# Detection of Na and K in the atmosphere of the hot Jupiter HAT-P-1b with
P200/DBSP

Guo Chen (陈果) CAS Key Laboratory of Planetary Sciences, Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, People’s Republic of
China  CAS Center for Excellence in Comparative Planetology, Hefei 230026,
People’s Republic of China  Hongchi Wang (王红池) CAS Key Laboratory of Radio
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, People’s Republic of China  Roy van Boekel Max-Planck-Institut für
Astronomie, Königstuhl 17, 69117 Heidelberg, Germany  Enric Pallé Instituto de
Astrofísica de Canarias, Vía Láctea s/n, E-38205 La Laguna, Tenerife, Spain
Departamento de Astrofísica, Universidad de La Laguna, E-38206 La Laguna,
Tenerife, Spain

###### Abstract

We present a new optical transmission spectrum of the hot Jupiter HAT-P-1b
based on two transits observed with the Double Spectrograph (DBSP) on the
Palomar 200-inch (P200) telescope. The DBSP transmission spectrum, covering a
wavelength range from 3250 to 10007 Å, is consistent with that observed with
the Hubble Space Telescope (HST), but the former has a finer spectral
resolution. The DBSP spectrum alone reveals the presence of a pressure
broadened line wing for Na, the line cores for both Na and K, and tentative
evidence for H2O. We obtain consistent results from the spectral retrieval
analyses performed on the DBSP-only dataset and the DBSP, HST, and Spitzer
combined dataset. Our retrievals suggest a mostly clear atmosphere for
HAT-P-1b, with a cloud coverage of $22^{+5}_{-3}$% that is dominated by
enhanced haze. We derive subsolar abundances for Na, K, and C, and subsolar-
to-solar for O. Future observations with James Webb Space Telescope and
ground-based high-resolution spectrographs should be able to not only confirm
the presence of these species but also stringently constrain the formation and
migration pathways for HAT-P-1b.

Exoplanet atmospheres (487); Exoplanet atmospheric composition (2021);
Transmission spectroscopy (2133); Hot Jupiters (753); Exoplanets (498)

††facilities: Palomar 200-inch (DBSP)††software:  george (Ambikasaran et al.,
2015), batman (Kreidberg, 2015), emcee (Foreman-Mackey et al., 2013), corner
(Foreman-Mackey, 2016), PLATON (Zhang et al., 2019, 2020), PyMultiNest
(Buchner et al., 2014), Matplotlib (Hunter, 2007), TEPCat (Southworth, 2011),
VizieR (Ochsenbein et al., 2000)

##  1 Introduction

Observational characterization of exoplanet atmospheres has long been pursued
since the first discovery of non-transiting and transiting exoplanets around
main-sequence stars (Mayor & Queloz, 1995; Charbonneau et al., 2000, 2002;
Vidal-Madjar et al., 2003). With the continuous developments of transit
spectrophotometry, direct spectroscopy, and high-resolution Doppler
spectroscopy, abundant spectral features induced by atoms and molecules have
been detected in dozens of exoplanets (Madhusudhan, 2019). The ultrahot gas
giants are generally found to be dominated by ionized or neutral atoms with
inverted thermal profiles, while the cooler ones by molecules without
inversions (Stangret et al., 2022; Changeat et al., 2022).

Among the various species detected in exoplanet atmospheres, Na and K are
important to understand rainout process (Line et al., 2017; Mollière et al.,
2022), photoionization (Lavvas et al., 2014), radiative cooling (Huang et al.,
2017), and wind patterns (Seidel et al., 2020, 2021). Meanwhile, Na and K play
a crucial role in constraining the reference pressure levels (Welbanks &
Madhusudhan, 2019; Pinhas et al., 2019) and cloud properties (Kellogg et al.,
2017; Manjavacas et al., 2021) with their pressure broadened line wings. The
inference of pressure broadening is still rare (Nikolov et al., 2018; Chen et
al., 2018; Pearson et al., 2019; Chen et al., 2020; Alam et al., 2021; Ahrer
et al., 2022), which relies on high-quality transit spectrophotometry in the
optical.

HAT-P-1b is a classical hot Jupiter orbiting the secondary component of a G
type binary system (Bakos et al., 2007). With an inflated radius of 1.319
RJup, a relatively low mass of 0.525 MJup, and an equilibrium temperature of
1322 K (Nikolov et al., 2014), HAT-P-1b is expected to have an atmospheric
scale height of $H/R_{\star}=0.00078$ that can produce large amplitudes of
transmission spectral features in clear atmospheres. Located in a parameter
space similar to the hot Jupiters exhibiting pressure broadening (i.e.,
1200–1500 K, 0.2–0.6 MJup, $>$1.0 RJup; Chen et al., 2020), HAT-P-1b has a
high priority for the search of Na and K.

Indeed, several photometric and spectrophotometric campaigns have been
conducted to characterize HAT-P-1b’s atmospheric compositions (Wakeford et
al., 2013; Nikolov et al., 2014; Wilson et al., 2015; Montalto et al., 2015;
Sing et al., 2016; Todorov et al., 2019) and thermal structure (Todorov et
al., 2010; de Mooij et al., 2011). The transmission spectra acquired with the
Hubble space telescope (HST) show the presence of both H2O and Na (Wakeford et
al., 2013; Nikolov et al., 2014; Sing et al., 2016). In particular, Nikolov et
al. (2014) reported an excess absorption at Na (3.3$\sigma$) by comparing the
30 Å Na narrow band to the blue and red neighboring 600 Å broad bands. But it
is not confirmed in the ground-based observations (Montalto et al., 2015;
Todorov et al., 2019) due to limited spectrophotometric precision. On the
other hand, using the 12 Å tunable filters, Wilson et al. (2015) reported a
strong detection of K (4.3$\sigma$ at line wing and 6.1$\sigma$ at line core)
by comparing the line core and wing to two narrow passbands far outside the K
feature. However, such comparison is based on data taken on different dates
with distinct systematics and limited out-of-transit measurements.

In this paper, we report the detection of Na and K in the newly acquired
optical transmission spectrum of HAT-P-1b, based on uniformly spaced narrow
passbands around the Na and K wavelengths. We present the observation summary
in Section 2 and detail the data reduction in Section 3. We describe the
light-curve modeling process and derive the transmission spectra in Section 4.
We perform Bayesian spectral retrieval analyses on the transmission spectra in
Section 5. We compare our results with literature and interpret HAT-P-1b’s
atmosphere in Section 6. Finally, we present our conclusions in Section 7.

Table 1: Observation summary Transit | Date | Start | End | Dichroic | Channel | $t_{\mathrm{exp}}$ | Airmass | Seeing-limited | Weather
---|---|---|---|---|---|---|---|---|---
# | UT | UT | UT |  |  | (sec) |  |  $\Delta\lambda$ at $\lambda$ (Å) |
1 | 2012-09-15 | 04:29 | 09:09 | D52 | Blue | 60 | 1.18-1.00-1.10 | 5.9 (4518) | mostly clear
1 | 2012-09-15 | 04:29 | 09:09 | D52 | Red | 60 | 1.18-1.00-1.10 | 8.1 (7699) | mostly clear
2 | 2016-07-27 | 05:09 | 10:17 | D68 | Blue | 30 | 2.12-1.01-1.01 | 3.8 (5893) | mostly clear
2 | 2016-07-27 | 05:09 | 10:19 | D68 | Red | 180 | 2.12-1.01-1.01 | 3.6 (7699) | mostly clear
Figure 1: Example stellar spectra of HAT-P-1 (dark colored) and its reference
star (light colored). Two transits were observed by P200/DBSP with the D52 and
D68 dichroics, respectively. Vertical dotted lines indicate the borders of
adopted spectroscopic passbands. The blue and red regions show the adopted
wavelength ranges to calculate the white light curves for Transit 1, while
green and purple for Transit 2, respectively. The spectral resolution has been
degraded for display purpose.

##  2 Observations

We observed two transits of HAT-P-1b using the Double Spectrograph (DBSP; Oke
& Gunn, 1982) installed on the Palomar 200-inch (P200) Hale telescope in
California, USA. The target star HAT-P-1 (BD+37 4734B, $G\mathrm{mag}=10.2$;
Gaia Collaboration et al., 2021) and a reference star (BD+37 4734A,
$G\mathrm{mag}=9.6$, 11$\farcs$3 from HAT-P-1; Gaia Collaboration et al.,
2021) were simultaneously monitored by a 128′′-long and 10′′-wide slit. After
the slit, the light was splitted into the blue and red channels with a
dichroic, and then dispersed by two gratings and recorded by two
2048$\times$4096 CCDs separately. The blue and red CCDs have a pixel scale of
0$\farcs$389 and 0$\farcs$293, respectively. A summary of the two transit
observations is given in Table 1.

The first transit was observed on the night of 2012 September 14 (Transit 1).
The dichroic D52 was used to split light at 5200 Å, along with the 600/4000
(i.e., 600 lines mm-1 blazed at 4000 Å) grating for the blue channel and the
316/7500 grating for the red channel, resulting in an average dispersion of
1.1 Å (blue) and 1.5 Å (red) per pixel. The order-blocking filter RG610 was
employed in the red channel. The observations were conducted continuously for
4.7 hours, covering the complete transit event and $\sim$50 minutes for both
pre-ingress and post-egress out-of-transit. The weather condition was mostly
clear, but the seeing was moderately variable during the ingress. We measured
a range of 1$\farcs$3–2$\farcs$7 and a median value of 1$\farcs$6 at around
7500 Å for the FWHM of the stellar spatial profiles, indicating a seeing-
limited spectral resolution of 6.8–13.7 Å. We adopted an exposure time of 60
seconds for both blue and red channels, and collected a total of 205 (blue)
and 201 (red) frames. The spectra of FeAr and HeNeAr arc lamps were acquired
through a 1′′-wide slit for subsequent wavelength calibrations.

The second transit was observed on the night of 2016 July 26 (Transit 2). The
dichroic D68 was used. The instrument setup team inadvertently swapped the
requested blue and red gratings. Consequently, the observations were conducted
with 600/10000 for the blue and 600/4000 for the red, resulting in an average
dispersion of 1.1 Å (blue) and 0.8 Å (red) per pixel. The incorrect placement
of gratings strongly reduced the photon count rate in the red channel (see
Figure 1). Both channels were left clear, without any order-blocking filter.
The observations lasted for 5.2 hours, covering the complete transit event
along with $\sim$55 minutes of pre-ingress and $\sim$65 minutes of post-
egress. The weather condition was mostly clear, and the seeing varied between
1$\farcs$2 and 1$\farcs$6 with a median value of 1$\farcs$4 at around 7500 Å,
corresponding to a seeing-limited resolution of 3.4–4.5 Å. We adopted an
exposure time of 30 seconds for the blue channel and 180 seconds for the red
channel, and collected a total of 344 (blue) and 88 (red) frames. The spectra
of FeAr and HeNeAr arc lamps were acquired through a 0$\farcs$5-wide slit.

