Formation of mass gap compact object and black hole binary from Population III stars
PProg. Theor. Exp. Phys. , 00000 (8 pages)DOI: 10.1093 / ptep/0000000000 Formation of mass gap compact ob ject andblack hole binary from Population III stars
Tomoya Kinugawa , Takashi Nakamura , and Hiroyuki Nakano Institute for Cosmic Ray Research, The University of Tokyo, Kashiwa, Chiba277-8582, Japan Department of Physics, Graduate School of Science, Kyoto University, Kyoto606-8502, Japan Faculty of Law, Ryukoku University, Kyoto 612-8577, Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We performed population synthesis simulations of Population III binary stars withMaxwellian kick velocity distribution when MGCOs (Mass Gap Compact Objectswith mass 2–5 M (cid:12) ) are formed. We found that for seven kick velocity dispersionmodels of σ k = 100–500 km/s, the mean mass of black hole (BH)-MGCO binary is ∼ (30 M (cid:12) , . M (cid:12) ). In numerical data of our simulations, we found the existence ofBH-MGCO binary with mass (22 . M (cid:12) , . M (cid:12) ) which looks like GW190814. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Subject Index xxxx, xxx Introduction
GW190814 [1] is a gravitational wave (GW) event observed by LIGO-Virgo collaboration during the first half of the third observation period, called O3a. Thisis a compact binary coalescence and the parameter estimation suggests that the binaryconsists of a black hole (BH) with mass of 22.2–24.3 M (cid:12) and a compact object with massof 2.50–2.67 M (cid:12) yielding a chirp mass of M chirp ∼ . . M (cid:12) . The mass of the smaller(secondary) object lies in 2–5 M (cid:12) , that is, between known neutron stars (NSs) and BHs.Therefore, the secondary compact object will be a NS with the maximum observed massor a BH with the minimum observed mass, so that we define a mass gap compact object(MGCO) as a compact object having mass 2–5 M (cid:12) . The merger rate density of this type ofbinaries is estimated as 1–23 Gpc − yr − [1]. So far, many proposals and discussions on theBH-MGCO binary with MGCO mass of ∼ . M (cid:12) were appeared after the announcementof GW190814 (see, e.g., Refs. [3–24]).We discussed in our previous study [25] in 2016, the detection rate and the chirp massdistribution of NS-BH binaries with mass of NS below 3 M (cid:12) by the population synthesissimulations of Population III (Pop III) stars. We found that the merger rate density of Pop M chirp = ( m m ) / / ( m + m ) / where m and m denote the mass of the primary and thesecondary objects, respectively. MGCO is different from “mass gap” (2.5–5 M (cid:12) ) used in Ref. [1] and “MassGap” (3–5 M (cid:12) ) definedin Ref. [2]. MGCOs include not only MassGap BHs, but also NSs with mass (cid:38) M (cid:12) , i.e., the massof MGCOs lies in 2–5 M (cid:12) . c (cid:13) The Author(s) 2015. Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License(http://creativecommons.org/licenses/by-nc/3.0), which permits unrestricted use,distribution, and reproduction in any medium, provided the original work is properly cited. a r X i v : . [ a s t r o - ph . H E ] J u l II NS-BH binaries is ∼ − yr − although it depends on the natal kick velocity of NSs.We also found that the chirp mass distribution of Pop III NS-BH binaries that merge withinthe Hubble time has a peak around 6 M (cid:12) .The results presented in Ref. [25] seems to be consistent with the estimation of Ref. [1]since in Ref. [25] we defined NS if its mass is below 3 M (cid:12) while the mass of secondary ofGW190814 is 2.50–2.67 M (cid:12) and the chirp mass of GW190814 is evaluated as 6.03–6.15 M (cid:12) .Thus, it is important to revisit our previous paper using the definition of MGCO and try toanswer the question raised as follows. What are “the processes by which the lightest BHs orthe most massive NSs form” in Ref. [1] ?In this letter, we summarize our previous study with additional analyses, and present ascenario to explain the BH-MGCO binary of GW190814. Analysis
In Ref. [25], we have calculated NS-BH formations and estimated the num-ber of NS-BH binaries merging within the Hubble time by using the population synthesissimulations of Pop III stars [26]. The key ingredient is to introduce the NS kick velocityof 200–500 km / s that is evaluated from the observation of the proper motion of the pulsar.The effect of kick velocity is important to decrease the merging time of NS-BH binaries. Forcomparison, we have calculated not only the Pop III NS-BH binaries, but also Pop I and IINS-BH binaries.To do the above analysis in our population synthesis Monte Carlo simulations, we haveconsidered six metallicity cases from Z = 0 (Pop III) to Z = Z (cid:12) (Pop I) where Z (cid:12) is the solarmetallicity, the initial mass, mass ratio, separation and eccentricity distribution functionsas binary initial conditions, the Roche lobe overflow, the common envelope phase, the tidaleffect, the supernova (SN) effect, and the gravitational radiation