The Assembly of Milky Way-like Galaxies Since z~2.5 (1304.2391v2)

Abstract: Galaxies with the mass of the Milky Way dominate the stellar mass density of the Universe but it is uncertain how and when they were assembled. Here we study progenitors of these galaxies out to z=2.5, using data from the 3D-HST and CANDELS Treasury surveys. We find that galaxies with present-day stellar masses of log(M)~10.7 built ~90% of their stellar mass since z=2.5, with most of the star formation occurring before z=1. In marked contrast to the assembly history of massive elliptical galaxies, mass growth is not limited to large radii: the mass in the central 2 kpc of the galaxies increased by a factor of 3.2+-0.8 between z=2.5 and z=1. We therefore rule out simple models in which bulges were fully assembled at high redshift and disks gradually formed around them. Instead, bulges (and black holes) likely formed in lockstep with disks, through bar instabilities, migration, or other processes. We find that after z=1 the growth in the central regions gradually stopped and the disk continued to build, consistent with recent studies of the gas distributions in z~1 galaxies and the properties of many spiral galaxies today.

• The paper shows that Milky Way-mass galaxies built approximately 90% of their stellar mass since z~2.5 through sustained star formation.
• It utilizes cumulative number density matching with HST and SDSS surveys to trace progenitors’ mass and structural evolution across cosmic time.
• The analysis reveals uniform radial mass growth, challenging simple bulge-disk formation models and offering critical benchmarks for galaxy formation simulations.

The paper "The Assembly of Milky Way-like Galaxies Since z~2.5" (1304.2391) investigates how galaxies with stellar masses similar to the Milky Way (approximately $5 \times 10^{10}$ M$_{\odot}$ at $z=0$) have grown and changed their structure over the past ~12 billion years, from redshift $z \sim 2.5$ to the present day. The paper utilizes data from the 3D-HST and CANDELS Hubble Space Telescope surveys, complemented by Sloan Digital Sky Survey (SDSS) data for the local universe.

The core methodology involves tracing the progenitors of present-day Milky Way-mass galaxies by selecting galaxies at higher redshifts that have the same cumulative co-moving number density. This technique assumes that the rank order of galaxies by stellar mass is largely conserved over cosmic time, which has been shown to be a reasonable approximation in simulations. By identifying these progenitors across different redshift bins, the authors construct a statistical picture of the average assembly history.

Based on this selection, the paper finds that galaxies destined to become Milky Way-like built approximately 90% of their stellar mass since $z=2.5$. The majority of this mass assembly occurred relatively early, before $z=1$, through significant star formation. This implied star formation history, derived directly from the mass evolution curve, is consistent with independently measured star formation rates of the selected galaxies obtained from spectral energy distribution (SED) fitting. This suggests that the mass growth was predominantly driven by star formation rather than major mergers, which are found to be more important for the growth of more massive galaxies at later times.

A key finding concerns the spatial distribution of this mass growth. By stacking images of the selected galaxies in different redshift bins and analyzing their radial surface density profiles, the authors demonstrate that the mass growth from $z=2.5$ to $z \sim 1$ was remarkably uniform across all radii. The central regions (within $r=2$ kpc) increased their stellar mass by a factor of $3.2^{+0.8}_{-0.7}$ between $z=2.5$ and $z=1$, while the outer regions also grew significantly. This contrasts sharply with the assembly history of more massive elliptical galaxies, which show strong inside-out growth, having formed dense cores at high redshift and adding mass primarily to their outer envelopes later. The finding that central regions grew substantially at the same time as disks rules out simple two-phase formation models where bulges are fully assembled early and disks form around them later. Instead, it supports scenarios where central components (bulges) and disks form concurrently, possibly driven by secular processes within the disk itself, such as bar instabilities, radial migration, or the dynamics of gas accretion in clumpy, turbulent disks observed at high redshift.

After $z \sim 1$, the pace of mass growth slows considerably, particularly in the central regions, which show little significant mass increase between $z=1$ and $z=0$. Disk growth continues, leading to the characteristic structure of present-day spiral galaxies with less active bulges and still star-forming (albeit at a lower rate) disks.

