Horizontal branch structure, age, and chemical composition for very metal-poor extragalactic globular clusters

This paper presents the results of analysing the integrated light (IL) low-resolution spectra of globular clusters (GCs) in the M31 and Centaurus A groups of galaxies. The sample consists of eight very metal-poor GCs ($\rm [Fe/H]\le -2$ dex) with high signal-to-noise ratio spectra acquired with the telescopes: the 6-m SAO RAS (BTA), the Southern African Large (SALT) and the 6.5-m Magellan (MMT). We study the influence of contribution of the horizontal branch stars on the hydrogen Balmer line profiles in the IL spectra. By modelling the Balmer lines, as well as the metal lines in the observed spectra, we determine the optimum parameters of stellar evolution isochrones and, consequently, the parameters of the atmospheres of the cluster stars. For all the studied GCs, the parameters of horizontal branch stars set by the selected isochrones, the corresponding ages, and carbon abundances are presented for the first time. The abundances of several other elements (Mg, Ca, Ti, Cr, and Mn) were determined for five GCs for the first time. All the studied GCs have blue horizontal branches and are older than 10 Gyr. Their chemical abundances, with the exception of Mg and Mn, are in good agreement with the abundances of stars in the Galactic field. The reasons of low [Mg/Fe] and of high [Mn/Fe] are discussed. Study of the fundamental properties of stellar populations in old globular clusters facilitates a better understanding of the formation processes of their parent galaxies and nucleosynthesis in the early Universe.


INTRODUCTION
Analysis of the integrated light (IL) spectra of star clusters is one of the effective tools for determining their age and metallicity and studying the formation and evolution of their host galaxies (see, for example, Lee et al. 2023;Cabrera-Ziri et al. 2022;Larsen et al. 2022;Leath et al. 2022;Fan et al. 2020, and references therein).It has been shown in a number of studies that determination of the age of old globular clusters (GCs) from the IL spectra is associated with the problem of taking into account the radiation of the horizontal branch (HB) stars corresponding to the core helium burning phase of stellar evolution.If one does not include the IL spectra of HB stars in the analysis, then the uncertainty in estimating the age of old GCs greatly increases, since the contribution to the spectra of stars with higher helium mass fraction (Y) populating the bluer parts of HBs imitates younger age (Koleva et al. 2008;Cabrera-Ziri et al. 2022;Leath et al. 2022;D'Antona et al. 2005).To take into account the radiation of HB stars, for example, the Balmer absorption line indices were studied ★ E-mail: sme@sao.ru(Schiavon et al. 2004;Leath et al. 2022;Percival & Salaris 2011), the flux contribution of hot HB stars was added to standard isochrones (Cabrera-Ziri et al. 2022;Koleva et al. 2008), or isochrones including HBs were used Sharina et al. (2020) (hereafter, S20 and references therein).The results of building the model IL spectra of GCs using the synthetic or observed spectra of stars and the results of analysing the distribution of stars in the colour-magnitude diagram (CMD) depend on the stellar evolution models used.However, it is not yet possible to take into account variations of some parameters during stellar evolution, for example, the variety of the convective overshoot conditions in stars depending on their chemical composition, mass, and evolutionary stage (Viani et al. 2018;D'Antona et al. 2018, and references therein).Star clusters of the same age and metallicity can have different HBs with a predominance of blue or red stars, which may occur due to differences in Y and in the mass-loss efficiency of red giants (see, e.g., Tailo et al. 2020;D'Antona et al. 2005;Percival & Salaris 2011;Lee et al. 2000).The result of studying the IL spectra of GCs also depends on the quality of the observed data.Often it is difficult to take into consideration the level of the foreground and Table 1.Literature and our (marked with superscript 0) characteristics of the eight GCs in M31: (1, 2, 3) the name of the GC, the designation of it used in this article and the name of the host galaxy; (4) the right ascension and declination of the object for the epoch J2000.0;(5,6) the absolute magnitude and radial velocity; (7,8,9) the age in Gyr, Z, and Y of the isochrone that we used in modelling the cluster spectrum.For all the GCs, except for EXT8, the isochrones by Bertelli et al. (2008) were used.For EXT8, the best solution was provided by the canonical scaled-solar isochrone by Pietrinferni et al. (2004).In the second lines of columns (5, 6, and 7), the literature data are given for each object from the papers: Larsen et al. (2022)   [GPH2009] KK NGC5128 13:22:02.0636±4 0 13.6±0.47 00.00013±0.000030.26 +0.04 −0.01 08.1 -9.8 G09 635±2 F20 6.5 F20 background contamination and stochastic variations in the number of stars at different evolutionary stages within the studied aperture.
In this paper, we study the IL spectra of the representatives of very metal-poor extragalactic GCs ([Fe/H] ≤ −2 dex).GCs with such metallicity are few in our and other galaxies and predominantly have blue HBs (Harris 2010;Beasley et al. 2019).Our analysis of lowresolution spectra (/Δ ∼ 1000) of GCs in nearby galactic groups is based on the method and results by S20 for the Galactic GCs in a wide metallicity range.The present study further improves this method.We study the influence of the properties of HB stars (T eff and luminosity) on Balmer line profiles in the IL spectra of GCs and introduce an automatic procedure of selecting the isochrones of stellar evolution for IL spectra modelling.In order to study the HB morphology, we separately consider two parameters: depth and width at half intensity (FWHM) of the Balmer lines in the IL spectra of GCs.Comparing the results of the analysis of the IL spectra of the Galactic GCs by S20 with the properties of stars on the CMD of these objects, we determine the accuracy of estimating the effective temperature T eff and luminosity of HB stars from the IL spectra.Our study will answer the question whether all the sample very metal-poor extragalactic GCs have blue HBs as their Galactic counterparts.

SAMPLE OF GLOBULAR CLUSTERS
The sample of objects is built based on the results of our observations at the 6-m telescope of the Russian Academy of Sciences (hereafter: BTA) in 2020 -2021 and at the Southern African Large Telescope (SALT) in 2019 -2020.We also use the spectra acquired by Caldwel et al. (2011) and references therein) during their observations with the Hectospec spectrograph of the 6.5-m MMT telescope (Fabricant et al. 2005).Caldwel et al. (2009Caldwel et al. ( , 2011) ) determined the radial velocities, ages, and metallicities for these and many other clusters in M31 from Hectospec observations by measuring the Lick absorption indices and comparing them with the modelled values.We selected only old GCs with [Fe/H] ≤ −2 dex from the sample of Caldwel et al. (2011) and analysed the spectra with high signal-to-noise ratio (SNR).According to our experience, the spectra with SNR ≥ 100 per pixel in the resulting one-dimensional spectrum at a wavelength of 4500 Å provide accurate results.The analysis of spectra of higher metallicity GCs will be presented elsewhere.In the columns 4 -6 of Table 1 main characteristics from the literature for the studied objects are presented: equatorial coordinates, absolute magnitudes in the V band of the Johnson-Cousins photometric system and radial velocities.In the second column of Table 1, symbolic designations for the objects' names used throughout this paper are given.The columns 7 -9 contain parameters of evolutionary isochrones selected by the analysis of the IL spectra.The IL spectra and their reduction will be characterised in Sec. 3. The methods of the spectra analysis will be described in Sec. 4.

