1 Outline
In Section 2, we present the description of
2 Description of
2.1 Main characteristic
2.2 Key ingredients
Key ingredients in
The
2.3 Initialization of the SP for the standard models
A
· The initial mass function
(IMF) of the primaries, which gives the relative number of primaries in the mass range m1 → m1 + dm1. The initial mass of the primary
is chosen from the approximation to the IMF of Miller & Scalo (1979) as given
by Eggleton, Fitchett & Tout (1989, hereafter EFT),
(1)
where X is a random variable
uniformly distributed in the range [0,1], and m1 is the primary mass in
units of M⊙.
· The initial secondary-mass
distribution, which is assumed to be correlated with the initial primary-mass
distribution in the standard models. So, this depends on the initial primary
mass and the initial mass ratio, q,
distribution, which is assumed to be a uniform form (EFT; Mazeh et al., 1992;
Goldberg & Mazeh, 1994),
(2)
where q = m2/m1 and m2 is the secondary mass in units of M⊙.
· The distribution of orbital separations (or
periods). This is taken as constant in log a (where a is the separation)
for wide binaries and falls off smoothly at close separations:
(3)
where asep » 0.070, a0 = 10R⊙, a1 = 5.75 ´ 106R⊙ and p » 1.2.
· The eccentricity distribution. A uniform form is
assumed:
e = X, (4)
where X is a random
variable.
2.4 Inclusion
of sdBs
Han et al. (2002, 2003) proposed a
binary model for the formation of hot subdwarf B stars (sdBs) in binaries and
single hot sdBs (three formation channels), and Han, Podsiadlowski &
Lynas-Gray (2007) have presented the ISEDs of SPs with the binary interactions
of sdBs. These are combined into
We use the all channels of
2.5
Construction of galaxies with different galaxy types
Based on the ISEDs of SPs and various SFRs, we
generate the ISEDs of galaxies with different galaxy types, including Burst-,
E-, S0-, Sa, Sb, Sc, Sd-, Irr-type galaxies and five classes of galaxies with
short e-folding timescales (Composite stellar populations, CSP).
E-type galaxy is constructed by advantage of a delta-form SFR, Irr-type
galaxy by a constant-form SFR and the other-type galaxies by exponentially
decreasing SFRs with different timescales:
(5)
where τ is the e-folding timescale, MPG(t) = [1−exp(−t/τ )] −Mstars−Mremnants is the mass of gas that has been processed into
stars and then returned to the interstellar medium (ISM) due to stellar
evolution at time t, Mstars and Mremnants are the masses of stars and
remnants at t and ε denotes the fraction of MPG(t) that can be recycled into new star formation. The timescales are τ = 0.1, 0.3, 0.5, 0.7, 0.9, 1, 2, 3, 5, 10, 15 and 30 Gyr, respectively, the last six
timescales corresponding to E, S0, Sa-Sc and Sd types. During the construction
of galaxies with different galaxy types, ε = 0, i.e., the gas could not be recycled into new star formation.
2.6 Nebular continuum, Q(H), LHa and LHb
We obtain the number of ionizing photons Q(H) by integrating the photons below 912Å, i.e.
(6)
where Fν is the stellar flux
in Hz, ν is frequency and h
is the Planck constant (= 6.6262 ´ 10−27 erg s). Moreover, we assume that all the star
formation is traced by the ionized gas, and use Case B recombination at
electron temperature Te=10 000K and number density ne =
Under the above assumptions, the emission of nebular continuum can be
obtained by
where c is the light velocity and Γ is the emission coefficient for hydrogen
and helium (He/H=0.1), which includes free-free and free-bound contributions
and the emission coefficient due to the two-photon continuum. The Γ coefficient
is wavelength-dependent and is taken from Aller (1984) and Ferland (1980).
The luminosities of Hα and Hβ can be obtained by
the following expression:
where αB is the recombination
coefficient to the excited level in hydrogen, which depends on the electronic
temperature, jB and αB are from Ferland (1980) and
the ratio α/β is taken from Osterbrock (1989).
3 Algorithms
3.1 ISEDs
The integrated spectral energy distributions
(ISEDs) are obtained by
where fλ(τ,Z) is the spectra of stars with mass M and metallicity Z at a relative age of τ , ϕ(M) is the IMF, ψ(t-τ ) is the SFR, Ml and Mu are the lower and upper mass limits of the IMF.