as binary interactions, andtwo kick velocity models with σ k = 265 km / s and σ k = 500 km / s where σ k is the dispersionof a Maxwellian distribution for kick velocity.Next, we briefly summarize the results. The chirp mass of Pop III NS-BH binaries mergingwithin the Hubble time is heavier than those of Pop I and II ones. The peak values of chirpmass distributions is ∼ M (cid:12) in the case of Pop III while it is ∼ M (cid:12) in the cases of Pop Iand II. These peak values almost do not depend on the kick velocity values σ k .The NS-BH merger rates at the present day depend on the progenitors and kick velocities(see Table 3 in Ref. [25] for the details). The sum of the merger rates of Pop I and II becomes19.7 Gpc − yr − and 6.38 Gpc − yr − for σ k = 265 km / s and 500 km / s, respectively. For thePop III case, we have found the NS-BH merger rates at the present day as 1.25 Gpc − yr − and 0.956 Gpc − yr − for σ k = 265 km / s and 500 km / s, respectively. In the previous study,we have assumed that the mass range of neutron stars are 1 . M (cid:12) . Thus, GW190814belongs to the previous Pop III NS-BH result.In this letter, we further focus on compact object binaries which consist of a BH and aMGCO with mass of 2–5 M (cid:12) . We calculate 10 Pop III binary evolutions and the merger ratesof BH-MGCO binaries, using the same setup of the previous Pop III NS-BH case [25]. Forsimplicity, we use the simple SN remnant model given in Refs. [26, 27]. A low mass progenitor( M ZAMS (cid:46) M (cid:12) ) experiences a SN and the Fe core remains as the remnant, where M ZAMS is the zero age main sequence mass. On the other hand, a high mass progenitor ( M ZAMS (cid:38) M (cid:12) ) becomes a direct collapse, and the whole stellar mass becomes the remnant mass. .0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 M chirp [ M ] d N / d M c h i r p / N t o t a l [ / M ] Fig. 1
The chirp mass distribution of BH-MGCO binaries which merge within the Hubbletime for 7 kick models with σ k = 100 , , , , , N total =10 is the total number of binaries which we have simulated. The chirp mass distribution doesnot strongly depend on the kick velocity. The averaged individual masses are summarizedin Table 1.An intermediate progenitor (22 M (cid:12) (cid:46) M ZAMS (cid:46) M (cid:12) ) experiences a failed SN and the fallbacked remnant mass linearly increases with increasing progenitor mass.Here, we assume that the SN remnants which have a mass less than 5 M (cid:12) experience SNkick, and we use the Maxwellian distribution for the kick velocity distribution. We calculatenot only kick velocity dispersion models of the previous paper of σ k = 265 km/s and 500km/s, but also σ k = 100 , , , N total = 10 isthe total number of binaries which we have simulated. The chirp mass distribution does notstrongly depend on the kick velocity and has a peak at M chirp ∼ M (cid:12) . Notice here that thechirp mass of GW190814 is ∼ M (cid:12) . Figure 2 shows the merger rate densities for each model.The peak of merger rate density depends on the kick velocity. Almost all BH-MGCO binariescannot merge within the Hubble time without the natal kick. The natal kick changes thebinary orbit and makes the binary be able to merge within the Hubble time. If the typicalkick velocity is small, the binary orbits do not change so much that the typical merger timetends to be long. Thus, the smaller kick velocity the model has, the lower redshift the peakof merger rate is.Since the typical chirp mass of BH-MGCO binary of ∼ M (cid:12) is almost the same as that ofGW190814, we searched if similar BH-MGCO binary to GW190814 exists in our simulationdata. As a result, we found one with mass (22 . M (cid:12) , . M (cid:12) ). Figure 3 shows the evolutionarypath of this binary. The binary is born as the zero age main sequence binary consisting of54 . M (cid:12) and 14 . M (cid:12) stars. The primary evolves to a giant and starts a mass transfer. z d N / d t [ / y r / G p c ] Fig. 2
The merger rate densities for 7 kick models with σ k = 100 , , , , , . M (cid:12) BHand 2 . M (cid:12) compact object which is either the lightest BH or the most massive NS. Thisexample might be a possible answer to the question of “What are the processes by whichthe lightest BHs or the most massive NSs form in Ref. [1] ?” in Introduction .To estimate the event rate of Pop III BH-MGCO binaries, we use an inspiral-merger-ringdown waveform presented in Ref. [28] which is based on Refs. [29, 30], The signal-to-noiseratio (SNR) of GW events is calculated in 4 strain-noise fitted curves (see Fig. 4) whichare prepared by using Ref. [31] for LIGO O3a-Livingston (O3a-L) (green) and LIGO O5(magenta), Ref. [32] (see also Ref. [33]) for Einstein Telescope (ET-B) (red), and Ref. [34]for Cosmic Explorer (CE2) (purple). Then, for example, the maximum observable redshift z max by setting the averaged SNR = 8 for the GW190814 binary with m = 23 . M (cid:12) and m = 2 . M (cid:12) becomes z max = 0 . .
