Neuro-Parametric Spectral Classification of Black Hole and Neutron Star X-ray Binary Systems

TL;DR

The paper addresses the challenge of distinguishing black hole and neutron star X-ray binaries from X-ray spectra by applying deep neural networks to RXTE data. It develops two input schemes—flux-only and flux-with-errors—and shows that incorporating uncertainties yields higher, more robust accuracies (≈94% vs ≈91%). By fitting the spectra with a simple bbody+powerlaw model, it extracts physically meaningful parameters (kT, Γ, fratio, χ^2_red) and demonstrates that a five-parameter neural classifier achieves comparable performance to the full-spectrum network, with kT and Γ identified as primary drivers. The results provide interpretable, physics-based insights into the network's decisions and propose a mission-agnostic framework for compact-object classification in current and future X-ray surveys.

Abstract

We perform the classification of black hole and neutron star X-ray binary systems using deep neural networks applied to archival RXTE X-ray spectral data. We first construct two neural network models: one trained using only spectral flux values and another trained using both fluxes and their associated errors. Both models achieve high classification accuracies of ~90-94 %. To gain physical interpretability of these networks, we fit all spectra with a simple phenomenological model consisting of a thermal disk component and a power-law. From this analysis, we identify the blackbody temperature, power-law index, the ratio of blackbody to power-law flux, the reduced $χ^2$, and the variance of the data as key parameters that likely contribute to the classification. We validate this inference by designing an additional neural network trained exclusively on this reduced parameter set, without using the spectral data directly. This parameter-based model achieves a classification accuracy comparable to that of the spectral models. Our results show that deep neural networks can not only classify compact objects in X-ray binaries with high accuracy but can also be interpreted in terms of physically meaningful spectral parameters derived from conventional X-ray spectral analysis. This framework offers a promising, mission-agnostic approach for compact object classification in current and future X-ray surveys.

Figures (7)

• Figure 1: Distribution of RXTE observational coverage for the X-ray binary sample analysed in this work. The left panel shows black hole X-ray binaries (BH XRBs), while the right panel shows neutron star X-ray binaries (NS XRBs). For each source, the bar height indicates the total accumulated RXTE exposure time in kiloseconds (left y-axis, shown on a logarithmic scale), while the bar colour encodes the average source count rate in counts/sec, as indicated by the colour bar. The total number of individual RXTE observations available for each source is annotated above the corresponding bar. Sources are ordered by increasing total exposure within each class, highlighting the wide dynamic range in both exposure time and source brightness across the sample.
• Figure 2: Representative RXTE energy spectra for the X-ray binary sample analysed in this work. The left panel shows black hole X-ray binaries (BH XRBs), while the right panel shows neutron star X-ray binaries (NS XRBs). For each source, we display the spectrum corresponding to the observation with the highest average count rate, chosen to maximise signal-to-noise. The spectra are shown in units ($\text{Counts~} \text{s}^{-1} \text{keV}^{-1}$) as a function of energy in the 5–25 keV range, with statistical uncertainties indicated by error bars. Each coloured curve corresponds to a different source, illustrating the diversity in spectral shapes and flux normalisations within and between the two populations.
• Figure 3: Two-dimensional projections of the full set of 43-dimensional RXTE energy spectra using linear and non-linear dimensionality-reduction techniques. The left panel shows the projection onto the first two principal components (PC1 and PC2) obtained via Principal Component Analysis (PCA), which preserves the directions of maximum variance in the original spectral space. The right panel shows the corresponding embedding produced by t-distributed Stochastic Neighbor Embedding (t-SNE), which emphasizes local neighborhood structure. Each point represents a single energy spectrum, with black hole X-ray binaries (BH XRBs) shown in red and neutron star X-ray binaries (NS XRBs) in green. These projections enable a qualitative assessment of overlap, clustering, and separability between the two source classes in reduced-dimensional space.
• Figure 4: Neural network architectures used in this work. The left panel shows the Spectral Model (SM), which consists of a single input layer with 43 flux bins, followed by two hidden layers of different sizes and a two-node output layer. The middle panel displays the Spectral–Error Model (SEM), where the input layer is a two-dimensional array comprising 43 spectral flux bins and their corresponding errors, followed by two hidden layers and a two-node output layer. The right panel shows the Parameter Model (PM), which uses a five-dimensional input vector of best-fit spectral parameters: blackbody temperature (kT), photon index ($\Gamma$), blackbody-to-power-law flux ratio (fratio = F${bb}$/F${pl}$), reduced $\chi^2$, and variance, derived from spectral fitting, followed by a single hidden layer and a two-node output layer. The PM is discussed in section \ref{['sec:highlight']}. All colors used for the three networks are consistent with those in Figure \ref{['fig:SM_SEM_scc']}, which shows the accuracy distributions of the three models.
• Figure 5: Comparison of accuracy distributions between the Spectra Model (SM, orange), Spectra-Error Model (SEM, blue), and the Parameter model (PM, green, see section \ref{['sec:highlight']}). Dashed lines represent Gaussian approximations of the underlying distributions, and vertical dotted lines mark the mean values. The SEM consistently outperforms the SM and PM, indicating the utility of incorporating error arrays into the training process.