Early galaxy formation and its implications for dark matter, 21cm cosmology and multi-messenger astronomy
Pratika Dayal
DELPHi ODIN The team in Groningen
Ruslan Brilenkov
Maxime Trebitsch Anne Hutter
Pratika Dayal
Laurent Legrand Jonas Bremer
Olmo Piana Key collaborators and collaborations Rychard Bouwens: Leiden University, The Netherlands Volker Bromm: University of Texas at Austin, USA Marco Castellano: Observatory of Rome, Italy Benedetta Ciardi: Max Planck Institute for Astrophysics, Germany Tirthankar Choudhury: National Centre for Radio Astronomy, India James Dunlop: Institute for Astronomy, U.K. Andrea Ferrara: Scuola Normale Superiore, Italy Stefan Gottloeber: Leibniz institute for Astrophysics, Germany Hiroyuki Hirashita: ASIAA, Taiwan Umberto Maio: Leibniz institute for Astrophysics, Germany Antonella Maselli: University of Barcelona, Spain Andrei Mesinger: Scuola Normale Superiore, Italy LISA Volker Mueller: Leibniz institute for Astrophysics, Germany Noam Libeskind: Leibniz institute for Astrophysics, Germany Fabio Pacucci: Harvard, USA Laura Pentericci: Observatory of Rome, Italy Elena Rossi: Leiden University, The Netherlands Catherine Trott: ICRAR, Perth, Australia Livia Vallini: Nordita, Stockholm, Sweden Marta Volonteri: Observatory of Paris, France Gustavo Yepes: Universita Autonoma di Madid, Spain… EUCLID HST The outstanding challenges
• Hints on the (warm) nature of dark matter using early galaxies
• Hints on (warm) nature of dark matter using 21cm data
• Early galaxies and GW events from LISA Hints on the (warm) nature of dark matter using early galaxies and 21cm data Hierarchical structure formation in CDM z = 20
z = 10
z =7
z =6 CDM Mass roughly ~100 GeV Lighter the WDM particle, more is the suppression of small scale structure z = 20
z = 10
z =7
z =6 3keV Lighter the WDM particle, more is the suppression of small scale structure z = 20
z = 10
z =7
z =6 1.5keV Since the merger tree starts building up later in WDM models..
Galaxies containing gas
Galaxies devoid of gas
Star formation in galaxies
Stellar mass
Smooth accretion of dark matter and gas from the intergalactic medium
Tuesday, 10 June 14 Since the merger tree starts building up later in WDM models..
Galaxies containing gas
Galaxies devoid of gas
Star formation in galaxies
Stellar mass
Smooth accretion of dark matter and gas from the intergalactic medium
Tuesday, 10 June 14 Early galaxies in WDM models 7
..it leads to a delayed assembly of stellar mass
CDM Galaxies assemble faster 5 keV • in 1.5 keV WDM models 3 keV compared to CDM. This is because they start off 1.5 keV bigger and are less feedback limited as a consequence.
~400 million
Log (Total stellar mass assembled) (Total Log years
Redshift PD+2015, ApJ, 806, 67
Figure 3. Average stellar mass assembly of galaxies as a function of z.Forthefinalz =4M value quoted in each panel, we show ⇤ the stellar mass build up for the four di↵erent DM models considered: CDM (solid black line), 5keV WDM (blue short-dashed line), 3keV WDM (red long-dashed line) and 1.5keV WDM (violet dot-dashed line). Gray, blue, red and purple shaded regions show the 1 dispersion for the CDM and WDM models of mass 5, 3and1.5keV,respectively.Asseen,high-z star formation is more rapid in WDM models. For example, z =4galaxieswithM =108.5M assemble 90% of their stellar masses within the previous 1.03 (0.64) Gyr in ⇤ CDM (1.5 keV WDM). This younger stellar population means that for a given stellar mass, WDM galaxies are more UV luminous. distinction of WDM with respect to CDM is most notable in stellar population. A useful observational probe of this trend the dearth of small halos, near the atomic cooling threshold is the mass to light relation, which links the total stellar mass (e.g. Fig. 1). The lack of these progenitor building blocks (M )andtheUVmagnitude(MUV ). ⇤ results in a sudden appearance of galaxies in WDM models, In Fig. 4 we show the M MUV relation for our DM ⇤ with little scatter in the assembly history. models. The M MUV relation for CDM (and mx > 3keV ⇤ As shown in Sec. 3.1, the higher particle mass WDM WDM) galaxies brighter than MUV = 15 is well fit by a models are di cult to distinguish from CDM with the as- power law: sembly histories for mx > 3 keV WDM models only di↵ering log M = MUV + , (14) from CDM in the high-z tails. Indeed, stellar mass assembly ⇤ histories in CDM and the 5 keV WDM model di↵er by less where = 0.38 and =2.4 0.1z. This relation is in good than 50 Myr, throughout the range shown in Fig. 3. agreement both with estimates using abundance matching (e.g. Kuhlen & Faucher-Giguere 2012; Schultz et al. 2014) and direct observational estimates for LBGs (Grazian et al., 3.3 Mass to light relation A&A submitted); we show the last group’s results in the In the previous section we saw that galaxies in WDM models z =7panelwhoalsofindaslopeof = 0.4. assemble their stars more rapidly compared to CDM. This As seen from Eqn. 14, the normalisation ( )ofthe rapid assembly translates to a younger, more UV luminous M MUV relation decreases with increasing z (although ⇤ c 0000 RAS, MNRAS 000,000–000 Mass-to-light ratios are cosmologyEarly dependent! galaxies in WDM models 7 Log (Stellarmass) Log
PD+2015, ApJ, 806, 67;
-15 -20 UV Magnitude
Light WDM models show lower M/L ratios (i.e. more luminosity per unit stellar mass) compared to CDM
Fig. 4.— Mass-to-light relation showing galaxy stellar mass as a function of UV magnitude for z 7 12 as marked. In each panel we ' show average M values for given MUV bins from our fiducial model for the four DM models considered in this work: CDM (solid black line), 5keV WDM⇤ (blue short-dashed line), 3keV WDM (red long-dashed line) and 1.5keV WDM (violet dot-dashed line). At z 7, violet points show the values for real galaxies in the CANDELS and HUDF fields, with yellow points showing the observed medians in' each UV bin as inferred by Grazian et al. (A&A submitted). In each panel, dashed vertical lines show the 10 104 s integration limits of the JWST. 3.2. Assembling early galaxies 3.3. Mass to light relation We now explore the build-up of the LFs shown in the In the previous section we saw that galaxies in WDM previous section. Due to the suppression of small-scale models assemble their stars more rapidly compared to structure in WDM models, star-formation is delayed and CDM. This rapid assembly translates to a younger, more more rapid (e.g Calura et al. 2014; Sitwell et al. 2014). UV luminous stellar population. A useful observational We quantify this for our galaxy evolution models in Fig. probe of this trend is the mass to light relation, which 3, in which we show the stellar mass assembly histories links the total stellar mass (M ) and the UV magnitude 8.5 ⇤ for four di↵erent mass bins ranging from M = 10 (MUV ). 10 ⇤ 10 M . In Fig. 4 we show the M MUV relation for our ⇤ As expected in hierarchical structure formation, the DM models. The M MUV relation for CDM (and ⇤ larger the final stellar mass, the earlier it started forming mx 3 keV WDM) galaxies brighter than MUV = 15 (i.e. with flatter assembly histories). For example, z = is well fit by a power law: 4 galaxies with M = 1010M build up 90% of their ⇤ stellar mass within the last 1.26 Gyr in CDM. Smaller log M = MUV + , (14) galaxies with M = 108.5M in CDM take only 1.03 Gyr ⇤ to build-up 90%⇤ of the stellar mass. This distinction where = 0.38 and =2.4 0.1z. This relation is even more dramatic in WDM models. For example, is in good agreement both with estimates using abun- z = 4 galaxies with M = 108.5 (1010)M assemble 90% dance matching (e.g. Kuhlen & Faucher-Giguere 2012; of their stellar masses⇤ within the previous 0.64 (1.12) Schultz et al. 2014) and direct observational estimates Gyr, for mx =1.5 keV. The distinction of WDM with for LBGs (Grazian et al., A&A submitted); we show the respect to CDM is most notable in the dearth of small last group’s results in the z = 7 panel who also find a halos, near the atomic cooling threshold (e.g. Fig. 1). slope of = 0.4. The lack of these progenitor building blocks results in As seen from Eqn. 14, the normalisation ( ) of the a sudden appearance of galaxies in WDM models, with M MUV relation decreases with increasing z (although ⇤ little scatter in the assembly history. the slope remains unchanged), i.e. a given UV luminosity As shown in Sec. 3.1, the higher particle mass WDM is produced by lower M galaxies with increasing z.This models are di cult to distinguish from CDM with the is due to the fact these galaxies⇤ are hosted by increasingly assembly histories for mx 3 keV WDM models only (with z) rare, biased halos, farther on the exponential tail di↵ering from CDM in the high-z tails. Indeed, stellar of the HMF, whose fractional growth is more rapid. mass assembly histories in CDM and the 5 keV WDM While there is little di↵erence between the M MUV ⇤ model di↵er by less than 50 Myr, throughout the range relation for CDM and mx 3 keV WDM, this relation shown in Fig. 3. starts diverging from the CDM one at MUV 19 at all z =7 12 in the 1.5 keV WDM model. The' relation Early galaxies in WDM models 5
Early galaxies in WDM models 5 UV LFs in Cold versus Warm DM models 4 Dayal et al. Scaling Halo mass function
Schultz+2014
Fig. 2.— The evolving LBG UV LF at z 7 12 in di↵erent DM models, computed with our fiducial semi-analytical galaxy formation model. In all panels, lines show the results' using the fiducial model that invokes a total of two redshift and mass-independent free parameters: the star formation e ciency (f 0.04) and the fraction of SN energy driving winds (fw =0.1). In all panels lines show theoretical results for CDM (black solid line)⇤ and⇡ WDM with particle masses of 5keV (blue short-dashed), 3keV (red long-dashed) and 1.5keV(violetdot-dashed);dashedverticallinesshowthe10 104 s integration limits of the JWST. In all panels, points show observational results (see Fig. 1 for references).
