arXiv subjects

Dohyeong Kim

Publications and source records attributed to Dohyeong Kim.

82 records · Page 5Linked to original sources

arXiv2017

Integral points on the complement of plane quartics

Let $Y$ be the complement of a plane quartic curve $D$ defined over a number field. Our main theorem confirms the Lang-Vojta conjecture for $Y$ when $D$ is a generic smooth quartic curve, by showing that its integral points are confined in a curve except for a finite number of exceptions. The required finiteness will be obtained by reducing it to the Shafarevich conjecture for K3 surfaces. Some variants of our method confirm the same conjecture when $D$ is a reducible generic quartic curve which consists of four lines, two lines and a conic, or two conics.

math.NT↗

arXiv2015

Descent for the punctured universal elliptic curve, and the average number of integral points on elliptic curves

We show that the average number of integral points on elliptic curves, counted modulo the natural involution on a punctured elliptic curve, is bounded from above by $2.1 \times 10^8$. To prove it, we design a descent map, whose prototype goes at least back to Mordell, which associates a pair of binary forms to an integral point on an elliptic curve. Other ingredients of the proof include the upper bounds for the number of solutions of a Thue equation by Evertse and Akhtari-Okazaki, and the estimation of the number of binary quartic forms by Bhargava-Shankar. Our method applies to $S$-integral points to some extent, although our present knowledge is insufficient to deduce an upper bound for the average number of them. We work out the numerical example with $S=\{2\}$.

math.NT↗

arXiv2015

Discovery of A Faint Quasar at z~6 and Implications for Cosmic Reionization

Recent studies suggest that faint active galactic nuclei may be responsible for the reionization of the universe. Confirmation of this scenario requires spectroscopic identification of faint quasars ($M_{1450}>-24$ mag) at $z \gtrsim6$, but only a very small number of such quasars have been spectroscopically identified so far. Here, we report the discovery of a faint quasar IMS J220417.92+011144.8 at z~6 in a 12.5 deg$^{2}$ region of the SA22 field of the Infrared Medium-deep Survey (IMS). The spectrum of the quasar shows a sharp break at $\sim8443~\rmÅ$, with emission lines redshifted to $z=5.944 \pm 0.002$ and rest-frame ultraviolet continuum magnitude $M_{1450}=-23.59\pm0.10$ AB mag. The discovery of IMS J220417.92+011144.8 is consistent with the expected number of quasars at z~6 estimated from quasar luminosity functions based on previous observations of spectroscopically identified low-luminosity quasars . This suggests that the number of $M_{1450}\sim-23$ mag quasars at z~6 may not be high enough to fully account for the reionization of the universe. In addition, our study demonstrates that faint quasars in the early universe can be identified effectively with a moderately wide and deep near-infrared survey such as the IMS.

astro-ph.GA↗

arXiv2015

Accretion Rates of Red Quasars from the Hydrogen P$β$ line

Red quasars are thought to be an intermediate population between merger-driven star-forming galaxies in dust-enshrouded phase and normal quasars. If so, they are expected to have high accretion ratios, but their intrinsic dust extinction hampers reliable determination of Eddington ratios. Here, we compare the accretion rates of 16 red quasars at $z \sim 0.7$ to those of normal type 1 quasars at the same redshift range. The red quasars are selected by their red colors in optical through near-infrared (NIR) and radio detection. The accretion rates of the red quasars are derived from the P$β$ line in NIR spectra, which is obtained by the SpeX on the Infrared Telescope Facility (IRTF) in order to avoid the effects of dust extinction. We find that the measured Eddington ratios ($L_{\rm bol}$/$L_{\rm Edd} \simeq 0.69$) of red quasars are significantly higher than those of normal type 1 quasars, which is consistent with a scenario in which red quasars are the intermediate population and the black holes of red quasars grow very rapidly during such a stage.

