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Takashi Nakamura

Publications and source records attributed to Takashi Nakamura.

At least 73 records · Page 4Linked to original sources
arXiv2015

Isotropic Detectable X-ray Counterparts to Gravitational Waves from Neutron Star Binary Mergers

Neutron star binary mergers are strong sources of gravitational waves (GWs). Promising electromagnetic counterparts are short gamma-ray bursts (GRBs) but the emission is highly collimated. We propose that the scattering of the long-lasting plateau emission in short GRBs by the merger ejecta produces nearly isotropic emission for $\sim 10^4$ s with flux $10^{-13}-10^{-10}$ erg cm$^{-2}$ s$^{-1}$ at 100 Mpc in X-ray. This is detectable by Swift XRT and wide field X-ray detectors such as ISS-Lobster, Einstein Probe, eROSITA and WF-MAXI, which are desired by the infrared and optical follow-ups to localize and measure the distance to the host galaxy. The scattered X-rays obtain linear polarization, which correlates with the jet direction, X-ray luminosity and GW polarizations. The activity of plateau emission is also a natural energy source of a macronova (or kilonova) detected in short GRB 130603B without the $r$-process radioactivity.

astro-ph.HE↗
arXiv2015

Optical Synchrotron Precursors of Radio Hypernovae

We examine the bright radio synchrotron counterparts of low-luminosity gamma-ray bursts (llGRBs) and relativistic supernovae (SNe) and find that they can be powered by spherical hypernova (HN) explosions. Our results imply that radio-bright HNe are driven by relativistic jets that are choked deep inside the progenitor stars or quasi-spherical magnetized winds from fast-rotating magnetars. We also consider the optical synchrotron counterparts of radio-bright HNe and show that they can be observed as precursors several days before the SN peak with an r-band absolute magnitude of M_r ~ -14 mag. While previous studies suggested that additional trans-relativistic components are required to power the bright radio emission, we find that they overestimated the energy budget of the trans-relativistic component by overlooking some factors related to the minimum energy of non-thermal electrons. If an additional trans-relativistic component exists, then a much brighter optical precursor with M_r ~ -20 mag can be expected. Thus, the scenarios of radio-bright HNe can be distinguished by using optical precursors, which can be detectable from < 100 Mpc by current SN surveys like the Kiso SN Survey, Palomar Transient Factory, and Panoramic Survey Telescope & Rapid Response System.

astro-ph.HE↗
arXiv2015

A complete Riemann zeta distribution and the Riemann hypothesis

Let $σ,t\in{\mathbb{R}}$, $s=σ+\mathrm{i}t$, $Γ(s)$ be the Gamma function, $ζ(s)$ be the Riemann zeta function and $ξ(s):=s(s-1)π^{-s/2}Γ(s/2)ζ(s)$ be the complete Riemann zeta function. We show that $Ξ_σ(t):=ξ(σ-\mathrm{i}t)/ξ(σ)$ is a characteristic function for any $σ\in{\mathbb{R}}$ by giving the probability density function. Next we prove that the Riemann hypothesis is true if and only if each $Ξ_σ(t)$ is a pretended-infinitely divisible characteristic function, which is defined in this paper, for each $1/2<σ<1$. Moreover, we show that $Ξ_σ(t)$ is a pretended-infinitely divisible characteristic function when $σ=1$. Finally we prove that the characteristic function $Ξ_σ(t)$ is not infinitely divisible but quasi-infinitely divisible for any $σ>1$.

math.ST↗
arXiv2015

Detectability of bigravity with graviton oscillations using gravitational wave observations

