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The H2 – CO conversion factor
In spite of the high optical depth of the 12CO line, as noted by Phillips et al. (1979), there are theoretical and empirical basis for the use of CO as a tracer of the mass of the Giant Molecular Clouds (GMCs) in luminous galaxies. There is an empirical correlation between the virial masses of molecular clouds with known sizes and linewidths, and their CO luminosities for some Local Group galaxies (see Fig. 1.4). The same measures for external galaxies are diﬃcult because a high spatial resolution is needed. However, since the few extragalactic molecular clouds seem apparently similar to those in the Milky Way (Young & Scoville, 1991), the use of the Galactic H2 to CO proportionality for external galaxies is, at least partially, justified.
This proportionality is defined as the conversion factor X between the H2 column density of the molecular hydrogen N (H2) and the intensity of CO emission integrated over the line profile: X = N (H2)/ICO (1.3).
Thermal radio continuum emission
The radio continuum emission from a normal galaxy consists of two compo-nents: a non-thermal component produced via synchrotron emission and a thermal one due to a free-free emission from HII regions.
Thermal re-irradiation of starlight by dust quickly overwhelms these components above ν ∼200 GHz (λ ∼1.5 mm), defining a practical upper bound to the frequencies of the radio observations. Observing the spectrum of the starburst galaxy M 82 (Fig. 1.5), we can note the typical relative in-tensities of synchrotron radiation, free-free (bremsstrahlung) emission, and the dust re-irradiation. The free-free emission emerges from HII regions containing ionizing stars, where the electrons in the interstellar plasma are subject to coulomb inter-action with ions, and they travel on hyperbolic trajectories in which they are accelerated and radiate. This emission, called “free-free” because the elec-tron passes from an unbound state to another unbound state -though it loses energy- has an intensity proportional to the production rate of Lyman con-tinuum photons. However, isolating the free-free component and measuring its flux density is very diﬃcult observationally because the flat-spectrum free-free emission is usually weaker than the steep-spectrum synchrotron emission below ν ∼30 GHz (see Fig. 1.5).
The specific emissivity, in c.g.s. units, at a certain temperature T (in K) for an ionized plasma of electrons with Maxwellian velocity distribution and numerical density ne (in cm−3), and a density ni (in cm−3) of ions with atomic number Z, is given by: Jbr ≃ 6.8 × 10−38T −1/2e−hν/kT nineZ2g¯f f (1.8).
in units of erg s−1 Hz−1 cm−3, and where g¯f f is the average Gaunt factor. The g¯f f value has been determined for a great number of diﬀerent situations, and for typical radio frequencies g¯f f varies as T 0.15ν−0.1 (Spitzer, 1978).
Using the radiative transport equation, the brightness of an object emit-ting via bremsstrahlung is given by: 4πkbr Bbr = Jbr (1 − eτ ) (1.9).
The Virial Theorem for molecular clouds
The condition for a molecular cloud or a clump within it to be gravitationally bound can be inferred from the virial theorem, which can be written: 1 ¨ (2.1) 2I =2(T −T0)+EM +W.
where I is the moment of inertia, T is the total kinetic energy (including thermal), EM is the net magnetic energy, and W is the gravitational energy (see McKee et al., 1993, for more details). The kinetic energy term can been expressed as: T = ZVcl 2 Pth + 2 ρv2 dV = 2 P¯Vcl (2.2).
that includes both the thermal and non-thermal pressure inside the cloud. The surface term can be expressed as T0 = 3/2P0 Vcl , where P0 is about equal to the total thermal plus non-thermal pressure in the ambient medium (McKee & Zweibel, 1992). Finally, the gravitational term can be written as (Bertoldi & McKee, 1992): W = −3PGVcl (2.3)
where the gravitational pressure PG is the mean weight of the material in the cloud. With these results, the steady-state virial theorem becomes: EM EM P¯=P0 + PG 1− |W| (2.4).
In this form, the virial theorem has an immediate intuitive meaning: the mean pressure inside the cloud is the surface pressure plus the weight of the material inside the cloud, reduced by the magnetic field. In the absence of an external gravitational field, W energy of the cloud: 3 GE2 W = − a M 5 R.