astro-ph.GA↗

arXiv2015

Rest-frame Optical Spectra and Black Hole Masses of 3<z<6 Quasars

We present the rest-frame optical spectral properties of 155 luminous quasars at 3.3<z<6.4 taken with the AKARI space telescope, including the first detection of H$α$ emission line as far out as z~6. We extend the scaling relation between the rest-frame optical continuum and line luminosity of active galactic nuclei (AGNs) to the high luminosity, high redshift regime that has rarely been probed before. Remarkably, we find that a single log-linear relation can be applied to the 5100${\rm Å}$ and H$α$ AGN luminosities over a wide range of luminosity (10$^{42}$<$L_{5100}$<10$^{47}$ergs/s) or redshift (0<z<6), suggesting that the physical mechanism governing this relation is unchanged from z=0 to 6, over five decades in luminosity. Similar scaling relations are found between the optical and the UV continuum luminosities or line widths. Applying the scaling relations to the H$β$ black hole mass ($M_{\rm BH}$) estimator of local AGNs, we derive the $M_{\rm BH}$ estimators based on H$α$, MgII, and CIV lines, finding that the UV-line based masses are overall consistent with the Balmer-line based, but with a large intrinsic scatter of 0.40dex for the CIV estimates. Our 43 $M_{\rm BH}$ estimates from H$α$ confirm the existence of BHs as massive as ~10$^{10}M_{\odot}$ out to z~5, and provide a secure footing for previous MgII-line based studies that a rapid $M_{\rm BH}$ growth has occurred in the early universe.

astro-ph.GA↗

arXiv2015

The AKARI 2.5-5.0 Micron Spectral Atlas of Type-1 Active Galactic Nuclei: Black Hole Mass Estimator, Line Ratio, and Hot Dust Temperature

We present 2.5-5.0 $μ$m spectra of 83 nearby ($0.002\,<\,z\,<\,0.48$) and bright ($K<14$mag) type-1 active galactic nuclei (AGNs) taken with the Infrared Camera (IRC) on board $\it{AKARI}$. The 2.5-5.0 $μ$m spectral region contains emission lines such as Br$β$ (2.63 $μ$m), Br$α$ (4.05 $μ$m), and polycyclic aromatic hydrocarbons (PAH; 3.3 $μ$m), which can be used for studying the black hole (BH) masses and star formation activities in the host galaxies of AGNs. The spectral region also suffers less dust extinction than in the ultra violet (UV) or optical wavelengths, which may provide an unobscured view of dusty AGNs. Our sample is selected from bright quasar surveys of Palomar-Green (PG) and SNUQSO, and AGNs with reverberation-mapped BH masses from Peterson et al. (2004). Using 11 AGNs with reliable detection of Brackett lines, we derive the Brackett-line-based BH mass estimators. We also find that the observed Brackett line ratios can be explained with the commonly adopted physical conditions of the broad line region (BLR). Moreover, we fit the hot and warm dust components of the dust torus by adding photometric data of SDSS, 2MASS, $\it{WISE}$, and $\it{ISO}$ to the $\it{AKARI}$ spectra, finding hot and warm dust temperatures of $\sim1100\,\rm{K}$ and $\sim220\,\rm{K}$, respectively, rather than the commonly cited hot dust temperature of 1500 K.

astro-ph.GA↗

arXiv2015

A modular approach to Thue-Mahler equations

Let $h(x,y)$ be a non-degenerate binary cubic form with integral coefficients, and let $S$ be an arbitrary finite set of prime numbers. By a classical theorem of Mahler, there are only finitely many pairs of relatively prime integers $x,y$ such that $h(x,y)$ is an $S$-unit. In the present paper, we reverse a well known argument, which seems to go back to Shafarevich, and use the modularity of elliptic curves over $\mathbb{Q}$ to give upper bounds for the number of solutions of such a Thue-Mahler equation. In addition, our methods gives an effective method for determining all solutions, and we use Cremona's Elliptic Curve Database to give a wide range of numerical examples.