211 for LIGO O5, 5 . . M (cid:12) for eachkick model, and the event rates in [yr − ] based on the maximum observable redshifts z max (shown as values in parenthesis for each detector) of this typical binaries for 4 GW detectorconfigurations. For the O3a-L detector, the maximum event rate of GWs is 0.268 yr − forthe kick model of σ k = 150 km/s. For the O5, ET-B and CE2 detectors, the maximum event ig. 3 Evolutionary path of a Pop III BH-MGCO binary similar to GW190814. MS,CHeB, HeSB, and nHe mean the main sequence, Core He burning, He shell burning, andnaked He stars, respectively. The naked He star is the remnant after the common envelopephase. V orb , and V kick are the orbital velocity just before the SN, and the natal kick velocity,respectively. a (in the solar radius R (cid:12) ) and e denote the orbital separation and eccentricity,respectively.rate of GWs are found as 3.62 yr − for the σ k = 100 km/s, 2070 yr − for the σ k = 265 km/sand 3830 yr − for the σ k = 300 km/s, respectively. Discussion
In a binary system, a heavier BH is formed first. After that, a lighterNS is formed. At this time, a part of the blown outer layer with a mass of ∼ M (cid:12) falls ig. 4 Strain-noise fitted curves for 4 GW detector configurations: LIGO O3a-Livingston(O3a-L, green), LIGO O5 (O5, magenta), Einstein Telescope (ET-B) (red) and CosmicExplorer (CE2) (purple). These fitting curves are obtained by using Refs. [31–34]. Wehave lower frequency cutoffs of 10 Hz, 1 Hz and 5 Hz for O3a-L and O5, ET-B and CE2,respectively.back, and the NS becomes a BH with a mass of ∼ . M (cid:12) . Normally, this binary BH takesmuch longer time to coalesce than the Hubble time, but considering the kick velocity ofthe MGCO, the binary coalescence will occur with in the Hubble time. Figure 5 showsmass distributions of MGCOs which merge within the Hubble time for each kick velocitymodel. As a future prediction, the lighter BHs can have various masses, and some may beNS. What seemed strange in the LIGO-Virgo paper [1] is commonplace in this scenario.The mass distribution of MGCOs (Fig. 5) does not depend on the kick velocity models,but depends on the SN remnant model. Future detections of MGCOs may give a strongconstraint on the SN remnant model. As a summary, the lighter compact objects will alwaysbecome BH or NS which is close to the maximum mass of NS in the scenario of this letter. Acknowledgment
T. K. acknowledges support from University of Tokyo Young Excel-lent researcher program. T. N. acknowledges support from JSPS KAKENHI Grant No.JP15H02087. H. N. acknowledges support from JSPS KAKENHI Grant Nos. JP16K05347and JP17H06358. able 1
Averaged masses ( (cid:104) m (cid:105) , (cid:104) m (cid:105) ) of BH-MGCO binaries in the solar mass M (cid:12) and event rates in [yr − ] for 4 GW detector configurations: LIGO O3a-Livingston (O3a-L),LIGO O5 (O5), Einstein Telescope (ET-B) and Cosmic Explore (CE2) in 7 kick models with σ k = 100 , , , , , z max (values in parenhtesis for each detector), and thenthe event rates for each detector are derived by using the merger rate density calculated bythe population synthesis simulations of Pop III stars. Although we can observe z ∼
40 byusing the CE detector, the merger rate density is approximately 0 for z (cid:38) .
75 in the casesof σ k = 100 and 150 km/s, and for z (cid:38) .
30 in the cases of σ k = 200 , , ,
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