Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 6 November 2018 (MN LATEX style file v2.2)
A binary model for the UV-upturn of elliptical galaxies
Z. Han1⋆, Ph. Podsiadlowski2, A.E. Lynas-Gray2
1 National Astronomical Observatories / Yunnan Observatory, the Chinese Academy of Sciences, Kunming, 650011, China
2 University of Oxford, Department of Physics, Keble Road, Oxford, OX1 3RH
6 November 2018
ABSTRACT
The discovery of a flux excess in the far-ultraviolet (UV) spectrum of elliptical galaxies was a
major surprise in 1969. While it is now clear that this UV excess is caused by an old population
of hot helium-burning stars without large hydrogen-rich envelopes, rather than young stars,
their origin has remained a mystery. Here we show that these stars most likely lost their
envelopes because of binary interactions, similar to the hot subdwarf population in our own
Galaxy. We have developed an evolutionary population synthesis model for the far-UV excess
of elliptical galaxies based on the binary model developed by Han et al. (2002, 2003) for the
formation of hot subdwarfs in our Galaxy. Despite its simplicity, it successfully reproduces
most of the properties of elliptical galaxies with a UV excess: the range of observed UV
excesses, both in (1550 − V ) and (2000 − V ), and their evolution with redshift. We also
present colour-colour diagrams for use as diagnostic tools in the study of elliptical galaxies.
The model has major implications for understanding the evolution of the UV excess and of
elliptical galaxies in general. In particular, it implies that the UV excess is not a sign of age,
as had been postulated previously, and predicts that it should not be strongly dependent on the
metallicity of the population, but exists universally from dwarf ellipticals to giant ellipticals.
Key words: galaxies: elliptical and lenticular, cD – galaxies : starburst – ultraviolet: galaxies
– stars: binaries: close – stars: subdwarfs
1 INTRODUCTION
A long-standing problem in the study of elliptical galaxies is the
far-ultraviolet (UV) excess in their spectra. Traditionally, elliptical
galaxies were supposed to be passively evolving and not contain
any young stars that radiate in the far-UV. Therefore, the discovery
of an excess of radiation in the far-UV by the Orbiting Astronom-
ical Observatory mission 2 (OAO-2) (Code 1969) came as a com-
plete surprise. Indeed, this was one of the first major discoveries
in UV astronomy and became a basic property of elliptical galax-
ies. This far-UV excess is often referred to as the “UV-upturn”,
since the flux increases in the spectral energy distributions of el-
liptical galaxies as the wavelength decreases from 2000 to 1200Å.
The UV-upturn is also known as UV rising-branch, UV rising flux,
or simply UVX (see the review by O’Connell 1999).
The UV-upturn phenomenon exists in virtually all ellipti-
cal galaxies and is the most variable photometric feature. A fa-
mous correlation between UV-upturn magnitude and metallicity
was found by Burstein et al. (1988) from International Ultravi-
olet Explorer Satellite (IUE) spectra of 24 quiescent early-type
galaxies (hereafter BBBFL relation). The UV-upturn could be
important in many respects: for the formation history and evo-
lutionary properties of stars, the chemical enrichment of galax-
ies, galaxy dynamics, constraints to the stellar age and metal-
⋆ E-mail: zhanwenhan@hotmail.com
licity of galaxies and realistic “K-corrections” (O’Connell 1999;
Yi, Demarque & Oemler 1998; Brown 2004; Yi 2004). In particu-
lar, the UV-upturn has been proposed as a possible age indica-
tor for giant elliptical galaxies (Bressan, Chiosi & Tantalo 1996;
Chiosi, Vallenari & Bressan 1997; Yi et al. 1999). The origin of the
UV-upturn, however, has remained one of the great mysteries
of extragalactic astrophysics for some 30 years (Brown 2004),
and numerous speculations have been put forward to explain it:
non-thermal radiation from an active galactic nucleus (AGN),
young massive stars, the central stars of planetary nebulae (PNe)
or post-asymptotic giant branch (PAGB) stars, horizontal branch
(HB) stars and post-HB stars (including post-early AGB stars
and AGB-manqué stars) and accreting white dwarfs (Code 1969;
Hills 1971; Gunn, Stryker & Tinsley 1981; Nesci & Perola 1985;
Mochkovitch 1986; Kjærgaard 1987; Greggio & Renzini 1990).
Using observations made with the the Hopkins Ultraviolet Tele-
scope (HUT) and comparing them to synthetic spectra, Ferguson
et al. (1991) and subsequent studies by Brown, Ferguson & David-
sen (1995), Brown et al. (1997), and Dorman, O’Connell & Rood
(1995) were able to show that the UV upturn is mainly caused by
extreme horizontal branch (EHB) stars. Brown et al. (2000b) de-
tected EHB stars for the first time in an elliptical galaxy (the core
of M 32) and therefore provided direct evidence for the EHB origin
of the UV-upturn.
EHB stars, also known as subdwarf B (sdB) stars, are
core-helium-burning stars with extremely thin hydrogen envelopes
c© 0000 RAS
http://arxiv.org/abs/0704.0863v3
2 Han, Podsiadlowski & Lynas-Gray
(Menv ≤ 0.02M⊙), and most of them are believed to have masses
around 0.5M⊙ (Heber 1986; Saffer et al. 1994), as has recently
been confirmed asteroseismologically in the case of PG 0014+067
(Brassard et al. 2001). They have a typical luminosity of a few
L⊙, a lifetime of ∼ 2 × 10
8yr, and a characteristic surface
temperature of ∼ 25 000K (Dorman, Rood & O’Connell 1993;
D’Cruz et al. 1996; Han et al. 2002). The origin of those hot,
blue stars, as the major source of the far UV radiation, has
remained an enigma in evolutionary population synthesis (EPS)
studies of elliptical galaxies. Two models, both involving single-
star evolution, have previously been proposed to explain the
UV-upturn: a metal-poor model (Lee 1994; Park & Lee 1997)
and a metal-rich model (Bressan, Chiosi & Fagotto 1994;
Bressan, Chiosi & Tantalo 1996; Tantalo et al. 1996;
Yi et al. 1995; Yi, Demarque & Kim 1997;
Yi, Demarque & Oemler 1997; Yi, Demarque & Oemler 1998).
The metal-poor model ascribes the UV-upturn to an old metal-
poor population of hot subdwarfs, blue core-helium-burning stars,
that originate from the low-metallicity tail of a stellar population
with a wide metallicity distribution (Lee 1994; Park & Lee 1997).
This model explains the BBBFL relation since elliptical galaxies
with high average metallicity tend to be older and therefore have
stronger UV-upturns. The model tends to require a very large age
of the population (larger than the generally accepted age of the
Universe), and it is not clear whether the metal-poor population is
sufficiently blue or not. Moreover, the required low-metallicity ap-
pears inconsistent with the large metallicity inferred for the major-
ity of stars in elliptical galaxies (Zhou, Véron-Cetty & Véron 1992;
Terlevich & Forbes 2002; Thomas et al. 2005).
In the metal-rich model the UV-upturn is caused by metal-
rich stars that lose their envelopes near the tip of the first-
giant branch (FGB). This model (Bressan, Chiosi & Fagotto 1994;
Yi, Demarque & Oemler 1997) assumes a relatively high metallic-
ity – consistent with the metallicity of typical elliptical galaxies
(∼ 1 − 3 times the solar metallicity). In the model, the mass-
loss rate on the red-giant branch, usually scaled with the Reimer’s
rate (Reimers 1975), is assumed to be enhanced, where the co-
efficient ηR in the Reimer’s rate is taken to be ∼ 2 − 3 times
the canonical value. In order to reproduce the HB morphology
of Galactic globular clusters, either a broad distribution of ηR is
postulated (D’Cruz et al. 1996), or, alternatively, a Gaussian mass-
loss distribution is applied that is designed to reproduce the dis-
tribution of horizontal-branch stars of a given age and metallicity
(Yi, Demarque & Oemler 1997). This model also needs a popula-
tion age that is generally larger than 10 Gyr. To explain the BBBFL
UV-upturn – metallicity relation, the Reimer’s coefficient ηR is as-
sumed to increase with metallicity, and the enrichment parameter
for the helium abundance associated with the increase in metallic-
ity, ∆Y
, needs to be > 2.5.
Both of these models are quite ad hoc: there is neither obser-
vational evidence for a very old, low-metallicity sub-population in
elliptical galaxies, nor is there a physical explanation for the very
high mass loss required for just a small subset of stars. Further-
more, the onset of the formation of the hot subdwarfs is very sud-
den as the stellar population evolves, and both models require a
large age for the production of the hot stars. As a consequence, the
models predict that the UV upturn of elliptical galaxies declines
rapidly with redshift. However, this does not appear to be con-
sistent with recent observations with the Hubble Space Telescope
(HST) (Brown et al. 1998; Brown et al. 2000a; Brown et al. 2003).
The recent survey with the Galaxy Evolution Explorer (GALEX)
satellite (Rich et al. 2005) showed that the intrinsic UV-upturn
seems not to decrease in strength with redshift.
The BBBFL relation shows that the (1550 − V ) colour be-
comes bluer with metallicity (or Lick spectral index Mg2), where
(1550 − V ) is the far-UV magnitude relative to the V magni-
tude. The relation could support the metal-rich model. However,
the correlation is far from being conclusively established. Ohl et al.
(1998) studied the far-UV colour gradients in 8 early-type galax-
ies and found no correlation between the FUV-B colour gradients
and the internal metallicity gradients based on the Mg2 spectral
line index, a result not expected from the BBBFL relation. De-
harveng, Boselli & Donas (2002) studied the far-UV radiation of
82 early-type galaxies, a UV-flux selected sample, and compared
them to the BBBFL sample, investigating individual objects with
a substantial record in the refereed literature spectroscopically1 .
They found no correlation between the (2000 − V ) colour and
the Mg2 spectral index. Rich et al. (2005) also found no correla-
tion in a sample of 172 red quiescent early-type galaxies observed
by GALEX and the Sloan Digital Sky Survey (SDSS). Indeed, if
there is a weak correlation in the data, the correlation is in the
opposite sense to that of BBBFL: metal-rich galaxies have red-
der (FUV − r)AB (far-UV magnitude minus red magnitude). On
the other hand, Boselli et al. (2005), using new GALEX data, re-
ported a mild positive correlation between (FUV − NUV )AB,
which is the far-UV magnitude relative to the near-UV, and metal-
licity in a sample of early-type galaxies in the Virgo Cluster. Donas
et al. (2006) use GALEX photometry to construct colour-colour
relationships for nearby early-type galaxies sorted by morphologi-
cal type. They also found a marginal positive correlation between
(FUV − NUV )AB and metallicity. These correlations, however,
do not necessarily support the BBBFL relation, as neither Boselli
et al. (2005) nor Donas et al. (2006) show that (FUV − r)AB cor-
relates significantly with metallicity. Therefore, this apparent lack
of an observed correlation between the strength of the UV-upturn
and metallicity casts some doubt on the metal-rich scenario.