3.2 Lick/IDS indices
The integrated absorption-feature index of the
Lick/IDS system is a flux-weighed one. For the ith atomic absorption line, it is expressed in equivalent width (W, in Å),
where wi(τ,Z) is the equivalent width of the ith index of stars with mass M and metallicity Z at a relative age of τ , and fi,Cλ(τ,Z) is the continuum flux at the midpoint of the ith ’feature’ passband; and for the ith molecular line, the feature index is expressed in magnitude,
where ci(τ,Z) is the magnitude of the ith index of stars with mass M and metallicity Z at age τ . The indices
include CNl, CN2, ..., HδF and HγF.
The wi(τ,Z) and ci(τ,Z) in Eqs. 10 and 11
can be obtained by the empirical fitting functions (FF) of Worthey et al.
(1994) and Trager et al. (1998).
The wi(τ,Z) and ci(τ,Z) in Eqs. 10 and 11
also can be obtained by direct computation (DC) from high-resolution spectra.
For the DC method, wi(τ,Z) and ci(τ,Z) can be obtained
from spectra at Lick/IDS resolution or at the original spectral resolution. For
the former, the high-resolution spectra are needed to degrade to those at
Lick/IDS resolution by applying a Gaussian broadening function,
where fλ,hs and fλ,Lick are the high-resolution spectra and the broaden spectra at Lick/IDS resolution,
Here, FWHM2hs and FWHM2Lick are the FWHM of the high-resolution spectra and spectra at Lick/IDS
resolution.
3.3 Magnitudes and filters
The magnitudes are obtained by the following:
where magi(τ,Z) is the ith magnitude of
stars with mass M and metallicity Z at age τ.
The Vega magnitudes include Johnson-Cousins’s U, B, V, R, I and 2MASS’ J, H and K magnitudes.
AB magnitudes include SDSS’ u, g, r, i, z, GALEX’s Fuv, Nuv and HST-WFPC
4 Description
of data
4.1 All data
Basel_csp_fneb.tar.gz Basel_sp_MLR.tar.gz sdb_csp_quan.tar.gz
Basel_csp_ISED.tar.gz Bluered_sp_idxty.tar.gz sdb_sp_ISED.tar.gz
Basel_csp_quan.tar.gz Bluered_sp_ISED.tar.gz sdb_sp_MAGS.tar.gz
Basel_sp_idxff.tar.gz HRES_sp_ISED.tar.gz sdb_sp-MLR.tar.gz
Basel_sp_ISED.tar.gz sdb_csp_fneb.tar.gz
Basel_sp_MAGS.tar.gz sdb_csp_ISED.tar.gz
4.2 All code
rdidxff_sp.f rdised_fneb.f rdised_sp-hs.f rdmags_sp2.f
rdidxty_sp.f rdised_fneb-sdb.f rdised_sp-sdb.f rdmags_sp2-sdb.f
rdised_csp.f rdised_sp-bl.f rdLha_fneb.f rdmlr_sp.f
rdised_csp-sdb.f rdised_sp-br.f rdLha_fneb-sdb.f rdmlr_sp-sdb.f
4.3 Data for
SPs
We provide the stellar mass and magnitudes (bolometric,
GALEX [Fuv, Nuv], SDSS [u, g, r, i and z], Johnson-cousins [U, B, V, R and I], 2MASS [J, H and K] and HSTWFPC2 [32] magnitudes) at
seven metallicities, 90 ages for SPs with and without binary interactions (Basel_sp_MAGS.tar.gz, including 14 files [xxxyy_sp.mags, xxx=metallicity, yy=bb/ss]), and the
code of reading these data (rdmags_sp2.f, in
Fortran). The data in each file has the
following format:
age/yr
|
mt
|
Mbol
|
Fuv
|
Nuv
|
U
|
...
|
0.10000E+06
|
1.00000
|
-1.66541
|
0.03800
|
0.27886
|
0.79083
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
The variables have the following meanings:
age:
|
age in units of yr;
|
mt:
|
stellar mass in units of M⊙;
|
Mbol:
|
bolometric magnitude;
|
Mags:
|
GALEX, SDSS, UBVRI, 2MASS and HST-WFPC2 magnitudes.