Figure 2: White light curves for the two transits observed by P200/DBSP. The
left panel presents the raw flux time series of the target and reference
stars. The three right panels present the reference-calibrated light curves:
before systematics correction, after systematics correction, and best-fitting
residuals.

##  3 Data reduction

We reduced the P200/DBSP raw data based on our established long-slit transit
spectroscopy pipeline, which was first developed to reduce the Gran Telescopio
Canarias (GTC) long-slit spectroscopic data (e.g., Chen et al., 2017b, a,
2018, 2020, 2021a) and then adapted to reduce the DBSP data in Chen et al.
(2021b). For completeness, we give below a brief summary of our data reduction
procedures.

The two-dimensional (2D) raw spectral images were calibrated for overscan,
bias, flat field, sky, and cosmic rays. The one-dimensional (1D) spectra were
extracted using the APALL task of IRAF (Tody, 1986, 1993) with the optimal
extraction algorithm (Horne, 1986). The wavelength solutions were constructed
from the arc lines using the fourth-order B-spline function, implemented by
the IDL script bspline_iterfit.pro written by D. Schlegel and S. Burles. The
spectral drifts over time were determined by measuring stellar line centers in
each spectrum, and the misalignments between target and reference stars were
calculated through the cross-correlation of telluric absorption lines. The
wavelength solutions were shifted to match the rest-frame air values to
correct for the offsets resulting from any imperfect alignment to the slit
center. The 1D spectra were kept in the original pixel space without
linearization, while the drifts and misalignments were corrected in the
wavelength solutions. To create the white and spectroscopic light curves, the
mid-exposure time was extracted and converted to Barycentric Julian Dates in
Barycentric Dynamical Time ($\mathrm{BJD}_{\mathrm{TDB}}$; Eastman et al.,
2010), and the flux was then integrated within a certain pixel range which was
converted from the requested bandpass using the wavelength solutions.

In contrast to our previous studies where we selected the best aperture radius
among a wide range of sizes, here we restrained ourselves from large aperture
radii due to the small separation of 11.3′′ between the target and reference
stars. For both observing runs, we adopted an aperture radius of 4 pixels in
the blue channel and 5.5 pixels in the red channel, equivalent to roughly
1.6′′ for both channels. This choice was a compromise between light-curve
scatter minimization and dilution minimization. Larger aperture radii would
increase the reference star’s flux inside the target star’s aperture, and vice
versa, which would result in a diluted transit signal in the target light
curve and a leaked transit signal in the reference light curve.

To estimate the dilution, we adopted an approach similar to that of Todorov et
al. (2019), in which we mirrored the undiluted part of the diluting star’s PSF
to remove the diluting star and performed a simple spectral extraction using
the same spectral trace of the original star. Due to seeing variation, the
dilution is expected to show temporal variation. When the planet was fully
inside the stellar disk, we measured a dilution to target flux of $<$0.04%
(D52-blue), $<$0.16% (D52-red), $<$0.08% (D68-blue), $<$0.03% (D68-red) for
the white light curves. The dilution was relatively flat in most wavelengths
except for $\lambda>9500$ Å, where a steep rise occurred and the maximum
dilution appeared at the longest wavelengths ($<$0.5% for D52-red and $<$0.2%
for D68-red) in the exposure with the maximum seeing. We experimented with and
without dilution correction in the light curve creation to inspect its impact
on the transmission spectrum. We found that such correction would cause a
typical change in transit depth at 0.14$\sigma$, much smaller than the
1$\sigma$ uncertainty but with noisier behavior. Therefore, we did not perform
the dilution correction on our data.

Figure 1 gives an example of the extracted 1D stellar spectra for the target
and reference stars. To create the white light curves, the target and
reference fluxes were individually integrated in the wavelength ranges of
3250–5018 Å (D52-blue), 6168–10007 Å (D52-red), 4168–6768 Å (D68-blue), and
6778–10007 Å (D68-red), respectively. The target flux time series were then
divided by that of the reference and then normalized by the out-of-transit
level. To create the spectroscopic light curves, similar procedures were
performed in the designed narrow bands. The full wavelength range was divided
into 38 narrow bands, most of which had a width of 200 Å while two groups of
five bands around the Na and K wavelengths had a width of 30 Å and 50 Å,
respectively. The four white light curves are shown in Figure 2, and the
spectroscopic light curves are shown in Appendix A.

Table 2: Priors and posteriors of the parameter estimation for white light curves.  Parameter | Prior | Posterior estimate
---|---|---
$i$ [∘] | $\mathcal{U}(80,90)$ | $85.652^{+0.058}_{-0.058}$
$a/R_{\star}$ | $\mathcal{U}(7,12)$ | $9.864^{+0.069}_{-0.069}$
|  | Transit 1 | Transit 2
$T_{\mathrm{mid}}$ [$\mathrm{BJD}_{\mathrm{TDB}}-2450000$] | $\mathcal{U}(6185.770,6185.810)$ | $6185.79050^{+0.00015}_{-0.00015}$ | –
$T_{\mathrm{mid}}$ [$\mathrm{BJD}_{\mathrm{TDB}}-2450000$] | $\mathcal{U}(7596.805,7596.845)$ | – | $7596.82464^{+0.00016}_{-0.00016}$
|  | D52-blue | D52-red | D68-blue | D68-red
$R_{\mathrm{p}}/R_{\star}$ | $\mathcal{U}(0.07,0.17)$ | $0.1189^{+0.0008}_{-0.0008}$ | $0.1171^{+0.0015}_{-0.0015}$ | $0.1164^{+0.0014}_{-0.0014}$ | $0.1182^{+0.0013}_{-0.0013}$
$\sigma_{\mathrm{j}}$ [$10^{-6}$] | $\mathcal{U}(0.1,5000)$ | $417^{+28}_{-28}$ | $341^{+20}_{-20}$ | $459^{+25}_{-25}$ | $186^{+21}_{-21}$
$\ln A$ | $\mathcal{U}(-10,-1)$ | $-6.2^{+0.6}_{-0.6}$ | $-7.2^{+0.7}_{-0.6}$ | $-7.8^{+0.4}_{-0.3}$ | $-6.7^{+0.8}_{-0.6}$
$\ln\tau_{t}$ | $\mathcal{U}(-6,5)$ | $1.4^{+2.3}_{-1.5}$ | $-1.8^{+0.6}_{-0.5}$ | $0.9^{+2.7}_{-2.5}$ | $-0.7^{+0.8}_{-0.8}$
$\ln\tau_{x}$ | $\mathcal{U}(-5,5)$ | $4.0^{+0.6}_{-0.9}$ | $3.9^{+0.8}_{-1.2}$ | $0.2^{+0.7}_{-0.6}$ | $2.1^{+0.8}_{-0.7}$
$\ln\tau_{y}$ | $\mathcal{U}(-5,5)$ | $3.8^{+0.8}_{-1.0}$ | $2.9^{+1.3}_{-1.1}$ | $1.0^{+0.6}_{-0.6}$ | $3.1^{+1.1}_{-0.9}$
$\ln\tau_{s}$ | $\mathcal{U}(-5,5)$ | $2.4^{+0.6}_{-0.6}$ | $2.2^{+0.7}_{-0.8}$ | $2.0^{+0.4}_{-0.4}$ | $3.3^{+0.9}_{-0.8}$
$u_{1}$ | $\mathcal{N}(0.607,0.063^{2})$ | $0.59^{+0.04}_{-0.04}$ | – | – | –
$u_{2}$ | $\mathcal{N}(0.198,0.048^{2})$ | $0.20^{+0.04}_{-0.04}$ | – | – | –
$u_{1}$ | $\mathcal{N}(0.281,0.036^{2})$ | – | $0.27^{+0.03}_{-0.03}$ | – | –
$u_{2}$ | $\mathcal{N}(0.294,0.018^{2})$ | – | $0.29^{+0.02}_{-0.02}$ | – | –
$u_{1}$ | $\mathcal{N}(0.410,0.047^{2})$ | – | – | $0.38^{+0.03}_{-0.03}$ | –
$u_{2}$ | $\mathcal{N}(0.286,0.028^{2})$ | – | – | $0.28^{+0.03}_{-0.03}$ | –
$u_{1}$ | $\mathcal{N}(0.256,0.033^{2})$ | – | – | – | $0.25^{+0.03}_{-0.03}$
$u_{2}$ | $\mathcal{N}(0.290,0.016^{2})$ | – | – | – | $0.29^{+0.02}_{-0.02}$

##  4 Light-curve analysis

As in our previous work (Chen et al., 2018, 2020, 2021b, 2021a), we treated
the observed light curves as Gaussian processes (GP; Rasmussen & Williams,
2006), which was first introduced to model transmission spectroscopy by Gibson
et al. (2012). Both white and spectroscopic light curves are expected to be
composed of the transit signal and correlated systematics. The python package
george (Ambikasaran et al., 2015) was employed to implement the GP, where the
transit model was adopted as the mean function and the Matérn $\nu=3/2$ kernel
function was adopted as the GP covariance matrix.

The transit model was implemented by batman (Kreidberg, 2015) with the
quadratic limb-darkening law, which was parameterized by orbital inclination
($i$), scaled semi-major axis ($a/R_{\star}$), planet-to-star radius ratio
($R_{\mathrm{p}}/R_{\star}$), mid-transit time ($T_{\mathrm{mid}}$), and limb-
darkening coefficients ($u_{1}$, $u_{2}$). The orbital period ($P$) was fixed
to 4.46529976 d from Nikolov et al. (2014), while the eccentricity was fixed
to zero.

For the GP covariance matrix, multiple state vectors were considered as the
input variables, including time ($t$), spectral drifts ($x$), spatial drifts
($y$), and seeing ($s$; as represented by spatial FWHM). The latter three have
been standardized, i.e., subtracted by the mean value and then divided by the
standard deviation. The associated free parameters were the covariance
amplitude ($A$) and multiple correlation length scales ($\tau_{k}$, where
$k=\\{t,x,y,s\\}$). To account for potential underestimation of white noise, a
free parameter $\sigma_{\mathrm{j}}$ was added in quadrature to the propagated
photon-noise dominated flux uncertainties.

During parameter estimation, uniform or log-uniform priors were adopted for
all the parameters, except for the limb-darkening coefficients. Normal priors
were imposed on the limb-darkening coefficients, with the mean and width
values being prepared in advance, which were calculated from the ATLAS9
stellar atmosphere models using a python script written by Espinoza & Jordán
(2015). The stellar model grid with $T_{\star}=6000$ K, $\log g=4.5$, and
$\mathrm{[Fe/H]}=0.0$ was used to derive the mean values, while the grids with
$T_{\star}=5750$ K and $T_{\star}=6250$ K were used to calculate a mean
difference from that with $T_{\star}=6000$ K as the width values.

