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Takashi Nakamura

Publications and source records attributed to Takashi Nakamura.

At least 55 records · Page 3Linked to original sources
arXiv2016

Hearables: Multimodal physiological in-ear sensing

Future health systems require the means to assess and track the neural and physiological function of a user over long periods of time and in the community. Human body responses are manifested through multiple modalities, such as the mechanical, electrical and chemical; yet current physiological monitors (actigraphy, heart rate) largely lack in both the desired cross-modal and non-stigmatizing aspects. We address these challenges through an inconspicuous and comfortable earpiece, equipped with miniature multimodal sensors, which benefits from the relatively stable position of the ear canal with respect to vital organs to robustly measure the brain, cardiac and respiratory functions. Comprehensive experiments validate each modality within the proposed earpiece, while its potential in health monitoring is illustrated through case studies. We further demonstrate how combining data from multiple sensors within such an integrated wearable device improves both the accuracy of measurements and the ability to deal with artifacts in real-life scenarios.

physics.med-ph↗
arXiv2016

Pre-DECIGO can get the smoking gun to decide the astrophysical or cosmological origin of GW150914-like binary black holes

Pre-DECIGO consists of three spacecraft arranged in an equilateral triangle with 100km arm lengths orbiting 2000km above the surface of the earth. It is hoped that the launch date will be in the late 2020s. Pre-DECIGO has one clear target: binary black holes (BBHs) like GW150914 and GW151226. Pre-DECIGO can detect $\sim 30M_\odot-30M_\odot$ BBH mergers up to redshift $z\sim 30$. The cumulative event rate is $\sim 1.8\times 10^{5}\,{\rm events~yr^{-1}}$ in the Pop III origin model of BBHs like GW150914, and it saturates at $z\sim 10$, while in the primordial BBH (PBBH) model, the cumulative event rate is $ \sim 3\times 10^{4}\,{\rm events~ yr^{-1}}$ at $z=30$ even if only $0.1\%$ of the dark matter consists of PBHs, and it is still increasing at $z=30$. In the Pop I/II model of BBHs, the cumulative event rate is $(3-10)\times10^{5}\,{\rm events~ yr^{-1}}$ and it saturates at $z \sim 6$. We present the requirements on orbit accuracy, drag free techniques, laser power, frequency stability, and interferometer test mass. For BBHs like GW150914 at 1Gpc, SNR$\sim 90$ is achieved with the definition of Pre-DECIGO in the $0.01-100$Hz band. Pre-DECIGO can measure the mass spectrum and the $z$-dependence of the merger rate to distinguish various models of BBHs like GW150914. Pre-DECIGO can also predict the direction of BBHs at $z=0.1$ with an accuracy of $\sim 0.3\,{\rm deg}^2$ and a merging time accuracy of $\sim 1$s at about a day before the merger so that ground-based GW detectors further developed at that time as well as electromagnetic follow-up observations can prepare for the detection of merger in advance. For intermediate mass BBHs at a large redshift $z > 10$, the QNM frequency after the merger can be within the Pre-DECIGO band so that the ringing tail can also be detectable to confirm the Einstein theory of general relativity with SNR$\sim 35$. [abridged]

astro-ph.HE↗
arXiv2016

Zeta distributions generated by multidimensional polynomial Euler products with complex coefficients

In the present paper, we treat multidimensional polynomial Euler products with complex coefficients on ${\mathbb{R}}^d$. We give necessary and sufficient conditions for the multidimensional polynomial Euler products to generate infinitely divisible, quasi-infinitely divisible but non-infinitely divisible or not even characteristic functions by using Baker's theorem. Moreover, we give many examples of zeta distributions on ${\mathbb{R}}^d$ generated by the multidimensional polynomial Euler products with complex coefficients. Finally, we consider applications to analytic number theory.

math.PR↗
arXiv2016

Gravitational wave quasinormal mode from Population III massive black hole binaries in various models of population synthesis

Focusing on the remnant black holes after merging binary black holes, we show that ringdown gravitational waves of Population III binary black holes mergers can be detected with the rate of $5.9-500~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$ for various parameters and functions. This rate is estimated for the events with SNR$>8$ for the second generation gravitational wave detectors such as KAGRA. Here, ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value of the Population III star formation rate and the fraction of binaries, respectively. When we consider only the events with SNR$>35$, the event rate becomes $0.046-4.21~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$. This suggest that for remnant black hole's spin $q_f>0.95$ we have the event rate with SNR$>35$ less than $0.037~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$, while it is $3-30~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$ for the third generation detectors such as Einstein Telescope. If we detect many Population III binary black holes merger, it may be possible to constrain the Population III binary evolution paths not only by the mass distribution but also by the spin distribution.