Star formation in molecular clouds
The star formation is a process which owes its origin to the gravitational collapse of molecular cloud clumps into cores. Accordingly with the virial theorem (Eq. 2.1), if the force due to the gas pressure dominate over the force of gravity the cloud expand, while if the kinetic energy is too low, the cloud collapse. If a molecular clump gets cold and dense enough that its mass is greater than the Jeans mass1, it collapse under its own gravity in a free-fall time tf f = 3 1/2 5×107 ≃ , where G is the gravitational constant 4πGρ¯ [nH (cm−3)] and ρ¯ is the mean mass density. This collapse is nearly isothermal as a result of an eﬃcient cooling by molecular lines and dust grains, which re-radiate in the IR range the observed gravitational potential energy. Neglecting the magnetic field eﬀects, in order to support the weight of the cloud’s outer layers, the thermal pressure must increase toward the center and, since T is constant, this translates into a rising density toward the cloud center. Therefore the inner part of the cloud begins to collapse well before the outer regions: this process is called inside-out collapse.
Following Shu et al. (1987), it is customary to describe the star forma-tion process in six phases, represented in Fig. 2.2. The first phase consists of the development of dense cores inside molecular clouds. The onset of the inside-out gravitational collapse and the formation of a protostar pro-vides the next phase. Subsequently, the formation of an accretion disk and a bipolar outflow occurs, as a consequence of the conservation of angular momentum. The infall of material is stropped and the surrounding dust envelope is swept away, leaving a visible star-disk system. As long as the star slowly contracts toward the main sequence, coagulating dust grains and forming planetesimals in the disk, its central temperature increases until hy-drogen ignites and halts further contraction: a new main-sequence star is born, possibly surrounded by a planetary system. For a main-sequence star, the nuclear energy becomes suﬃcient to support the star against collapse. Although from the observational point of view it is generally diﬃcult to es-tablish the evolutionary stage of an object, the theoretical point of view is clear: in the protostellar phase the luminosity is entirely provided by the accretion, in the pre-main-sequence phase by contraction, and, once in the Zero Age Main Sequence (ZAMS) phase, by the nuclear burning of hydrogen.
CO-H2 conversion factor
As said in the Chapter 1, a diﬃculty linked to the measurement of the X value is that it is determined by various factors, such as the metallicity, the temperature, the cosmic ray density, and the UV radiation field (see, for instance, Boselli et al., 2002).
Theory and observations suggest that the gas temperatures in systems with high SFR can be quite high, so the use of the standard conversion factor will lead to serious systematic overestimates of the amount of the molecular gas. This consideration is probably valid not only for the galaxies with unusually high global rates of star formation, such as the infrared-luminous galaxies discovered by IRAS, but also for the nuclear regions of many less infrared-luminous galaxies.
Also the dependence of the CO-H2 conversion factor on the metallicity is quite controversial. Some calculations show that CO emission from an ensemble of clouds in an external galaxy does not depends strongly on me-tallicity as long as the individual clouds are optically thick in CO (Dickman et al., 1986). However, models of individual low-metallicity clouds suggest that such clouds are optically thin in CO, which produce a strong depen-dence of the CO-H2 conversion factor on metallicity (see Maloney & Black, 1988). If the CO-H2 conversion factor is strongly dependent on the metal-licity, then molecular gas masses in irregular galaxies, in the outer regions of spiral galaxies, and in other low metallicity systems may be significantly underestimated. Galaxies with lower metallicity generally have a higher X factor: Wilson (1995), studying 5 Local Group galaxies, have found that the X conversion factor increases as the metallicity of the host galaxy de-creases, with the conversion factor increasing by a factor of 4.7 for a factor of 10 decrease in metallicity. The X value also seems to change with the morphological type of the galaxies. Nakai & Kuno (1995), studying the CO-H2 conversion factor in the M 51 galaxy and comparing their results with those present in litera-ture for other nearby galaxies, have found that galaxies early-type -earlier than Scd (M 31, M 33, M 51, NGC 891)- show values from comparable to smaller (≈ 1-3) than the mean Galactic value, while extremely late-type or irregular galaxies (IC 10, NGC 55, LMC, SMC), which moreover have a low abundance of heavy elements, tend to show larger values (> 4).
Another interesting aspect is the suspicion of a relation existing be-tween the X conversion factor and the ICO . Galaxies or observed positions with small ICO (ICO < 20-40 K km s−1) show a larger X. Nakai & Kuno (1995) showed that the galaxy M 51 is an example of this behaviour: ICO < 20 K km s−1 and the X derived value is a factor 2.6 lower than the mean Galactic value (see Fig. 2.4).
