to calculate spectra from these model atmospheres because they
have a different chemical composition than what is expected at that position
in the grid. A possibility to bypass this issue is to perform interpolation in
the computed fluxes as described by Westendorp Plaza et al. (2023), which was
found by Mészáros & Allende Prieto (2013) to be more accurate than
interpolation of the model atmospheres. However, the iNNterpol code was not
yet available when our calculations were made. Spectra related to model
atmospheres with parameters from Table 3 are not published. In total, 157 155
model atmospheres formed the basis of the spectral synthesis, 99 027 of MARCS,
and 58 128 of ATLAS9.

##  3 Spectral synthesis

###  3.1 Radiative transfer and continuum opacities

The new synthetic BOSZ library is computed with Synspec (Hubeny et al. 2021)
and its Python wrapper called
Synple555https://github.com/callendeprieto/synple. After reading the model
atmosphere, the code prepares the solution of the equation of state, reads the
atomic and molecular line lists to compute the total line opacity, adds the
continuum opacity, and then solves the radiative transfer equation. While
Synple can handle NLTE models, all spectra described in this work are
synthesized under the assumption of local thermodynamic equilibrium (LTE).
Synple reads the composition from the model atmosphere file, ensuring
consistency between these two calculation steps, that is, ensuring that the
solar composition is the same as that of the model atmospheres.

Partition functions of 29 molecules from the ExoMol project (Tennyson &
Yurchenko 2012; Tennyson et al. 2016) are implemented in Synspec as described
in detail by Hubeny et al. (2021). All calculations use generic opacities from
Allende Prieto et al. (2018), except for molecules (see the next section).
There is only a short overview her; all the details of the opacity updates are
presented in Allende Prieto et al. (2018). Bound-free opacities of H-, H I,
H${}_{2}^{+}$, CH, and OH and the first two ionization stages of He, C, N, O,
Na, Mg, Al, Si, Ca, and Fe are included in the calculations with free-free
opacities from H-, H${}_{2}^{+}$, and He-. The atomic line list is the 2017
version from the Kurucz website666http://kurucz.harvard.edu/ with the updates
to the van der Waals damping constants added by Allende Prieto et al. (2018).
The Stark broadening of hydrogen lines were taken from Tremblay & Bergeron
(2009).

###  3.2 Opacities of molecules

Figure 2: Atomic and molecular absorption in dwarf stars with
[M/H]=[$\alpha$/M]=[C/M]= 0, log $g$ = 4.5 as a function of wavelength, and
$T_{\rm eff}$. The color indicates the strength of the absorption. The top-
left panel shows the atomic absorption only.

Significant updates were made to the molecular line list compared to Bohlin et
al. (2017) and Allende Prieto et al. (2018) by including line lists from the
ExoMol project. The improved atom physical data of molecular transitions and
increased number of lines makes it possible to compute more accurate synthetic
spectra, than with older line lists.

The old BOSZ grid included the following 12 molecules (from the 2015 version
of the Kurucz database): C2, CH, CN, CO, H2, H2O, MgH, NH, OH, SiH, SiO, and
TiO. This list is expanded here, and altogether, 11 new molecules are
considered: AlH, AlO, CaH, CaO, CrH, FeH, MgO, NaH, OH+, TiH, and VO. All but
two of the molecules included in the new calculations were compiled by Robert
Kurucz using various literature sources, as listed in Table 4. The absorption
profiles of 19 molecules appear in Figure 2 as a function of wavelength and
$T_{\rm eff}$. AlH, H2, NaH, and TiH are not shown due to their very weak
absorption within our parameter range.

The following molecules are the same in both the old and new calculations: C2,
H2, CO, and SiO. However, many previously used molecular line lists have been
updated using new line lists calculated as part of the ExoMol project
(Tennyson & Yurchenko 2012; Tennyson et al. 2016, for references, see Table
4). The most important decision was to replace the line lists of H2O and TiO.
The H2O line data of the old BOSZ grid were from Partridge & Schwenke (1997),
which is replaced by the one calculated for ExoMol by Barton et al. (2017a, b)
and formatted for Synspec by Hubeny et al. (2021). TiO is also taken from
ExoMol database calculated by McKemmish et al. (2019), instead of Schwenke
(1998), which was used for the previous BOSZ grid. The original ExoMol TiO
line data contained nearly 108 lines, which was truncated down to the
strongest $8.3\cdot 10^{6}$ lines, as described in Hubeny et al. (2021). The
partition functions for molecules have also been updated following the ExoMol
calculations.