The gravitational waveforms in the ghost-free bigravity theory exhibit deviations from those in general relativity. The main difference is caused by graviton oscillations in the bigravity theory. We investigate the prospects for the detection of the corrections to gravitational waveforms from coalescing compact binaries due to graviton oscillations and for constraining bigravity parameters with the gravitational wave observations. We consider the bigravity model discussed by the De Felice-Nakamura-Tanaka subset of the bigravity model, and the phenomenological model in which the bigravity parameters are treated as independent variables. In both models, the bigravity waveform shows strong amplitude modulation, and there can be a characteristic frequency of the largest peak of the amplitude, which depends on the bigravity parameters. We show that there is a detectable region of the bigravity parameters for the advanced ground-based laser interferometers, such as Advanced LIGO, Advanced Virgo, and KAGRA. This region corresponds to the effective graviton mass of $μ\geq 10^{-17}~{\rm cm}^{-1}$ for $\tilde{c}-1 \geq 10^{-19}$ in the phenomenological model, while $μ\geq 10^{-16.5}~{\rm cm}^{-1}$ for $κξ_c^2 \geq 10^{0.5}$ in the De Felice-Nakamura-Tanaka subset of the bigravity model, respectively, where $\tilde{c}$ is the propagation speed of the massive graviton and $κξ_c^2$ corresponds to the corrections to the gravitational constant in general relativity. These regions are not excluded by existing solar system tests. We also show that, in the case of $1.4-1.4M_{\rm sun}$ binaries at the distance of $200~{\rm Mpc}$, $\logμ^2$ is determined with an accuracy of ${\cal O}$(0.1)\% at the 1$σ$ level for a fiducial model with $μ^2=10^{-33}~{\rm cm}^{-2}$ in the case of the phenomenological model.

gr-qc↗
arXiv2014

Soft X-ray Extended Emissions of Short Gamma-Ray Bursts as Electromagnetic Counterparts of Compact Binary Mergers; Possible Origin and Detectability

We investigate the possible origin of extended emissions (EEs) of short gamma-ray bursts with an isotropic energy of ~ 10^(50-51) erg and a duration of a few 10 s to ~ 100 s, based on a compact binary (neutron star (NS)-NS or NS-black hole (BH)) merger scenario. We analyze the evolution of magnetized neutrino-dominated accretion disks of mass ~ 0.1 M_sun around BHs formed after the mergers, and estimate the power of relativistic outflows via the Blandford-Znajek (BZ) process. We show that a rotation energy of the BH up to > 10^52 erg can be extracted with an observed time scale of > 30 (1+z) s with a relatively small disk viscosity parameter of alpha < 0.01. Such a BZ power dissipates by clashing with non-relativistic pre-ejected matter of mass M ~ 10^-(2-4) M_sun, and forms a mildly relativistic fireball. We show that the dissipative photospheric emissions from such fireballs are likely in the soft X-ray band (1-10 keV) for M ~ 10^-2 M_sun possibly in NS-NS mergers, and in the BAT band (15-150 keV) for M ~ 10^-4 M_sun possibly in NS-BH mergers. In the former case, such soft EEs can provide a good chance of ~ 6 yr^-1 for simultaneous detections of the gravitational waves with a ~ 0.1 deg angular resolution by soft X-ray survey facilities like Wide-Field MAXI.

astro-ph.HE↗
arXiv2014

Measuring Speed of Gravitational Waves by Observations of Photons and Neutrinos from Compact Binary Mergers and Supernovae

Detection of gravitational waves (GW) provides us an opportunity to test general relativity in strong and dynamical regimes of gravity. One of the tests is checking whether GW propagates with the speed of light or not. This test is crucial because the velocity of GW has not ever been directly measured. Propagation speed of a GW can deviate from the speed of light due to the modification of gravity, graviton mass, and the nontrivial spacetime structure such as extra dimensions and quantum gravity effects. Here we report a simple method to measure the propagation speed of a GW by directly comparing arrival times between gravitational waves, and neutrinos from supernovae or photons from short gamma-ray bursts. As a result, we found that the future multimessenger observations of a GW, neutrinos, and photons can test the GW propagation speed with the precision of ~10^{-16} improving the previous suggestions by 8-10 orders of magnitude. We also propose a novel method that distinguishes the true signal due to the deviation of GW propagation speed from the speed of light and the intrinsic time delay of the emission at a source by looking at the redshift dependence.

gr-qc↗
arXiv2014

Short Gamma Ray Burst Formation Rate from BATSE data using E_p-L_p correlation and the minimum gravitational wave event rate of coalescing compact binary