Both models ignore the effects of binary evolution. On
the other hand, hot subdwarfs have long been studied in our
own Galaxy (Heber 1986; Green, Schmidt & Liebert 1986;
Downes 1986; Saffer et al. 1994), and it is now well established
that the vast majority of (and quite possibly all) Galactic hot
subdwarfs are the results of binary interactions. Observation-
ally, more than half of Galactic hot subdwarfs are found in
binaries (Ferguson, Green & Liebert 1984; Allard et al. 1994;
Thejll, Ulla & MacDonald 1995; Ulla & Thejll 1998;
Aznar Cuadrado & Jeffery 2001; Maxted et al. 2001;
Williams et al. 2001; Reed & Stiening 2004), and orbital
parameters have been determined for a significant sam-
ple (Jeffery & Pollacco 1998; Koen, Orosz & Wade 1998;
Saffer, Livio & Yungelson 1998; Kilkenny et al. 1999;
Moran et al. 1999; Orosz & Wade 1999; Wood & Saffer 1999;
Maxted, Marsh & North 2000; Maxted et al. 2000;
Maxted et al. 2001; Napiwotzki et al. 2001; Heber et al. 2002;
Heber et al. 2004; Morales-Rueda, Maxted & Marsh 2004;
Charpinet et al. 2005; Morales-Rueda et al. 2006).
There has also been substantial theoretical progress
(Mengel, Norris & Gross 1976; Webbink 1984;
Iben & Tutukov 1986; Tutukov & Yungelson 1990;
D’Cruz et al. 1996; Sweigart 1997). Recently, Han et al. (2002;
1 Note, however, that some of the galaxies show hints of recent star forma-
tion (Deharveng, Boselli & Donas 2002).
c© 0000 RAS, MNRAS 000, 000–000
A binary model for the UV-upturn of elliptical galaxies 3
2003) proposed a binary model (hereafter HPMM model) for the
formation of hot subdwarfs in binaries and single hot subdwarfs.
In the model, there are three formation channels for hot subdwarfs,
involving common-envelope (Paczyński 1976) ejection for hot
subdwarf binaries with short orbital periods, stable Roche lobe
overflow for hot subdwarfs with long orbital periods, and the
merger of helium white dwarfs to form single hot subdwarfs.
The model can explain the main observational characteristics
of hot subdwarfs, in particular, their distributions in the orbital
period–minimum companion mass diagram and in the effective
temperature–surface gravity diagram, their distributions of orbital
period and mass function, their binary fraction and the fraction of
hot subdwarf binaries with white dwarf (WD) companions, their
birth rates and their space density. More recent observations (e.g.
Lisker et al. 2004, 2005) support the HPMM model, and the model
is now widely used in the study of hot subdwarfs (e.g. Heber et al.
2004, Morales-Rueda, Maxted & Marsh 2004, Charpinet et al.
2005, Morales-Rueda et al. 2006).
Hot subdwarfs radiate in UV, and we can apply the HPMM
scenario without any further assumptions to the UV-upturn problem
of elliptical galaxies. The only assumption we have to make is that
the stellar population in elliptical galaxies, specifically their binary
properties, are similar to those in our own galaxy. Indeed, as we
will show in this paper, the UV flux from hot subdwarfs produced
in binaries is important. This implies that any model for elliptical
galaxies that does not include these binary channels is necessarily
incomplete or has to rely on the apriori implausible assumption that
the binary population in elliptical galaxies is intrinsically different.
The main purpose of this paper is to develop an apriori EPS model
for the UV-upturn of elliptical galaxies, by employing the HPMM
scenario for the formation of hot subdwarfs, and to compare the
model results with observations.
The outline of the paper is as follows. We describe the EPS
model in Section 2 and the simulations in Section 3. In Section 4
we present the results and discuss them, and end the paper with a
summary and conclusions in Section 5.
2 THE MODEL
EPS is a technique for modelling the spectrophotomet-
ric properties of a stellar population using our knowledge
of stellar evolution. The technique was first devised by
Tinsley (Tinsley 1968) and has experienced rapid develop-
ment ever since (Bruzual & Charlot 1993; Worthey 1994;
Bressan, Chiosi & Fagotto 1994; Tantalo et al. 1996;
Zhang et al. 2002; Bruzual & Charlot 2003; Zhang et al. 2004a).
Recently, binary interactions have also been incorporated
into EPS studies (Zhang et al. 2004b; Zhang et al. 2005a;
Zhang, Li & Han 2005b; Zhang & Li 2006) with the rapid
binary-evolution code developed by Hurley, Tout & Pols (2002).
In the present paper we incorporate the HPMM model into EPS by
adopting the binary population synthesis (BPS) code of Han et al.
(2003), which was designed to investigate the formation of many
interesting binary-related objects, including hot subdwarfs.
2.1 The BPS code and the formation of hot subdwarfs
The BPS code of Han et al. was originally devel-
oped in 1994 and has been updated regularly ever
since (Han, Podsiadlowski & Eggleton 1994; Han 1995;
Han, Podsiadlowski & Eggleton 1995; Han et al. 1995; Han 1998;
Han et al. 2002; Han et al. 2003; Han & Podsiadlowski 2004).
With the code, millions of stars (including binaries) can be evolved
simultaneously from the zero-age main sequence (ZAMS) to the
white-dwarf (WD) stage or a supernova explosion. The code can
simulate in a Monte-Carlo way the formation of many types of
stellar objects, such as Type Ia supernovae (SNe Ia), double degen-
erates (DDs), cataclysmic variables (CVs), barium stars, planetary
nebulae (PNe) and hot subdwarfs. Note that “hot subdwarfs” in this
paper is used as a collective term for subdwarf B stars, subdwarf O
stars, and subdwarf OB stars. They are core-helium-burning stars
with thin hydrogen envelopes and radiate mainly in the UV (see
Figure 1 for the formation channels of hot subdwarfs).
The main input into the BPS code is a grid of stellar models.
For the purpose of this paper, we use a Population I (pop I) grid
with a typical metallicity Z = 0.02. The grid, calculated with
Eggleton’s stellar evolution code (Eggleton 1971; Eggleton 1972;
Eggleton 1973; Han, Podsiadlowski & Eggleton 1994;
Pols et al. 1995; Pols et al. 1998), covers the evolution of normal
stars in the range of 0.08 − 126.0M⊙ with hydrogen abundance
X = 0.70 and helium abundance Y = 0.28, helium stars in
the range of 0.32 − 8.0M⊙ and hot subdwarfs in the range of
0.35−0.75M⊙ (see Han et al. 2002, 2003 for details). Single stars
are evolved via interpolations in the model grid. In this paper, we
use tFGB instead of logm as the interpolation variable between
stellar evolution tracks, where tFGB is the time from the ZAMS to
the tip of the FGB for a given stellar mass m and is calculated from
fitting formulae. This is to avoid artefacts in following the time
evolution of hot subdwarfs produced from a stellar population.
The code needs to model the evolution of binary stars as well
as of single stars. The evolution of binaries is more complicated due
to the occurrence of Roche lobe overflow (RLOF). The binaries of
main interest here usually experience two phases of RLOF: the first
when the primary fills its Roche lobe which may produce a WD
binary, and the second when the secondary fills its Roche lobe.
The mass gainer in the first RLOF phase is most likely a
main-sequence (MS) star. If the mass ratio q = M1/M2 at the
onset of RLOF is lower than a critical value, qcrit, RLOF is
stable (Paczyński 1965; Paczyński, Ziółkowski & Żytkow 1969;
Plavec, Ulrich & Polidan 1973; Hjellming & Webbink 1987;
Webbink 1988; Soberman, Phinney & van den Heuvel 1997;
Han et al. 2001). For systems experiencing their first phase of
RLOF in the Hertzsprung gap, we use qcrit = 3.2 as is supported
by detailed binary-evolution calculations of Han et al. (2000).
For the first RLOF phase on the FGB or asymptotic giant branch
(AGB), we mainly use qcrit = 1.5. Full binary calculations
(Han et al. 2002) demonstrate that qcrit ∼ 1.2 is typical for
RLOF in FGB stars. We do not explicitly include tidally enhanced
stellar winds (Tout & Eggleton 1988; Eggleton & Tout 1989;
Han et al. 1995) in our calculation. Using a larger value for qcrit
is equivalent to including a tidally enhanced stellar wind to
some degree while keeping the simulation simple (see HPMM
for details). Alternatively, we also adopt qcrit = 1.2 in order to
examine the consequences of varying this important criterion.
For stable RLOF, we assume that a fraction αRLOF of the
mass lost from the primary is transferred onto the gainer, while
the rest is lost from the system (αRLOF = 1 means that RLOF is
conservative). Note, however, that we assume that mass transfer is
always conservative when the donor is a MS star. The mass lost
from the system also takes away a specific angular momentum α
in units of the specific angular momentum of the system. The unit
is expressed as 2πa2/P , where a is the separation and P is the or-
bital period of the binary (see Podsiadlowski, Joss & Hsu 1992 for
c© 0000 RAS, MNRAS 000, 000–000
4 Han, Podsiadlowski & Lynas-Gray
Porb = 0.1− 10 days
MsdB = 0.40− 0.49M⊙
D. CE only (q > 1.2− 1.5)
Unstable RLOF leads to dynamical mass transfer
Common-envelope (CE) phase
Short-period hot subdwarf binary with MS companion
C. Stable RLOF+CE (q < 1.2− 1.5)
Stable RLOF
Wide WD binary with MS companion
Unstable RLOF leads to dynamical mass transfer
Common-envelope (CE) phase
Short-period hot subdwarf binary with WD companion
Common-Envelope Channels
B. Stable RLOF (q < 1.2 − 1.5)
Stable RLOF near the tip of FGB
Wide hot subdwarf binary with MS companion
Porb = 10− 500 days
MsdB = 0.30− 0.49M⊙
MsdB = 0.40− 0.65M⊙
MsdB = 0.45− 0.49M⊙
A. Single hot subdwarfs
Envelope loss near the tip of FGB by stellar wind (rotation, Z ?)
