# Chemical analysis of two extremely metal-poor stars HE 2148$-$2039 and HE
2155$-$2043111Based on data collected at Subaru Telescope, which is operated
by the National Astronomical Observatory of Japan. The data are retrieved from
the JVO portal (http://jvo.nao.ac.jp/portal/v2/) operated by the NAOJ

Meenakshi Purandardas Indian Institute of Astrophysics, Koramangala, Bangalore
560034, India;  Department of physics, Bangalore university, Jnana Bharathi
Campus, Karnataka 560056, India  Aruna Goswami Indian Institute of
Astrophysics, Koramangala, Bangalore 560034, India;

(Received December xx, 2020; Revised XXXX; Accepted xxx)

###### Abstract

We present elemental abundance results for HE 2148$-$2039 and HE 2155$-$2043
based on a detailed high-resolution spectroscopic analysis. The high-
resolution SUBARU/HDS spectra used for our analysis have a resolution of
R$\sim$60 000. Although limited information based on photometry and low-
resolution spectroscopy are available, we present for the first time an
abundance analysis based on high-resolution spectra for both the objects. Our
analysis shows that the two objects are extremely metal-poor with [Fe/H]$<$
$-3$. Among the neutron-capture elements, abundances of only Sr and Ba could
be determined in our programme stars. For both the objects [Ba/Fe] is found to
be $<$ 0\. While strontium is under abundant in HE 2148$-$2039 with
[Sr/Fe]$\sim$ $-2.02$, Sr is near solar in HE 2155$-$2043\. The locations of
the programme stars in the absolute carbon abundance, A(C) vs. [Fe/H] diagram
show that HE2148$-$2039 is a CEMP-no Group II object and HE 2155$-$2043 is a
CEMP-no Group III object. Observed [Sr/Ba] ratios are characteristics of a
fast rotating massive star progenitor for HE2155$-$2043 and a metal-poor
Asymptotic giant branch (AGB) star for HE2148$-$2039\. The estimated [Sc/Mn]
as well as [C/Cr] ratios in HE2155$-$2043 show that the surface chemical
composition of this object is mono-enriched. The surface chemical composition
of HE 2148$-$2039 is also found to be mono-enriched based on [Mg/C] ratio.
With respect to their locations in the [C/N] vs. Teff diagram, HE 2148$-$2039
shows signatures of mixing, and HE2155$-$2043 falls in the unmixed region of
[C/N] vs. Teff plot. Kinematic analysis shows that both the objects belong to
Galactic halo population.

stars: abundances— stars: chemically peculiar—stars: Population II

††journal: ApJ

##  1 Introduction

The Halo of our Galaxy holds a large number of stars that are older than the
Milky Way (Frebel, 2018). Understanding the chemical compositions of Galactic
halo stars can give insight into various stellar progenitors and help to
better understand the nature of nucleosynthetic pathways at earlier times.
First generation stars are thought to be massive stars. They are expected to
synthesize elements up to iron peak including Sr or Ba by weak slow neutron-
capture (-s) process (Frischknecht et al., 2012). About half of the heavy
elements were produced only after the low- and intermediate- mass stars were
formed and evolved to their asymptotic giant branch (AGB) phase (Lugaro et
al., 2003; Herwig, 2005; Karakas & Lattanzio, 2014). Core collapse supernovae,
neutron star mergers etc. are the other known sources of heavy elements, the
rapid neutron-capture (r-) process elements (Arcones & Thielemann, 2013;
Rosswog et al., 2014; Abbott et al., 2017; Drout et al., 2017; Shappee et al.,
2017).

Metal-poor ([Fe/H] $<$ $-1.0$) stars with enhanced carbon ([C/Fe] ${\geq}$
0.7, Aoki et al. (2007)) are known as carbon-enhanced metal-poor (CEMP) stars.
Various sky survey programmes such as HES/HK surveys (Christlieb et al., 2001;
Wisotzki et al., 2000; Beers et al., 1985, 1992; Beers, 1999a, b) dedicated to
explore the metal-poor stars revealed that the fraction of carbon-enhanced
metal-poor stars increases with decrease in metallicty (Cohen et al., 2005;
Frebel et al., 2006a; Carollo et al., 2012; Lee et al., 2013; Placco et al.,
2014b; Beers et al., 2017). CEMP stars show different levels of enhancement of
neutron-capture elements. Based on the enhancement of neutron-capture
elements, CEMP stars are classified into different groups: CEMP-s, CEMP-r,
CEMP-r/s and CEMP-no (Beers & Christlieb, 2005). A detailed study and a
comprehensive analysis of the classification criteria put forward by different
authors for CEMP stars, as well as production scenarios can be found in
Goswami et al. (2021). CEMP-s stars exhibit the enhancement of s-process
elements ([Ba/Fe] $>$ 1.0, and [Ba/Eu] $>$ 0.5). CEMP-r/s stars show over
abundances of both s- and r- process elements (0.0 $<$ [Ba/Eu] $<$ 0.5). The
widely accepted scenario to explain the observed enhancement of heavy elements
in these groups of CEMP stars involves a binary mass transfer process (Herwig,
2005; Bisterzo et al., 2012). According to this scenario, these stars accreted
the heavy elements synthesised by the companion during its AGB phase. Radial
velocity variations exhibited by CEMP-s and CEMP-r/s stars also support the
binary mass transfer scenario (McClure & Woodsworth, 1990; Hansen et al.,
2016a). CEMP-r stars are the most rarely observed objects and exhibit
enhancement of r-process elements ([Eu/Fe] $>$ 1.0). CS 22892-052 is the
CEMP-r star first reported by McWilliam et al. (1995) and Sneden et al. (2003)
which is found to be unlikely in a binary system (Hansen et al., 2011). Hansen
et al. (2015) compared the elemental abundance patterns estimated in two
CEMP-r stars HE 0010$-$3422 and HE 0448$-$4806, in their sample with the
yields from metal-poor AGB stars with different masses. Massive AGB models
could reproduce only some of the observed abundances for the neutron capture
elements in HE 0010$-$3422 which requires radial velocity monitoring to
confirm its binarity. For HE 0448$-$4806, none of the AGB models could give a
good fit for the observed abundances. Hansen et al. (2015) suggest that the
observed abundance anomalies in CEMP-r stars are not the result of mass
transfer from a binary companion but may be inherited from the interstellar
medium from which the star was formed.

Unlike the other groups of CEMP stars, CEMP-no stars do not show any
enhancement of neutron-capture elements. CEMP-no stars constitute ${\sim}$ 20%
of very metal-poor ([Fe/H] $<$ $-2.0$) stars, ${\sim}$ 40% of extremely metal-
poor ([Fe/H] $<$ $-3.0$) stars, and ${\sim}$ 80% of ultra metal-poor ([Fe/H]
$<$ $-4.0$) stars and the fraction increases with lower metallicities
(Banerjee et al., 2018). CEMP-no stars mostly occur as single stars (Norris et
al., 2013; Starkenburg et al., 2014; Hansen et al., 2016c). Only a very few of
the CEMP-no stars are known to be confirmed binaries. Hansen et al. (2016c)
reported that 17% of CEMP-no stars in their sample of 24 stars are binaries.
Arentsen et al. (2019) suggest that the CEMP-no star may be in a binary system
and the companion is an extremely metal-poor star and once passed through the
AGB phase but that has not produced any significant amount of s-process
elements. Another scenario proposed to explain the origin of CEMP-no stars is
that they are formed from an interstellar medium polluted by Spin stars
(Meynet et al., 2010; Chiappini, 2013) or Faint supernovae that underwent
mixing and fall back (Umeda & Nomoto, 2005; Nomoto et al., 2013; Tominaga et
al., 2014) or metal-free massive stars (Heger & Woosley, 2010). Hansen et al.
(2016c) suggest that all these sources may contribute towards the observed
abundance patterns of CEMP-no stars. CEMP-no stars are expected to be the
direct descendants of the first generation stars (Ito et al., 2013; Spite et
al., 2013; Placco et al., 2014b; Hansen et al., 2016b). Many studies show that
the surface composition of CEMP-no stars match well with that expected for
population III stars (Christlieb et al., 2004; Meynet et al., 2006; Frebel et
al., 2008; Nomoto et al., 2013; Keller et al., 2014; Bonifacio et al., 2015;
Yoon et al., 2016; Placco et al., 2016; Choplin et al., 2017; Ezzeddine et
al., 2019).