BTA and SALT data
Observations of the sample GCs were carried out with BTA and with SALT (Buckley et al. 2006;O'Donoghue et al. 2006).
The SCORPIO-I focal reducer (Afanasiev et al. 2005) mounted at BTA was used in the long-slit spectroscopy mode.Equipped with the VPHG1200B grism, the reducer provides the spectral range of 3600−5400 Å and the spectral resolution FWHM ∼ 5.5 Å (full width at half-maximum) with a slit width of 1 ′′ .We used the Robert Stobie Spectrograph (RSS) (Burgh et al. 2003;Kobulnicky et al. 2003) at SALT in the long-slit mode with a slit width 1.25 ′′ , the grating pg0900, blocking filter pc03400 and the Camera Station parameter 26.5.The spectra cover a spectral range of 3700-6700 Å with a reciprocal dispersion of 0.97 Å pixel −1 and spectral resolution of FWHM = 5Å.The log of observations is presented in Table 2.The table columns for each cluster observed on a particular date show: (2) the date of observation, (3) the exposure time, (4) the SNR per pixel at a wavelength of 4500 Å obtained after reduction of the one-dimensional spectra, and (5) the FWHM of stellar images.
The long-slit spectra were reduced using the MIDAS (Banse et al. 1983) and IRAF (Tody 1993) software packages.The primary reduction of CCD images, the cosmic ray removal, and the linearisation of the two-dimensional spectra using the successively obtained spectra of the He-Ne-Ar lamp were performed in MIDAS.The dispersion relations constructed for each object provided a wavelength calibration accuracy of about 0.16 Å.The sky background subtraction was performed in IRAF using the background procedure.The one-dimensional spectra were extracted in IRAF using the apsum procedure with correction of the spectrum curvature along the dispersion.

The 6.5-m MMT telescope data
The used MMT spectra of GCs B317, B2, and B165 from the observation archive of the Hectospec spectrograph of the 6.5-m MMT telescope (Fabricant et al. 2005).The spectra of the clusters are given in the Hectospec spectrograph archive after reducing.They were obtained with a grid of 270 lines/mm with a dispersion of 1.21 Å/pixel in the spectral range of 3650 − 9200 Å.In the columns of Table 3, for each cluster observed on a specific date, the following archive data from the Hectospec spectrograph of the 6.5-m MMT telescope (Fabricant et al. 2005) are given: (2) the date of observations, (3) the total exposure time, (4) the SNR per pixel in the reduced one-dimensional spectrum, and (5) the program identifier.We co-added the reduced BTA one-dimensional spectrum of B317 in the spectral range of 3900 − 5400 Å to the corresponding MMT spectra Tab.3.The spectral resolution is FWHM ∼ 5 Å.Before co-adding, the Hectospec spectra were normalised to a wavelength resolution similar to that of SCORPIO-I.The dependence of the spectral resolution on the wavelength and the subsequent smoothing of the spectra to the required resolution were determined based on the study of the line spread function (LSF) of the spectrograph using the UlySS software package of the University of Lyon (Koleva et al. 2008(Koleva et al. , 2009)).The UlySS web page gives examples of building the LSF: http://ulyss.univ-lyon1.fr/tuto_base.html.The spectrum of any object can be represented by a convolution of the spectrum belonging to the object itself and the LSF describing the properties of the instrument.The LSF can be determined using the spectra of: 1) the twilight sky, 2) the calibration lamp in a spectrograph, or 3) the compact object (a standard star, a globular cluster).1, and the element abundances presented in Table 4.
When observing the extended objects (for example, galaxies) occupying most of the CCD frame, the first or second way of building the LSF is used.Since the globular clusters under study at a distance of M31 can be seen as compact objects, it is possible to use their spectra to build the LSF.This LSF will describe the instrument function for that particular part of the CCD frame.Examples of LSFs built for the spectra obtained with the SCORPIO-I (BTA) and Hectospec (MMT) spectrographs are shown in Fig. 1.
To measure the radial velocities of GCs (Table 1) from their IL spectra, we used the UlySS package with the PEGASE-HR model grids (Le Borgne et al. 2004), the Salpeter IMF (Salpeter 1955), and the ELODIE (Prugniel & Soubiran 2001) stellar library.We used the instrumental LSFs built with UlySS to determine the radial velocities.
The resulting one-dimensional spectra of the clusters are shown in Fig. 2 compared with the synthetic ones calculated by the methods from the present paper and described in Section 4 with selected isochrone parameters and element abundances given in Table 1 and  Table 4, respectively.The normalisation of the observed spectra to the synthetic ones was performed with the methods given in Appendix A that describes our procedure for the automatic selection of an isochrone for the optimum description of the observed IL spectrum.

SUMMARISING THE METHOD OF IL SPECTRA ANALYSIS
The procedure of our analysis of the IL spectra of GCs is as follows (see also S20).Age, Y, and the approximate value of [Fe/H], determined from the isochrone parameter Z, are selected, first, using the isochrone fitting procedure described below in Sec.4.2 and Appendix A. Then the chemical composition including the iron abundance is specified by fitting the intensities of individual absorption features in the IL spectrum using the calculation of the synthetic spectra of GCs, that is, in fact, the chemical composition of GCs is compared with the solar one.The abundances of chemical elements are determined by varying them until the best agreement is achieved between the observed and model profiles of the spectral feature associated with a particular element.This scheme may be far from ideal but it works for the purposes of our study, as have been shown by the tests using the spectra of the Galactic GCs described in this and previous papers (Sharina et al. 2014(Sharina et al. , 2017(Sharina et al. , 2020)).Note that in the analysis of IL spectra of extragalactic GCs, we use only the comparison of the observed and synthetic IL spectra.However, in order to evaluate the results of our analysis and continue to improve our method, it is also important for us to compare the isochrones selected with our method for the specific GCs and the observed CMDs, if any.In the following, we will depict the details of the method more specifically.

Calculating the Synthetic IL Spectra of GCs
Synthetic IL spectra are computed with the CLUSTER software package (S20) in accordance with the selected abundances of chemical elements, stellar mass function, and stellar parameters T eff and log(g), defined by the chosen isochrone of stellar evolution.We use the plane-parallel hydrostatic models of stellar atmospheres set by the ATLAS 9 model grid (Castelli & Kurucz 2003) based on the solar metal distribution from Grevesse & Sauval (1998) 1 .We apply the air wavelengths for our analysis 2 .The program CLUSTER has been developed with the methods of synthetic stellar spectra calculation described by Shimansky et al. (2003).This is performed in the course of numerical modelling of the radiative transfer in stellar atmospheres obtained by interpolation to the required parameters with the method described by Suleimanov (1996).More specifically, cubic interpolation in T eff and linear in log(g) is used, which makes it possible to obtain the distributions of depth and gas pressure, as well as the spectrum of escaping radiation with an accuracy of 1% (Suleimanov 1996).In the plane-parallel models of stellar atmospheres the distribution of temperature, pressure, and concentration of atoms and ions depending on the optical depth is determined by the given parameters of the star: T eff , log(g), and metallicity.When computing the synthetic spectra of individual stars, for the given specific stellar parameters and chemical composition, the concentrations of atoms and ions are calculated depending on the depth in the atmosphere, and 1 Lists of atomic and molecular spectral lines are available on the R. L. Kurucz website (http://kurucz.harvard.edu/linelists.html). 2 The IAU standard for conversion from air to vacuum wavelengths is given in Morton (1991).
the contribution of each atom or ion to the emission and absorption coefficients at the given wavelength is determined.
Model IL spectra of GCs ( ()) are computed using the synthetic spectra of the stars ((,m)) according to the given mass function () with the initial mass (m) taken from the isochrones of stellar evolution: We calculate synthetic IL spectra with the stellar mass function by Chabrier (2005) (formula 2).It is in agreement with both the theoretical distribution for low-mass stars (Padoan & Nordlund 2004) and the HST-observed mass function for nearby stars (Zheng et al. 2001).In the mass range of stars in old globular clusters, this function is close to those derived by Salpeter (1955) and Kroupa (2001).