(HMF) at that redshift assuming a fixed halo mass-to- TABLE 1 light ratio. Indeed, Schultz et al. (2014) propose that For the redshift shown in column 1, we show the observed the cumulative number densityFig. of 2.—high-redshiftThe evolving galaxies LBG UVfaint-end LF at z slope7 of12 the in UV di↵erent LF (McLure DM models, et al. 2009,computed 2013) with in our fiducial semi-analytical galaxy formation could be used to constrain mmodel.. We caution In all howeverpanels, lines that showcolumn the results 2.' Columns using 3 the and fiducial 4 show the model faint-end that invokes slope of a the total of two redshift and mass-independent free x fiducial UV LFs with the 1 errors for CDM and 1.5keV constraints on WDM obtainedparameters: through such the star abundance formation e ciency (f 0.04) and the fraction of SN energy driving winds (fw =0.1). In all panels lines show theoretical results for CDM (black solidWDM, line)⇤ respectively. and⇡ WDM Thewith faint-end particle massesslopes for of 5keV the (blue short-dashed), 3keV (red long-dashed) and matching directly rely on the assumed halo mass UV theoretical UV LF have been computed4 over the absolute 1.5keV(violetdot-dashed);dashedverticallinesshowthe10$ magnitude range 1018 sM integration14. limits of the JWST. In all panels, points show observational luminosity relation, which Schultz et al. (2014) take to UV be independent of the DM modelresults and (see assume Fig. 1 for a power- references). z ↵obs ↵CDM ↵1.5keV law extrapolation towards small(HMF) masses. at that As we redshift shall see assuming a7 fixed1.90 halo+0.14 mass-to-1.96 0.18 1.85 0.11 0.15 ± ± TABLE 1 below, this need not be the case.lightFig. 1.— ratio.The Indeed, evolving LBG Schultz UV LFs et al.at z (2014)8 7 2.0212 propose+0 for.22 the four2.06 that di0↵.22erentFor DM1.93 models the0.13 redshift considered, shown obtained in column by scaling 1, we the show appropriate the observed ' 0.23 ± ± Before presenting resultsHMFthe from cumulative with our a complete halo mass number model independent density star of formation high-redshift9 e ciency galaxies of2.21f =00.32.9%faint-end at2.01z 07and.16 slopef =1 of.3% the for UVz > LF8. (McLure In all panels, et al. lines 2009, show 2013) in ⇤± ±' ⇤ which includes feedback, intheoreticalcould Fig. be 1 we usedresults show to for constrain UV CDM LFs (blackm solid. We line) caution10 and WDM however with2 particle.31 that0.45 massescolumn2.10 of 5keV0.18 2. (blue Columns short-dashed), 3 and 4⇠ show3keV (red the long-dashed) faint-end slope and of the x 4 ± ± obtained simply by multiplying1.5keV(violetdot-dashed);dashedverticallinesshowthe10 the HMFs by a con- 11 102.39s integration0.32 fiducial2.22 limits0.28 of UV the LFs JWST. with In all the panels1 pointserrors show for observational CDM and 1.5keV constraints on WDM obtained through such abundance ± ± stant mass-to-light ratio. Matchingresults: (a) toz the7: observations Oesch et al. (2010, filled12 cyan squares), Bouwens2.62 0 et.53 al. (2010,2.34 WDM, empty0.44 blue respectively. circles), Bouwens The faint-end et al. (2011, slopes filled yellow for the requires a halo star formationcircles),matching e Castellanociency directly' with et al. rely values (2010, on the empty assumed purple triangles), halo mass McLure UV± et al. (2010, theoretical filled± red triangles), UV LF have McLure been et computed al. (2013, empty over orange the absolute circles)luminosity and Bowler relation, et al. which (2014, filled Schultz purple et circles); al. (2014) (b) z take$8: Bouwens to et al. (2010, emptymagnitude blue circles), range Bouwens18 M etUV al. (2011,14. filled f =(0.9, 1.3)% for z =(7, 8 10); we use f =0.013 ' ⇤ yellowbe independent circles), McLure⇤ of theet al. DM (2010, model filled green and triangles), assume a Bradley power- et al. (2012, empty purple squares) and McLure et al. (2013, empty for all z 11 and 12 givenorange the lack circles), of data(c) z at9: these McLure et al. (2013, empty blue circles) and Oesch et al. (2013,z empty↵ greenobs squares)↵CDM and, (d) z 10:↵1. Bouwens5keV ' law extrapolation' towards small masses. As we shall see +0.14 ' z. A constant halo mass etUV al. luminosity (2014, empty mapping green circles); al- thevalue downward of ↵ pointing2 inferred triangle observationally represents the upper-limit (e.g.7 McLure of1. the90 z 10 data1.96 at M0UV.18 191.85.25. 0.11 $ ' 0.'15 ± ' ± lows us to estimate which halosbelow, host this observable need galaxies: not be the case.et al. 2013). In spite of this peel-away, the faint-end8 2.02+0 .22 2.06 0.22 1.93 0.13 On the other hand, a galaxy that has progenitors in- bright-end where galaxies0.23 can form± stars with the± maxi- e.g. galaxies with MUV 15Before ( 20) reside presenting in halos with resultsslope from values our for complete all the four model DM models explored here9 are 2.21 0.32 2.01 0.16 8.6 8.8 10.8 11' .2 herits a certain amount of stars and gas from them fol- mum e ciency. Although this model± need not be unique± Mh 10 (10 )Mwhichat z includes=7 12. feedback, inequally Fig. compatible 1 we show with UV current LFs observations, including10 2.31 0.45 2.10 0.18 ' lowing merging events. In addition, this galaxy also ob- in describing the observed LF, we stress± again that± our From Fig. 1 we can also estimateobtained the simply viability by of dis- multiplyingthe deepest the HMFsz 7, 8 by data a obtained con- from the Hubble11 Ul- 2.39 0.32 2.22 0.28 ' ± ± tinguishing between di↵erenttainsstant DM a models.mass-to-light part of We its see DM ratio. that (and Matching gas)tra mass Deep Field throughto the 2012 observations smooth- (HUDF12; Ellismain et al. conclusions 2013;12 McLure are driven by2.62 the relative0.53 2 di.34↵erences0.44 3 the WDM LFs with mx = 3accretionrequires (5) keV are from a essentially halo the star IGM: indis- formation whileet in al. principle e 2013). ciency With a cosmolog- with its higher values sensitivitybetween the,the cosmologies,JWST which are± more robust ± to as- tinguishable from CDM downicalf to=(0 ratio an absolute.9 of, 1. DM3)% magnitude and for baryonsz =(7,could8 can10); be potentially accreted we use constrain ontof =0 the. the013 UVtrophysical LF and hence uncertainties.↵ to of MUV 15 ( 14); this ishalo,for about⇤ all UVB 0.5z (1.5) photo-heating11 magnitudes and 12 given feedbackfainter the suppresses lack magnitudes, of data the allowing⇤ avail- at these constraints on mx. fainter than' the range of the next generation of instru- EARLY GALAXY EVOLUTION IN DIFFERENT DARK ablez. A gas constant reservoir' halo for accretion mass UV insideHowever, luminosity the ionized the UV mapping IGM LFs areas al- more3. complex,value of shaped↵ by 2 inferred observationally (e.g. McLure ments such as the JWST. However, the UV LF for WDM the star-formation histories of each galaxy. While galax-MATTER MODELS explainedlows us to in estimate Sec. 2.2. which Thus,$ halos the total host initial observable gas mass galaxies: in et al. 2013).' In spite of this peel-away, the faint-end with mx =1.5 keV starts tothe “peel-away” galaxy at fromz is the CDM sum of the newly accreted gas mass, We now show how high-z galaxy assembly varies with e.g.10 galaxies with MUV 153 ( 20) reside in halos with slope values for all the four DM models explored here are UV LF at a value of Mh 10 M at all z = 7 to 12, We use the detection limits for as well as8 that.6 8.8 brought10.8 in11' by.2 its merging progenitors.4 the DM particle mass considered, and its impact on ob- and exhibits faint-end slope'M valuesh 10 shallower (10 than the )Ma10at z =7 1012.sobservationprovidedatequally compatible with current observations, including This' updated gas mass is thenhttp://www.stsci.edu/jwst/instruments/nircam/sensitivity/table. used to calculate the servables including the UV LF, the