He WD merger (1 or 2 CE phases)
Figure 1. Single and binary channels to produce hot subdwarfs, core-helium-burning stars with no or small hydrogen-rich envelopes. (A) Single hot subdwarfs
may result from large mass loss near the tip of the first giant branch (FGB), as in the metal-rich model, or from the merger of two helium white dwarfs. (B)
Stable Roche lobe overflow (RLOF) near the tip of the FGB produces hot subdwarfs in wide binaries. (C + D) Common-envelope evolution leads to hot
subdwarfs in very close binaries, where the companion can either be a white dwarf (C) or a main-sequence star (D). The simulations presented in this paper
include all channels except for the metal-rich single star channel.
c© 0000 RAS, MNRAS 000, 000–000
A binary model for the UV-upturn of elliptical galaxies 5
details). Stable RLOF usually results in a wide WD binary. Some
of the wide WD binaries may contain hot subdwarf stars and MS
companions if RLOF occurs near the tip of the FGB (1st stable
RLOF channel for the formation of hot subdwarfs). In order to re-
produce Galactic hot subdwarfs, we use αRLOF = 0.5 and α = 1
for the first stable RLOF in all systems except for those on the MS
(see HPMM for details).
If RLOF is dynamically unstable, a common envelope (CE)
may be formed (Paczyński 1976), and if the orbital energy de-
posited in the envelope can overcome its binding energy, the CE
may be ejected. For the CE ejection criterion, we introduced two
model parameters, αCE for the common envelope ejection effi-
ciency and αth for the thermal contribution to the binding energy
of the envelope, which we write as
αCE ∆Eorb > Egr − αth Eth, (1)
where ∆Eorb is the orbital energy that is released, Egr is the grav-
itational binding energy and Eth is the thermal energy of the en-
velope. Both Egr and Eth are obtained from full stellar structure
calculations (see Han, Podsiadlowski & Eggleton 1994 for details;
also see Dewi & Tauris 2000) instead of analytical approximations.
CE ejection leads to the formation of a close WD binary. Some of
the close WD binaries may contain hot subdwarf stars and MS com-
panions if the CE occurs near the tip of the FGB (1st CE channel
for the formation of hot subdwarfs). We adopt αCE = αth = 0.75
in our standard model, and αCE = αth = 1.0 to investigate the
effect of varying the CE ejection parameters.
The WD binary formed from the first RLOF phase continues
to evolve, and the secondary may fill its Roche lobe as a red giant.
The system then experiences a second RLOF phase. If the mass
ratio at the onset of RLOF is greater than qcrit given in table 3 of
Han et al. (2002), RLOF is dynamically unstable, leading again to a
CE phase. If the CE is ejected, a hot subdwarf star may be formed.
The hot subdwarf binary has a short orbital period and a WD com-
panion (2nd CE channel for the formation of hot subdwarfs). How-
ever, RLOF may be stable if the mass ratio is sufficiently small. In
this case, we assume that the mass lost from the mass donor is all
lost from the system, carrying away the same specific angular mo-
mentum as pertains to the WD companion. Stable RLOF may then
result in the formation of a hot subdwarf binary with a WD com-
panion and a long orbital period (typically ∼ 1000 d, 2nd stable
RLOF channel for the formation of hot subdwarfs).
If the second RLOF phase results in a CE phase and the CE
is ejected, a double white dwarf system is formed (Webbink 1984;
Iben & Tutukov 1986; Han 1998). Some of the double WD systems
contain two helium WDs. Angular momentum loss due to gravita-
tional wave radiation may then cause the shrinking of the orbital
separation until the less massive white dwarf starts to fill its Roche
lobe. This will lead to its dynamical disruption if
0.7− 0.1(M2/M⊙) (2)
or M1 >∼ 0.3M⊙, where M1 is the mass of the donor (i.e.
the less massive WD) and M2 is the mass of the gainer
(Han & Webbink 1999). This is expected to always lead to a com-
plete merger of the two white dwarfs. The merger can also produce
a hot subdwarf star, but in this case the hot subdwarf star is a single
object (He WD merger channel for the formation of hot subdwarfs).
If the lighter WD is not disrupted, RLOF is stable and an AM CVn
system is formed.
In this paper, we do not include a tidally enhanced stellar wind
explicitly as was done in Han et al. (1995) and Han (1998). In-
stead we use a standard Reimers wind formula (Reimers 1975) with
η = 1/4 (Renzini 1981; Iben & Renzini 1983; Carraro et al. 1996)
which is included in our stellar models. This is to keep the simu-
lations as simple as possible, although the effects of a tidally en-
hanced wind can to some degree be implicitly included by using
a larger value of qcrit. We also employ a standard magnetic brak-
ing law (Verbunt & Zwaan 1981; Rappaport, Verbunt & Joss 1983)
where appropriate (see Podsiadlowski, Han & Rappaport 2002 for
details and further discussion).
2.2 Monte-Carlo simulation parameters
In order to investigate the UV-upturn phenomenon due to hot sub-
dwarfs, we have performed a series of Monte-Carlo simulations
where we follow the evolution of a sample of a million binaries
(single stars are in effect treated as very wide binaries that do not
interact with each other), including the hot subdwarfs produced in
the simulations, according to our grids of stellar models. The sim-
ulations require as input the star formation rate (SFR), the initial
mass function (IMF) of the primary, the initial mass-ratio distribu-
tion and the distribution of initial orbital separations.
(1) The SFR is taken to be a single starburst in most of our
simulations; all the stars have the same age (tSSP) and the same
metallicity (Z = 0.02), and constitute a simple stellar population
(SSP). In some simulations a composite stellar population (CSP) is
also used (Section 3.3).
(2) A simple approximation to the IMF of Miller & Scalo
(1979) is used; the primary mass is generated with the formula of
Eggleton, Fitchett & Tout (1989),
0.19X
(1−X)0.75 + 0.032(1 −X)0.25
, (3)
where X is a random number uniformly distributed between 0 and
1. The adopted range of primary masses is 0.8 to 100.0M⊙. The
studies by Kroupa, Tout & Gilmore (1993) and Zoccali et al. (2000)
support this IMF.
(3) The mass-ratio distribution is quite uncer-
tain. We mainly take a constant mass-ratio distribution
(Mazeh et al. 1992; Goldberg & Mazeh 1994; Heacox 1995;
Halbwachs, Mayor & Udry 1998; Shatsky & Tokovinin 2002),
) = 1, 0 ≤ q
≤ 1, (4)
where q′ = 1/q = M2/M1. As alternatives we also consider a
rising mass ratio distribution
) = 2q
, 0 ≤ q
≤ 1, (5)
and the case where both binary components are chosen randomly
and independently from the same IMF.
(4) We assume that all stars are members of binary systems
and that the distribution of separations is constant in log a (where
a is the orbital separation) for wide binaries and falls off smoothly
at close separations:
an(a) =
αsep(
)m, a ≤ a0;
αsep, a0 < a < a1,
where αsep ≈ 0.070, a0 = 10R⊙, a1 = 5.75 × 10
6 R⊙ =
0.13 pc, and m ≈ 1.2. This distribution implies that there is an
equal number of wide binary systems per logarithmic interval and
that approximately 50 per cent of stellar systems are binary systems
with orbital periods less than 100 yr.
c© 0000 RAS, MNRAS 000, 000–000
6 Han, Podsiadlowski & Lynas-Gray
2.3 Spectral library
In order to obtain the colours and the spectral energy distribu-
tion (SED) of the populations produced by our simulations, we
have calculated spectra for hot subdwarfs using plane-parallel
static model stellar atmospheres computed with the ATLAS9 stel-
lar atmosphere code (Kurucz 1992) with the assumption of local
thermodynamic equilibrium (LTE). Solar metal abundances were
adopted (Anders & Grevesse 1989) and line blanketing is approx-
imated by appropriate opacity distribution functions interpolated
for the chosen helium abundance. The resulting model atmosphere
grid covers a wide range of effective temperatures (10, 000 ≤
Teff ≤ 40, 000K with a spacing of ∆T = 1000K), gravities
(5.0 ≤ log g ≤ 7.0 with ∆ log g = 0.2), and helium abundances
(−3 ≤ [He/H ] ≤ 0), as appropriate for the hot subdwarfs pro-
duced in the BPS code. For the spectrum and colours of other single
stars, we use the latest version of the comprehensive BaSeL library
of theoretical stellar spectra (see Lejeune et al. 1997, 1998 for a de-
scription), which gives the colours and SEDs of stars with a wide
range of Z, log g and Teff .
2.4 Observables from the model
Our model follows the evolution of the integrated spectra of stellar
populations. In order to compare the results with observations, we
calculate the following observables as well as UBV colours in the
Johnson system (Johnson & Morgan 1953).
(i) (1550−V ) is a colour defined by BBBFL. It is a combination
of the short-wavelength IUE flux and the V magnitude and is used
to express the magnitude of the UV-upturn:
(1550− V ) = −2.5 log(fλ,1250−1850/fλ,5055−5945), (7)
where fλ,1250−1850 is the energy flux per unit wavelength averaged
between 1250 and 1850Å and fλ,5055−5945 the flux averaged be-
tween 5055 and 5945Å (for the V band):
(ii) (1550 − 2500) is a colour defined for the IUE flux by Dor-
man, O’Connell & Rood (1995).