Since the CEMP-no stars are the bonafide second generation stars (Placco et
al., 2015; Hansen et al., 2016c; Yoon et al., 2016), the abundance analysis of
these stars can give important clues about the early Galactic nucleosynthesis.
In this work, we have presented a detailed abundance analysis of two CEMP-no
stars, HE 2148$-$2039 and HE 2155$-$2043 using high-resolution spectra. The
paper is organized as follows: Section 2 presents a brief summary of previous
works found in literature on the two programme stars. The source of the
spectra is presented in section 3. Determination of stellar atmospheric
parameters, mass and age of the programme stars are discussed in section 4.
Abundance analysis is discussed in section 5. Section 6 presents a discussion
on our results. Kinematic analysis is discussed in section 7. Conclusions are
drawn in Section 8.

##  2 Previous studies: A brief summary

U, B and V magnitudes for the two objects HE 2148$-$2039 and HE 2155$-$2043
are reported in Beers et al. (2007). Frebel et al. (2006b) reported a
metallicity [Fe/H] $\sim$ $-3.55$ and a carbon abundance [C/Fe] $\sim$ 1.56
for the object HE 2155$-$2043 based on medium resolution ($\sim$ 2Å)
spectroscopy. For the object HE 2155$-$2043, Hansen et al. (2016a) reported
atmospheric parameters Teff = 5200 K, log g = 2.4, and $\zeta$ = 1.5 kms-1
with a metallicity [Fe/H] $\sim$ $-3.0$. They have determined the abundances
of strontium, nitrogen and carbon for this object based on the analysis of
medium resolution (R$\sim$ 7450) spectra obtained with X-shooter spectrograph.
They obtained [Sr/Fe] $\sim$ 0.20, [N/Fe] $\sim$ 0.0 and [C/Fe] $\sim$ 0.70.
They could not determine the abundance of Ba as its absorption features were
too weak in the spectrum of this object. They classified the object HE
2155$-$2043 as CEMP-no star based on their analysis. The most recent study
available for the object HE 2155$-$2043 is by Beers et al. (2017). They have
reported the atmospheric parameters Teff = 5016 K, log g = 2.87, [Fe/H] $\sim$
$-3.27$ and carbon abundance of [C/Fe] $\sim$ 0.81 based on an analysis of
medium resolution (R $\sim$ 2000) spectra using non-SEGUE Stellar Parameter
Pipeline (n-SSPP). They have also determined a radial velocity of $\sim$ $-92$
kms-1 for this object. Although some aspects of our programme stars have been
addressed in previous studies, results based on high-resolution spectroscopic
analysis are missing. We present for the first time an abundance analysis for
both the objects based on high-resolution spectra.

##  3 Source of spectra

Programme stars are selected from the list of metal-poor candidates of the
Hamburg/ESO survey (Christlieb, 2003). We have used the high resolution
spectra of the two programme stars obtained using the High Dispersion
Spectrograph (HDS) of the 8.2 m Subaru Telescope at a resolution $\sim$ 60
000. The wavelength calibrated spectra were retrieved from the JVO portal
(http://jvo.nao.ac.jp/portal/v2/) operated by National Astronomical
Observatory of Japan where the data are publicly available. The wavelength
coverage of the spectra spans from 4100 to 6850Å, with a small gap between
5440 and 5520Å. This gap occurs due to the physical separation between the two
CCDs. The detectors are two EEV CCDs with 2048$\times$4096 pixels with two by
two on-chip binning. Examples of sample spectra are shown in Figure 1 (Upper
panel). The basic data for the programme stars are listed in Table 1. A low
resolution spectrum of the programme star HE 2148$-$2039 obtained using the
Himalayan Faint Object Spectrograph Camera (HFOSC) attached to 2-m Himalayan
Chandra Telescope (HCT) at the Indian Astronomical Observatory (IAO), Hanle on
20 October 2020 is also shown in Figure 1 (Lower panel), that covers a
wavelength range from 3840 to 6800Å. HFOSC is an optical imager cum
spectrograph used for low- and medium-resolution grism spectroscopy. We have
obtained spectra in grism 7 and 8 that cover the wavelength regions from 3800
- 6840 Å with a resolution of R $\sim$ 1330 and 5800 - 9000 Å with a
resolution of R $\sim$ 2190 respectively.

Table 1: Basic data for the programme stars

Star |  RA$(2000)$ |  Dec.$(2000)$ | B | V | J | H | K | Exposure | Date of obs. | Source
---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  |  | (seconds) |  | of spectrum
HE 2148$-$2039 | 21 51 06.85 |  $-20$ 25 48.26 |  14.67$\pm$0.03a |  14.03$\pm$0.02a |  12.48$\pm$0.02 |  12.03$\pm$0.02 |  11.96$\pm$0.02 | 1800 | 08-12-2003 | Subaru/HDS
|  |  |  13.99$\pm$0.03b |  14.72$\pm$0.04b |  |  |  | 2700 | 20-10-2020 | HCT/HFOSC
HE 2155$-$2043 | 21 58 42.27 |  $-20$ 58 42.27 |  14.10a |  13.15$\pm$0.02a |  11.57$\pm$0.02 |  11.09$\pm$0.02 |  11.02$\pm$0.02 | 1800 | 27-06-2004 | Subaru/HDS
|  |  |  13.19$\pm$0.03b |  13.96$\pm$0.01b |  |  |  |  |  |

a SIMBAD, b APASS DR10 catalog

Figure 1:  Upper panel: High resolution spectra of the programme stars in the
wavelength region 5160 to 5190 Å.
Lower panel: A low resolution spectrum of HE 2148$-$2039 in the wavelength
region 3840 to 6800 Å acquired with HCT/HFOSC.

##  4 Spectroscopic stellar parameters

Radial velocities of the programme stars are determined by measuring the shift
in the wavelength for a large number of unblended and clean lines in the
spectra. Estimated radial velocities are presented in Table 2.

Stellar parameters are determined following the detailed procedures described
in our earlier paper Purandardas et al. (2019b). Here we mention briefly the
main points. Atmospheric parameters of the programme stars are determined from
the measured equivalent widths of a number of clean and unblended Fe I and Fe
II lines. The number of (Fe I and Fe II) lines measured on the stars’ spectra
are limitted and the lines are found to be very weak; (9, 1) and (25, 3)
respectively for HE 2148$-$2039 and HE 2155$-$2043\. Only those lines with
excitation potential in the range 0.0 - 5.0 eV are considered for the
analysis. We have made use of the recent version of MOOG (Sneden 1973, updated
version 2013) for the analysis assuming the local thermodynamic equilibrium
(LTE). Model atmospheres are selected from Kurucz grid of model atmospheres
with no convective overshooting (http://cfaku5.cfa.hardvard.edu/). Solar
abundances are adopted from Asplund et al. (2009). The effective temperature
of a programme star is taken to be that value for which the trend between the
abundances obtained from Fe I lines and the excitation potential gives zero
slope. A trend between the abundances derived from Fe I lines and the reduced
equivalent width with a zero slope defines the microturbulent velocity of the
star. Under this temperature and microturbulent velocity, the surface gravity
log g, is determined for which the abundances obtained from the Fe I and Fe II
lines are nearly the same. The derived atmospheric parameters and radial
velocities of the programme stars are listed in Table 2. The derived Teff
estimates when compared with the estimates from Gaia DR2 are found to be lower
by 314 K in the case of HE 2148$-$2039 and by 382 K in the case of HE
2155$-$2043\. This discrepancy may be due to the fact that the RMS error in
Teff provided by Gaia DR2 is found to increase with decreasing metallicity of
the stars with smallest error around solar metallicity. The Gaia Teff
estimates are good in the metallicity range $-$2 $\leq$ [Fe/H] $\leq$ 0.5 as
their training sample of stars are in this metallicity range. Outside this
range of metallicity, the Teff estimates are found to be more biased and
overestimated (Gaia Collaboration et al., 2018). The plot showing the
estimated abundances from Fe I and Fe II lines as a functions of excitation
potential and equivalent widths are shown in Figure 2. The equivalent widths
of the Fe I and Fe II lines used for deriving the atmospheric parameters are
presented in Table 3.

