Editing Galaxy formation and evolution (section)

===Baryonic Physics===

To shape the population of galaxies, the hydrodynamical equations must be supplemented by a variety of astrophysical processes mainly governed by baryonic physics.

====Gas cooling====

Processes, such as collisional excitation, ionization, and inverse [[Compton scattering]], can cause the internal energy of the gas to be dissipated. In the simulation, cooling processes are realized by coupling cooling functions to energy equations. Besides the primordial cooling, at high temperature,<math>\ 10^5K< T < 10^7K\,</math>, heavy elements (metals) cooling dominates.<ref name="WiersmaSchayeSmith2009">{{cite journal | last1 = Wiersma | first1 = Robert P. C. | last2 = Schaye | first2 = Joop | last3 = Smith | first3 = Britton D. | title = The effect of photoionization on the cooling rates of enriched, astrophysical plasmas | journal = Monthly Notices of the Royal Astronomical Society | date = 11 February 2009 | volume = 393 | issue = 1 | pages = 99–107 | issn = 0035-8711 | eissn = 1365-2966 | doi = 10.1111/j.1365-2966.2008.14191.x | doi-access = free | pmid = | url = | arxiv = 0807.3748 | bibcode = 2009MNRAS.393...99W | s2cid = 118405953 }}</ref> When <math>\  T < 10^4K\,</math>, the fine structure and molecular cooling also need to be considered to simulate the cold phase of the [[interstellar medium]].

====Interstellar medium====

Complex multi-phase structure, including relativistic particles and magnetic field, makes simulation of interstellar medium difficult. In particular, modeling the cold phase of the interstellar medium poses technical difficulties due to the short timescales associated with the dense gas. In the early simulations, the dense gas phase is frequently not modeled directly but rather characterized by an effective polytropic equation of state.<ref name="SpringelHernquist2003">{{cite journal | last1 = Springel | first1 = V. | last2 = Hernquist | first2 = L. | title = Cosmological smoothed particle hydrodynamics simulations: a hybrid multiphase model for star formation | journal = Monthly Notices of the Royal Astronomical Society | date = 21 February 2003 | volume = 339 | issue = 2 | pages = 289–311 | issn = 0035-8711 | eissn = 1365-2966 | doi = 10.1046/j.1365-8711.2003.06206.x | pmid = | url = | doi-access = free | arxiv = astro-ph/0206393 | bibcode = 2003MNRAS.339..289S }}</ref> More recent simulations use a [[multimodal distribution]]<ref name="HopkinsQuataertMurray2012">{{cite journal | last1 = Hopkins | first1 = Philip F. | last2 = Quataert | first2 = Eliot | last3 = Murray | first3 = Norman | title = The structure of the interstellar medium of star-forming galaxies | journal = Monthly Notices of the Royal Astronomical Society | date = 16 March 2012 | volume = 421 | issue = 4 | pages = 3488–3521 | issn = 0035-8711 | doi = 10.1111/j.1365-2966.2012.20578.x | doi-access = free | pmid = | url = | arxiv = 1110.4636 | bibcode = 2012MNRAS.421.3488H | s2cid = 119199512 }}</ref><ref name="AgertzKravtsovLeitner2013">{{cite journal | last1 = Agertz | first1 = Oscar | last2 = Kravtsov | first2 = Andrey V. | last3 = Leitner | first3 = Samuel N. | last4 = Gnedin | first4 = Nickolay Y. | title = Toward a Complete Accounting of Energy and Momentum from Stellar Feedback in Galaxy Formation Simulations | journal = The Astrophysical Journal | date = 21 May 2013 | volume = 770 | issue = 1 | page = 25 | issn = 0004-637X | eissn = 1538-4357 | doi = 10.1088/0004-637X/770/1/25 | pmid = | url = | arxiv = 1210.4957 | bibcode = 2013ApJ...770...25A | s2cid = 118587852 }}</ref> to describe 
the gas density and temperature distributions, which directly model the multi-phase structure. However, more detailed physics processes needed to be considered in future simulations, since the structure of the interstellar medium directly affects [[star formation]].

