Galaxy formation in the epoch of reionization 


One of the key goals of DELPHI is to shed light on the interplay between galaxy formation and reionization. A few key results from our work on this topic are highlighted below:

1. We have recently had our invited review on "Early galaxy formation and its large-scale effects" published in Physics Reports (Dayal & Ferrara, 2018, Physics Reports, 780, 1). In this review, we combine the information gleaned from different theoretical models/studies to build a coherent picture of the Universe in its early stages which includes the physics of galaxy formation along with the impact that early structures had on large-scale processes as cosmic reionization and metal enrichment of the intergalactic medium. A few key points from the review are noted below


A timeline of the first billion years of the Universe (Sec. 2). According to our current understanding, immediately after its inception in the Big Bang, the Universe underwent a period of accelerated expansion (inflation) after which it cooled adiabatically. At a redshift z~1100, matter and radiation decoupled (decoupling) giving rise to the cosmic microwave background (CMB) and electrons and protons recombined to form hydrogen and helium (recombination). This was followed by the cosmic ``Dark Ages" when no significant radiation sources existed. These cosmic dark ages ended with the formation of the first stars (at z~30). These first stars started producing the first photons that could reionize hydrogen into electrons and protons, starting the "Epoch of cosmic Reionization" which had three main stages: the pre-overlap phase where each source produced an ionized region around itself, the overlap  phase when nearby ionized regions started overlapping and the post-overlap phase when the IGM was effectively completely ionized. (Reionization simulation credit: Dr. Anne Hutter).


Metal enrichment of the Intergalactic medium (IGM; Sec. 6). The plot shows the cumulative fractional contribution to the IGM metal enrichment from galaxies below the halo mass value on the x-axis. As marked, the solid, dashed and dot-dashed lines show the results at z=5, 10 and 15, respectively. The horizontal solid, dashed and dot-dashed lines show cumulative fractional contributions of 90%, 50% and 25%, respectively. As shown, while galaxies below a (log) halo mass of 7.8 solar masses contribute half of the total IGM metal budget at z=15, this value shifts to higher values of  9.5solar masses by z=5. Changing the model assumptions, such as assuming outflows to be preferentially metal-rich (w>1) or metal-poor (w<1) can increase and decrease the fractional contributions. Further, assuming a constant star formation efficiency for all halos, as opposed to a mass-dependent value, will result in a larger fractional contribution from lower masses as marked.


The key reionization sources (IGM; Sec. 7). The plots shows the cumulative fractional contribution to reionization photons from galaxies below the halo mass value on the x-axis. The solid lines show results without any reionization (UV) feedback. Dashed lines show results for a maximal UV feedback scenario where all galaxies with a virial velocity < 50 km/sare assumed to be devoid of baryons due to photo-evaporation. The horizontal lines show the 25, 50 and 90% fractions. As seen, while halos with (log) mass below 8.7 solar masses can provide half of the reionization photons, using a halo mass dependent star formation efficiency, this value increases to (log) halo mass <= 9.8 solar masses if only galaxies above the chosen virial velocity can support star formation. Changing the model assumptions (on the escape fraction and star formation efficiency dependence on halo mass) will result in a larger fractional contribution from higher (lower) mass galaxies. 


The cosmic star formation rate density (IGM; Sec. 8). Points show observational data collected by various ground- and space-based campaigns The black lines shows DELPHI (Dayal et al. 2014) results integrated down to a UV magnitude limit of -17.7 (solid line), -15 (dashed line) and for all galaxies (dot-dashed line). The dot-dashed gold line and the dashed red line show results from the DRAGONS project (Mutch et al. 2016) and the EAGLE simulations (Schaye et al. 2015), respectively. We also show the SFRD-z trend inferred from low-z galaxies which evolves as (1+z)^-3.6 (short-dashed blue line) with z>8 Lyman Break Galaxies showing a much steeper fall-off as (1+z)^-10.9 (long-dashed blue line). Although showing different slopes for the z-evolution of the SFRD, as of now, all three models (DELPHI, DRAGONS and EAGLE) are in accord with the observations within error bars

2. We have also recently submitted our paper entitled "The hierarchical assembly of galaxies and black holes in the first billion years: predictions for the era of gravitational wave astronomy" (Dayal et al. 2018) to MNRAS. In this work we include black hole (BH) seeding, growth and feedback into our semi-analytic galaxy formation model, Delphi. Our model now fully tracks the, accretion- and merger-driven, hierarchical assembly of the dark matter halo, baryonic and BH masses of high-redshift (z>5) galaxies. We use a minimal set of mass- and z-independent free parameters associated with star formation and BH growth (and feedback) and include suppressed BH growth in low-mass galaxies to explore a number of physical scenarios including: (i) two types of BH seeds (stellar and those from Direct Collapse BH; DCBH); (ii) the impact of reionization feedback; and (iii) the impact of instantaneous versus delayed galaxy mergers on the baryonic growth. We find that while both reionization feedback and delayed galaxy mergers have no sensible impact on the evolving ultra-violet luminosity function, the latter limits the maximum BH masses achieved at these high-z. We then use this model, baselined against all available high-z galaxy and BH data-sets, to predict the LISA detectability of merger events at z>5. As expected, the merger rate is dominated by stellar BH mergers for all scenarios and our model predicts an expected upper limit of about 20 mergers in the case of instantaneous merging and no reionization feedback over the 4-year mission duration. Including the impact of delayed mergers and reionization feedback reduces this to about 12 events over the same observational time-scale.


The ultra-violet luminosity function (UV LF) from z~5-10 as marked in the panels. In each panel, the violet points show the available Lyman Break Galaxy data collected both using space- and ground-based observatories and the yellow points show the Active Galactic Nuclei data collected observationally. In each panel, lines show model UV LFs for galaxies and black holes for the following models that bracket the range of UV LFs allowed in the presence/absence of a UVB and for both instantaneous and delayed (by a merging timescale) merger: ins1 (galaxies solid black line; BH solid gray line), ins4 (galaxies short dashed red line; short dashed light-red line), tdf1 (galaxies long dashed green line; BH long-dashed light green line) and tdf4 (galaxies dot-dashed blue line; BH dot-dashed purple line).


The BH merger event rate (per year) expected as a function of redshift for two models that bracket the physical range probed: left panel: ins1 and right panel: tdf4. In each panel, the dot-dashed purple line shows the results for all mergers (without any cut in signal to noise ratio) while the solid black line shows the results for all mergers using a value of signal-to-noise SNR>7. The latter is deconstructed into the contribution from (SNR>7) type1 (stellar BH-stellar BH mergers; green dashed line), type2 "light DCBH" seed (stellar BH-DCBH mergers; dark blue dashed line) and type3 "light DCBH" seed (DCBH-DCBH mergers; red dashed line) mergers. Further, the long-dashed light blue line and dot-dashed pink line show results for mergers with SNR>7 using a heavier DCBH seed mass of 10^4-5 solar masses for type 2 and type 3 mergers, respectively.