Figure 3: Examples of the new BOSZ synthetic spectra as a function of
wavelength. Top panel: Example of low-resolution ($R$ = 500) solar composition
spectra on the main sequence (log $g$ = 4.5) between 2800 and 16 000 K. Middle
panel: Medium resolution ($R$ = 5000) sequence in the optical and near-IR.
Bottom panel: High-resolution spectra ($R$ = 50 000) near the Mg triplet lines
between 515 and 520 nm.

Many of the new molecules have significant absorption impacting the atmosphere
of stars cooler than 5000 K, as depicted in Figure 2. These molecules are
primarily: CaH, FeH, OH+, and VO. CaH is important in the optical range
between 400 and 900 nm below 5000 K, while FeH lines appear in the near IR
between 800 and 1700 nm at similar temperatures to CaH. VO lines in the range
of 500 and 900 nm are generally weak in the spectra of main sequence stars,
but become stronger in the atmosphere of giant stars between below 3500 K. OH+
has wide absorption features between 1.5 and 8 $\mu$m that were not accounted
in Bohlin et al. (2017). Another improvement is the inclusion of the extensive
list of CH from Masseron et al. (2014) that affects the spectra of stars
between 3500 and 7000 K.

###  3.3 Parameters of the spectral synthesis

All models were calculated with four microturbulent velocity values, $v_{\rm
micro}$= 0, 1, 2, and 4 km s-1, which is a significant update from the old
BOSZ grid that has only 2 km s-1. All spectra span a range from 50 nm to 32
$\mu$m using air wavelengths above 200 nm and vacuum wavelength below 200 nm.
Due to the immerse calculation time required, the wavelength range was divided
into 50 regions and calculated in parallel using the mpsyn routine of Synple.
The top panel of Figure 3 illustrates the full wavelength and $T_{\rm eff}$
range of solar composition main sequence stars (log $g$ = 4.5). Four $v_{\rm
micro}$ calculations for each model atmosphere produce a total of 628 620
synthetic spectra. The number of spectra available for each mini-grid can be
seen in Table 2. The updated BOSZ grid is available via the Mikulski Archive
for Space Telescopes (MAST) at the STScI as a High Level Science
Product777https://archive.stsci.edu/prepds/bosz via
https://dx.doi.org/10.17909/T95G68.

The wavelength step of the original synthesis ($\Delta\lambda_{o}$),
automatically chosen in Synple, is calculated the following way:

$\Delta\lambda_{o}=\frac{\lambda_{\rm range}}{c\cdot
0.785}\cdot\sqrt{0.1289^{2}\cdot\frac{T_{\rm min}}{100}+\frac{v_{\rm
micro}^{2}}{2}},$ (1)

where $\lambda_{\rm range}$ is the wavelength range, $c$ is the speed of
light, and $T_{\rm min}$ is the minimum temperature of the model atmosphere.
This step is one third of the thermal and microturbulent broadening at the
lowest temperature of the atmosphere for an atomic mass of 100. Thus, each
original spectrum has a slightly different sampling and resolution spanning a
range roughly between 200 000 and 600 000 depending on the main atmospheric
parameters. The file name of these original spectra contains the “rorig”
string and has three columns: the wavelength in $\AA$, the Eddington first
moment ($H$, surface brightness) of the spectra, and the continuum. The flux
($F$) at the stellar surface is calculated as

$F=4\pi H,$ (2)

where $H$ is in erg s-1 cm-2 $\AA^{-1}$.

Synspec solves the radiative transfer equation assuming plane-parallel
geometry, irrespective of the geometry of the input model atmosphere, which in
the case of MARCS for low gravity stars are spherical models. While the
original spectra are included in the database, the following lower resolutions
are also provided: $R$ = 500, 1000, 2000, 5000, 10 000, 20 000, and 50 000.
The middle panel of Figure 3 shows examples of $R$ = 5000 spectra in the
optical and near-IR, while the bottom panel illustrates high-resolution, $R$ =
50 000 spectra of the Mg Ib triplet lines in the optical.