Isochrone Selection for Calculating the IL Spectrum
In this study, we mainly use the isochrones of stellar evolution by Bertelli et al. (2008) (hereafter, B08)3 including the helium burning phase.The minimum initial stellar mass for the isochrones by B08 is 0.15  ⊙ .The selected isochrones are based on the solar abundances from Grevesse & Noels (1993) and on the initial metallicity of the Sun Z = 0.017 (Grevesse & Sauval 1998), i.e. close to the abundance scale on which the ATLAS 9 code is based.Tab. 5 shows the mass fractions of hydrogen (X), helium (Y), and metals (Z) adopted in our analysis with the ATLAS 9 model atmospheres (Castelli & Kurucz 2003) compared to several compilations of the solar chemical composition (Grevesse & Noels 1993;Grevesse & Sauval 1998;Caffau et al. 2011).The BASTI (Pietrinferni et al. 2004) 4 isochrones are based on the solar abundances from Grevesse & Noels (1993).The new BASTI models (Hidalgo et al. 2018;Pietrinferni et al. 2021) 5 employ the Caffau et al. (2011) solar metal distribution.One can ensure that the solar chemical element distribution adopted for our analysis is closer to the distributions by Grevesse & Noels (1993) and Grevesse & Sauval (1998) than to the distribution by Caffau et al. (2011) used in the new BASTI models.
The temperature and luminosity of HB and other stars depend on many factors including He, CNO and metal abundances.Therefore, the change in the abundance scale in our analysis is not straightforward and will be studied elsewhere.The B08 isochrones were computed with the mass loss by stellar wind during the red giant branch (RGB) of low-mass stars taken into account using the mass loss rate parameter Reimers (1975)  = 0.35.This value is close the  parameter range directly estimated with Kepler for HB stars in two old open clusters by Miglio et al. (2012).Miglio et al. (2012) compared the difference between the average mass of low-luminosity RGB and red clump stars to theoretical predictions using, among others, B08 isochrones.
Selection of the isochrone for calculating the synthetic IL spectrum can be performed using an automatic procedure that minimizes the deviations between the synthetic spectrum and the observed one normalised to the synthetic.The program is written in the Python language v3.8.8 6 using the Numpy and Scipy 7 packages.The description of the program is given in the Appendix A to the paper.For Table 4.The first line for each object shows the LTE abundances of chemical elements obtained by us for seven GCs in M31 from the modelling of their IL spectra (marked with superscript 0 ).The second line shows the literature LTE abundances for each object, if any.Superscripts L22, C11, and F20 mean references to the papers by Larsen et al. (2022), Colucci et al. (2011) andFahrion et al. (2020)

EXT8
-2.8±0.15 00.00±0.14 0-0.40±0.17 00.35±0.090 0.30±0.18 0-0.2±0.19 0 0.3±0.2 0-2.81±0.04L22 -0.27±0.22L22 0.37±0.06L22 0.24±0.08L22 -0.16±0.16L22 0.89±0.17L22 KK -2.15±0.13 00.15±0.020 -0.05±0.12 00.6±0.060 0.15±0.060 0.35±0.080 0.1±0.3 0-1.84±0.05F20 Table 5.Chemical composition of the Sun in terms of the mass fractions of hydrogen (X), helium (Y), and metals (Z) adopted in our analysis with the ATLAS 9 model atmospheres (Castelli & Kurucz 2003)  this purpose, a grid of the synthetic IL spectra is used calculated with the specified chemical composition, as well as the specified set of parameters of isochrones and [Fe/H] of the utilized models of stellar atmospheres.In the process of the isochrone assortment (see Appendix A for more details), the synthetic spectrum that best matches the observed one is selected from the pre-calculated grid ones by minimization of the  2 function: where obj i and err i are the elements of the cluster observed spectrum and error spectrum, theor i is a synthetic spectrum set by the isochrone parameters q1, q2, q3, and q4 (Y, the logarithm of age, the metallicity of the isochrone Z, and the metallicity of model atmospheres [Fe/H] atm ).Before calculating , the continuum level of the observed spectrum is normalised to the level of the synthetic continuum.
To model the spectrum of the GC with the lowest metallicity in our sample, Ext 8 (Tab.1), we used a scaled-solar canonical BASTI (Pietrinferni et al. 2004) isochrone with the mass loss rate parameter (Reimers 1975)  = 0.4.In the BASTI canonical models by Pietrinferni et al. (2004) based on the solar abundances from Grevesse & Noels (1993), Y is related to metallicity as follows: dY/dZ ∼ 1.4.The BASTI isochrones with various values of Y at a given metallicity Pietrinferni et al. (2006) are based on alpha-enhanced heavy elements distribution and do not include HBs.The alpha-enhanced canonical BASTI isochrones Pietrinferni et al. (2006) with the opacities from Ferguson et al. (2005) include HBs and are available only for the Henormal composition: dY/dZ ∼ 1.4.For the above mentioned reasons, in this study we use only the isochrones in the solar abundance scale by Grevesse & Noels (1993) or Grevesse & Sauval (1998) which are close to each other.We do not use the new BASTI isochrones (Hidalgo et al. 2018;Pietrinferni et al. 2021) based on the solar abundances from Caffau et al. (2011).
To illustrate in more detail the reasons for our choice of isochrones, in Tab.B1 (Appendix B) we compare T eff and L(L ⊙ ) for the three main stages of stellar evolution: the maximum in T eff along the Main sequence (MSTO point), the tip of the red giant branch (TRGB), and the start of quiescent core He burning (HB).Isochrones with an age of 12.5 Gyr and Z = 0.0001 by B08, by Pietrinferni et al. (2004)  Pairwise compared isochrones differ only in one of the following parameters: the helium mass fraction (Y), the mass-loss efficiency  according to the Reimers (1975) formula, and availability of taking into account the effect of atomic diffusion (Diff = Y or N).We also compare the scaled-solar canonical BASTI isochrones by Pietrinferni et al. (2004) and Hidalgo et al. (2018) with the equal parameters Y, , and Diff; the scaled-solar with the alpha-enhanced canonical BASTI isochrones (Pietrinferni et al. (2004) and Pietrinferni et al. (2006)) with other similar parameters; and the scaled-solar with the alpha-enhanced new BASTI isochrones (Hidalgo et al. (2018) and Pietrinferni et al. (2021)) with other similar parameters.Here are some conclusions that follow from this comparison.When moving from the scaled-solar canonical BASTI isochrones (Pietrinferni et al. 2004) to the new scaled-solar BASTI isochrones (Hidalgo et al. 2018) These significant variations in T eff and L(L ⊙ ) arising, when the initial solar chemical composition changes, impose restrictions on our use of isochrones.We will come back to other comparison results given in Appendix B later.

