コロキウム要旨 / Colloquium ABSTRACTS

Dr. Shotaro YAMASAKI (Hebrew University of Jerusalem)

Deciphering Multiwavelength Transient Activity of Strongly Magnetized Neutron Stars: From Magnetar Flares to Galactic Fast Radio Bursts

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Strongly magnetized neutron stars show energetic transient activity in both X-ray and radio bands, such as magnetar flares, faint pulsed radio emission, and bright short-duration radio bursts in reminiscence of cosmological fast radio bursts (FRBs). Magnetar flares are believed to be related to an electron/positron pair plasma produced by a sudden dissipation of magnetic energy in the stellar vicinity. Such a plasma could be either trapped to the stellar surface by strong magnetic fields or launched as a relativistic outflow, which would play important roles in producing/suppressing the simultaneous emission in radio bands. In this talk, I will first present our recent work on (1) how magnetar flare spectra form inside the magnetosphere. Then, I will discuss (2) the potential link between magnetar flares and pulsed radio emission and (3) the plasma properties that are compatible with X-ray and radio bursts co-detected from the Galactic FRB source, SGR 1935+2154.


Millimeter and submillimeter observations of nearby merging galaxies

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Hello, my name is Tomonari Michiyama, a new pos-doc at OUTAP from April 2021. As Ph.D. research, I have conducted sub-mm observes for nearby merging galaxies. In Michiyama et al., (2016), we show the enhancement of star formation efficiency in merging galaxies based on ASTE CO(3-2) survey for nearby galaxies, In Michiyama et al., (2018), we found dense gas outflows from one merging galaxies NGC 3256 using ALMA. In Michiyama et al., (2020a), we investigate the star formation activity in the same galaxy NGC 3256 using hydrogen recombination line; Ha and Hb (using MUSE/VLT) and H40a using ALMA. Now I am interested in ALMA [CI] observations for nearby merging galaxies. We discovered a merging galaxy whose [CI] is faint and CO is bright (NGC 6052). Such a faint [CI] may indicate a very young starburst triggered by a merger process (Michiyama et al., 2020b, Michiyama et al. 2021 submitted). If you are interested in ALMA observations, please let me know and start collaborations!

Prof Emer. Kazunari SHIBATA (Kyoto University)

From Jets to Superflares : Extraordinary Activity of Magnetized Plasmas in the Universe

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The development of astronomical observations of various objects in 20th century has revealed that the universe is full of explosions (flares or bursts) and plasma outflows such as high-speed jets. Why is our universe filled with such extraordinary activity?

When I started astrophysical research in 1977, I was fascinated with a puzzle why the nuclei of distant galaxies produce relativistic jets, collimated supersonic outflows. Soon after I learned observations of astrophysical jets, I learned solar observations, which show the importance of magnetic field in the production of flares and jets, though detailed physics is still not understood well at that time. I hypothesized that the jets may be accelerated by magnetic force both on the Sun and galaxies: in the case of the galaxies, magnetic field may be twisted by the rotation of accretion disk plasma, whereas on the Sun magnetic field can be twisted in the solar convection zone. During the untwisting process of a twisted magnetic flux tube, the jet may be accelerated. Then I started magnetohydrodynamic (MHD) numerical simulations of both solar and astrophysical jets. Fortunately, I succeeded in reproducing astrophysical jets from magnetized accretion disks using time dependent MHD simulations for the first time (1985, 1986). I was also lucky since I became a member of space solar observation missions Yohkoh (1991-2000) and Hinode (2007-present), and discovered X-ray jets in the corona (1992), as well as chromospheric anemone jets (2007). Both phenomena were successfully explained by the magnetic reconnection model. From observations of flares and jets on the Sun, I realized the importance of plasmoid ejections in magnetic reconnection (1995), and proposed the unified model of flares and jets on the basis of the plasmoid-induced reconnection and fractal reconnection (2001).

More recently, as an extension of solar flare studies, I was fortunate enough to discover superflares on solar type stars with young colleague (2012), which may be important for the existence or survivability of human beings and life on the Earth and exoplanets.

In conclusion, through these studies, I learned the reason why our universe is filled with extraordinary activity is that magnetized plasmas are so active and dynamic.