M/L relation and the newFrom stellar Fig. mass 1 we formed can also in the estimate galaxy the as described viability of by dis- the deepest z 7, 8 data obtained from the Hubble Ul- tinguishing between di↵erent DM models. We see that SMD.tra Deep Field' 2012 (HUDF12; Ellis et al. 2013; McLure Eqn. 11. The total stellar mass in this galaxy is now the 3 the WDM LFs with mx = 3 (5) keV are essentially indis- et al. 2013). With its higher sensitivity ,theJWST sum of mass of the newly-formed stars, and that brought 3.1. Ultraviolet luminosity functions intinguishable by its progenitors. from CDM down to an absolute magnitude could potentially constrain the UV LF and hence ↵ to of MUV 15 ( 14); this is about 0.5 (1.5) magnitudes Thefainter evolving magnitudes, UV LF is allowing the most constraints robust piece on ofm in-x. Our fiducial' parameters are selected to match the ob- > servedfainter UV than LF. the Specifically, range of the we next take generationf =0.038 of and instru- formationHowever, available the for UVz LFs7 galaxies, are more with complex, the obser- shaped by ments such as the JWST. However, the⇤ UV LF for WDM vational estimates for a number⇠ of di↵erent groups (e.g. fw =0.1 which result in a good fit to available data the star-formation histories of each galaxy. While galax- atwithz m7x =110 for.5 keV all the starts four to DM “peel-away” models considered from the (see CDM Oesch et al. 2010; Bouwens et al. 2010, 2011; Castellano UV' LF at a value of M 1010M at all z = 7 to 12, et al. 2010;3 McLureWe et use al. 2010, the 2013; detection Bowler et al. 2014;limits for Fig. 2). Roughly speaking,h fw a↵ects the faint-end slope and exhibits faint-end slope' values shallower than the Bradleya10 et al. 2012;10 Oesch4 sobservationprovidedat et al. 2013; Bouwens et al. of the UV LF where feedback is most e↵ective, while http://www.stsci.edu/jwst/instruments/nircam/sensitivity/table. f determines the amplitude and normalization at the 2014) being in good agreement. The simplest approach ⇤ to obtaining a UV LF is to scale the halo mass function Early galaxies in WDM modelsEarly galaxies in WDM models 5 5
Early galaxies in WDM models 5
Early galaxies in WDM models 5 UV LFs in Cold versus Warm DM models 4 Dayal et al. Scaling Halo mass function Fiducial model Early galaxies in WDM models 5
Schultz+2014 PD+2015
Fig. 2.— The evolving LBG UV LF at z 7 12 in di↵erent DM models, computed with our fiducial semi-analytical galaxy formation Fig. 2.— The evolving LBG UV LF at z model.7 12Fig. in In di 2.—↵ allerentThe panels, DM evolving models, lines LBG show computed UV the LF results with at z' our7 using fiducial12 in the di semi-analytical↵ fiducialerent DM model models, galaxy that computed formation invokes with a total our fiducial of two semi-analytical redshift and galaxy mass-independent formation free ' model. In all panels, lines show the results'parameters: using model. the fiducial In the all star panels, model formation linesthat invokes show e ciency the a resultstotal (f of using two0.04) redshift the and fiducial the and fraction model mass-independent that of SN invokes energy free a total driving of two winds redshift (fw and=0. mass-independent1). In all panels free lines show Including baryons (and SF) decreases⇤ ⇡ the difference between CDM and 1.5 parameters: the star formation e ciency (f theoretical0parameters:.04) and results the the fraction for star CDM formation of SN (black energy e solidciency driving line) (f winds and0.04) WDM (fw and=0 with the.1). fraction particleIn all panels of masses SN lines energy of show 5keV driving (blue winds short-dashed), (fw =0.1). In 3keV all panels (red long-dashed) lines show and theoretical results for CDM (black solid line)⇤1. and⇡5keV(violetdot-dashed);dashedverticallinesshowthe10theoretical WDM with results particle for massesCDM (black of 5keV solid (blue line)keV⇤ short-dashed), and⇡WDM WDM models with 3keV particle10 4 (reds integration long-dashed) masses of limits 5keV and (blue of the short-dashed), JWST. In all 3keV panels, (red points long-dashed) show observational and 1.5keV(violetdot-dashed);dashedverticallinesshowthe10results1.5keV(violetdot-dashed);dashedverticallinesshowthe10 (see Fig. 10 14 fors integration references). limits of the JWST. In all panels, 10 points4 s integration show observational limits of the JWST. In all panels, points show observational results (see Fig. 1 for references). results (see Fig. 1 for references). (HMF) at that redshift assuming a fixed halo mass-to- TABLE 1 (HMF) at that redshift assuming a fixedlight(HMF) halo ratio. mass-to- at Indeed, that redshift Schultz assuming et al. a (2014) fixed halo propose mass-to- that For the redshift shown in column 1, we show the observed the cumulative number density of high-redshiftTABLE galaxies 1 faint-end slope of theTABLE UV LF 1 (McLure et al. 2009, 2013) in light ratio. Indeed, Schultz et al. (2014)light propose ratio. that Indeed,For Schultz the redshift et al. (2014) shown in propose column that 1, we showFor thecolumn the observed redshift 2. Columns shown 3 in and column 4 show 1, we the show faint-end the observed slope of the could be used to constrain mx. We caution however that the cumulative number densityFig. of 2.—high-redshiftThethe evolving cumulative galaxies LBG number UVfaint-end LF density at z slope7 of of high-redshift12 the in UV di↵erent LF (McLure galaxies DM models, et al.faint-end 2009,computedfiducial 2013) slope UV with in LFs of our the with fiducial UV the LF (McLure1 semi-analytical errors et al. for 2009, galaxy CDM 2013) formation and in 1.5keV constraints on WDM obtained through such abundance columnWDM, 2. Columns respectively. 3 and 4 show The the faint-end faint-end slopes slope of for the the could be used to constrain mmodel.. We caution In allcould howeverpanels, be used lines that to show constraincolumn the results 2.mx' Columns. We using caution 3 the and fiducial however 4 show the model that faint-end that invokes slope of a the total of two redshift and mass-independent free x matching directly relyfiducial on the UV assumed LFs with halo the 1 mass errorsUV for CDMfiducialtheoretical and 1 UV.5keV LFs UV with LF the have1 beenerrors computed for CDM over and the1.5keV absolute parameters: the star formation e ciency (f 0.04) and the fraction of SN energy driving winds (fw =0.1). In all panels lines show constraints on WDM obtained throughluminosity suchconstraints abundance relation, on WDM which obtained Schultz through et al. such (2014) abundance take$ to WDM, respectively.magnitude The range faint-end18 slopesMUV for14 the. theoretical results for CDM (black solidWDM, line)⇤ respectively. and⇡ WDM Thewith faint-end particle massesslopes for of 5keV the (blue short-dashed), 3keV (red long-dashed) and matching directly rely on the assumedbe halo independentmatching mass directlyUV of the relytheoretical DM on the model assumed UV and LF have haloassume been mass a computed power-UV overtheoretical the absolute UV LF have been computed over the absolute 1.5keV(violetdot-dashed);dashedverticallinesshowthe10$ Fig. 2.— The evolving 10$4 LBGs integration UV LF at limitsz 7 of12magnitudez the in JWST. di↵↵erentobs range In DM all models, panels,18↵CDMM computed points14 show. with↵1.5keV observational our fiducial semi-analytical galaxy formation luminosity relation, which Schultz etlaw al. (2014)luminosity extrapolation take relation, to towards which small Schultzmodel.magnitude masses. et In al. all range As (2014) panels, we shall18 linestakeM show to seeUV the14 results. ' using the fiducial+0.14 model thatUV invokes a total of two redshift and mass-independent free results (see Fig. 1 for references). 