astro-ph.HE↗
arXiv2016

Zeros of polynomials of derivatives of zeta functions

Let $P_s \in \mathcal{D}_s[X_0,X_1, \ldots,X_l]$ be a polynomial whose coefficients are the ring of all general Dirichlet series which converge absolutely in the half-plane $\Re (s) > 1/2$. In the present paper, we show that the function $P_s(L(s), L^{(1)}(s),\ldots, L^{(l)}(s))$ has infinitely many zeros in the vertical strip $D:= \{ s \in {\mathbb{C}} : 1/2 < \Re (s) <1\}$ if $L(s)$ is hybridly universal and $P_s \in \mathcal{D}_s[X_0,X_1, \ldots,X_l]$ is a polynomial such that at least one of the degree of $X_1,\ldots,X_l$ is greater than zero. As a corollary, we prove that the function $(d^k / ds^k) P_s(L(s))$ with $k \in {\mathbb{N}}$ has infinitely many zeros in the strip $D$ when $L(s)$ is hybridly universal and $P_s \in \mathcal{D}_s[X]$ is a polynomial with degree greater than zero. The upper bounds for the numbers of zeros of $P_s(L(s), L^{(1)}(s),\ldots, L^{(l)}(s))$ and $(d^k / ds^k) P_s(L(s))$ are studied as well.

math.NT↗
arXiv2016

The detection of quasinormal mode with $a/M \sim 0.95$ would prove a sphere $99\%$ soaking in the ergoregion of the Kerr space-time

Recent numerical relativity simulations of mergers of binary black holes suggest that the maximum final value of $a/M$ is $\sim 0.95$ for the coalescence of two equal mass black holes with aligned spins of the same magnitude $a/M=0.994$ which is close to the upper limit $a/M=0.998$ of accretion spin-up shown by Thorne. Using the WKB method, we suggest that if quasinormal modes with $a/M \sim 0.95$ are detected by the second generation gravitational wave detectors, we could confirm the strong gravity space-time based on Einstein's general relativity up to $1.33M$ which is only $\sim 1.014$ times the event horizon radius and within the ergoregion. One more message about black hole geometry is expected here. If the quasinormal mode is different from that of general relativity, we need to find the true theory of gravity which deviates from general relativity only near the black hole horizon.

gr-qc↗
arXiv2016

How close can we approach the event horizon of the Kerr black hole from the detection of the gravitational quasinormal modes?

Using the WKB method, we show that the peak location ($r_{\rm peak}$) of the potential, which determines the quasinormal mode frequency of the Kerr black hole, obeys an accurate empirical relation as a function of the specific angular momentum $a$ and the gravitational mass $M$. If the quasinormal mode with $a/M \sim 1$ is observed by gravitational wave detectors, we can confirm the black-hole space-time around the event horizon, $r_{\rm peak}=r_+ +O(\sqrt{1-q})$ where $r_+$ is the event horizon radius. While if the quasinormal mode is different from that of general relativity, we are forced to seek the true theory of gravity and/or face to the existence of the naked singularity.

gr-qc↗
arXiv2016

Possible confirmation of the existence of ergoregion by the Kerr quasinormal mode in gravitational waves from Pop III massive black hole binary

The existence of the ergoregion of the Kerr space-time has not been confirmed observationally yet. We show that the confirmation would be possible by observing the quasinormal mode in gravitational waves. As an example, using the recent population synthesis results of Pop III binary black holes, we find that the peak of the final merger mass ($M_f$) is about $50~\rm M_{\odot}$, while the fraction of the final spin $q_f = a_f/M_f > 0.7$ needed for the confirmation of a part of ergoregion is $\sim 77\%$. To confirm the frequency of the quasinormal mode, ${\rm SNR} > 35$ is needed. The standard model of Pop III population synthesis tells us that the event rate for the confirmation of more than $50\%$ of the ergoregion by the second generation gravitational wave detectors is $\sim 2.3$ ${\rm events\ yr^{-1}\ (SFR_p/(10^{-2.5}\ M_\odot yr^{-1}\ Mpc^{-3}))} \cdot (\rm [f_b/(1+f_b)]/0.33)$ where ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value of the Pop III star formation rate and the fraction of binaries, respectively.

astro-ph.HE↗
arXiv2016

The detection of Quasinormal Mode of Pop III Binary Black Hole merger with final $M \sim 60M_\odot$ and $a/M \sim 0.7$ would confirm the strong gravity space-time around $\sim 2M$ which is only $\sim 1.17$ times the event horizon radius