On the contribution of isochrone points to the IL spectrum of a GC
The grids of model atmospheres by Castelli & Kurucz (2003) that we use set the following parameter limitations for any [Fe/H] values: 0.0 < log(g) < 5.0 and temperature 3400K < T eff < 45000 K.If for the current isochrone point, one parameter goes beyond the specified limits, the nearest boundary value is assigned to it.This procedure does not affect the accuracy of calculations, since, as a rule, cool low-mass MS stars making a small contribution to the spectrum of the cluster go beyond the indicated ranges.We found out that when analysing the low-resolution IL spectra of GCs it is acceptable to take into account only the isochrone points with a contribution larger than 0.2% to the IL spectrum.The detailed description of the procedure for selecting the isochrone points is presented in Appendix C. Note that when using this procedure we do not change the original parameters of the isochrone points (T eff , logg, R, and M).An example of the result selecting the isochrone points to calculate the IL spectrum is presented in Fig. C1, which argues that, when the number of points is reduced, the structure of the isochrone and the total relative contribution of the isochrone points to the overall spectrum are preserved.

ON THE INFLUENCE OF THE HB STARS ON THE BALMER LINES IN THE IL SPECTRA
It has been established in a number of studies (see Sec. 1), that HB stars make a significant contribution to the IL spectra of GCs.
In the following, we will study the changes in the intensities, i.e.FWHM and depth (I core ), of the Balmer lines in the IL spectra of very low-metallicity GCs depending on the age.Our experience shows that separate consideration of these two parameters characterizing absorption lines is useful due to the fact that stars at different evolutionary stages contribute in different proportions to the IL spectra, and FWHM and I core in the spectra of stars depend on the parameters of their atmospheres.For example, the hydrogen lines of hot HB stars are wide and deep, while the lines of RGB stars are narrow and shallow.FWHM and I core of the Main sequence and subgiant branch stars have different, intermediate values between those for the HB and RGB stars.In this section, we consider the isochrones with varying Y and Z = 0.0001 ([Fe/H] ∼ −2.23 dex) (B08).In the Appendix D we examine the isochrones by B08 with Z = 0.0004 ([Fe/H] = −1.63dex).Since, as a result of our analysis of the spectrum of EXT8, the metallicity of this GC turned out to be lower than the metallicities in the model grid of B08, in this case we used the isochrone by Pietrinferni et al. (2004) (left panel of Fig. D1).Note that we measure the parameters FWHM and I core in the H  , H  , and H  hydrogen lines normalised to unity in the wavelength regions: 4089.05− 4115.4Å, 4318.4 − 4363.5 Å, and 4815.8 − 4896.5 Å, respectively.
Figs. D1, D2 in the Appendix D show how the isochrones vary with age and Y.In particular, with the increase of age, the effective temperatures of the MSTO stars decrease, while for the hottest HB stars, on the contrary, they increase.With the increase of age, the luminosity of the MSTO stars and of the hottest HB stars decrease.Similar conclusions concerning the variations with age are valid for the scale-Solar canonical BASTI isochrones Pietrinferni et al. (2004) with Z = 0.00001 (left panel of Fig. D1).
Fig. 3 compares the variation of the parameters logT eff (on the left) and logL (on the right) with age for the MSTO stars and stars at the HB blue end (see also Fig. D3 in the Appendix D for the case of Z = 0.0004).The temperatures of the MSTO stars decrease with age.The luminosities of the MSTO stars and the hottest HB stars behave similarly.On the other hand, logT eff for the stars at the HB hot end increases non-linearly with age at different rates for different Y.If we consider the B08 isochrone, then the higher the Y value, the hotter the HB first point.
The considered variations of the parameters logT eff and logL significantly affect the FWHM and I core of the Balmer lines in the spectra of GCs which will be illustrated below.Fig. 4 shows the variation of I core and FWHM with age for three Balmer hydrogen lines in the synthetic IL spectra of GCs with the metallicity Z = 0.0001 (see also Fig. D4 in the Appendix D for the case of Z = 0.0004).The model dependences in Figs 4 and 5 are built for the spectral resolution FWHM = 5.5 Å.The synthetic spectra were obtained using the B08 isochrones for Y = 0.23, 0.26, and 0.30 (Fig. 5).Fig. 4 shows that FWHM and I core vary monotonously with age.The higher the value of I core , the shallower the line becomes, i.e., closer to the continuum level.Similar changes of I core and FWHM with age for three Balmer hydrogen lines can be seen in the case of Z = 0.0004 (Fig. D4 in the Appendix D).
If helium burning stages of stellar evolution are taken into account when building the IL synthetic spectra (Fig. 5), the behaviour of the FWHM and I core variation is no longer monotonous with age.First, the depth and FWHM decrease with the increase of age, mainly due  to the fact that T eff and L of the MSTO stars decrease, but T eff of the HB stars does not increase in such a quick way as to compensate for this decrease.
As soon as T eff for the hottest HB stars exceed T eff for the MSTO stars, and as T eff of the hottest HB stars continues to increase (see Fig. D1 in the Appendix D and Fig. 3), the hydrogen lines start getting deeper and wider.This continues until the moment, when T eff reaches ∼ 9000 K for the HB stars, at which the hydrogen line intensities begin to decrease again.This is due to the intense hydrogen ionization at the given temperature.Thus, the growth rate of FWHM and I core for the HB stars varies depending on age.This is due to how quickly their temperature and contribution to the IL spectrum varies with age.Similar changes of I core and FWHM with age for three Balmer hydrogen lines can be seen in the case of using the isochrones by B08 with HBs and Z = 0.0004 (Fig. D5 in the Appendix D). Lee et al. (2000) and Percival & Salaris (2011) detected a nonmonotonic variation of the Lick H  index, when hot HB stars were considered.The details of the modelling of the horizontal branch morphologies are different in our and those studies.The general conclusion is that underestimation of the contribution of the HB stars to the IL spectra results in underestimation of the age of GCs.In the work by Percival & Salaris (2011), there is an important conclusion about the difficulty of taking into account statistical fluctuations in the number of stars on the HB in the spectra of real GCs when determining their age and metallicity.Percival & Salaris (2011) found that the extension of the real HB in the CMD, and accordingly, the H  indices differ from the modelled ones by setting an average mass and implementing the Gaussian spread in masses of individual stars coming on to the HB for each stellar evolutionary model.

