Understanding the tsunami with a simple model

In this paper, we use the approximation of shallow water waves (Margaritondo G 2005 Eur. J. Phys. 26 401) to understand the behaviour of a tsunami in a variable depth. We deduce the shallow water wave equation and the continuity equation that must be satisfied when a wave encounters a discontinuity in the sea depth. A short explanation about how the tsunami hit the west coast of India is given based on the refraction phenomenon. Our procedure also includes a simple numerical calculation suitable for undergraduate students in physics and engineering

TRINITY III: Quasar Luminosity Functions Decomposed by Halo, Galaxy, and Black Hole Masses and Eddington Ratios from z=0-10

We present the redshift evolution of quasar luminosity functions decomposed by halo mass, galaxy mass, supermassive black hole (SMBH) mass, and Eddington ratio, as well as SMBH kinetic/radiative energy output ratios from TRINITY, a flexible empirical model that self-consistently infers the halo--galaxy--SMBH connection that match observational data. Key findings include: 1) The normalization of QLF increases by ~3-4 dex from z~10 to z~4, due to the fast mass build-up of different SMBH populations; 2) From z~4 to z~1, less massive galaxies and SMBHs make up bigger and bigger fractions of QLFs, due to the AGN downsizing effect; 3) At z~0, massive haloes/galaxies/SMBHs are responsible for most bright quasars due to low Eddington ratios among all SMBHs; 4) The bright ends of quasar luminosity functions (QLFs) are dominated by SMBHs that are at least 0.3 dex over-massive relative to the median SMBH mass-galaxy mass relation; 5) QLFs at z~6-7 are dominated by SMBHs accreting at Eddington ratios 0.1 < $\eta_\mathrm{rad}$ < 1, but super-Eddington AGNs contribute more significantly to QLFs towards z~9-10.Comment: 18 pages, 14 figures. Accepted by MNRAS. Comments welcome

TRINITY II: The Luminosity-dependent Bias of the Supermassive Black Hole Mass--Galaxy Mass Relation for Bright Quasars at z=6z=6

Using recent empirical constraints on the dark matter halo--galaxy--supermassive black hole (SMBH) connection from $z=0-7$, we infer how undermassive, typical, and overmassive SMBHs contribute to the quasar luminosity function (QLF) at $z=6$. We find that beyond $L_\mathrm{bol} = 5 \times 10^{46}$ erg/s, the $z=6$ QLF is dominated by SMBHs that are at least 0.3 dex above the $z=6$ median $M_\bullet-M_*$ relation. The QLF is dominated by typical SMBHs (i.e., within $\pm 0.3$ dex around the $M_\bullet-M_*$ relation) at $L_\mathrm{bol} \lesssim 10^{45}$ erg/s. At $z\sim 6$, the intrinsic $M_\bullet-M_*$ relation for all SMBHs is slightly steeper than the $z=0$ scaling, with a similar normalization at $M_* \sim 10^{11} M_\odot$. We also predict the $M_\bullet-M_*$ relation for $z=6$ bright quasars selected by different bolometric luminosity thresholds, finding very good agreement with observations. For quasars with $L_\mathrm{bol} > 3 \times 10^{46}$ ($10^{48}$) erg/s, the scaling relation is shifted upwards by $\sim0.35$ (1.0) dex for $10^{11} M_\odot$ galaxies. To accurately measure the intrinsic $M_\bullet-M_*$ relation, it is essential to include fainter quasars with $L_\mathrm{bol} \lesssim 10^{45}$ erg/s. At high redshifts, low-luminosity quasars are thus the best targets for understanding typical formation paths for SMBHs in galaxies.Comment: 5 pages, 3 figures. Submitted to MNRAS Letters. Comments welcome

TRINITY IV: Predictions for Supermassive Black Holes at z≳7z \gtrsim 7

We present predictions for the high-redshift halo-galaxy-supermassive black hole (SMBH) connection from the TRINITY model. Constrained by a comprehensive compilation of galaxy ($0\leq z \leq 10$) and SMBH datasets ($0\leq z \leq 6.5$), TRINITY finds: 1) The number of SMBHs with $M_\bullet > 10^9 M_\odot$ in the observable Universe increases by six orders of magnitude from $z\sim10$ to $z\sim2$, and by another factor of $\sim 3$ from $z\sim2$ to $z=0$; 2) The $M_\bullet > 10^9/10^{10} M_\odot$ SMBHs at $z\sim 6$ live in haloes with $\sim (2-3)/(3-5) \times 10^{12} M_\odot$; 3) the new JWST AGNs at $7\lesssim z \lesssim 11$ are broadly consistent with the median SMBH mass-galaxy mass relation for AGNs from TRINITY; 4) Seeds from runaway mergers in nuclear star clusters are viable progenitors for the SMBHs in GN-z11 ($z=10.6$) and CEERS_1019 ($z=8.7$); 5) $z=6-10$ quasar luminosity functions from wide area surveys by, e.g., Roman and Euclid, will reduce uncertainties in the $z=6-10$ SMBH mass-galaxy mass relation by up to $\sim 0.5$ dex.Comment: 15 pages, 12 figures, submitted to MNRAS. Questions and comments are welcome