Structurally, Milky Way progenitors show less dramatic evolution compared to more massive galaxies. Their effective radii increased by a factor of $\sim 1.8$ and their Sersic index (a measure of light concentration) changed from $\sim 1.5$ to $\sim 2.5$ since $z=2.5$. This size growth scaling, $r_e \propto M^{0.27 \pm 0.04}$, is much shallower than that observed for massive galaxies ($r_e \propto M^{2.0 \pm 0.1}$) and is similar to the slope of the size-mass relation for late-type galaxies in the local universe. This indicates that while their mass increased significantly, their overall structure evolved relatively modestly, maintaining characteristics consistent with disk-dominated systems throughout much of their assembly history.

For practical implementation and application, this research highlights several aspects:

1. Data Requirements: To paper galaxy evolution this way, large, deep, multi-wavelength photometric and spectroscopic/grism surveys are essential across a wide range of redshifts. The combination of high-resolution HST imaging (CANDELS) and spectral information (3D-HST grism) is crucial for measuring sizes, morphologies, stellar masses, and star formation rates accurately for large samples of distant galaxies. SDSS provides the necessary low-redshift baseline.
2. Analysis Pipeline: A robust data processing pipeline is required, including:
   • Photometric redshift estimation and stellar population synthesis fitting to derive stellar masses and SFRs.
   • Image processing for stacking, including alignment, normalization, and background subtraction.
   • Advanced techniques for PSF deconvolution or correction to recover intrinsic galaxy profiles accurately, which is critical for measuring central densities and sizes. Tools like GALFIT are commonly used for this.
   • Methods for measuring radial profiles and structural parameters from potentially complex galaxy morphologies.
3. Statistical Methods: The number density matching technique requires reliable stellar mass functions across cosmic time. Statistical analysis like bootstrapping is vital for estimating uncertainties in measurements from stacked images and derived parameters.
4. Computational Resources: Processing and analyzing the volume of data from surveys like 3D-HST and CANDELS, performing SED fitting for thousands of galaxies, stacking images, and running profile fitting algorithms are computationally intensive tasks.

import numpy as np from scipy.interpolate import interp1d z_local = 0.1 mass_local = np.array([10**10.6, 10**10.7, 10**10.8]) # Example log mass density_local = np.array([1.5e-3, 1.1e-3, 0.8e-3]) # Example cumulative density (Mpc^-3) mf_local = interp1d(density_local, mass_local) target_mass_local = 10**10.7 target_density = 1.1e-3 # Mpc^-3 redshifts_high_z = [0.6, 1.0, 1.5, 2.0, 2.4] evolved_masses_log = [] mass_z1 = np.array([10**10.0, 10**10.2, 10**10.4]) density_z1 = np.array([2.0e-3, 1.1e-3, 0.6e-3]) mf_z1 = interp1d(density_z1, mass_z1) try: mass_at_z1 = mf_z1(target_density) evolved_masses_log.append(np.log10(mass_at_z1)) print(f"Mass at z=1.0 for density {target_density:.1e}: {np.log10(mass_at_z1):.2f} log Msun") except ValueError: print(f"Target density {target_density:.1e} outside the range for z=1.0 mass function.") def get_milky_way_progenitor_mass_log(z): return 10.7 - 0.045 * z - 0.13 * z**2 print(f"Mass at z=2.5 according to Eq. 1: {get_milky_way_progenitor_mass_log(2.5):.2f} log Msun") print(f"Mass at z=1.0 according to Eq. 1: {get_milky_way_progenitor_mass_log(1.0):.2f} log Msun") print(f"Mass at z=0.1 according to Eq. 1: {get_milky_way_progenitor_mass_log(0.1):.2f} log Msun")

The paper provides strong observational constraints that are crucial for refining cosmological galaxy formation simulations. By showing that MW-like galaxies assemble differently than more massive galaxies (more uniform growth vs. inside-out growth, star formation-dominated vs. merger-driven growth), it highlights the need for models to accurately reproduce these different mass-dependent assembly pathways. The detailed quantitative measurements of mass growth at different radii and structural parameter evolution offer specific targets for simulation validation. The identified limitations, such as the impact of stellar migration on observed profiles, suggest directions for future research, including spatially-resolved studies of gas kinematics and distribution at high redshifts.