Mr. Kengo SHIBATA, Kazuki TOMARU and Kaoru YANAGISAWA (Osaka University)

B4 presentation practice

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Prof Emer. Masanori IYE (NAOJ)

Origin and distribution of spin vortex field in the Universe

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Let me start with a brief historical review on the controversy and the theory of spiral structure of galaxies, whether the spirals are trailing or leading. We made a modern observational reassessment on this issue and confirmed that all the spirals are trailing as people usually assume nowadays. This affirmation enables us to judge the sign of the line-of-sight component of the spin vector of spiral galaxies just by identifying whether the spiral winding pattern in the sky is S-wise or Z-wise. We use this robust one-bit information to study the distribution of spin vectors in the Universe.

Regarding the origin of galaxy spins, there were classic ideas e.g., "Primordial Whirl" or "Pan-cake Shock" advocated in the last century. "Tidal Torque Theory" appears to be the standard theoretical paradigm to explain non spherical dark halo acquiring the angular momentum from the surrounding gravitational field that results in the spin up of galaxies as the matter cloud shrinks. However, quantitative detailed studies on this subject by analyzing the numerical simulation of structure formation in LCDM universe appear just beginning and no serious observational verification has yet been made.

The authors group is compiling a large catalog of spiral galaxies with their spiral winding direction, S-wise or Z-wise, as determined from SDSS, PanStarrs, DES, ESO-DSS, and HSC imaging surveys by visual inspection and by deep learning software. We developed a formalism to quantify the statistical properties, e.q. the anisotropic dipole amplitude in the distribution of S/Z spirals and evaluate its statistical significance by means of 3D random flight simulations. We report the result of applying this method to study the distribution of SDSS galaxies in the local Universe where Shamir(2017,2020) claimed to find significant anisotropy.

Mr. Abednego WILIARDY (Osaka University)

AGN Feedback Model in Galaxy Simulation

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Modelling AGN feedback has been a challenge in cosmological simulation. As it has been widely accepted, almost every galaxy hosts a supermassive black hole (SMBH) in their nuclei and they are called active galactic nuclei (AGN) when observed as a luminous source. Considering the feedback released by an AGN in the form of radiation, wind and jet is important to explain galaxy mass function and star formation quenching. Simulating all of these processes is essential to get better understanding in galaxy formation and evolution. However, in large-scale galaxy simulations, the resolution is insufficient to resolve the detailed sub-parsec scale structure of the AGN and subgrid models are required to accommodate it in simulations. Following previous work, two modes of AGN feedback are implemented according to the SMBH accretion rate, i.e. quasar mode and radio mode. Quasar mode takes place when the accretion rate is high by using geodesic dome bins to assign energy isotropically, but considering the obscuration by a dusty torus. On the other hand, radio mode takes place by introducing ghost particle treatment to distribute thermal heat from collimated jet, producing outflow and low density lobes emanating from galaxy center, following the features of observed jet.

Mr. Nicolas LEDOS (Osaka University)

Cold stream accretion: development of magnetohydrodynamical simulation code with heat conduction and preliminary study of stream stability

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Cold gas streams (T ~ 104K) are crucial to explain the star formation in high-redshift galaxies, and they are strongly supported by cosmological hydrodynamic simulations. However, the dynamics and the lifetime of such streams is subject to Kelvin Helmholtz instabilities (KHI). Recent studies aim to theorize the survival conditions of cold stream, but the interplay of the different physics is still not fully understood. In this talk, I will mainly present two topics: my preliminary work and research plan on the study of cold stream undergoing KHI, as well as, the development of a high spatial order heat conduction solver for the study of cold accretion.

Dr. Nikole M. NIELSEN (Swinburne University of Technology)

The Circumgalactic Medium at Cosmic Noon with KCWI

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The star formation history of the universe reveals that galaxies most actively build their stellar mass at cosmic noon (z=1-3), roughly 10 billion years ago, with a decrease toward present-day. The resulting metal-enriched material ejected from these galaxies due to supernovae and stellar feedback is deposited into the circumgalactic medium (CGM), which is a massive reservoir of diffuse, multiphase gas out to radii of ~200 kpc. The CGM is the interface between the intergalactic medium and the galaxy, through which accreting filaments of near-pristine gas must pass to contribute new star formation material to the galaxy and outflowing gas is later recycled. Simulating these baryon cycle flows is crucial for accurately modeling galaxy evolution. While the CGM is well-studied at z<1, little attention has been paid to the reservoir when star formation is most active due to the difficulty in identifying the host galaxies. The installation of the Keck Cosmic Web Imager (KCWI), an integral field spectrograph, on Keck II has opened a new window to quickly identify galaxies via their Lyman alpha emission at this redshift. I will introduce a new survey to build a catalog of absorber-galaxy pairs at z=2-3 with KCWI. With the combination of HST images, high-resolution quasar spectra, and the cutting-edge KCWI data, this survey aims to examine CGM kinematics and metallicities and relate them to the host galaxy star formation rates and orientations to reveal the baryon cycle at cosmic noon.

