The search for subsolar mass primordial black holes (PBHs) poses a
challenging problem due to the low signal-to-noise ratio, extended signal
duration, and computational cost demands, compared to solar mass binary black
hole events. In this paper, we explore the possibility of investigating the
mass range between subsolar and planetary masses, which is not accessible using
standard matched filtering and continuous wave searches. We propose a
systematic approach employing the Viterbi algorithm, a dynamic programming
algorithm that identifies the most likely sequence of hidden Markov states
given a sequence of observations, to detect signals from small mass PBH
binaries. We formulate the methodology, provide the optimal length for
short-time Fourier transforms, and estimate sensitivity. Subsequently, we
demonstrate the effectiveness of the Viterbi algorithm in identifying signals
within mock data containing Gaussian noise. Our approach offers the primary
advantage of being agnostic and computationally efficient.
The search for subsolar mass primordial black holes (PBHs) is a challenging problem due to various factors such as low signal-to-noise ratio, extended signal duration, and high computational cost demands. However, in this paper, we propose a systematic approach utilizing the Viterbi algorithm, a dynamic programming algorithm, to detect signals from small mass PBH binaries in the mass range between subsolar and planetary masses.
We start by formulating the methodology for our approach and provide the optimal length for short-time Fourier transforms. This step is crucial in order to enhance the sensitivity of our detection method. By estimating sensitivity, we can make the most of the limited resources available for detecting subsolar mass PBHs.
Next, we demonstrate the effectiveness of the Viterbi algorithm by applying it to mock data containing Gaussian noise. This allows us to evaluate its performance and validate its capability to identify signals from small mass PBH binaries accurately.
One of the primary advantages of our approach is its agnostic nature. It does not rely on specific assumptions about the signal properties or underlying physics. This flexibility makes our method applicable in a wide range of scenarios, enhancing its potential to detect subsolar mass PBHs.
Moreover, our approach is computationally efficient compared to other existing methods for detecting PBHs. This efficiency reduces the computational cost demands, making it more feasible to search for subsolar mass PBHs.
Future Roadmap: Challenges and Opportunities
Challenges:
- The low signal-to-noise ratio remains a significant challenge in the search for subsolar mass PBHs. As we move forward, finding innovative ways to improve signal detection and reduce noise interference will be crucial.
- The extended signal duration also poses a challenge. Devising methods to accurately detect and analyze long-duration signals while minimizing false positives will be an important area of research.
- The computational cost demands, although reduced by our approach, may still be a limiting factor. Exploring techniques to further optimize the computational efficiency without compromising accuracy will be necessary for wider implementation.
Opportunities:
- Further advancements in signal processing algorithms and techniques can offer new opportunities to improve the detection sensitivity for subsolar mass PBHs. Investigating alternative algorithms and combining them with the Viterbi algorithm may yield even better results.
- The increasing availability of computational resources, such as high-performance computing clusters and cloud services, opens up opportunities to scale up the analysis and search for subsolar mass PBHs across larger datasets.
- Collaboration among researchers and institutions can enhance the knowledge sharing and facilitate the development of a unified approach towards detecting subsolar mass PBHs. Sharing data, methodologies, and insights will accelerate progress in this field.
In conclusion, our proposed systematic approach utilizing the Viterbi algorithm shows promise in addressing the challenges associated with the search for subsolar mass PBHs. While there are challenges to overcome, there are also exciting opportunities on the horizon. By continuing to refine our methods, collaborate, and leverage advancements in technology, we can unlock new discoveries and deepen our understanding of the universe.