A&A 462, 495-506 (2007)
DOI: 10.1051/0004-6361:20065468
G. Galletta1 - V. Casasola1,3 - L. Piovan1,4 - E. Merlin1 - D. Bettoni2
1 - Dipartimento di Astronomia, Università di Padova, Vicolo
dell'Osservatorio 2, 35122 Padova, Italy
2 - INAF - Osservatorio Astronomico di Padova, Vicolo dell
'Osservatorio 5, 35122 Padova, Italy
3 -
Observatoire de Paris-LERMA, 61 Av. de l'Observatoire, 75014 Paris, France
4 -
Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, Garching bei München,
Germany
Received 20 April 2006 / Accepted 20 September 2006
Abstract
Aims. We study the relations existing between fluxes emitted at the CO(1-0) line, 60 and 100 m wavelengths, and the B and soft X-ray wavebands for galaxies of all morphological types. The large set of data that we created allowed us to revisit some of the already known relations between the different tracers of the interstellar medium (ISM): the link between the FIR flux and the CO line emission, the relation between X-ray emission in non-active galaxies and the blue or FIR luminosity.
Methods. Using both catalogues of galaxies and works in the literature, we collected fluxes in the FIR, 21 cm, and CO(1-0) lines and in the soft X-ray for two samples, consisting of normal and interacting galaxies, respectively. By joining these samples, we have data for a total of 2953 galaxies, not all observed in these four wavebands.
Results. All the relations found are discussed in the frame of the star formation activity that is the link for most of them. We note that when an active star formation is present, it may link the galaxy fluxes at almost all wavelengths, from X to microwaves. In contrast, in early-type galaxies where the current star formation rate has faded, the X-FIR fluxes link disappears. This result for early-type galaxies is discussed and explained in detail in the frame of a suitable theoretical model, obtained by coupling chemo-dynamical N-body simulations with a dusty spectrophotometric code of population synthesis.
Key words: galaxies: ISM - galaxies: fundamental parameters - infrared: ISM - radio lines: ISM - X-rays: ISM
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Figure 1:
The relation between the flux from the CO(1-0) line and
at 100 ![]() |
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At present, different tracers of the gas are known, such as
millimetric lines for the cold molecular gas, the 21 cm line for
atomic hydrogen at 100 K, IR bands for molecules at thousands
of degrees, UV lines, and X-ray emission for hotter gas. The dust
distribution is also traced by FIR emission at 60 and 100
m, if
the grains are warm (Bregman et al. 1992), or at 170
m, if they are
colder (Popescu et al. 2002). The diffusion of large archives of
observations at the above wavelengths (except for molecular lines) has
allowed the compilation of catalogues in the past years containing
a huge number of galaxies. Using these catalogues and the works
presented in the literature, we collected fluxes in FIR, 21 cm,
CO(0-1) line, and soft X-ray for two broad samples of normal
(Bettoni et al. 2003a) and interacting (Casasola et al. 2004a) galaxies. By joining
these samples, we have amassed data for a total of 2953 galaxies,
not all observed in these four wavebands. The fluxes measured
with the different tracers now allow a study of the
link between dust, gas, and stars based on hundreds of
galaxies.
It is known that the fluxes emitted by a galaxy at very different
wavelengths may be linked by means of the star formation
mechanism (see Ranalli et al. 2003; David et al. 1992).
For instance, the formation of massive stars generates
heating of the dust clouds they are embedded in, by absorption
of their UV radiation, and produces a re-emission of this energy in
the FIR. This process links the current star formation rate
to the IR emission at 60 and 100 m (Thronson & Telesco 1986). The
ionizing radiation of stars may also produce evaporation of the
molecular clouds. Inside these clouds, where the particle density is
high enough to produce a significant number of collisions between H2 and CO molecules, these are excited and produce
photons, but in optically thick regions. The warming by the UV
stellar light makes these regions less dense, thereby making visible the CO lines at their edge. Because of this mechanism, these lines are
considered tracers of the cold molecular hydrogen that does not emit
observable lines. The newly formed stars are also responsible for the
X-ray emission produced by very massive stars, by core-collapse SN,
and by high-mass X-ray binaries. According to the mechanisms
described above, we expect that galaxies with active star formation will
have a FIR emission, but also CO and X-ray emissions induced by the
more massive stars, linked by different kinds of relations.
When the star formation decreases or vanishes, the FIR emission decreases as well, but it may be fed by the stellar light absorbed and re-emitted in the infrared by dust (cirrus), while low-mass X-ray binaries and type I SN contribute to the high energy galaxy spectrum. In addition, AGB stars, surrounded by dust, and the cooling flows of the interstellar medium ejected by supernovae may together produce additional IR and X emission.
