Current Detectors, Future Detectors, and Prospects of Multi-Band

Chapter I: Introduction

1.4 Current Detectors, Future Detectors, and Prospects of Multi-Band

Direct detections of gravitational waves (GWs) by the LIGO Scientific Collabora- tion [11, 26–34] are historic. As detector upgrades come online next generation 3G detectors, such as Cosmic Explorer (CE) [18, 22, 35, 36] and Einstein Telescope (ET) [37, 38], are planned to probe the cosmic horizon of GW events. Figure 1.3 displays the range to which future detectors such as CE and ET can observe. To demonstrate 3G detectors’ level of sensitivity, compared to current detectors, fig- ure 1.4 displays detector noise curves with GW signals simulated from IMRPhe- nomD using PyCBC [39]. Planned upgrades, e.g., A+ and Voyager, are also shown.

These GW events are sampled from two different mass distributions, where the sampling procedure will be discussed in the next section.

The surprisingly high masses of kilohertz signals observed so far have provided interesting prospects of multi-band GW astronomy. Some of the systems observed by

Figure 1.3: Horizon of current and future GW detectors for compact binaries.

Dotted lines are detectors, white lines marking the redshift, and dots represent binary sources (yellow for NS-NS and white for BH-BH). The sources are equal mass systems with a merger of 100 Myrs. Image take from Ref [18, 22].

LIGO to date would also have been observable by a space-based Laser Interferometer Space Antenna (LISA) [40]. Given space-based detectors, observing in conjunction with Adv. LIGO, GW150914-like systems will be detectable in the centihertz range, merging in Adv. LIGO’s band on a timescale of less than a decade [40]. In December of 2015, the European Space Agency launched LISA Pathfinder, a technology demonstration mission that has been a great success [41]. The results have also provided updated noise curves for a new LISA design set to launch in the next 20 years [17]. One of the science objectives for LISA is to keep a GW150914- like system detectable in the LISA band with a (signal-to-noise) SNR threshold 𝜌LISA ≥ 7 during the four year space mission. This would advance GW astronomy to begin observing GW signals across multiple bandwidths. Once a GW150914-

10⁰ 10¹ 10² 10³ 10⁴ f[Hz^−1/2]

10⁻²⁵ 10⁻²⁴ 10⁻²³ 10⁻²² 10⁻²¹ 10⁻²⁰

p S(f)[Hz−1/2 ]

Power-Law

10⁰ 10¹ 10² 10³ 10⁴ f[Hz^−1/2]

Log-Uniform

Adv. LIGO A+

Voyager ET CE

Figure 1.4: Current and next generation detectors. For each detector the curves represent the noise PSD

√

𝑆_𝑛 where𝑛 representing the noise curve for LIGO, A+, Voyager, Einstein Telescope, and Cosmic Explorer. A realization of 1000 sources

√

𝑆_ℎ = 2|ℎ˜|√︁

𝑓 are sampled from an optimally oriented power-law (left panel) and log-uniform (right panel) mass distribution. Total mass of the systems are restricted to≤ 100𝑀_⊙. Here𝑧is sampled from a uniform comoving volume without a specific star formation assumed. No SNR restrictions are imposed on the displayed source signals (implemented via IMRPhenomD).

like system advances to 1 decihertz, the signal will enter Adv. LIGO’s band on a timescale of two weeks. This advance warning allows electromagnetic observers to concentrate on the source’s sky location for any (although rare) EM counterpart and perform additional tests of GR. This prospect of multi-band GW astronomy also has a promising future in the decihertz regime with latest proposed TianGO [23] and other proposed detectors [24, 25].

