Research Interests

With the terrestrial based Laser Interferometer Gravitational-Wave Observatory (LIGO) [1] continuing to take its initial data at design sensitivity, and plans for future improvements secured, the first direct detection of gravitational radiation is imminent. Moreover, as other large scale interferometric detectors come online and future spaceborne detectors expand the observable spectrum, the newly formed network of gravitational wave observatories will allow astronomers to continuously view the Universe through a previously undetected form of radiation [2].

Before the information content contained in the gravitational wave spectrum can be used as a viable tool in astronomical studies, we must first design and build highly sensitive detectors capable of measuring the radiation that weakly couples to matter. Important components in wthe initial phases of these instruments are in developing realistic models for source populations; simulating the detector response to arbitrary input waves; and the development of sophisticated data analysis techniques capable of extracting multiple, correlated signals within the output time series. Furthermore, since gravitational wave astronomy is a new and yet unproven field, it is vital in these early days to establish an understanding and support from the astronomical community and the general public through education and public outreach projects. It is in these areas of research that my work has focused.

Population Modeling of Gravitational Wave Sources

Galactic Gravitational Wave Background

Located within our own galaxy are in excess of 108 compact binaries whose emitted gravitational radiation lies within the bandwidth (10-5 - 1 Hz) of the proposed Laser Interferometer Space Antenna (LISA). Except for a limited number of bright outliers, this large binary population will form a confusion limited background the results of which is to introduce an effective noise into the detector [3, 4]. In the strictest sense the confusion limited background is defined as the signal strength level at which gravitational wave sources can no longer be extracted from the detector's output.

In a paper I wrote with Neil Cornish (Montana State) and an undergraduate at Montana State, Seth Timpano, we produced a simulated time series for how the galactic gravitational wave background would appear in the LISA data [5]. The main results of this study was to estimate the expected power spectral density associated with the background and the number of individual (bright) galactic binaries we may hope to identify in the LISA data.

For the above study we only investigated the galactic background that would arise from our Galaxy's main disk structure. While a suitable starting point, it is well known that our Galaxy contains further structure that may house additional gravitational wave sources. In a study with Kelly Holley-Bockelmann (Vanderbilt) and Lee Samuel Finn (Penn State) we are building a more faithful model of the galaxy that includes both a thick and thin disk, a central bulge, and a halo. In a series of papers we plan to develop our galactic model; construct a statistical method for identifying and measuring large scale parameters (e.g. total mass, scale lengths, etc.); and perform a numerical experiment to demonstrate the capabilities of our approach.

Extreme Mass Ratio Bursts

An important source of low frequency gravitational waves are the capture and subsequent inspiral of compact objects (~1 Msun) into the massive black holes (104-7 Msun) located at the centers of galaxies. These systems, known as extreme mass ratio inspirals (EMRIs), have received considerable attention recently both because their signals are complex and will be difficult to isolate in the data [6], and because their signals may provide a direct test of strong field gravity [7].

EMRIs by definition are captured objects destined to plunge into the massive black hole. However, prior to this fate EMRIs originated on extremely elongated orbits bound not to the central black hole but to the central stellar population, which includes the massive black hole as a perturbation. Since the orbits are highly elongated (i.e. eccentricities near unity and large orbital periods) the periapse passage is highly relativistic and will thus produce a burst of gravitational radiation. It had been thought that this radiation would be too weak to be observed, but in a study with Holley-Bockelmann and Finn we calculated an event rate that would indicate that such bursts signals may be detectable by LISA on average once every three weeks [8].

Our initial investigation made the simplest assumptions about the stellar populations, radiation generation, and detection capabilities. Future research will investigate the severity of our initial assumptions.