Prof. Shin'ichiro ANDO (University of Amsterdam)

Particle dark matter searches and small-scale distribution

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What is dark matter? This is one of the most fundamental questions in cosmology, particle physics, and astrophysics. It was long hypothesised to be made of weakly interacting massive particles (WIMPs), which can be probed with colliders, direct and indirect experiments. The dark matter distribution at sub-galactic scales makes important role in predicting and interpreting the signal from some of these experiments. Here I introduce an attempt to build semi-analytic models of dark matter distribution, especially dark matter subhalos, discuss why we need such models, and show that models are well in agreement with the results of N-body simulations. I then show implications of this model, ranging from enhancement of the signals from dark matter annihilation, and interpretations of WIMP constraints using dwarf spheroidal galaxies. I will also mention possible extension of the models to accommodate different kinds of dark matter particles such as warm and self-interacting dark matter.

Mr. Keita FUKUSHIMA (Osaka University)

Star Formation and Chemical Enrichment in Protoclusters

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The galaxy cluster precursor ProtoCluster(PC) is undergoing active galaxy formation. Active star formation in PC results in the formation of abundant metals and rapid chemical evolution. Theoretical studies of chemical evolution are important because they can be compared with observations to reveal the history of chemical evolution in the universe and put limits on the simulation's feedback models. In this colloquium, I will present the results of the study of the star formation history and chemical evolution of the PC using Gadget3-Osaka. I will also discuss my master's thesis plans and future prospects.

Mr. Yuri OKU (Osaka University)

Supernova feedback in galaxy formation

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Supernova feedback has been widely recognized as an essential process in galaxy formation. Supernova explosion heats up and blows out surrounding gas by depositing energy of typically 10^51 erg and plays an important role in the self-regulation of star formation in galaxies. In this talk, I will discuss the following three topics I have worked on for this one and half years;1) the statistical properties of galaxies, 2) the momentum input by clustered supernovae, and 3) development of supernova feedback model in galaxy formation simulation. I will also talk about my plan for a master thesis and future prospects.

Prof. Ji-hoon KIM (Seoul National University)

Solving the Mysteries of Galaxy and Supermassive Black Hole Formation in the Era of High-resolution Simulations and Machine Learning

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The community of numerical galaxy formation has benefited greatly from the ever-improving computing technology over the past decades. I will discuss the new possibilities in the upcoming era of high-resolution numerical galaxy formation and machine learning, and highlight efforts to overcome the accompanying challenges. As one example, I will describe a state-of-the-art cosmological simulation of a high-redshift quasar-host galaxy that includes sophisticated treatments of feedback from star-forming clumps and supermassive black holes (SMBHs). I will demonstrate that previously undiscussed types of interplay between galactic components may hold important clues about the growth of SMBHs. In another example,I will introduce a machine-assisted pipeline that estimates baryonic properties of a galaxy based purely on its dark matter (DM) properties in a large-scale DM-only simulation.

Prof. Tomoaki ISHIYAMA (Chiba University)

Supercomputer simulations of dark matter structure formation in the Universe

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We report the results of ultralarge cosmological N-body simulations of small and large scale structure formation in the Universe. First, we introduce the Uchuu suite of large high-resolution cosmological N-body simulations. The largest simulation, named Uchuu, consists of 2.1 trillion dark matter particles in a box of 2.0 Gpc/h. The highest resolution simulation, called Shin-Uchuu, consists of 262 billion particles in a box of 140 Mpc/h. Combining these simulations we can follow the evolution of dark matter haloes (and subhaloes) spanning from dwarf galaxies to massive galaxy cluster hosts. We present basic statistics, dark matter power spectra and halo mass function, to demonstrate the huge dynamic range and superb statistics of the Uchuu simulations. We also provide parameters of a mass-concentration model, which describes the evolution of halo concentrations, that reproduces our simulation data within 5% error for haloes with masses spanning nearly eight orders of magnitude at redshift 0<z<14. We make publicly available various N-body products, as part of Uchuu Data Release 1, on the Skies & Universes site. In this talk, we also introduce the ongoing project for the small scale structure formation: a new semi-analytic model of Pop III formation with high resolution cosmological N-body simulations.

