Host-Galaxy Stellar Mass Correction

• Host-Galaxy Stellar Mass Correction is the practice of applying systematic bias adjustments to stellar mass estimates from SED fitting, mitigating issues like outshining and photometric limitations.
• It leverages empirical relations, such as sSFR-dependent corrections and redshift adjustments, to harmonize unresolved mass estimates with spatially resolved measurements.
• These corrections are vital for refining SN Ia host mass correlations and reducing uncertainties in cosmological inferences and high-redshift galaxy studies.

Host-Galaxy Stellar Mass Correction refers to a class of empirically derived or physically motivated adjustments applied to stellar mass estimates or related astrophysical diagnostics, accounting for systematic biases inherent to the measurement, environment, or physical properties of the galaxy. This concept is widely implemented in galaxy SED fitting, transient (especially Type Ia supernova) cosmology, and studies relying on host mass scaling relations, to mitigate biases introduced by photometric limitations, outshining, host-dependent population differences, or selection effects.

1. Motivation and Definition

Stellar mass, as inferred from integrated photometry or SED fitting, is subject to biases arising from observational limitations, unresolved stellar populations, outshining by young stars, or host selection biases. These systematic effects are particularly acute in the following contexts:

• Broad-band SED fits of spatially unresolved galaxies, where young, blue stellar populations can bias mass-to-light ratios low by masking older populations.
• Cosmological applications relying on correlations between transients and host properties, for example the "mass step" in SN Ia Hubble residuals.
• High-redshift regimes where wavelength coverage and restframe bias systematically underestimate stellar masses due to lack of sensitivity to evolved stars.

Correcting for these effects—i.e., applying a Host-Galaxy Stellar Mass Correction—entails an empirically or physically grounded recalibration of the originally estimated mass or associated property, as a function of specific host or observational parameters.

2. Empirical SED-Based Mass Corrections

Outshining Bias and sSFR Dependence

Integrated SED fitting systematically underestimates stellar mass in star-forming galaxies, an effect traced to the "outshining bias" whereby luminous young populations dominate the optical/UV light and obscure underlying high mass-to-light ratio old components. Sorba & Sawicki (2015) quantify the correction as:

$$m_{\rm resolved} = \frac{m_{\rm unresolved}}{-0.057\,\log_{10}(\mathrm{sSFR}) + 0.34}$$

where sSFR is in yr$^{-1}$. This adjustment yields negligible correction for quiescent galaxies ($\log_{10}(\mathrm{sSFR}) \lesssim -11.5$), with the underestimation growing to $\sim 13\%$ at intermediate sSFR, and up to 25% at the highest sSFRs. The origin is validated via spatial resolution tests: the bias emerges when physical scales exceed $\sim3\,\mathrm{kpc/pixel}$, comparable to spiral arm widths (Sorba et al., 2015).

Similar bias at higher redshift is addressed by Sorba & Sawicki (2018), which provides a piecewise analytic correction dependent on log sSFR, with more extreme corrections (up to a factor of 5) at sSFR $\gtrsim 10^{-8}$ yr$^{-1}$ (Sorba et al., 2018).

Correction Application

The correction is applied by inserting the measured unresolved mass and sSFR into the given relation, yielding mass estimates compatible with spatially resolved measurements. Validity is formally demonstrated for low-redshift ($z\lesssim 0.02$) galaxies, but the prescription extends to higher redshifts with caveats regarding population differences and SED coverage.

3. Corrections in Supernova Cosmology

The SN Ia "Mass Step"

Host-galaxy stellar mass correlates with Hubble residuals (HRs) of Type Ia supernovae after light-curve standardization. The empirical "mass step" is modeled as a linear term in the standardization relation:

$$\mathrm{HR} = \gamma \log_{10}(M_{\rm host}/M_\odot) + C$$

with best-fit $\gamma$ in the range $-0.057$ to $-0.11$\,mag/dex across several surveys and methodologies (Gupta et al., 2011, Campbell et al., 2016, Rose et al., 2020). Corrections are applied either as:

$$\Delta\mu_{\rm mass} = \gamma\;[\log_{10}(M_{\rm host}/M_\odot) - \log_{10}(M_{\rm thr}/M_\odot)]$$

or via a step-function at a pivot mass (e.g., $10^{10}\,M_\odot$). Implementation is incorporated directly in likelihood-based cosmological inference, ensuring α, β, and the host-mass term are fit simultaneously to avoid bias and correlation between nuisance parameters (Rose et al., 2020, Popovic et al., 2021).

Systematics and Model Extensions

Systematic uncertainties in the host mass estimation propagate into the SN distance error budget; random errors (∼0.03 dex with UV-NIR photometry) and systematic uncertainties (∼0.1 dex from SED modeling) lead to an uncertainty in the correction of ≲0.006 mag. The mass–residual correlation is robust (>5σ), more significant than age or metallicity correlations in most samples, and persists across different galaxy types. However, recent hierarchical and spectroscopic modeling suggests a fraction (∼35%) of the observed mass step may stem from luminosity-independent spectral variations (Jones et al., 2022), and some or all may be attributed to differing dust laws between hosts (Popovic et al., 2021).

