arXiv subjects

Takashi Nakamura

Publications and source records attributed to Takashi Nakamura.

At least 37 records · Page 2Linked to original sources

arXiv2020

Chirp Mass and Spin of Binary Black Holes from First Star Remnants

We performed Population III (Pop III) binary evolution by using population synthesis simulations for seven different models. We found that Pop III binaries tend to be binary black holes (BBHs) with chirp mass $M_{\rm chirp} \sim 30~M_{\odot}$ and they can merge at present day due to long merger time. The merger rate densities of Pop III BBHs at $z=0$ ranges 3.34--21.2 $\rm /yr/Gpc^3$ which is consistent with the aLIGO/aVIRGO result of 9.7--101 $\rm /yr/Gpc^3$. These Pop III binaries might contribute to some part of the massive BBH gravitational wave (GW) sources detected by aLIGO/aVIRGO. We also calculated the redshift dependence of Pop III BBH mergers. We found that Pop III low spin BBHs tend to merge at low redshift, while Pop III high spin BBHs do at high redshift, which can be confirmed by future GW detectors such as ET, CE, and DECIGO. These detectors can also check the redshift dependence of BBH merger rate and spin distribution. Our results show that except for one model, the mean effective spin $\left\langle χ_{\rm eff} \right\rangle$ at $z=0$ ranges $0.02$--$0.3$ while at $z=10$ it does $0.16$--$0.64$. Therefore, massive stellar-mass BBH detection by GWs will be a key for the stellar evolution study in the early universe.

astro-ph.HE↗

arXiv2020

The values of zeta functions composed by the Hurwitz and periodic zeta functions at integers

For $s \in {\mathbb{C}}$ and $0 < a <1$, let $ζ(s,a)$ and ${\rm{Li}}_s (e^{2πia})$ be the Hurwitz and periodic zeta functions, repectively. For $0 < a \le 1/2$, put $Z(s,a) := ζ(s,a) + ζ(s,1-a)$, $P(s,a) := {\rm{Li}}_s (e^{2πia}) + {\rm{Li}}_s (e^{2πi(1-a)})$, $Y(s,a) := ζ(s,a) - ζ(s,1-a)$ and $O(s,a):= -i \bigl( {\rm{Li}}_s (e^{2πia}) - {\rm{Li}}_s (e^{2πi(1-a)}) \bigr)$. Let $n \ge 0$ be an integer and $b := r/q$, where $q>r>0$ are coprime integers. In this paper, we prove that the values $Z(-n,b)$, $π^{-2n-2} P(2n+2,b)$, $Y(-n,b)$ and $π^{-2n-1} O(2n+1,b)$ are rational numbers, in addition, $π^{-2n-2} Z(2n+2,b)$, $P(-n,b)$, $π^{-2n-1} Y(2n+1,b)$ and $O(-n,b)$ are polynomials of $\cos (2π/q)$ and $\sin (2π/q)$ with rational coefficients. Furthermore, we show that $Z(-n,a)$, $π^{-2n-2} P(2n+2,a)$, $Y(-n,a)$ and $π^{-2n-1} O(2n+1,a)$ are polynomials of $0<a<1$ with rational coefficient, in addition, $π^{-2n-2} Z(2n+2,a)$, $P(-n,a)$, $π^{-2n-1} Y(2n+1,a)$ and $O(-n,a)$ are rational functions of $\exp (2 πia)$ with rational coefficients. Note that the rational numbers, polynomials and rational functions mentioned above are given explicitly. Moreover, we show that $P(s,a) \equiv 0$ for all $ 0 < a < 1/2$ if and only if $s$ is a negative even integer. We also prove similar assertions for $Z(s,a)$, $Y(s,a)$, $O(s,a)$ and so on. In addition, we prove that the function $Z(s,|a|)$ appears as the spectral density of some stationary self-similar Gaussian distributions.

math.NT↗

arXiv2020

Current status of space gravitational wave antenna DECIGO and B-DECIGO

Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is the future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could be produced during the inflationary period right after the birth of the universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in the heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1,000 km. Three clusters of DECIGO will be placed far from each other, and the fourth cluster will be placed in the same position as one of the three clusters to obtain the correlation signals for the detection of the primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder of DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand the multi-messenger astronomy.