Comparison of the Distribution of Stars on the Observed CMDs with the Isochrones Selected when Modelling the IL Spectra
Before considering the comparison of isochrones with the parameters determined from analysing the IL spectra and the stellar photometry data of extragalactic GCs available in the literature, let us turn to such a comparison for the Galactic GCs analysed by S20.Accurate stellar photometry for them was performed by Piotto et al. (2002) and by Sarajedini et al. (2007) in the B, V and V, I filters of the Johnson Cousins photometric system, respectively.Following S20, we plot Parameter/ CMDs of the GCs as colour corrected for extinction versus absolute magnitude, i.e., (B − V) 0 versus   (Piotto et al. 2002), or ( − ) 0 versus M I (Sarajedini et al. 2007).Then we superimpose the B08 isochrones with the parameters determined by S20 onto the CMDs and estimate for 35 Galactic GCs the differences between T eff and L(L ⊙ ) observed for the cluster HB stars and the isochronous ones.We estimate T eff of bright hot stars on the blue end of the HB and logL(L ⊙ ) of the mid-HB stars by interpolation of theoretical relations for HB stars: colour versus T eff and absolute magnitude versus logL(L ⊙ ).A detailed description of this procedure is given in the Appendix E. While this is a crude approximation, taking into account, among other factors, the scatter of the colours and magnitudes of HB stars, this comparison with deep photometry data will help us to reveal the caveats and limitations of our method.
Figure 6 shows the estimated and observed T eff and L(L ⊙ ) values in comparison with the corresponding theoretical ones.The standard deviation from the isochronous luminosity value in the I filter for the mid-HB stars has a scatter of about std(I HB ) = 0.19 ± 0.1 mag.On average over the sample of 35 Galactic GCs, this value corresponds to: ΔL ∼ 15L ⊙ (Fig. 6).It should be noted that for half of the sample objects, this value does not exceed Δ ∼ 4 ⊙ .When considering the results of the comparison of the isochrones in Tab.B1 (Appendix B), discussed in Sec.4.2, the largest discrepancy in L(L ⊙ ) for the HB is expected between the isochrones with different .The isochrones with the higher  demonstrate the lower logL(L ⊙ ) for HB (case (f) in Tab.B1).Therefore, one of the reasons for the differences in logL(L ⊙ ) in the selected isochrones and the data for the real HB stars on the CMD may be the difference in the average values  for a cluster from those isochronous.Another reason for large deviations of the luminosity of HB stars from the corresponding isochronous values (ΔL ≥ 10L ⊙ ) may be the contribution of hot stars of GCs, beyond the HB luminosity, such as blue straggler stars, asymptotic giant branch (AGB), and variable stars to the IL spectrum.Also, field stars of the corresponding temperature that do not belong to GCs can contribute.
The average colour scatter (( − ) 0 , (B − V) 0 ) of bright hot stars on the blue end of the HB for 35 Galactic GCs is ∼0.1 mag.The typical deviation of the average colours (T eff ) of stars in the HB blue part from the corresponding values at the isochrone points selected from the IL spectra of clusters by S20 is smaller than one percent for the HBs cooler than ∼8000 K, and 3% for HBs with T eff ∼ 10000 K (Fig. 6).For hotter HBs, the deviation can reach 4-6%.However, there are GCs with HBs cooler than ∼10000 K and with large ΔT eff (Fig. 6).These are GCs with complex HB morphology, such as NGC6171, NGC6441, and NGC6569.These GCs exhibit a rich-populated red part of the HB and a small number of stars in the blue part of the HB, which may nevertheless fall into the IL spectrum.It follows from Tab. B1 (Appendix B) that the greatest differences in T eff of the HB blue end, up to 2000 K, occur between the isochrones with different Y and the isochrones with different  and other equal parameters (cases (c) -(f) in Tab.B1).Therefore, the reason for the large deviations of the isochronous T eff of the HB blue end from the average T eff estimated for the blue end HB stars may be differences in the average values of  and Y for a cluster from those isochronous.Significant deviations from the model values of T eff and logL(L ⊙ ) occur for clusters close to the Galactic plane, as well as those shielded from us by the Galactic plane.Probability of the contribution of field stars to such IL spectra increases significantly.The parameters of isochrones selected from the IL spectra and, therefore, T eff and logL(L ⊙ ) will turn out to be distorted for the main evolutionary stages, if field stars of any temperature and luminosity have contributed to the IL spectrum.In general, based on the sample of 35 Galactic GCs, we can conclude that for ∼75% of the sample it is possible to determine the parameters of HB stars quite confidently with regard to the above-mentioned caveats.Similar problems can be expected for extragalactic GCs, especially for those observed in dense fields of field stars.
It should be noted that, in addition to contamination problems, limitations on the accuracy of selecting the stellar evolution isochrone to describe the observed IL spectrum can be imposed by the specific features of the stellar evolution models used.For example, inclusion of atomic diffusion in the BASTI models (Pietrinferni et al. 2021;Hidalgo et al. 2018) significantly improved the result of approximating theoretical isochrones to the results of photometry of the MSTO stars.On the other hand, atomic diffusion increases the mass of the He-core at the He ignition for a given initial chemical composition and decreases the He abundance in the stellar envelope.The luminosity and T eff of core He-burning stars are higher in Pietrinferni et al. (2021) than those in the previous -enhanced BASTI models (Pietrinferni et al. 2006).In Tab.B1 (case (g)) (Appendix B) we compare the BASTI new (Hidalgo et al. 2018) scaled-solar isochrones with taking or not into account the effect of atomic diffusion (Diff = Y or N).It can be seen that T eff of the HB blue end is higher in the case of Diff = Y by approximately 400 K from that in the case Diff = N.Another limitation is that it is not yet possible to take into account variations of some parameters during stellar evolution, for example, the variety of the convective overshoot conditions in stars treated in the models of the stellar evolution according to the mixing length theory by Böhm-Vitense (1958) (see, e.g., Viani et al. 2018;D'Antona et al. 2018, and references therein).The mixing length and the mass-loss efficiency parameters are assigned fixed values in the models.However, in real GCs they can vary from star to star.Recently, the first direct estimates of the mass loss of the Galactic GCs on the RGB using asteroseismology methods have appeared.(Howell et al. 2023).
Using Fig. 3, as well as Figs.D1, D2, and D3 in the Appendix D, one can estimate the maximum T eff of HB stars belonging to our sample GCs in accordance with the isochrones selected from the IL spectra (Table 1).The most blue extended HBs host GCs HIII, C39, and Ext 8 with the maximum T eff ∼ 12600K.The nuclear GC in KK197 hosts hot HBs stars with T eff ∼ 10000K.The maximum T eff of other four GCs (PA, B317, B2, and B165) is 8000-9000 K.

HIII and B317
In the following we will check the correspondence of the isochrones that we selected, when modelling the IL spectra of the GCs, to the observed CMDs of these objects.We built the Hess diagrams for HIII and B317 (Fig. 7) using the stellar photometry by Sharina et al. (2006) 9 performed with the images from WFPC2 HST.The circular apertures for selecting stars within and around the clusters remained the same as those determined in the original paper.The colour intensity in each bin (0.1 mag × 0.1 mag) on the Hess diagrams means the number of stars labelled under the colour-bars at the bottom  6, column 4).These benchmarks are quite acceptable for solving the problem, since the number of stars near the TRGB of the clusters is small and the field stars, making a significant contribution in terms of population to the CMD, differ little in colour and luminosity from the stars belonging to the objects under study.Table 6 shows our and literature (m − M) 0 and E(B − V), as well as the absolute magnitude of the HB level (column 5) calculated with formula (2) from Federici et al. (2012) and our [Fe/H] estimates from Table 1.The second column gives the corresponding apparent magnitude of the HB level (a thin solid line in Fig. 7 ) calculated from M V (HB), (m − M) 0 , and E(B − V) in Table 6.