(1550− 2500) = −2.5 log(fλ,1250−1850/fλ,2200−2800). (8)
(iii) (2000 − V ) is a colour used by Deharveng, Boselli &
Donas (2002) in their study of UV properties of the early-
type galaxies observed with the balloon-borne FOCA experiment
(Donas et al. 1990; Donas, Milliard & Laget 1995):
(2000− V ) = −2.5 log(fλ,1921−2109/fλ,5055−5945). (9)
(iv) (FUV − NUV )AB, (FUV − r)AB, (NUV − r)AB are
colours from GALEX and SDSS. GALEX, a NASA Small Ex-
plorer mission, has two bands in its ultraviolet (UV) survey:
a far-UV band centered on 1530 Å and a near-UV band cen-
tered on 2310 Å (Martin et al. 2005; Rich et al. 2005), while SDSS
has five passbands, u at 3551 Å, g at 4686 Å, r at 6165 Å, i at
7481 Å, and z at 8931 Å (Fukugita et al. 1996; Gunn et al. 1998;
Smith et al. 2002). The magnitudes are in the AB system of Oke &
Gunn (1983):
(FUV −NUV )AB = −2.5 log(fν,1350−1750/fν,1750−2750), (10)
(FUV − r)AB = −2.5 log(fν,1350−1750/fν,5500−7000), (11)
(NUV − r)AB = −2.5 log(fν,1750−2750/fν,5500−7000), (12)
where fν,1350−1750 , fν,1750−2750 , fν,5500−7000 are the energy
Table 1. Simulation sets (metallicity Z = 0.02)
Set n(q′) qc αCE αth
Standard SSP simulation set with tSSP varying upto 15 Gyr
1 constant 1.5 0.75 0.75
SSP simulation sets with varying model parameters
2 uncorrelated 1.5 0.75 0.75
3 rising 1.5 0.75 0.75
4 constant 1.2 0.75 0.75
5 constant 1.5 1.0 1.0
CSP simulation sets with a tmajor and variable tminor and f
6 constant 1.5 0.75 0.75
Note - n(q′) = initial mass-ratio distribution; qc = the critical mass ratio
above which the first RLOF on the FGB or AGB is unstable; αCE = CE
ejection efficiency; αth = thermal contribution to CE ejection; tSSP = the
age of a SSP; tmajor = the age of the major population in a CSP; tminor =
the age of the minor population in a CSP; f = the ratio of the mass of the
minor population to the total mass in a CSP.
fluxes per unit frequency averaged in the frequency bands corre-
sponding to 1350 and 1750 Å, 1750 and 2750 Å, 5500 and 7000 Å,
respectively.
(v) βFUV is a far-UV spectral index we defined to measure the
SED slope between 1075 and 1750 Å:
fλ ∼ λ
βFUV , 1075 < λ < 1750 Å, (13)
where fλ is the energy flux per unit wavelength. In this paper, we
fit far-UV SEDs with equation (13) to obtain βFUV. In the fitting
we ignored the part between 1175 and 1250Å for the theoretical
SEDs from our model, as this part corresponds to the Lα line. We
also obtained βFUV via a similar fitting for early-type galaxies ob-
served with the HUT (Brown et al. 1997; Brown 2004) and the IUE
(Burstein et al. 1988). We again ignored the part between 1175 and
1250Å for the HUT SEDs, while the IUE SEDs do not have any
data points below 1250Å.
3 SIMULATIONS
In order to investigate the UV-upturn systematically, we performed
six sets of simulations for a Population I composition (X = 0.70,
Y = 0.28 and Z = 0.02). The first set is a standard set with
the best-choice model parameters from HPMM. In Sets 2 to 5 we
systematically vary the model parameters, and Set 6 models a com-
posite stellar population (Table 1).
3.1 Standard simulation set
In the HPMM model, hot subdwarfs are produced through binary
interactions by stable RLOF, CE ejection or He WD mergers. The
main parameters in the HPMM model are: n(q′), the initial mass
ratio distribution, qc, the critical mass ratio above which the 1st
RLOF on the FGB or AGB is unstable, αCE, the CE ejection ef-
ficiency parameter, and αth, the contribution of thermal energy to
the binding energy of the CE (see Sections 2.1 and 2.2 for details).
The model that best reproduces the observed properties of hot sub-
dwarfs in our Galaxy has n(q′) = 1, qc = 1.5, αCE = 0.75,
αth = 0.75, (see section 7.4 of Han et al. 2003). These are the
parameters adopted in our standard simulation.
c© 0000 RAS, MNRAS 000, 000–000
A binary model for the UV-upturn of elliptical galaxies 7
In our standard set, we first construct a SSP containing a mil-
lion binaries (Section 2.2). The binaries are formed simultaneously
(i.e. in a single starburst) and with the same metallicity (Z = 0.02).
The SSP is evolved with the BPS code (Section 2.1), and the results
are convolved with our spectral libraries (Section 2.3) to produce
integrated SEDs and other observables. The SEDs are normalised
to a stellar population of mass 1010M⊙ at a distance of 10 Mpc.
3.2 Simulation sets with varying model parameters
In order to investigate the importance of the model parameters, we
also carried out simulation sets in which we systematically varied
the main parameters. Specifically, we adopted three initial mass-
ratio distributions: a constant mass-ratio distribution, a rising mass-
ratio distribution, and one where the component masses are uncor-
related and drawn independently from a Miller-Scalo IMF (Sec-
tion 2.2). We also varied the value of qc in the instability criterion
for the first RLOF phase on the FGB or AGB from 1.5 to 1.2, the
parameter αCE for CE ejection efficiency and the parameter αth
for the thermal contribution to CE ejection from 0.75 to 1.0.
3.3 Simulation sets for composite stellar populations
Many early-type galaxies show evidence for some moderate
amount of recent star formation (Yi et al. 2005; Salim et al. 2005;
Schawinski et al. 2006). Therefore, we also perform simulations in
which we evolve composite stellar populations. Here, a compos-
ite stellar population (CSP) consists of two populations, a major
old one and a minor younger one. The major population has solar
metallicity and an age of tmajor, where all stars formed in a single
burst tmajor ago, while the minor one has solar metallicity and an
age tminor, where all stars formed in a starburst starting tminor ago
and lasting 0.1 Gyr. The minor population fraction f is the ratio of
the mass of the minor population to the total mass of the CSP (for
f = 100% the CSP is actually a SSP with an age tminor).
4 RESULTS AND DISCUSSION
4.1 Simple stellar populations
4.1.1 Evolution of the integrated SED
In our standard simulation set, we follow the evolution of the in-
tegrated SED of a SSP (including binaries) of 1010M⊙ up to
tSSP = 15Gyr. The SSP is assumed to be at a distance of 10 Mpc
and the evolution is shown in Figure 2. Note that hot subdwarfs
originating from binary interactions start to dominate the far-UV
after ∼ 1Gyr.
We have compiled a file containing the spectra of the SSP with
ages from 0.1 Gyr to 15 Gyr and devised a small FORTRAN code to
read the file (and to plot the SEDs with PGPLOT). The file and the
code are available online2. In order to be able to apply the model
directly, we have also provided in the file the spectra of the SSP
without any binary interactions considered. This provides an easy
way to examine the differences in the spectra for simulations with
and without binary interactions.
2 The file and the code are available on the VizieR data base of the astro-
nomical catalogues at the Centre de Données astronomiques de Strasbourg
(CDS) web site (http://cdsarc.u-strasbg.fr/) and on ZH’s personal website
(http://www.zhanwenhan.com/download/uv-upturn.html).
Figure 2. The evolution of the restframe intrinsic spectral energy distri-
bution (SED) for a simulated galaxy in which all stars formed at the same
time, representing a simple stellar population (SSP). The stellar population
(including binaries) has a mass of 1010M⊙ and the galaxy is assumed to
be at a distance of 10 Mpc. The figure is for the standard simulation set, and
no offset has been applied to the SEDs.
4.1.2 Evolution of the UV-upturn
The colours of the SSP evolve in time, and Table 2 lists the
colours of a SSP (including binaries) of 1010M⊙ at various
ages for the standard simulation set. In order to see how the
colours evolve with redshift, we adopted a ΛCDM cosmology
(Carroll, Press & Turner 1992) with cosmological parameters of
H0 = 72km/s/Mpc, ΩM = 0.3 and ΩΛ = 0.7, and assumed
a star-formation redshift of zf = 5 to obtain Figures 3 and 4.
The figures show the evolution of the restframe intrinsic colours
and the evolution of the far-UV spectral index with redshift (look-
back time). As these figures show, the UV-upturn does not evolve
much with redshift; for an old stellar population (i.e. with a red-
shift z ∼ 0 or an age of ∼ 12Gyr), (1550 − V ) ∼ 3.5,
(UV −V ) ∼ 4.4, (FUV −r)AB ∼ 6.7, (1550−2500) ∼ −0.38,
(FUV −NUV )AB ∼ 0.42 and βFUV ∼ −3.0.
4.1.3 Colour-colour diagrams
Colour-colour diagrams are widely used as a diagnostic tool in the
study of stellar populations of early-type galaxies. We present a
few such diagrams in Figures 5 and 6 for the standard simulation
set. In these figures, most curves have a turning-point at ∼ 1Gyr,
at which hot subdwarfs resulting from binary interactions start to
dominate the far-UV.
c© 0000 RAS, MNRAS 000, 000–000
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8 Han, Podsiadlowski & Lynas-Gray
Figure 5. Colour-colour diagrams for the standard simulation set. Ages are denoted by open triangles (0.01 Gyr), open squares (0.1 Gyr), open circles (1 Gyr),
filled triangles (2 Gyr), filled squares (5 Gyr), filled circles (10 Gyr) and filled stars (15 Gyr).
c© 0000 RAS, MNRAS 000, 000–000
A binary model for the UV-upturn of elliptical galaxies 9
Figure 6. Similar to Figure 5, but with (B − V ) as the abscissa.
c© 0000 RAS, MNRAS 000, 000–000
10 Han, Podsiadlowski & Lynas-Gray
Figure 7. Integrated restframe intrinsic SEDs for hot subdwarfs for different formation channels. Solid, thin dark grey and thick light grey curves are for the
stable RLOF channel, the CE ejection channel and the merger channel, respectively. The merger channel starts to dominate at an age of tSSP ∼ 3.5Gyr. The
figure is for the standard simulation set with a stellar population mass of 1010M⊙ (including binaries), and the population is assumed to be at a distance of
10 Mpc.
c© 0000 RAS, MNRAS 000, 000–000
A binary model for the UV-upturn of elliptical galaxies 11
Table 2. Colour evolution of a simple stellar population (including binaries) of 1010M⊙ for the standard simulation set. This table is also available in
machine-readable form on the VizieR data base of the astronomical catalogues at the Centre de Données astronomiques de Strasbourg (CDS) web site
(http://cdsarc.u-strasbg.fr/) and on ZH’s personal website (http://www.zhanwenhan.com/download/uv-upturn.html).