To study the activity of the galaxies at different wavebands, we
collected data on galaxies starting from the original data on fluxes
in the 60, 100 m, CO(1-0) lines, and in the soft X-ray used to compile
our catalogues (Bettoni et al. 2003b; Casasola et al. 2004b). The merging of these two
catalogues produces 1764 known values of
FIR fluxes (1837 have 100
m flux), 391 soft X-ray fluxes, and 434 values for the CO(1-0) line luminosity. We extracted the values of the distance moduli,
blue absolute magnitudes, and morphological classification for all of them
from the LEDA catalogue (Paturel et al. 1997).
These are 1038 galaxies with evident signs of interactions or disturbed morphologies according to the catalogues of Arp (1966), Arp & Madore (1987), and Vorontsov-Velyaminov (1959). We shall refer to them as "perturbed galaxies''. The remaining 1915 galaxies that appear neither morphologically nor dynamically perturbed are called "normal galaxies''. In our sample, we have 253 galaxies that have a spectral classification for the nucleus, and 231 of these appear to host an AGN (Seyfert 1, 2 or transition type, Seyfert 3 or Liners) according to the classifications of Ho et al. (1997) and Véron-Cetty & Véron (2003). Most of the remaining 2722 galaxies lack information about nuclear spectrum or have spectra of HII regions (22 starburst spectra). They are not included in any AGN catalogue and, for this reason, we refer to them in the following discussion as "non active galaxies'' and to the others as "active galaxies''. With all these data, we crossed the various tracers to understand and revisit the main relations existing between X, FIR, CO, and B luminosities.
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Figure 2: Left: the X-ray luminosity plotted vs. blue luminosity, in solar units, for late-type, non-active galaxies. The relation corresponding to emission caused by discrete sources, indicated in Eq. (4) is plotted as a dotted line. Right: X-ray luminosity vs. FIR luminosity, in solar units for the late-type, non-active galaxies. The linear relation indicated in Eq. (7) is plotted as a dashed line. |
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The relations existing between different cold components of the ISM, such as
the molecular gas and the dust, have been studied for many years
(Sanders & Mirabel 1985; Solomon & Sage 1988; Bregman et al. 1992). They find that the global galaxy luminosity
derived from CO(1-0) line is directly related with the flux at 100 m.
With our large sample we tested these relations using galaxies
of different morphological types and activity or interaction.
In Fig. 1 we plotted the logarithm of the flux measured from CO(1-0)
line vs. the logarithm of the IRAS flux at 100 m. In our plots, we have
193 galaxies with classification from E to Sb and 178 from Sbc to Sm. The
relation found by Bregman et al. (1992) for a sample of early-type galaxies,
,
is also
plotted as comparison.
The relations are evident with this wider sample of galaxies. In these diagrams, active and non-active galaxies appear mixed together without clear differences and have been plotted together. The same behaviour appears for interacting and non interacting galaxies, which are not distinguished in our plots.
For all the galaxy types, we find:
We note that irregular galaxies are not fitted by these relations but are widespread. In our sample there are just 10 galaxies and their representative points have not been plotted in Fig. 1.
We are interested in understanding what relations exist between ,
the X-ray
luminosity, and the other global galaxy properties. From the literature, it is
known that a proportionality exists between
produced by
discrete sources and LB, the blue luminosity of the whole galaxy.
This relation has been studied by Ciotti et al. (1991) and compared by Beuing et al. (1999)
with soft X-ray fluxes measured by the ROSAT satellite. It appears that late-type
galaxies have a global X-ray luminosity directly proportional to LB, while
early-type systems are dominated by emission produced by hot diffuse gas, and
their
is proportional to the square power of the blue luminosity, as
discussed by Beuing et al. (1999). For this reason, the early and late-type
galaxies are discussed separately.