The posterior distributions of free parameters were explored by the affine-
invariant Markov chain Monte Carlo (MCMC) as implemented by emcee (Foreman-
Mackey et al., 2013). When model comparison was necessary, the Bayesian
multimodal nested sampling algorithm (Feroz et al., 2009) was applied using
PyMultiNest (Buchner et al., 2014).

###  4.1 White light curves

We jointly fitted the four white light curves, which shared the same values of
$i$ and $a/R_{\star}$ for all and the same values of $T_{\mathrm{mid}}$ for
the same transit. For both transits, we adopted all four inputs {$t$, $x$,
$y$, $s$} in the GP covariance matrix, which showed the highest Bayesian
evidence as calculated by PyMultiNest among the experiments with either single
input or different combinations of them. We used emcee to explore the
posterior distributions of the 40 free parameters. Three runs of 120 walkers
were performed, with the first two in 1000 steps for initial burn-in and the
third in 50000 steps (but thinned every ten) for final production.

Figure 2 shows the best-fit light-curve models compared to the observations.
The root mean square (rms) of the best-fit light-curve residuals reach 448,
333, 484, 182 parts per million (ppm), for D52-blue, D52-red, D68-blue,
D68-red, respectively, which correspond to 2.32$\times$, 4.72$\times$,
2.42$\times$, 2.28$\times$ photon noise. Table 2 gives the priors and
posteriors for the free parameters in the joint analysis of white light
curves. Our derived values of $i$ and $a/R_{\star}$ agree well with those of
Nikolov et al. (2014), i.e., $i=85\fdg 634\pm 0\fdg 056$ and
$a/R_{\star}=9.853\pm 0.071$.

Table 3: Mid-transit times of HAT-P-1b.

Epoch | Mid-transit | O$-$C | Reference
---|---|---|---
| ($\mathrm{BJD}_{\mathrm{TDB}}-2450000$) | (sec) |
$-$517 | 3979.930708 $\pm$ 0.000690 |  $-$121.9 | 2
$-$516 | 3984.397768 $\pm$ 0.009000 | 30.2 | 1
$-$515 | 3988.862738 $\pm$ 0.000760 | 1.8 | 2
$-$513 | 3997.792768 $\pm$ 0.000540 |  $-$47.4 | 2
$-$513 | 3997.794248 $\pm$ 0.000470 | 80.4 | 2
$-$511 | 4006.724028 $\pm$ 0.000590 | 9.7 | 2
$-$509 | 4015.654147 $\pm$ 0.001070 |  $-$31.8 | 2
$-$497 | 4069.238716 $\pm$ 0.002900 | 52.3 | 2
$-$431 | 4363.946769 $\pm$ 0.000910 |  $-$96.5 | 3
$-$427 | 4381.809249 $\pm$ 0.001250 | 14.2 | 3
$-$48 | 6074.157370 $\pm$ 0.000180 |  $-$23.4 | 4
$-$47 | 6078.623070 $\pm$ 0.000180 | 11.2 | 4
$-$39 | 6114.345370 $\pm$ 0.000200 | 2.8 | 4
$-$30 | 6154.532530 $\pm$ 0.000180 |  $-$43.6 | 5
$-$23 | 6185.790501 $\pm$ 0.000153 | 31.9 | 8
$-$22 | 6190.255420 $\pm$ 0.000180 |  $-$1.0 | 4
$-$19 | 6203.649839 $\pm$ 0.000950 |  $-$128.8 | 6
$-$15 | 6221.512610 $\pm$ 0.000220 | 7.0 | 5
$-$10 | 6243.839084 $\pm$ 0.000076 | 5.0 | 7
233aaThis epoch was not used in the linear regression. It was listed here for completeness. | 7328.907659 $\pm$ 0.000034 | 71.2 | 7
293 | 7596.824638 $\pm$ 0.000163 |  $-$15.0 | 8
549 | 8739.942711 $\pm$ 0.000667 | 103.3 | 9
550 | 8744.407173 $\pm$ 0.001247 | 31.0 | 9
551 | 8748.873683 $\pm$ 0.000769 | 135.6 | 9
552 | 8753.337067 $\pm$ 0.000697 |  $-$30.0 | 9
553 | 8757.802413 $\pm$ 0.000708 |  $-$25.9 | 9
554 | 8762.267168 $\pm$ 0.000593 |  $-$73.0 | 9

Note. — The zero epoch and orbital period are revised as
$T_{0}(\mathrm{BJD}_{\mathrm{TDB}})=2456288.492023\pm 0.000063$ and
$P=4.46529962\pm 0.00000039$ d, respectively.

References. — 1. Bakos et al. (2007); 2. Winn et al. (2007); 3. Johnson et al.
(2008); 4. Nikolov et al. (2014); 5. Montalto et al. (2015); 6. Turner et al.
(2016); 7. Todorov et al. (2019); 8. This work (DBSP); 9. This work (TESS).

Figure 3: Residuals of the mid-transit times after a linear ephemeris
regression. For clarity, the epochs are grouped into four rows. The red line
and shaded region present the best-fit model and 1$\sigma$ confidence region
from this work, while the blue shows that derived from Nikolov et al. (2014).

####  4.1.1 Update of transit ephemeris

With our two newly measured transit timings, we attempted to revise the
transit ephemeris of HAT-P-1b. We collected other transit timing measurements
from Bakos et al. (2007), Winn et al. (2007), Johnson et al. (2008), Nikolov
et al. (2014), Montalto et al. (2015), Turner et al. (2016), and Todorov et
al. (2019), and converted them into $\mathrm{BJD}_{\mathrm{TDB}}$ using the
online applet111https://astroutils.astronomy.osu.edu/time/ developed by
Eastman et al. (2010) if a different time standard was adopted. We did not
include the transit timings of Wilson et al. (2015) since the reported best-
fit values did not have sufficient significant digits. We also excluded the
transit timing measured by Gemini GMOS B600 presented in Todorov et al.
(2019), which was derived from a light curve with strong systematics and the
uncertainty was likely underestimated.

We noticed that HAT-P-1 was observed by the Transiting Exoplanet Survey
Satellite (TESS; Ricker et al., 2014) in Sector 16 between 2019 September 12
and October 6. The data were collected in full frame images (FFIs) with a
cadence of 30 minutes. In order to expand the time span and update the transit
ephemeris, we downloaded the light curve produced by the MIT Quick Look
Pipeline (Huang et al., 2020a, b). For the subsequent timing measurements, we
adopted the detrended flux (labeled as KSPSAP_FLUX). For each transit, we
extracted an individual light curve in a window of three times transit
duration on both sides of each expected mid-transit time.

The TESS light curves were modeled in an approach similar to DBSP. In the
transit model, we fixed the values of $i$ and $a/R_{\star}$ to those listed in
Table 2, and adopted the nonlinear limb-darkening law with the coefficients
fixed to pre-calculated values ($c_{1}=0.5404$, $c_{2}=0.0740$,
$c_{3}=0.2020$, $c_{4}=-0.1518$). The radius ratio was fitted with a normal
prior $\mathcal{N}(0.11802,0.00018^{2})$. A dilution parameter was freely
fitted to correct for potential imperfect dilution correction in the MIT Quick
Look Pipeline. For the GP covariance matrix, only time was adopted as the
single input. The long cadence has been considered by first generating a
super-sampled model and then binning it into current cadence.

Table 4.1 gives the full list of literature transit timings, two DBSP timings,
and six TESS timings. We employed emcee to perform a linear regression to the
transit epochs ($E$) and timings ($T_{\mathrm{C}}$) to derive the zero epoch
timing ($T_{0}$) and orbital period ($P$): $T_{\mathrm{C}}=T_{0}+EP$. We used
a free parameter to rescale the timing uncertainties to account for potential
underestimation. The zero epoch was chosen as the one that minimized the
uncertainty of $T_{0}$. Finally, we derived

$\displaystyle T_{0}$ $\displaystyle=$ $\displaystyle 2456288.492023\pm
0.000063~{}\mathrm{BJD}_{\mathrm{TDB}},$ (1) $\displaystyle P$
$\displaystyle=$ $\displaystyle 4.46529962\pm 0.00000039~{}\mathrm{d},$ (2)

which are consistent with that of Nikolov et al. (2014) but with smaller
uncertainties. The derived uncertainty rescaling factor is $1.3\pm 0.2$.
Figure 3 shows the comparison between our newly derived transit ephemeris and
that of Nikolov et al. (2014).