log(tSSP) MV B − V 15− V 20 − V 25− V 15− 25 FUV − r NUV − r FUV −NUV βFUV
-1.000 -22.416 0.173 -1.274 -0.953 -0.447 -0.827 1.483 1.296 0.188 0.775
-0.975 -22.346 0.165 -1.245 -0.938 -0.432 -0.813 1.503 1.304 0.199 0.941
-0.950 -22.306 0.175 -1.195 -0.901 -0.396 -0.799 1.555 1.346 0.209 1.100
-0.925 -22.289 0.185 -1.106 -0.829 -0.326 -0.780 1.644 1.421 0.223 1.305
-0.900 -22.232 0.194 -1.053 -0.788 -0.286 -0.767 1.699 1.466 0.233 1.479
-0.875 -22.168 0.192 -1.019 -0.766 -0.265 -0.754 1.730 1.487 0.243 1.659
-0.850 -22.135 0.199 -0.959 -0.717 -0.215 -0.744 1.792 1.542 0.250 1.842
-0.825 -22.053 0.199 -0.969 -0.723 -0.216 -0.753 1.780 1.537 0.243 1.968
-0.800 -22.000 0.200 -0.945 -0.701 -0.189 -0.756 1.802 1.561 0.241 2.182
-0.775 -21.949 0.205 -0.892 -0.660 -0.148 -0.744 1.855 1.605 0.250 2.407
-0.750 -21.923 0.207 -0.789 -0.587 -0.086 -0.703 1.955 1.674 0.281 2.656
-0.725 -21.885 0.211 -0.682 -0.514 -0.025 -0.658 2.058 1.743 0.316 2.935
-0.700 -21.839 0.218 -0.569 -0.437 0.041 -0.609 2.169 1.816 0.353 3.314
-0.675 -21.804 0.221 -0.468 -0.367 0.101 -0.569 2.266 1.882 0.384 3.565
-0.650 -21.767 0.223 -0.377 -0.307 0.152 -0.529 2.355 1.939 0.416 3.832
-0.625 -21.732 0.230 -0.272 -0.235 0.215 -0.486 2.459 2.009 0.451 4.087
-0.600 -21.689 0.235 -0.166 -0.167 0.273 -0.439 2.565 2.075 0.490 4.343
-0.575 -21.644 0.242 -0.051 -0.092 0.337 -0.388 2.681 2.148 0.532 4.583
-0.550 -21.606 0.246 0.074 -0.015 0.403 -0.329 2.806 2.222 0.583 4.879
-0.525 -21.546 0.250 0.188 0.048 0.456 -0.268 2.918 2.280 0.638 5.176
-0.500 -21.512 0.263 0.315 0.122 0.522 -0.207 3.055 2.359 0.695 5.384
-0.475 -21.478 0.274 0.444 0.196 0.587 -0.144 3.189 2.433 0.757 5.503
-0.450 -21.424 0.285 0.556 0.254 0.637 -0.081 3.316 2.495 0.820 5.524
-0.425 -21.377 0.292 0.688 0.322 0.694 -0.005 3.458 2.560 0.898 5.603
-0.400 -21.335 0.308 0.872 0.421 0.777 0.095 3.661 2.660 1.001 5.881
-0.375 -21.290 0.319 1.015 0.497 0.840 0.175 3.825 2.736 1.089 5.642
-0.350 -21.253 0.340 1.172 0.591 0.919 0.253 4.011 2.834 1.176 5.545
-0.325 -21.217 0.362 1.374 0.706 1.015 0.360 4.246 2.951 1.295 5.507
-0.300 -21.162 0.375 1.543 0.795 1.084 0.459 4.440 3.036 1.404 5.764
-0.275 -21.121 0.394 1.723 0.903 1.168 0.555 4.651 3.143 1.507 5.827
-0.250 -21.068 0.410 1.897 1.012 1.245 0.653 4.846 3.242 1.604 6.004
-0.225 -21.028 0.434 2.116 1.152 1.344 0.772 5.095 3.374 1.721 5.839
-0.200 -20.994 0.462 2.339 1.305 1.448 0.890 5.343 3.517 1.826 5.968
-0.175 -20.965 0.495 2.597 1.485 1.571 1.026 5.629 3.682 1.947 5.989
-0.150 -20.937 0.524 2.778 1.632 1.671 1.107 5.820 3.816 2.004 6.248
-0.125 -20.930 0.572 2.964 1.814 1.804 1.159 6.018 3.994 2.024 6.113
-0.100 -20.864 0.590 3.123 1.932 1.873 1.250 6.184 4.092 2.091 5.806
-0.075 -20.801 0.603 3.274 2.038 1.933 1.340 6.336 4.174 2.162 5.673
-0.050 -20.730 0.622 3.440 2.142 1.992 1.448 6.522 4.264 2.258 5.434
-0.025 -20.664 0.639 3.655 2.254 2.056 1.599 6.768 4.355 2.413 4.681
0.000 -20.583 0.649 3.771 2.336 2.096 1.675 6.897 4.415 2.482 3.445
0.025 -20.511 0.666 3.822 2.424 2.144 1.677 6.955 4.488 2.467 2.006
0.050 -20.419 0.672 3.737 2.484 2.171 1.566 6.860 4.528 2.332 0.404
0.075 -20.313 0.666 3.569 2.517 2.176 1.393 6.672 4.534 2.137 -0.684
0.100 -20.259 0.685 3.420 2.607 2.241 1.179 6.509 4.612 1.897 -1.360
0.125 -20.201 0.707 3.441 2.738 2.323 1.118 6.536 4.719 1.817 -1.734
0.150 -20.150 0.722 3.547 2.866 2.398 1.149 6.646 4.814 1.832 -1.868
0.175 -20.081 0.731 3.603 2.974 2.455 1.148 6.704 4.888 1.816 -2.019
0.200 -20.028 0.750 3.642 3.094 2.525 1.117 6.748 4.983 1.766 -2.148
0.225 -19.973 0.766 3.731 3.240 2.606 1.125 6.837 5.085 1.752 -2.270
4.1.4 The far-UV contribution for different formation channels
of hot subdwarfs
In our model, there are three channels for the formation of hot sub-
dwarfs. In the stable RLOF channel, the hydrogen-rich envelope of
a star with a helium core is removed by stable mass transfer, and
helium is ignited in the core. The hot subdwarfs from this channel
are in binaries with long orbital periods (typically ∼ 1000 d). In the
CE ejection channel, the envelope is ejected as a consequence of the
spiral-in in a CE phase. The resulting hot subdwarf binaries have
c© 0000 RAS, MNRAS 000, 000–000
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12 Han, Podsiadlowski & Lynas-Gray
Table 2. continued
log(tSSP) MV B − V 15 − V 20− V 25− V 15− 25 FUV − r NUV − r FUV −NUV βFUV
0.250 -19.906 0.773 3.804 3.359 2.664 1.140 6.902 5.157 1.745 -2.342
0.275 -19.853 0.790 3.886 3.492 2.735 1.151 6.992 5.254 1.739 -2.457
0.300 -19.789 0.799 3.936 3.571 2.781 1.155 7.042 5.311 1.731 -2.466
0.325 -19.746 0.811 4.005 3.684 2.842 1.162 7.115 5.389 1.726 -2.573
0.350 -19.664 0.812 4.010 3.761 2.870 1.140 7.119 5.428 1.691 -2.680
0.375 -19.588 0.815 4.007 3.821 2.895 1.111 7.113 5.462 1.651 -2.706
0.400 -19.533 0.818 3.968 3.879 2.932 1.036 7.067 5.499 1.568 -2.759
0.425 -19.484 0.827 3.922 3.915 2.968 0.954 7.025 5.539 1.486 -2.787
0.450 -19.412 0.830 3.854 3.931 2.987 0.867 6.957 5.557 1.401 -2.828
0.475 -19.374 0.846 3.856 4.009 3.049 0.807 6.965 5.629 1.336 -2.865
0.500 -19.337 0.857 3.817 4.041 3.096 0.720 6.924 5.673 1.251 -2.851
0.525 -19.288 0.869 3.743 4.041 3.127 0.615 6.857 5.703 1.154 -2.857
0.550 -19.201 0.864 3.653 4.026 3.128 0.525 6.763 5.693 1.070 -2.896
0.575 -19.170 0.879 3.666 4.082 3.189 0.477 6.782 5.758 1.024 -2.914
0.600 -19.089 0.876 3.654 4.103 3.203 0.451 6.767 5.770 0.996 -2.930
0.625 -19.055 0.891 3.708 4.188 3.271 0.437 6.828 5.850 0.978 -2.944
0.650 -18.992 0.896 3.666 4.179 3.290 0.376 6.785 5.862 0.923 -2.925
0.675 -18.957 0.904 3.695 4.230 3.340 0.355 6.817 5.914 0.903 -2.933
0.700 -18.880 0.905 3.667 4.239 3.357 0.310 6.788 5.928 0.860 -2.955
0.725 -18.812 0.906 3.635 4.238 3.371 0.264 6.754 5.936 0.818 -2.962
0.750 -18.758 0.913 3.631 4.247 3.402 0.229 6.754 5.966 0.788 -2.944
0.775 -18.710 0.925 3.682 4.310 3.453 0.229 6.814 6.029 0.785 -2.958
0.800 -18.680 0.936 3.676 4.325 3.502 0.174 6.810 6.071 0.739 -2.956
0.825 -18.576 0.929 3.615 4.290 3.492 0.123 6.745 6.050 0.695 -2.964
0.850 -18.556 0.947 3.606 4.314 3.560 0.046 6.744 6.113 0.631 -2.974
0.875 -18.473 0.945 3.629 4.348 3.583 0.046 6.765 6.138 0.627 -2.979
0.900 -18.429 0.959 3.591 4.338 3.626 -0.035 6.735 6.173 0.562 -2.980
0.925 -18.362 0.958 3.552 4.319 3.647 -0.095 6.691 6.176 0.514 -2.988
0.950 -18.339 0.981 3.613 4.391 3.729 -0.116 6.767 6.271 0.496 -2.986
0.975 -18.236 0.972 3.528 4.322 3.711 -0.184 6.675 6.231 0.445 -2.992
1.000 -18.191 0.982 3.570 4.374 3.768 -0.198 6.724 6.292 0.432 -2.989
1.025 -18.100 0.975 3.499 4.320 3.764 -0.265 6.645 6.263 0.382 -2.998
1.050 -18.100 0.995 3.481 4.321 3.843 -0.362 6.634 6.321 0.313 -3.005
1.075 -18.036 1.004 3.514 4.359 3.898 -0.384 6.672 6.376 0.296 -3.002
1.100 -18.044 1.032 3.541 4.396 3.997 -0.456 6.712 6.465 0.247 -2.998
1.125 -17.947 1.029 3.473 4.338 3.998 -0.525 6.641 6.441 0.201 -2.999
1.150 -17.884 1.033 3.473 4.345 4.039 -0.566 6.641 6.468 0.173 -2.995
1.175 -17.800 1.030 3.463 4.338 4.062 -0.600 6.626 6.475 0.151 -2.995
Note - tSSP = population age in Gyr; MV = absolute visual magnitude; B − V = (B − V ); 15− V = (1550 − V ); 20− V = (2000 − V ); 25 − V =
(2500 − V ); 15− 25 = (1550 − 2500); FUV − r = (FUV − r)AB; NUV − r = (FUV − r)AB; FUV −NUV = (FUV −NUV )AB; βFUV =
far-UV spectral index.
very short orbital periods (typically ∼ 1 d). In the merger channel,
a helium WD pair coalesces to produce a single object. Hot sub-
dwarfs from the merger channel are generally more massive than
those from stable RLOF channel or the CE channel and have much
thinner (or no) hydrogen envelope. They are therefore expected to
be hotter. See Han et al. (2002; 2003) for further details.