Table 2: Derived atmospheric parameters and radial velocities of the programme
stars.

Star |  Teff | log g | $\zeta$ | [Fe I/H] | [Fe II/H] |  Vr |  Vr | Ref
---|---|---|---|---|---|---|---|---
| (K) | cgs |  (km s-1) |  |  |  (km s-1) |  (km s-1) |
|  ($\pm$100) |  ($\pm$0.2) |  ($\pm$0.2) |  |  |  | (SIMBAD) |
HE 2148$-$2039 | 5000 | 2.0 | 2.80 |  $-3.30$$\pm$0.14 | $-3.35$ |  14.95 $\pm$ 0.14 | - | 1
| 5314 |  |  |  |  |  |  | 2
HE 2155$-$2043 | 4800 | 0.4 | 1.21 |  $-3.43$$\pm$0.06 |  $-3.49$$\pm$0.04 |  $-68.92$ $\pm$ 0.53 | $-92$ | 1
| 5182 |  |  |  |  |  |  | 2

Ref: 1: This work; 2: Gaia DR2

Table 3: Equivalent widths (in mÅ) of Fe lines used for deriving atmospheric
parameters.

Wavelength(Å) | Element |  $E_{low}$(eV) | log gf |  HE 2148$-$2039 |  HE 2155$-$2043
---|---|---|---|---|---
4143.869 | Fe I | 1.557 | -0.45 | - | 87.7(4.07)
4147.670 |  | 1.484 | -2.10 | - | 31.9(4.20)
4187.038 |  | 2.449 | -0.55 | - | 44.4(4.07)
4337.046 |  | 1.557 | -1.69 | - | 40.4(4.02)
4427.309 |  | 0.051 | -3.04 | - | 67.9(4.01)
4447.718 |  | 2.222 | -1.34 | - | 23.2(4.07)
4466.551 |  | 2.832 | -0.59 | - | 29.6(4.19)
4531.147 |  | 1.485 | -2.15 | - | 29.7(4.13)
4871.317 |  | 2.868 | -0.41 | - | 31.9(4.05)
4994.129 |  | 0.915 | -3.08 | - | 22.9(4.12)
5006.117 |  | 2.832 | -0.77 | 32.2(4.45) | -
5049.819 |  | 2.279 | -1.42 | - | 22.0(4.11)
5051.634 |  | 0.915 | -2.79 | - | 31.3(4.02)
5083.338 |  | 0.958 | -2.96 | - | 26.7(4.13)
5166.281 |  | 0.000 | -4.19 | - | 21.5(3.99)
5171.595 |  | 1.485 | -1.79 | 47.5(4.13) | 47.5(4.02)
5192.343 |  | 2.998 | -0.52 | - | 20.8(4.02)
5194.941 |  | 1.557 | -2.09 | 28.5(4.23) | 31.2(4.09)
5232.939 |  | 2.940 | -0.19 | 29.6(3.93) | 38.2(4.00)
5266.555 |  | 2.998 | -0.49 | - | 24.9(4.09)
5324.178 |  | 3.211 | -0.24 | - | 23.8(4.06)
5497.516 |  | 1.011 | -2.85 | 23.3(4.22) | -
5501.464 |  | 0.958 | -2.95 | - | 22.2(3.96)
5506.778 |  | 0.990 | -2.79 | 25.6(4.19) | 34.7(4.12)
5586.756 |  | 3.368 | -0.21 | - | 17.7(4.02)
6136.615 |  | 2.453 | -1.40 | - | 19.2(4.12)
6252.554 |  | 2.404 | -1.69 | 15.0(4.11) | -
6393.602 |  | 2.433 | -1.62 | 18.6(4.47) | -
6494.980 |  | 2.404 | -1.27 | 18.9(4.09) | 22.4(3.99)
4508.288 | Fe II | 2.856 | -2.21 | - | 16.8(3.98)
4515.339 |  | 2.844 | -2.48 | - | 10.5(3.99)
4923.927 |  | 2.891 | -1.32 | 41.9(4.15) | -
5234.625 |  | 3.221 | -2.05 | - | 12.4(4.03)

The numbers in the parenthesis in columns 5-6 give the derived abundances from
the respective line.
log gf values are taken from kurucz atomic line list
(https://www.cfa.harvard.edu).

Table 4: Estimates of log g using parallax method  Star name | Parallax | $M_{bol}$ |  log(L/L⊙) |  Mass(M⊙) | log g | log g (Spectroscopic)
---|---|---|---|---|---|---
| (mas) |  |  |  | (cgs) | (cgs)
HE 2148$-$2039 |  0.12$\pm$0.03 |  $-0.77$$\pm$1.00 |  2.21$\pm$0.21 |  0.95$\pm$0.55 |  1.98$\pm$0.13 |  2.0$\pm$0.2
HE 2155$-$2043 |  0.13$\pm$0.05 |  $-1.63$$\pm$0.52 |  2.55$\pm$0.40 |  1.00$\pm$0.30 |  1.54$\pm$0.28 |  0.4$\pm$0.2
Figure 2:  The iron abundances of programme stars as a function of excitation
potential (left panels) and equivalent width (right panels). In all the
panels, the open circles indicate Fe I lines and solid triangles represent Fe
II lines.

###  4.1 Mass and age

Mass and age of the programme stars are estimated from their positions in the
H-R diagram, log(L/L⊙) vs. Teff. Luminosities of the stars are determined
using the relation,

$log(L/L_{\odot})=(M_{\odot}-M_{bol})/2.5$

where M⊙ is the bolometric magnitude for the sun, and

$M_{bol}=Mv+BC-Av$

Mv is calculated using the equation,

$Mv=V-(5log(d))+5$

The visual magnitude (V) of the star is taken from SIMBAD and the parallax
values are adopted from Gaia (Gaia collaboration et al. 2016, 2018b,
https://gea.esac.esa.int/archive/). Bolometric corrections are calculated
using the empirical calibrations of Alonso et al. (1999). Interstellar
extinction required for the estimation of bolometric magnitude is calculated
using the formula as given by Chen et al. (1998). The evolutionary tracks and
isochrones corresponding to Z = 0.0008 are taken from the Girardi et al.
(2000) database to estimate the mass and age of the stars. Locations of the
programme stars in the H-R diagram (Figure 3) show that they are in the
ascending stage of the giant branch with near solar masses. The estimated ages
of the objects HE 2148$-$2039 and HE 2155$-$2043 are 5.6 and 5.0 Gyrs
respectively as derived from the parallax method. However, we note that, the
errors in the age estimates are as high as 7Gyr for both the objects which may
be due to the high errors in the parallax estimates that are ${\sim}$ 38% and
25% for HE 2155$-$2043 and HE 2148$-$2039 respectively. The parallax error
propagates to the luminosity estimates that could cause uncertainties in
accurate age determination from the isochrones in the H-R diagram.

The surface gravity, log g, is calculated using the relation,

$log(g/g_{\odot})=log(M/M_{\odot})+4log(T_{eff}/T_{eff\odot})+0.4(M_{bol}-M_{bol\odot})$

Where log g⊙ = 4.44, Teff⊙ = 5770K, and Mbol⊙ = 4.75 mag (Yang et al., 2016).
The estimated mass and surface gravity of the programme stars are tabulated in
Table 4.

Figure 3: The locations of HE 2148$-$2039 and HE 2155$-$2043 in the H-R
diagram are shown. The isochrone tracks for log(age) 10.20, 10.0, 9.9, 9.8,
9.70, 9.60, 9.40 and 9.25 are shown from bottom to top in the upper panel. The
evolutionary tracks for 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.3, 1.4, 1.5 and 1.7 M⊙
are shown from bottom to top in the bottom panel.