Figure 4: Top panel: comparison between the transmission spectra acquired by P200/DBSP in two transits. Bottom panel: comparison between the combined P200/DBSP transmission spectrum and the HST/STIS transmission spectrum. The vertical dashed lines mark the locations of the Na and K doublets. Figure 5: Ultra-narrow band transmission spectra around the Na (top) and K (bottom) lines. The cyan line and shaded regions show the median model and 1$\sigma$/2$\sigma$ confidence regions from the Bayesian spectral retrieval. Also shown for comparison are the 30 Å (Na) and 50 Å (K) bands in the full P200/DBSP spectrum. Table 4: Derived transmission spectrum of HAT-P-1b. $\lambda$ (Å) |  $u_{1}$ prior |  $u_{2}$ prior | $R_{\mathrm{p}}/R_{\star}$ | $R_{\mathrm{p}}/R_{\star}$ |  | RMS/Photon noise
---|---|---|---|---|---|---
|  |  | Weighted | Transit 1 | Transit 2 |  | Transit 1 | Transit 2
3250–4018 | $\mathcal{N}(0.735,0.095^{2})$ | $\mathcal{N}(0.108,0.083^{2})$ | $0.1194^{+0.0011}_{-0.0012}$ | $0.1194^{+0.0011}_{-0.0012}$ | – |  | 1.41 | –
4018–4418 | $\mathcal{N}(0.677,0.071^{2})$ | $\mathcal{N}(0.148,0.059^{2})$ | $0.1191^{+0.0006}_{-0.0006}$ | $0.1191^{+0.0006}_{-0.0006}$ | – |  | 1.38 | –
4418–4618 | $\mathcal{N}(0.584,0.059^{2})$ | $\mathcal{N}(0.220,0.042^{2})$ | $0.1169^{+0.0008}_{-0.0008}$ | $0.1169^{+0.0008}_{-0.0008}$ | – |  | 1.37 | –
4618–4818 | $\mathcal{N}(0.538,0.058^{2})$ | $\mathcal{N}(0.247,0.039^{2})$ | $0.1157^{+0.0009}_{-0.0009}$ | $0.1159^{+0.0010}_{-0.0010}$ | $0.1148^{+0.0024}_{-0.0024}$ |  | 1.52 | 1.17
4818–5018 | $\mathcal{N}(0.482,0.060^{2})$ | $\mathcal{N}(0.275,0.040^{2})$ | $0.1152^{+0.0014}_{-0.0014}$ | $0.1155^{+0.0018}_{-0.0018}$ | $0.1149^{+0.0021}_{-0.0021}$ |  | 1.19 | 1.16
5018–5218 | $\mathcal{N}(0.483,0.057^{2})$ | $\mathcal{N}(0.259,0.038^{2})$ | $0.1161^{+0.0019}_{-0.0019}$ | – | $0.1161^{+0.0019}_{-0.0019}$ |  | – | 1.20
5218–5418 | $\mathcal{N}(0.451,0.050^{2})$ | $\mathcal{N}(0.273,0.031^{2})$ | $0.1169^{+0.0017}_{-0.0017}$ | – | $0.1169^{+0.0017}_{-0.0017}$ |  | – | 1.26
5418–5618 | $\mathcal{N}(0.426,0.049^{2})$ | $\mathcal{N}(0.283,0.029^{2})$ | $0.1170^{+0.0023}_{-0.0020}$ | – | $0.1170^{+0.0023}_{-0.0020}$ |  | – | 1.32
5618–5818 | $\mathcal{N}(0.405,0.046^{2})$ | $\mathcal{N}(0.290,0.026^{2})$ | $0.1181^{+0.0020}_{-0.0022}$ | – | $0.1181^{+0.0020}_{-0.0022}$ |  | – | 1.22
5818–5848 | $\mathcal{N}(0.389,0.046^{2})$ | $\mathcal{N}(0.299,0.026^{2})$ | $0.1204^{+0.0018}_{-0.0017}$ | – | $0.1204^{+0.0018}_{-0.0017}$ |  | – | 1.09
5848–5878 | $\mathcal{N}(0.387,0.045^{2})$ | $\mathcal{N}(0.297,0.025^{2})$ | $0.1183^{+0.0027}_{-0.0028}$ | – | $0.1183^{+0.0027}_{-0.0028}$ |  | – | 1.04
5878–5908 | $\mathcal{N}(0.392,0.046^{2})$ | $\mathcal{N}(0.286,0.028^{2})$ | $0.1232^{+0.0008}_{-0.0007}$ | – | $0.1232^{+0.0008}_{-0.0007}$ |  | – | 1.11
5908–5938 | $\mathcal{N}(0.382,0.045^{2})$ | $\mathcal{N}(0.298,0.025^{2})$ | $0.1206^{+0.0020}_{-0.0022}$ | – | $0.1206^{+0.0020}_{-0.0022}$ |  | – | 1.03
5938–5968 | $\mathcal{N}(0.379,0.045^{2})$ | $\mathcal{N}(0.299,0.025^{2})$ | $0.1173^{+0.0016}_{-0.0013}$ | – | $0.1173^{+0.0016}_{-0.0013}$ |  | – | 1.04
5968–6168 | $\mathcal{N}(0.370,0.043^{2})$ | $\mathcal{N}(0.297,0.023^{2})$ | $0.1187^{+0.0018}_{-0.0018}$ | – | $0.1187^{+0.0018}_{-0.0018}$ |  | – | 1.33
6168–6368 | $\mathcal{N}(0.355,0.042^{2})$ | $\mathcal{N}(0.297,0.022^{2})$ | $0.1181^{+0.0009}_{-0.0009}$ | $0.1175^{+0.0014}_{-0.0014}$ | $0.1187^{+0.0013}_{-0.0013}$ |  | 1.58 | 1.19
6368–6568 | $\mathcal{N}(0.322,0.043^{2})$ | $\mathcal{N}(0.309,0.021^{2})$ | $0.1179^{+0.0008}_{-0.0008}$ | $0.1174^{+0.0009}_{-0.0009}$ | $0.1191^{+0.0014}_{-0.0014}$ |  | 1.59 | 1.23
6568–6768 | $\mathcal{N}(0.311,0.041^{2})$ | $\mathcal{N}(0.308,0.021^{2})$ | $0.1179^{+0.0011}_{-0.0011}$ | $0.1182^{+0.0014}_{-0.0014}$ | $0.1174^{+0.0019}_{-0.0019}$ |  | 1.55 | 1.15
6768–6968 | $\mathcal{N}(0.317,0.039^{2})$ | $\mathcal{N}(0.296,0.020^{2})$ | $0.1166^{+0.0010}_{-0.0010}$ | $0.1179^{+0.0016}_{-0.0016}$ | $0.1157^{+0.0013}_{-0.0013}$ |  | 1.58 | 1.15
6968–7168 | $\mathcal{N}(0.305,0.038^{2})$ | $\mathcal{N}(0.295,0.019^{2})$ | $0.1162^{+0.0010}_{-0.0010}$ | $0.1167^{+0.0013}_{-0.0013}$ | $0.1156^{+0.0016}_{-0.0016}$ |  | 1.39 | 1.10
7168–7368 | $\mathcal{N}(0.295,0.036^{2})$ | $\mathcal{N}(0.293,0.018^{2})$ | $0.1168^{+0.0011}_{-0.0011}$ | $0.1169^{+0.0017}_{-0.0017}$ | $0.1168^{+0.0015}_{-0.0015}$ |  | 1.54 | 1.31
7368–7557 | $\mathcal{N}(0.283,0.035^{2})$ | $\mathcal{N}(0.292,0.017^{2})$ | $0.1169^{+0.0010}_{-0.0010}$ | $0.1161^{+0.0014}_{-0.0014}$ | $0.1179^{+0.0015}_{-0.0015}$ |  | 1.60 | 1.31
7557–7607 | $\mathcal{N}(0.278,0.035^{2})$ | $\mathcal{N}(0.293,0.017^{2})$ | $0.1182^{+0.0013}_{-0.0013}$ | $0.1175^{+0.0014}_{-0.0014}$ | $0.1213^{+0.0030}_{-0.0030}$ |  | 1.32 | 1.12
7607–7657 | $\mathcal{N}(0.275,0.034^{2})$ | $\mathcal{N}(0.293,0.016^{2})$ | $0.1175^{+0.0012}_{-0.0012}$ | $0.1173^{+0.0013}_{-0.0013}$ | $0.1191^{+0.0033}_{-0.0033}$ |  | 1.21 | 1.46
7657–7707 | $\mathcal{N}(0.272,0.034^{2})$ | $\mathcal{N}(0.292,0.016^{2})$ | $0.1188^{+0.0013}_{-0.0013}$ | $0.1194^{+0.0016}_{-0.0016}$ | $0.1178^{+0.0022}_{-0.0022}$ |  | 1.13 | 1.16
7707–7757 | $\mathcal{N}(0.271,0.034^{2})$ | $\mathcal{N}(0.291,0.016^{2})$ | $0.1179^{+0.0015}_{-0.0015}$ | $0.1168^{+0.0017}_{-0.0017}$ | $0.1207^{+0.0029}_{-0.0029}$ |  | 1.21 | 1.06
7757–7807 | $\mathcal{N}(0.266,0.035^{2})$ | $\mathcal{N}(0.294,0.016^{2})$ | $0.1163^{+0.0012}_{-0.0012}$ | $0.1171^{+0.0019}_{-0.0019}$ | $0.1157^{+0.0016}_{-0.0016}$ |  | 1.12 | 1.07
7807–8007 | $\mathcal{N}(0.263,0.035^{2})$ | $\mathcal{N}(0.292,0.016^{2})$ | $0.1171^{+0.0011}_{-0.0011}$ | $0.1170^{+0.0020}_{-0.0020}$ | $0.1171^{+0.0013}_{-0.0013}$ |  | 1.59 | 1.23
8007–8207 | $\mathcal{N}(0.256,0.035^{2})$ | $\mathcal{N}(0.291,0.016^{2})$ | $0.1175^{+0.0010}_{-0.0010}$ | $0.1172^{+0.0013}_{-0.0013}$ | $0.1178^{+0.0014}_{-0.0014}$ |  | 1.53 | 1.21
8207–8407 | $\mathcal{N}(0.248,0.034^{2})$ | $\mathcal{N}(0.289,0.016^{2})$ | $0.1175^{+0.0009}_{-0.0009}$ | $0.1177^{+0.0015}_{-0.0015}$ | $0.1174^{+0.0012}_{-0.0012}$ |  | 1.55 | 1.26
8407–8607 | $\mathcal{N}(0.233,0.032^{2})$ | $\mathcal{N}(0.286,0.014^{2})$ | $0.1170^{+0.0009}_{-0.0009}$ | $0.1167^{+0.0015}_{-0.0015}$ | $0.1172^{+0.0011}_{-0.0011}$ |  | 1.56 | 1.15
8607–8807 | $\mathcal{N}(0.226,0.032^{2})$ | $\mathcal{N}(0.287,0.015^{2})$ | $0.1179^{+0.0008}_{-0.0008}$ | $0.1169^{+0.0015}_{-0.0015}$ | $0.1182^{+0.0009}_{-0.0009}$ |  | 1.55 | 1.31
8807–9007 | $\mathcal{N}(0.224,0.031^{2})$ | $\mathcal{N}(0.287,0.014^{2})$ | $0.1176^{+0.0009}_{-0.0009}$ | $0.1174^{+0.0015}_{-0.0015}$ | $0.1177^{+0.0011}_{-0.0011}$ |  | 1.57 | 1.12
9007–9207 | $\mathcal{N}(0.221,0.030^{2})$ | $\mathcal{N}(0.284,0.013^{2})$ | $0.1176^{+0.0011}_{-0.0011}$ | $0.1175^{+0.0018}_{-0.0018}$ | $0.1177^{+0.0013}_{-0.0013}$ |  | 1.44 | 1.41
9207–9407 | $\mathcal{N}(0.208,0.030^{2})$ | $\mathcal{N}(0.288,0.013^{2})$ | $0.1182^{+0.0011}_{-0.0011}$ | $0.1174^{+0.0016}_{-0.0016}$ | $0.1188^{+0.0014}_{-0.0014}$ |  | 1.37 | 1.22
9407–9607 | $\mathcal{N}(0.205,0.030^{2})$ | $\mathcal{N}(0.287,0.013^{2})$ | $0.1177^{+0.0010}_{-0.0010}$ | $0.1185^{+0.0013}_{-0.0013}$ | $0.1163^{+0.0017}_{-0.0017}$ |  | 1.37 | 1.18
9607–9807 | $\mathcal{N}(0.216,0.025^{2})$ | $\mathcal{N}(0.275,0.010^{2})$ | $0.1194^{+0.0011}_{-0.0011}$ | $0.1189^{+0.0017}_{-0.0017}$ | $0.1197^{+0.0014}_{-0.0014}$ |  | 1.41 | 1.47
9807–10007 | $\mathcal{N}(0.210,0.025^{2})$ | $\mathcal{N}(0.277,0.010^{2})$ | $0.1180^{+0.0011}_{-0.0011}$ | $0.1177^{+0.0019}_{-0.0019}$ | $0.1182^{+0.0014}_{-0.0014}$ |  | 1.50 | 1.26

###  4.2 Spectroscopic light curves

We fitted the raw spectroscopic light curves individually, without applying
the divide-white method to remove the common-mode systematics as in our
previous work (e.g., Chen et al., 2021a). This was mainly because these DBSP
spectroscopic light curves came from four “passbands” with very different
response function (i.e., D52-blue, D52-red, D68-blue, D68-red; see Figure 1).
According to Jiang et al. (2022)’s benchmark test on transiting white dwarfs,
the divide-white method could potentially introduce an overall offset in the
transmission spectrum. With four white light curves from different passbands
in hand, it would be difficult to handle the “offset” problem if the divide-
white method was adopted.