Figure 7 shows the SEDs of the hot subdwarfs produced from
the different formation channels at various ages. It shows that hot
subdwarfs from the RLOF channel are always important, while the
CE channel becomes important at an age of ∼ 1Gyr. The merger
channel, however, catches up with the CE channel at ∼ 2.5Gyr
and the stable RLOF channel at ∼ 3.5Gyr, and dominates the far-
UV flux afterwards.
4.1.5 The effects of the model assumptions
In order to systematically investigate the dependence of the UV-
upturn on the parameters of our model, we now vary the major
model parameters: n(q′) for the initial mass-ratio distribution, qc
for the critical mass ratio for stable RLOF on the FGB or AGB,
αCE for the CE ejection efficiency and αth for the thermal con-
tribution to the CE ejection. We carried out four more simulation
sets (Table 1). Figures 3 and 4 show the UV-upturn evolution
of the various simulation sets. These figures show that the initial
mass-ratio distribution is very important. As an extreme case, the
mass-ratio distribution for uncorrelated component masses (Set 2)
makes the UV-upturn much weaker, by ∼ 1mag in (1550 − V )
or (FUV − r)AB, as compared to the standard simulation set. On
the other hand, a rising distribution (Set 3) makes the UV-upturn
stronger. Binaries with a mass-ratio distribution of uncorrelated
c© 0000 RAS, MNRAS 000, 000–000
A binary model for the UV-upturn of elliptical galaxies 13
Figure 3. The evolution of restframe intrinsic colours (1550 − V ),
(2000−V ) and (FUV − r)AB with redshift (lookback time) for a simple
stellar population (including binaries). Solid, dashed, dash-dotted, dotted,
dash-dot-dot-dot curves are for simulation sets 1 (standard set), 2, 3, 4, 5,
respectively. Ages are denoted by open triangles (0.01 Gyr), open squares
(0.1 Gyr), open circles (1 Gyr), filled triangles (2 Gyr), filled squares (5 Gyr)
and filled circles (10 Gyr).
component masses tend to have bigger values of q (the ratio of
the mass of the primary to the mass of the secondary), and mass
transfer is more likely to be unstable. As a result, the numbers of
hot subdwarfs from the stable RLOF channel and the merger chan-
nel are greatly reduced, and the UV-upturn is smaller in strength.
Binaries with a rising mass-ratio distribution tend to have smaller
values of q and therefore produce a larger UV-upturn. A lower qc
(Set 4) leads to a weaker UV-upturn, as the numbers of hot sub-
dwarfs from the stable RLOF channel and the merger channel are
reduced. A higher CE ejection efficiency αCE and a higher thermal
contribution factor αth (Set 5) result in an increase in the number
of hot subdwarfs from the CE channel, but a decrease in the number
from the merger channel, and the UV-upturn is not affected much
as a consequence.
4.1.6 The importance of binary interactions
Binaries evolve differently from single stars due to the occurrence
of mass transfer. Mass transfer may prevent mass donors from
evolving to higher luminosity and can produce hotter objects than
expected in a single-star population of a certain age (mainly hot
Figure 4. Similar to Figure 3, but for colours (1550 − 2500), (FUV −
NUV )AB, and far-UV spectral index βFUV.
subdwarfs and blue stragglers3). To demonstrate the importance of
binary interactions for the UV-upturn explicitly, we plotted SEDs of
a population for two cases in Figure 8. Case 1 (solid curves) is for
our standard simulation set, which includes various binary interac-
tions, while case 2 (light grey curves) is for a population of the same
mass without any binary interactions. The figure shows that the hot
subdwarfs produced by binary interactions are the dominant con-
tributors to the far-UV for a population older than ∼ 1Gyr. Note,
however, that blue stragglers resulting from binary interactions are
important contributors to the far-UV between 0.5 Gyr and 1.5 Gyr.
In order to assess the importance of binary interactions for the
UV upturn, we define factors that give the fraction of the flux in a
particular waveband that originates from hot subdwarfs produced
in binaries: bFUV = F
FUV/F
total
FUV , where F
FUV is the integrated
flux between 900Å and 1800Å radiated by hot subdwarfs (and
their descendants) produced by binary interactions, and F totalFUV is
the total integrated flux between 900Å and 1800Å . We also de-
fined other similar factors, b1550, b2000, and b2500, for passbands
of 1250Å to 1850Å , 1921Å to 2109Å, and 2200Å to 2800Å,
respectively. Figure 9 shows the time evolution of those factors. As
3 Blue stragglers are stars located on the main sequence well beyond
the turning-point in the colour-magnitude diagram of globular clusters
(Sandage 1953), which should already have evolved off the main sequence.
Collisions between low-mass stars and mass transfer in close binaries are
believed to be responsible for the production of these hotter objects (e.g.
Pols & Marinus 1994, Chen & Han 2004, Hurley et al. 2005).
c© 0000 RAS, MNRAS 000, 000–000
14 Han, Podsiadlowski & Lynas-Gray
Figure 8. Integrated restframe intrinsic SEDs for a stellar population (including binaries) with a mass of 1010M⊙ at a distance of 10 Mpc. Solid curves are
for the standard simulation set with binary interactions included, and the light grey curves for the same population, but no binary interactions are considered;
the two components evolve independently.
c© 0000 RAS, MNRAS 000, 000–000
A binary model for the UV-upturn of elliptical galaxies 15
Figure 9. Time evolution of the fraction of the energy flux in different UV wavebands originating from hot subdwarfs (and their descendants) formed in
binaries for the standard simulation set.
the figure shows, the hot-subdwarf contribution becomes increas-
ingly important in the far- and near-UV as the population ages.
4.2 The model for composite stellar populations
Early-type galaxies with a recent minor starburst can be modelled
as a composite stellar population (CSP). A CSP contains a ma-
jor population with an age of tmajor and a minor population of
age tminor and mass fraction f (Section 3.3). Figure 10 shows the
colour–colour diagram for CSPs with tmajor = 10Gyr with vary-
ing tminor and f . Note that the curves of different f start to con-
verge to the SSP curve, the curve of f = 100%, for tminor >
1Gyr. This implies that there exists a strong degeneracy between
the age of the minor population and the mass fraction.
4.3 Theory versus observations
4.3.1 The fitting of the far-UV SED
In our binary population synthesis model, we adopted solar metal-
licity. To test the model, we chose NGC 3379, a typical elliptical
galaxy with a metallicity close to solar (Gregg et al. 2004) to fit
the far-UV SED. Figure 11 presents various fits that illustrate the
effects of different sub-populations with different ages and differ-
ent amounts of assumed extinction. As the figure shows, acceptable
fits can be obtained for the various cases. Our best fits require the
presence of a sub-population of relatively young stars with an age
< 0.5Gyr, making up ∼ 0.1% of the total population mass.
The existence of a relatively young population could imply the
existence of some core-collapse supernovae in these galaxies. If we
assume that an elliptical galaxy has a stellar mass of 1011M⊙ and
0.1% of the mass was formed during the last 0.4 Gyr, then a mean
star formation rate would be 0.25M⊙/yr, about one tenth that of
the Galaxy. Core-collapse supernovae would be possible. Indeed, a
Type Ib supernova, SN 2000ds, was discovered in NGC 2768, an
elliptical galaxy of type E6 (Van Dyk, Li & Filippenko 2003).
4.3.2 The UV-upturn magnitudes versus the far-UV spectral
index
There is increasing evidence that many elliptical galaxies had
some recent minor star-formation events (Schawinski et al. 2006;
Kaviraj et al. 2006), which also contribute to the far-UV excess. To
model such secondary minor starbursts, we have constructed CSP
galaxy models, consisting of one old, dominant population with an
assumed age tmajor = 10Gyr and a younger population of vari-
able age, making up a fraction f of the stellar mass of the system.
Our spectral modelling shows that a recent minor starburst mostly
affects the slope in the far-UV SED, and we therefore defined a far-
UV slope index βFUV (Section 2.4). In order to assess the impor-
tance of binary interactions, we also defined a binary contribution
c© 0000 RAS, MNRAS 000, 000–000
16 Han, Podsiadlowski & Lynas-Gray
Figure 10. The diagram of (FUV − NUV )AB versus (FUV − r)AB for a composite stellar population (CSP) model of elliptical galaxies with a major
population age of tmajor = 10Gyrs (Set 6). Solid curves are for given minor population fractions f and are plotted in steps of ∆ log(f) = 0.5, as indicated.
Light grey curves are for fixed minor population ages tminor and are plotted in steps of ∆ log(tminor/Gyr) = 0.1, as indicated. The colours are presented
in the restframe. The thick solid curve for f = 100% actually shows the evolution of a simple stellar population with age tminor.
factor bFUV (Section 4.1.6), which is the fraction of far-UV flux
radiated by hot subdwarfs produced by binary interactions.
Figure 12 shows the far-UV slope as a function of UV ex-
cess, a potentially powerful diagnostic diagram which illustrates
how the UV properties of elliptical galaxies evolve with time in a
dominant old population with a young minor sub-population. For
comparison, we also plot observed elliptical galaxies. Some of the
observed galaxies are from Astro-2 observations with an aperture
of 10′′ ×56′′ (Brown et al. 1997), some are from IUE observations
with an aperture of 10′′ × 20′′ (Burstein et al. 1988). The value of
βFUV for NGC 1399, however, is derived from Astro-1 HUT ob-
servation with an aperture of 9′′.4 × 116′′ (Ferguson et al. 1991),
and its (1550 − V ) comes from the IUE observations. As the far-
UV light is more concentrated toward the centre of the galaxy than
the optical light (Ohl et al. 1998), the value of (1550−V ) for NGC
1399 should be considered an upper limit for the galaxy area cov-
ered by the observation. The galaxies plotted are all elliptical galax-
ies except for NGC 5102, which is a S0 galaxy, and the nucleus of
M 31, which is a Sb galaxy. Active galaxies or galaxies with large
errors in βFUV from BBBFL have not been plotted.