Dr. Taiki KAWAMURO (Universidad Diego Portales)

Spatially-resolved Chandra and ALMA studies of molecular gas destruction due to AGN X-ray emission

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The active galactic nucleus (AGN) generally emits a large amount of X-rays, and the high-energy emission is expected to significantly alter the thermal and chemical properties of the surrounding interstellar medium (ISM). An interesting, theoretical prediction is the destruction of molecular gas. Given a positive correlation between the molecular gas and star-formation-rate surface densities, that suggests that the X-ray radiation has the potential to suppress star formation eventually. Also, the gas phase of the AGN outflow, capable of impacting the galaxy growth, may be altered as well, and therefore the understanding is related to the observation of the outflow and the discussion of its role.

In this colloquium, I will talk about our recent studies of nearby AGNs that focused on the AGN X-ray radiative impact. While we revealed the ISM subject to AGN X-ray radiation with Chandra, ALMA was used to constrain the ISM properties therein. Thanks to their sub-arcsec resolutions, the ISM was resolved at quite high resolutions down to ~10 pc. An interesting finding was faint molecular gas emission in regions likely subject to the AGN X-ray radiation. Motivated by this, we quantitatively discussed the possibility that the molecular gas was destroyed by the X-ray radiation. Based on ALMA data, we constrained molecular gas densities, and found that they were low enough to be interpreted by the X-ray destruction.

Mr. Kosuke NAMEKATA (Kyoto University)

Stellar superflares on late-type stars and the effects on planets

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Solar flares are explosive phenomena on the solar surface. They often produce high XUV radiations and mass ejections which have potential risks to damage human technologies. On other stars, such as M dwarfs and young stars, larger ‘superflares’ (more than ten times larger than the most energetic solar flares) are known to frequently occur, severely affecting the exoplanet habitability. Moreover, it is recently found that superflares actually occur on the slowly rotating Sun-like stars, which supports the possibility of superflares on the current Sun. In this context, there is an increasing interest in the questions “How do the magnetic activities of central stars affect the planet environment?” or “Can our Sun produce superflares?”. Our purpose is to answer these questions by revealing the mechanisms and properties of such stellar extreme events. We have investigated the photometric properties of the stellar superflares and large starspots with the data of Kepler Space Telescope and found that its basic mechanism is common with solar phenomena (i.e. the release of magnetic energy). Moreover, we have recently started optical spectroscopic observations of stellar superflares with the Kyoto Univerisity 3.8-m Seimei Telescope. We found the properties of radiations and the first evidence of stellar mass ejection, which would enable us to estimate its impacts on planets. In this colloquium, I will talk about recent progress and future prospects.

Prof. Yoshiyuki INOUE (Osaka University)

Introduction to High Energy & Black Hole Astrophysics

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I will briefly introduce high energy astrophysics and some recent exciting topics such as Fermi bubbles and cosmic gamma-ray background radiation. Then, I will talk about various types of black holes from primordial to supermassive. Lastly, I also would like to talk about the coronae of active supermassive black holes. Black hole coronae, ~100 keV hot plasma, are believed to exist based on the X-ray observations. However, we still do not know the formation process of those coronae. By introducing our recent ALMA results and theoretical prediction of its multi-messenger properties, I would like to discuss the nature of black hole corona with you.

Prof. Yusei KOYAMA (Subaru Telescope)

Panoramic and Microscopic Views of Galaxy Evolution Near and Far

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I present an overview of our observing campaign of distant (proto-)clusters using wide-field facilities of the Subaru Telescope, aiming to unveil the large-scale structures around massive clusters at 0.4<z<2.6, and to study the nature of young progenitors of present-day cluster galaxies. I will also present our recent multi-wavelength approaches to understand the "quenching" of star formation in nearby galaxies - I would like to discuss the "real" effect of galaxy morphologies on the star formation efficiency of galaxies. Finally, I will introduce our next-generation, wide-field adaptive optics (GLAO) development project at Subaru ("ULTIMATE-Subaru" project). This is a big instrumentation program to build a major facility instrument of Subaru in 2020s and beyond. It is predicted that GLAO can deliver FWHM=0.2-arcsec image quality at K-band over ~20-arcmin FoV at Maunakea - expecting a great synergy with future wide-field IR space missions to be launched in 2020s.