For each spectroscopic light curve, we fixed the values of $i$, $a/R_{\star}$,
and $T_{\mathrm{mid}}$ to those listed in Table 2. We adopted the same four
inputs {$t$, $x$, $y$, $s$} in the GP covariance matrix as in the white light
curve analysis. Consequently, there were nine free parameters for each
spectroscopic light curve: $R_{\mathrm{p}}/R_{\star}$, $u_{1}$, $u_{2}$,
$\sigma_{\mathrm{j}}$, $\ln A$, $\ln\tau_{t}$, $\ln\tau_{x}$, $\ln\tau_{y}$,
$\ln\tau_{s}$. We configured emcee to perform three runs of 32 walkers, with
the first two runs in 1000 steps for initial burn-in and the third in 5000
steps for final production.

To produce the final transmission spectrum, we combined the four segments of
transmission spectra, and recorded in the overlapping wavelengths the weighted
mean along with the propagated uncertainty. Table 4 presents the adopted
priors for the two limb-darkening coefficients, the derived transmission
spectra, and the ratio between the rms of best-fit light-curve residuals and
photon noise. In general, we achieved an rms of 1.19–1.52$\times$,
1.12–1.60$\times$, 1.03–1.33$\times$, 1.06–1.47$\times$ photon noise in the
spectroscopic light curve analysis.

Figure 4 shows the four segments of DBSP transmission spectra and the final
DBSP transmission spectrum compared to the HST/STIS transmission spectrum
(taken from Sing et al., 2016). The DBSP segments are consistent with each
other in the common wavelength ranges. When compared to HST/STIS, the DBSP
spectrum agrees with the former in most wavelengths except for
$4000\leq\lambda\leq 5000$ Å. If we fit the DBSP spectrum to the HST/STIS
spectrum after the latter is linearly interpolated on the DBSP grid, with an
offset as the only free parameter, they would appear consistent with each
other at 0.3$\sigma$ confidence level ($\chi^{2}=29.7$ for 37 degrees of
freedom, hereafter dof). On the other hand, the DBSP spectrum is consistent
with a flat line only at 4.4$\sigma$ ($\chi^{2}=85.5$ for 37 dof), indicating
that the DBSP spectrum is not flat.

###  4.3 Ultra-narrow bands in search of Na and K

In addition to the 38 spectroscopic bands, we also created two groups of
ultra-narrow bands, with a bin width of $\sim$12 Å, centered at the Na and K
lines, respectively. The 12 Å bin width is slightly larger than the seeing-
limited resolutions (see Table 1), and can be directly compared to the results
of Wilson et al. (2015), in which the GTC tunable 12 Å filters were used. Our
Na group consisted of 15 uniform bins centered at 5893 Å, while our K group
consisted of 11 bins centered at 7665 Å and 7699 Å, of which nine bins had a
width of 12 Å and two bins in-between K doublet 11 Å.

In our observations, Na was only covered by D68-blue in Transit 2, while K was
covered by both transits. However, due to low count rate and sparse cadence of
D68-red in Transit 2, we decided to only use the D52-red data for the ultra-
narrow band analysis. In this case, we applied the divide-white method to
remove the common-mode systematics. We defined 5800-6000 Å and 7600-7800 Å as
the local “white” bands for Na and K, respectively, which were modeled in the
same way as in Section 4.2. The priors on limb-darkening coefficients were
$u_{1}\sim\mathcal{N}(0.385,0.045^{2})$ and
$u_{2}\sim\mathcal{N}(0.296,0.026^{2})$ for 5800-6000 Å and
$u_{1}\sim\mathcal{N}(0.271,0.034^{2})$ and
$u_{2}\sim\mathcal{N}(0.292,0.016^{2})$ for 7600-7800 Å. We derived
$R_{\mathrm{p}}/R_{\star}=0.1193\pm 0.0014$ for 5800-6000 Å and
$R_{\mathrm{p}}/R_{\star}=0.1176\pm 0.0010$ for 7600-7800 Å, respectively.

We derived the common-mode systematics by dividing the local “white” light
curves by their best-fit transit models, and then removed them from the 12
Å-bin Na and K ultra-narrow band light curves. Finally, we fitted the
corrected Na and K light curves in the same way as in Section 4.2 to derive
the Na and K transmission spectra. Figure 5 shows the derived Na and K
transmission spectra, which clearly hint a peak centered at Na and two peaks
centered at the doublet of K. The derived Na and K transmission spectra are
presented in the tables in Appendix A.

From Wilson et al. (2015)’s tunable filter transit observations, we can obtain
a radius difference of $\Delta R_{\mathrm{p}}/R_{\star}=0.0021\pm 0.0018$
between 7664.9 Å and 7582 Å, which were observed simultaneously by switching
between these two filters. Based on the DBSP 12 Å bin at 7665 Å and 50 Å bin
at 7582 Å, we derived a radius difference of $\Delta
R_{\mathrm{p}}/R_{\star}=0.0020\pm 0.0022$, fully consistent with that of
Wilson et al. (2015). However, we note that Wilson et al. (2015)’s significant
detection of K was based on the comparison between 7664.9 Å and the weighted
mean of 6792 Å and 8844 Å. Since the latter two were observed on very
different dates with distinct systematics, we did not include them in this
comparison.

Table 5: Parameter estimation for spectral retrievals assuming patchy clouds.  Parameter | Prior | Equilibrium chemistry |  | Free chemistry
---|---|---|---|---
|  | DBSP | DBSP+HST+Spitzer |  | DBSP | DBSP+HST+Spitzer
$R_{\mathrm{1bar}}$(RJ) | $\mathcal{U}(0.5,2)$ | $1.313^{+0.007}_{-0.009}$ | $1.298^{+0.006}_{-0.008}$ |  | $1.291^{+0.011}_{-0.012}$ | $1.256^{+0.009}_{-0.008}$
$T_{\mathrm{iso}}$(K) | $\mathcal{U}(500,1700)$ | $1082^{+175}_{-134}$ | $959^{+81}_{-40}$ |  | $1562^{+95}_{-158}$ | $1643^{+40}_{-110}$
$\log P_{\mathrm{cloud}}$(bar) | $\mathcal{U}(-6,2)$ | $-1.5^{+2.2}_{-2.8}$ | $-1.0^{+2.1}_{-2.4}$ |  | $-1.7^{+2.3}_{-2.5}$ | $-1.8^{+2.4}_{-2.0}$
$\log A_{\mathrm{RS}}$ | $\mathcal{U}(0,10)$ | $3.2^{+3.8}_{-2.4}$ | $7.8^{+1.1}_{-1.5}$ |  | $2.2^{+4.3}_{-1.6}$ | $8.3^{+1.0}_{-0.7}$
$\gamma$ | $\mathcal{U}(-20,2)$ | $-7.1^{+5.8}_{-7.6}$ | $-10.7^{+4.9}_{-5.8}$ |  | $-5.4^{+4.6}_{-7.0}$ | $-15.8^{+4.4}_{-2.7}$
$\phi$ | $\mathcal{U}(0,1)$ | $0.06^{+0.12}_{-0.05}$ | $0.21^{+0.07}_{-0.06}$ |  | $0.11^{+0.26}_{-0.08}$ | $0.22^{+0.05}_{-0.03}$
$\mathrm{C/O}$ | $\mathcal{U}(0.05,2)$ | $0.48^{+0.85}_{-0.29}$ | $0.25^{+0.23}_{-0.14}$ |  | – | –
$\log Z$(Z☉) | $\mathcal{U}(-1,3)$ | $0.52^{+0.45}_{-0.47}$ | $0.50^{+0.43}_{-0.55}$ |  | – | –
$\log X_{\mathrm{Na}}$ | $\mathcal{U}(-12,0)$ | – | – |  | $-4.3^{+1.6}_{-1.0}$ | $-6.3^{+0.5}_{-0.4}$
$\log X_{\mathrm{K}}$ | $\mathcal{U}(-12,0)$ | – | – |  | $-8.5^{+1.7}_{-1.8}$ | $-9.7^{+1.3}_{-1.4}$
$\log X_{\mathrm{TiO}}$ | $\mathcal{U}(-12,0)$ | – | – |  | $-11.2^{+0.7}_{-0.5}$ | $-11.5^{+0.4}_{-0.3}$
$\log X_{\mathrm{VO}}$ | $\mathcal{U}(-12,0)$ | – | – |  | $-10.9^{+0.9}_{-0.8}$ | $-11.1^{+0.7}_{-0.6}$
$\log X_{\mathrm{H_{2}O}}$ | $\mathcal{U}(-12,0)$ | – | – |  | $-3.1^{+0.7}_{-0.8}$ | $-3.2^{+0.3}_{-0.3}$
$\log X_{\mathrm{CH_{4}}}$ | $\mathcal{U}(-12,0)$ | – | – |  | $-6.9^{+3.5}_{-3.3}$ | $-8.5^{+2.4}_{-2.3}$
$\log X_{\mathrm{CO}}$ | $\mathcal{U}(-12,0)$ | – | – |  | – | $-7.6^{+2.9}_{-2.8}$
$\log X_{\mathrm{CO_{2}}}$ | $\mathcal{U}(-12,0)$ | – | – |  | – | $-9.1^{+1.9}_{-1.9}$
$\log X_{\mathrm{HCN}}$ | $\mathcal{U}(-12,0)$ | – | – |  | – | $-7.5^{+3.2}_{-2.9}$
$\log X_{\mathrm{NH_{3}}}$ | $\mathcal{U}(-12,0)$ | – | – |  | – | $-6.2^{+2.1}_{-3.8}$