7 1.90 0.15 1.96 0.18 1.85 0.11 be independent of the DM model andbelow, assumebe independent this a power- need not of thebe the DM case. modelparameters: and assume the star a formation power- e ciency (f 0.04) and the+0 . fraction22 of SN± energy driving± winds (fw =0.1). In all panels lines show z ↵obs ↵CDM ↵1.5keV ⇤ z 8 ↵obs2.02 0.23 ↵CDM2.06 0.22↵1.5keV1.93 0.13 Before presenting results fromtheoretical our results complete for CDM model (black solid line) and⇡ WDM with particle masses± of 5keV (blue± short-dashed), 3keV (red long-dashed) and law extrapolation towards small(HMF) masses. at that Aslaw we extrapolation redshift shall see assuming towards asmall fixed masses. halo+0.14 As mass-to- we shall see 7 9 1.90+0.14 1.96 2.021.18 0.321.85 20..0111 0.16 7 1.90 0.15 1.96 0.18 1.85 0.11 0.15 4TABLE 1 which includes feedback, in1 Fig..5keV(violetdot-dashed);dashedverticallinesshowthe10 1 we show UV± LFs ± 10 s integration ± ± limits of ± the JWST.± In all panels, points show observational below, this need not be the case. below, this need not be the case. +0 .22 8 10 2.02+0.22 2.06 2.031.22 0.451.93 20..1013 0.18 lightFig. 1.— ratio.The Indeed, evolving LBG Schultz UV LFs et al.at z (2014)8results7 2.0212 (see propose for0 Fig..23 the 1 forfour2.06 that references). di0↵.22erentFor DM1.93 models the0.13 redshift considered, shown0 obtained. 23 in column by scaling± 1, we the show appropriate the± observed obtainedBefore simply presenting by multiplying results' from the our HMFs complete by± model a con- ± 11 ±2.39 0 .32 ±2.22 0.28 Before presenting resultsHMFthe from cumulative with our a complete halo mass number model independent density star of formation high-redshift9 e ciency galaxies of2.21f =00.32.9%faint-end at2.01z 07and.16 slope9f =1 of.3% the for UVz >2 LF.218. (McLure In0.32 all± panels,2. et01 al. lines0.16 2009,± show 2013) in stant mass-to-light ratio. Matching to the observations⇤ ⇤12 ±2.62 0 .53 ±2.34 0.44 which includes feedback, intheoretical Fig. 1 we results showwhich for UV CDM includes LFs (black feedback, solid line) in(HMF) and Fig. WDM 1 at we that with show particle redshift UV± LFs masses assuming column of±' 5keV a 2. fixed (blue Columns10 halo short-dashed), mass-to- 3 and 4⇠2 show3keV.31 0 (red. the45± long-dashed) faint-end2.10 0.18 slope± and of the could berequires used to constrain a halo starmx formation. We caution10 e ciency however with2.31 that0 values.45 2.10 0.18 TABLE 1 obtained simply by multiplying the HMFs by4 ± a con- ± ± ± obtained simply by multiplying1.5keV(violetdot-dashed);dashedverticallinesshowthe10 thef HMFs=(0 by.9, a1.3)% con- for z =(7, 118light10); ratio. we use Indeed, 102f.39s=0 integration Schultz0.32.013fiducial2 et.22 limits al.0.28 (2014) of UV the11 LFs JWST. propose with In all the that panels12.39 pointsForerrors0.32 the show2 forredshift.22 observational CDM0.28 shown and 1 in.5keV column 1, we show the observed constraints on WDM obtained through such abundance ± ±WDM, respectively. The ± faint-end slopes± for the stant mass-to-light ratio. Matchingresults: (a) toforz⇤ thestant all7: observationsz Oesch mass-to-light11 et al. and (2010, 12 ratio. given filled Matching12 cyanthe the cumulative squares), lack to of the Bouwens data observations number2.62⇤ at0 et. these53 density al. (2010,2.34 of empty0 high-redshift.44 12 blue circles), galaxies Bouwens2.62 etfaint-end0. al.53 (2011,2.34 slope filled0.44 of yellow the UV LF (McLure et al. 2009, 2013) in circles),matching Castellano directly'requires et' al. rely a (2010, halo on the empty star assumed formation purple triangles), halo e ciency mass McLure withUV± et values al. (2010, theoretical filled± red triangles), UV LF have McLure been et± computed al.column (2013, 2. empty Columns over± orange the 3 and absolute 4 show the faint-end slope of the requires a halo star formation e ciencyz. A constantwith values halo mass UVcould luminosity be used to$ mapping constrain al-mx. Wevalue caution of ↵ however2 that inferred observationally (e.g. McLure circles)luminosity and Bowler relation, et al. which (2014, filled Schultz purple$ et circles); al. (2014) (b) z take8: Bouwens to et al. (2010, emptymagnitude blue circles), range Bouwens18fiducialM etUV al.UV (2011, LFs14 with. filled the 1 errors for CDM and 1.5keV f =(0.9, 1.3)% for z =(7, 8 10); welows usef us=(0f to=0 estimate.9,.1013.3)% for whichz =(7 halos,constraints8 host10); observable we on use' WDMf =0 galaxies: obtained.013 throughet al. such 2013). abundance' In spite of this peel-away, the faint-end ⇤ yellowbe independent circles),for McLure⇤ all⇤ ofz theet al.11 DM (2010, and model filled12 given green and the triangles), assume lack of a Bradley data power-⇤ at et these al. (2012, empty purple squares) and McLure etWDM, al. (2013, respectively. empty The faint-end slopes for the for all z 11 and 12 givenorange the lack circles),e.g. of data(c) galaxiesz at9: these withMcLureM etUV al. (2013,15matching ( empty20) blue reside directly circles) in halos rely and on Oesch with the et assumed al.slope (2013,z halo values empty mass↵ green forobs all squares)UV the four↵CDM and,theoretical DM (d) modelsz 10:↵ UV1. explored Bouwens5keV LF have here been are computed over the absolute ' 8.6 '8.8 10.8 11' .2 +0$.14 z. A constant halo mass etlawUV al. luminosityextrapolation (2014,M emptyh z. mapping A10 green' constant towards circles); al-(10 halo small thevalue mass downward masses.)M of ↵luminosityUVat pointing luminosity Asz2=7 inferred we triangle relation, shall12. mapping observationally represents see which al- Schultz thevalue upper-limit (e.g.equally et of McLure al.↵ (2014) compatible of the2z take inferred10 to with data observationally at currentM observations,' 19magnitude (e.g..25. McLure range including18 MUV 14. 7 1.90 0.15 1.96 0UV.18 1.85 0.11 $ From' Fig. 1 we can also$ estimate' the viability of dis- the deepest ' z '7, 8 data obtained± ' from± the Hubble Ul- lows us to estimate which halosbelow, host this observable needlows us galaxies: not to estimatebe the case.et which al. 2013). halosbe independenthost In observable spite of of this galaxies: the peel-away, DM modelet the al.and faint-end8 2013). assume2.02 In a+0 spite power-.22 of2 this.06 peel-away,0.22 1. the93 faint-end0.13 tinguishing between di↵erent DM models. We see that tra Deep Field'0 2012.23 (HUDF12; Ellisz et al.↵obs 2013; McLure↵CDM ↵1.5keV e.g. galaxies with MUV 15OnBefore ( 20) the reside other presentinge.g. in hand, halos galaxies with a results withgalaxyMslopeUV from that values has our15 ( progenitors for complete20) all reside the four in in-model halos DM models withbright-end exploredslope where values here galaxiesare for all the can four form DM± stars models with explored the± maxi- here+0.14 are law extrapolation towards small masses.9 As we shall see 2.21 0.32 7 2.011.9003.16 1.96 0.18 1.85 0.11 8.6 8.8 10.8 11' .2 herits a certainthe WDM amount LFs8.6 8 with of.8 stars10m.x8 and=11' . 32 gas (5) keV from are them essentially fol- indis-mum e ciency.et al. 2013). Although With this its model higher± need sensitivity not be unique± ,the0.15 JWST Mh 10 (10 )Mwhichat z includes=7 M12.h feedback,10 (10 inequally Fig. )M compatible 1below, weat showz this=7 with need UV12. current not LFs be observations, the case.equally including10 compatible with current2.31 0 observations,.45 2.10 including0+0 .18.22 ± ± ' tinguishable ' from CDM down to an absolute magnitude could potentially constrain the UV8 LF2. and02 0. hence23 2.↵06 to0.22 1.93 0.13 From Fig. 1 we can also estimatelowingobtained merging the simply viabilityFrom events. by of Fig. dis- multiplying In 1 weaddition, canthe also deepest thethis estimateBefore galaxyHMFsz 7 the, 8 presenting also by data viability ob-a obtained con- of results dis-in from describing from thethe Hubble our deepest the complete Ul-observedz 7, 8 model data LF, obtained we stress± from again the that Hubble± our Ul- ± ± of MUV 15 ( 14); this is about 0.5 (1.5) magnitudes fainter11 magnitudes, allowing2.39 0 constraints.32 9 2.22 on0.28m . 