Dr. Sunmyon CHON (Tohoku University)

Supermassive star formation via super competitive accretion in slightly metal-enriched clouds

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Direct collapse black hole (DCBH) formation with mass 10^5 M is a promising scenario for the origin of high-redshift supermassive black holes. It has been supposed that the DCBH can only form in the primordial gas since the metal enrichment enhances the cooling ability and causes the fragmentation into smaller pieces. What actually happens in such an environment, however, has not been explored in detail. Here, we study the impact of the metal enrichment on the clouds, conducting hydrodynamical simulations to follow the cloud evolution with different degree of the metal enrichment. What we have found is that supermassive stars can form when Z/Zsun <~ 10^-4. Although dust cooling promotes fragmentation, a massive accreting flow feeds the gas to the central massive stars, which grows supermassive. Once the metallicity exceeds 10^−3 Zsun and metal-line cooling becomes operative, the central star cannot grow supermassive. Our results open up a new window for seed BHs, which relaxes the condition on metallicity and enhances the seed BH abundance.

Prof. Hidenobu YAJIMA (University of Tsukuba)

Formation of dusty massive galaxies and massive black holes in protocluster regions

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Revealing the formation mechanism of massive galaxies in overdense regions is one of the key issues in today’s astrophysics. Recent observations have discovered a lot of protocluster candidates with dusty massive galaxies and massive black holes. However, the galaxy formation in the protoclusters has not been understood yet. Using cosmological simulations with zoom-in initial conditions, we study the galaxy formation in protocluster regions in the early Universe. We find that star formation in massive galaxies proceeds as in the mean-density field and stellar radiation is attenuated by interstellar dust. Massive black holes with M > 10^8 solar mass are formed in the massive galaxies and their growth rates are suppressed due to AGN feedback at z < 6.
In addition to the above large-scale simulations, we perform radiative-hydrodynamic simulations of star cluster formation in low-metallicity clouds. The low-metallicity star clusters are fundamental components in understanding galaxy formation. In this talk, I will show these simulation results and discuss future work.

Prof. Luca BAIOTTI (Osaka University)

Gravitational waves from neutron star mergers and their relation to the nuclear equation of state

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With reference to observed gravitational wave events GW170817 and GW190425, I introduce ideas and techniques to extract information about the equation of state of matter at very high densities from gravitational waves emitted before, during and after the merger of binary neutron stars. In passing, I also touch on the possibility that what we observe in gravitational waves are not neutron stars, but something more exotic.

Prof. Kohei INAYOSHI (KIAA - Peking University)

Radiative inefficient accretion flows onto static and moving massive black holes from the galactic nuclei to the outskirts of galaxies

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 Supermassive black holes (SMBHs) are ubiquitously harbored at the centers of massive nearby galaxies. The vast majority of SMBHs in the local universe show levels of activity much lower than those expected from gas supplying rates onto the galactic nuclei, and only a small fraction of silent SMBHs can turn into active galactic nuclei (AGN). Performing 2D hydrodynamical simulations of BH accretion that resolve the relevant physical scales from the BH influence radius down to an accretion disk, we study the state transitional behavior of accreting BHs in galactic nuclei from radiatively inefficient phases to cold disk accretion. The simulation result naturally explains (1) the reason for the offset between the observed luminosities and theoretical predictions for nearby quiescent SMBHs, and (2) the conditions to fuel gas into the nuclear SMBH.

 Furthermore, we extend our simulation to 3D and study mass accretion onto wandering BHs at the outskirts of massive (elliptical) galaxies. Those wandering BHs are expected to be populated via ejection from the galactic nuclei through BH interactions associated with galaxy mergers. We find that the mass accretion rate on a moving BH in plasma with density fluctuations is limited at ~10% of the canonical Bondi-Hoyle-Littleton rate due to angular momentum of the inflowing gas. Combining the result with a semi-analytical model of disk radiation spectra, we find that those BHs, supposed to be 1% of the nuclear SMBHs in mass, are bright at the millimeter band. Millimeter observations with ALMA and the next generation Very Large Array will enable us to hunt wandering BH population and push the detectable mass limit below ~10^7 Msun for massive nearby ellipticals, e.g., M87, and ~10^5 Msun for Milky Way.

