Host-Subtracted Median Stack

• The paper introduces a host-subtraction technique that scales and subtracts matched host galaxy spectra from JWST/NIRSpec observations to isolate BH* emission in high-redshift Little Red Dots.
• The methodology constructs a robust median stack of host-subtracted spectra by aligning and normalizing individual SEDs, revealing diagnostic features such as ultra-strong Balmer breaks and steep decrements.
• Diagnostic findings, including narrow [O III] emissions and blackbody-like continua, indicate a dense, optically thick, gas-enshrouded accreting phase distinct from typical stellar populations or AGN.

A host-subtracted median stack is an empirical spectral methodology for isolating the intrinsic emission of compact nuclear engines in galaxies, notably "black hole stars" (BH*s) at the core of high-redshift Little Red Dots (LRDs), by subtracting the host galaxy’s contribution from the observed spectrum. This technique, as implemented in JWST/NIRSpec PRISM studies of LRDs, reconstructs a population-level spectral energy distribution (SED) of the central BH* component by leveraging the spatial and spectral properties of [O III]5008 Å emission to scale and subtract matched host spectra. The resulting median stack demonstrates diagnostic features—including ultra-strong Balmer breaks, steep Balmer decrements, and blackbody-like continua—consistent with a dense, optically thick, gas-enshrouded accreting phase distinct from normal stellar populations or AGN (Sun et al., 28 Jan 2026).

1. Sample Definition and Spectral Alignment

The host-subtracted median stack was performed on a curated set of 98 Little Red Dot sources, selected from 116 initial JWST/NIRSpec PRISM spectra spanning $z \sim 2.3$ to $8.4$, and drawn from DAWN v4.4 and proprietary MoM/IFU programs. Selection criteria imposed a V-shape rest-frame continuum ($\beta_{\mathrm{UV}} < -0.2$, $\beta_{\mathrm{opt}} > 0$, $\beta_{\mathrm{UV}} - \beta_{\mathrm{opt}} < 0.5$), point-source morphology in F444W, median S/N $\geq 2$ per pixel in every 1000 Å bin between 3000–6000 Å, and at least 90% valid pixels. Spectra were shifted to the rest frame and resampled onto a common wavelength grid using flux-conserving interpolation.

2. Host Tracing via [O III] 5008 Å

Disentangling the central BH* from the host galaxy relies on the empirical fact that [O III]5008 Å emission in LRDs is narrow (FWHM ≈ 50–200 km s$^{-1}$), correlates tightly with the UV continuum, and vanishes in pure BH* cases. Collisional de-excitation at nebular densities ($n_{\mathrm{H}} \gtrsim 10^{9}–10^{12}$ cm$^{-3}$) suppresses [O III], rendering it a clean tracer of host emission. Hosts were identified for each LRD by matching in $|\Delta z| < 1.5$ and $|\Delta\log L_{[\mathrm{O\,III}]}| < 0.5$ dex, then flux-scaled to match the LRD’s [O III] using

$$\alpha_{ij} = \frac{L_{[\mathrm{O\,III}],i}^{\mathrm{LRD}}}{L_{[\mathrm{O\,III}],j}^{\mathrm{host}}}$$

for each LRD $i$ and candidate host $j$.

3. Subtraction and Median Stacking Procedure

For each LRD $i$ and host $j$, rest-frame host candidate spectra $G_j(\lambda)$ are resampled onto the LRD’s grid. The host-subtracted spectrum for that pairing is: $$F_{i,j}^{\mathrm{sub}}(\lambda) = F_i(\lambda) - \alpha_{ij} G_j(\lambda)$$ Per-object host-subtracted SEDs are constructed by taking the median across all $N_i \approx 78$ host candidates per LRD: $$F_i^{\mathrm{sub}}(\lambda) = \mathrm{median}_{j=1\ldots N_i}(F_{i,j}^{\mathrm{sub}}(\lambda))$$ These spectra are normalized at 5500 Å, then the median across all 98 LRDs yields the final host-subtracted median BH* stack: $$F_{\mathrm{stack}}^{\mathrm{sub}}(\lambda) = \mathrm{median}_{i=1\ldots98}(F_i^{\mathrm{sub}}(\lambda))$$

4. Error Estimation and Robustness

Uncertainties in the stacked SED are quantified via a combined Monte Carlo and bootstrap approach. For each trial, one host-subtracted spectrum is randomly selected per LRD, with the set bootstrap-resampled and the median SED recalculated. This process is repeated 10,000 times, and at each $\lambda$ the $16$th–$84$th percentile range defines the $\pm1\sigma$ confidence envelope. Pixel-level measurement errors are incorporated implicitly through the host match distribution. Mock tests demonstrate recovery of key quantities to within $1\sigma$.