Each of the seven sets of resolutions has its own equally sampled logarithmic
wavelength space for simplicity. To save disk space, the sets of files for the
seven lowest resolution values have only the flux and continuum columns with
their common wavelengths specified separately. The wavelengths have at least 2
points per resolution element at the lowest temperature (2800 K) for the solar
composition. There are 7500 wavelength points at $R$ = 500, which is set as
the reference value. Using this approach, the higher temperature spectra are
usually over-sampled by more than a factor of 2. The logarithmic wavelength
step ($\Delta\lambda_{R}$) as a function of resolution is calculated with the
following equation:

$\Delta\lambda_{R}=\frac{\ln(\lambda_{\rm max})-\ln(\lambda_{\rm
min})}{7500\cdot R/500},$ (3)

where $\lambda_{\rm max}=320\,000\leavevmode\nobreak\ \AA$, $\lambda_{\rm
min}=500\leavevmode\nobreak\ \AA$, and $R$ is the resolving power. The
wavelength sampling can be downloaded in separate files for each resolution
from the BOSZ website at MAST, or each wavelength value for a particular
resolution can be calculated with the equation

$\lambda_{R,i}=e^{ln(500)+\Delta\lambda_{R}\cdot i},$ (4)

where the $i$ integer starts at 0 and ends with $7500\cdot R/500-1$.

In FGKM-type stars, the flux is near zero well above 50 nm. To avoid having
unreliably small fluxes in the seven sets of lower-resolution spectra, all
line flux values are replaced by 0 and continuum fluxes by 1 when the original
flux is below 10-6 erg s-1 cm-2$\AA^{-1}$, which ensures that the same number
of rows are in all files of the same resolution. The original output of the
synthesis, the highest-resolution spectra (“rorig” files) retain all fluxes,
regardless of their values.

Line identifications are saved in the “lineid” files for $v_{\rm micro}$ = 0
km s-1, but not for the other microturbulent velocities. These files have
three columns: wavelength in $\AA$, a string of line identifications, and the
equivalent width ($W$) in $\AA$. Weak lines with $W<0.1\ \AA$ are not listed.
The new BOSZ grid contains 5 186 115 files, one for each of the eight
resolutions for all 628 620 spectra and one line id file per model atmosphere
for the $v_{\rm micro}$ = 0 km s-1 case, totaling 12.7 TB in size in gzip
format.

###  3.4 Differences between ATLAS9 and MARCS spectra

Between 7500 and 8000 K, both ATLAS9 and MARCS model atmospheres are published
to quantify the difference between the two types of model atmospheres. MARCS
replaces ATLAS9 models below 7500 K, but the differences due to the changes in
model atmosphere structure are discussed before examining the changes between
the new and old BOSZ grid. For this reason, four new spectra with ATLAS9
models at 3500, 4000, 5000, and 6000 K are calculated using the solar
composition, log $g$ = 4.5, $v_{\rm micro}$ = 2 km s-1, and all the updates to
the opacities. This set of four new cool ATLAS9 models quantifies the effects
of changes in the atmospheric structures at lower temperatures. The ratio of
differences between the MARCS and ATLAS9 spectra and the ATLAS9 spectra at $R$
= 5000 appear in the three panels of Figure 4. The top panel shows the
wavelength region between 100 nm and 32 $\mu$m, the middle panel depicts the
optical and near-IR between 350 and 1000 nm, and the bottom panel illustrates
the IR region between 1000 nm and 32 $\mu$m.

The difference of absolute fluxes between MARCS and ATLAS9 at 8000 K is on
average $\pm$0.5% at solar composition between 350 and 1000 nm and on average
$\pm$0.3 % between 1000 nm and 32 $\mu$m. JWST covers 800 nm to 30 $\mu$m.
Larger than average differences in the optical and IR appear in the cores of
very deep absorption lines where the flux itself is near zero. These ratios of
small values appear as spikes in the panels of Figure 4, and are likely
associated with a more limited extent of the MARCS models in the outermost
atmospheric layers. The MARCS fluxes are also larger by 5$-$10% than ATLAS9
for the coolest models of 3500 and 4000 K in the optical and near IR up to 5
$\mu$m, but the differences decrease as the wavelength increases (middle and
bottom panels of Figure 4). Such systematic flux offsets in the optical and IR
start to disappear at temperatures higher than 4000 K, and the agreement is
within 2% between 5 and 32 $\mu$m.