Using 72 Short Gamma Ray Bursts (SGRBs) with well determined spectral data observed by BATSE, we determine their redshift and the luminosity by applying $E_p$--$L_p$ correlation for SGRBs found by \cite{tsutsui13}. For 53 SGRBs with the observed flux brighter than $4 \times 10^{-6}~{\rm erg~cm^{-2}s^{-1}}$, the cumulative redshift distribution up to $z=1$ agrees well with that of 22 {\it Swift}~SGRBs. This suggests that the redshift determination by the $E_p$--$L_p$ correlation for SGRBs works well. The minimum event rate at $z=0$ is estimated as $ρ_{SGRB}(0) = 6.3_{-3.9}^{+3.1} \times 10^{-10}~{\rm events~Mpc^{-3}yr^{-1}}$ so that the minimum beaming angle is $0.6^\circ-7.8^\circ$ assuming the merging rate of $10^{-7}-4\times 10^{-6}~{\rm events~Mpc^{-3}yr^{-1}}$ suggested from the binary pulsar data. Interestingly, this angle is consistent with that for SGRB130603B of $\sim 4^\circ-8^\circ$\citep{fong13b}. On the other hand, if we assume the beaming angle of $\sim 6^\circ$ suggested from four SGRBs with the observed value of beaming angle, the minimum event rate including off-axis SGRBs is estimated as $ρ_{SGRB,all}^{min}(0)=1.15_{-0.71}^{+0.57}\times 10^{-7}~{\rm events~Mpc^{-3}yr^{-1}}$. If SGRBs are induced by coalescence of binary neutron stars (NSs) and/or black holes (BHs), this event rate leads to the minimum gravitational-wave detection rate of $\rm 3.9_{-2.4}^{+1.9} (152_{-94}^{+75})~events~y^{-1}$ for NS-NS (NS-BH) binary, respectively, by a worldwide network with KAGRA, advanced-LIGO, advanced-Virgo, and GEO.

astro-ph.HE↗
arXiv2014

Possible Indirect Confirmation of the Existence of Pop III Massive Stars by Gravitational Wave

We perform population synthesis simulations for Population III (Pop III) coalescing binary neutron stars (NS-NSs), neutron star - black hole binaries (NS-BHs), and binary black holes (BH-BHs) which merge within the age of the universe. We found that the typical mass of Pop III BH-BHs is $\sim 30\ \rm{M}_{\odot}$ so that the inspiral chirp signal of gravitational waves can be detected up to z=0.28 by KAGRA, Adv. LIGO, Adv. Virgo and GEO network. Our simulations suggest that the detection rate of the coalescing Pop III BH-BHs is $140 (68) \cdot ({\rm SFR}_{\rm p}/10^{-2.5} \rm{M}_{\odot} {\rm yr}^{-1} {\rm Mpc}^{-3}) \cdot {\rm Err}_{\rm sys} ~{\rm events} ~{\rm yr}^{-1}$ for the flat (Salpeter) initial mass function (IMF), respectively, where $\rm SFR_p$ and $\rm Err_{sys}$ are the peak value of the Pop III star formation rate and the possible systematic errors due to the assumptions in Pop III population synthesis, respectively. $\rm Err_{sys}=1$ correspond to conventional parameters for Pop I stars. From the observation of the chirp signal of the coalescing Pop III BH-BHs, we can determine both the mass and the redshift of the binary for the cosmological parameters determined by Planck satellite. Our simulations suggest that the cumulative redshift distribution of the coalescing Pop III BH-BHs depends almost only on the cosmological parameters. We might be able to confirm the existence of Pop III massive stars of mass $\sim 30~\rm M_{\odot}$ by the detections of gravitational waves if the merger rate of the Pop III massive BH-BHs dominates that of Pop I BH-BHs.

astro-ph.HE↗
arXiv2014

Hurwitz zeta and Euler-Zagier-Hurwitz type of double zeta distributions and real zeros of these zeta functions

In this paper, we give Hurwitz zeta distributions with $0 < σ\ne 1$ by using the Gamma function. During the proof process, we show that the Hurwitz zeta function $ζ(σ,a)$ does not vanish for all $0 <σ<1$ if and only if $a \ge 1/2$. Next we define Euler-Zagier-Hurwitz type of double zeta distributions not only in the region of absolute convergence but also the outside of the region of absolute convergence. Moreover, we show that the Euler-Zagier-Hurwitz type of double zeta function $ζ_2 (σ_1,σ_2\,;a)$ does not vanish when $0<σ_1<1$, $σ_2>1$ and $1<σ_1+σ_2<2$ if and only if $a \ge 1/2$.

math.NT↗
arXiv2013

Blue Supergiant Model for Ultra-Long Gamma-Ray Burst with Superluminous-Supernova-Like Bump