gr-qc↗

arXiv2020

On a basis for Euler-Zagier double zeta functions with non-positive components

For a non-negative integer $N$, let $\mathcal{Z}_{N}:=\sum^N_{c = 0} \mathbb{Q} \cdot ζ(-c,s+c)$, where the right-hand side is the vector space spanned by the Euler-Zagier double zeta functions over $\mathbb{Q}$. In this paper, we show that $\mathcal{Z}_{N} =\bigoplus^{N}_{c = 0 : \text{even}} \mathbb{Q} \cdot ζ(-c,s+c)$, where $\bigoplus$ is the direct sum of vector spaces. Moreover, we give a family of relations that exhaust all $\mathbb{Q}$-linear relations on $\mathcal{Z}_{N}$.

math.NT↗

arXiv2019

Zeros and the functional equation of the quadrilateral zeta function

In this paper, we show that all real zeros of the bilateral Hurwitz zeta function $Z(s,a):=ζ(s,a) + ζ(s,1-a)$ with $1/4 \le a \le 1/2$ are on only the non-positive even integers exactly same as in the case of $(2^s-1) ζ(s)$. We also prove that all real zeros of the bilateral periodic zeta function $P(s,a):={\rm{Li}}_s (e^{2πia}) + {\rm{Li}}_s (e^{2πi(1-a)})$ with $1/4 \le a \le 1/2$ are on only the negative even integers just like $ζ(s)$. Moreover, we show that all real zeros of the quadrilateral zeta function $Q(s,a):=Z(s,a) + P(s,a)$ with $1/4 \le a \le 1/2$ are on only the negative even integers. On the other hand, we prove that $Z(s,a)$, $P(s,a)$ and $Q(s,a)$ have at least one real zero in $(0,1)$ when $0<a<1/2$ is sufficiently small. The complex zeros of these zeta functions are also discussed when $1/4 \le a \le 1/2$ is rational or transcendental. As a corollary, we show that $Q(s,a)$ with rational $1/4 < a < 1/3$ or $1/3 < a < 1/2$ does not satisfy the analogue of the Riemann hypothesis even though $Q(s,a)$ satisfies the functional equation that appeared in Hamburger's or Hecke's theorem and all real zeros of $Q(s,a)$ are located at only the negative even integers again as in the case of $ζ(s)$.

math.NT↗

arXiv2019

Implementation and Performance of Barnes-Hut N-body algorithm on Extreme-scale Heterogeneous Many-core Architectures

In this paper, we report the implementation and measured performance of our extreme-scale global simulation code on Sunway TaihuLight and two PEZY-SC2 systems: Shoubu System B and Gyoukou. The numerical algorithm is the parallel Barnes-Hut tree algorithm, which has been used in many large-scale astrophysical particle-based simulations. Our implementation is based on our FDPS framework. However, the extremely large numbers of cores of the systems used (10M on TaihuLight and 16M on Gyoukou) and their relatively poor memory and network bandwidth pose new challenges. We describe the new algorithms introduced to achieve high efficiency on machines with low memory bandwidth. The measured performance is 47.9, 10.6 PF, and 1.01PF on TaihuLight, Gyoukou and Shoubu System B (efficiency 40\%, 23.5\% and 35.5\%). The current code is developed for the simulation of planetary rings, but most of the new algorithms are useful for other simulations, and are now available in the FDPS framework.

astro-ph.IM↗

arXiv2019

Spectral Puzzle of the Off-Axis Gamma-Ray Burst in GW170817

Gravitational waves from a merger of two neutron stars (NSs) were discovered for the first time in GW170817, together with diverse electromagnetic counterparts, providing a direct clue to the origin of short gamma-ray bursts (sGRBs). The associated sGRB 170817A was much fainter than typical, suggesting off-axis emission from a relativistic jet. However the observed prompt spectrum is inconsistent with the spectral (Amati) relation and causes the compactness problem in the simplest off-axis model. We focus on this spectral puzzle and suggest a possible key that the off-axis emission generally comes from the off-center jet, neither the jet core nor the line-of-sight jet, if the jet structure is exponentially faint outward as inferred from observations. The off-center jet could be loaded with baryon or cocoon. The off-axis model predicts that roughly $\sim 10\%$ events are brighter at smaller viewing angles than sGRB 170817A, although the exact event rate sensitively depends on uncertainties of the off-center structure. The model also predicts outliers to Amati relation, providing future tests to reveal the central engine activities.