##  5 Abundance analysis

Abundance analyses of the programme stars are performed using the measured
equivalent widths as well as using the spectral synthesis calculation of clean
and symmetric lines due to various elements. Lines are identified by
overplotting the Arcturus spectrum on the individual spectrum of the programme
stars. A master linelist is prepared with the measured equivalent widths and
line information such as excitation potential and log gf values of the
spectral lines taken from the Kurucz database (https://www.cfa.harvard.edu).
Abundances of light elements, C and N, odd-Z element Na, $\alpha$ elements Mg,
Ca, Sc and Ti and Fe-peak elements Cr, Mn, Co and Ni are determined whenever
possible. Among the neutron-capture elements, we could estimate the abundances
of only Sr and Ba. Lines due to other heavy elements are either absent or too
weak to measure. The lines used to derive the abundances of various elements
are presented in Table 5.

Table 5: Lines used for deriving elemental abundances

Wavelength(Å) | Element |  $E_{low}$(eV) | log gf | HE 2148$-$2039 | HE 2155$-$2043
---|---|---|---|---|---
5889.951 | Na I | 0.000 | 0.10 | 95.4(2.65) | 131.1(4.06)
5895.920 |  | 0.000 | -0.20 | 73.1(2.69) | 114.0(3.94)
5172.684 | Mg I | 2.711 | -0.40 | 118.7(4.08) | 141.8(5.59)
5183.600 |  | 2.720 | -0.18 | 123.2(3.93) | -
4318.652 | Ca I | 1.899 | -0.21 | - | 19.3(3.48)
6122.217 |  | 1.885 | -0.41 | - | 20.0(3.47)
6162.173 |  | 1.899 | 0.10 | 26.0(3.11) | 28.4(3.20)
6439.075 |  | 2.525 | 0.47 | 16.8(3.19) | 18.6(3.26)
4320.732 | Sc II | 0.605 | -0.26 | 29.8(-0.25) | 43.6(-0.28)
4374.457 |  | 0.618 | -0.44 | - | 31.7(-0.40)
4415.557 |  | 0.595 | -0.64 | - | 26.2(-0.39)
4417.719 | Ti II | 1.164 | -1.43 | 22.0(1.77) | 40.8(1.85)
4443.794 |  | 1.080 | -0.70 | - | 65.1(1.74)
4468.507 |  | 1.130 | -0.60 | - | 60.4(1.54)
4563.761 |  | 1.221 | -0.96 | 50.4(1.83) | 46.1(1.54)
5226.540 |  | 1.565 | -1.30 | 16.6(1.88) | -
4289.717 | Cr I | 0.000 | -0.36 | - | 63.1(2.58)
4030.753 | Mn I | 0.000 | -0.47 | - | 65.7(2.27)
4121.311 | Co I | 0.922 | -0.32 | - | 38.9(2.18)
5476.900 | Ni I | 1.826 | -0.89 | - | 30.6(3.13)
4077.709 | Sr II | 0.000 | 0.17 | - | 95.1(-0.30)
4215.519 |  | 0.000 | -0.14 | - | 88.4(-0.26)
4934.076 | Ba II | 0.000 | -0.15 | 41.5(-1.67) | 14.9(-2.72)

The numbers in the parenthesis in columns 5-6 give the derived abundances from
the respective line. log gf values are taken from kurucz atomic line list
(https://www.cfa.harvard.edu)

###  5.1 Carbon and Nitrogen

The abundance of carbon is determined using the spectrum synthesis calculation
of CH band at 4315 Å. In both the programme stars, CH bands are clearly
detectable. Hence we have used the carbon abundance obtained from the
synthesis of CH band throughout our analysis. The spectrum synthesis
calculation of CH band gives [C/Fe] $\sim$ 1.15 and 2.05 respectively for HE
2148$-$2043 and HE 2155$-$2043\. As the CH band region of HE 2148$-$2043 is
found to be very noisy, the carbon abundance obtained for this object is taken
as the upper limit. The best spectrum synthesis fit that we could obtain for
the CH band for HE 2148$-$2043 is shown in Figure 4. The C2 bands at 5165 and
5635 Å are weak and marginally detectable.

Figure 4: Synthesis of CH band around 4315 Å. Dotted line represents
synthesized spectra and the solid line indicates the observed spectra. Short
dashed line represents the synthetic spectra corresponding to $\Delta$ [C/Fe]
= -0.3 and long dashed line corresponds to $\Delta$[C/Fe] = +0.3. Solid cyan
line corresponds to a spectral synthesis fit obtained without CH. Figure 5:
Synthesis of CN band around 4215 Å. Dotted line represents synthesized spectra
and the solid line indicates the observed spectra. Short dashed line
represents the synthetic spectra corresponding to $\Delta$[N/Fe] = -0.3 and
long dashed line corresponds to $\Delta$[N/Fe] = +0.3. Solid cyan line
corresponds to a spectral synthesis fit obtained without CN.

Abundance of nitrogen is estimated using the spectrum synthesis calculation of
CN band at 4215 Å. Nitrogen is found to be enhanced in both the stars with
[N/Fe] $\sim$ 3.86 and 2.10 in HE 2148$-$2039 and HE 2155$-$2043 respectively.
As the region around 4215 Å is noisy in HE 2148$-$2039, the nitrogen abundance
obtained for this star is taken as the upper limit. The best spectrum
synthesis fit that we could obtain for the CN band for this object is shown in
Figure 5. The molecular linelists for carbon and nitrogen are taken from
Sneden et al. (2014) and Ram et al. (2014). We could not determine oxygen in
both the stars as the lines [OI] 6300.3 and 6363.7 Å are highly blended and
the near infrared oxygen triplet lines are out of the spectral coverage.

###  5.2 Na, Mg, Ca, Sc, Ti

The abundance of Na is estimated using the equivalent width measurements as
well as the spectrum synthesis calculation of the lines Na I 5889.95 and
5895.92 Å. While sodium is found to be enhanced in HE 2155$-$2043 with [Na/Fe]
$\sim$ 0.98, it is under abundant in HE 2148$-$2039 with [Na/Fe] $\sim$
$-0.32$. Abundance of Mg is determined using the measured equivalent widths as
well as using the spectrum synthesis calculation of lines Mg I 5172.68 and
5183.60 Å. HE 2155$-$2043 exhibits enhancement of Mg with [Mg/Fe] $\sim$ 1.57.
Magnesium is found to be under abundant in HE 2148$-$2039 with [Mg/Fe] $\sim$
$-0.35$. We have used the equivalent width measurements of three Ca I lines
(Table 5) to estimate the abundance of Ca in HE 2155$-$2043\. For HE
2148$-$2039 the spectrum synthesis calculation of line Ca I 6162.17 is
performed to determine the abundance of Ca. Calcium is slightly enhanced in HE
2155$-$2043, and near solar in HE 2148$-$2039.

The abundance of Sc is determined using the equivalent width measurements of
three Sc II lines (Table 5) in HE 2155$-$2043\. The spectrum synthesis
calculation of Sc II 4320.73 Å is performed to estimate the abundance of Sc in
HE 2148$-$2039\. Scandium abundance is found to be near solar in both the
programme stars with [Sc/Fe] $\sim$ $-0.19$ and $-0.02$ in HE 2148$-$2039 and
HE 2155$-$2043 respectively. The abundance of Ti is measured using the
equivalent width measurements of four Ti I lines (Table 5). The abundance is
nearly same in both the stars with a value [Ti/Fe] ${\sim}$ 0.20.

###  5.3 Cr, Co, Mn, Ni

The abundances of Cr, Co, Mn and Ni could be determined only in HE
2155$-$2043\. In HE 2148$-$2039, these lines are found to be blended and not
useful for abundance determination. Abundance of Cr is determined using the
spectrum synthesis calculation of Cr I 4289.72 Å that gives [Cr/Fe] $\sim$
$-0.10$. The spectrum synthesis calculation of Mn I 4030.75 Å gives a near
solar value. The abundance of Co is determined using the spectrum synthesis
calculation of Co I 4121.31 Å that gives [Co/Fe] $\sim$ 0.90. The spectrum
synthesis of the line Ni I 5476.90 Å is used to derive the abundance of Ni.
Nickel is only slightly enhanced in this object with [Ni/Fe] $\sim$ 0.30.