Long GRBs (LGRBs) have typical duration of ~ 30 s and some of them are associated with hypernovae, like Type Ic SN 1998bw. Wolf-Rayet stars are the most plausible LGRB progenitors, since the free-fall time of the envelope is consistent with the duration, and the natural outcome of the progenitor is a Type Ic SN. While a new population of ultra-long GRBs (ULGRBs), GRB 111209A, GRB 101225A, and GRB 121027A, has a duration of ~ 10^4 s, two of them are accompanied by superluminous-supernova (SLSN) like bumps, which are <~ 10 times brighter than typical hypernovae. Wolf-Rayet progenitors cannot explain ULGRBs because of too long duration and too bright SN-like bump. A blue supergiant (BSG) progenitor model, however, can explain the duration of ULGRBs. Moreover, SLSN-like bump can be attributed to the so-called cocoon-fireball photospheric emissions (CFPEs). Since a large cocoon is inevitably produced during the relativistic jet piercing though the BSG envelope, this component can be a smoking-gun evidence of BSG model for ULGRBs. In this paper, we examine u, g, r, i, and J-band light curves of three ULGRBs and demonstrate that they can be fitted quite well by our BSG model with the appropriate choices of the jet opening angle and the number density of the ambient gas. In addition, we predict that for 121027A, SLSN-like bump could have been observed for ~ 20 - 80 days after the burst. We also propose that some SLSNe might be CFPEs of off-axis ULGRBs without visible prompt emission.

astro-ph.HE↗
arXiv2013

Any non-monomial polynomial of the Riemann zeta-function has complex zeros off the critical line

In this paper, we show that any polynomial of zeta or $L$-functions with some conditions has infinitely many complex zeros off the critical line. This general result has abundant applications. By using the main result, we prove that the zeta-functions associated to symmetric matrices treated by Ibukiyama and Saito, certain spectral zeta-functions and the Euler-Zagier multiple zeta-functions have infinitely many complex zeros off the critical line. Moreover, we show that the Lindelöf hypothesis for the Riemann zeta-function is equivalent to the Lindelöf hypothesis for zeta-functions mentioned above despite of the existence of the zeros off the critical line. Next we prove that the Barnes multiple zeta-functions associated to rational or transcendental parameters have infinitely many zeros off the critical line. By using this fact, we show that the Shintani multiple zeta-functions have infinitely many complex zeros under some conditions. As corollaries, we show that the Mordell multiple zeta-functions, the Euler-Zagier-Hurwitz type of multiple zeta-functions and the Witten multiple zeta-functions have infinitely many complex zeros off the critical line.

math.NT↗
arXiv2013

Luminous supernova-like UV/optical/infrared transients associated with ultra-long gamma-ray bursts from metal-poor blue supergiants

Metal-poor massive stars may typically end up their lives as blue supergiants (BSGs). Gamma-ray bursts (GRBs) from such progenitors could have ultra-long duration of relativistic jets. For example Population III (Pop III) GRBs at z ~ 10-20 might be observable as X-ray rich events with a typical duration of T_90 ~ 10^4(1+z) sec. Recent GRB111209A at z = 0.677 has an ultra long duration of T_90 ~ 2.5*10^4 sec so that it have been suggested that the progenitor might be a metal-poor BSGs in the local universe. Here, we suggest luminous UV/optical/infrared emissions associated with such a new class of GRB from metal poor BSGs. Before the jet head breaks out the progenitor envelope, the energy injected by the jet is stored in a hot-plasma cocoon, which finally emerges and expands as a baryon-loaded fireball. We show that the photospheric emissions from the cocoon fireball could be intrinsically very bright (L_peak ~ 10^(42-44) erg/sec) in UV/optical bands (E_peak ~ 10 eV) with a typical duration of ~ 100 days in the rest frame. Such cocoon emissions from Pop III GRB might be detectable in infrared bands at ~ years after Pop III GRBs at up to z ~ 15 by up-coming facilities like JWST. We also suggest that GRB111209A might have been rebrightening in UV/optical bands up to an AB magnitude of < 26. The cocoon emissions from local metal-poor BSGs might have been already observed as luminous supernovae without GRB since they can be seen from the off-axis direction of the jet.

astro-ph.HE↗
arXiv2013

Possible existence of viable models of bi-gravity with detectable graviton oscillations by gravitational wave detectors

We discuss graviton oscillations based on the ghost free bi-gravity theory. We point out that this theory possesses a natural cosmological background solution which is very close to the case of general relativity. Furthermore, interesting parameter range of the graviton mass, which can be explored by the observations of gravitational waves, is not at all excluded by the constraint from the solar system tests. Therefore the graviton oscillation with possible inverse chirp signal would be an interesting scientific target of KAGRA, adv LIGO, adv Virgo and GEO.