If, instead of the blue luminosity, we use the galaxy area
,
calculated
from the apparent diameter measured at the 25 mag arcsec2 isophote and
converted in kpc2, we
discover that the relation is still present, but with a wider spread. It becomes
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(5) |
A relation similar to that of Ciotti et al. (1991) has been found by some authors
(Ranalli et al. 2003; Griffiths & Padovani 1990; David et al. 1992), but using 60 m fluxes or FIR
luminosities. The values of
are calculated using the formula
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(6) |
From our data it is possible to find a relation between
and
that fits the values of late-type galaxies. We found
,
similar to the
found by
Ranalli et al. (2003) for fluxes between 0.5 and 2 keV and to the
found by David et al. (1992) using fluxes between 0.5
and 4.5 keV. Forcing the relation to a linear proportionality between
and
we find:
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Figure 3: Left: the X-ray luminosity plotted vs. blue luminosity, for early-type, non-active galaxies. The relation corresponding to emission caused by diffuse gas, valid for early-type galaxies and indicated in Eq. (10) is plotted as a full line. Right: X-ray luminosity vs. FIR luminosity for the early-type galaxies. The linear relation for late-type, non-active galaxies indicated in Eq. (7) is plotted as a dashed line. |
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We note that the B and FIR luminosities are also connected in late-type
galaxies by means of a linear relation fitted by:
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(8) |
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(9) |
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Figure 4: Left: the X-ray luminosity plotted vs. blue luminosity for active galaxies, separated according to the type of activity. The relation corresponding to emission caused by diffuse gas, valid for early-type galaxies and indicated in Eq. (10) is plotted as a full line. Right: X-ray luminosity vs. FIR luminosity for the active galaxies. The linear relation for late-type galaxies indicated in Eq. (7) is plotted as a dashed line. |
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The relation still holds if
(kpc2) is used. It becomes
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(11) |
Many galaxies with high blue luminosity, indication of high masses and of a recent star formation, lie quite far from the mean line, with different behaviour than late-type galaxies.
If the X-ray fluxes are compared with FIR luminosity, the disagreement with
the behaviour found in late-type galaxies is more evident. The plot
vs.
for early-type galaxies shows the representative points of the
galaxies above the relation (7) for late-type galaxies
(Fig. 3, right panel). To understand this apparent disagreement, we
should use a theoretical analysis of the FIR emission, as explained
in Sect. 4.
To cast light on the nature of the relations observed
between ,
LB, and
for early-type
galaxies, one has to consider the various
components of a galaxy (stars, gas, and dust) and to understand
their mutual interactions as far as the spectral energy
distribution (SED) is concerned. There are two basic schemes for
modelling the formation and evolution of early type galaxies: (1) the
semi-analytical models on which a great deal of our understanding of
the chemo-spectro-photometric properties is derived; and (2) the
N-Body Tree-SPH simulations that, in contrast, have been used only
occasionally to study spectro-photometric properties of
early type galaxies. In the following part of this section
we proceed as follows. First, we analyse the drawbacks of
semi-analytical models, in particular dealing with the calculation
of the infrared emission of early-type galaxies. Second, we discuss
how dynamical simulations and a dusty
spectrophotometric code, when mixed together, allow us to move forward
a step in the calculations of the SEDs properties. Third, we show
in detail how our model has been built and the coupling between
dynamics and dusty population synthesis was done.
The semi-analytical models approximate a galaxy to a point-mass system in which gas is turned into stars by means of suitable recipes for star formation, and heavy elements are produced by stellar nucleosynthesis and stellar winds/explosions. The standard evolutionary population synthesis technique (EPS) is usually applied to derive the SED of the galaxy, with models able to explain many global features of early type galaxies, as amply described by many authors (Arimoto & Yoshii 1989; Gibson 1997; Tantalo et al. 1998; Bressan et al. 1994; Tantalo et al. 1996; Arimoto & Yoshii 1987). There are three important and problematic issues of these models to be discussed for our purposes.
First, to determine the age at which the galactic wind
sets (Larson 1974; Larson & Dinersten 1975), we need some hypothesis about dark
and baryonic matter with their relative distributions and about the
heating and cooling efficiency of the various mechanisms to
properly evaluate the total gravitational potential well and to
describe the thermal history of the gas. In this scheme it turns
out that the galactic wind occurs typically for ages
Gyr,
later in a massive early-type galaxy and much earlier in galaxies of lower mass
(Arimoto & Yoshii 1989; Gibson 1997; Tantalo et al. 1998,1996; Bressan et al. 1994; Arimoto & Yoshii 1987; Chiosi et al. 1998).
The maximum duration of star-forming activity therefore follows
the trend
in these models.
This trend of the SFH is, however, contrary to what is required by the
observed trend forward the
-enhancement for early type galaxies,
which implies that the maximum duration of the star forming activity
should decrease when the galaxy mass increases
(see Tantalo & Chiosi 2004; Kuntschner 2000; Trager et al. 2000b; Thomas et al. 2005; Bressan et al. 1996; Trager et al. 2000a, for more details on the
enhancement in
-elements and the SFH of early-type
galaxies).