5. Spectral Diagnostics and Physical Interpretation

The host-subtracted median stack is characterized by a Balmer break of

$$\Delta D = \frac{F_\nu(4000\pm50\,\mathrm{Å})}{F_\nu(3700\pm50\,\mathrm{Å})} = 6.50^{+3.70}_{-1.72}$$

significantly exceeding the stellar-population maximum ($\lesssim 3$). The continuum blueward of 3000 Å is weak; redward of 4000 Å, it rises steeply. A Planck function fitted to the emission redward of 4200 Å yields $T_{\mathrm{eff}} = 4047^{+156}_{-155}$ K, $L_{\mathrm{bol}} = 10^{43.9 \pm 0.1}$ erg s$^{-1}$, and $R_{\mathrm{eff}} = 1321^{+168}_{-153}$ au. The stack exhibits a Balmer decrement $$\mathrm{H}\alpha/\mathrm{H}\beta = 16.2^{+2.2}_{-2.2}$$, pointing to collisional excitation and high densities. Key equivalent widths (rest-frame, host-subtracted) include EW(H$\alpha$) = $827.6^{+62.8}_{-64.7}$ Å, EW(H$\beta$) = $73.5^{+8.6}_{-7.4}$ Å, EW(O I 8446 + Fe II complexes) = $18.5^{+2.4}_{-2.4}$ Å. In the host stack (at 5500 Å normalization), EW([O III]5008) = $1106.4^{+86.7}_{-79.6}$ Å, EW(H$\alpha$) = $939.0^{+54.6}_{-62.5}$ Å, EW(C III]1908) = $11.6^{+5.0}_{-4.7}$ Å.

6. Wavelength Dependence of BH* and Host Contributions

The BH* contribution as a fraction of total LRD emission varies markedly by wavelength. Defining

$$f_{\mathrm{BH^*}}(\lambda) = \frac{F_{\mathrm{stack}}^{\mathrm{sub}}(\lambda)}{F_{\mathrm{stack}}^{\mathrm{sub}}(\lambda) + F_{\mathrm{host\,stack}}(\lambda)}$$

typical values are $f_{\mathrm{BH^*}}(\lambda)\sim20\%$ in the UV ($<3500$ Å), $\sim50\%$ at the Balmer break (3700–4000 Å), and $>90\%$ at $\lambda > 1\, \mu$m (longward of H$\alpha$). The sharp transition in $f_{\mathrm{BH^*}}$ explains the characteristic V-shape continua of LRDs and their wavelength-dependent morphologies.

7. Implications for Black Hole Growth in Young Galaxies

The empirical host-subtracted stacking reveals population-level evidence for gas-enshrouded BH*s as the dominant central engines of LRDs. The distinct suite of spectral features—ultra-strong Balmer break, extreme broad H$\alpha$, steep Balmer decrement, Fe II and O I fluorescence, and a blackbody-like continuum peak—cannot be produced by conventional stellar populations or AGN. Instead, these match radiative transfer models of BH*s with envelope densities $n_{\mathrm{H}}\sim10^9$–$10^{12}$ cm$^{-3}$. LRD hosts are typically low-mass galaxies ($M_\star \sim 10^8\,M_\odot$, $M_{\mathrm{UV}}\sim-18.5$) undergoing bursty star formation and exhibiting enhanced emission line luminosities. The inferred high duty cycle ($\sim1\%$) and brief lifetime ($\sim10$ Myr) of the BH* phase imply that rapid, transient BH*-driven accretion episodes are a universal stage in massive black hole assembly at high redshift. Thus, every typical LRD hosts such a dense BH* engine, and the host-subtracted median stack methodology provides robust, population-level confirmation of their prevalence (Sun et al., 28 Jan 2026).