##  5 Atmospheric spectral retrieval

We performed Bayesian spectral retrieval analyses on the transmission spectrum
of HAT-P-1b to constrain its atmospheric properties. We employed the forward
modeling module of the PLATON code (Zhang et al., 2019, 2020) and used
PyMultiNest to explore the Bayesian evidence ($\mathcal{Z}$) and posterior
distributions of the retrieval analyses. PLATON uses metallicity ($Z$) and the
carbon-to-oxygen ratio (C/O) to parameterize the equilibrium chemistry model
based on abundance grids computed by GGchem (Woitke et al., 2018), which
includes the same 34 atomic and molecular species as in Exo-Transmit (Kempton
et al., 2017) but excluding C2H6 and SH. In our retrieval analyses, we adopted
the opacities with a resolution of $\mathcal{R}=10000$ and assumed an
isothermal temperature ($T_{\mathrm{iso}}$) for the atmosphere. We used the
cloud-top pressure ($P_{\mathrm{cloud}}$) and the parametric form of
$\sigma=A_{\mathrm{RS}}\sigma_{0}\lambda^{-\gamma}$ ($A_{\mathrm{RS}}$: an
enhancement factor over nominal H2 Rayleigh scattering) to account for clouds
and hazes, which were assumed to occupy a fraction ($\phi$) of terminator
atmosphere while the rest clear as in MacDonald & Madhusudhan (2017). The
planet radius at a reference pressure of 1 bar ($R_{\mathrm{1bar}}$) was set
as a free parameter. The planet mass was fixed to 0.525 MJ and the stellar
radius was fixed to 1.174 R☉, taken from Nikolov et al. (2014).

We used 1000 live points in PyMultiNest, which typically resulted in an
uncertainty of $\sim$0.1 for $\ln\mathcal{Z}$. We considered different model
hypotheses in the following subsections. We adopted the criteria of Trotta
(2008) to assess the model preference, where
$\ln\mathcal{B}_{10}=\ln\mathcal{Z}_{1}-\ln\mathcal{Z}_{0}=1.0,2.5,5.0$ were
interpreted as the starting points of “weak”, “moderate”, and “strong”
evidence to prefer model hypothesis 1 over hypothesis 0. For the subsequent
retrieval analyses, the derived parameters are listed in Table 5, and their
associated joint posterior distributions are presented in Appendix B. The
statistics of the retrieval analyses are given in Table 6.

Table 6: Statistics from Bayesian spectral retrieval analyses.  Model | DBSP |  | DBSP+HST+Spitzer
---|---|---|---
| dof |  $\chi^{2}_{\mathrm{MAP}}$aa$\chi^{2}_{\mathrm{MAP}}$ stands for the $\chi^{2}$ of the maximum a posteriori (MAP) model. | $\ln\mathcal{Z}$ | $\Delta\ln\mathcal{Z}$ | FSbbFrequentist significance (FS) was converted from the Bayes factor $\mathcal{B}_{10}=\mathcal{Z}_{1}/\mathcal{Z}_{0}$ following Trotta (2008) and Benneke & Seager (2013). FS is only calculated for those with $|\Delta\mathcal{Z}|\geq 1.0$. A positive FS value indicates that the reference model is favored over the model in comparison. |  | dof |  $\chi^{2}_{\mathrm{MAP}}$aa$\chi^{2}_{\mathrm{MAP}}$ stands for the $\chi^{2}$ of the maximum a posteriori (MAP) model. | $\ln\mathcal{Z}$ | $\Delta\ln\mathcal{Z}$ | FSbbFrequentist significance (FS) was converted from the Bayes factor $\mathcal{B}_{10}=\mathcal{Z}_{1}/\mathcal{Z}_{0}$ following Trotta (2008) and Benneke & Seager (2013). FS is only calculated for those with $|\Delta\mathcal{Z}|\geq 1.0$. A positive FS value indicates that the reference model is favored over the model in comparison.
1\. Wide coverage spectrum: equilibrium chemistry
Patchy clouds | 30 | 33.8 | 248.38 | 0 | Ref. |  | 72 | 85.4 | 550.99 | 0 | Ref.
Uniform clouds | 31 | 32.3 | 245.88 |  $-$2.5 | 2.8$\sigma$ |  | 73 | 93.0 | 544.80 |  $-$6.2 | 3.9$\sigma$
2\. Wide coverage spectrum: free chemistry w/ patchy clouds
Full model | 26 | 23.2 | 247.30 | 0 | Ref. |  | 64 | 65.3 | 547.71 | 0 | Ref.
No Na | 27 | 63.0 | 231.97 |  $-$15.3 | 5.9$\sigma$ |  | 65 | 113.3 | 533.49 |  $-$14.2 | 5.7$\sigma$
No K | 27 | 23.8 | 247.09 |  $-$0.2 | – |  | 65 | 67.4 | 547.83 | 0.1 | –
No TiO | 27 | 22.6 | 248.87 | 1.6 |  $-$2.4$\sigma$ |  | 65 | 65.4 | 551.28 | 3.6 |  $-$3.2$\sigma$
No VO | 27 | 23.7 | 248.56 | 1.3 |  $-$2.2$\sigma$ |  | 65 | 66.2 | 550.27 | 2.6 |  $-$2.8$\sigma$
No H2O | 27 | 25.5 | 245.92 |  $-$1.4 | 2.2$\sigma$ |  | 65 | 76.9 | 543.85 |  $-$3.9 | 3.3$\sigma$
No CH4 | 27 | 23.6 | 247.11 |  $-$0.2 | – |  | 65 | 66.6 | 548.67 | 1.0 |  $-$2.0$\sigma$
No CO | – | – | – | – | – |  | 65 | 66.5 | 548.48 | 0.8 | –
No CO2 | – | – | – | – | – |  | 65 | 65.9 | 548.58 | 0.9 | –
No HCN | – | – | – | – | – |  | 65 | 66.1 | 548.34 | 0.6 | –
No NH3 | – | – | – | – | – |  | 65 | 69.5 | 547.40 |  $-$0.3 | –
3\. Na ultra-narrow band spectrum: free chemistry w/ uniform clouds
Full model | 11 | 7.7 | 96.21 | 0 | Ref. |  | – | – | – | – | –
No Na | 12 | 26.8 | 89.25 |  $-$7.0 | 4.1$\sigma$ |  | – | – | – | – | –
4\. K ultra-narrow band spectrum: free chemistry w/ uniform clouds
Full model | 7 | 6.9 | 72.15 | 0 | Ref. |  | – | – | – | – | –
No K | 8 | 22.3 | 66.55 |  $-$5.6 | 3.8$\sigma$ |  | – | – | – | – | –

###  5.1 DBSP transmission spectrum

We first focused on the interpretation of our DBSP transmission spectrum. We
started with the retrieval with the assumption of equilibrium chemistry. Only
$R_{\mathrm{1bar}}$ and $\log Z$ show well constrained distributions, with the
latter being $3.3^{+6.0}_{-2.2}\times$ solar metallicity. The other parameters
are either unconstrained ($\log P_{\mathrm{cloud}}$, $\log A_{\mathrm{RS}}$,
$\gamma$), bimodal ($T_{\mathrm{iso}}=1082^{+175}_{-134}$ K), or strongly
skewed to the lower boundary ($\phi<0.27$, $\mathrm{C/O}<1.57$, 90% upper
limit). We find that the assumption of patchy clouds (free $\phi$) is
moderately favored over uniform clouds ($\phi$ fixed to 1) by the DBSP
spectrum given the latter has a reduced model evidence of
$\Delta\ln\mathcal{Z}=-2.5$ (see Table 6). However, both models can fit the
DBSP spectrum at 1$\sigma$ confidence levels according to the $\chi^{2}$
statistic.

To explore the species responsible for the observed spectral signatures, we
also performed the retrieval analysis with the assumption of free chemistry.
In contrast to the equilibrium chemistry case, we only included the gas
opacities of Na, K, TiO, VO, H2O, and CH4 in addition to H2 and He, each of
the former six had the volume mixing ratio ($X_{i}$) as a free parameter,
which is constant across all pressures. Figure 6 shows the retrieved models
assuming free chemistry. As presented in Table 5, we obtained a much higher
temperature of $T_{\mathrm{iso}}=1562^{+95}_{-158}$ K strongly skewed to the
upper boundary ($>$1338 K, 90% lower limit), while $\log P_{\mathrm{cloud}}$,
$\log A_{\mathrm{RS}}$, and $\gamma$ remained unconstrained. The cloud
coverage was still skewed to the lower boundary ($\phi<0.51$, 90% upper
limit).

We then removed each of the six gas opacities one by one from the full model
in additional retrievals. Such experiments reveal that the presence of Na is
strongly favored because its absence would cause a significant decrease in
model evidence ($\Delta\ln\mathcal{Z}=-15.3$; 5.9$\sigma$). The DBSP spectrum
also moderately favors the presence of H2O ($\Delta\ln\mathcal{Z}=-1.4$;
2.2$\sigma$). On the other hand, the presence of TiO or VO are disfavored at
2.4$\sigma$ and 2.2$\sigma$, respectively.

####  5.1.1 Na and K ultra-narrow band transmission spectra

We also performed the retrieval analysis on the Na and K ultra-narrow band
transmission spectra individually. Due to fewer available data points compared
to the full DBSP spectrum and much narrower wavelength coverage, we only
included $T_{\mathrm{iso}}$, $R_{\mathrm{1bar}}$, $P_{\mathrm{cloud}}$, and
$X_{\mathrm{Na}}$ (or $X_{\mathrm{K}}$) as free parameters, but fixed the
other parameters ($\gamma=-4$, $\log A_{\mathrm{RS}}=0$, $\mathrm{C/O}=0.53$,
$\log Z=0$, $\phi=1$). The prior on $T_{\mathrm{iso}}$ was still uniform, but
the upper boundary was extended to 3000 K. Consequently, we derived
$T_{\mathrm{iso,Na}}=2095^{+268}_{-340}$ K and $\log
X_{\mathrm{Na}}=-4.7^{+2.2}_{-2.2}$ for the Na transmission spectrum, and
$T_{\mathrm{iso,K}}=1725^{+392}_{-413}$ K and $\log
X_{\mathrm{K}}=-5.3^{+2.6}_{-3.3}$ for the K transmission spectrum. As shown
in Figure 5 and Table 6, the retrieved models can fit the Na and K
transmission spectra very well.

We then muted the opacities of Na and K in an additional run of retrieval
analysis, in order to inspect how the Na and K spectral signatures contribute
to the models. Exclusion of Na and K would reduce the model evidence by
$\Delta\ln\mathcal{Z}=-7.0$ for Na and $\Delta\ln\mathcal{Z}=-5.6$ for K,
indicating that the presence of Na and K were both strongly favored in the
ultra-narrow band transmission spectra.

