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Astron. Astrophys. 342, 655-664 (1999)

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4. Evolution

In this section we demonstrate that the low density as found in LSB galaxies, by itself is not sufficient to reproduce the low observed SFRs of LSB galaxies. Low metallicity gas is required to explain the properties of LSB galaxies.

To show this we construct two model galaxies using the structural parameters of F563-1. Model H represents an LSB galaxy with a solar metallicity gas. Although we use the structural parameters relevant for F563-1, the model is in effect a model HSB galaxy, which is "stretched out" to give the low (surface) densities found in LSB galaxies. This model therefore tests the low-density hypothesis.

The other model, L, has the same structural parameters as H, but in addition we lowered the cooling efficiency of the gas below [FORMULA] K by a factor of seven. Cooling below [FORMULA] K is dominated by metals, so lowering the efficiency is equivalent to lowering the metallicity by an equal amount. Model L thus most closely approximates what is currently known observationally about LSB galaxies. In summary we adopt the cooling function of a solar abundance gas in model H. This cooling function is later changed in model L to simulate the effects of low metallicity.

We assume that the physics regulating the star formation is the same for LSB and HSB galaxies, and therefore use the star formation recipe described in Sect. 2 and applied to HSB galaxies in Gerritsen & Icke (1997, 1998). After initialization we let the two model galaxies evolve for 2.3 Gyr. The models rapidly settled into equilibrium, any longer time interval would have produced identical results.

In this section we first discuss the evolution of the stellar disk. The stellar disk evolves rather independently from the gas disk and star formation. Hence we effectively explore the consequences of the disk/halo decomposition, notably on the stability and thickness of the stellar disk. Second, we discuss the evolution of the SFR with time for both simulations. For a physical interpretation of the difference in SFRs we present phase diagrams of the ISM in both simulations.

4.1. Stellar disk

Fig. 1 shows the stability parameter Q for the stellar disk at [FORMULA] Gyr (that is 2 Gyr after the start of the simulation which started at [FORMULA]), where Q is defined as


with [FORMULA] the epicycle frequency (Toomre 1964). [FORMULA] denotes a (local) instability, while [FORMULA] means stability. For both simulations [FORMULA] in the center and rises to [FORMULA] in the outer parts of the disk. There is no evolution in the stability. Once the system has settled after the start of the simulation, the radial behavior of Q as shown is reached. The value of course depends on the input parameters, notably the stellar mass, but it is clear that the stellar disks of LSBs are more stable than the stellar disks of HSBs, where Q is of order 2 (Bottema 1993, van der Hulst et al. 1993).

In both simulations the scale height of the stellar disk decreases by approximately a factor of 1.3. The initial scale height corresponded to the scale height of an Sc galaxy (van der Kruit & Searle 1982). The final axial ratio for the galaxy model is about 15. As particle scattering during the simulation tends to increase the thickness of the disk, we conclude that the stellar disks of LSB galaxies are thinner than those of HSB galaxies. We will return to this in more detail in Sect. 5.1.

4.2. Star formation and ISM

Fig. 3 shows the SFR versus time. In model H the SFR settles after a short adjustment at a value of [FORMULA]/yr and declines slowly with time. The SFR in model L settles at [FORMULA]/yr.

[FIGURE] Fig. 3. The evolution of the SFR versus time. The lower line shows the SFR from simulation L, the upper line represents simulation H. Data are averaged over 9 Myr

For both simulations the SFR varies on time scales of a few tens of Myr and the amplitude of these variations can exceed [FORMULA]/yr. The rapid variability in the SFR is due to the discrete nature of star formation in our simulation. New star particles have a mass of approximately [FORMULA] and thus represent (large) stellar clusters. In this way our simulations incorporate the idea that most stars in real galaxies form in stellar clusters. For a small number of star forming regions (as in LSB galaxies) this will in real life also lead to a rapidly fluctuating, but on average low SFR.

In simulation L the strength of the star formation peak is large compared to the average SFR. These fluctuations in star formation activity will actually dominate the color of the galaxy, with large fluctuations giving rise to blue colors. The same star formation fluctuations will also be present in HSB galaxies, but due to the higher SFR the large number of fluctuations will give the impression of a high, relatively constant SFR.

We thus find that it is not so much the absolute value of the average SFR which determines the colors, but the contrast of any SF fluctuation with respect to the average SFR. For the LSB galaxies the large contrast leads to blue colors.

In order to understand the behavior of the star formation activity in the simulations we constructed phase diagrams of the ISM. Fig. 4 shows the temperature versus density for all gas particles in both simulations. The top panel shows simulation L while the bottom panel shows the phase diagram for simulation H. Most particles have a temperature of [FORMULA] K. In simulation H a large fraction of the particles has a temperature of about 100 K. This simulation shows a dominant two-phase structure, and resembles the ISM in simulations of HSB galaxies (Gerritsen & Icke 1998). Quantitatively, the cold gas fraction ([FORMULA] K) makes up 37% of the total gas mass in simulation H and only 4% in simulation L. This reflects the cooling properties of the gas: in simulation L seven times less heat input is required to keep the gas at [FORMULA] K as in simulation H.

[FIGURE] Fig. 4. Phase diagrams (temperature versus number density) for the simulations. Top panel shows simulation L, bottom panel shows simulation H; each dot represents an SPH particle. The individual particles at the top of each diagram are hot SN particles. Simulation H clearly shows a two-phase structure, while in simulation L almost all gas is in the warm ([FORMULA] K) phase (85%)

Consequently simulation L contains virtually only a warm, one-phase ISM. The simulated absence of metals prevents the ISM from cooling efficiently. As molecular gas is only formed in/from the cold component of the ISM, the 4% mentioned above is actually an upper limit to the amount of molecular gas that could form in such a galaxy. The amount of cold molecular gas in sites for star formation would thus be negligible. From these models we expect the disks of LSB galaxies to contain only negligible amounts of molecular gas. This is consistent with observations by Schombert et al. (1990) and de Blok & van der Hulst (1998b), who find upper limits of less than 10%.

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© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999