###  5.4 Sr, Ba

Among the neutron-capture elements, we could determine the abundances of only
Sr and Ba in our programme stars. Spectrum synthesis of Sr II 4215.52 Å is
used to estimate the abundance of Sr in HE 2148$-$2039 and is found to be
under abundant with [Sr/Fe] $\sim$ $-2.02$. In this star, the Sr II 4077.71 Å
line could not be detected. The spectrum synthesis calculation of these two
lines give [Sr/Fe] $\sim$ $-0.04$ for HE 2155$-$2043.

The abundance of Ba is estimated using the spectrum synthesis calculation of
Ba II 4934.08 Å in both the stars considering the hyperfine structure and Ba
isotopic ratios taken from McWilliam (1998) and Arlandini et al. (1999)
respectively. The other prominent lines Ba II 5853.66 and 6141.71 Å, are found
to be extremely weak. Barium is under abundant in both the programme stars
with [Ba/Fe] $\sim$ $-0.84$ and $-1.64$ for HE 2148$-$2039 and HE 2155$-$2043
respectively. The spectrum synthesis fits for Sr and Ba lines in HE
2155$-$2043 are shown in the Figure 6.

We have checked for several absorption features due to other neutron-capture
elements in the spectra of our program stars that are generally observed in
extremely metal-poor stars. But these lines were found to be either absent or
too weak to be used for abundance determination. The abundance results for our
programme stars are presented in Table 6.

Figure 6: Synthesis of Sr II line around 4215.52 Å and Ba II line around 4934
Å. Dotted line represents synthesized spectra and the solid line indicates the
observed spectra. Short dashed line represents the synthetic spectra
corresponding to $\Delta$ [X/Fe] = -0.3 and long dashed line corresponds to
$\Delta$[X/Fe] = +0.3 Table 6: Elemental abundances in HE 2148$-$2039 and HE
2155$-$2043

|  |  |  HE 2148$-$2039 |  HE 2155$-$2043
---|---|---|---|---
| Z |  Solar log$\epsilon^{\ast}$ |  log$\epsilon$ | [X/H] | [X/Fe] |  log$\epsilon$ | [X/H] | [X/Fe]
C (CH band) | 6 | 8.43 |  $<$ 6.28$\pm$0.20(syn) |  $<$ $-2.15$ |  $<$ 1.15 |  7.05$\pm$0.20(syn) | $-1.38$ | 2.05
N | 7 | 7.83 |  $<$ 8.39$\pm$0.20(syn) |  $<$ 0.56 |  $<$ 3.86 |  6.50$\pm$0.20(syn) | $-1.33$ | 2.10
Na I | 11 | 6.24 |  2.62$\pm$0.20(syn) | $-3.62$ | $-0.32$ |  3.79$\pm$0.20(syn) | $-2.45$ | 0.98
Mg I | 12 | 7.60 |  3.95$\pm$0.20(syn) |  $-$3.65 | $-0.35$ |  5.74$\pm$0.20(syn) | $-1.86$ | 1.57
Ca I | 20 | 6.34 |  3.07$\pm$0.20(syn) |  $-$3.27 | 0.03 |  3.35$\pm$0.14(4) | $-2.99$ | 0.44
Sc II | 21 | 3.15 |  $-0.39$$\pm$0.20(syn) |  $-$3.54 | $-0.19$ |  $-0.36$$\pm$0.07(3) | $-3.51$ | $-0.02$
Ti II | 22 | 4.95 |  1.82$\pm$0.06(3) |  $-$3.13 | 0.22 |  1.67$\pm$0.15(4) | $-3.28$ | 0.21
Cr I | 24 | 5.64 | - | - | - |  2.11$\pm$0.20(syn) | $-3.53$ | $-0.10$
Mn I | 25 | 5.43 | - | - | - |  2.04$\pm$0.20(syn) | $-3.39$ | 0.04
Fe I | 26 | 7.50 |  4.20$\pm$0.17(9) |  $-$3.30 | - |  4.07$\pm$0.06(25) | $-3.43$ | -
Fe II | 26 | 7.50 | 4.15(1) |  $-$3.35 | - |  4.01$\pm$0.04(3) | $-3.49$ | -
Co I | 27 | 4.99 | - | - | - |  2.46$\pm$0.20(syn) | $-2.53$ | 0.90
Ni I | 28 | 6.22 | - | - | - |  3.09$\pm$0.20(syn) | $-3.13$ | 0.30
Sr II | 38 | 2.87 |  $-2.50$$\pm$0.20(syn) | $-5.37$ | $-2.02$ |  $-0.66$$\pm$0.20(syn) | $-3.53$ | $-0.04$
Ba II | 56 | 2.18 |  $-2.01$$\pm$0.20(syn) | $-4.19$ | $-0.84$ |  $-2.95$$\pm$0.20(syn) | $-5.13$ | $-1.64$

$\ast$ Asplund (2009), The number inside the parenthesis shows the number of
lines used for the abundance determination.

Table 7: Elemental abundances in HE 2155$-$2043 at log g = 0.40 and log g =
1.54

|  |  |  Teff = 4800, log g = 0.40, $\xi$ = 1.21 |  Teff = 4800, log g = 1.54, $\xi$ = 1.21 |
---|---|---|---|---|---
| Z |  Solar log$\epsilon^{\ast}$ |  log$\epsilon$ | [X/H] | [X/Fe] |  log$\epsilon$ | [X/H] | [X/Fe] | Difference
C (CH band) | 6 | 8.43 |  7.05$\pm$0.20(syn) | $-1.38$ | 2.05 |  6.75$\pm$0.20(syn) | $-1.68$ | 1.66 | 0.39
N | 7 | 7.83 |  6.50$\pm$0.20(syn) | $-1.33$ | 2.10 |  6.80$\pm$0.20(syn) |  $-$1.03 | 2.31 | 0.21
Na I | 11 | 6.24 |  3.79$\pm$0.20(syn) | $-2.45$ | 0.98 |  3.83$\pm$0.20(syn) |  $-$2.41 | 0.93 | 0.05
Mg I | 12 | 7.60 |  5.74$\pm$0.20(syn) | $-1.86$ | 1.57 |  5.44$\pm$0.20(syn) |  $-$2.16 | 1.18 | 0.39
Ca I | 20 | 6.34 |  3.35$\pm$0.14(4) | $-2.99$ | 0.44 |  3.27$\pm$0.14(4) |  $-$3.07 | 0.27 | 0.17
Sc II | 21 | 3.15 |  $-0.36$$\pm$0.07(3) | $-3.51$ | $-0.02$ |  -0.11$\pm$0.07(3) |  $-$3.26 | 0.09 | 0.11
Ti II | 22 | 4.95 |  1.67$\pm$0.15(4) | $-3.28$ | 0.21 |  1.88$\pm$0.15(4) |  $-$3.07 | 0.28 | 0.07
Cr I | 24 | 5.64 |  2.11$\pm$0.20(syn) | $-3.53$ | $-0.10$ |  2.27$\pm$0.20(syn) |  $-$3.37 |  $-$0.03 | 0.07
Mn I | 25 | 5.43 |  2.04$\pm$0.20(syn) | $-3.39$ | 0.04 |  1.43$\pm$0.20(syn) |  $-$4.00 |  $-$0.66 | 0.70
Fe I | 26 | 7.50 |  4.07$\pm$0.06(25) | $-3.43$ | - |  4.16$\pm$0.06(25) | $-3.34$ | - | 0.09
Fe II | 26 | 7.50 |  4.01$\pm$0.04(3) | $-3.49$ | - |  4.15$\pm$0.04(3) | $-3.35$ | - | 0.14
Co I | 27 | 4.99 |  2.46$\pm$0.20(syn) | $-2.53$ | 0.90 |  2.18$\pm$0.20(syn) |  $-$2.81 | 0.53 | 0.37
Ni I | 28 | 6.22 |  3.09$\pm$0.20(syn) | $-3.13$ | 0.30 |  3.00$\pm$0.20(syn) |  $-$3.22 | 0.12 | 0.18
Sr II | 38 | 2.87 |  $-0.66$$\pm$0.20(syn) | $-3.53$ | $-0.04$ |  $-$0.61$\pm$0.20(syn) |  $-$3.48 |  $-$0.13 | 0.09
Ba II | 56 | 2.18 |  $-2.95$$\pm$0.20(syn) | $-5.13$ | $-1.64$ |  $-$2.68$\pm$0.20(syn) |  $-$4.86 |  $-$1.51 | 0.13