Recent population synthesis simulations of Pop III stars suggest that the event rate of coalescence of $\sim 30M_\odot$--$30M_\odot$ binary black holes can be high enough for the detection by the second generation gravitational wave detectors. The frequencies of chirp signal as well as quasinormal modes are near the best sensitivity of these detectors so that it would be possible to confirm Einstein's general relativity. Using the WKB method, we suggest that for the typical value of spin parameter $a/M\sim 0.7$ from numerical relativity results of the coalescence of binary black holes, the strong gravity of the black hole space-time at around the radius $2M$, which is just $\sim 1.17$ times the event horizon radius, would be confirmed as predicted by general relativity. The expected event rate with the signal-to-noise ratio $> 35$ needed for the determination of the quasinormal mode frequency with the meaningful accuracy is $0.17$--$7.2$~${\rm events~yr^{-1}~(SFR_p/(10^{-2.5}~M_\odot~yr^{-1}~Mpc^{-3}))} \cdot (\rm [f_b/(1+f_b)]/0.33)$ where ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value of the Pop III star formation rate and the fraction of binaries, respectively. As for the possible optical counter part, if the merged black hole of mass $M\sim 60M_\odot$ is in the interstellar matter with $n\sim 100~{\rm cm^{-3}}$ and the proper motion of black hole is $\sim 1~{\rm km~s^{-1}}$, the luminosity is $\sim 10^{40}~{\rm erg~ s^{-1}}$ which can be detected up to $\sim 300~{\rm Mpc}$, for example, by Subaru-HSC and LSST with the limiting magnitude 26.

astro-ph.HE↗
arXiv2015

Real zeros of Hurwitz-Lerch zeta functions in the interval $(-1,0)$

For $0 < a \le 1$, $s,z \in {\mathbb{C}}$ and $0 < |z|\le 1$, the Hurwitz-Lerch zeta function is defined by $Φ(s,a,z) := \sum_{n=0}^\infty z^n(n+a)^{-s}$ when $σ:=\Re (s) >1$. In this paper, we show that $Φ(σ,a,z) \ne 0$ when $σ\in (-1,0)$ if and only if [I] $z=1$ and $(3-\sqrt{3}) /6 \le a \le 1/2$ or $(3+\sqrt{3}) /6 \le a \le 1$, [II] $z \in [-1,1)$ and $(1-z)(1-a) \le 1$, [III] $z \not \in {\mathbb{R}}$ and $0<a \le 1$. In addition, we give a new proof of the functional equation of $Φ(s,a,z)$.

math.NT↗
arXiv2015

X-raying extended emission and rapid decay of short gamma-ray bursts

Extended emission is a mystery in short gamma-ray bursts (SGRBs). By making time resolved spectral analyses of brightest nine events observed by ${\it Swift}$ XRT, we obviously classify the early X-ray emission of SGRBs into two types. One is the extended emission with exponentially rapid decay, which shows significant spectral softening during hundreds seconds since the SGRB trigger and is also detected by ${\it Swift}$-BAT. The other is a dim afterglow only showing power-law decay over $10^4$ s. The correlations between the temporal decay and spectral indices of the extended emissions are inconsistent with the $α$-$β$ correlation expected for the high-latitude curvature emission from a uniform jet. The observed too-rapid decay suggests the emission from a photosphere or a patchy surface, and manifests the stopping central engine via such as magnetic reconnection at the black hole.

astro-ph.HE↗
arXiv2015

The detection rate of Inspiral and Quasi-normal modes of Pop III binary black holes which can confirm or refute the General Relativity in the strong gravity region

Using our population synthesis code, we found that the typical chirp mass of Pop III BH-BHs is $\sim30~\msun$ with the total mass of $\sim60~\msun$ so that the inspiral chirp signal as well as quasi normal mode (QNM) of the merging BH are interesting targets of KAGRA. The detection rate of the coalescing Pop III BH-BHs is $\sim$180 $\rm events~yr^{-1}$$(\rm SFR_p/(10^{-2.5}~\msun \rm~yr^{-1}~Mpc^{-3}))\cdot([f_b/(1+f_b)]/0.33)\cdot Err_{sys}$ in our standard model where $\rm SFR_{p},~f_b$ and $\rm Err_{sys}$ are the peak value of the Pop III star formation rate, the binary fraction and the systematic error with $\rm Err_{sys}=1$ for our standard model, respectively. To evaluate the robustness of chirp mass distribution and the range of $\rm Err_{sys}$, we examine the dependence of the results on the unknown parameters and the distribution functions. We found that the chirp mass has a peak at $\sim 30 ~\msun$ in most of parameters and distribution functions as well as $\rm Err_{sys}$ ranges from 0.046 to 4. The minimum rate corresponds to the worst model which we think unlikely so that unless $ {\rm ~(SFR_p/(10^{-2.5}~\msun~yr^{-1}~Mpc^{-3}))\cdot([f_b/(1+f_b)]/0.33) \ll 0.1}$, we expect the Pop III BH-BHs merger rate of at least one event per year by KAGRA. Nakano, Tanaka \& Nakamura (2015) show that if S/N of QNM is larger than 35, we can confirm or refute the General Relativity (GR) more than 5 sigma level. In our standard model, the detection rate of Pop III BH-BHs whose S/N is larger than 35 is $3.2~\rm events~yr^{-1}$$(\rm SFR_p/(10^{-2.5}~\msun \rm~yr^{-1}~Mpc^{-3}))\cdot([f_b/(1+f_b)]/0.33)\cdot Err_{sys}$. Thus, there is a good chance to check whether GR is correct or not in the strong gravity region.