EXT8
EXT8 is remote from M31 GC residing in the halo of this galaxy.Its deep CMD Larsen et al. (2021) (hereafter: L21) is much less polluted by field stars and the photometric depth is greater than in the case of HIII and B317.There are quite a lot of stars near the TRGB on the CMD of EXT8, and the HB is clearly visible (L21).Fig. 8 shows the CMD of EXT8 built from the L21 results in a radius of 30 pc (200 pix × 0.15 pc/pixel) from the centre of the object.The large black dots in Fig. 8 demonstrate the stellar photometry in the drc images in the F606W and F814W filters11 selected by photometric errors (dF606W < 0.1 mag and dF814W < 0.1 mag) and by the ALLFRAME sharpness parameter which was set to be in the range from −0.1 to 0.22.After this selection, the ALLFRAME chi-square parameter for the stellar images in two filters appears to be smaller than 13.Note that the photometry table in the flc images from L2112 does not contain the sharpness and chi-square parameters.Therefore, the selection for these data was performed only by the photometry errors.The small black dots in Fig. 8 demonstrate the stellar photometric data in the flc images from L21 selected by the photometric errors as follows.We have set the errors on the magnitudes in two  filters (dF606W and dF814W) and R.M.S. on the F606W and F814W magnitudes to be smaller than 0.1 mag.Such a limitation on the photometry errors was not chosen by chance, since according to artificial star experiments in L21 (see their fig.3), the photometric errors should be smaller than 0.1 mag for the RGB and HB stars.In addition to the RGB and HB stars, the stars bluer than the RGB as well as the stars brighter than the HB, which are apparently the field stars, remain in the cluster region after the selections.In the mF814W filter, the stars being in terms of brightness approximately at the level of the TRGB and bluer than it are located mainly in the central part of EXT8 and have, on average, high values of chi-square and sharpness.
It can be seen in Fig. 8 that the solar-scaled canonical BASTI isochrone (Pietrinferni et al. 2004) chosen by us for analysing the EXT8 IL spectrum with the parameters Z = 0.00001, Age = 11 Gyr, and Y = 0.245 adequately describes the RGB and HB clusters.It should be noted though that the metallicity of this isochrone [Fe/H] ∼ −3.23 dex is lower than the value obtained from the analysis of the IL spectra [Fe/H] ∼ −2.8 dex (Table 4).We used (m − M) 0 = 24.5 mag and E(B − V) = 0.06 mag obtained by L21.To convert the BASTI isochrone data from VEGAMAG WFC3 UVIS to the STMAG system, we used the corrections from L21: Δ 606 = 0.246 mag and Δ 814 = 1.259 mag.Note that the instability strip in the selected isochrone (Fig. 8) approximately coincides with that on the CMD and with that found by L21.The colour boundaries for the instability strip: M 606 − M 814 from −0.8 to −0.5 (L21), or m 606 − m 814 from −0.736 to −0.436, since A 606 = 0.168 mag and A 814 = 0.104 mag.This analysis suggests that our choice of the isochrone (Table 1) is not bad.Let us turn to Tab.B1(case (j)) (Appendix B).It demonstrates a comparison of T eff and L(L ⊙ ) for the MSTO, TRGB, and HB in the scaled-solar canonical BASTI isochrones (Pietrinferni et al. 2004) with the metallicities [/] = −3.27dex and [/] = −2.27dex and other equal parameters used by us in the analysis of the IL spectrum of Ext 8.The value [/] = −2.8dex is approximately halfway between these two metallicities.If we divide the differences in T eff and L(L ⊙ ) by 2, then we can notice the following most significant differences between the isochrones.The HB is cooler by ∼ 65 K and brighter by ∼ 60L ⊙ , and the luminosity of the TRGB is higher by about ∼ 100L ⊙ for the isochrone with [/] = −2.8dex compared to the isochrone used.Since the agreement between the observed and model spectra in the region of the Balmer lines is not ideal (Fig. 2), especially in the core and wings of the H  line, then these discrepancies can be attributed to the above-mentioned differences in T eff and L(L ⊙ ) for the MSTO, TRGB, and HB.

Chemical Composition of the sample GCs
Fig. 9 shows a comparison of the chemical composition for the sample GCs with the corresponding abundances obtained with highresolution spectroscopy for the field stars of the Galaxy (Lucchesi et al. 2022;Eitner et al. 2020;Ishigaki et al. 2013;Smith et al. 2003;Venn et al. 2004) and GCs of M31 from the papers by Larsen et al. (2022), Colucci et al. (2014), andSakari et al. (2016).An overall agreement between the abundances for our sample GCs and the literature data can be seen.However, it should be noted that there are differences ≤ 0.2 dex between the literature and our LTE abundances for GCs (see also 4).The exception is the lower [Mn/Fe] value we obtained compared to that by Larsen et al. (2022) (9, panel e).We estimated the Mn abundance using the blend near 4033Å (see Fig. 1).The total contribution of the intense Mn I 4030.76,4031.79,4033.07,4033.58,4033.65,4034.49,and 4035.72 Å lines to this blend generally about 1.5 times exceeds the contribution of Fe.It should be noted that, in general, [Mn/Fe] for GCs is on average higher than that for field stars.Low Mn abundances in dwarf galaxies served as indication of sub-Chandrasekhar-mass white dwarf progenitors of SNe Ia in these objects (de los Reyes et al. 2020).
It should also be noted that almost all GCs of our sample, except B317 and B165, have low ([Mg/Fe] ≲ 0) in comparison with field stars for which [Mg/Fe] ∼ 0.4 dex.Mg is the so-called -element mainly produced by explosive C-burning in massive stars and in corecollapse supernovae (CCSNe).Unlike Mg, Ca, whose abundance appears normal compared to field stars (Fig. 9), is mainly produced in CCSNe and SNe Ia.Low [Mg/Fe] values for GCs obtained from IL spectra were considered as evidence for the presence of multiple stellar populations in GCs (e.g.Larsen et al. 2022).Low [Mg/Fe] ∼ −0.24 dex were obtained by Sharina et al. (2018) from the IL spectra of low-metallicity Galactic GCs NGC 6341 and NGC 7078 observed with the CARELEC spectrograph at the 1.93-m telescope of the Haute-Provence Observatory.These results are consistent with the discovery by Masseron et al. (2019) of extreme Mg-depleted stars in these GCs and of Mg-Al anticorrelation among the clusters' stars.The depletion reaches [Mg/Fe] ∼ −0.5 dex.Even stronger Mgdepletion likely exists for Ext 8 and B2, as follows from the analysis of their IL spectra (Larsen et al. (2022), Table 4 this paper).
[C/Fe] values that we determined from the IL spectra in the optical range, are consistent with that of the field stars, but on average higher than [C/Fe] for RGB stars in Galactic GCs (Roediger et al. 2014) and for GCs in M31 from IL spectroscopic observations in the H band (Sakari et al. 2016).The main contribution to the IL spectrum in this wavelength range is made by RGB stars.On the other hand, IL spectra in the optical range include the contribution from all the cluster stars.Note that MSTO stars make a significant contribution to the IL spectrum in the optical range.It is known from the literature that the abundances of light elements: Li, C, N, and O in stellar atmospheres change during the dredge-up processes on the RGB (Kraft 1994;Gratton et al. 2000).Thus, the difference between [C/Fe] values obtained from analysing IL spectra of GCs and the corresponding C abundances of RGB stars in GCs are due to the change of the chemical composition of the stellar atmospheres during their evolution.
Regarding the accuracy of [C/Fe] estimates using low-resolution IL spectra, it should be noted that the contribution of carbon to the CH band at 4240 − 4330 Å is approximately five times greater than the contribution of oxygen.The abundances of other elements (Ti, Mg, Si, Ca, Al, and Fe), whose lines contribute the CH band, can be determined independently using other absorption features in the spectrum.An additional test for the correctness of [C/Fe] obtained from the CH band is provided by other molecular lines involving C, for example, CN band at 4120 − 4220 Å.There are no O-dominated spectral features in the studied spectra.Therefore, [O/Fe] is estimated indirectly and depends on [C/Fe].The abundance of oxygen was set within the limits: [O/Fe] ∼ 0.3 ÷ 0.5 dex.In S20, it was demonstrated that [C/Fe] for the Galactic GCs obtained with our method is higher by about 0.4 dex than those obtained with high-resolution spectroscopy for some of the brightest stars in these clusters.However, there are no systematic differences between IL [C/Fe] abundances obtained using the same spectra of Galactic GCs from Schiavon et al. (2005) by Conroy et al. (2018) and S20.