====Star formation====

As cold and dense gas accumulates, it undergoes gravitational collapse and eventually forms stars. To simulate this process, a portion of the gas is transformed into collisionless star particles, which represent coeval, single-metallicity stellar populations and are described by an initial underlying mass function. Observations suggest that star formation efficiency in molecular gas is almost universal, with around 1% of the gas being converted into stars per free fall time.<ref name="BigielLeroyWalter2011">{{cite journal | last1 = Bigiel | first1 = F. | last2 = Leroy | first2 = A. K. | last3 = Walter | first3 = F. | last4 = Brinks | first4 = E. | last5 = de Blok | first5 = W. J. G. | last6 = Kramer | first6 = C. | last7 = Rix | first7 = H. W. | last8 = Schruba | first8 = A. | last9 = Schuster | first9 = K.-F. | last10 = Usero | first10 = A. | last11 = Wiesemeyer | first11 = H. W. | title = A Constant Molecular Gas Depletion Time in Nearby Disk Galaxies | journal = The Astrophysical Journal | date = 3 March 2011 | volume = 730 | issue = 2 | page = L13 | issn = 2041-8205 | eissn = 2041-8213 | doi = 10.1088/2041-8205/730/2/L13 | pmid = | url = | arxiv = 1102.1720 | bibcode = 2011ApJ...730L..13B | s2cid = 18832882 }}</ref> In simulations, the gas is typically converted into star particles using a probabilistic sampling scheme based on the calculated star formation rate. Some simulations seek an alternative to the probabilistic sampling scheme and aim to better capture the clustered nature of star formation by treating star clusters as the fundamental unit of star formation. This approach permits the growth of star particles by accreting material from the surrounding medium.<ref name="LiGnedinGnedin2017">{{cite journal | last1 = Li | first1 = Hui | last2 = Gnedin | first2 = Oleg Y. | last3 = Gnedin | first3 = Nickolay Y. | last4 = Meng | first4 = Xi | last5 = Semenov | first5 = Vadim A. | last6 = Kravtsov | first6 = Andrey V. | title = Star Cluster Formation in Cosmological Simulations. I. Properties of Young Clusters | journal = The Astrophysical Journal | date = 3 January 2017 | volume = 834 | issue = 1 | page = 69 | eissn = 1538-4357 | doi = 10.3847/1538-4357/834/1/69 | pmid = | url = | arxiv = 1608.03244 | doi-access = free | bibcode = 2017ApJ...834...69L }}</ref> In addition to this, modern models of galaxy formation track the evolution of these stars and the mass they return to the gas component, leading to an enrichment of the gas with metals.<ref name="VogelsbergerGenelSijacki2013">{{cite journal | last1 = Vogelsberger | first1 = Mark | last2 = Genel | first2 = Shy | last3 = Sijacki | first3 = Debora|author3-link= Debora Šijački | last4 = Torrey | first4 = Paul | last5 = Springel | first5 = Volker | last6 = Hernquist | first6 = Lars | title = A model for cosmological simulations of galaxy formation physics | journal = Monthly Notices of the Royal Astronomical Society | date = 23 October 2013 | volume = 436 | issue = 4 | pages = 3031–3067 | issn = 0035-8711 | eissn = 1365-2966 | doi = 10.1093/mnras/stt1789 | pmid = | url = | doi-access = free | arxiv = 1305.2913 }}</ref>