Overall, the model covers the observed range of properties
reasonably well. Note in particular that the majority of galaxies
lie in the part of the diagram where the UV contribution from
binaries is expected to dominate (i.e. where bFUV > 0.5). The
location of M 60 and M 89 in this figure implies f ∼ 0.01%
and tminor ∼ 0.11Gyr with bFUV ∼ 0.5. Interestingly, inspec-
tion of the HUT spectrum of M 60 (see the mid-left panel of fig-
ure 3 in Brown et al. (1997)) shows the presence of a marginal
C IV absorption line near 1550Å. Chandra observations show that
M 89 has a low luminosity AGN (Xu et al. 2005). This would make
(1550 − V ) bluer and may also provide indirect evidence for low
levels of star formation.
The galaxy NGC 1399 requires special mention, as it is UV-
bright and the young star-hypothesis was believed to have been
ruled out due to the lack of strong C IV absorption lines in its HUT
spectrum (Ferguson et al. 1991). However, any young star signa-
ture, if it exists, would have been diluted greatly in the HUT spec-
trum, as the aperture of the HUT observation is much larger than
that of the IUE observation covering mainly the galaxy nucleus.
Our model is sensitive to both low levels and high levels of
star formation. It suggests that elliptical galaxies had some star for-
mation activity in the relatively recent past (∼ 1Gyr ago). AGN
and supernova activity may provide qualitative supporting evidence
for this picture, since the former often appears to be accompanied
c© 0000 RAS, MNRAS 000, 000–000
A binary model for the UV-upturn of elliptical galaxies 17
Figure 11. Far-UV SED fitting of NGC 3379, a standard elliptical galaxy. The grey histogram represents the HUT observations of Brown et al. (1997) with
337 bins, while the other curves are based on our theoretical model with different assumptions about a minor recent population and different amounts of
extinction. The age of the old, dominant population, tmajor , is assumed to be 10 Gyr in all cases. The minor population, making up a total fraction f of the
stellar mass of the galaxy, is assumed to have experienced a starburst tminor ago, as indicated, lasting for 0.1 Gyr. To model the effects of dust extinction,
we applied the internal dust extinction model of Calzetti et al. (2000). For a given f and E(B − V ), we varied the galaxy mass and the age of the minor
population. For each case, the curves give the fits obtained. Note that the best fits require the presence of a minor young population.
by active star formation, while supernovae, both core collapse and
thermonuclear, tend to occur mainly within 1 – 2 Gyr after a star-
burst in the most favoured supernova models. In Figure 12, we have
plotted 13 early-type galaxies altogether. Using the Padova-Asiago
supernova online catalogue4, which lists supernovae recorded ever
since 1885, we found 8 supernovae in six of the galaxies: SN 1885A
(Type I) in M 31, SN 1969Q (type unavailable) in M 49, SN 2004W
(Type Ia) in M 60, SN 1939B (Type I) in M 59, SN 1957B (Type Ia),
SN 1980I (Type Ia), SN 1991bg (Type Ia) in M 84 and SN 1935B
(type unavailable) in NGC 3115. The majority of supernovae in
these galaxies appear to be of Type Ia.
4.3.3 Colour-colour diagrams
Similar to the above subsection, we have constructed composite
stellar population models for elliptical galaxies consisting of a ma-
jor old population (tmajor = 10Gyr) and a minor younger popula-
tion, but for colour-colour diagrams.
4 http://web.pd.astro.it/supern/snean.txt
Figure 13 shows the appearance of a galaxy in the colour-
colour diagrams of (1550 − V ) versus (1550 − 2500) (panel (a))
and (2000−V ) versus (1550−2500) (panel (b)) in the CSP model
for different fractions f and different ages of the minor popula-
tion. Solid squares in panel (a) of the figure are for quiescent early-
type galaxies observed with IUE by BBBFL and the data points
are taken from table 2 of Dorman, O’Connell & Wood (1995). The
observed data points are located in a region without recent star for-
mation or with a very low level of recent star formation (f <
0.1%).
Therefore, the observations are naturally explained with our model.
Panel (a) shows the epoch when the effects of the starburst fade
away, leading to a fast evolution of the galaxy colours, and the dia-
gram therefore provides a potentially powerful diagnostic to iden-
tify a minor starburst in an otherwise old elliptical galaxy that oc-
curred up to ∼ 2Gyr ago. For larger ages, the curves tend to con-
verge in the (1550− 2500) versus (1550− V ) diagram. Note that
this is not so much the case in the (1550−2500) versus (2000−V )
diagram, which therefore could provide better diagnostics.
Figure 14 is a diagram of (B−V ) versus (2000−V ) for a CSP
with a major population age tmajor = 10Gyr and variable minor
population age tminor and various minor population mass fractions
c© 0000 RAS, MNRAS 000, 000–000
http://web.pd.astro.it/supern/snean.txt
18 Han, Podsiadlowski & Lynas-Gray
Figure 12. Evolution of far-UV properties [the slope of the far-UV spectrum, βFUV, versus (1550 − V )] for a composite stellar population (CSP) model
of elliptical galaxies with a major population age of tmajor = 10Gyrs (Set 6). The mass fraction of the younger population is denoted as f and the time
since the formation as tminor [squares, triangles or dots are plotted in steps of ∆log(t) = 0.025]. Note that the model for f = 100% shows the evolution
of a simple stellar population with age tminor . The legend is for bFUV , which is the fraction of the UV flux that originates from hot subdwarfs resulting from
binary interactions. The effect of internal extinction is indicated in the top-left corner, based on the Calzetti internal extinction model with E(B − V ) = 0.1
(Calzetti et al. , 2000). For comparison, we also plot galaxies with error bars from HUT (Brown et al. , 1997) and IUE observations (BBBFL). The galaxies
with strong signs of recent star formation are denoted with an asterisk (NGC 205, NGC 4742, NGC 5102).
f . Overlayed on this diagram is figure 2 of Deharveng, Boselli &
Donas (2002) for observational data points of early-type galaxies.
NGC 205 and NGC 5102 (the circles with crosses above the line
(2000 − V ) = 1.4) are known to have direct evidence of massive
star formation (Hodge 1973; Pritchet 1979); therefore Deharveng,
Boselli & Donas (2002) individually examined the seven galaxies
with (2000−V ) < 1.4 in their sample for suspected star formation.
CGCG 119053, CGCG 97125, VCC 1499 (the three solid squares
with big stars) showed hints of star formation, NGC 4168 (the solid
square with a big triangle) has a low-luminosity Seyfert nucleus
and CGCG 119030 (the solid square with a big diamond) could be
a spiral galaxy instead of an elliptical galaxy. However, no hint of
star formation has been found for VCC 616 (the solid square on the
far-left above the line (2000 − V ) = 1.4) and CGCG 119086 (the
solid square on the far-right above the line (2000−V ) = 1.4). Our
model can explain the observations satisfactorily except for CGCG
119086, which needs further study.
Figure 15 shows the diagrams of (FUV − r)AB versus
(FUV −NUV )AB for a CSP galaxy model with a major popula-
tion age tmajor = 10Gyr and variable minor population age tminor
and various minor population mass fractions f . In these diagrams,
the colours are not shown in the restframe, but have been redshifted
(i.e. the wavelength is (1 + z) times the restframe wavelength,
where z is the redshift); panel (a) is for a redshift of z = 0.05
and panel (b) for z = 0.15. Overlayed on the two panels are qui-
escent early-type galaxies observed with GALEX by Rich et al.
(2005). The observed galaxies are for a redshift range 0 < z < 0.1
(panel (a)) and 0.1 < z < 0.2 (panel (b)). We note that most of the
quiescent galaxies are located in the region with f <
In Figures 13 to 15, we adopted a major population age of
tmajor = 10Gyr, and the colours are intrinsic. However, adopt-
ing a different age for the major population can change the dia-
grams; for example, a larger age leads to bluer (1550 − 2500) or
(FUV −NUV ) colours. In contrast, internal dust extinction shifts
the curves towards redder colours (Calzetti et al. 2000). Consider-
ing the uncertainties in the modelling, we take our model to be in
reasonable agreement with the observations.
c© 0000 RAS, MNRAS 000, 000–000
A binary model for the UV-upturn of elliptical galaxies 19
Figure 13. The diagrams of (1550−V ) versus (1550−2500) (a) and (2000−V ) versus (1550−2500) (b) for a composite stellar population (CSP) model
of elliptical galaxies with a major population age of tmajor = 10Gyrs (Set 6). Solid curves are for given minor population fractions f and are plotted, from
left to right, in steps of ∆ log(f) = 0.5, as indicated. Light grey curves are for fixed minor population ages tminor and are plotted, from top to bottom, in
steps of ∆ log(tminor/Gyr) = 0.1 , as indicated. Note that the colours are given in the restframe and intrinsic. The thick solid curve for f = 100% actually
shows the evolution of a simple stellar population with age tminor . Solid squares are for quiescent early-type galaxies observed with IUE by BBBFL and the
data points are taken from Dorman, O’Connell & Wood (1995).
4.3.4 UV-upturn magnitudes and their evolution with redshift
There is an observed spread in the (1550−V ), (1550−2500) and
(2000 − V ) colours of early-type galaxies. As can be seen from
Figures 12, 13, and 14, this spread is satisfactorily explained by
our model.
Brown et al. (2003) showed with HST observations that the
UV-upturn does not evolve much with redshift, a result apparently
confirmed by Rich et al. (2005) with GALEX observation of a large
sample. This is contrary to the prediction of both the metal-poor
and the metal-rich model, as both models require a large age for
the hot subdwarfs and therefore predict that the UV-upturn should
decline rapidly with redshift. Our binary model, however, predicts
that that UV-upturn does not evolve much with redshift (see Fig-
ures 3 and 4), consistent with the recent observations.
Lee et al. (2005) and Ree et al. (2007) studied the look-back
time evolution of the UV-upturn from the brightest elliptical galax-
ies in 12 clusters at redshift z < 0.2 with GALEX. Compared
to local giant elliptical galaxies, they found that the UV-upturn of
the 12 galaxies is redder. However, the local giant elliptical galax-
ies are quite special. NGC 1399 and M 87, with the strongest
UV-upturn, have the largest known specific frequencies of globu-
lar clusters (Ostrov, Geisler & Forte 1993), and M 87 hosts an ac-
tive galactic nuclei (AGN) with the best-known jet (Curtis 1918;
Waters & Zepf 2005). Given a larger sample of elliptical galaxies,
no matter how luminous they are, and a bigger redshift range, the
UV-upturn is not found to decline with redshift.