CONCLUDING REMARKS
The distribution of GCs by colour and metallicity is bimodal in many massive galaxies with prominent metallicity peaks near [Fe/H] = −1.6 dex and [Fe/H] = −0.6 dex (Harris 2010;Beasley et al. 2019).Very low metallicity GCs are rare, massive, and predominantly have blue HBs (Harris 2010;Beasley et al. 2019).Their chemical composition and chemical anomalies among their stars is a subject of extensive studies.Recently, extremely low-metallicity GC Ext 8 in M31 has been discovered (Larsen et al. 2022).This discovery changed our understanding about the so-called 'metallicity floor', i.e., the minimum metallicity of a GC surviving in the Universe (Beasley et al. 2019).Our study contributes to investigation of very metal-poor GCs.We determine the properties of HBs, i.e., T eff and luminosity of HB stars set by the isochrones of stellar evolution for GCs with [Fe/H] ≤ −2 dex.We improve the method by S20 developed for determination of the age, metallicity Z, specific helium abundance Y, and the abundances of several chemical elements: Fe, C, Mg, Ca, Mn, Ti, and Cr.Using the low-resolution IL spectra of GCs, we explore how the FWHM and the depth of the Balmer absorption lines change depending on the isochrone used and on the properties of HB stars.We show a comparison between the parameters of HB stars on the isochrones used to model the IL spectra (S20) and the corresponding observed characteristics of HB stars from the Galactic GCs (see details in Sec.6.1).This comparison allows us to identify caveats of the employed method.We conclude that the main sources of errors in the isochrone selection with our method of modelling the intensities of the Balmer hydrogen lines in the IL spectra of GCs are the lack of knowledge about the actual mass losses of the RGB stars in the clusters under study (we used the isochrones with the fixed mass-loss efficiency parameters  (Reimers 1975)), foreground and background contamination and stochastic variations in the number of stars at different evolutionary stages within the studied aperture.
Our research has shown that all GCs in the sample are old (10 ≤  ≤ 13.6 Gyr) and have blue HBs.Using the dependences between T eff and the age (Fig. 3 and Figs.D1, D2 and D3 in the Appendix D), we estimated the maximum T eff of HB stars belonging to our sample GCs, in accordance with the isochrones selected from the IL spectra (Table 1).Studying the IL spectra of HIII, C39, and Ext 8 reveals that they have blue extended HBs with the maximum T eff ∼ 12600K.The nuclear GC in KK197 hosts hot HBs stars with T eff ∼ 10000K.The maximum T eff of HB stars in other four GCs (PA, B317, B2, and B165) is 8000-9000 K.
Chemical abundances of Ca, Ti, C, and Cr correspond well to the abundances of stars in the Galactic field (Sec.6.2 and Fig. 9).Carbon abundances determined from the IL spectra of GCs are higher than the corresponding data for RGB stars in the Galactic GCs (Roediger et al. 2014) and for GCs in M31 from the IL spectroscopic observations in the H band (Sakari et al. 2016).This is due to the change in chemical composition of stellar atmospheres during their evolution (Sec.6.2).Almost all GCs of our sample, except for B317 and B165, have low Mg abundances ([Mg/Fe] ≲ 0) compared to field stars, whose [Mg/Fe] ∼ 0.4 dex.This is an indication of the presence of multiple populations (Larsen et al. 2022) and of extremely Mg-depleted stars (Masseron et al. 2019) in these GCs.Manganese abundances are higher in our sample GCs, than those in field stars.Low Mn abundances in dwarf galaxies were explained by the presence of sub-Chandrasekhar-mass white dwarf progenitors of SNe Ia (de los Reyes et al. 2020).
It can be concluded that there are similarities between the properties of very low-metallicity ancient GCs in different galaxies and different environments, which indicates similar evolutionary processes.However, individual parameters of stars in GCs, such as T eff , luminosity, and chemical composition, undergo changes depending on local physical conditions.continuum level of the model spectrum, the maximum intensity in the range of ±1 Å is taken.The resulting continuum points are linearly interpolated over the whole length of the observed and model spectra.As a result, the observed spectrum is divided by the continuum of the observed spectrum and multiplied by the pseudo-continuum of the model spectrum.
Fig. A1 shows the results of experiments on the selection of the isochrone parameters for a hundred of spectra obtained from one synthetic one calculated with the B08 isochrone parameters Y = 0.26, log(Age) = 10.0,Z = 0.0004, and metallicity of model atmospheres [Fe/H] = −2.0dex by adding random noise using the Monte Carlo method.The average SNR in each spectrum is 100.In this case, when artificially noisy model spectra are used as the studied spectra, the error spectra are random noise which is on average 1/100 with respect to signal.Four diagonal panels in Fig. A1 show the probability distributions for each of the parameters: Y, log(Age), Z, and [Fe/H].Other panels of Fig. A1 show the joint probability distributions for these parameters computed with kernel density estimates using the Gaussian kernels.The 1 and 2 error contours are drawn in the panels of Fig. A1.The dispersions of the parameters that we have determined are as follows:  = 0.008, 0.034, 1.43E-5 and 0.018 for Y, log(Age), Z and [Fe/H], respectively.The cross marks the parameters of the isochrone of the synthetic spectrum used in the experiment.Fig. A1 shows the correlation between the parameters Y and log(Age) determined by the algorithm, as well as the correlation between the metallicity of the isochrone Z and the metallicity of the model atmospheres [Fe/H].The correlation between Z and [Fe/H] can be explained as follows.The mass fraction of chemical elements heavier than helium, Z, includes abundances of many chemical elements including Fe and iron peak elements14 .The correlation between Y and log(Age) indicates the difficulty of separating these parameters while analysing the IL spectra.This issue was discussed in Section 5 in more detail.
The program and the set of synthetic spectra computed with the B08 isochrones and a fixed chemical composition will be accessible via GitHub.for the three main evolutionary stages, correspondingly, using the canonical isochrones with  = 0.2 and  = 0.4.(case b) Significant changes of T eff at the HB take place when moving from the scaled-solar isochrones by B08 to the scaled-solar canonical BASTI isochrones (Pietrinferni et al. 2004).With all similar parameters, including the initial Solar chemical composition, these models differ in their input physics, which, as can be seen, primarily affects T eff for the HB.Pairwise comparison of the remaining corresponding isochrone parameters in case (b) does not show large differences.Since these models are based on the same initial Solar chemical composition, there may not be so large differences in T eff at Table B1.Results of comparison of T eff and L(L ⊙ ) for the three main evolutionary stages (MSTO, TRGB, and HB).The isochrones with an age of 12.5 Gyr and Z = 0.0001 by B08, by Pietrinferni et al. (2004) and Pietrinferni et al. (2006)   the HB when comparing other B08 and scaled-solar canonical BASTI (Pietrinferni et al. 2004) isochrones with all equal parameters.The largest differences in T eff at the HB between the models are expected with the change of Y (cases c, d and e) or  (case f).With the increase of Y, or the increase of the mass loss from  = 0 to  = 0.3, T eff for the HB increases by about 2000 K. Additionally, as Y increases, L(L ⊙ ) at the TRGB point decreases by approximately 100L ⊙ , and T eff also changes at the MSTO by approximately 30-50 K.With the increase of , no other significant changes are observed besides the growth of T eff at the HB point.
When moving from the scaled-solar to alpha-enhanced isochrones by the same authors, no major changes in T eff and L(L ⊙ ) are observed for the three main evolutionary stages (cases h and i).
(j) In this case, a comparison of the scaled-solar canonical BASTI isochrones (Pietrinferni et al. 2004) with different metallicities and other equal parameters is considered.This comparison was performed in order to approximately estimate the differences in T eff and L(L ⊙ ) for the three stages of stellar evolution during the transition from the BASTI isochrone (Pietrinferni et al. 2004) with [/] = −3.2dex, which we used to model the spectrum of Ext 8 (Tab. 1) to the BASTI isochrone (Pietrinferni et al. 2004) with [/] = −2.8dex.We obtained the latter value when model-ing the intensity of the Fe lines in the spectrum of Ext 8 (Tab.4).The metallicity [/] = −2.8dex is approximately halfway between the successive (1 and 2) values of [/] in Tab.B1 (case (j)).If we divide the differences in T eff and L(L ⊙ ) by 2, then we can notice the following most significant differences between the isochrones.The HB is cooler by ∼ 65 K and brighter by ∼ 60L ⊙ , and the luminosity of the TRGB is higher by about ∼ 100L ⊙ for the isochrone with [/] = −2.8dex compared to the isochrone used.