Differences increase substantially, at least to 10% in the UV, for all
temperatures between 3500 and 8000 K. In this wavelength region, the MARCS
models have larger flux than the ATLAS9 models, and this discrepancy between
the two types of models increases with decreasing wavelength. The MARCS UV
excess reaches 8-10 times the ATLAS9 spectrum at the shortest wavelengths; but
at such short wavelengths, the flux in both models is very low. This
discrepancy is most likely the result of the continuous opacity changes in the
UV region and the different model atmosphere structures.

Figure 4: Fractional differences between MARCS and ATLAS9 flux relative to the
ATLAS9 flux. Top panel: Spectra shown from $T_{\rm eff}$ = 3500 K to 8000 K
and between 100 nm and 32 $\mu$m. A large discrepancy exists in the UV for all
temperatures. Middle panel: Relative differences in the optical and near-IR,
where the offset is usually within 10%. Bottom panel: Relative differences are
the smallest in the IR between 1 and 32 $\mu$m. The large spikes above 15
$\mu$m originate from slight spectral mismatches in the resampling. Figure 5:
Fractional differences between the flux of the new and old BOSZ grid relative
to the old grid. Top panel: showing the full spectral range between 100 nm and
32 $\mu$m. Middle panel: Relative differences in the optical range. Bottom
panel: Relative differences in the IR.

###  3.5 Description of file names

File names are consistent, so the parameters of any spectra can be easily
recovered. All new names starts with “bosz2024_” and then the standard naming
scheme follows. An example of naming a spectrum file with $T_{\rm eff}$ = 5000
K, log $g$ = 5, [M/H] = 0, $v_{\rm micro}$ = 0, $R$ = 500, and solar scaled
[$\alpha$/M], [C/M] abundances is

$\rm{mp\\_t5000\\_g+5.0\\_m+0.00\\_a+0.00\\_c+0.00\\_v0\\_r500\\_resam,}$

where the first two strings define the model atmosphere, “mp”: MARCS plan-
parallel model, “ms”: MARCS spherical model, “ap”: ATLAS9 plan-parallel model.
The “_t5000” string indicates the effective temperature, which ranges between
2800 and 16000. The “_g+5.0” string is the surface gravity that ranges between
$-$0.5 and 5.5. The “_m-0.00” denotes the metallicity covering $-$2.50 to
0.75. The “_a+0.00” string shows the $\alpha$ abundance ($-$0.25 to 0.50), and
the “_c+0.00” string is the carbon abundance ($-$0.75 to 0.5). All the allowed
values are listed in Tables 1 and 2.

After the strings indicating the main atmospheric parameters, the
microturbulent velocity follows as “_v0,” for which the allowed values are 0,
1, 2, and 4. The resolution is “_r500” and allowed values are: 500, 1000,
2000, 5000, 10000, 20000, and 50000. For the original resolution, “rorig”
appears here. The lower-resolution spectra were resampled, as indicated by the
“_resam” string. For the original resolution, the original wavelength sampling
is kept, so this string is “_noresam.” In the files containing the line
identifications this part is called “_lineid.”

##  4 Comparisons of the new and old BOSZ libraries

###  4.1 Changes in the model fluxes

There are substantial changes in the fluxes of the new spectra when compared
to the old BOSZ grid, as illustrated in Figure 5. The top panel shows the
differences in flux relative to the old models in the common wavelength range
of 100 nm and 32 $\mu$m, the middle panel shows the optical, the bottom panel
depicts the IR region. All comparisons are for temperatures in the common
$T_{\rm eff}$ range between 3500 and 16000 K using solar composition, log $g$
= 4.5, $v_{\rm micro}$ = 2 km s-1, and R = 5000. Two factors cause these
changes: 1. the replacement of ATLAS9 with MARCS models, and 2. updates to the
continuous and line opacities. The largest differences between the two sets of
models appear in the UV. As seen in Section 3.4, differences in the UV between
MARCS and ATLAS9 are substantial and probably on par with changes in
opacities.

Except for the UV region, the differences in the model atmosphere structure
modestly affects the overall flux only for the coolest stars below 4000 K. The
large variations of flux displayed in Figure 5 originate from the adoption of
new continuous and line opacities. Changes in the continuous opacities mostly
show up in the spectra of the $T_{\rm eff}$ = 10000 and 16000 K stars
(greenish yellow and yellow lines in the panels of Figure 5). Up to 10$-$15%
changes in the fluxes occur at these temperatures near the Balmer jump between
360 and 400 nm, and at 850 and 900 nm near the Paschen jump. The discrepancy
in the hydrogen lines remains in the IR but decreases to about 5$-$7%, at the
most.