Second, after the galactic wind phase, star formation no longer
occurs and the evolution is merely passive. However, AGB and RGB
stars continue to lose gas in amounts that are comparable
to those before the galactic wind (Chiosi 2000). What is
the fate of this gas? One may imagine that the large amount of gas
lost by stars will expand into the dark matter halo and heat up to
an energy and overwhelm the gravitational potential, and will escape
the galaxy. Most likely a sort of dynamical equilibrium is reached
in which gas is continuously ejected by stars and lost by the
galaxy. It may happen therefore that some amount of gas is always
present in the galaxy. The question is not obvious because, if an
early type galaxy is free of gas and contains only stars, the SED is
expected to drop off long ward of about
,
and no IR emission
should be detected. However, as already pointed out long ago
by Guhathakurta et al. (1986) and Knapp et al. (1989) (see also Fig. 3), many
early-type galaxies of the local universe emit in the IR. The origin
of this flux in the MIR/FIR is most likely due to the dust present
in a diffuse ISM that, once emits at those wavelengths
heated up by the galactic radiation field.
Therefore to match the IR emission, one
has to allow for some amount of diffuse ISM. An interesting
question is therefore how much gas can be present today in
an elliptical galaxy and how it is distributed across the galaxy.
Even if we can correctly estimate the amount of gas ejected by
stars, the fate of this gas goes beyond the possibilities of
classical semi-analytical models.
As a third point, note that, when we fold many SSPs to calculate a galaxy SED using the classical EPS technique, we simply convolve their fluxes with the SFH of the galaxy. Many classical spectrophotometric semi-analytical models of galaxies are built in this way: there is no dust at the level of SSPs and again no dust at the level of the galaxy model (see e.g. Buzzoni 2002; Tantalo et al. 1998; Arimoto & Tarrab 1990; Kodama & Arimoto 1997; Tantalo et al. 1996; Arimoto & Yoshii 1987; Buzzoni 2005; Bruzual & Charlot 1993). To calculate the emission by dust, a higher level of sophistication is required for the model. Indeed, one has to develop a model in which the sources of radiation and the emitting/absorbing medium are distributed, so as to face and solve the problem of the radiative transfer simulating the interactions in a realistic way among the various physical components of a galaxy. Among recent models of this kind are those by Silva et al. (1998), Devriendt et al. (1999), and Takagi et al. (2003).
Two drawbacks of the semi-analytical models therefore concern (1) the description of galactic wind, which is supposed to occur within a finite time interval; and (2) the star formation history that is reversed, allowing longer SFH for more massive galaxies. These two problems, combined with a lack of geometrical information about the distribution of gas and dust, make semi-analytical models unsuitable properly for calculating the IR emission of early type galaxies. To improve upon them we need to use the results from dynamical simulations. They have been shown to be able to properly model the ejection of gas by the galaxy as a sort of continuous process, taking place whenever a gas particle heated up by various mechanism has acquired a higher velocity than the escape velocity (see e.g. Springel 2001; Chiosi & Carraro 2002; Carraro et al. 1998; Kawata 2001). They are able to reproduce the SF history of early-type galaxies both in the context of the monolithic collapse scenario (Chiosi & Carraro 2002; Kawata 2001) and recently in the context of hierarchical scenario (De Lucia et al. 2006). Finally, the galaxy is no longer a mass point, but a fully three-dimensional structure of the galaxy is available with spatial distribution of stars and gas.
With the aid of N-Body Tree-SPH
simulations based on quasi-cosmological initial conditions in the
standard-cold dark matter scenario (S-CDM), Merlin & Chiosi (2006) modelled the formation
and evolution of two early-type galaxies of different total mass
(dark + baryonic matter in the cosmological proportions 9:1). The
total masses under considerations are
(Model A) and
(Model B). The galaxies
have been followed from their separation from the global expansion
of the universe to their collapse to virialized structures, the
formation of stars, and subsequent nearly passive evolution. They are
followed for a long period of time, i.e. 13 Gyr (Model A) and 5 Gyr
(Model B), or at least well beyond the stages of active star
formation that occurs within the first 3 to 4 Gyr (see below). The
models take into account radiative cooling by several processes,
heating by energy feed back from supernova explosions (both types I
and II), and chemical enrichment. All the models conform to the
so-called revised monolithic scheme, because mergers of
substructures have occurred very early in the life of the galaxy. Some
parameters and results of the two models are summarised in Table 1. Note that the shape of the resulting galaxies is
nearly spherical both in dark matter and stars.
Table 1:
Initial parameters for the dynamical simulations of
Merlin & Chiosi (2006) in the Standard CMD scenario, where masses are in units
of
,
radii are in kpc, and ages are in Gyr.