Forward Modeling for Gravitational Wave Detectors

As with any measurement in astronomy the telescope acts as a filter between the incident radiation and the data analyst. Understanding the filtering process, sometimes referred to as forward modeling, is essential in order to extract the full scientific potential hidden in the data. The same is true in gravitational wave astronomy. In fact, forward modeling plays a significant role for spaceborne gravitational wave detectors because it is through the continual orbital motion of the detector that only certain information (e.g. sky location) becomes encoded in the data.

My first research project in the field of gravitational wave astronomy was on describing the response function for LISA [9]. Based on this original work Cornish and I constructed The LISA Simulator an open software package that simulates LISA's response to an arbitrary input gravitational wave [10]. As part of the software package we developed a somewhat idealized model for the instrument noise. At that time the fidelity in our noise model was high enough for the development of first generation data analysis algorithms. However, enough advancements have been made that it is now time to revisit the instrument noise model. A new noise model would incorporate the expected correlations in the various instrument noise sources along with random and scheduled data gaps. Using this model, which could be plugged in as a module into codes that simulate data streams, further advancements could be made in data analysis algorithms.

Development of Data Analysis Techniques

Gravitational wave detectors return a set of time series. Encoded within these time series are the superposition of all gravitational wave signals received during a particular observational run, co-added to a complicated, time dependent instrumental noise signal. The goal for the data analyst is to coax out individual signals from these time series in order to make scientific inferences about the emitting systems or populations. The next two subsections describes efforts I am currently involved with for developing techniques to extract scientific information from gravitational wave data.

Galactic Binary Detection

Lying above the galactic confusion background mentioned earlier will be a number of individual sources whose signals are stronger than the local rms value of the background [5]. As a result, they will be resolvable within the LISA data streams. Moreover, due to the large orbital periods and low component masses associated with the galactic binaries LISA will observe, the inspiral to merger timescale due to the emission of gravitational radiation (and thus energy lost) is much longer than the mission lifetime. In turn, their signals will be ever present in the detector output. It is these galactic binaries that are prime targets for data analysis techniques.

Even though these target sources are relatively bright, significant correlations may still exist between their signals. Consequently, sophisticated data analysis techniques capable of resolving the individual systems will be required. In collaboration with Neil Cornish and Ron Hellings (Montana State) we are developing a scheme capable of identifying and characterizing these bright binaries [11].

Bayesian Analyses

The previously described algorithm makes the assumption that we know the exact signal structure prior to the analysis (i.e. its functional form). An alternative approach is to select the best signal model from a library of possible models based on the actual data. This can be achieved using a Bayesian model selection criteria [12]. In terms of my involvement in the development of data analysis techniques, it is here, using Bayesian analysis approaches that I expect to spend a considerable amount of my future research pursuing.

Together with Lee Samuel Finn we have mapped out a series of Bayesian analysis projects that would benefit the development of both LISA and LIGO science data analyses. With Edward Cazalas (an undergraduate at Penn State), Matthew Francis (New Jersey Institute of Technology), and Deirdre Shoemaker (Penn State) we are completing a project where we calculate the conditions in which it is possible to measure a changing orbital frequency for galactic binaries in the LISA band. Other projects include selecting the appropriate waveform model for studying black hole binary inspirals and tracking the evolution of parameter estimates for continuous sources as additional data is collected.

Education and Public Outreach

There is a common belief that since gravitational radiation is a consequence of Einstein's theory of General Relativity a thorough understanding of this advance topic is required in order to understand gravitational wave astronomy. While this is true for a select few studies associated with the details of radiation production from highly relativistic sources, the vast majority of the field can easily be understood using undergraduate level physics (for example, see Schutz [13]). The next few subsections describe a sequence of outreach activities and articles designed to help communicate the field of gravitational wave astronomy at the undergraduate level.