$\ast$ Asplund et al. (2009), The number inside the parenthesis shows the
number of lines used for the abundance determination.
Column 10 represents the difference in the abundances obtained for log g =
0.40 and log g = 1.54

##  6 Discussion

Before we present a detailed discussion and interpretation of the abundance
results obtained from the spectroscopic analysis for the two programme stars,
we would like to comment on the adopted surface gravity value for the star HE
2155$-$2043\. The value of log g for which Fe II lines give the same abundance
as obtained from the Fe I lines, is taken as the spectroscopic log g value of
the star and in general, the spectroscopic log g match with their counter
parts obtained from the parallax method within the errors. For the object HE
2155$-$2043, the three Fe II lines used return a value 0.4 for log g. This
value is very different from the log g (1.54) as obtained from the parallax
method. We have therefore calculated the abundances for all the elements at
both the values of log g keeping the spectroscopic temperature and the
corresponding microturbulent velocity constant. The abundance obtained using
log g = 1.54 are presented in Table 7. The observed difference may be due to
the high carbon enhancement in the object. For a star which shows strong
enhancement in carbon, the evolutionary track is shifted towards lower
temperatures which causes inconsistency between the atmospheric parameters
determined from the evolutionary track and that derived from the spectral
analysis as the exact location of the giant branch is sensitive to the opacity
in the atmosphere of a star (Marigo, 2002; Jorissen et al., 2016). The error
in parallax for HE 2155$-$2043 is around 38% which can also contribute towards
the observed deviation. The difference in the abundance values for various
elements obtained using the log g from parallax and that from spectroscopy
ranges from 0.05 to 0.70 dex. However the classification of HE 2155$-$2043 as
CEMP-no star remains the same. An example for the spectrum synthesis of Mn for
log g = 1.54 and log g = 0.40 is shown in Figure 7.

Figure 7: Synthesis of Mn I line around 4030.75 Å for log g = 0.40 and 1.54.
Dotted line represents synthesized spectra and the solid line indicates the
observed spectra. Short dashed line represents the synthetic spectra
corresponding to $\Delta$[Mn/Fe] = -0.3 and long dashed line corresponds to
$\Delta$[Mn/Fe] = +0.3

###  6.1 Locations of the programme stars in the A(C) vs. [Fe/H] diagram and
classification:

The existance of different carbon production mechanisms among CEMP stars were
explored by many authors. Spite et al. (2013) identified the existance of a
bimodality among the CEMP stars in a plot of absolute carbon abundance as a
function of metallicity, based on a sample of $\sim$ 50 stars. They showed
that the stars in their sample with metallicity $>$ $-3.0$ occupy the region
around A(C) $\sim$ 8.25 which they have taken as higher carbon ”plateau”.
Objects that fall around this band are mostly composed of CEMP-s and CEMP-r/s
stars. The stars with [Fe/H] $<$ $-3.4$ occupy a region around A(C) $\sim$ 6.5
and found to be dominated by CEMP-no stars. These observations led to their
interpretation that two different carbon production mechanisms exist among
CEMP stars. Bonifacio et al. (2015) and Hansen et al. (2015) confirmed this
bimodality based on even larger sample of stars. The knowledge of binary
status of the stars of the two different carbon bands may provide important
clues regarding the nature of their progenitors.

Location of a carbon star in the absolute carbon abundance A(C) vs.
metallicity [Fe/H] diagram (Yoon et al., 2016) could be an important indicator
of its class. We have therefore attempted to classify the programme stars from
their locations in such a plot (Figure 8). Yoon et al. (2016) compiled high-
resolution abundance data for 305 CEMP stars and found that the distribution
of these CEMP stars in the A(C) vs. [Fe/H] diagram is bimodal with two
distinct peaks, the high-carbon region centered around A(C) = 7.96 and the
low-carbon region centered around A(C) = 6.28. The CEMP-s and CEMP-r/s stars
are found to occupy the high-carbon region and are called as the Group I
objects. The majority of CEMP-no stars are found to occupy the low-carbon
region. Among the CEMP-no stars, the group that show a clear trend with
respect to [Fe/H] is called the group II objects, and those that do not show
any trend with respect to [Fe/H] are classified as Group III objects. The
Group III and the lower end of Group I has a very thin separation. It is in
this region the object HE 2155$-$2043 lies close to the lower boundary of the
region for Group I, and the upper boundary for the Group III objects making it
difficult to clearly classify this object based on this diagram alone.
However, on the basis of its very low barium abundance [Ba/Fe] ${\sim}$
$-$1.6, the object can be classified as a CEMP-no star. It is to be noted
that, in general the CEMP-s and CEMP-r/s stars show [Ba/Fe] ${\geq}$ 1.0. We
have applied the necessary correction factors (Placco et al., 2014a) to our
estimated carbon abundances of the programme stars using the public online
tool 222http://vplacco.pythonanywhere.com/ for placing them in Figure 8. The
corrections applied to the estimated carbon abundances are 0.01 and 0.37 for
HE 2148$-$2039 and HE 2155$-$2043 respectively. It is clearly seen from the
figure that the object HE 2148$-$2039 could be a bonafied CEMP-no star as it
falls in the region occupied by CEMP-no Group II objects.

###  6.2 Analysis of the observed abundance patterns in the program stars

Understanding how the CEMP-no stars become enriched in various elements can
provide insight into their nucleosynthetic pathways and the formation history.
The estimated abundances of alpha, Fe-peak and the neutron-capture elements
such as Sr and Ba in the two programme stars match well with the observed
abundance patterns of these elements in other extremely metal-poor objects
reported by various studies. Carbon and nitrogen are found to be enhanced in
both the programme stars. HE 2148$-$2039 shows very high nitrogen abundance
with [N/Fe] $\sim$ 3.87. Such a high value of nitrogen abundance is not
uncommon among extremely metal-poor objects. Roederer et al. (2014) reported
an enhancement in nitrogen with [N/Fe] $>$ 3.0 for the objects CS 22171$-$037,
CS 22177$-$009, CS 22884$-$108 and CS 22960$-$053 with similar metalicities.

Figure 8: A(C) vs. [Fe/H] diagram for CEMP stars compiled by Yoon et al.
(2016). In this plot Cyan colour indicates CEMP-r/s stars: binary stars are
represented by eight sided star and stars with no information on their binary
status are indicated by cross symbols. Open and filled red circles indicate
binary and single CEMP-s stars respectively. CEMP-s stars with no information
on their binarity are represented using red open triangles. Open and filled
hexagons in blue represent binary and single CEMP-no stars respectively. CEMP-
no stars with no information on their binarity are indicated by blue open
squares. Group III CEMP-no stars are represented using green symbols: binary
and single stars are represented by open and filled pentagons respectively.
Skeleton triangles represent stars with no information about binary status.
Programme stars are represented using magenta colour, HE 2148$-$2039 is
represented by a filled triangle and HE 2155$-$2043 is represented by a filled
square.

