Moderate Influence of Halo Spin on Stellar Mass Distributions in Dwarf and Massive Galaxies

In empirical models of galaxy formation, galaxy properties are largely determined by the characteristics of their host dark matter halos. Key processes, including gas accretion, temperature, angular momentum retention, and star formation efficiency, are influenced by these halo properties (e.g., Rubin et al. 2010, 2015; Lehner et al. 2014; Fardal et al. 2001; Kereš et al. 2005; van de Voort et al. 2012; Nelson et al. 2013; Noguchi 2023; Guo et al. 2011; Yang et al. 2012; Behroozi et al. 2010; Girelli et al. 2020; Silk 1977). For example, halos with shallower potential wells and lower concentrations exhibit more pronounced feedback effects, which leads to reduced star formation efficiencies, lower stellar mass fractions, and more extended stellar distributions (Kravtsov et al. 2018; Sales et al. 2022; Hopkins et al. 2012; Sawala et al. 2015). Based on hydro-dynamical simulations, in low-mass halos, gas inflow is dominated by “cold mode” accretion, resulting in subsonic flows that create “hot” structures with more diffuse stellar distributions (Noguchi 2018, 2022; Kalita et al. 2022). In contrast, gas accretion in massive halos occurs through a “hot mode”, where supersonic inflows lead to thin, disk-like “cold” structures with significant angular momentum (Noguchi 2018; Hafen et al. 2022).

Despite extensive research, the influence of halo spin on galaxy structure and evolution remains incompletely understood. It is generally accepted that the spin of a dark matter halo impacts the stellar distribution in massive late-type galaxies (Mo et al. 1998; van den Bosch 1998; Diemand et al. 2005; Desmond et al. 2017; Kim & Lee 2013). However, for low-mass galaxies, high-resolution simulations indicate that halo spin may not play as critical a role as it does in massive counterparts, although it may be essential in forming diffuse stellar distributions in ultra-diffuse galaxies (Yang et al. 2023; Di Cintio et al. 2019; Rong et al. 2017; Amorisco & Loeb 2016; Benavides et al. 2023).

To date, research on the effects of halo spin on stellar distributions has been inconclusive, particularly in observational studies where halo spin determination poses significant challenges. Observational halo spin measurements have largely focused on small, high-surface-brightness samples (e.g., Cappellari et al. 2006, 2013; Wang et al. 2020; Rong et al. 2018), often introducing selection biases. This limitation complicates efforts to accurately investigate the correlation between halo spin and stellar distribution.

Large HI surveys conducted with single-dish telescopes provide a unique opportunity to obtain HI spectra for a large number of galaxies, offering essential dynamical data to estimate halo spin parameters for HI-rich galaxies. Since these samples are selected based on HI column densities rather than stellar characteristics, they present an unbiased approach for examining the relationship between halo spin and stellar distribution.

In this study, we estimate halo spins for HI-bearing galaxies selected from the Arecibo Legacy Fast Alfa Survey (ALFALFA; Giovanelli et al. 2005; Haynes et al. 2018) and analyze their relationship with stellar density. Section 2 describes the data sample and our approach for estimating halo spin. Section 3 provides a statistical analysis of the correlation between stellar density and halo spin. Our conclusions are summarized and discussed in Section 4.

Our final sample comprises $6,680$ galaxies with stellar masses spanning $10^{7}$ to $10^{11}$ $\rm M_{\odot}$. Panels a and b of Fig. 1 illustrate the relationship between $S_{\star}$ and $\lambda_{\rm{h}}$ for the low-mass ($M_{\star}<10^{9}\ M_{\odot}$) and massive ($M_{\star}>10^{9}\ M_{\odot}$) galaxies, respectively.The blue and red points with error bars represent the median $\lambda_{\rm{h}}$ values and their $1\sigma$ uncertainties across different $\log S_{\star}$ bins. A linear fit to these medians yields $\log\lambda_{\rm{h}}=(-0.09\pm 0.09)\log S_{\star}-(0.16\pm 0.59)$ for the low-mass galaxies, and $\log\lambda_{\rm{h}}=(-0.11\pm 0.09)\log S_{\star}+(0.04\pm 0.73)$ for high-mass galaxies. The correlation coefficients of -0.21 and -0.31 suggest a weak correlation in low-mass galaxies and a moderate correlation in high-mass galaxies.