The third drawback of the classical semi-analytical model was the lack of a description of the dusty component, which for our purposes needs to be included. The semi-analytical chemo-spectro-photometric model developed by Piovan et al. (2006b) allows us to overcome this issue. It takes into account not only the geometrical structure of galaxies of different morphological types, but also the effect of dust in converting the UV and optical light in FIR radiation. In brief, the Piovan et al. (2006b) model follows the infall scheme, allows for the onset of galactic winds, and contains three main components: (i) the diffuse interstellar medium composed of gas and dust whose emission and extinction properties have been studied in detail by Piovan et al. (2006a); (ii) the large complexes of molecular clouds in which new stars are formed; and (iii) the stars of any age and chemical composition. The total gas and star mass provided by the chemical model are distributed over the whole volume by means of suitable density profiles, one for each component and depending on the galaxy type (spheroidal, disk, and disk plus bulge). The galaxy is then split into suitable volume elements to each of which the appropriate amounts of stars, molecular clouds and interstellar medium are assigned. Each elemental volume absorbs radiation from all other volumes and from the interstellar medium in between. The elemental volume also emits the absorbed light again and produces radiation by the stars that it contains. On the other hand, the star formation, the initial mass function, and the chemical enrichment of the Piovan et al. (2006b) model are very similar to those by Bressan et al. (1994), Tantalo et al. (1996), Tantalo et al. (1998), and Portinari et al. (1998).
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Figure 5:
Top panel: the masses of stars (continuous line) and
gas (dashed line) for the dynamical model of
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The description of an early-type galaxy as far as predicting its spectro-photometric infrared properties can therefore be realised with a suitable combination of dynamical and spectro-photometric approaches. Coupling the dynamical models with spectro-photometric synthesis requires a number of steps that deserve some remarks.
As the spectro-photometric code of Piovan et al. (2006b) suited to
describing early-type galaxies is written in spherical symmetry, we
have to derive suitable spherical distributions for the density of
stars and gas to be used into the model. The task is facilitated by
the nearly spherical shape of the dynamical models. To this aim, we
consider the sphere of radius
centred at the centre of
mass of the stellar component. The sphere is then divided into a
number of thin spherical shells whose derived average density of
stars and gas is shown in Fig. 6. Even if the
centre of mass of the star and gas distributions may not be exactly
coincident, this is not relevant here, so the same coordinate centre
can be used for both components.
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Figure 6:
The averaged density profiles of gas and stars for the model of
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where "i'' stands for "stars'' or "gas'', and
are the corresponding core radii. The above
representation is suited more to our aims than is the classical King
law. The fits are shown in Fig. 6. They
are normalized in such a way that the integral over the galaxy
volume corresponds to the amount of gas contained inside
.
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Figure 7:
Basic quantities of the chemical models for a prototype
early-type galaxy of
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Figure 8:
The same as in Fig. 7, but for the model with
total baryonic mass of
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Knowing the amount of gas, we need to specify the fraction of it in the form of dust to finally be able to derive the whole SED from X to FIR and look for relationships between the luminosity in the X, B, and FIR pass-bands we want to interpret. Our models, both semi-analytical and chemo-dynamical, are not suitable to describing the evolution of the compositions and abundances of both gas and dust phases. The relative proportions of the various components of the dust would require detailed study of the evolution of the dusty environment and complete information on the dust yields, as in the models of Dwek (1998,2005). This would lead to a better and more physically sounded correlation between the composition of dust and the star formation and chemical enrichment history of the galaxy itself, although at the price of increasing the complexity and the uncertainty of the problem.
The key parameter in calculating the amount of dust is the dust-to-gas
ratio, defined as
,
where
and
are the total dust and hydrogen mass, respectively. For the Milky
Way and the galaxies of the Local Group,
is estimated to
vary from about 1/100 to 1/500 and typical values
,
,
and
are used for the
Milky Way (MW) and the Large and Small Magellanic Clouds (LMC and
SMC). These dust-to-gas mass ratios describe a decreasing sequence,
going from the MW to the LMC and SMC. Since these galaxies also
describe a sequence of decreasing metallicity, a simple assumption
is to hypothesize
in such a way as to match the
approximate results for MW, LMC, and SMC:
.
This relation
simply implies that the higher the metal content of a galaxy, the
higher the abundance of grains per H atom. However, the
metallicity difference not only implies a difference in the
absolute abundance of heavy elements in the dust, but also a
difference in the composition pattern as a function of the
star formation history (Dwek 1998,2005). Despite these
uncertainties (Devriendt et al. 1999), the relation
is often adopted to evaluate the amount of dust in galaxy models
(e.g. Silva et al. 1998) by simply scaling the dust content adopted
for the ISM of the MW to the metallicity under consideration.