4.3.5 Implication for star formation history of early-type
galaxies
Boselli et al. (2005) studied the UV properties of 264 early-type
galaxies in the Virgo cluster with GALEX. They showed that
(FUV − NUV )AB ranges from 3 to 0, consistent with the the-
oretical range shown in panel (b) of Figure 4. The colour index
(FUV −NUV )AB of those galaxies becomes bluer with luminos-
ity from dwarfs (LH ∼ 10
8LH,⊙) to giants (LH ∼ 10
11.5LH,⊙),
i.e. a luminous galaxy tends to have a bluer (FUV − NUV )AB.
Panel (b) of Figure 4 shows that (FUV −NUV )AB becomes bluer
with population age for tSSP > 1Gyr. Taking the stellar popu-
lations as an “averaged” SSP, we may conclude that a luminous
c© 0000 RAS, MNRAS 000, 000–000
20 Han, Podsiadlowski & Lynas-Gray
Figure 14. The diagrams of (B−V ) versus (2000−V ) for a composite stellar population (CSP) model of elliptical galaxies with a major population age of
tmajor = 10Gyrs (Set 6). Solid curves are for given minor population fractions f and are plotted, from left to right, in steps of ∆ log(f) = 0.5, as indicated.
Light grey curves are for fixed minor population ages tminor and are plotted, from top to bottom, in steps of ∆ log(tminor/Gyr) = 0.1, as indicated. The
thick solid curve for f = 100% actually shows the evolution of a simple stellar population with age tminor. Note that the colours are intrinsic and are plotted
in the restframe. Overlayed on this diagram is figure 2 of Deharveng, Boselli & Donas (2002), in which solid squares are for their sample observed with the
FOCA experiment and open circles (including circles with crosses) are for the sample of BBBFL observed with IUE. Crosses denote objects that have been
studied in detail with HUT or HST. For galaxies bluer than (2000−V ) = 1.4, solid squares with big stars and circles with crosses are for galaxies with recent
star formation. NGC 4168 (solid square with a big triangle) has a low-luminosity Seyfert nucleus. CGCG 119030 (solid square with a big diamond) could be
misclassified as an elliptical, as it is classified as a spiral in the NASA/IPAC Extragalactic Database (NED).
early-type galaxy is older, or in other words, the less luminous an
early-type galaxy is, the younger the stellar population is or the
later the population formed.
4.4 The UV-upturn and metallicity
As far as we know, metallicity does not play a significant role
in the mass-transfer process or the envelope ejection process for
the formation of hot subdwarfs, although it may affect the prop-
erties of the binary population in more subtle ways. We there-
fore expect that (FUV − r)AB or (1550 − V ) from our model
is not very sensitive to the metallicity of the population, This is
in agreement with the recent large sample of GALEX observa-
tions by Rich et al. (2005). Boselli et al. (2005) and Donas et al.
(2006) studied nearby early-type galaxies with GALEX. Neither of
them show that (FUV − r)AB correlates significantly with metal-
licity, However, both of them found a positive correlation between
(FUV −NUV )AB and metallicity. This can possibly be explained
with our model. The UV-upturn magnitudes (FUV − r)AB or
(1550−V ) does not evolve much with age for tSSP > 1Gyr while
(FUV −NUV )AB decreases significantly with age (see Figures 3
and 4). A galaxy of high metallicity may have a larger age and
therefore a stronger (FUV −NUV )AB.
4.5 Comparison with previous models
Both metal-poor and metal-rich models are quite ad hoc and require
a large age for the hot subdwarf population (Section 1), which im-
plies that the UV-upturn declines rapidly with look-back time or
redshift. In our model, hot subdwarfs are produced naturally by en-
velope loss through binary interactions, which do not depend much
on the age of the population older than ∼ 1Gyr, and therefore
our model predicts little if any evolution of the UV-upturn with
redshift. Note, however, that (FUV − NUV )AB declines signifi-
cantly more with redshift than (FUV −r)AB, as the contribution to
the near-UV from blue stragglers resulting from binary interactions
becomes less important for an older population.
The metal-rich model predicts a positive correlation between
the magnitude of the UV-upturn and metallicity; for example,
(1550 − V ) correlates with metallicity. However, such a correla-
c© 0000 RAS, MNRAS 000, 000–000
A binary model for the UV-upturn of elliptical galaxies 21
Figure 15. The diagrams of (FUV − r)AB versus (FUV −NUV )AB for a composite stellar population (CSP) with a major population age of tmajor =
10Gyrs (Set 6). Solid curves are for given minor population fractions f and are plotted, from bottom to top, in steps of ∆ log(f) = 0.5, as indicated. Light
grey curves are for fixed minor population ages tminor and are plotted, from left to right, in steps of ∆ log(tminor/Gyr) = 0.1, as indicated. The thick solid
curve for f = 100% actually shows the evolution of a simple stellar population with age tminor. Note that the colours are intrinsic but not in the restframe.
Panel (a) assumes a redshift of z = 0.05 and panel (b) z = 0.15. Overlayed on this diagram is figure 3 of Rich et al. (2005), in which circles are for their
sample observed with GALEX for quiescent early-type galaxies. Filled circles (panel (a)) are observational data points for galaxies of 0 < z < 0.1 and open
circles (panel (b)) for 0.1 < z < 0.2.
c© 0000 RAS, MNRAS 000, 000–000
22 Han, Podsiadlowski & Lynas-Gray
tion is not expected from our binary model as metallicity does not
play an essential role in the binary interactions. Furthermore, even
though the metal-rich model could in principle account for the UV-
upturn in old, metal-rich giant ellipticals, it cannot produce a UV-
upturn in lower-metallicity dwarf ellipticals. In contrast, in a binary
model, the UV-upturn is universal and can account for UV-upturns
from dwarf ellipticals to giant ellipticals.
5 SUMMARY AND CONCLUSION
By applying the binary scenario of Han et al. (2002; 2003) for the
formation of hot subdwarfs, we have developed an evolutionary
population synthesis model for the UV-upturn of elliptical galaxies
based on a first-principle approach. The model is still quite simple
and does not take into account more complex star-formation histo-
ries, possible contributions to the UV from AGN activity, non-solar
metallicity or a range of metallicities. Moreover, the binary popu-
lation synthesis is sensitive to uncertainties in the binary modelling
itself, in particular the mass-ratio distribution and the condition for
stable and unstable mass transfer (Han et al. 2003). We have varied
these parameters and found these uncertainties do not change the
qualitative picture, but affect some of the quantitative estimates.
Despite its simplicity, our model can successfully reproduce
most of the properties of elliptical galaxies with a UV excess: the
range of observed UV excesses, both in (1550−V ) and (2000−V )
(e.g. Deharveng, Boselli & Donas, 2002), and their evolution with
redshift. The model predicts that the UV excess is not a strong
function of age, and hence is not a good indicator for the age
of the dominant old population, as has been argued previously
(Yi et al. 1999), but is very consistent with recent GALEX findings
(Rich et al. 2005). We typically find that the (1550 − V ) colour
changes rapidly over the first 1 Gyr and only varies slowly there-
after. This also implies that all old galaxies should show a UV
excess at some level. Moreover, we expect that the model is not
very sensitive to the metallicity of the population. The UV-upturn
is therefore expected to be universal.
Our model is sensitive to both low levels and high levels of
star formation. It suggests that elliptical galaxies had some star for-
mation activity in the relatively recent past (∼ 1Gyr ago). AGN
and supernova activity may provide supporting evidence for this
picture.
The modelling of the UV excess presented in this study is only
a starting point: with refinements in the spectral modelling, includ-
ing metallicity effects, and more detailed modelling of the global
evolution of the stellar population in elliptical galaxies, we propose
that this becomes a powerful new tool helping to unravel the com-
plex histories of elliptical galaxies that a long time ago looked so
simple and straightforward.
ACKNOWLEDGEMENTS
We are grateful to an anonymous referee for valuable comments
which help to improve the presentation, to Kevin Schawinski for
numerous discussions and suggestions, to Thorsten Lisker for in-
sightful comments leading to Section 4.3.5. This work was in part
supported by the Natural Science Foundation of China under Grant
Nos. 10433030 and 10521001, the Chinese Academy of Sciences
under Grant No. KJCX2-SW-T06 (Z.H.), and a Royal Society UK-
China Joint Project Grant (Ph.P and Z.H.).
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	Introduction
	The Model
	The BPS code and the formation of hot subdwarfs
	Monte-Carlo simulation parameters
	Spectral library
	Observables from the model
	Simulations
	Standard simulation set
	Simulation sets with varying model parameters
	Simulation sets for composite stellar populations
	Results and Discussion
	Simple stellar populations
	The model for composite stellar populations
	Theory versus observations
	The UV-upturn and metallicity
	Comparison with previous models
	Summary and Conclusion
	REFERENCES

  The discovery of a flux excess in the far-ultraviolet (UV) spectrum of
elliptical galaxies was a major surprise in 1969. While it is now clear that
this UV excess is caused by an old population of hot helium-burning stars
without large hydrogen-rich envelopes, rather than young stars, their origin
has remained a mystery. Here we show that these stars most likely lost their
envelopes because of binary interactions, similar to the hot subdwarf
population in our own Galaxy. We have developed an evolutionary population
synthesis model for the far-UV excess of elliptical galaxies based on the
binary model developed by Han et al (2002, 2003) for the formation of hot
subdwarfs in our Galaxy. Despite its simplicity, it successfully reproduces
most of the properties of elliptical galaxies with a UV excess: the range of
observed UV excesses, both in $(1550-V)$ and $(2000-V)$, and their evolution
with redshift. We also present colour-colour diagrams for use as diagnostic
tools in the study of elliptical galaxies. The model has major implications for
understanding the evolution of the UV excess and of elliptical galaxies in
general. In particular, it implies that the UV excess is not a sign of age, as
had been postulated previously, and predicts that it should not be strongly
dependent on the metallicity of the population, but exists universally from
dwarf ellipticals to giant ellipticals.

Introduction
	The Model
	The BPS code and the formation of hot subdwarfs
	Monte-Carlo simulation parameters
	Spectral library
	Observables from the model
	Simulations
	Standard simulation set
	Simulation sets with varying model parameters
	Simulation sets for composite stellar populations
	Results and Discussion
	Simple stellar populations
	The model for composite stellar populations
	Theory versus observations
	The UV-upturn and metallicity
	Comparison with previous models
	Summary and Conclusion
	REFERENCES