Table 5: Atmospheric parameters of selected CALSPEC stars. |  |  Old Grid |  |  |  |  New Grid |  |
---|---|---|---|---|---|---|---|---
Star |  $T_{\rm eff}$ |  log $g$ |  [M/H] |  E(B$-$V) |  $T_{\rm eff}$ |  log $g$ |  [M/H] |  E(B$-$V)
BD+60 1753 |  9480 |  3.75 |  0.04 |  0.017 |  9420 |  3.75 |  0.12 |  0.015
P330E |  5830 |  4.80 |  -0.21 |  0.028 |  5840 |  4.40 |  -0.09 |  0.029
KF06T2 |  4510 |  1.55 |  -0.26 |  0.053 |  4550 |  2.10 |  -0.11 |  0.069
Figure 6: Ratio of the new to original best fitting models for an A-, G-, and
K-type star. At the longer wavelengths, the old and new models agree mostly
within 1%. At shorter wavelengths, where the line blanketing is heavy,
differences are much larger. Figure 7: SEDs for the STIS data (black
diamonds), original model grid (green), and new model grid (red) in a region
of heavy line blanketing for BD+60 1753.

For the coolest temperatures from 3500 to 5000 K (dark and light blue lines in
Figure 5), the new BOSZ flux is significantly lower between 200 and 500 nm
than the old grid. Some of this must be related to the addition of OH+, which
has strong absorption bands in this wavelength region when $T_{\rm eff}$ $<$
5500 K (see Figure 2) and which was not included in the old BOSZ models.
Between 450 and 720 nm variations in flux from 20% to $-$40% appear at 3500 K
and 4000 K, but not at hotter temperatures. The cause of this change is most
likely the generally stronger absorption coming from the new TiO line list.
Most of the large spikes of differences in the optical occur in the core of
deep absorption lines, while the agreement is much better near the continuum.

The differences between the new and old BOSZ spectra are usually within
$\pm$10% when the wavelength is larger than 1 $\mu$m. The discrepancy between
the two versions of spectra increases as the temperature decreases, reaching a
maximum at 3500 K. Because the largest variation only occurs in the spectra of
the coolest models, the cause can be attributed to changes in the absorption
bands of H2O and the new addition of OH+. H2O is a significant absorber above
1 $\mu$m, and OH+ has absorption bands between 1.5 and 8 $\mu$m. While the
offset in fluxes is quite large when these molecules form in the atmosphere at
$T_{\rm eff}$ $<$ 5500 K, the agreement between the new and old models is
generally better than 1% when $T_{\rm eff}$ $>$ 5500 K. Thus, models for
CALSPEC stars cooler than 5500 K should have significant IR flux changes that
increase with decreasing temperature when fitting with the new BOSZ models.

###  4.2 Fitting CALSPEC stars

To understand the typical differences between models that best fit the HST
STIS and NICMOS observations, examples of an A-, G-, and K-type star are fit
with both the new and the original grid using the technique of Bohlin et al.
(2017, 2019, 2020). The model fitting finds the smallest $\chi^{2}$ by varying
four parameters: $T_{\mathrm{eff}}$, $\log g$, [M/H], and E(B-V), which are
the model effective temperature, surface gravity, metal abundance relative to
hydrogen, and the selective extinction. The average galactic extinction
prescription is from Gordon et al. (2022).

Table 5 compares the model parameter results from fitting with the original
and new model grids. There is fair agreement between the two sets of results
with a maximum difference in $T_{\rm eff}$ of 60 K for BD+60 1753. Figure 6
shows the ratios at a resolution R = 500 for new/old model SEDs that are
defined by the parameters of the best fitting models of Table 5. While model
parameters may differ, differences in our final SEDs are less than 1% over
most of the longer wavelengths. Below the 0.29 $\mu$m cutoff of the ratio for
P330E and KF06T2, those stars are very faint.