Prof. Kento MASUDA (Osaka University)

On the link between extrasolar giants and their inner planets

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 Doppler surveys showed long ago that extrasolar giant planets have a broad eccentricity distribution, hinting that their orbits have been dynamically excited due to post-formation perturbations such as planet-planet scattering. On the other hand, recent analyses of Doppler and transit survey data both indicate that most of the extrasolar giant planets orbiting beyond 1AU from the star are associated with inner systems of multiple smaller planets. Then, one might expect that those dynamically active outer giants significantly affect the orbits of the inner systems. I will discuss how such a view compares to the orbital architecture of exoplanetary systems inferred from transit and Doppler data.

Prof. Takayoshi SANO (Osaka University)

The magnetized Richtmyer-Meshkov instability in laser and astrophysical plasmas

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 Extreme plasma states observed in astrophysical phenomena can be created in the laboratory using large laser facilities such as the GEKKO laser at Osaka University. For example, the verification of the metallic hydrogen state under ultra-high pressure comparable to that of Jupiter's interior and the formation of collisionless shocks are being actively pursued. We are conducting laser experiments and MHD simulations on interfacial instabilities in magnetized plasmas associated with supernova explosions. Such a phenomenon is also an important process in laser fusion plasmas. In this presentation, I briefly introduce our laser astrophysics experiments and theoretical understandings on the amplification of magnetic fields by the Richtmyer-Meshkov instability.

Dr. Jackson M. NORRIS (Osaka University)

Intervening Quasar Absorption Lines and the Circumgalactic Medium

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 The circumgalactic medium (CGM) is important to our understanding of galaxy evolution. It is a complex multiphase system of accreting, outflowing, and recycled gas around galaxies. We will discuss some of the fundamental observational methods used to observe and interpret the CGM, with an emphasis on intervening quasar absorption line (QAL) systems. We will look at some of the findings of recent QAL studies, including an in-depth “cloud-by-cloud” analysis of individual QAL systems as well as statistical analyses that incorporate dozens of these systems to address the “missing baryon” and “missing metals” problems.

Prof. Shinsuke TAKASAO (Osaka University)

Accretion in various astrophysical objects

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 Accretion is a fundamental process in the formation of all the astrophysical objects. Theoretical studies are highly demanded, since growing objects are generally embedded in a dense gas and direct observations are very difficult. Many accreting systems should be considered in the framework of magnetohydrodynamics (MHD), because more than 99.9% of baryonic matter in the universe exists as a plasma that couple with magnetic fields. The boundary/initial conditions and major microphysics are different from one system to another, but they share key common physics. The aim of this talk is to give a general picture of the formation of astrophysical objects by pointing out key physics including MHD, and to show how we can unveil the link between the formation processes of astrophysical objects and their various activities; why protostars frequently produce huge explosions? when outflows start to be launched during the formation of disks around black holes? etc. The main part of this talk is devoted to show our recent results about protostellar accretion. In the end, I will briefly introduce our recent studies of other topics; accretion onto proto-gas giant planets, proto-neutron stars, and black holes.

Prof. Kentaro NAGAMINE (Osaka University)

ISM and Galaxy Formation from a theoretical / numerical perspective

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 The purpose of this talk is to give you a big picture (especially to the beginning new students) of galaxy formation studies, and how the recent works by our own students are related to these big ideas and directions of research. The main idea is simple and clear: “testing the concordance LambdaCDM model with structure formation both at the redshift frontier and idealized isolated systems.” In doing so, the feedback processes by stars/SNe/AGNs become key ingredients that control various phases of galaxy growth. I will discuss the results of GADGET3-Osaka SPH simulation by Shimizu+19, high-z galaxy formation work by Arata+’19 & ’20, H-alpha intensity map by Nakata’s M-thesis, the IGM tomography by upcoming PFS project by the Subaru telescope, and how all these are related with each other. The hope is that the B4/M1 students will find their own research topics from my talk.