The
and
galaxy models reach an average metallicity of solar and
slightly more than twice solar, respectively. To describe them, we
adopted the description of Piovan et al. (2006b,a) where a
model of dusty ISM is built by taking different metallicities into account.
The problem, however, remained unsettled for metallicities
higher than the solar one, where relative proportions holding good
for the MW average diffuse ISM model were adopted and the
amount of dust scaled with
.
Therefore, for the
galaxy with solar metallicity, the MW
diffuse-ISM model was adopted
,
while for the
model we
followed the
relation, using the MW average
pattern of dust composition.
The connection between the results of this model and the observed diagrams are discussed in the next section.
Our data confirm and extend the previous relations between
various tracers of the ISM in galaxies of different morphological
types. In the literature the relation found by Bregman et al. (1992) between
and S100 indicates a direct proportionality (slope = 1)
between the two fluxes and differs from that of Solomon & Sage (1988),
which exhibits a steeper gradient. Our relation (1)
agrees quite well with the proportionality found by Bregman et al. (1992),
the slope we found being equal to 1.06. The similarity between the
two curves in Fig. 1 is evident. As
described in the introduction, this link derives from the excitation of gas clouds by
the currently forming stars and by the warming of the dust in the galaxy.
In late-type galaxies )
our data show the existence of a
linear relation between soft X-ray fluxes and other indicators of
recent and current star formation, such as the B and FIR luminosity,
respectively (Eqs. (4) and (7)). This has been known
since the first X-ray observations of large samples
Fabbiano et al. (1992), and this connection between B and X-ray luminosity
in late type galaxies has been interpreted as due to the
contribution of discrete X-ray sources, whose number is proportional
to the quantity of already formed stars (Beuing et al. 1999; Ciotti et al. 1991). The
recent work of Kim & Fabbiano (2004), which is able to resolve the single
X-ray binaries in 14 galaxies, indicates that the X-ray luminosity
produced by discrete sources is related to B luminosity by a similar
relation, with an intercept value of -3.63, similar to our -3.85 of
Eq. (4).
In addition to the interstellar radiation, which is proportional to
the number of already formed stars, the X-ray emission is also produced
by HII regions, where there is an ongoing vigorous star
formation (David et al. 1992). This latter contribution appears more
evident in FIR light and may explain the existence of a similar
linear relation between
and
.
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Figure 9:
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In the FIR, however, mechanisms different from the emission from warm dust heated by the newly born stars predominate, since the star formation in most of these systems is almost exhausted. The FIR emission comes from circumstellar dusty shells around AGB stars and from an interstellar medium due to the outflow of dusty gas from AGB and RGB stars, as described in Sect. 4.
The key point for interpreting the observed trends is that we are
dealing with an emission coming from a more or less small amount of
dust distributed over the whole galaxy and heated by an average
interstellar radiation field due to all the stars of any age. The
situation is quite different from what happens, for instance, in
starburst galaxies where high optical depth dusty regions reprocess
the light coming from newly born stars embedded in the parental
environment. We can therefore conclude that in most of our
early-type galaxies, the mechanism of IR emission is not strictly
related to the star formation, and the link between the younger
generations of stars and dust emission is lost. For these reasons
one may expect that the soft X-ray luminosity in early type galaxies
is traced by the total blue luminosity but not by the FIR
luminosity. With the end of the star formation, the FIR
emission of these galaxies has faded out and an early type galaxy
with the same
of a late type will have a lower
.
This
could explain the location of the points in Fig. 3 (right
panel), on the left side of the linear relation.
To check if this interpretation is correct we try to apply the
detailed chemo-dynamical spectrophotometric model described in the
previous section, in such a way as to estimate the luminosities
produced by the stars in connection with the various phenomena
present inside the galaxy, taking the contribution by
dust into account as well. Since the theoretical model cannot derive the luminosity, we proceed in the following way.
The luminosities LB and
are directly derived
from the model. Then, we assume that the X-ray production of these
galaxies is proportional to LB according to our relation (10). In this way we may estimate the expected X-ray flux
and define a representative point in the
vs.
plot.
We start considering two template models in which all the
parameters are fixed using the clues coming from the dynamical
simulations of Merlin & Chiosi (2006), as described in Sect. 4. The King profiles represented in Fig. 6
are similar for all the components, with
and
kpc, while the dimension of the galaxy is an average one
corresponding to most of the galaxies available in the catalogue.
The SFH is exactly the one obtained by the dynamical simulations.
The two values of
and
obtained for the
and
baryonic mass
models are plotted in Fig. 9. The more massive galaxy
fits well into the region defined by the actually observed galaxies.