2.21 0.32 2.01 0.16 tains a part oftinguishing its DM (and between gas) di mass↵erent through DM' models. smooth- We see thatmain conclusionstra Deep Field are' 2012 driven (HUDF12; by the± Ellis relative et al. di 2013;↵erences± McLurex ± ± tinguishing between di↵erentstant DM models.mass-to-lightfainter We than' see ratio. that the range Matchingtra of Deep thewhich Field tonext the 2012 generation includes observations (HUDF12; feedback, of instru- Ellis in et al. Fig. 2013; 1However,12 weMcLure show the UV UV LFs LFs2.62 are0. more53 10 complex,2.34 0.44 shaped2.31 by0.45 2.10 0.18 3 ± 3 ± ± ± the WDM LFs with mx = 3accretionrequires (5) keV arements from a essentially halothe the such WDM star IGM: indis-as LFs the formation while with JWST.etm in al.x principle However,= e 2013). 3 (5)obtainedciency keV With a the are cosmolog- with simply UV essentially its LF higher values by for multiplying indis-WDMsensitivitybetweenet the,thethe the al. cosmologies,star-formation 2013). HMFsJWST Withby a which its con- histories higher are sensitivity more of each robust11 galaxy.,the to WhileJWST as- galax-2.39 0.32 2.22 0.28 tinguishable from CDM down to an absolute magnitude ± ± tinguishable from CDM downicalf to=(0 ratio an absolute.9with of, 1. DM3)%m magnitudex and for=1 baryons.z5 keV=(7 starts,could8 can10); be to potentially “peel-away” accretedstant we use mass-to-light constrain ontof from=0 the. the013 ratio. CDMUVtrophysical MatchingLF andcould hence uncertainties. to potentially the↵ to observations constrain the UV LF12 and hence ↵ to 2.62 0.53 2.34 0.44 10 3 ± ± of MUV 15 ( 14); this ishalo, about⇤ UVB 0.5UV (1.5) photo-heatingof LFM magnitudesUV at a value15 feedback ( of14);fainterM h this suppresses magnitudes, is10requires aboutM 0.5at the a (1.5) allowing⇤ all halo avail-z magnitudes= star constraints 7 to formation 12, onfainter em xciency. magnitudes,We with values use allowing the constraints detection on mx. limits for for all z 11 and' 12 given the lack of data at these 4 fainter than' the range of theable next gas generation reservoirand' fainter exhibits of for thaninstru- accretion faint-end the range insideHowever, slope of' the thef values next ionized=(0 the generation UV. shallower9, IGM1 LFs.3)% areas for of than more instru-z =(7 the3. complex,, EARLY8 10);a10However, shaped GALAXY we use by thef EVOLUTION UV=010 LFs.013sobservationprovidedat are IN more DIFFERENT complex, DARK shaped by z. A constant halo mass UV luminosity mapping al- valuehttp://www.stsci.edu/jwst/instruments/nircam/sensitivity/table. of ↵ 2 inferred observationally (e.g. McLure ments such as the JWST. However,explained the inUV Sec.ments LF for 2.2. such WDM Thus, as the$ the JWST.the total star-formation However, initialfor⇤ all gas thez histories UVmass11 LF and in for of 12each WDM given galaxy. the the While lack star-formation ofgalax- dataMATTER⇤ at histories these MODELS of each galaxy. While galax- lows us to estimate which halos host observable' galaxies: et al. 2013).' In spite of this peel-away, the faint-end with mx =1.5 keV starts tothe “peel-away” galaxy at fromwithz is themx CDM sum=1.5 of keV the starts newly to accretedz “peel-away”. A constant gas mass,from halo the mass CDMWeUV now luminosity show how mapping high-z galaxy al- assemblyvalue of ↵ varies2 with inferred observationally (e.g. McLure e.g.10 galaxies with MUV 153 ( 20) reside10 in halos with $ slope3 values for all the four DM models explored here are UV LF at a value of Mh 10 M at allUVz = LF 7 at to a 12, value of Mh Welows10 M us use toat estimate all thez = 7 which to detection 12, halos host limits observableWe for use galaxies: theet detection al. 2013).' limits In spite for of this peel-away, the faint-end as well as8 that.6 8.8 brought10.8 in11' by.2 its merging ' progenitors. 4 the DM particle mass considered,4 and its impact on ob- and exhibits faint-end slope'M valuesh 10 shallower and(10 exhibits than the faint-end)Ma10at slopez =7 values1012. shallowersobservationprovidedat than the equallya10 compatible 10 sobservationprovidedat with current observations, including This updated gas mass is then usede.g. to galaxies calculate with theMUV servables15 ( http://www.stsci.edu/jwst/instruments/nircam/sensitivity/table.20) including reside in the halos UV with LF, the M/Lslope relation values for and all the the four DM models explored here are From' Fig. 1 we can also estimatehttp://www.stsci.edu/jwst/instruments/nircam/sensitivity/table. the viability8.6 8.8 of dis-10.8 11' .2 the deepest z 7, 8 data obtained from the Hubble Ul- new stellar mass formed in the galaxyM ash described10 (10 by SMD.)M at z =7 12.' equally compatible with current observations, including tinguishing between di↵erent DM models.From' Fig. We 1see we that can also estimatetra Deep the Field viability 2012 of (HUDF12; dis- the Ellis deepest et al.z 2013;7, 8 data McLure obtained from the Hubble Ul- Eqn. 11. The total stellar mass in this galaxy is now the '3 sumthe WDM of mass LFs of the with newly-formedmx = 3 (5) stars, keV aretinguishing and essentially that brought between indis- di↵erentet DM al. models. 2013). We With see its that highertra sensitivity Deep Field 2012,the (HUDF12;JWST Ellis et al. 2013; McLure 3.1. Ultraviolet luminosity functions 3 intinguishable by its progenitors. from CDM down to anthe absolute WDM magnitudeLFs with mx = 3could (5) keV potentially are essentially constrain indis- theet al. UV 2013). LF and With hence its higher↵ to sensitivity ,theJWST of MUV 15 ( 14); this is about 0.5tinguishable (1.5) magnitudes from CDM downThefainter to evolving an magnitudes, absolute UV magnitudeLF is allowing the most constraintscould robust potentially piece on ofm constrain in-x. the UV LF and hence ↵ to Our fiducial' parameters are selected to match the ob- > servedfainter UV than LF. the Specifically, range of the we next take generationoff M=0UV .038 of15 and instru- ( 14); thisformation is aboutHowever, available 0.5 (1.5) the magnitudes for UVz LFs7 galaxies, arefainter more with complex,magnitudes, the obser- shaped allowing by constraints on mx. ' ⇠ fments=0 such.1 which as the result JWST. in aHowever, good fit thefainter to⇤ UV available than LF for the data WDM range ofvational thethe next star-formation estimates generation for of a historiesnumberinstru- of of di each↵However,erent galaxy. groups the While UV (e.g. LFs galax- are more complex, shaped by w ments such as the JWST. However, the UV LF for WDM atwithz m7x =110 for.5 keV all the starts four to DM “peel-away” models considered from the (see CDM Oesch et al. 2010; Bouwens et al. 2010,the star-formation 2011; Castellano histories of each galaxy. While galax- UV' LF at a value of M 1010M withat allmxz=1=.5 7 keV to 12, startset to al. “peel-away” 2010;3 McLureWe from et use the al. CDM 2010, the 2013; detection Bowler et al. 2014;limits for Fig. 2). Roughly speaking,h fw a↵ects the faint-end slope 10 3 ' UV LF at a value of Mh a1010 M at all z =104 7sobservationprovidedat to 12, We use the detection limits for and exhibits faint-end slope values shallower than the Bradley et al. 2012; Oesch et al. 2013; Bouwens et4 al. of the UV LF where feedback is mostand e↵ exhibitsective, while faint-end slope' http://www.stsci.edu/jwst/instruments/nircam/sensitivity/table. values shallower than the a10 10 sobservationprovidedat f determines the amplitude and normalization at the 2014) being in good agreement. Thehttp://www.stsci.edu/jwst/instruments/nircam/sensitivity/table. simplest approach ⇤ to obtaining a UV LF is to scale the halo mass function 10 Dayal et al.