Redshift-Dependent Correction

At higher redshifts, systematic underestimation of stellar mass increases due to lack of restframe optical data. Paulino-Afonso et al. (2022) provide a parameterization for the mass bias in griz-based SED fits as a function of redshift:

$$\Delta M(z) = (0.05 \pm 0.01)\,z - (0.20 \pm 0.02)\,z^2$$

These corrections reduce the estimated host-mass step and have minor, but non-negligible, impact on cosmological parameters in precision analyses (Paulino-Afonso et al., 2022).

4. Corrections for Massive and High-Redshift Galaxy Hosts

Surface-Brightness and Flux Loss Corrections

At the high-mass end, standard SDSS photometry underestimates total flux due to low surface-brightness wings. D’Souza et al. (2015) define a bin-dependent flux correction Δm, derived from stacking, and apply it as:

$$\log_{10}M_*^{\rm corr} = \log_{10}M_*^{\rm MPA} - 0.4\,\Delta m$$

The resulting shift in the stellar mass function increases the abundance of massive galaxies ($M_*\gtrsim 10^{11}\,M_\odot$) by a factor up to ∼3 (D'Souza et al., 2015).

IMF and Dynamical Corrections

For dynamical mass estimates and variable-IMF effects, Corrections to SED-based $M_*$ employ velocity dispersion ($\sigma_e$) and Sérsic index via a power-law or JAM model fit:

$\log_{10}\frac{M_*^{\alpha_{\rm JAM}}{M_*} = a + b\,s_e$

with calibration tables for (a, b) according to structural parameters and sample (Bernardi et al., 2017).

High-Redshift Quasar Host Corrections

In high-redshift quasar host studies, stellar mass estimates can be biased, typically via PSF subtraction residuals or underestimation of host light. Corrections based on forward modeling and simulated quasar subtraction yield maximum bias |Δlog M_*| ≲ 0.3 dex, generally smaller than typical uncertainties, and insufficient to reconcile extreme BH-to-host mass ratios at $z>6$ (Berger et al., 13 Jun 2025).

5. Mass Corrections in Non-SN Host Studies

Fast Radio Burst Hosts

For FRB host galaxy samples, corrections for stellar mass-to-light ratio (M/L) as a function of broad-band color and SFR are crucial to mitigate selection biases in flux-limited surveys. The referenced correction prescription:

$(M_*/L_r)_{\rm obs} = 10^{a + b(g-r)}$

with scatter σ_{M/L}=0.12 dex, is augmented by an SFR–M/L relation, shifting the host mass distribution and flattening the inferred low-mass slope of the FRB host-galaxy mass function (Loudas et al., 21 Feb 2025).

Dispersion Measure–Mass Correlations

Observed host-galaxy DM for low-redshift FRB hosts anti-correlates with stellar mass, described (over $10^9<M_*/M_\odot<10^{11}$) by:

$$\mathrm{DM}_{\rm host}(M_*) = 89 - 97\,\log_{10}(M_*/10^{10}M_\odot)$$

with intrinsic scatter $\sim60$ pc cm⁻³ (Leung et al., 22 Jul 2025).

6. Methodological and Practical Considerations

Implementation and Limitations

• Applicability: Corrections must be matched to the population, redshift, bandpass, and methodology for which they were derived. Use outside calibration range introduces uncertainty.
• Propagation: Correction uncertainties—both systematic and random—should be propagated into host-mass dependent analyses, especially in cosmological parameter estimation.
• Interpretation: Stellar mass is a proxy for multiple underlying physical properties (metallicity, age, dust content); correlations may result from complex astrophysical causality, not pure mass effects.

Summary of Key Correction Prescriptions

Context	Correction Basis	Formula (param.) evidence
SED fitting, unresolved SFR	sSFR-dependent, outshining	$$m_{\rm resolved} = m_{\rm unresolved}/(-0.057\log_{10}({\rm sSFR})+0.34)$$ (Sorba et al., 2015)
SN Ia HR–host mass	Linear regression (“mass step”)	$HR = \gamma\log_{10}(M_*/M_\odot)+b$; $\gamma\sim-0.057...-0.11$ (1107.60031602.02596Rose et al., 2020)
High-mass SDSS galaxies	Surface-brightness flux loss	$$\log_{10}M_*^{\rm corr} = \log_{10}M_* - 0.4\,\Delta m$$ (D'Souza et al., 2015)
FRB hosts	Color- and SFR-dependent $M/L$	$(M_*/L_r)_{\rm obs} = 10^{a+b(g-r)}$, SFR–M/L (Loudas et al., 21 Feb 2025)
IMF/dynamical	Velocity dispersion-based	$\log_{10}(M_*^{\alpha_{\rm JAM}/M_*}) = a + b\,s_e$ (Bernardi et al., 2017)
SN Ia host mass bias (z)	Redshift-dependent SED bandpass	$\Delta M(z) = 0.05z - 0.20z^2$ (Paulino-Afonso et al., 2022)

The adoption of an appropriate host-galaxy stellar mass correction is critical for quantitative extragalactic astrophysics wherever stellar mass or its systematics propagate into derived properties, cosmological inferences, or studies of galaxy–transient connections.