The calculated levels of emission
and
of this galaxy are very low, and for this
reason they belong to a region where we do not have enough
observations. Its weak
emission can be
explained by the dynamical evolution in which almost all the gas is
consumed to form stars so the galactic winds are very efficient
(see Chiosi & Carraro 2002, for more details about galactic winds in low-mass
galaxies). Therefore, even if the trend of this galaxy is
the expected one for early-type galaxies (the model stays above the
linear relation), nothing can be said with more certainty, because we lack
observed data in that region of the diagram.
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Figure 10:
Models
of the
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Much more interesting is the model of higher mass. The calculated luminosities of the model, with its exhaustion of its star formation, seem to agree well with the observations of early-type galaxies. However, the model needs to be checked against other possibilities, in order to understand how the various parameters of the model influence the spreading of early-type galaxies into the observational data. First of all we have to check the effects of the geometrical parameters and of the masses of stars/gas.
The effect of this huge increase in the mass of diffuse gas and dust (in
the original model at
kpc only
of the gas is
inside
)
is to shift the models straight toward the linear
relation. It can be explained in the following way. Increasing the
amount of diffuse gas/dust (with all the parameters fixed and the
star formation exhausted) implies more absorption of the stellar
radiation and therefore a lower LB (and
). On the
other hand,
remains almost unchanged or becomes lower.
The reason is that the strongly increased mass of dust makes the
average stellar radiation field weaker, therefore the increased
emission of dust (due to the bigger mass) peaks at wavelengths
longer than
,
leaving
almost unchanged. Even if
in this way we can shift the model toward the linear relation, the
situation is physically unrealistic, requiring a huge amount of
gas/dust concentrated in the centre of an early-type galaxy with
exhausted star formation, which is not commonly observed and also
not predicted by dynamical models.
This can be explained in the following way: for
and
both
0.5 and the diffuse ISM
and the stars are both concentrated in the inner region of the
galaxy with a density of stars/gas of many orders of magnitude higher
than the outer regions. This is the condition for producing high
,
because we find that the regions of higher density of
dust are the same in which there is also the higher average
radiation field heating dust. The spatial distribution of the ISM
favours the interaction with the stellar radiation. When we destroy
this coupling between stellar emission and density of gas, as we do
allowing for a uniform distribution of gas or stars or both, the
emission in the
becomes weaker. The weakening of the dusty
emission is stronger for the bigger radius of 20 kpc because in
all three cases one or both the components are distributed over
a huge galactic volume and we then have a low density of gas, eventually
coupled with weak radiation field. For the 6 kpc model, even if
the coupling in the central regions is destroyed, the galaxy is
small enough to keep a acceptable level of
,
even when the matter
is equally distributed across all the galaxy volume.
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Figure 11:
Models
of the more massive galaxy of
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The last and main point to be examined is how varying the star
formation history affects the position of the galaxies on the
vs.
plot. In Figs. 10 and 11,
the galaxies of different morphological types form a sequence that,
going from systems in which the star formation was exhausted long ago to
systems in which star formation is still active, moves toward the
linear relation and thereby suggesting the key role played by star
formation. First of all we calculate the
and
obtained by the SEDs and the models by Piovan et al. (2006b) of real
galaxies of the local universe: three
spiral galaxies
and
and two starburst
galaxies
and
.
The key point is that the SFHs of
these galaxies allow us to cover an acceptable
number of different star
formation histories. All these SFHs, unlike the ones of the ellipticals
obtained by dynamical simulations, never end; in the case of the
two starbursters, a strong burst of star formation is added in the
last millions of years. A huge amount of
therefore comes
from the young and deeply obscured region of star formation and not
only from the diffuse component.
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Figure 12:
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The results, presented in Fig. 12, show that
the three models of spirals stay near the linear relation, while the
two starbursters stay below the line, with the model of
,
powered by a huge burst of star formation falling well below the
linear relation. The stronger the emission coming from the
regions of star formation, the bigger the shift toward higher
and lower
(due to the lower LB). The results
from these models are quite similar to the observational data:
for
we get
with the observations giving
(10.37,7.01), for
we have
compared with
(11.99,7.60), and for M 82 we get
against
(9.79,6.31).
However, these galaxy models, even if they represent
real galaxies well, differ in many parameters from the early-type galaxy
model of
,
like geometry and mass.
These parameters, together with the SFH, obviously concur to
determine the position of the models on the
vs.
plot. To isolate the effect of the SFH, we first re-calculated the SFHs
of the five theoretical models above, rescaled to
the mass of
of the early-type galaxy
model. In Fig. 13 we can see four of the five SFH obtained.
