LISA and Binary Black Holes

Introduction to LISA

The Laser Interferometer Space Antenna (LISA) is the first generation of gravitational wave detectors to be based in space. The LISA observatory is comprised of three individual spacecraft flying in a triangular constellation, trailing behind the Earth in an orbit around the Sun. LISAs ground-based sibling, LIGO, is made in the shape of an L with two arms extending from a central vertex. By contrast, LISA is a triangle with three arms, any spacecraft where the arms meet can be thought of as a vertex similar to the corner of LIGO. In this way, LISA can be seen as three separate instruments. LISAs arms are a million times larger than LIGOs, enabling LISA to detect phenomenon at millihertz gravitational wave frequencies; by comparison, LIGO observes around kilohertz frequencies. LISA will allow us to observe phenomena we already observe in the electromagnetic spectrum in a different form. It will also allow us to observe interactions and objects that we can not currently see. Among the strongest sources LISA will see, and a source we have yet to see directly in other forms, is that of binary black holes - the object of my research!

Object of My Research

Starting Late June 2018

My team wanted to understand just how many massive binary black holes (MBH) will we observe when LISA is up and running. But not just any old MBH, how many we observe that are constantly inspiraling.

LISA will be able to observe different binaries at different phases of their evolution, from inspiral to merger to ringdown. These phases last varying lengths of time, depending on the mass; in particular, the inspiral time can last longer than LISAs observational time. I wanted to find out how many would we observe, what if there are so many we have to account for the noise they'll cause (such as the case for white dwarfs) or so few that we may want to consider the sensitivity of our detector.

How I Got The Data

In this project we account for a couple different sensitivity curves (Classic and Propsed LISA) to see the different SNR's we might come across. All these mights are because LISA is still in the design process. And just like LISAs design is still in the works, our understand of MBH are still in the works - we have yet to observe them directly in gravitational waves! This is why the MBH data I used in my research is from a simulation.

Illustris is a large-scale cosmological simulation designed to study structure and formation in the Universe. It is done over cosmic time in a volume cube with side length 106.5 Mpc, and tracks relevant interactions and processes between dark matter, gas, stars, and massive black holes. We extract from the Illustris simulation all merging MBH sources, determine if they are detectable by LISA, and then restrict our attention to sources that will produce observable mergers in a narrow window of time (within 100 years of the time LISA is observing). This time restriction ensures we capture the population of black holes that are observable by LISA and inspiraling without merging before LISA observations conclude. Using the statistics of the systems extracted from Illustris, we use Monte Carlo methods to create 8000 statistically equivalent LISA detection catalogs to assess our ability to probe this population of black holes.

Analysis of Said DATA

The 8000 catalogs are analyzed through three configurations: CLLF observing for 4 years, PL for 4 years, and PL for 10 years. The purple/blue/green/yellow diagrams capture the properties of the 8000 Monte Carlo LISA detection catalogs, with the color density showing the density of sources in the respective parameter space. Change in frequency, total mass, and time till coalescence properties are compared to the values SNR. The red horizontal line in the rightmost histograms accentuates an SNR over 5, this is considered a guaranteed detection.

Since these diagrams are using all 8000 catalogs the density really shows the probability of us observing a source like that when LISA lunches

Results! LISA Detection

There is a good possibility that we will observe one or a few inspiraling MBH when LISA is detecting gravitational waves! The chart shows the filters I put through the configurations we set. First, we took out the MBH that merger during the first constraint, observation time, because I am interested in the ones that don't merge! Then I calculated the SNR using post-Newtonian methods to get the average number of detectable Inspiraling MBH! Any positive SNR is detectable but an SNR over 5 is pin-pointable.

Divide this average number of detectable MBH by the years observing and you get how many inspiraling MBH are seen a year! I found that in 10 catalogs out of 8000, PL 4-year shows 0.5 detections; the rest of the PL data, for both 4 and 10-year observation, shows minimal to no MBH detection. CLLF sees a closer to 1 detection per year of observation.

The data here shows an indication of what is to be expected from inspiraling MBH sources when we are observing gravitational waves in this frequency range. With this data, we are also able to compare the different sensitivity methods that are planned for LISA. Future work will take into account these projected numbers to finalize LISAs full range of detection. Only then will we see if the MBH are a chorus among our data or a solo artist.

Considerations: We use Monte Carlo realizations of the LISA catalog to assess the variability in MBH detections that can be expected. However, this work is theoretical and is based on the data created in the Illustris simulation. This data has been shown to have lower detection rates for MBH than shown in gravitational wave literature.