====Stellar feedback====

Stars have an influence on their surrounding gas by injecting energy and momentum. This creates a feedback loop that regulates the process of star formation. To effectively control star formation, stellar feedback must generate galactic-scale outflows that expel gas from galaxies. Various methods are utilized to couple energy and momentum, particularly through supernova explosions, to the surrounding gas. These methods differ in how the energy is deposited, either thermally or kinetically. However, excessive radiative gas cooling must be avoided in the former case. Cooling is expected in dense and cold gas, but it cannot be reliably modeled in cosmological simulations due to low resolution. This leads to artificial and excessive cooling of the gas, causing the supernova feedback energy to be lost via radiation and significantly reducing its effectiveness.  In the latter case, kinetic energy cannot be radiated away until it thermalizes. However, using hydrodynamically decoupled wind particles to inject momentum non-locally into the gas surrounding active star-forming regions may still be necessary to achieve large-scale galactic outflows.<ref name="PillepichSpringelNelson2017">{{cite journal | last1 = Pillepich | first1 = Annalisa | last2 = Springel | first2 = Volker | last3 = Nelson | first3 = Dylan | last4 = Genel | first4 = Shy | last5 = Naiman | first5 = Jill | last6 = Pakmor | first6 = Rüdiger | last7 = Hernquist | first7 = Lars | last8 = Torrey | first8 = Paul | last9 = Vogelsberger | first9 = Mark | last10 = Weinberger | first10 = Rainer | last11 = Marinacci | first11 = Federico | title = Simulating galaxy formation with the IllustrisTNG model | journal = Monthly Notices of the Royal Astronomical Society | date = 12 October 2017 | volume = 473 | issue = 3 | pages = 4077–4106 | issn = 0035-8711 | eissn = 1365-2966 | doi = 10.1093/mnras/stx2656 | doi-access = free | pmid = | url = | arxiv = 1703.02970 }}</ref> Recent models explicitly model stellar feedback.<ref name="MuratovKerešFaucher-Giguère2015">{{cite journal | last1 = Muratov | first1 = Alexander L. | last2 = Kereš | first2 = Dušan | last3 = Faucher-Giguère | first3 = Claude-André | last4 = Hopkins | first4 = Philip F. | last5 = Quataert | first5 = Eliot | last6 = Murray | first6 = Norman | title = Gusty, gaseous flows of FIRE: galactic winds in cosmological simulations with explicit stellar feedback | journal = Monthly Notices of the Royal Astronomical Society | date = 13 October 2015 | volume = 454 | issue = 3 | pages = 2691–2713 | issn = 0035-8711 | eissn = 1365-2966 | doi = 10.1093/mnras/stv2126 | doi-access = free | pmid = | url = | arxiv = 1501.03155 }}</ref> These models not only incorporate supernova feedback but also consider other feedback channels such as energy and momentum injection from stellar winds, photoionization, and radiation pressure resulting from radiation emitted by young, massive stars.<ref name="StinsonBrookMacciò2012">{{cite journal | last1 = Stinson | first1 = G. S. | last2 = Brook | first2 = C. | last3 = Macciò | first3 = A. V. | last4 = Wadsley | first4 = J. | last5 = Quinn | first5 = T. R. | last6 = Couchman | first6 = H. M. P. | title = Making Galaxies In a Cosmological Context: the need for early stellar feedback | journal = Monthly Notices of the Royal Astronomical Society | date = 23 October 2012 | volume = 428 | issue = 1 | pages = 129–140 | issn = 0035-8711 | eissn = 1365-2966 | doi = 10.1093/mnras/sts028 | doi-access = free | pmid = | url = | arxiv = 1208.0002 }}</ref> During the [[Cosmic Dawn]], galaxy formation occurred in short bursts of 5 to 30 Myr due to stellar feedbacks.<ref>{{Cite journal |last1=Furlanetto |first1=Steven R |last2=Mirocha |first2=Jordan |date=22 February 2022 |title=Bursty star formation during the Cosmic Dawn driven by delayed stellar feedback |url=https://academic.oup.com/mnras/article/511/3/3895/6522193 |journal=[[Monthly Notices of the Royal Astronomical Society]] |language=en |volume=511 |issue=3 |pages=3895–3909 |doi=10.1093/mnras/stac310 |issn=0035-8711 |access-date=23 December 2023|doi-access=free |arxiv=2109.04488 }}</ref>