Intensity line ratios
The line ratio between diﬀerent molecular species or simply between two transitions of the same molecule is usually used to derive the physical con-ditions of the gas. It is well known that the filling factor of molecular clouds in a galaxy is often low. Thus, integrated intensities are generally not a good measure of the physical conditions of individual molecular clouds be-cause the signal is diluted by the large radio telescope beams, which also cover much empty space. Using the ratio of two integrated intensities helps cancel out the eﬀects of beam dilution, assuming that similar regions of space are responsible for the emission at both frequencies. The physical conditions recovered from the analysis of line ratios are the average con-ditions for all clouds within the beam. In other words, mapping a galaxy in many transitions helps to increase our understanding of the molecular gas dynamics, since diﬀerent transitions and molecules do not necessarily trace the same gas (e.g. Petitpas & Wilson, 1998; Kohno et al., 1999). As already said before, the CO molecule -for instance- doesn’t map regions at high density, and because stars are formed from dense cores of molecular clouds rather than their diﬀuse envelopes (e.g., Lada, 1992), it is essential to study the properties of dense molecular gas in order to understand star formation in galaxies and in starburst phenomena. Dense molecular mate-rial is investigated by observing the molecules referred to as “high-density tracers”, which require larger hydrogen density than that of CO for their collisional excitation, such as HCN, HCO+, CS, and so on (e.g., Henkel et al., 1998; Mauersberger et al., 2003; Nakanishi et al., 2005; Graci´-Carpio et al., 2006; Papadopoulos, 2007; Knudsen et al., 2007; Iono et al., 2007). For example, the CO(1-0) emission is excited even in low-density molecular gas (nH2 ∼500 cm−3), whereas HCN(1-0) emission traces very dense mole-cular clouds (nH2 > 104 cm−3) due to its larger dipole moment ( H CN = 3.0 debye, whereas CO = 0.10 debye).
Distribution and dynamics of the CO
Large-scale CO maps of nearby galaxies now available, extend our knowledge on global properties, radial gradients, and spiral structure of the molecular ISM. Millimetric interferometers reveal high velocity gradients in galaxy nuclei, and formation of embedded structures, like bars within bars.
Table of contents :
1 The Interstellar Medium
1.1 Components of the Interstellar Medium
1.2 Observation of different emissions in the ISM
1.2.1 X-ray and Extreme UV emissions
1.2.2 UV emission
1.2.3 Optical line emission
1.2.4 Infrared emission: radiation by dust
1.2.5 Radio line emission
1.3 Other emissions
1.3.1 γ-ray emission
1.3.2 Thermal radio continuum emission
1.3.3 Non-Thermal synchrotron emission
2 Molecular gas in galaxies
2.1 Molecular Clouds
2.2 Cloud structure
2.2.1 The Virial Theorem for molecular clouds
2.2.2 Structure analysis techniques
2.3 Star formation in molecular clouds
2.4 Molecular gas content
2.4.1 CO-H2 conversion factor
2.4.2 Intensity line ratios
2.5 Distribution and dynamics of the CO
2.5.1 Radial and vertical distribution
2.5.2 Dynamics: bars, shells and tidal dwarfs
2.6 CO as a function of type and environment
2.7 CO at high redshift
3 Relations between ISM tracers
3.1 Emissions and star formation
3.2 The sample
3.3.1 Cold gas and warm dust
3.3.2 X-ray component
3.4.1 Late-type galaxies
3.4.2 Early-type galaxies
3.5 Modelling early-type galaxies
3.5.1 The galactic radius and mass of stars and gas
3.5.2 The scale radii
3.5.3 The star formation history
4 Messier 81
4.1 The idea
4.3 Molecular gas emission
4.3.1 A and B receivers
4.3.2 HERA receiver
4.3.3 Line ratio
4.4 Clumping properties of the gas
4.4.1 Molecular Associations
4.4.2 GMAs masses
4.4.3 Virial equilibrium
4.4.4 The X factor for M 81
4.5 Comparison with previous works
4.6.1 The X problem
4.6.2 Heating of the gas
4.8 Future perspectives
5 NUGA survey: NGC 3147
5.1 NUGA project
5.1.1 Aims and results already obtained
5.2 NGC 3147 galaxy
5.3.1 IRAM single dish CO and HCN observations
5.3.2 IRAM interferometer CO observations
5.3.3 Near-infrared observations
5.3.4 Archival observations with Spitzer and GALEX
5.4 Single dish results
5.5 Interferometric results: Molecular gas properties
5.5.1 Morphology and mass of the CO rings
5.5.2 Kinematics of the CO rings
5.6 Comparison with Spitzer and GALEX
5.7 Computation of the torques
5.7.1 Near infrared images
5.7.2 Evaluation of the gravitational potential
5.7.3 Evaluation of gravity torques
6 Conclusions and Future Applications
6.1 Conclusions and obtained results
6.2 The future: ALMA
6.2.1 Synergy between ALMA and Herschel
7 Candidate’s list of papers