astro-ph.HE↗

arXiv2018

Scattered Short Gamma-Ray Bursts as Electromagnetic Counterparts to Gravitational Waves and Implications of GW170817 and GRB 170817A

In the faint short gamma-ray burst sGRB 170817A followed by the gravitational waves (GWs) from a merger of two neutron stars (NSs) GW170817, the spectral peak energy is too high to explain only by canonical off-axis emission. We investigate off-axis appearance of an sGRB prompt emission scattered by a cocoon, which is produced through the jet-merger-ejecta interaction, with either sub-relativistic or mildly-relativistic velocities. We show that the observed properties of sGRB 170817A, in particular the high peak energy, can be consistently explained by the Thomson-scattered emission with a typical sGRB jet, together by its canonical off-axis emission, supporting that an NS-NS merger is the origin of sGRBs. The scattering occurs at $\lesssim 10^{10}$--$10^{12}\,{\rm cm}$ not far from the central engine, implying the photospheric or internal shock origin of the sGRB prompt emission. The boundary between the jet and cocoon is sharp, which could be probed by future observations of off-axis afterglows. The scattering model predicts a distribution of the spectral peak energy that is similar to the observed one but with a cutoff around $\sim$ MeV energy, and its correlations with the luminosity, duration, and time lag from GWs, providing a way to distinguish it from alternative models.

astro-ph.HE↗

arXiv2018

Multiband Gravitational-Wave Astronomy: Observing binary inspirals with a decihertz detector, B-DECIGO

An evolving Japanese gravitational-wave (GW) mission in the deci-Hz band: B-DECIGO (DECihertz laser Interferometer Gravitational wave Observatory) will enable us to detect GW150914-like binary black holes, GW170817-like binary neutron stars, and intermediate-mass binary black holes out to cosmological distances. The B-DECIGO band slots in between the aLIGO-Virgo-KAGRA-IndIGO (hecto-Hz) and LISA (milli-Hz) bands for broader bandwidth; the sources described emit GWs for weeks to years across the multiband to accumulate high signal-to-noise ratios. This suggests the possibility that joint detection would greatly improve the parameter estimation of the binaries. We examine B-DECIGO's ability to measure binary parameters and assess to what extent multiband analysis could improve such measurement. Using non-precessing post-Newtonian waveforms with the Fisher matrix approach, we find for systems like GW150914 and GW170817 that B-DECIGO can measure the mass ratio to within $< 0.1\%$, the individual black-hole spins to within $< 10\%$, and the coalescence time to within $< 5\,$s about a week before alerting aLIGO and electromagnetic facilities. Prior information from B-DECIGO for aLIGO can further reduce the uncertainty in the measurement of, e.g., certain neutron star tidally-induced deformations by factor of $\sim 6$, and potentially determine the spin-induced neutron star quadrupole moment. Joint LISA and B-DECIGO measurement will also be able to recover the masses and spins of intermediate-mass binary black holes at percent-level precision. However, there will be a large systematic bias in these results due to post-Newtonian approximation of exact GW signals.

gr-qc↗

arXiv2018

Can an Off-axis Gamma-Ray Burst Jet in GW170817 Explain All the Electromagnetic Counterparts?

Gravitational waves from a merger of two neutron stars (NSs) were discovered for the first time in GW170817, together with diverse electromagnetic (EM) counterparts. To make constraints on a relativistic jet from the NS merger, we calculate the EM signals in (1) the short gamma-ray burst sGRB 170817A from an off-axis jet, (2) the optical-infrared macronova (or kilonova), especially the blue macronova, from a jet-powered cocoon, and (3) the X-ray and radio afterglows from the interaction between the jet and interstellar medium. We find that a typical sGRB jet is consistent with these observations, and there is a parameter space to explain all the observations in a unified fashion with an isotropic energy $\sim 10^{51}$-$10^{52}$ erg, opening angle $\sim 20^{\circ}$, and viewing angle $\sim 30^{\circ}$. The off-axis emission is less de-beamed than the point-source case because the viewing angle is comparable to the opening angle. We also analytically show that the jet energy accelerates a fair fraction of the merger ejecta to a sub-relativistic velocity $\sim 0.3$-$0.4$c as a cocoon in a wide parameter range. The ambient density might be low $\sim 10^{-3}$-$10^{-6}$ cm$^{-3}$, which can be tested by future observations of radio flares and X-ray remnants.