====Supermassive black holes====

Simulation of supermassive black holes is also considered, numerically seeding them in dark matter haloes, due to their observation in many galaxies<ref name="MoranShahinyanSugarman2014">{{cite journal | last1 = Moran | first1 = Edward C. | last2 = Shahinyan | first2 = Karlen | last3 = Sugarman | first3 = Hannah R. | last4 = Vélez | first4 = Darik O. | last5 = Eracleous | first5 = Michael | title = Black Holes at the Centers of Nearby Dwarf Galaxies | journal = The Astronomical Journal | date = 13 November 2014 | volume = 148 | issue = 6 | page = 136 | eissn = 1538-3881 | doi = 10.1088/0004-6256/148/6/136 | pmid = | url = | arxiv = 1408.4451 | bibcode = 2014AJ....148..136M | s2cid = 118487176 }}</ref> and the impact of their mass on the mass density distribution. Their mass accretion rate is frequently modeled by the Bondi-Hoyle model.

====Active galactic nuclei ====

[[Active galactic nuclei]] (AGN) have an impact on the observational phenomena of supermassive black holes, and further have a regulation of black hole growth and star formation. In simulations, AGN feedback is usually classified into two modes, namely quasar and radio mode. Quasar mode feedback is linked to the radiatively efficient mode of black hole growth and is frequently incorporated through energy or momentum injection.<ref name="SpringelDi MatteoHernquist2005">{{cite journal | last1 = Springel | first1 = Volker | last2 = Di Matteo | first2 = Tiziana |author2-link=Tiziana Di Matteo (astrophysicist)| last3 = Hernquist | first3 = Lars | title = Modelling feedback from stars and black holes in galaxy mergers | journal = Monthly Notices of the Royal Astronomical Society | date = August 2005 | volume = 361 | issue = 3 | pages = 776–794 | issn = 0035-8711 | eissn = 1365-2966 | doi = 10.1111/j.1365-2966.2005.09238.x | doi-access = free | pmid = | s2cid = 14866854 | url = http://nrs.harvard.edu/urn-3:HUL.InstRepos:41381734| arxiv = astro-ph/0411108 | bibcode = 2005MNRAS.361..776S }}</ref> The regulation of star formation in massive galaxies is believed to be significantly influenced by radio mode feedback, which occurs due to the presence of highly collimated jets of relativistic particles. These jets are typically linked to X-ray bubbles that possess enough energy to counterbalance cooling losses.<ref name="SijackiSpringelDi Matteo2007">{{cite journal | last1 = Sijacki | first1 = Debora|author1-link= Debora Šijački | last2 = Springel | first2 = Volker | last3 = Di Matteo | first3 = Tiziana |author3-link=Tiziana Di Matteo (astrophysicist)| last4 = Hernquist | first4 = Lars | title = A unified model for AGN feedback in cosmological simulations of structure formation | journal = Monthly Notices of the Royal Astronomical Society | date = 20 August 2007 | volume = 380 | issue = 3 | pages = 877–900 | issn = 0035-8711 | doi = 10.1111/j.1365-2966.2007.12153.x | pmid = | url = | doi-access = free | arxiv = 0705.2238 | bibcode = 2007MNRAS.380..877S}}</ref>

====Magnetic fields====

The ideal [[magnetohydrodynamics]] approach is commonly utilized in cosmological simulations since it provides a good approximation for cosmological magnetic fields. The effect of magnetic fields on the dynamics of gas is generally negligible on large cosmological scales. Nevertheless, magnetic fields are a critical component of the interstellar medium since they provide pressure support against gravity<ref name="Ferrière2001">{{cite journal | last1 = Ferrière | first1 = Katia M. | title = The interstellar environment of our galaxy | journal = Reviews of Modern Physics | date = 5 December 2001 | volume = 73 | issue = 4 | pages = 1031–1066 | issn = 0034-6861 | eissn = 1539-0756 | doi = 10.1103/RevModPhys.73.1031 | pmid = | url = | arxiv = astro-ph/0106359 | bibcode = 2001RvMP...73.1031F | s2cid = 16232084 }}</ref> and affect the propagation of cosmic rays.<ref name="KoteraOlinto2011">{{cite journal | last1 = Kotera | first1 = Kumiko | last2 = Olinto | first2 = Angela V. | title = The Astrophysics of Ultrahigh-Energy Cosmic Rays | journal = Annual Review of Astronomy and Astrophysics | date = 22 September 2011 | volume = 49 | issue = 1 | pages = 119–153 | issn = 0066-4146 | eissn = 1545-4282 | doi = 10.1146/annurev-astro-081710-102620 | pmid = | url = | arxiv = 1101.4256 | bibcode = 2011ARA&A..49..119K | s2cid = 118661799 }}</ref>