Our programme stars exhibit light element abundance patterns that are
distinctly different from each other indicating different production
mechanisms for these two stars. While HE 2155$-$2043 shows enhancement of Na
and Mg, these elements are underabundant in HE 2148$-$2039\. Previous studies
show that the enhancement of light elements such as Na, Mg, Al, and Si are
common among the majority of the extremely metal-poor stars (Aoki et al.,
2002; Frebel et al., 2005). For example, Roederer et al. (2014) reported such
a high enhancement in Na and Mg for the extremely metal-poor stars CS
29498-043, CS 22893-010 and HE 1012-1540. Aoki et al. (2002) and Masseron et
al. (2010) divided the CEMP-no stars into two categories with Mg- enhanced and
Mg- normal at extremely low metallicities. Yoon et al. (2016) show that CEMP-
no Group III stars exhibit enhancement of Na as well as Mg unlike CEMP-no
Group II stars that do not show any enhancement of these elements. The
locations of our programme stars in the [Na/Fe] vs. [Fe/H] and [Mg/Fe] vs.
[Fe/H] (Figure 9) show that the programme star HE 2148$-$2039 is a CEMP-no
Group II object and HE 2155$-$2043 is a CEMP-no Group III object. Their
locations in the A(Na) vs. A(C) and A(Mg) vs. A(C) (Figure 10) also support
the same. This again shows the existance of different progenitors among the
CEMP-no stars themselves, leading to two different groups.

Figure 9: Distribution of the [Na/Fe] and [Mg/Fe] as a function of metallicity
for CEMP-no stars. The data used in the plot are taken from Yoon et al.
(2016). Symbols used are same as in Figure 8 Figure 10: Distribution of the
A(Na) and A(Mg) as a function of A(C) for CEMP-no stars. The data used in the
plot are taken from Yoon et al. (2016). Symbols used are same as in Figure 8.

In Figures 11 and 12, we have shown a comparison between the estimated
elemental abundance ratios of the programme stars with their counterparts
observed in CEMP-s, CEMP-no and extremely metal-poor stars taken from various
sources in literature. The estimated abundance ratios are also compared with
their counterparts observed in two extremely metal poor CEMP-no stars
J1202-0020 and J1208-0029 of the Sylgr stellar streams (Roederer & Gnedin,
2019) in the same figures. It is clear from the figures that the abundance
ratios of the program stars match well with those observed in the literature
CEMP-no stars.

While the carbon is more enhanced in the two programme stars than the Sylgr
stellar stream CEMP-no stars, nitrogen is found to have similar values. The
${\alpha}$-elements in HE 2155$-$2043 are found to be over abundant and in HE
2148$-$2039 under abundant when compared with those observed in the two Sylgr
stellar stream stars. While the abundances of Fe-peak elements in HE
2155$-$2043 are found to be similar to that of Sylgr stellar stream stars, the
estimated abundances of Sr and Ba in the two programme stars are found to be
lower.

Figure 11: Abundance ratios of light elements with respect to metallicity
estimated in our programme stars. Symbols used are same as in Figure 8. The
abundance values for the CEMP-no stars are taken from Christlieb et al.
(2004),Plez & Cohen (2005),Yong et al. (2013), Hansen et al. (2014), Bonifacio
et al. (2015), Bessell et al. (2015) and Frebel (2018). The abundance values
for CEMP-s stars are taken from Lucatello et al. (2003), Barklem et al.
(2005), Cohen et al. (2006), Goswami et al. (2006), Aoki et al. (2007),
Karinkuzhi & Goswami (2015), Purandardas et al. (2019a) and Purandardas et al.
(2019b). Abundances of light elements observed in the programme stars are also
compared with the abundance patterns of extremely metal-poor objects (cyan
open circles) presented by Roederer et al. (2014) and with the extremely
metal-poor stars in the Sylgr stellar stream (blue open triangle) presented by
Roederer & Gnedin (2019) .  Figure 12:  Same as Figure 8 but for Sr and Ba.

###  6.3  Possible progenitors of the program stars

Frischknecht et al. (2012) studied the impact of rotation-induced mixing on
the neutron capture nucleosynthesis in rotating massive stars at low
metallicities using the Geneva stellar evolution code. Their studies show that
the s-process nucleosynthesis in massive stars produces elements upto Sr at a
metallicity, [Fe/H] $>$ $-2$. They obtained [Sr/Ba] $>$ 0 from low metallicity
massive rotating stars. Choplin et al. (2017) also showed that the [Sr/Ba]
ratio is higher in fast rotating massive stars than in AGB stars. Since
[Sr/Ba] ratio is different in AGB and fast rotating massive stars, it is a
useful descriptor to trace the formation sites (Hansen et al., 2019). The
estimated [Sr/Ba] ratio in HE 2155$-$2043 is $\sim$ 1.60. This implies that
the possible progenitor of this object may be a fast rotating massive star.

Yoon et al. (2016) suspect that the CEMP-no Group III objects may be
associated with spin star progenitors and Group II objects may be related to
the faint supernovae progenitors. However they remain open to other classes of
progenitors that may also contribute to the observed abundance anomalies. The
[Sr/Ba] ratio in HE 2148$-$2039 is $\sim$ $-1.18$. [Sr/Ba] ratio is found to
be less than 0 for metal-poor AGB stars (Cristallo et al., 2011; Hansen et
al., 2019). This may point towards a metal-poor AGB progenitor for HE
2148$-$2039\. According to Arentsen et al. (2019), CEMP-no stars can be in a
binary system. The primary companion is an extremely metal-poor star that once
passed through the AGB phase and it had not produced any significant amount of
s-process elements.

Hartwig et al. (2018) showed that [Mg/C] ratio can be used to tell if a CEMP
star was enriched by a single event (mono-enriched) or several pollution
events (multi-enriched) based on their model calculations. For mono-enriched
objects, [Mg/C] is found to be less than $-1.0$. Other elemental ratios such
as [Sc/Mn] $<$ 0.5, [C/Cr] $>$ 0.5 and [Ca/Fe] $>$ 2.0 can also indicate mono-
enrichment (Hartwig et al., 2018). The estimated [Mg/C] ratio in our programme
stars show that HE 2148$-$2039 is mono-enriched and HE 2155$-$2043 is multi-
enriched (Figure 13). But the observed [Ca/Fe] in HE 2148$-$2039 and HE
2155$-$2043 do not support mono-enrichment. The [Sc/Mn] and [C/Cr] ratios
estimated in HE 2155$-$2043 show that this object is enriched by a single
pollution event.

Figure 13: Location of programme stars in [Mg/C] vs. [Fe/H] plot. Filled
triangle represents HE 2148$-$2039 and filled square represents HE
2155$-$2043\. Filled circles represent the CEMP stars from literature (Norris
et al., 2007; Hollek et al., 2011; Ito et al., 2013; Yong et al., 2013; Cohen
et al., 2013; Hansen et al., 2014; Placco et al., 2014a; Roederer et al.,
2014; Placco et al., 2014a; Hansen et al., 2015; Li et al., 2015; Jacobson et
al., 2015; Bessell et al., 2015; Karinkuzhi & Goswami, 2015; Purandardas et
al., 2019a, b; Goswami et al., 2021; Shejeelammal et al., 2021)

###  6.4 Mixing diagnostic

Various mixing processes have been found to operate in stars (Spite et al.,
2006; Gratton et al., 2000). It is therefore important to understand whether
the stars have undergone any internal mixing. [C/N] ratio can give important
clues about the internal mixing process in a star. We have checked for the
signatures of any internal mixing in our programme stars based on the
estimated [C/N] ratios (Figure 14). Stars with [C/N] $>$ $-0.60$ are found to
be unmixed stars (Spite et al., 2005). While HE 2148$-$2039 shows signatures
of internal mixing, HE 2155$-$2043 falls in the unmixed region with [C/N] =
$-0.05$. An extra mixing is found to operate in stars with luminosity,
log(L/L⊙) $\sim$ 2.0 (Gratton et al., 2000; Spite et al., 2005). Since HE
2155$-$2043 has log(L/L⊙) $>$ 2.0, we expect signatures of mixing in this
object. But this object is found to fall in the unmixed category based on
[C/N] ratio. According to Spite et al. (2006), [C/N] ratio is not a clean
indicator of mixing, because, the abundances of carbon and nitrogen in the
interstellar medium from which these stars are formed show large variations.
But carbon isotopic ratio can be used as a good indicator of mixing, since it
is high in primordial matter (12C/13C $>$ 70) and it is insensitive to the
choice of atmospheric parameters for the stars (Spite et al. 2006). However we
could not estimate carbon isotopic ratio in our programme stars as the C2 swan
band around 4700 Å is found to be absent.

