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The cosmological evolution of galaxies is a fascinating subject which has experienced explosive growth lately due to the incredible rate of new observational data and the development of new methods and codes in this observationally and computationally intensive research field. In this review, we have discussed various aspects of galaxy evolution. The original paradigm of this evolution is being replaced slowly but persistently by a modified view - a process which is driven by a long list of recent discoveries.

Probably, nowhere is this more obvious than in our understanding of the main factor(s) behind galaxy growth. The cold accretion scenario has successfully challenged the merger-only picture. The new approach raised a number of challenging questions. How important is the accretion shock? What fraction of the gas is actually processed by the shock? How does the accretion flow join the growing disk? Via shocks or smoothly assembling in the outer disk? These outstanding questions will be answered shortly via high-resolution numerical simulations. On the other hand, observations must answer questions about the redshift evolution of cold accretion flows. Furthermore, the issue of the actual detection of flows in cosmological filaments is an open one and will help to resolve at least partly the problem of the missing baryons. And of course the increasing number of detected galaxies at redshifts corresponding to the re-ionisation epoch must answer the fundamental questions about the morphological types of the first galaxies, their mode of growth and the other scaling relations established at low redshifts, e.g., the morphology-density relation.

The subject of stellar and AGN feedback on galaxy evolution is truly a Pandora's box. The inclusion of feedback has clearly solved the overcooling problem. However, the current subgrid physics used to quantify SN feedback, and feedback from OB stellar winds, AGN and galactic winds has too many parameters to be fine-tuned. For AGN feedback, mechanisms more sophisticated than considering the AGN as a giant O star are needed. Does it quench the star formation and clean the galaxies of their ISM, or is this feedback much more anisotropic, producing much less disturbance for the rest of the host galaxy. At high redshifts, z ~ 6-10, does the QSO feedback induce or dampen galaxy formation?

How do galactic winds form? They are clearly detected in observations, but the underlying theory requires much more work. In fact, almost any model of the wind from any astrophysical object experiences difficulties in describing the physics of wind initiation.

There are too many bulgeless disks in the Universe. This comes as a surprise and as another challenge. One approach attempted successfully has related this phenomenon to the feedback problem. Indeed, back-of-the-envelope estimates show convincingly that the SNe can expel the ISM and therefore eliminate the bulge buildup in smaller galaxies. Additional work is required to understand the efficiency of this process. Could it be too efficient? Massive disks provide another challenge. In a number of cases cold gas has been detected in the central regions, but no indication of intensive star formation, at least not in the mode of massive clusters. How can one suppress the star formation while leaving the gas intact? One possibility lies in pumping the energy into turbulent motions in the gas. Observations will resolve this issue soon.

Where do stars form? This simple question has an interesting twist. Do stars form as a result of Jeans instability in the molecular gas? Or does the molecular gas itself form as a result of the Jeans instability in the neutral gas? This issue has immediate consequences for numerical simulations of galaxy evolution. Because we still cannot resolve the star-forming regions, what should be used as a density threshold for star formation?

The growing list of high-redshift galaxies presently extending to z ~ 10.4, and protoclusters extending to z ~ 8, will soon increase dramatically. We have already mentioned the importance of measuring the scaling relations at these redshifts, but even more basic parameters, like the galaxy LF, or the rate of star formation, must be measured as well. Is the evolution of the specific SFR so flat even at redshifts beyond 7?

Different challenges are expected to resolve the kinematics of cold gas in galactic centres. A high-resolution survey of gas morphology will probably be produced by ALMA. What fraction of this gas is in a relaxed orbital motion, and what fraction is in a `barred' state? What is the relation between the AGN host galaxy and the central SMBH? We know that Seyfert activity is probably not triggered by galaxy interactions or mergers. We also know that the brightest of AGN, the QSOs, can be fuelled by this process. Overall, a number of factors can fuel the accretion onto the SMBH, but it would be interesting to understand the statistics of local versus non-local sources of fuelling. If both are involved, where is the boundary between them?

The bulge buildup is partly a dissipative process, but it appears now that stellar-dynamical instabilities play an important role as well. The relation between the origin of peanut/boxy bulges and vertical buckling in stellar bars has been now established. But this instability is recurrent, and what determines the timescale of the onset of the next stage in this instability is not yet clear.

The fate of nuclear bars is really `lost' in the darkness. While purely stellar nested bars can live indefinitely, the gas can still make a difference, especially in gas-rich nuclear bars. What is their relation to the bulge build-up? And to AGN fuelling?

Finally, an outstanding issue is when and where the SMBHs form and how massive their seeds are. Are they formed at very high redshifts from Pop III remnants, or at lower redshifts in a direct collapse inside DM minihaloes of ~ 108 Modot? The separate problems in galaxy evolution we have discussed above join together to complicate this process. Does the accretion flow fragment or does the induced turbulence dampen the Jeans instability and does the seed SMBH form more massive? Is the angular momentum problem resolved in this case by the bars-in-bars mechanism? Observers can hope to detect the quasistars - the last stage before the horizon is formed. Or does the energy escape along the preferred channel without interacting and stopping the inflow? In this case, the evolution may bypass the quasistar stage. The detection of intermediate-mass black holes can help here.

I would like to complete these lecture notes with my favourite question asked by Stanislaw Lem in his novel Ananke: `Where is that order and whence came this mocking illusion?'


I am grateful to the organisers of the XXIII Winter School, Johan Knapen and Jesús Falcón-Barroso, for their financial support and patience, and for bringing together this highly enjoyable meeting. I thank Mitch Begelman, Jun-Hwan Choi and Michele Trenti for insightful discussions on some of the topics presented here. As this is not a full-fledged review, but encompasses a broad range of topics on galaxy evolution, I apologise if some references have been left out. My research is supported by NSF, NASA and STScI grants.

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