|
We provide the ratios of stellar mass to light for
various light (bolometric, Johnson-cousins [U, B, V, R and I], 2MASS [J, H and K]) at seven metallicities, 90 ages for
SPs with and without binary interactions (Basel_sp_MLR.tar.gz, including 14
files [xxxyy_sp.mlr, xxx=metallicity, yy=bb/ss]), and the code of reading these
data (rdmlr_sp.f, in Fortran). The data in each file has the following format:
age/yr
|
M/LBOL
|
M/LU
|
M/LB
|
M/LV
|
M/LR
|
M/LI
|
M/LJ
|
M/LH
|
M/LK
|
0.10000E+06
|
0.00267
|
0.00461
|
0.01262
|
0.02871
|
0.04398
|
0.06661
|
0.13231
|
0.19061
|
0.20961
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
The variables have the following meanings:
age:
|
age in units of yr;
|
M/L:
|
the ratios of stellar mass to bolometric, U, B, V, R, I, J, H and K magnitudes in
units of the corresponding one of Sun.
|
We provide the ISEDs at three resolutions (8-20Å, 0.3Å
and 0.1Å) for SPs at several metallicities, 90 ages for SPs with and without
binary interactions, and the code of reading these data. For the ISEDs at
different resolution, the wavelength and metallicity coverages are different.
· ISED at low
resolution: For the low-resolution ISEDs, the
wavelength ranges from 91 to 1600000Å, spectral resolution is 8-20Å and
metallicity has seven values and ranges from 0.0001 to 0.03 (Basel_sp_ISED.tar.gz, including 14 files [xxxyy_sp-bl. ised, xxx=metallicity (’m
90
|
0.1000E+06
|
0.1259E+06
|
0.1585E+06
|
0.1995E+06
|
0.2512E+06
|
...
|
1221
|
91.0
|
94.0
|
96.0
|
98.0
|
100.0
|
...
|
0.1228E-08
|
0.2945E-08
|
0.5112E-08
|
0.8653E-08
|
0.1432E-07
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
the 1st line: ages (90) in
units of yrs;
the 2nd line: wavelength (1221) in units of Å;
the 3rd-last lines: physics flux in units of Fλ/L⊙/M⊙.
· ISED at 0.3Å resolution: The wavelength ranges from 3000 to 7000Å, and metallicity
has four values and ranges from 0.004 to 0.03 (HRES_sp_ISED.tar.gz, including 8
files [xxxyy_sp-hr.ised, xxx=metallicity (’m
90
|
0.1000E+06
|
0.1259E+06
|
0.1585E+06
|
0.1995E+06
|
0.2512E+06
|
...
|
13323
|
3000.2
|
3000.5
|
3000.8
|
3001.1
|
3001.4
|
...
|
0.1694E-01
|
0.1695E-01
|
0.1688E-01
|
0.1681E-01
|
0.1677E-01
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
the 1st line: ages (90) in
units of yrs;
the 2nd line: wavelength (13323) in units of Å;
the 3rd-last lines: physics flux in units of Fλ/L⊙/M⊙.
· ISED at 0.1Å resolution The wavelength ranges from 3500 to 7000Å, and metallicity
has seven values and ranges from 0.0001 to 0.03 (Bluered_sp_ISED.tar.gz, including 14
files [xxxyy_sp-br.ised, xxx=metallicity (’m
90
|
0.1000E+06
|
0.1259E+06
|
0.1585E+06
|
0.1995E+06
|
0.2512E+06
|
...
|
27731
|
3500.0
|
3500.1
|
3500.2
|
3500.3
|
3500.4
|
...
|
0.1124E-01
|
0.1123E-01
|
0.1121E-01
|
0.1119E-01
|
0.1119E-01
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
the 1st line: ages (90) in
units of yrs;
the 2nd line: wavelength (27731) in units of Å;
the 3rd-last lines: physics
flux in units of Fλ/L⊙/M⊙.