astro-ph.HE↗

arXiv2018

Prompt emission from the counter jet of a short gamma-ray burst

The counter jet of a short gamma-ray burst (sGRB) has not yet been observed, while recent discoveries of gravitational waves (GWs) from a binary neutron star (NS) merger GW170817 and the associated sGRB 170817A have demonstrated that off-axis sGRB jets are detectable. We calculate the prompt emission from the counter jet of an sGRB and show that it is typically 23-26 mag in the optical-infrared band 10-10^3 sec after the GWs for an sGRB 170817A-like event, which is brighter than the early macronova (or kilonova) emission and detectable by LSST in the near future. We also propose a new method to constrain the unknown jet properties, such as the Lorentz factor, opening angle, emission radii, and jet launch time, by observing both the forward and counter jets. To scrutinize the counter jets, space GW detectors like DECIGO are powerful in forecasting the merger time (<~ 1 sec) and position (<~ 1 arcmin) (~ a week) before the merger.

astro-ph.HE↗

arXiv2017

How to confirm the existence of population III stars by observations of gravitational waves

We propose a method for confirmation of the existence of Population III (Pop III) stars with massive black hole binaries as GW150914 in gravitational wave (GW) observation. When we get enough number of events, we want to determine which model is closer to reality, with and without Pop III stars. We need to prepare various "Pop I/II models" and various "Pop I/II/III models" and investigate which model is consistent with the events. To demonstrate our analysis, we simulate detections of GW events for some examples of population synthesis models with and without Pop III stars. We calculate the likelihood ratio with the realistic number of events and evaluate the probability of identifying the existence of Pop III stars. In typical cases, our analysis can distinguish between Pop I/II model and Pop I/II/III model with 90% probability by 22 GW signals from black hole-black hole binary mergers.

astro-ph.HE↗

arXiv2017

In-ear EEG biometrics for feasible and readily collectable real-world person authentication

The use of EEG as a biometrics modality has been investigated for about a decade, however its feasibility in real-world applications is not yet conclusively established, mainly due to the issues with collectability and reproducibility. To this end, we propose a readily deployable EEG biometrics system based on a `one-fits-all' viscoelastic generic in-ear EEG sensor (collectability), which does not require skilled assistance or cumbersome preparation. Unlike most existing studies, we consider data recorded over multiple recording days and for multiple subjects (reproducibility) while, for rigour, the training and test segments are not taken from the same recording days. A robust approach is considered based on the resting state with eyes closed paradigm, the use of both parametric (autoregressive model) and non-parametric (spectral) features, and supported by simple and fast cosine distance, linear discriminant analysis and support vector machine classifiers. Both the verification and identification forensics scenarios are considered and the achieved results are on par with the studies based on impractical on-scalp recordings. Comprehensive analysis over a number of subjects, setups, and analysis features demonstrates the feasibility of the proposed ear-EEG biometrics, and its potential in resolving the critical collectability, robustness, and reproducibility issues associated with current EEG biometrics.

cs.CR↗

arXiv2017

Estimate of the radius responsible for quasinormal modes in the extreme Kerr limit and asymptotic behavior of the Sasaki-Nakamura transformation

The Sasaki-Nakamura transformation gives a short-ranged potential and a convergent source term for the master equation of perturbations in the Kerr space-time. In this paper, we study the asymptotic behavior of the transformation, and present a new relaxed necessary and sufficient condition of the transformation to obtain the short-ranged potential in the assumption that the transformation converges in the far distance. Also, we discuss quasinormal mode frequencies which are determined by the information around the peak of the potential in the WKB analysis. Finally, in the extreme Kerr limit, $a/M \to 1$, where $M$ and $a$ denote the mass and spin parameter of a Kerr black hole, respectively, we find the peak location of the potential, $r_p/M \lesssim 1 + 1.8 \,(1-a/M)^{1/2}$ by using the new transformation. The uncertainty of the location is as large as that expected from the equivalence principle.

gr-qc↗

arXiv2017

Multidimensional polynomial Euler products and infinitely divisible distributions on R^d