10 ObservationalDayal et al. imprints of light WDM particles: buildup of the 10 Dayal et al. 10 Dayal et al. cosmic stellar mass density
•
FigureRedshift 6. Redshift evolution evolution of stellar of mass the SMD density for with the four JWST-detectable DM models considered galaxies can in this work: CDM (black line), 5keV WDM (blue line), Figure 6. Redshift evolution of the SMD for theFigure four DM 6. Redshift models considered evolution in of this the work:SMD CDMfor the (black four DMline), models 5keV WDM considered (blue line),in this work: CDM (black line), 5keV WDM (blue line), 3 keV WDM (red line)allow and constraints 1.5keV WDM on WDM (violet mass line). of about The 2keV left and right panels show the SMD from galaxies that have already been 3Figure keV WDM 6. (redRedshift line) and 1.5keV evolution WDM (violet of3 keVthe line). WDM SMD The (red left for and line) the right and four panels 1.5keV DM show WDM models the SMD (violet from considered line). galaxies The left that in and have this right already work: panels been show CDM the (black SMD from line), galaxies 5keV that haveWDM already (blue been line), detected, i.e. MUV 6 18, and galaxies that are expected to be detected using a magnitude limit of MUV 6 16.5 for the JWST, detected,3 keV WDM i.e. MUV (red6 18, line) and galaxies and 1 that.5keVdetected, are expected WDM i.e. toM (violetUV be detected6 18, line). using and galaxies The a magnitude left that and limit are expected rightof MUV panels6 to be16. detected5 show for the using JWST, the SMDa magnitude from limit galaxies of MUV that6 16 have.5 for the already JWST, been respectively. As seen, while the SMD measured by the JWST will be indistinguishable for CDM and WDM with mx =3and5keV, respectively. As seen, while the SMD measuredrespectively. by the JWST As will seen, be while indistinguishable the SMD measured for CDM by and the WDM JWST withPD+2015, willmx be =3and5keV,ApJ, indistinguishable 806, 67; for CDM and WDM with mx =3and5keV, detected, i.e. MUV 18, and galaxiesour model predicts that are that theseexpected three models to be will detected have formedPD+2017, using about 3 ApJ, a (10) magnitude 836, times 16 more stellar limit mass of perMUV unit volume16 at.z5 for11 ( thez 13) JWST, our model predicts that these6 three models willour have model formed predicts about that 3 (10) these times three more models stellar will mass have per unit formed volume about at 3z (10)11 times (z 13) more stellar mass per unit6 volume at z' 11 (z' 13) compared to the 1.5keVcase,providingoneofthestrongesthintsonthenatureofDMusinghigh-' ' z galaxies. ' ' comparedrespectively. to the 1.5keVcase,providingoneofthestrongesthintsonthenatureofDMusinghigh- As seen, while thecompared SMD measured to the 1.5keVcase,providingoneofthestrongesthintsonthenatureofDMusinghigh- by the JWST will bez galaxies. indistinguishable for CDM and WDMz galaxies. with mx =3and5keV, our model predicts that these three models will have formed about 3 (10) times more stellar mass per unit volume at z 11 (z 13) ' ' > < >> << becompared instrumental to in the di↵erentiating 1.5keVcase,providingoneofthestrongesthintsonthenatureofDMusinghigh- the standardbebe instrumental CDM instrumental from in in diconstraints di↵erentiating↵erentiating on the whether the standard standardmx CDM CDM2keV from from or mx 2keV,constraintsconstraints solely on on whetherz galaxies.mmxx 2keV2keV or or mmxx 2keV,2keV, solely solely WDM models that invoke particles lighterWDM thenWDM 2keV. models models that that invokeusing invoke theparticles particles UV LF. lighter lighter then then⇠ 2keV. 2keV. ⇠ usingusing the the UV UV LF. ⇠⇠ ⇠⇠ The suppression of small scale structure leadsTheThe to de- suppression suppression of of small small scale scale structure structure leads leads to to de- de- layed and more rapid stellar assembly in the 1.5layedlayed keV WDM and and more more rapid stellar stellar> assembly assembly in in the the 1< 1.5.5 keV keV WDM WDM be instrumental in di↵erentiating the standard CDM from constraints on whether mx 2keV or mx 2keV, solely 4CONCLUSIONS 4CONCLUSIONS4CONCLUSIONSscenario (compared to the three other models)scenarioscenario which re- (compared (compared to to the the three three other other models) models) which which re- re- WDM models that invoke particles lighter thensults 2keV. in galaxies of a given stellarusing mass the being UVsultssults more LF. in in UV galaxies galaxies of a a⇠ given given stellar stellar mass mass being being⇠ more more UV UV The standard ⇤CDM cosmological model has been ex- TheThe standard standard⇤CDM⇤CDMluminous, cosmological cosmological i.e. a lower model model M/L has has ratio. been been While ex- ex- the M/Lluminous,luminous, relation i.e. i.e. a lower M/L M/L ratio. ratio. While While the the M/L M/L relation relation tremely successful at explaining the large scaletremelytremely structure successful successful of at at explaining explaining the the large large scale scale structure structure of of for CDM (and mx > 3 keV WDM)The is well-fit suppression byforfor the CDM CDM func- (and (and ofmx small> 33 keV keV scale WDM) WDM) structure is is well-fit well-fit by by leads the the func- func- to de- the Universe. However, it faces a numberthe ofthe problems Universe. Universe. on However, However, it it faces faces a a number number of of problems problems on on tional form log M = 0.38MUV +2.4 0.1z, thetionaltional M/L form form ra- log M = 00..3838MMUVUV +2+2..44 00.1.1zz,, the the M/L M/L ra- ra- small scales (e.g. the number of satellite galaxies and the ⇤ layed and more rapid stellar⇤ assembly in the 1.5 keV WDM smallsmall scales scales (e.g. (e.g. the thetion number number for the of of 1 satellite.5 satellite keV WDM galaxies galaxies starts and and diverging the the fromtiontion this for for rela- the the 1.5 keV WDM WDM starts starts diverging diverging from from this this rela- rela- DM halo profiles) that can potentially be solvedDM halo by invok- profiles) that can potentially be solved by invok- DM halo profiles) thattion can at M potentiallyUV = 19 be at solvedz 7,scenario by with invok- a z-evolution (comparedtiontion in at at bothMMUV to= the19 at at threezz 7,7, other with with a a zz models)-evolution-evolution in in which both both re- ing4CONCLUSIONS warm dark matter (WDM) comprised of low mass ( keV) ' UV ' inging warm warm dark dark matter matterthe (WDM) (WDM) slope and comprised comprised normalisation. of of low low mass mass The ( lower ( keV) keV) M/L ratiosthe slope in the and normalisation. ' The lower M/L ratios in the particles. Since WDM smears-out power on small scales, it sults in galaxiesthe slope of and a normalisation. given stellar The lower mass M/L being ratios more in the UV particles.particles. Since Since WDM WDM1.5 smears-out keV smears-out scenario power power partially on on small compensates small scales, scales, for it it the dearth1.5 keV of scenario low partially compensates for the dearth of low eThe↵ects are standard expected to be⇤CDM felt most cosmological strongly on the number model has been ex- 1.5 keV scenario partially compensates for the dearth of low e↵eects↵ects are are expected expected tomass to be be halos, felt felt most most as a strongly result strongly of which on on the theluminous, the number number UV LFs predicted i.e.mass a halos, by lower our as a M/L result of ratio. which the While UV LFs the predicted M/L by relation our densities and the assembly history of the earliest (low mass) mass halos, as a result of which the UV LFs predicted by our tremely successful at explainingdensitiesdensities the and large and the the assembly scale assemblysemi-analytic structure history history galaxy of of the the of evolutionearliest earliest (low (low model mass) mass) are moresemi-analytic similar than galaxy evolution model are more similar than galaxies that formed in the Universe. Here we explore how for CDM (andsemi-analyticmx > galaxy3 keV evolution WDM) model is are well-fit more similar by the than func- galaxiesgalaxies that that formed formedsimple in in the the estimates Universe. Universe. based Here Here on we we scaling explore explore of the how how halo masssimple functions. estimates based on scaling of the halo mass functions. the Universe. However, it faces> a number of problems on > simple estimates based on scaling of the halo mass functions. current and upcoming observations of high-currentz (z 7) and LBGs upcoming observations of high-z (z tional>7) LBGs form log M = 0.38MUV +2.4 0.1z, the M/L ra- current⇠ and upcoming observationsFinally we estimate of high- thez (z redshift7) LBGs evolution of the SMDs, can constrain the mass of WDM particles. can constrain the mass of WDM particles. ⇠ FinallyFinally⇤ we estimate the the redshift redshift evolution evolution of of the the SMDs, SMDs, small scales (e.g. the numbercan of satelliteconstrain the galaxies masswhich of provideWDM and particles. a the more direct⇠tion probe for of the the mass 1.5 assem- keV WDM starts diverging from this rela- We consider four di↵erent DM scenarios:We CDM consider and four di↵erent DM scenarios: CDM and whichwhich provide provide a more direct direct probe probe of of the the mass mass assem- assem- DM halo profiles) that can potentiallyWe consider be solved fourbly history di↵erent by (albeit invok- DM scenarios: requiring accurate CDM and multi-bandbly photom- history (albeit requiring accurate multi-band photom- WDM with mx =1.5, 3 and 5 keV. BuildingWDM on DM with mergermx =1.5, 3 and 5 keV. Building on DMtion merger at MUVbly= history19 (albeit at z requiring7, with accurate a multi-bandz-evolution photom- in both WDM with mx =1etry)..5, 3 and Integrating 5 keV. Building down to on a limit DM merger of M 16.5 (corre- trees, our galaxy formation model includes the key baryonic UV etry). Integrating down' to a limit of MUV 16.5 (corre- ing warm dark matter (WDM)trees, comprised our galaxy of formation low mass model ( includes keV) the key baryonic ' etry). Integrating down to a limit of MUV ' 16.5 (corre- trees, our galaxy formationsponding model to a conservative includes theJWST keythe baryonicthreshold), slope and wesponding find normalisation. that to a conservative TheJWST lowerthreshold), M/L' we ratios find that in the processes of star formation, feedback from bothprocesses supernovae of star formation, feedback from both supernovae sponding to a conservative JWST threshold), we find that particles. Since WDM smears-outprocesses power of star on formation,the small 1.5 keV scales, feedback WDM from it SMDs both evolve supernovae more rapidlythe with 1.5 red- keV WDM SMDs evolve more rapidly with red- (SN) explosions and photo-heating from reionization,(SN) explosions and and photo-heating from reionization,1.5 keV and scenariothe 1.5 partially keV WDM compensates SMDs evolve more for rapidly the dearth with red- of low (SN) explosions andshift photo-heating than those predicted from reionization, by CDM. and Specifically,shift we than find those predicted by CDM. Specifically, we find thee↵ects merger, are accretion expected and ejection to be driven felt growththe most merger, of strongly stellar accretion on and the ejection number driven growthmass of stellar halos, asshift a than result those of predicted which the by CDM. UV LFs Specifically, predicted we find by our and gas mass. Below we summarize our mainthe results. merger, accretionlog( andSMD ejection) 0 driven.44(1 + growthz) for CDM, of stellar with a steeperlog(SMD slope) 0.44(1 + z) for CDM, with a steeper slope and gas mass. Below we summarize/ our main results. log(SMD) / 0.44(1 + z) for CDM, with a steeper slope densities and the assembly historyand< gas of mass. the earliest Belowof we log( summarize (lowSMD) mass) our0.63(1 main + z results.) for WDM with mx =1.5keV. We find that the observed UV LF (MUV We find17) that is the observed UV/ LF (M
Sky-averaged absorption 21cm signal (EDGES)
Bowman et al., 2018, Nature, 555, 67 Figure 2. The global 21 cm di↵erential brightness temperature for the CDM, 5 keV, 3 keV and 1.5 keV WDM models, as marked, including both X-ray heating and an excess radio background (see Sec. 3.2). In each panel the black curve shows the EDGES result. The grey lines in each panel show models that satisfy the ARCADE-2 limits and where the signal is limited to z > 14. The red lines show models consistent with the EDGES result, both in terms of the redshift range of the signal as well as its amplitude⇠ ( T = 500 75mK). b ± As shown, the inclusion of an excess radio background results in free parameter combinations (fR and fX,h)yieldingresultsinagreement < with the EDGES data for the CDM and 5 keV WDM models. However, mx 3keVmodelscane↵ectively be ruled out since they are unable to reproduce either the redshift range or the amplitude of the observed⇠ signal. between the radio background and the SFRD results in an this case too, structure formation is delayed long enough in < absorption that extends much later than conventional mod- mx 3 keV WDM models so that they can be ruled out. els as well as the EDGES signal. Reproducing the EDGES ⇠Although our model contains various simplifying as- data requires such a background be turned o↵ (or equiva- sumptions at di↵erent stages (e.g., the various e ciency pa- lently, the gas be heated up beyond what is predicted by rameters related to X-ray heating are taken to be indepen- X-ray heating) at z 16. As of now, both the sources dent of z), it is clear that WDM models with m < 3 keV ⇠ x (metal free stars or cosmic rays associated with the first simply cannot form stars early enough to satisfy the⇠ EDGES stars and/or black holes) and reasons for the decay of such constraint. We have checked this by varying the free parame- a background at z<16 remain open questions. Despite this ters to their extreme limits, and found our conclusions to be and irrespective of the values of the free parameters used, in robust. Our constraints are thus comparable to constraints c 0000 RAS, MNRAS 000,000–000 Ruling out 3 keV WDM using EDGES 3
(Furlanetto et al. 2006a) where S↵ is a factor of order unity that accounts for the detailed atomic physics involved in the scattering process TS (z) T (z) ⌧ Tb(⌫)= 1 e , (1) (Furlanetto et al. 2006b; Hirata 2006). Further, J↵,the 1+z background Ly↵ photon flux, is calculated using the Del- where ⌧ is the 21 cm optical depth of the di↵use IGM and TS phi model as (Ciardi & Madau 2003) and T are the neutral hydrogen (H I) spin temperature and 3 c(1 + z) 1 dt0 the background radiation temperature, respectively. The op- J (z)= n˙ (z0) dz0, (6) ↵ 4⇡ ⌫0 dz tical depth is usually much less than unity. In this case, for Zz 0 the cosmological parameters used in the paper, the above where ⌫0 = ⌫↵(1 + z0)/(1 + z)with⌫↵ being the Ly↵ fre- expression simplifies to quency,n ˙ (z0) is the production rate of photons per unit Ruling out 3 keV WDM using EDGES⌫0 3 T (z) 1/2 frequency per unit comoving volume at redshift z0, c is the Tb(⌫) 10.1mK HI(z) 1 (1 + z) , (2) ⇡ TS (z) speed of light and t0 is the cosmic time corresponding to the ✓ ◆ (Furlanetto et al. 2006a) where S↵ is a factor of order unity thatredshift accountsz0. In for this the paper, we assume the spectrum of pho- where is the neutral hydrogen fraction. HI detailed atomic physics involved in thetons scattering around the process Ly↵ frequencies to be constant (Furlanetto TS (z) T (z) ⌧ In absence of any other radiation sources at radio fre- Tb(⌫)= 1 e , (1) (Furlanetto et al. 2006b; Hirata 2006).et al. Further, 2006b).J Note↵,the that we have implicitly assumed that all 1+z quencies 1420 MHz, the radiation temperature T (z)is ⇠ background Ly↵ photon flux, is calculatedLy↵ photons using the producedDel- in the galaxy escape into the IGM, given by the CMB temperature TCMB(z). The spin tem- where ⌧ is the 21 cm optical depth of the di↵use IGM and TS phi model as (Ciardi & Madau 2003) i.e. a Ly↵ photon escape fraction of f↵ = 1, resulting in our perature TS can be written as a weighted sum of various and T are the neutral hydrogen (H I) spin temperature and model overestimating the Ly↵ background. A more reason- 3 temperatures (Field 1958) such that 1 the background radiation temperature, respectively. The op- c(1 + z) abledt0 and physical value corresponding to f↵ < 1willonly J↵(z)= n˙ ⌫ (z0) dz0, (6) 1 1 1 0 4⇡ strengthendz0 our conclusions on the WDM particle mass by tical depth is usually much less than unity. In this case, for1 T + xcTk + x↵T↵ z T = , Z (3) the cosmological parameters used in the paper, the aboveS 1+x + x leading to a reduction in the Ly↵ background, and hence, where ⌫c0 = ⌫↵↵(1 + z0)/(1 + z)with⌫↵ being the Ly↵ fre- expression simplifies to the coupling co-e cient. where T is the gas kinetic temperature0 and T is the color k quency,n ˙ ⌫0 (z ) is the↵ production rate of photons per unit T (z) temperature1/2 of the Ly↵frequencyradiation per field. unit Further, comovingxc volumeand at redshift z0, c is the T (⌫) 10.1mK HI(z) 1 (1 + z) , (2) b x↵ are the coupling coe cients corresponding to the col- Ruling⇡ out 3 keV WDM usingTS (z) EDGES 3 speed of light and t0 is the cosmic time corresponding2.4 The gas to kinetic the temperature ✓ ◆ lisional excitations andredshift spin-flipz due0. In to this the paper, Ly↵ radiation we assume the spectrum of pho- where is the neutral hydrogen fraction. The next quantity of interest is the gas kinetic temperature (Furlanetto et al. 2006a) where S isHI a factor of order unity that accountsfield, respectively. for the For alltons practical around purposes the Ly one↵ frequencies can assume to be constant (Furlanetto In↵ absence of any other radiation sources at radio fre- which evolves as (Furlanetto et al. 2006b) detailed atomic physics involved in the scatteringT↵ = T processk. This is justifiedet by al. the 2006b). fact that Note the that optical we have depth implicitly assumed that all TS (z) T (z) ⌧ quencies 1420 MHz, the radiation temperaturefor Ly↵ photonsT (z)is is so high that they undergo a large number dT 2T 2 ✏ Tb(⌫)= 1 e , (1) (Furlanetto⇠ et al. 2006b; Hirata 2006). Further, J↵,the Ly↵ photons produced in the galaxy escape into thek = IGM,k i . (7) 1+z given by the CMB temperature TCMB(z).of The scatterings spin tem- – these are su cient to bring the Ly↵ radia- i background Ly↵ photon flux, is calculated using the Del- i.e. a Ly↵ photon escape fraction of f↵ = 1, resultingdz in our1+z 3H(z)(1 + z) kB n where ⌧ is the 21 cm optical depth of the di↵use IGM and T perature TS can be written as a weightedtion sum field of and various the gas into local equilibrium near the central X S phi model as (Ciardi & Madau 2003) model overestimating the Ly↵ background.The first A more term reason- on the right hand side corresponds to the cool- and T are the neutral hydrogen (H I) spin temperature and temperatures (Field 1958) such that frequency of Ly↵ radiation (Pritchard & Loeb 2012). 