Figure 6: Spectral retrieval analysis performed on the P200/DBSP data assuming
free chemistry. The cyan line and shaded regions show the median and
1$\sigma$/2$\sigma$ confidence regions of the retrieved models. Figure 7: Top
panel presents the complete transmission spectrum of HAT-P-1b, with data from
P200/DBSP, HST/STIS, HST/WFC3, and Spitzer. Bottom panel presents the close-up
view of the optical wavelength range. The shaded areas show the retrieved
atmospheric models assuming free chemistry.

###  5.2 Complete transmission spectrum

For HAT-P-1b, high quality transmission spectrum has been observed from space
by HST/STIS (Nikolov et al., 2014), HST/WFC3 (Wakeford et al., 2013), and
Spitzer (Nikolov et al., 2014), covering a wavelength range from 3000 to 51000
Å. Our DBSP spectrum has a wavelength coverage similar to that of HST/STIS,
but has finer wavelength grids around the Na and K lines, thereby
complementary to HST/STIS in corresponding wavelengths. We collected the
revised HST and Spitzer data from Sing et al. (2016), and performed the
equilibrium chemistry and free chemistry retrieval analyses on the DBSP, HST,
and Spitzer combined dataset (hereafter complete spectrum), similar to that in
Section 5.1. A major difference is that more gas opacities were added in the
free chemistry retrieval of the complete spectrum, including Na, K, TiO, VO,
H2O, CH4, CO, CO2, HCN, and NH3. The retrieval results assuming free chemistry
are shown in Figure 7, while those assuming equilibrium chemistry can be found
in Appendix B.

The resulting parameters were in general consistent between the retrievals
performed on the DBSP spectrum and the complete spectrum. For both equilibrium
chemistry and free chemistry scenarios, the largest difference came from the 1
bar planet radius, which was smaller in the complete spectrum retrievals in
both scenarios. The cloud-top pressure remained unconstrained. The scattering
slope had a 90% upper limit of $\gamma<-5.0$ in the equilibrium chemistry and
$\gamma<-8.0$ in the free chemistry scenarios, respectively, but the latter
was strongly skewed to the lower boundary. The Rayleigh scattering enhancement
factor and the cloud coverage were constrained to $A_{\mathrm{RS}}\sim 10^{8}$
and $\phi\sim 0.22$ in both scenarios, respectively. For the equilibrium
chemistry scenario, the derived metalicities were almost the same based on
either the DBSP spectrum or the complete spectrum, while the C/O ratio was
skewed to the lower boundary with a narrower distribution in the complete
spectrum retrievals ($\mathrm{C/O}<0.54$, 90% upper limit). On the other hand,
the free chemistry scenario only resulted in well constrained volume mixing
ratios for Na and H2O, with smaller uncertainties ($\log
X_{\mathrm{Na}}=-6.3^{+0.5}_{-0.4}$, $\log
X_{\mathrm{H_{2}O}}=-3.2^{+0.3}_{-0.3}$) than those from the DBSP spectrum
($\log X_{\mathrm{Na}}=-4.3^{+1.6}_{-1.0}$, $\log
X_{\mathrm{H_{2}O}}=-3.1^{+0.7}_{-0.8}$).

Similar to the results from the DBSP spectrum, the equilibrium chemistry
retrieval of the complete spectrum favored the assumption of patchy clouds at
3.9$\sigma$, while the free chemistry retrieval favored the presence of Na
(5.7$\sigma$) and H2O (3.3$\sigma$), but disfavored TiO (3.2$\sigma$), VO
(2.8$\sigma$), and CH4 (2.0$\sigma$). Therefore, the DBSP spectrum delivered
very consistent information with that of the 3000–51000 Å complete spectrum,
with larger uncertainties though.

##  6 Discussion

###  6.1 Comparison with literature results

Our new DBSP observations of HAT-P-1b have revealed a broad spectral signature
around the Na line at 5.9$\sigma$, indicating the presence of a pressure
broadened line wing for Na. The reasonable precision and spectral resolution
of DBSP allow the creation of uniformly spaced 12 Å transmission spectra
centered at Na and K, resulting in the detection of the line cores of both Na
(4.1$\sigma$) and K (3.8$\sigma$) doublets.

To search for excess absorption at the Na and K lines, the approach of
comparing a central narrow band to the neighboring wide bands has been widely
adopted in both space- and ground-based transit spectrophotometry due to
limited narrow-band precision and spectral resolution (e.g., Nikolov et al.,
2014). An alternative way is to perform quasi-simultaneous narrow-band
photometry by switching between two tunable filters designed to cover the core
and wing of a spectral line (e.g., Wilson et al., 2015). However, both
approaches have the risk of obtaining false positive detections due to noise
fluctuation in only one or two narrow bands.

In contrast, tens of uniform narrow bands centered around the target line
could in principal perform better in retaining the noise fluctuation and
potential excess absorption signal. The latter has been successfully
implemented to detect Na in several exolplanets (e.g., Sing et al., 2011; Chen
et al., 2017b, 2018, 2020; Nikolov et al., 2018; Pearson et al., 2019; Ahrer
et al., 2022). Our detection of Na and K in HAT-P-1b is another example.

Several studies have performed spectral retrieval analyses on HAT-P-1b’s HST
and Spitzer combined dataset (Barstow et al., 2017; Pinhas et al., 2019;
Welbanks et al., 2019). Our retrieval approach approximately follows Pinhas et
al. (2019) and Welbanks et al. (2019), in particular the assumption of cloudy
and clear sectors. The latter two have obtained almost the same retrieval
results. Welbanks et al. (2019) reported the detection of H2O at 3.2$\sigma$
($\log X_{\mathrm{H_{2}O}}=-2.5^{+0.8}_{-0.7}$) and marginal evidence of Na at
1.3$\sigma$ ($\log X_{\mathrm{Na}}=-8.6^{+1.2}_{-1.8}$). With the addition of
the newly acquired DBSP data, we are able to detect H2O at 3.3$\sigma$ ($\log
X_{\mathrm{H_{2}O}}=-3.2^{+0.3}_{-0.3}$) and Na at 5.7$\sigma$ ($\log
X_{\mathrm{Na}}=-6.3^{+0.5}_{-0.4}$). The retrieval performed on the DBSP data
alone results in a H2O volume mixing ratio ($\log
X_{\mathrm{H_{2}O}}=-3.1^{+0.7}_{-0.8}$), almost the same as that from the
DBSP, HST, and Spitzer combined dataset, revealing a weak evidence for the
9300 Å H2O feature. On the other hand, we derive a well constrained cloud
fraction of $0.22^{+0.05}_{-0.03}$, much smaller than
$\sim$$0.5^{+0.1}_{-0.1}$ reported in Pinhas et al. (2019) and Welbanks et al.
(2019).

###  6.2 Interpreting the atmosphere of HAT-P-1b

Our retrieval results suggest that HAT-P-1b’s terminator atmosphere is mostly
clear, with a small fraction of $\sim$22% covered by clouds and hazes. The
inference of a large clear region is probably due to the presence of the
pressure broadened line wing of Na and prominent spectral signature of H2O.
However, we are not able to detect the pressure broadening of the K line. This
is not a rare phenomenon in hot Jupiters. Presence of Na pressure broadening
and absence of K pressure broadening have been also found in WASP-96b (Nikolov
et al., 2018, 2022), WASP-21b (Chen et al., 2020), and WASP-62b (Alam et al.,
2021).

In our retrieved cloudy and hazy region, haze is the dominant scattering
opacity source. Arfaux & Lavvas (2022) recently studied the photochemical
hazes in the atmospheres of ten hot Jupiters based on a self-consistent model
including haze microphysics, disequilibrium chemistry, and radiative feedback.
HAT-P-1b is among the planets showing degeneracies, for which the low-haze or
haze-free solution was presented in their discussion. According to their
neglected hazy solution, HAT-P-1b would have a haze density of 8 particle cm-3
for a mass flux of 10-12 g cm-2 s-1. This might be the case for the cloudy and
hazy region as retrieved by our analyses.

In the equilibrium chemistry retrieval of the DBSP, HST, and Spitzer combined
dataset, we obtained a low C/O of 0.25${}^{+0.23}_{-0.14}$ and a metallicity
of 3.2${}^{+5.3}_{-2.3}$$\times$ solar metallicity. Our retrieved metallicity
is fully consistent with the value of 3.6${}^{+5.8}_{-2.6}$ derived by Pinhas
et al. (2019). The low C/O value is a natural result of non-detection of
carbon-baring molecules as evidenced by the free chemistry retrieval. The
latter has resulted in a better goodness of fit than the equilibrium chemistry
retrieval according to the reduced $\chi^{2}_{\mathrm{MAP}}$. The non-
detection might be caused by the lack of resolvable carbon-related spectral
signatures in the current wavelength coverage, where H2O is the dominant
opacity source. The Spitzer data could in principal provide constraints on
carbon-baring molecules, but could be easily biased by systematics when only
two very broad bands are available.

We calculate the C/H, O/H, Na/H, K/H ratios relative to solar values (Asplund
et al., 2009) in logarithmic scale from the free chemistry retrieval results,
and obtain $\mathrm{[C/H]}<-0.18$ (90% upper limit),
$\mathrm{[O/H]}=-0.15^{+0.32}_{-0.28}$,
$\mathrm{[Na/H]}=-0.77^{+0.50}_{-0.40}$, and $\mathrm{[K/H]}<-1.25$ (90% upper
limit), of which only the O and Na abundances are constrained. All the
abundances appear sub-solar, except for O being consistent with the solar
value within uncertainties. As the major O carrier, the abundance of H2O is
consistent with the solar value of $-3.3$ (Asplund et al., 2009; Madhusudhan,
2012; Pinhas et al., 2019). When compared to that of the host star, i.e.,
$\mathrm{[C/H]}=-0.001\pm 0.031$, $\mathrm{[O/H]}=+0.088\pm 0.035$, and
$\mathrm{[Na/H]}=+0.090\pm 0.011$ (Liu et al., 2014), the planetary abundances
are in the range of substellar to stellar.

With a low C/O ratio ($<$0.54, 90% upper limit), a low C/H ratio
($<$0.7$\times$solar, 90% upper limit), and a solar O/H ratio
(0.4–1.5$\times$solar, 68.3% confidence interval), HAT-P-1b could be formed
through either core accretion with disk migration or gravitational instability
with disk-free migration according to the formation-migration pathways
presented by Madhusudhan et al. (2014). On the other hand, HAT-P-1b has a
refractory-to-oxygen ratio of $\mathrm{[R/O]}=-0.67^{+0.52}_{-0.45}$ based on
Na, K, TiO, and VO from our free chemistry retrieval, which favors an icy
instead of rocky-rich planetesimal enrichment (Lothringer et al., 2021).
However, the R/O ratio is proposed for ultrahot Jupiters, while HAT-P-1b’s
equilibrium temperature is much cooler than them. A large fraction of the
refractory elements could have been condensed into solids, thus absence from
observable atmosphere.