It is known to be difficult to find out whether a certain multivariable function to be a characteristic function when its corresponding measure is not tirivial to be or not to be a probability measure on R^d. Such results were not obtained for a long while. In this paper, multidimensional polynomial Euler product is defined as a generalization of the polynomial Euler product. By applying the Kronecker's approximation theorem, a necessary and sufficient condition for some polynomial Euler products to generate characteristic functions is given. Furthermore, by using the Baker's theorem, that of some multidimensional polynomial Euler products is also given. As one of the most important properties of probability distributions, the infinite divisibility of them is studied as well.

math.PR↗

arXiv2017

Automatic sleep monitoring using ear-EEG

The monitoring of sleep patterns without patient's inconvenience or involvement of a medical specialist is a clinical question of significant importance. To this end, we propose an automatic sleep stage monitoring system based on an affordable, unobtrusive, discreet, and long-term wearable in-ear sensor for recording the Electroencephalogram (ear-EEG). The selected features for sleep pattern classification from a single ear-EEG channel include the spectral edge frequency (SEF) and multi- scale fuzzy entropy (MSFE), a structural complexity feature. In this preliminary study, the manually scored hypnograms from simultaneous scalp-EEG and ear-EEG recordings of four subjects are used as labels for two analysis scenarios: 1) classification of ear-EEG hypnogram labels from ear-EEG recordings and 2) prediction of scalp-EEG hypnogram labels from ear-EEG recordings. We consider both 2-class and 4-class sleep scoring, with the achieved accuracies ranging from 78.5 % to 95.2 % for ear-EEG labels predicted from ear-EEG, and 76.8 % to 91.8 % for scalp-EEG labels predicted from ear-EEG. The corresponding kappa coefficients, which range from 0.64 to 0.83 for Scenario 1 and from 0.65 to 0.80 for Scenario 2, indicate a Substantial to Almost Perfect agreement, thus proving the feasibility of in-ear sensing for sleep monitoring in the community.

physics.med-ph↗

arXiv2016

Jet-powered supernovae of $\sim 10^5\,M_{\odot}$ population III stars are observable by $Euclid$, $WFIRST$, $WISH$, and $JWST$

Supermassive black holes observed at high redshift $z\gtrsim6$ could grow from direct collapse black holes (DCBHs) with mass $\sim10^5\,M_{\odot}$, which result from the collapse of supermassive stars (SMSs). If a relativistic jet is launched from a DCBH, it can break out of the collapsing SMS and produce a gamma-ray burst (GRB). Although most of the GRB jets are off-axis from our line of sight, we show that the energy injected from the jet into a cocoon is huge $\sim10^{55-56}\,{\rm{erg}}$, so that the cocoon fireball is observed as ultra-luminous supernovae of $\sim10^{45-46}\rm{\,erg\,s^{-1}}$ for $\sim5000 [(1+z)/16] \rm{\,days}$. They are detectable by the future telescopes with near infrared bands, such as, $Euclid$, $WFIRST$, $WISH$, and $JWST$ up to $z\sim20$ and $\sim 100$ events per year, providing a direct evidence of the DCBH scenario.

astro-ph.HE↗

arXiv2016

The possible existence of Pop III NS-BH binary and its detectability

In the population synthesis simulations of Pop III stars, many BH (Black Hole)-BH binaries with merger time less than the age of the Universe $(τ_{\rm H})$ are formed, while NS (Neutron Star)-BH binaries are not. The reason is that Pop III stars have no metal so that no mass loss is expected. Then, in the final supernova explosion to NS, much mass is lost so that the semi major axis becomes too large for Pop III NS-BH binaries to merge within $τ_{\rm H}$. However it is almost established that the kick velocity of the order of $200-500{\rm~ km~s^{-1}}$ exists for NS from the observation of the proper motion of the pulsar. Therefore, the semi major axis of the half of NS-BH binaries can be smaller than that of the previous argument for Pop III NS-BH binaries to decrease the merging time. We perform population synthesis Monte Carlo simulations of Pop III NS-BH binaries including the kick of NS and find that the event rate of Pop III NS-BH merger rate is $\sim 1 {\rm Gpc^{-3} yr^{-1}}$. This suggests that there is a good chance of the detection of Pop III NS-BH mergers in O2 of Advanced LIGO and Advanced Virgo from this autumn.

astro-ph.HE↗