Astrophysics and cosmology with a decihertz gravitational-wave detector: TianGO

We present the astrophysical science case for a space-based, decihertz gravitational-wave (GW) detector. We particularly highlight an ability to infer a source’s sky location, both when combined with a network of ground-based detectors to form a long triangulation baseline, and by itself for the early warning of merger events. Such an accurate location measurement is the key for using GW signals as standard sirens for constraining the Hubble constant. This kind of detector also opens up the possibility to test type Ia supernovae progenitor hypotheses by constraining the merger rates of white dwarf binaries with both super- and sub-Chandrasekhar masses separately. We will discuss other scientific outcomes that can be delivered, including the constraint of structure formation in the early Universe, the search for intermediate-mass black holes, the precise determination of black hole spins, the probe of binary systems’ orbital eccentricity evolution, and the detection of tertiary masses around merging binaries.

Figure 1

Sensitivities of future ground-based and space gravitational-wave detectors. The sensitivities are averaged over sky location and polarization. The LISA curve includes two 60° interferometers and the ET curve includes three 60° interferometers. The curve labeled “GW150914” is $2\sqrt{f}h$, where $h$ is the waveform of the first gravitational wave detected [20] starting 5 years before merger.

Figure 2

Horizons for equal mass compact binaries oriented face on for the detectors shown in Fig. 1. The maximum detectable distance, defined as the distance at which a source has an SNR of 8 in a given detector, is computed for 48 source locations uniformly tiling the sky. The horizon is the maximum distance at which the best source is detected; 50% of these sources are detected within the dark shaded band, and 90% of the sources are detected within the light shaded band. If a source stays in a space detector’s sensitivity band for more than 5 years, the 5-year portion of the system’s evolution that gives the best SNR in each detector is used.

Figure 3

Sky localization, luminosity distance, and volume localization precision as a function of redshift for a binary black hole system with ${\mathcal{M}}_c=25M_{\odot }$, $q=1.05$, and an inclination $\iota =30°$ and TianGO in a 5° Earth-trailing orbit. A notional density of $0.01\text{galaxies}/{\mathrm{Mpc}}^3$ is used to convert $\mathrm{\Delta }{V}_C$ to the expected number of galaxies. Figure 13 shows the same for face-on binaries.

Figure 4

Angular uncertainty as determined by TianGO alone for a face-on BNS (at 12 source locations uniformly tiling the sky) with $(M_1,M_2)=(1.4M_{\odot },1.35M_{\odot })$ as a function of GW frequency or time to coalescence.

Figure 5

Upper panel: the GW frequency $f_{\mathrm{gw}}$ for WD binaries with different total masses $(M_1+M_2)$ and mass ratios $q\equiv M_1/M_2\ge 1$ at the onset of Roche-lobe overflow. Bottom panel: angle-averaged SNR seen by TianGO, assuming a source distance of 10 kpc and an observation period of 5 years.

Figure 6

Tidal interactions for a $0.72M_{\odot }–0.6M_{\odot }$ WD binary. Upper panel: orbital energy dissipation/transfer rates $\dot{E}$ in different channels. Lower panel: total GW frequency shift of the binary over a 5-year observation period, $\mathrm{\Delta }f$, as a function of the initial GW frequency $f_0$. Frequency shifts greater than $1/T_{\mathrm{obs}}$ are resolvable.

Figure 7

Uncertainties in inferring the mass ratio, $\mathrm{\Delta }q$, for WD binaries with different total masses.

Figure 8

Uncertainties in the precession spin parameter ${\chi }_{\mathrm{p}}$ for TianGO (left) and a network of five Voyager-like detectors (right). We vary the source’s chirp mass and mass ratio, while fixing $({\chi }_{\mathrm{eff}},{\chi }_{\mathrm{p}})=(-0.3,0.6)$. The source is assumed to be at $z=2$ and the sky location is marginalized over. Note that the color scales are different in the two panels.

Figure 9

Similar to Fig. 8 but showing the uncertainties in ${\chi }_{\mathrm{eff}}$, for binaries with $({\chi }_{\mathrm{eff}},{\chi }_{\mathrm{p}})=(0.05,0)$. Note that the uncertainties $\mathrm{\Delta }{\chi }_{\mathrm{eff}}$ are amplified by a factor of 100 in the plots, and that the color scales are different in the two panels.

Figure 10

Evolution of the characteristic strain amplitude $h_c$ for the first four orbital harmonics of a BH binary with $M_1=M_2=30M_{\odot }$ at $z=0.3$. The solid (dashed) curves represent systems with an initial eccentricity of $1-e_0={10}^{-3}({10}^{-2})$ and $a_0=0.1\mathrm{AU}$. The x axis corresponds to the frequency of each harmonic [Eq. (9)]. The thin black traces represent the sky-averaged sensitivity (in $\sqrt{5f{S}_a(f)}$) for LISA, TianGO, and (a single) Voyager, respectively. The pluses, dots, and crosses correspond, respectively, to instants 5 years, 1 day, and 1 hour prior to the final merger.

Figure 11

Similar to Fig. 10, but for an IMRI system with $(M_1,M_2)=({10}^3{M}_{\odot },10M_{\odot })$ starting at $a_0=1\mathrm{AU}$. The solid (dashed) traces correspond to an initial eccentricity of $1-e_0={10}^{-3}({10}^{-2})$.

Figure 12

Fractional uncertainties in the linear velocity (top panels) and angular velocity (bottom panels) of the outer orbit for an inner binary with masses $(30M_{\odot },30M_{\odot })$ and an initial frequency of 0.017 Hz, corresponding to a system that merges in 5 years. The system is 400 Mpc from the Earth and ${\varphi }_{\mathrm{mod}}=0$. In the left panels, we fix $v_{\mathrm{mod}}/c=0.02$ and vary ${\mathrm{\Omega }}_{\mathrm{mod}}$, and in the right panels, we fix ${\mathrm{\Omega }}_{\mathrm{mod}}=2\pi /0.5\mathrm{yr}$ and vary $v_{\mathrm{mod}}$. Blue pluses and orange dots represent the uncertainties obtained with TianGO and LISA, respectively.

Figure 13

The same as Fig. 3 except for face on binaries.