· indices via
fitting function method: We provide the
Lick/IDS indices by FF method (Wi and Ci in Eqs. 10 and 11), the pseudo-continuum flux [Fi,Cλ(t,Z) = ∫t0∫MuMl fi,Cλ(τ,Z) ϕ(M) ψ(t-τ ) dM dt, the meaning of fi,Cλ(τ,Z) can be seen from Eqs. 10 and 11] and pseudo-continuum wavelength
for SPs with and without binary interactions at seven metallicities and 90 ages
(Basel_sp_idxff.tar.gz, including 14 files [xxxyy_sp.idxff, xxx=metallicity (’m
01
|
02
|
03
|
...
|
27
|
28
|
...
|
52
|
53
|
…
|
Age
|
CN1
|
CN2
|
...
|
FCN1,Cλ
|
FCN2,Cλ
|
...
|
wCN1,Cλ
|
wCN2,Cλ
|
…
|
100000.0
|
-0.162
|
-0.093
|
…
|
0.852E-02
|
0.864E-02
|
|
4159.625
|
4159.625
|
…
|
...
|
...
|
...
|
|
|
...
|
...
|
...
|
...
|
…
|
the 1st line:
|
number;
|
the 2nd line:
|
age, indices, Fi,Cλ and wi,Cλ:
|
age:
|
ages (90) in units of yrs;
|
EWi/Ci:
|
indices obtained by fitting functions in units of
Å or mag, including CN1, CN2, Ca4227, G4300,
Fe4383, Ca4455, Fe4531, Fe4668, Hb, Fe5015, Mg1, Mg1, Mgb, Fe5270, Fe5335, Fe5406, Fe5709, Fe5782, NaD,
TiO1, TiO2, HδA, HγA,
HδF,
HAF;
|
Fi,Cλ:
|
integrated pseudo-continuum flux in units of Fλ/L⊙/M⊙;
|
wi,Cλ:
|
pseudo-continuum wavelength in units of Å.
|
· indices via
direct computation method: We also provide
the Lick/IDS indices by DC method, the pseudo-continuum flux and
pseudo-continuum wavelength for SPs with and without binary interactions at
seven metallicities and 90 ages (Bluered_sp_idxty.tar.gz, including 14 files [xxxyy_sp-br.idxty, xxx=metallicity
(’m
01
|
02
|
03
|
...
|
27
|
28
|
...
|
52
|
53
|
…
|
Age
|
CN1
|
CN2
|
...
|
FCN1,Cλ
|
FCN2,Cλ
|
...
|
wCN1,Cλ
|
wCN2,Cλ
|
…
|
100000.0
|
-0.162
|
-0.093
|
…
|
0.852E-02
|
0.864E-02
|
|
4159.625
|
4159.625
|
…
|
...
|
...
|
...
|
|
|
...
|
...
|
...
|
...
|
…
|
the 1st line:
|
number;
|
the 2nd line:
|
age, indices, Fi,Cλ and wi,Cλ:
|
age:
|
ages (90) in units of yrs;
|
EWi/Ci:
|
indices obtained by fitting functions in units of
Å or mag, including CN1, CN2, Ca4227, G4300,
Fe4383, Ca4455, Fe4531, Fe4668, Hb, Fe5015, Mg1, Mg1, Mgb, Fe5270, Fe5335, Fe5406, Fe5709, Fe5782, NaD,
TiO1, TiO2, HδA, HγA,
HδF,
HAF;
|
Fi,Cλ:
|
integrated pseudo-continuum flux in units of Fλ/L⊙/M⊙;
|
wi,Cλ:
|
pseudo-continuum wavelength in units of Å.
|
4.4 Data for
CSP
We provide the low-resolution ISEDs for
13 types of galaxies at seven metallicities and 90 ages on the basis of SP with
and without binary interactions (Basel_csp_ISED.tar.gz, including 182 files [xxxyy_csp_zz.ised, xxx=metallicity
(’m
90
|
0.1000E+06
|
0.1259E+06
|
0.1585E+06
|
0.1995E+06
|
0.2512E+06
|
...
|
1221
|
91.0
|
94.0
|
96.0
|
98.0
|
100.0
|
...
|
0.1228E-08
|
0.2945E-08
|
0.5112E-08
|
0.8653E-08
|
0.1432E-07
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
the 1st line:
|
ages (90) in units of
yrs;
|
the 2nd line:
|
wavelength (1221) in
units of Å;
|
the 3rd -last lines:
|
physics flux in units of Fλ/L⊙/M⊙.