Considering that environmental factors can affect galaxy size and thereby stellar density (Moore et al. 1996; Mayer et al. 2001; Mastropietro et al. 2005; Smith et al. 2015; Kazantzidis et al. 2011), we control for environmental influences by using the galaxy group catalog from Saulder et al. (2016), constructed with a friends-of-friends algorithm based on SDSS DR12 (Alam et al. 2015) and 2MASS Redshift Survey (Huchra et al. 2012) data, accounting for biases like the Malmquist bias and “Fingers of God” effect.

We further refine the sample to include only isolated galaxies, defined as those located more than three times the virial radius from any galaxy group or cluster (Rong et al. 2024a) to minimize effects of tidal stripping and ram-pressure stripping (Mamon et al. 2004; Gill et al. 2005; Oman et al. 2013; Zinger et al. 2018). Panels c and d of Fig. 1 display the relationship between $\lambda_{\rm{h}}$ and $S_{\star}$ for this isolated sample. Linear fits yield $\log\lambda_{\rm{h}}=(-0.08\pm 0.09)\log S_{\star}-(0.20\pm 0.60)$ for isolated low-mass galaxies and $\log\lambda_{\rm{h}}=(-0.11\pm 0.09)\log S_{\star}+(0.03\pm 0.69)$ for isolated high-mass galaxies, with correlation coefficients of -0.18 and -0.30, indicating the persistence of weak to moderate correlations between $S_{\star}$ and $\lambda_{\rm{h}}$ across galaxy masses, independent of environmental effects.

Using a semi-analytic approach, we estimate halo spin parameters ($\lambda_{\rm{h}}$) for HI-rich galaxies in the ALFALFA survey and examine how the stellar surface density ($S_{\star}$) varies with halo spin in isolated low- and high-mass samples. Our analysis reveals a moderate correlation between $\lambda_{\rm{h}}$ and $S_{\star}$ in both galaxy samples, implying that halo spin significantly influences gas cooling, star formation, and feedback processes within galaxies. This finding is consistent with prior results in Rong et al. (2024a) but indicates that the correlation between halo spin and stellar surface density is weaker than that between halo spin and HI-to-stellar mass ratios (Liu et al. 2024).

As proposed by Rong et al. (2024a), high-spin halos acquire gas with high angular momentum, which resists momentum loss and slows its inward motion and cooling. This process restricts the accumulation of cold gas at the galactic center, reducing the fuel for star formation (Peng & Renzini 2020). Consequently, gas inflow and star formation are more gradual, minimizing supernova-driven feedback and limiting gas expulsion from the halo. Instead, gas is displaced outward within the halo, weakening the central gravitational potential and promoting an extended stellar distribution as stars and dark matter migrate outward (Di Cintio et al. 2017; Yang et al. 2024). Our results suggest that this halo-spin-dependent formation scenario may apply universally across galaxy types.

However, the weaker correlation observed between $\lambda_{\rm{h}}$ and $S_{\star}$ compared to that between $\lambda_{\rm{h}}$ and HI-to-stellar mass ratios (Liu et al. 2024), suggests that stellar distribution may also be shaped by additional mechanisms beyond halo spin alone, indicating a more complex set of processes at work in galaxy evolution.

Note that we utilize a semi-analytic method to estimate the halo spin, which may introduce relatively large uncertainties. For example, the application of equation (1) relies on the assumption of spherically symmetric dark matter halo systems, a universally applicable baryonic Tully-Fisher relation with a slope of 3.5, and the same specific angular momenta of cool gas and halo. The assumed geometry and kinematics of the cool gas disk may also be overly idealized. As a result, the estimated spins from equation (1) are statistically higher than those of dark matter halos in simulations (e.g., Bett et al. 2007). However, since the spins of both galaxy samples with low and high stellar surface densities are likely overestimated, the correlation between $\lambda_{\rm{h}}$ and $S_{\star}$ cannot be attributed to spin overestimation. Nevertheless, this relationship underscores the robust correlation between the two galaxy characteristics, and further observational investigations are warranted to re-examine the moderate correlation between them.