##  7 Conclusions

We have presented a new optical transmission spectrum of HAT-P-1b based on two
transits observed with P200/DBSP. The DBSP transmission spectrum exhibits a
pressure broadened line wing at the Na line and a tentative H2O absorption
signature at around 9300 Å. The line cores of Na and K are spectrally resolved
when the passband bin width is as narrow as 12 Å. Our spectral retrieval
analyses on the DBSP spectrum reveal a mostly clear atmosphere for HAT-P-1b,
with the presence of Na line wing detected at 5.9$\sigma$, Na line core at
4.1$\sigma$, K line core at 3.8$\sigma$, and H2O at 2.2$\sigma$. The results
from the retrievals of the DBSP, HST/STIS, HST/WFC3, and Spitzer combined
dataset are consistent with that performed on the DBSP data alone, but are
generally more precise and the significance of H2O increases to 3.3$\sigma$.
The current available dataset suggests a metallicity of
3.2${}^{+5.3}_{-2.3}$$\times$ solar, a C/O ratio lower than 0.54 at 90%
confidence level, subsolar values for Na, K, C, and a subsolar-to-solar value
for O.

Future high-resolution Doppler spectroscopy could resolve Na and K and provide
insight into the atmospheric dynamics in the upper atmosphere of HAT-P-1b. The
JWST GTO-1201 program and any future JWST observations should be able to put
stringent constraints on all the important oxygen, carbon, and nitrogen
carriers, enabling an in-depth exploration of HAT-P-1b’s formation and
migration history.

G. C. acknowledges the support by the National Natural Science Foundation of
China (Grant No. 42075122, 12122308), the Natural Science Foundation of
Jiangsu Province (Grant No. BK20190110), Youth Innovation Promotion
Association CAS (2021315), and the Minor Planet Foundation of the Purple
Mountain Observatory. The authors would like to thank Carolyn Heffner and
Kajsa Peffer for their great supports during the observations, Sheng Jin for
carrying out the second observation, Nikku Madhusudhan and Neale Gibson for
their help at the early stage of this work. This research uses data obtained
through the Telescope Access Program (TAP), which has been funded by the TAP
member institutes. Observations obtained with the Hale Telescope at Palomar
Observatory were obtained as part of an agreement between the National
Astronomical Observatories, Chinese Academy of Sciences, and the California
Institute of Technology. We acknowledge the use of TESS High Level Science
Products (HLSP) produced by the Quick-Look Pipeline (QLP) at the TESS Science
Office at MIT, which are publicly available from the Mikulski Archive for
Space Telescopes (MAST). Funding for the TESS mission is provided by NASA’s
Science Mission directorate.

##  Appendix A Spectroscopic light curves

The raw spectroscopic light curves, along with the systematics corrected ones
and the best-fit residuals, are presented in Figure 8 for D52-blue, Figure 9
for D52-red, Figure 10 for D68-blue, and Figure 11 for D68-red, respectively.
The derived Na and K ultra-narrow band transmission spectra are presented in
Table 7.

Table 7: Ultra-narrow band transmission spectra of HAT-P-1b. $\lambda$ (Å) |  $u_{1}$ prior |  $u_{2}$ prior | $R_{\mathrm{p}}/R_{\star}$
---|---|---|---
Na transmission spectrumaaThe Na transmission spectrum was derived from
common-mode corrected spectroscopic light curves, and the common-mode
systematics was derived from the 5800-6000 Å band, with
$R_{\mathrm{p}}/R_{\star}=0.1193\pm 0.0014$.
5803–5815 | $\mathcal{N}(0.395,0.045^{2})$ | $\mathcal{N}(0.294,0.025^{2})$ | $0.1179^{+0.0010}_{-0.0010}$
5815–5827 | $\mathcal{N}(0.391,0.046^{2})$ | $\mathcal{N}(0.298,0.026^{2})$ | $0.1172^{+0.0010}_{-0.0010}$
5827–5839 | $\mathcal{N}(0.388,0.046^{2})$ | $\mathcal{N}(0.300,0.026^{2})$ | $0.1192^{+0.0009}_{-0.0010}$
5839–5851 | $\mathcal{N}(0.389,0.045^{2})$ | $\mathcal{N}(0.297,0.025^{2})$ | $0.1195^{+0.0016}_{-0.0021}$
5851–5863 | $\mathcal{N}(0.388,0.045^{2})$ | $\mathcal{N}(0.297,0.025^{2})$ | $0.1188^{+0.0012}_{-0.0013}$
5863–5875 | $\mathcal{N}(0.386,0.046^{2})$ | $\mathcal{N}(0.298,0.026^{2})$ | $0.1188^{+0.0010}_{-0.0010}$
5875–5887 | $\mathcal{N}(0.391,0.046^{2})$ | $\mathcal{N}(0.288,0.028^{2})$ | $0.1219^{+0.0034}_{-0.0032}$
5887–5899 | $\mathcal{N}(0.394,0.047^{2})$ | $\mathcal{N}(0.282,0.029^{2})$ | $0.1242^{+0.0031}_{-0.0031}$
5899–5911 | $\mathcal{N}(0.387,0.046^{2})$ | $\mathcal{N}(0.292,0.027^{2})$ | $0.1210^{+0.0010}_{-0.0010}$
5911–5923 | $\mathcal{N}(0.383,0.045^{2})$ | $\mathcal{N}(0.297,0.025^{2})$ | $0.1211^{+0.0010}_{-0.0010}$
5923–5935 | $\mathcal{N}(0.381,0.045^{2})$ | $\mathcal{N}(0.298,0.025^{2})$ | $0.1189^{+0.0010}_{-0.0010}$
5935–5947 | $\mathcal{N}(0.380,0.045^{2})$ | $\mathcal{N}(0.298,0.025^{2})$ | $0.1179^{+0.0011}_{-0.0010}$
5947–5959 | $\mathcal{N}(0.379,0.045^{2})$ | $\mathcal{N}(0.299,0.025^{2})$ | $0.1175^{+0.0010}_{-0.0010}$
5959–5971 | $\mathcal{N}(0.376,0.044^{2})$ | $\mathcal{N}(0.300,0.024^{2})$ | $0.1179^{+0.0010}_{-0.0010}$
5971–5983 | $\mathcal{N}(0.375,0.044^{2})$ | $\mathcal{N}(0.301,0.024^{2})$ | $0.1160^{+0.0011}_{-0.0010}$
K transmission spectrumbbThe K transmission spectrum was derived from common-
mode corrected spectroscopic light curves, and the common-mode systematics was
derived from the 7600-7800 Å band, with $R_{\mathrm{p}}/R_{\star}=0.1176\pm
0.0010$.
7623–7635 | $\mathcal{N}(0.275,0.035^{2})$ | $\mathcal{N}(0.294,0.017^{2})$ | $0.1160^{+0.0009}_{-0.0009}$
7635–7647 | $\mathcal{N}(0.275,0.034^{2})$ | $\mathcal{N}(0.293,0.016^{2})$ | $0.1165^{+0.0007}_{-0.0007}$
7647–7659 | $\mathcal{N}(0.274,0.033^{2})$ | $\mathcal{N}(0.292,0.015^{2})$ | $0.1169^{+0.0021}_{-0.0020}$
7659–7671 | $\mathcal{N}(0.273,0.033^{2})$ | $\mathcal{N}(0.290,0.015^{2})$ | $0.1195^{+0.0017}_{-0.0017}$
7671–7682 | $\mathcal{N}(0.272,0.033^{2})$ | $\mathcal{N}(0.291,0.016^{2})$ | $0.1188^{+0.0013}_{-0.0013}$
7682–7693 | $\mathcal{N}(0.272,0.034^{2})$ | $\mathcal{N}(0.292,0.016^{2})$ | $0.1184^{+0.0007}_{-0.0007}$
7693–7705 | $\mathcal{N}(0.271,0.034^{2})$ | $\mathcal{N}(0.293,0.016^{2})$ | $0.1193^{+0.0006}_{-0.0006}$
7705–7717 | $\mathcal{N}(0.271,0.034^{2})$ | $\mathcal{N}(0.292,0.016^{2})$ | $0.1174^{+0.0009}_{-0.0014}$
7717–7729 | $\mathcal{N}(0.273,0.034^{2})$ | $\mathcal{N}(0.291,0.016^{2})$ | $0.1183^{+0.0007}_{-0.0007}$
7729–7741 | $\mathcal{N}(0.273,0.034^{2})$ | $\mathcal{N}(0.290,0.016^{2})$ | $0.1169^{+0.0006}_{-0.0007}$
7741–7753 | $\mathcal{N}(0.270,0.034^{2})$ | $\mathcal{N}(0.290,0.016^{2})$ | $0.1167^{+0.0006}_{-0.0007}$
Figure 8: Spectroscopic light curves in the D52-blue channel obtained with
P200/DBSP on the night of 2012 September 14. From left to right presents the
reference-calibrated raw light curves, systematics corrected light curves, and
best-fitting residuals, respectively. Figure 9: Same as Figure 8, but for the
D52-red channel. Figure 10: Spectroscopic light curves in the D68-blue channel
obtained with P200/DBSP on the night of 2016 July 26. From left to right
presents the reference-calibrated raw light curves, systematics corrected
light curves, and best-fitting residuals, respectively. Figure 11: Same as
Figure 10, but for the D68-red channel.

##  Appendix B Additional plots from the Bayesian spectral retrieval

The retrieved transmission spectra assuming equilibrium chemistry are shown in
Figure 12, which is in a similar manner to the free chemistry retrievals as
shown in Figure 7.

The joint posterior distributions of the equilibrium chemistry retrievals are
shown in Figure 13, while those of the free chemistry retrievals in Figure 14.
In both figures, the blue contours refer to the retrievals on the DBSP data,
while the red ones refer to those on the DBSP, HST, and Spitzer combined data.
To save space, the volume mixing ratios of CO, CO2, HCN, and NH3 are omitted
in the plot, which are unconstrained.

Figure 12: Top panel presents the complete transmission spectrum of HAT-P-1b,
with data from P200/DBSP, HST/STIS, HST/WFC3, and Spitzer. Bottom panel
presents the close-up view of the optical wavelength range. The shaded areas
show the retrieved atmospheric models assuming equilibrium chemistry.  Figure
13: Corner plot for spectral retrieval analyses assuming equilibrium
chemistry. Figure 14: Corner plot for spectral retrieval analyses assuming
free chemistry.

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