gr-qc↗
arXiv2012

Multidimensional Shintani zeta functions and zeta distributions on R^d

The class of Riemann zeta distribution is one of the classical classes of probability distributions on R. Multidimensional Shintani zeta function is introduced and its definable probability distributions on R^d are studied. This class contains some fundamental probability distributions such as binomial and Poisson distributions. The relation with multidimensional polynomial Euler product, which induces multidimensional infinitely divisible distributions on R^d, is also studied.

math.PR↗
arXiv2012

Long Duration X-Ray Flash and X-Ray Rich Gamma Ray Burst from Low Mass Population III Star

Recent numerical simulations suggest that Population III (Pop III) stars were born with masses not larger than $\sim 100 M_{\odot}$ but typically $\sim 40M_{\odot}$. By self-consistently considering the jet generation and propagation in the envelope of these low mass Pop III stars, we find that a Pop III blue super giant star has the possibility to raise a gamma-ray burst (GRB) even though it keeps a massive hydrogen envelope. We evaluate observational characters of Pop III GRBs and predict that Pop III GRBs have the duration of $\sim 10^5$ sec in the observer frame and the peak luminosity of $\sim 5 \times 10^{50} {\rm erg} {\rm sec}^{-1}$. Assuming that the $E_p-L_p$ (or $E_p-E_{γ, \rm iso}$) correlation holds for Pop III GRBs, we find that the spectrum peak energy falls $\sim$ a few keV (or $\sim 100$ keV) in the observer frame. We discuss the detectability of Pop III GRBs by future satellite missions such as EXIST and Lobster. If the $E_p-E_{γ, \rm iso}$ correlation holds, we have the possibility to detect Pop III GRBs at $z \sim 9$ as long duration X-ray rich GRBs by EXIST. On the other hand, if the $E_p-L_p$ correlation holds, we have the possibility to detect Pop III GRBs up to $z \sim 19$ as long duration X-ray flashes by Lobster.

astro-ph.HE↗
arXiv2012

Gamma-Ray Bursts are precise distance indicators similar to Type Ia Supernovae?

We estimate the distance modulus to long gamma-ray bursts (LGRBs) using the Type I Fundamental Plane, a correlation between the spectral peak energy $E_{\rm p}$, the peak luminosity $L_{\rm p}$, and the luminosity time $T_{\rm L}$ ($\equiv E_{\rm iso}/L_{\rm p}$ where $E_{\rm iso}$ is isotropic energy) for small Absolute Deviation from Constant Luminosity(ADCL). The Type I Fundamental Plane of LGRBs is calibrated using 8 LGRBs with redshift $z<1.4$. To avoid any assumption on the cosmological model, we use the distance modulus of 557 Type Ia supernovae (SNeIa) from the Union 2 sample. This calibrated Type I Fundamental Plane is used to measure the distance moduli to 9 high-redshift LGRBs with the mean error $\bar σ_μ=0.31$, which is comparable with that of SNe Ia $\bar σ_μ=0.26$ where $μ$ stands for the distance modulus. The Type I Fundamental Plane is so tight that our distance moduli have very small uncertainties. From those distance moduli, we obtained the constraint $Ω_{\rm M}=0.22\pm0.04$ for flat $Λ$CDM universe. Adding 9 LGRBs distance moduli ($z>1.4$) to 557 SNeIa distance moduli ($z<1.4$) significantly improves the constraint for non-flat $Λ$CDM universe from ($Ω_{\rm M}, Ω_{\rm Λ}$)=($0.29\pm0.10$, $0.76\pm0.13$) for SNeIa only to ($Ω_{\rm M}, Ω_{\rm Λ}$)=($0.23\pm0.06$, $0.68\pm0.08$) for SNeIa and 9 LGRBs.

astro-ph.CO↗
arXiv2012

Behaviors of multivariable finite Euler products in probabilistic view

Finite Euler product is known to be one of the classical zeta functions in number theory. In [1], [2] and [3], we have introduced some multivariable zeta functions and studied their definable probability distributions on R^d. They include functions which generate infinitely divisible, not infinitely divisible characteristic functions and not even to be characteristic functions. In this paper, we treat some multivariable finite Euler products and show how they behave in view of such properties.

math.PR↗