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.

Figure 1

Average distributions of redshifted chirp mass $\mathcal{M}$ of simulated BH-BH binary detections for a 1-month period, and a simulated observation result for a 1-month period of GW detection simulation in KAGRA. The horizontal axis is the redshifted chirp mass. The vertical axis is the detection rate per redshifted chirp mass of BH-BH binary mergers [$/{\mathrm{M}}_{\odot }/\mathrm{month}$]. The dotted (blue) and solid (red) lines correspond to the average distributions of redshifted chirp mass $\mathcal{M}$ of simulated BH-BH binary detections for a 1-month period of Pop I/II Standard model and that of Pop III IMF:Flat, respectively. The dashed (black) line corresponds to sum of the Pop I/II model and the Pop III model, i.e., Pop I/II/III model. The crosses and its error bars show the simulated BH-BH binary detection events and its statistical errors on a 1-month period simulation, respectively.

Figure 2

Distributions of the log-likelihood ratio $\ln \mathrm{\Lambda }(\overrightarrow{\mathcal{M}})$ for equivalent a 1-month period of observation. We use the detection rate of Pop I/II/III BH-BH binary mergers rounded off to the nearest integer as the value of $n$. In the case of the combination of standard model and IMF:Flat, the detection rate of $31.99+4.685=36.675$ is rounded off to the nearest integer as $n=37$. The horizontal axis is the log-likelihood ratio. The vertical axis is the probability distribution function of the log-likelihood ratio. The dashed (blue) and solid (red) lines represent distributions of the $\ln \mathrm{\Lambda }({\overrightarrow{\mathcal{M}}}^{\mathrm{I}/\mathrm{II}})$ and $\ln \mathrm{\Lambda }({\overrightarrow{\mathcal{M}}}^{\mathrm{I}/\mathrm{II}/\mathrm{III}})$, respectively. The dotted (black) line shows the log-likelihood ratio threshold $\ln {\mathrm{\Lambda }}_{\mathrm{th}}$. The probability of identifying the existence of Pop III stars $P$ defined in Eq. (15) is estimated to be 98.0% at $n=37$ events.

Figure 3

The probability of identifying the existence of Pop III stars $P$ as a function of the number of simulated BH-BH binary detections $n$. The horizontal axis is the number of simulated BH-BH binary detections $n$. The vertical axis shows the probability of identifying the existence of Pop III stars $P$.

Figure 4

Same as Fig. 1 but for more examples of population synthesis models. From top to bottom panel, Pop III models are Kinugawa’s IMF:Flat, IMF:Logflat, and IMF:Salpeter, respectively. From left to right panel, Pop I/II models are Dominik’s standard model, high BH kicks model, and delayed SN model, respectively.

Figure 5

Same as Figure 2 but for more examples of population synthesis models. From top to bottom panel, Pop III models are Kinugawa’s IMF:Flat, IMF:Logflat, and IMF:Salpeter, respectively. From left to right panel, Pop I/II models are Dominik’s standard model, high BH kicks model, and delayed SN model, respectively.

Figure 6

Same as Fig. 3 but for more examples of population synthesis models.