Template Matching Activity

Contrary to most traditional electromagnetic telescopes, gravitational wave detectors are not imaging telescopes. Instead they return a set of noisy time series. For most students it is not clear how to do astronomy without the use of pictures. In a template activity I designed with Shane Larson (Weber State), Michelle Larson (Utah State), and an undergraduate at Penn State, Kristina Zaleski, we introduce students to the notion of how to detect a signal within a noisy time series [14]. In short, the activity has students match an idealized signal (i.e. a template) to a sample of noisy data by overlaying a sequence of templates and deciphering which matches best to the data. We have successfully applied our template activity with students as early as the fifth grade. Recently the activity has been featured in the educational support materials packaged with the NSF's Einstein's Messengers DVD video about LIGO.

Information Extraction Activity

The template activity described above teaches the students about making a detection within a noisy time stream. Once that detection has been made the next issue to address is how to characterize the signal, i.e. what can be said about the emitting system. To address this next step in the gravitational wave data analysis ladder we have developed a second activity in which the students use the leading order formulas for gravitational waveform descriptions to extract information about the emitting systems [15]. The activity involves the students physically measuring values on plots of a detected waveform, and then translating the information into physical quantities such as the distance to the binary. This activity is also featured in the educational support material for the Einstein's Messengers DVD.

References

  1. A. Abramovici et al., LIGO: The Laser Interferometer Gravitational-Wave Observatory, Science 256, 325-333 (1992)

  2. L. J. Rubbo, S. L. Larson, M. B. Larson, & K. D. Zaleski, Gravitational Waves: New Observatories for New Astronomy, The Physics Teacher 44, 420-423 (2006)

  3. D. Hils and P. L. Bender and R. F. Webbink, Gravitational Radiation from the Galaxy, Astrophysical Journal 360, 75-94 (1990)

  4. G. Nelemans, L. R. Yungelson, & S. F. Portegies Zwart, The Gravitational Wave Signal from the Galactic Disk Population of Binaries Containing Two Compact Objects, Astronomy & Astrophysics 375, 890-898 (2001)

  5. S. E. Timpano, L. J. Rubbo, & N. J. Cornish, Characterizing the Galactic Gravitational Wave Background with LISA, Physical Review D 73, 122001 (2006)

  6. L. Barack & C. Cutler, LISA Capture Sources: Approximate Waveforms, Signal-to-Noise Ratios, and Parameter Estimation Accuracy, Physical Review D 69, 082005 (2004)

  7. S. A. Hughes, (Sort of) Testing Relativity with Extreme Mass Ratio Inspirals, arXiv/gr-qc/0608140 (2006)

  8. L. J. Rubbo, K. Holley-Bockelmann, & L. S. Finn, Event Rate for Extreme Mass Ratio Burst Signals in the Laser Interferometer Space Antenna Band, Astrophysical Journal Letters 649, L25-L28 (2006)

  9. N. J. Cornish & L. J. Rubbo, LISA Response Function, Physical Review D 67, 022001 (2003)

  10. L. J. Rubbo, N. J. Cornish, & O. Poujade, Forward Modeling of Space-Borne Gravitational Wave Detectors, Physical Review D 69, 082003 (2004)

  11. L. J. Rubbo, N. J. Cornish, & R. W. Hellings, Slice & Dice: Identifying and Removing Bright Galactic Binaries from LISA Data, arXiv/gr-qc/0608112 (2006)

  12. L. J. Rubbo, When is Enough Good Enough in Gravitational Wave Source Modeling?, arXiv/gr-qc/0608114 (2006)

  13. B. F. Schutz, Gravitational Waves on the Back of an Envelope, American Journal of Physics 52, 412-419 (1984)

  14. M. B. Larson, L. J. Rubbo, K. D. Zaleski, & S. L. Larson, Science Icebreaker Activities: An Example from Gravitational Wave Astronomy, The Physics Teacher 44, 416-419 (2006)

  15. L. J. Rubbo, S. L. Larson, M. B. Larson, & D. R. Ingram, Hands-On Gravitational Wave Astronomy: Extraction of Astrophysical Information from Simulated Signals, arXiv/physics/0610028 (2006)