|
4.5 Data for
nebular continuum
We provide the stellar (Fste,λ), nebular (Fneb,λ)and total continuum (Ftot,λ = Fste,λ + Fneb,λ) for 13 types of galaxies at seven metallicities on the basis of SP with
and without binary interactions (Basel_csp_fneb.tar.gz,
including 182 files [xxxyy_csp_zz.fneb, xxx=metallicity (’m
90
|
0.1000E+06
|
0.1259E+06
|
0.1585E+06
|
0.1995E+06
|
0.2512E+06
|
...
|
1221
|
91.0
|
94.0
|
96.0
|
98.0
|
100.0
|
...
|
0.1228E-08
|
0.2945E-08
|
0.5112E-08
|
0.8653E-08
|
0.1432E-07
|
...
|
...
|
0.0000E+00
|
0.0000E+00
|
0.0000E+00
|
0.0000E+00
|
0.0000E+00
|
...
|
..
|
0.1026E-15
|
0.2760E-15
|
0.5152E-15
|
0.9353E-15
|
0.1655E-14
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
the 1st line:
|
ages (90) in units of
yrs;
|
the 2nd line:
|
wavelength (1221) in
units of Å;
|
the 3rd +(k-1) ´3 lines:
|
stellar continuum
(physics flux) in units of Fλ/M⊙;
|
the 4th +(k-1) ´3 lines:
|
nebular continuum
(physics flux) in units of Fλ/M⊙;
|
the 5th +(k-1) ´3 lines:
|
total continuum (physics
flux) in units of Fλ/M⊙.
|
4.6 Data for Q(H), LHα and LHb
We provide the number of ionizing
photons Q(H), the luminosities LHα and LHb of for 13 types of galaxies at seven metallicities
on the basis of SP with and without binary
interactions (Basel_csp_quan.tar.gz, including 182 files [xxxyy_csp_zz.quan, xxx=metallicity (’m
age/yr
|
Nphot
|
L(Ha)
|
L(Hb)
|
L(bol)
|
0.10000E+06
|
40.35264
|
28.48618
|
28.03025
|
30.37387
|
...
|
...
|
...
|
...
|
...
|
The variables have the following
meanings:
age:
|
age in units of yr;
|
Nphot:
|
the logarithmic number of
ionizing photons;
|
L(Ha):
|
the logarithmic
luminosity of Hα line in units of
erg s−1;
|
L(Hb):
|
the logarithmic
luminosity of Hβ line in units of
erg s−1;
|
L(bol):
|
the logarithmic
bolometric luminosity in units of erg s−1. (~ LFIR)
|
5 Description
of data considering sdBs
We comprising the binary interactions
of sdBs into our models, and give the results of SPs, galaxies with different
types, nebular emission and luminosities of Hα and Hβ. Because this set of models is only
for SPs with binary interactions, the number of files is an half of the above
set in Section 4.
5.1 Data for
SPs
We provide the low-resolution ISEDs,
stellar mass, magnitudes and mass-to-light ratios at several metallicities, 90
ages for SPs with binary interactions of sdBs.
· stellar
mass and magnitudes: the format is the same as
that in Section
· mass-to-light
ratios: the format is the same as that in Section
· low-resolution
ISEDs: the format is the same as that of SPs at low resolution
in Section
5.2 Data for
galaxies with different types
We provide the ISEDs for 13 types of
galaxies at seven metallicities on the basis of SP with the binary interactions
of sdBs (sdb_csp_ISED.tar.gz, including 91 files [xxxbb_csp_zz-sdb. ised, xxx=metallicity
(’m
5.3 Data for nebular
continuum, Q(H), LHα and LHb
We provide the nebular continuum, Q(H), LHα and LHb for 13 types of galaxies at seven metallicities on
the basis of SP with the binary interactions of sdBs
(sdb_csp_fneb.tar.gz & sdb_csp_quan.tar.gz, with each tar file including 91 files [xxxbb_csp_zz-sdb.fneb
& xxxbb_csp_zz-sdb.quan, xxx=metallicity (’m
6 Sole effect
of binary interactions
Ongoing.
7 Example
7.1 On the
BC03 models
Ongoing.
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