One major advantage to multi-band observations is the accurate sky-localization, which, along with an identified host galaxy [42], will give an independent mea- surement of the luminosity distance and redshift. This will also allow accurate study of GW cosmology and the possibility of studying weak-lensing potentials. At cosmological distances every GW source will be gravitationally lensed, causing a magnification or demagnification of the observed shear signal at the detector. The presence of this signal can be inferred statistically. Ref. [43] analyzed precision measurements of fundamental cosmological parameters, including measuring the

10⁻³ 10⁻¹ 10¹ 10³ f[Hz^−1/2]

10⁻²⁵ 10⁻²⁴ 10⁻²³ 10⁻²² 10⁻²¹ 10⁻²⁰ 10⁻¹⁹ 10⁻¹⁸ 10⁻¹⁷

p S(f)[Hz−1/2 ]

Power-Law

10⁻³ 10⁻¹ 10¹ 10³

f[Hz^−1/2]

Log-Uniform

LISA TianGO DECIGO Adv. LIGO A+

CE

Figure 1.5: Demonstration of multiband GW astronomy. This is the same sampling procedure of Figure 1.3 where noise curves

√

𝑆_𝑛for Voyager and Einstein Telescope are excluded. Millihertz and decihertz space-based detectors LISA, TianGO [23], and DECIGO [24, 25] are added. This example of multiband GW astronomy restricts each source to merge on a timescale of 10 years.

gravitational-lensing convergence power spectrum, in which errors on the absolute luminosity distance is dominated by effects of gravitational lensing magnification.

Here the power spectrum from weak lensing shear is not only sensitive to distances between the observer, lens, and source, but also to the distribution of lenses. Mea- suring this distribution of lens and mapping the weak lensing potential will provide insight to growth of density perturbations. Ch. 2 will further investigate prospects of testing GR in the decihertz range.

To demonstrate, during the early inspiral of binary black holes (BBHs) Keplerian motion can, to zeroth order, be used to describe their motion and come to a descrip- tion of the leading order evolution of the binary due to GW emission [44]. Here the orbital period 𝑃 of the binary is related to the semi-major axis𝑎 as𝑃2 ∝ 𝑎3. The dominant GW frequency 𝑓 is twice the orbital frequency of the binary, thus we can say 𝑎 ∝ 𝑓^−2/3. Ref. [44] provides a description of the time evolution of a circular binary due to GW emission, inspiraling and coalescing on a timescale𝑇_𝑐(𝑎) ∝ 𝑎⁴.

Between two frequencies 𝑓

lowand 𝑓

upthis explicitly comes out as, 𝑇 = 5

256𝜂 𝐺 𝑀

𝑐3

𝐺 𝑀 𝑐3

𝜋 𝑓low

−8/3

− 𝐺 𝑀

𝑐3

𝜋 𝑓up

−8/3!

(1.78) In this interval, the SNR accumulated is integrated from 𝑓

low to 𝑓

up. For example, all detections with Adv. LIGO have had𝑇_𝑐varying from less than a second to a little under two seconds while accumulating an 𝜌 ∼10−30 at O1/O2 sensitivities. The most massive, GW150914, would have advanced from 1.7 to 10 centihertz in 4 years.

The inspiral-merger-ringdown waveform, from the early inspiral to coalescence, of a GW150914-like system has 𝜌

LISA =7 and at design 𝜌

LIGO =97. Here the lower frequency of the IMR waveform is set so that 𝑓

up =10 Hz when calculating 𝜌

LISA. The observing time is then set to LISA’s space mission of 𝑇 = 4 years. Then, using (1.78) we can estimate what the lower frequency is, which comes out to 1.7 centihertz for a (36,29)𝑀_⊙ system. The total time to coalesce from 1.7 centihertz is 4.03 years. This exemplifies the type of system expected to be observed in both bands. More massive systems will have lower 𝑓

low when 𝑓

up = 10 Hz and𝑇 = 4 years are fixed, allowing more SNR to be accumulated while still merging on a time scale of ∼ 4 years. Figure 1.5 extends the signals observed in figure 1.4 to where

𝑓low is chosen so that the binaries coalesce in exactly 10 years.