Second, we fixed all the geometrical parameters to the same
values as for the average model of the
early type galaxy. The additional parameters, i.e. the escape
time of young stars from parental molecular clouds, the library of
SEDs of young dusty regions and the mass of gas in the diffuse and
molecular component, are fixed to the values used in
Piovan et al. (2006b) for spirals and starbursters, as appropriate.
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Figure 13:
Different adopted star formation histories for the model of
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Figure 14:
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In Fig. 14 we finally show the results
obtained as a function of the SFH for the galaxy of
,
keeping all the other parameters fixed. It is
interesting to observe that, since now the star formation never ends
and the galactic wind is not included, the classical semi-analytical
chemical evolution can be much more safely coupled to the
spectro-photometric code. The effect of varying the SFH at fixed
mass is to enhance the
,
keeping the
almost fixed
and shifting the points toward the linear relation at higher
infrared luminosities. This is ultimately due to the strong and
efficient reprocessing of the light coming from very young stars,
occurring in the dusty star-forming regions. As a consequence of
this, models with starburst-like SFHs shift, as expected, toward
higher
luminosity than do models with spiral-like SFH,
because of the stronger star formation and, therefore, emission
from young dusty regions. This can be also understood if we look in
detail at the relative contribution to
coming from the
regions of star formation (let us define it
and represent
it as usual in
)
and from the diffuse interstellar
medium
.
We get the values (
), (
), (
)
for the three models with spiral-like SFHs, while we
have (
)
and (
)
for the models with starburst-like SFHs. The stronger
the contribution from star forming regions, the higher is
when keeping LB (and
)
almost unchanged. Models
slightly dominated by the ISM contribution, but with a significant
contribution coming from obscured newly born stars are more suitable
to the linear relation of spirals.
It is worth noticing that in Fig. 14 we show both the
results obtained by applying the early-type linear relation between
and LB - Eq. (10) - and the late-type one -
Eq. (4). Since, however, the SFHs used (see Fig. 13) are typical of late type galaxies (or starbursters), it is
physically much sounder to apply Eq. (4) to obtain the
luminosity. As a last point, we also calculated a sequence of
models in which one of the SFHs of the spirals has been chosen
(namely the one of NGC 6946) with all the parameters fixed and only
the mass varied. As we see from Fig. 14, the effect
of varying the mass is to shift the object diagonal by almost along
the relation. This is explained simply by the smaller amounts of
stars/gas emitting radiation.
We have been able to describe the relations existing in a galaxy between the various tracers of the ISM and to fix the coefficients of the relations existing between FIR, B, and X-ray luminosity, both for early- and late-type galaxies.
The large set of data we used allowed us to more clearly redefine the
relationship between the CO and the 100 m fluxes. We found
that the relation, first obtained by Bregman et al. (1992) for early type
galaxies, is also valid for late type galaxies. In these galaxies, the
X-ray flux also appears linked to B and FIR emissions.
The only relation lacking from observations, i.e. the one
between
and
,
was studied by the use of the most
recent chemo-dynamical models coupled with dusty evolutionary
population synthesis.
The calculated luminosities of the models seem to confirm our
hypothesis about a connection between the exhaustion of the star
formation and the "migration'' of the early type galaxies above the
linear relation in the
vs.
plot. In the frame of our
assumptions, we may therefore conclude that the prediction of our
dusty chemo-dynamical models of galaxy evolution is consistent with
the observed lack of a direct relation between
and
for early type galaxies and is due to the different mechanisms for
producing FIR light in galaxies where the active star formation
is no longer active. In most of our early-type galaxies, the
mechanism of IR emission is no longer strictly related to the ongoing
star formation and to the reprocessing of the radiation in the dense
regions where new stars are born. The FIR emission therefore comes
most likely from circumstellar dusty shells around AGB stars and
from an interstellar diffuse medium due to the outflow of dusty gas
from AGB and RGB stars.
Finally, we can summarize that: (i) the SFH
of the galaxies seems to have the stronger effect on the
position of early-type galaxies in the
vs.
plot; (ii)
other parameters, like the radius of the galaxy and the scale radii
of stars and gas, play a secondary role, even if they can
significantly contribute to the scatter of the models in the region
above the linear relation; (iii) the mass is the main parameter in
explaining the scatter of the points along the linear relation.
Acknowledgements
This research was partially funded by the University of Padua with Funds ex 60% 2005. We acknowledge Prof. C. Chiosi for useful discussions of the theoretical subjects of this paper. L. Piovan is pleased to acknowledge the hospitality and stimulating environment provided by the Max-Planck-Institut für Astrophysik in Garching where part of the work was done during his visit as an EARA fellow on leave from the Department of Astronomy of the Padua University. We also thank the referee for the detailed and useful comments about this topic.