astro-ph.SR↗
arXiv2015

Real zeros of Hurwitz-Lerch zeta and Hurwitz-Lerch type of Euler-Zagier double zeta functions

Let $0 < a \le 1$, $s,z \in {\mathbb{C}}$ and $0 < |z|\le 1$. Then the Hurwitz-Lerch zeta function is defined by $Φ(s,a,z) := \sum_{n=0}^\infty z^n(n+a)^{-s}$ when $σ:=\Re (s) >1$. In this paper, we show that the Hurwitz zeta function $ζ(σ,a) := Φ(σ,a,1)$ does not vanish for all $0 <σ<1$ if and only if $a \ge 1/2$. Moreover, we prove that $Φ(σ,a,z) \ne 0$ for all $0 <σ<1$ and $0 < a \le 1$ when $z \ne 1$. Real zeros of Hurwitz-Lerch type of Euler-Zagier double zeta functions are studied as well.

math.NT↗
arXiv2015

Can direct collapse black holes launch gamma-ray bursts and grow to supermassive black holes?

The existence of black holes (BHs) of mass ~ 10^{9} M_sun at z > 6 is a big puzzle in astrophysics because even optimistic estimates of the accretion time are insufficient for stellar mass BHs of ~ 10 M_sun to grow into such supermassive BHs. A resolution of this puzzle might be the direct collapse of supermassive stars with mass M ~ 10^{5} M_sun into massive seed BHs. We find that if a jet is launched from the accretion disk around the central BH, the jet can break out the star because of the structure of the radiation pressure-dominated envelope. Such ultra-long gamma-ray bursts with duration of ~ 10^{4} - 10^{6} s and flux of 10^{-11} - 10^{-8} erg s^{-1} cm^{-2} could be detectable by Swift. We estimate an event rate of < 1yr^{-1}. The total explosion energy is > 10^{55} - 10^{56} erg. The resulting negative feedback delays the growth of the remnant BH by about 70 Myr or evacuates the host galaxy completely.

astro-ph.HE↗
arXiv2015

Joint universality for Lerch zeta-functions

For $0<α, λ\leq 1$, the Lerch zeta-function is defined by $L(s;α, λ)$$:= \sum_{n=0}^\infty e^{2πiλn} (n+α)^{-s}$, where $σ>1$. In this paper, we prove joint universality for Lerch zeta-functions with distinct $λ_1,\ldots,λ_m$ and transcendental $α$.

math.NT↗
arXiv2015

Possible golden events for ringdown gravitational waves

There is a forbidden region in the parameter space of quasinormal modes of black holes in general relativity. Using both inspiral and ringdown phases of gravitational waves from binary black holes, we propose two methods to test general relativity. We also evaluate how our methods will work when we apply them to Pop III black-hole binaries with typical masses. Adopting the simple mean of the estimated range of the event rate, we have the expected rate of 500 ${\rm yr^{-1}}$. Then, the rates of events with signal-to-noise ratios greater than 20 and greater than 50 are 32 ${\rm yr^{-1}}$ and 2 ${\rm yr^{-1}}$, respectively. Therefore, there is a good chance to confirm (or refute) the Einstein theory in the strong gravity region by observing the expected quasinormal modes.

astro-ph.HE↗
arXiv2015

Value distribution for the derivatives of the logarithm of $L$-functions from the Selberg class in the half-plane of absolute convergence

In the present paper, we show that, for every $δ>0$, the function $(\log {\mathcal{L}}(s))^{(m)}$, where $m\in {\mathbb{N}} \cup \{ 0\}$ and ${\mathcal{L}} (s) := \sum_{n=1}^\infty a(n) n^{-s}$ is an element of the Selberg class ${\mathcal{S}}$, takes any value infinitely often in any strip $1<\Re(s) <1+δ$, provided $\sum_{p\leq x} |a (p)|^2 \sim κπ(x)$ for some $κ>0$. In particular, ${\mathcal{L}} (s)$ takes any non-zero value infinitely often in the strip $1<\Re(s)<1+δ$, and the first derivative of ${\mathcal{L}} (s)$ vanishes infinitely often.

math.NT↗