APPENDIX C: SELECTION OF ISOCHRONE POINTS FOR SPECTRUM MODELLING
When working with the B08 isochrones, we have developed the following procedure allowing us to check the significance of the contribution of each isochrone point to the IL spectrum of a GC and to possibly exclude the points with a very small contribution from our calculations.It should be noted that the masses at consecutive points often coincide in the isochrones by B08.This is due to the fact that the mass changes slowly along the RGB and the AGB, and the values of the evolving masses are printed with not enough decimal digits.As a result, the term dm in formula 4.1 is equal to zero.
The isochrone points with coinciding mass values near the TRGB, or on the AGB are of particular concern.Such stars have high luminosity.If a mass at the certain isochrone point coincide with the previous one, then the contribution of the next isochrone point to the IL spectrum may turn out to be implausibly large, greater than 5%.In addition to solving the above issues, development of a procedure for selecting the isochrone points, when modelling IL spectra, helps reduce calculation time.
The total luminosity of stars at the given wavelength  for an isochrone point with the number n can be approximately estimated as follows: where L() is the luminosity to be found at the given wavelength, B() n is the Planck function, F(M n ) is the mass function, ΔM n = (M n+1 − M n )/2 is half of the mass interval between consecutive points.In this study, we estimated the contribution of points to the IL of the cluster in the continuum at the wavelength  = 5000 Å.The points with a contribution smaller than 0.2 % to the IL spectrum of a GC were excluded from consideration.The removed points should not differ in temperature by no more than Δ log T eff = 0.01 dex and in surface gravity by no more Δ log g = 0.06 dex from neighbouring ones.These selection conditions were obtained experimentally.
It should be noted that, when an isochrone point is removed, the contribution of the next point to the IL spectrum increases due to the increase of its ΔM value.Therefore, two consecutive points could not be excluded simultaneously.The process of excluding the points was iterative, and before each iteration, the values L() n of all the points were calculated over again.Note, that in this process we do not change the original parameters of the isochrone points (T eff , logg, R, and M).An example of the result of the described procedure is presented in Fig. C1.Panel (a) presents the initial distribution of the isochrone points according to their T eff and log g.Panel (b) shows the points selected for calculating the synthetic IL spectrum.The circles of various sizes on the panel legends of Fig. C1 denote the contribution of the points in the IL spectrum.The asterisk marks the RGB tip.Fig. C1 (b) argues that, when the number of points is reduced, the structure of the isochrone and the total relative contribution of the isochrone points to the overall spectrum are preserved.

Figure 1 .
Figure 1.Variation of the measured shifts and broadening of the spectral lines in the twilight spectrum as a function of wavelength in observations with the SCORPIO-I and Hectospec spectrographs.

Figure 2 .
Figure 2. Comparison of the spectra of the studied clusters with the model ones calculated with the methods described in Section 4, with the isochrone parameters given in Table1, and the element abundances presented in Table4.

Figure 3 .
Figure 3. Effective temperatures and luminosities of the MSTO stars and the hottest HB stars depending on age.The B08 isochrones are used for Z=0.0001.The data for different isochrones are highlighted in colour as explained in the legend.

Figure 4 .
Figure 4. Variation of I core and FWHM with age for three Balmer hydrogen lines in the synthetic IL spectra of GCs with the metallicity Z = 0.0004.The spectra were obtained using the B08 isochrones (the solid, dashed, and dash-dotted lines for Y = 0.23, 0.26, and 0.30, respectively) ignoring the HB stars.

Figure 5 .
Figure 5. Same as in the previous figure but with the HB stars included.

Figure 6 .
Figure6.Differences between T eff (left) and logL(L ⊙ ) (right) observed for the cluster HB stars and the isochronous ones B08 (see Sec. 6.1 for details).The isochrones, with which the observed CMDs were compared, were selected by S20 examining the IL spectra of the GCs from the library ofSchiavon et al. (2005).The observed T eff and logL(L ⊙ ) are plotted along the X axes in the diagrams.

Figure 7 .
Figure 7.Comparison of the isochrones selected in the IL spectrum modelling (Table 1) with the Hess diagrams built from the observed CMDs of the clusters H III (a) and B 317 (b) (see Sec. 6.1.1 for details).

Figure 8 .
Figure 8.Comparison of the isochrone selected in the modelling of the EXT8 spectrum (Table 1) shown in red and the photometry results for this cluster from Larsen et al. (2021) (see Section 6.1.2for details).

Figure A1 .
Figure A1.Results of the Monte Carlo experiments (see Appendix A) for details.

Figure C1 .
Figure C1.Illustration of the result of selecting the isochrone points to calculate the IL spectrum (see Appendix C for details).The original distribution of the isochrone points according to their     and log  is shown in panel (a).The resulting distribution is shown in panel (b).

Figure D1 .
Figure D1.Isochrones by Pietrinferni et al. (2004) (BASTI) with the metallicity Z = 0.00001 and Bertelli et al. (2008) (B08) with the metallicity Z = 0.0001 and different age and Y.The X and Y axes, respectively, show the logarithm of the effective temperature in kelvins (logT eff ) and the luminosity logarithm in solar luminosities (logL).Different colours represent the isochrones of different ages (in Gyr).The evolutionary stages of the MSTO and HB stars are marked in the left-hand panel.

Figure D2 .
Figure D2.Isochrones by Bertelli et al. (2008) (B08) with the metallicity Z = 0.0004 and different age and Y.The X and Y axes, respectively, show the logarithm of the effective temperature in kelvins (logT eff ) and the luminosity logarithm in solar luminosities (logL).Different colours represent the isochrones of different ages (in Gyr).The evolutionary stages of the MSTO and HB stars are marked in the left-hand panel.

Figure D3 .
Figure D3.Effective temperatures (on the left) and luminosities (on the right) of the MSTO stars and the hottest HB stars depending on age.The B08 isochrones are used for Z=0.0004.The data for different isochrones are highlighted in colour as explained in the legend.

Figure D4 .
Figure D4.Variation of I core and FWHM with age for three Balmer hydrogen lines in the synthetic IL spectra of GCs with the metallicity Z = 0.0004.The spectra were obtained using the B08 isochrones (the solid, dashed, and dash-dotted lines for Y = 0.23, 0.26, and 0.30, respectively) ignoring the HB stars.

Figure D5 .
Figure D5.Same as in the previous figure but with the HB stars included.
and in stellar evolutionary models.See text for details.
Pietrinferni et al. (2021)al.(2018)andPietrinferni et al. (2021)(BASTI new) are considered.Subscripts SS and  mean that we consider the scaled-solar or alpha-enhanced isochrones.See the text for details.