math.NT↗

arXiv2014

On the transfer congruence between $p$-adic Hecke $L$-functions

We prove the transfer congruence between $p$-adic Hecke $L$-functions for CM fields over cyclotomic extensions, which is a non-abelian generalization of the Kummer's congruence. The ingredients of the proof include the comparison between Hilbert modular varieties, the $q$-expansion principle, and some modification of Hsieh's Whittaker model for Katz' Eisenstein series. As a first application, we prove explicit congruence between special values of Hasse-Weil $L$-function of a CM elliptic curve twisted by Artin representations. As a second application, we prove the existence of a non-commutative $p$-adic $L$-function in the algebraic $K_1$-group of the completed localized Iwasawa algebra.

math.NT↗

arXiv2014

The Infrared Medium-Deep Survey II: How to Trigger Radio-AGN? Hints from Their Environments

Activity at the centers of galaxies, during which the central supermassive black hole is accreting material, is nowadays accepted to be rather ubiquitous and most probably a phase of every galaxy's evolution. It has been suggested that galactic mergers and interactions may be the culprits behind the triggering of nuclear activity. We use near-infrared data from the new Infrared Medium-Deep Survey (IMS) and the Deep eXtragalactic Survey (DXS) of the VIMOS-SA22 field and radio data at 1.4 GHz from the FIRST survey and a deep VLA survey to study the environments of radio-AGN over an area of ~25 sq. degrees and down to a radio flux limit of 0.1 mJy and a J-band magnitude of 23 mag AB. Radio-AGN are predominantly found in environments similar to those of control galaxies at similar redshift, J-band magnitude, and U-R rest-frame absolute color. However, a sub-population of radio-AGN is found in environments up to 100 times denser than their control sources. We thus preclude merging as the dominant triggering mechanism of radio-AGN. Through the fitting of the broadband spectral energy distribution of radio-AGN in the least and most dense environments, we find that those in the least dense environments show higher radio-loudness, higher star formation efficiencies, and higher accretion rates, typical of the so-called high-excitation radio-AGN. These differences tend to disappear at z>1. We interpret our results in terms of a different triggering mechanism for these sources that is driven by mass-loss through winds of young stars created during the observed ongoing star formation.

astro-ph.GA↗

arXiv2010

New Estimators of Black Hole Mass in Active Galactic Nuclei with Hydrogen Paschen Lines

More than 50% of Active Galactic Nuclei (AGNs) are suspected to be red and affected by dust-obscuration. Meanwhile, popular spectral diagnostics of AGNs are based on optical or ultraviolet light, making the dust obscuration as a primary concern for understanding the general nature of AGNs and supermassive black holes residing in them. To provide with a method of investigating properties of the dusty AGNs, we derive new black hole (BH) mass estimators based on velocity widths and luminosities of Near Infrared (NIR) hydrogen emission lines such as P$α$ and P$β$, and also investigate the line ratios of these Hydrogen lines. To derive the BH mass ($M_{\rm BH}$) estimators, we used a sample of 37 unobscured Type-1 AGNs with a $M_{\rm BH}$ range of $10^{6.8}$-$10^{9.4} M_{\odot}$, where $M_{\rm BH}$ come from either reverberation mapping method or single-epoch measurement method using Balmer lines. Our work shows that $M_{\rm BH}$ can be estimated from the Paschen line luminosities and the velocity widths to the accuracy of 0.18 - 0.24 dex (rms scatter). We also show that the mean line ratios of the Paschen lines and the Balmer lines are $\mathrm{\frac{Hα}{Pα}} \simeq 9.00$, $\mathrm{\frac{Hβ}{Pα}} \simeq 2.70$, which are consistent with a Case B recombination under a typical AGN broad line region environment. These ratios can be used as reference points when estimating the amount of dust extinction over the broad line region (BLR) for red AGNs. We expect the future application of the new BH mass estimators on red, dusty AGNs to provide a fresh view of obscured AGNs.

astro-ph.CO↗