Figure 7 depicts an example of the difficulties in modeling the data in a
region of heavy line blanketing, where some features of the observed STIS SED
(black diamonds) are not reproduced by either the new (red) or the original
(green) model grid. To approximately match the STIS resolution, the models
have R = 500. The strong doublet at 0.15267 $\mu$m and 0.15334 $\mu$m could be
mostly interstellar SiII, which is not included in the models. The new grid
matches the observation better at the shortest and longest wavelengths, while
the original grid fits better in some intermediate regions. Both grids are
$>$7e-13 in comparison to the $\approx$5e-13 STIS flux at 0.1537 $\mu$m. Thus,
for applications in the observed STIS wavelength range, the observed CALSPEC
flux is preferred to any model.

##  5 Conclusions

The new set of BOSZ models, available from
MAST888https://archive.stsci.edu/prepds/bosz at the Space Telescope Science
Institute, contains 628 620 model spectra calculated with Synspec using an LTE
approximation. The spectra cover a wavelength range between 50 nm and 32
$\mu$m, using eight different resolutions from 500 to roughly 200 000,
depending on the $T_{\rm eff}$. Spectra with varying metallicities from $-$2.5
to 0.75 dex, [$\alpha$/M] from $-$0.25 to 0.5 dex, and [C/M] from $-$0.75 to
0.5 dex have been calculated. The hottest spectra in the new grid are at
$T_{\rm eff}$ = 16000 K using ATLAS9 model atmospheres; the inclusion of MARCS
models below 8000 K extends the grid down to 2800 K, where 23 molecular line
lists, many from the ExoMol project, play an important role in shaping the IR
spectrum.

As a result of using MARCS models at lower temperatures and updates in the
continuous and line opacities, there are large differences between the new and
old BOSZ grid in the common wavelengths of 100 nm and 32 $\mu$m. Above 10000
K, flux changes of up to 10$-$15% occur near the Balmer jump between 360 and
400 nm and at 850 and 900 nm near the Paschen jump, while the IR hydrogen
lines have smaller differences than in the optical. In the IR, variations
occur in the spectra of the coolest models, with changes of up to $\pm$10%,
which are mostly due to absorption bands of a new H2O line list from ExoMol
and to the new addition of OH+. Due to the updated molecular line lists,
CALSPEC stars cooler than 5500 K have significant IR flux changes compared to
the old BOSZ spectra, which increase with decreasing temperature.

Using both the new and old BOSZ grid, the best fitting models for an A-, G-,
or K-type star from the CALSPEC database illustrate the typical differences
between the three pairs of resulting SEDs. The main parameters, $T_{\rm eff}$,
log $g$, and [M/H], agree well; as expected from the direct model comparisons,
the largest differences can be seen in the UV region. While none of the models
can exactly reproduce all observed UV features, the new models match the
observations slightly better than the old ones.

###### Acknowledgements.

We thank the referee for his/her comments that significantly improved the
paper. This project has been supported by the LP2021-9 Lendület grant of the
Hungarian Academy of Sciences. On behalf of the ”Calculating the Synthetic
Stellar Spectrum Database of the James Webb Space Telescope” project we are
grateful for the possibility to use HUN-REN Cloud (see Héder et al. 2022;
https://science-cloud.hu/) which helped us achieve the results published in
this paper. B.Cs. acknowledges support from the Lendület Program LP2023-10 of
the Hungarian Academy of Sciences. C.A.P. acknowledges financial support from
the Spanish Ministry MICINN projects AYA2017-86389-P and PID2020-117493GB-I00.
Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions. SDSS-IV acknowledges support and resources from
the Center for High Performance Computing at the University of Utah. The SDSS
website is www.sdss.org. SDSS-IV is managed by the Astrophysical Research
Consortium for the Participating Institutions of the SDSS Collaboration
including the Brazilian Participation Group, the Carnegie Institution for
Science, Carnegie Mellon University, Center for Astrophysics — Harvard &
Smithsonian, the Chilean Participation Group, the French Participation Group,
Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli
Institute for the Physics and Mathematics of the Universe (IPMU) / University
of Tokyo, the Korean Participation Group, Lawrence Berkeley National
Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-
Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik
(MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE),
National Astronomical Observatories of China, New Mexico State University, New
York University, University of Notre Dame, Observatário Nacional / MCTI, The
Ohio State University, Pennsylvania State University, Shanghai Astronomical
Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma
de México, University of Arizona, University of Colorado Boulder, University
of Oxford, University of Portsmouth, University of Utah, University of
Virginia, University of Washington, University of Wisconsin, Vanderbilt
University, and Yale University.

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