Improved Mock Galaxy Catalogs for the DEEP2 Galaxy Redshift Survey from Subhalo Abundance and Environment Matching

We develop empirical methods for modeling the galaxy population and populating cosmological N-body simulations with mock galaxies according to the observed properties of galaxies in survey data. We use these techniques to produce a new set of mock catalogs for the DEEP2 Galaxy Redshift Survey based on the output of the high-resolution Bolshoi simulation, as well as two other simulations with different cosmological parameters, all of which we release for public use. The mock-catalog creation technique uses subhalo abundance matching to assign galaxy luminosities to simulated dark-matter halos. It then adds color information to the resulting mock galaxies in a manner that depends on the local galaxy density, in order to reproduce the measured color-environment relation in the data. In the course of constructing the catalogs, we test various models for including scatter in the relation between halo mass and galaxy luminosity, within the abundance-matching framework. We find that there is no constant-scatter model that can simultaneously reproduce both the luminosity function and the autocorrelation function of DEEP2. This result has implications for galaxy-formation theory, and it restricts the range of contexts in which the mocks can be usefully applied. Nevertheless, careful comparisons show that our new mocks accurately reproduce a wide range of the other properties of the DEEP2 catalog, suggesting that they can be used to gain a detailed understanding of various selection effects in DEEP2.Comment: 24 pages, 13 figures, matches version accepted for publication in ApJS. Catalogs are available for download from the URL referenced in the Appendi

Reproducing the Stellar Mass/Halo Mass Relation in Simulated LCDM Galaxies: Theory vs Observational Estimates

We examine the present-day total stellar-to-halo mass (SHM) ratio as a function of halo mass for a new sample of simulated field galaxies using fully cosmological, LCDM, high resolution SPH + N-Body simulations.These simulations include an explicit treatment of metal line cooling, dust and self-shielding, H2 based star formation and supernova driven gas outflows. The 18 simulated halos have masses ranging from a few times 10^8 to nearly 10^12 solar masses. At z=0 our simulated galaxies have a baryon content and morphology typical of field galaxies. Over a stellar mass range of 2.2 x 10^3 to 4.5 x 10^10 solar masses, we find extremely good agreement between the SHM ratio in simulations and the present-day predictions from the statistical Abundance Matching Technique presented in Moster et al. (2012). This improvement over past simulations is due to a number systematic factors, each decreasing the SHM ratios: 1) gas outflows that reduce the overall SF efficiency but allow for the formation of a cold gas component 2) estimating the stellar masses of simulated galaxies using artificial observations and photometric techniques similar to those used in observations and 3) accounting for a systematic, up to 30 percent overestimate in total halo masses in DM-only simulations, due to the neglect of baryon loss over cosmic times. Our analysis suggests that stellar mass estimates based on photometric magnitudes can underestimate the contribution of old stellar populations to the total stellar mass, leading to stellar mass errors of up to 50 percent for individual galaxies. These results highlight the importance of using proper techniques to compare simulations with observations and reduce the perceived tension between the star formation efficiency in galaxy formation models and in real galaxies.Comment: Submitted to ApJ 9 pages, 5 figure

How Common are the Magellanic Clouds?

We introduce a probabilistic approach to the problem of counting dwarf satellites around host galaxies in databases with limited redshift information. This technique is used to investigate the occurrence of satellites with luminosities similar to the Magellanic Clouds around hosts with properties similar to the Milky Way in the object catalog of the Sloan Digital Sky Survey. Our analysis uses data from SDSS Data Release 7, selecting candidate Milky-Way-like hosts from the spectroscopic catalog and candidate analogs of the Magellanic Clouds from the photometric catalog. Our principal result is the probability for a Milky-Way-like galaxy to host N_{sat} close satellites with luminosities similar to the Magellanic Clouds. We find that 81 percent of galaxies like the Milky Way are have no such satellites within a radius of 150 kpc, 11 percent have one, and only 3.5 percent of hosts have two. The probabilities are robust to changes in host and satellite selection criteria, background-estimation technique, and survey depth. These results demonstrate that the Milky Way has significantly more satellites than a typical galaxy of its luminosity; this fact is useful for understanding the larger cosmological context of our home galaxy.Comment: Updated to match published version. Added referenc

Constructing Fresnel reflection coefficients by ruler and compass

A simple and intuitive geometical method to analyze Fresnel formulas is presented. It applies to transparent media and is valid for perpendicular and parallel polarizations. The approach gives a graphical characterization particularly simple of the critical and Brewster angles. It also provides an interpretation of the relation between the reflection coefficients for both basic polarizations as a symmetry in the plane

Fresnel coefficients as hyperbolic rotations

We describe the action of a plane interface between two semi-infinite media in terms of a transfer matrix. We find a remarkably simple factorization of this matrix, which enables us to express the Fresnel coefficients as a hyperbolic rotation.Comment: 6 pages, 3 figure