====Cosmic rays====

Cosmic rays play a significant role in the interstellar medium by contributing to its pressure,<ref name="Cox2005">{{cite journal | last1 = Cox | first1 = Donald P. | title = The Three-Phase Interstellar Medium Revisited | journal = Annual Review of Astronomy and Astrophysics | date = 1 September 2005 | volume = 43 | issue = 1 | pages = 337–385 | issn = 0066-4146 | eissn = 1545-4282 | doi = 10.1146/annurev.astro.43.072103.150615 | pmid = | bibcode = 2005ARA&A..43..337C | url = }}</ref> serving as a crucial heating channel,<ref name="WolfireHollenbachMcKee1995">{{cite journal | last1 = Wolfire | first1 = M. G. | last2 = Hollenbach | first2 = D. | last3 = McKee | first3 = C. F. | last4 = Tielens | first4 = A. G. G. M. | last5 = Bakes | first5 = E. L. O. | title = The neutral atomic phases of the interstellar medium | journal = The Astrophysical Journal | date = April 1995 | volume = 443 | page = 152 | issn = 0004-637X | eissn = 1538-4357 | doi = 10.1086/175510 | pmid = | bibcode = 1995ApJ...443..152W | url = }}</ref> and potentially driving galactic gas outflows.<ref name="BoothAgertzKravtsov2013">{{cite journal | last1 = Booth | first1 = C. M. | last2 = Agertz | first2 = Oscar | last3 = Kravtsov | first3 = Andrey V. | last4 = Gnedin | first4 = Nickolay Y. | title = Simulations of Disk Galaxies with Cosmic Ray Driven Galactic Winds | journal = The Astrophysical Journal | date = 18 October 2013 | volume = 777 | issue = 1 | page = L16 | issn = 2041-8205 | eissn = 2041-8213 | doi = 10.1088/2041-8205/777/1/L16 | pmid = | url = | arxiv = 1308.4974 | bibcode = 2013ApJ...777L..16B | s2cid = 59518603 }}</ref> The propagation of cosmic rays is highly affected by magnetic fields. So in the simulation, equations describing the cosmic ray energy and flux are coupled to [[magnetohydrodynamics]] equations.<ref name="ThomasPfrommer2019">{{cite journal | last1 = Thomas | first1 = T | last2 = Pfrommer | first2 = C | title = Cosmic-ray hydrodynamics: Alfvén-wave regulated transport of cosmic rays | journal = Monthly Notices of the Royal Astronomical Society | date = 25 January 2019 | volume = 485 | issue = 3 | pages = 2977–3008 | issn = 0035-8711 | eissn = 1365-2966 | doi = 10.1093/mnras/stz263 | doi-access = free | pmid = | url = | arxiv = 1805.11092 }}</ref>

====Radiation Hydrodynamics====

Radiation hydrodynamics simulations are computational methods used to study the interaction of radiation with matter. In astrophysical contexts, radiation hydrodynamics is used to study the epoch of reionization when the Universe had high redshift. There are several numerical methods used for radiation hydrodynamics simulations, including ray-tracing, [[Monte Carlo]], and moment-based methods. Ray-tracing  involves tracing the paths of individual photons through the simulation and computing their interactions with matter at each step. This method is computationally expensive but can produce very accurate results.