Figure 14: Position of the programme stars in the [C/N] vs. Teff diagram.
Filled triangle represents HE 2148$-$2039 and filled square represents HE
2155$-$2043\. Filled circles represent the CEMP stars from literature (Spite
et al., 2006; Aoki et al., 2007; Hansen et al., 2014; Goswami et al., 2016;
Purandardas et al., 2019a, b; Goswami et al., 2021; Shejeelammal et al., 2021)

##  7 Kinematic analysis

We have determined the space velocities of the programme stars following the
methods as given in Bensby et al. (2003). The space velocity of the star with
respect to the local standard of rest (LSR) is given by

$(U,V,W)_{LSR}=(U,V,W)+(U,V,W)_{\odot}$ km/s.

where, $(U,V,W)_{\odot}=(11.1,12.2,7.3)$ km/s Schönrich et al. (2010) is the
solar motion with respect to LSR , and

$\left[\begin{array}[]{lll}&U&\\\ &V&\\\
&W&\end{array}\right]=B\left[\begin{array}[]{lll}&k\mu_{\alpha}/\pi&\\\
&k\mu_{\delta}/\pi&\\\ &\rho&\end{array}\right]$

where B = T.A, T represents the transformation matrix connecting Galactic
coordinates and equatorial coordinates which is given by

$T=\left[\begin{array}[]{ccc}-0.0548756&-0.8734371&-0.4838350\\\
+0.4941094&-0.4448296&+0.7469822\\\
-0.8676661&-0.1980764&+0.4559838\end{array}\right]$

A represents the coordinate matrix which is defined as:

$A=\left[\begin{array}[]{ccc}-sin\alpha&-cos\alpha sin\delta&+cos\alpha
cos\delta\\\ +cos\alpha&-sin\alpha sin\delta&sin\alpha cos\delta\\\
0&+cos\delta&sin\delta\end{array}\right]$

Where $\alpha$ is the right ascension and $\delta$ is the declination in
degrees, k = 4.74057 km s-1, $\mu_{\alpha}$ is the proper motion in right
ascension, in arcsec yr-1, $\mu_{\delta}$ is the proper motion in declination,
in arcsec yr-1, $\rho$ is the radial velocity in kms-1 and $\pi$ is the
parallax in arcsec. The proper motion and the parallax of the star are taken
from (Gaia Collaboration et al. (2016), Gaia Collaboration et al. (2018)) and
the radial velocity is taken to be the value which we have estimated. The
coordinate system that we used for U, V and W is right handed and it is
therefore, they are positive in the directions of the Galactic center,
Galactic rotation, and the North Galactic Pole (NGP) respectively (Johnson &
Soderblom, 1987). The total spacial velocity of the star is

$V_{spa}^{2}=U_{LSR}^{2}+V_{LSR}^{2}+W_{LSR}^{2}$

We have also determined the membership of the star into the thin disc, thick
disc or the halo population. We have followed the procedures as given in Reddy
et al. (2006), Bensby et al. (2003, 2004), Mishenina et al. (2004) based on
the assumption that the Galactic space velocity of the star has Gaussian
distribution:

$f(U,V,W)=K\times\exp[-\frac{U_{LSR}^{2}}{2\sigma_{U}^{2}}-\frac{(V_{LSR}-V_{asy})^{2}}{2\sigma_{V}^{2}}-\frac{W_{LSR}^{2}}{2\sigma_{W}^{2}}]$

Where $K=\frac{1}{(2\pi)^{\frac{3}{2}}\sigma_{U}\sigma_{V}\sigma_{W}}$
The values for characteristic velocity dispersion $\sigma_{U}$, $\sigma_{V}$
and $\sigma_{W}$ and the asymmetric drift $V_{asy}$ are adopted from Reddy et
al. (2006). The results of the kinematic analysis of the programme stars are
presented in Table 8. Both the programme stars are found to be the members of
the halo of the Galaxy. This is in agreement with the studies by Carollo et
al. (2014) that the CEMP-no stars are mostly found to be associated with the
outer-halo population and the CEMP-s and CEMP-r/s stars are mostly found in
the inner-halo. Tumlinson (2007) suggests that the dominant progenitors of the
CEMP population in the outer-halo are more massive stars than that for the
inner-halo population for which the intermediate-mass stars might be the
possible progenitors.

Table 8: Spatial velocity and probability estimates for the programme stars Star name |  ULSR |  VLSR |  WLSR |  Vspa |  pthin |  pthick |  phalo | Population
---|---|---|---|---|---|---|---|---
|  (kms-1) |  (kms-1) |  (kms-1) |  (kms-1) |  |  |  |
HE 2148$-$2039 |  $-112.80$$\pm$31.69 |  $-109.10$$\pm$30.34 |  $-163.95$$\pm$38.32 |  226.95$\pm$58 | 0.00 | 0.08 | 0.91 | Halo
HE 2155$-$2043 |  $-192.29$$\pm$71.87 |  $-442.13$$\pm$186.01 |  $-253.59$$\pm$135.62 |  544.76$\pm$239.06 | 0.00 | 0.00 | 1.00 | Halo

##  8 Conclusion

We have presented the results of the high-resolution spectroscopic analysis of
two stars HE 2148$-$2039 and HE 2155$-$2043\. Our analysis shows that the
objects are extremely metal-poor with [Fe/H] $\sim$ $-3.30$ and $-3.43$ for HE
2148$-$2039 and HE 2155$-$2043 respectively. The observed abundances of
carbon, A(C) = 6.29 and 7.42 (after applying necessary corrections) and the
estimated [Ba/Fe] of $-0.84$ and $-1.64$ for HE 2148$-$2039 and HE 2155$-$2043
respectively confirm the programme stars to be CEMP-no stars.

Among the neutron-capture elements, abundances of only Sr and Ba could be
determined in our programme stars. Strontium is found to be under-abundant in
HE 2148$-$2039 and is near solar in HE 2155$-$2043\. The [Sr/Ba] ratio of HE
2155$-$2043 indicates that the possible progenitor for this object could be a
fast rotating massive metal-poor star. [Sr/Ba] = $-1.18$ for HE 2148$-$2039
indicates a metal-poor AGB progenitor for this object. The lines due to other
neutron-capture elements are found to be either absent or too weak to measure.

The abundances of Na, and Mg estimated in our programme stars show that HE
2148$-$2039 is a CEMP-no Group II object and HE 2155$-$2043 is a CEMP-no Group
III object as per the classification scheme of Yoon et al. (2016). While the
estimated abundance ratios of [Sc/Mn] and [C/Cr] in HE 2155$-$2043 show that
this object is enriched by a single pollution event, the estimated [Mg/C]
ratio indicates that the object is enriched by multiple pollution events. As
we could not determine the abundances of Sc, Mn and Cr in HE 2148$-$2039, the
formation history of this object could not be constrained based on these
abundances. But the estimated [Mg/C] ratio of this object shows that this is a
mono-enriched object.

[C/N] ratio can act as an indicator of mixing. Locations of the two objects in
the [C/N] vs. Teff plot show that the object HE 2148$-$2039 had undergone
significant internal mixing and HE 2155$-$2043 does not show any signatures of
mixing. Kinematic analysis shows that both the programme stars belong to the
halo population of the Galaxy.

Low-mass extremely metal-poor stars are ideal candidates to study the nature
of the very first stars as these objects are believed to bear the chemical
imprints of the oldest metal-poor stars. However, most of the extremely metal-
poor stars exhibit diversity in elemental abundance patterns indicating
different formation mechanisms. Although there have been many studies, the
formation mechanisms of these stars and their diverse abundance patterns are
far from being completely understood. The high-resolution spectroscopic
studies available for these stars are also currently limited in number. This
underscores the need for high resolution spectroscopic studies for larger
sample that would provide robust observational constraints for theoretical
studies.

##  9 ACKNOWLEDGEMENT

Funding from the DST SERB project EMR/2016/005283 is gratefully acknowledged.
We thank the referee for many constructive suggestions and useful comments on
the manuscript which improved this paper. This work made use of the SIMBAD
astronomical database, operated at CDS, Strasbourg, France, the NASA ADS, USA
and data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC),
(https://www.cosmos.esa.int/web/gaia/dpac/consortium).

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