3 able and physical value correspondingRuling to f↵ < out1willonly 3 keV WDM using EDGES 3 1 0 ing due to the adiabatic expansion of the Universe while the the background radiation temperature, respectively. The op- c(1 + z) 1 1 dt 1 We now discuss how the coupling coe cients and the J↵(z)= n˙ ⌫ (z0) d z0, (6) strengthen our conclusions on the WDMsecond particle term mass accounts by for the heating and cooling processes 1 4⇡ T + xcT0k +dxz↵T↵gas kinetic temperature are calculated. tical depth is usually much less than unity. In this case, for TS = Rulingz out 3 keV0 WDM, using(3) EDGES 3 Z (Furlanetto et al. 2006a) leading to a reduction in the Lywhere↵ background,summarisedS is a factor and below. hence, of order The quantity unity that✏i is accounts the energy for injected the the cosmological parameters used in the paper, the above 1+xc + x ↵ ↵ where ⌫0 = ⌫↵(1 + z0)/(1 + z)with⌫↵ being the Ly↵ fre- the coupling co-e cient. detailedinto atomic (or taken physics out from) involved the in gas the per scattering second per process unit phys- expression simplifies to where Tk is the gas kinetic temperature and T↵ is the colorTS (z) T (z) ⌧ (Furlanetto et al. 2006a) 0 where S↵ is a factor of order unity that accounts for the quency,n ˙ ⌫0 (z ) is the production rate of photons2.3 T perb The(⌫)= unit coupling co-e cients1 e , (1) (Furlanettoical volume et al. through 2006b; process Hiratai 2006)., n is the Further, total numberJ↵,the of gas temperature of the Ly↵ radiation field. Further, xc and detailed atomic physics involved0 in the scattering1+z process T (z) TS (z)1/2T (z) frequency⌧ per unit comoving volume at redshift z , c is the backgroundparticles Ly↵ andphotonkB is Boltzmann’s flux, is calculated constant. using The the keyDel- heating Tb(⌫) 10.1mK HI(z) 1 Tb(⌫)=(1 + z) , (2) 1 e x,↵ are the(1) coupling(Furlanetto coe cients et al. corresponding 2006b;The Hirata coupling to 2006). the coe col- Further, cients2.4J used↵,the inThe this gas work kinetic are calculated temperature as ⇡ TS (z) 1+z speed of light and t0 is the cosmic timewhere corresponding⌧ is the 21 to cm the optical depth of the di↵use IGM and TS phi modeland ascooling (Ciardi processes & Madau relevant 2003) at high-z include: ✓ ◆ lisional excitationsbackground and spin-flip Ly↵ duephoton to the flux,follows: Ly is↵ calculatedradiation using the Del- redshift z0. In this paper, we assumeand theT spectrum are the of neutral pho- hydrogen (H I) spin temperature and (i) Compton heating/cooling: The rate of heat- where HI is the neutralwhere hydrogen⌧ is the fraction. 21 cm optical depth of the di↵use IGM and TS phi model as (Ciardi & Madau(i) 2003)The collisional couplingThe next coe quantity cient, xc of, is interest determined is the gas kinetic temperature3 tonsfield, around respectively. the Ly↵ frequencies For all practical to bethe purposes constant background (Furlanettoone can radiation assume temperature, respectively. The op- ing/cooling duec(1 to + z Compton) 1 scatteringdt0 of residual electrons and T are the neutral hydrogen (H I) spin temperature and which evolves as (Furlanetto et al. 2006b) J↵(z)= n˙ ⌫ (z0) dz0, (6) In absence of any other radiation sources at radio fre- T↵ = Tk. This is justified by the fact thatby the3 three optical di↵ deptherent channels, namely, hydrogen-hydrogen (H- 0 the background radiation temperature, respectively.et al. 2006b). The op- Note that we have implicitlyticalc(1 depth + assumedz) is1 usually that all muchdt0 less than unity. In this case, for with background4⇡ photonsz is given bydz0 quencies 1420 MHz, the radiation temperature T (z)is J↵(z)= H), hydrogen-electronn˙ (z0) dz0, (H-e) and(6) hydrogen-proton (H-p) col- Z Lyfor↵ photons Ly↵ photons produced is so in high the that galaxy they escape undergo into a the large IGM,⌫0 number dTk 2Tk 2 ✏i ⇠ tical depth is usually much less than unity. In this case, for the cosmological4⇡ z parametersdz0 used in the paper, the above 2✏comp e 8 T u given by the CMB temperature TCMB(z). The spin tem- of scatterings – these are su cient to bringlisions.Z the Ly The↵ radia- results in a total coupling coe= cient of where ⌫0 = ⌫↵(1. + z0)/=(1(7) + z)with⌫↵ being(T the LyT ↵)(8)fre- the cosmological parameters used in the paper,i.e. a Ly the↵ abovephoton escape fraction of fexpression↵ = 1, resulting simplifies in our to dz 1+z 3H(z)(1 + z) i kB n k perature TS can be written as a weighted sum of various where ⌫0 = ⌫↵(1 + z0)/(1 + z)with⌫↵ being the Ly↵ fre- quency,n ˙ ⌫ (z0) is3nk theB production1+ e + f rateHe 3 ofme photonsc per unit modeltion overestimating field and the gas the into Ly↵ localbackground. equilibrium A more near reason- the central T H i X 0 expression simplifies to x = ⇤ T n , (4) temperatures (Field 1958) such that quency,n ˙ ⌫ (z0) is the production rate of photonsc perTheT unit first(z) term10 onk thei right hand sidefrequency corresponds per unit to the comoving cool- volume at redshift z0, c is the 4 frequency of Ly↵ radiation (Pritchard0 & Loeb 2012). A10T 1/2 where e =(1 HI) is the ionization fraction ( e 10 ; able and physical value corresponding to Tfb(↵⌫)< 1willonly10.1mK HI(z) 1 i=H,e,p (1 + z) , (2) T (z) frequency per unit comoving volume at redshift z0,ingc is due the to the adiabatic expansionspeed of the of Universe light and whilet0 is the the cosmic time corresponding to' the 1 1 1 strengthen1We/2 nowour conclusions discuss how on the the coupling WDM particle coe ⇡cients mass and by the TSX(z) Bharadwaj & Ali 2004), u is the energy density of back- 1 T + Txbc(T⌫)k +10x.1mK↵T↵ HI(z) 1 (1 + z) , (2) ✓ ◆ T (z) speed of light and t0 is the cosmic time correspondingsecond to the term accounts for the heatingredshift andz cooling0. In this processes paper, we assume the spectrum of pho- TS = ⇡ , (3)S gas kinetic temperature are calculated. where T =68.5 mK is the temperature corresponding to ground photons, T is the Thomson cross-section, fHe = 1+x + x ✓ ◆ leading to a reduction in the Ly↵ background,where HI is and the hence,⇤ neutral hydrogen fraction. c ↵ redshift z0. In this paper, we assume the spectrumsummarised of pho- below. The quantitytons✏ is around the energy the Ly injected↵ frequencies to be constant (Furlanetto where is the neutral hydrogen fraction.the coupling co-e cient. the 21 cm transition, A10 is the corresponding Einstein- i 0.08 is the helium fraction by number and me is the elec- where T is the gas kinetic temperatureHI and T is the color tons around the Ly↵ frequenciesIn absence to of be any constant other radiation(Furlanetto sources at radioH i fre- k In absence of any other↵ radiation sources at radio fre- coe cient for spontaneousinto emission (or taken and out10 from) is the the gas spe-et per al. second 2006b).tron mass. per Note unit that phys- we have implicitly assumed that all quencies 1420 MHz, the radiation temperature T (z)is temperature of the Ly↵ radiation field. Further, xc and et al. 2006b). Note that wecific have rate implicitly coe cient assumed for spin that de-excitation all by collisions with quencies 1420 MHz, the radiation temperature2.3T The (z)is coupling co-e cients ⇠ ical volume through process i, n Lyis↵ thephotons total(ii) number produced X-ray heating/cooling of gas in the galaxy: The escape X-ray into photons the IGM, produced Ly↵ photons producedgiven by in the the galaxy CMB escape temperature into theT IGM,(z). The spin tem-H i x↵ are the coupling coe cients⇠ corresponding to the col- Ruling out 3CMB keV WDM using EDGES 3 given by the CMB temperature TCMB21cm(z).2.4 The signal Thespin tem- gas kineticredshift temperature and amplitudeparticles scale of species withi withparticles star number formation and densitykB isni.The Boltzmann’s 10 co-i.e. constant. a Lyby↵ early Thephoton key sources escape heating (e.g., fraction accreting of f↵ black= 1, resulting holes, miniquasars, in our lisional excitations and spin-flip due to the Ly↵ radiation The coupling coe i.e.cients a Ly used↵ photon in thisperature escape work fractionT areS can calculated of bef↵ = written 1, as resulting as a in weighted our sum of various perature TS can be written as a weighted sum of various e cients are calculatedand using cooling the fitting processes functions relevant given at inmodel high-zsupernova overestimatinginclude: shocks the or Ly X-ray↵ background. binaries) can A more heat up reason- gas. The (Furlanetto etThe al.follows: next 2006a) quantity ofmodel interest overestimating is therate gastemperatures kinetic thedensity Ly temperature↵ background. (Fieldwhere 1958)S A suchis more a factor that reason- of order unity that accounts for the field, respectively. For alltemperatures practical purposes (Field 1958) one can such assume that Kuhlen et al. (2006)↵ and Liszt(i) (2001). Compton heating/coolingable: and Theamount physical rate of heating of value heat- correspondingdepends both on to thef↵ number< 1willonly of photons which evolves(i) The as collisional (Furlanettoable couplingand et physical al. 2006b)coe valuecient, correspondingx , is determined to f↵ < 1willonly T↵ = Tk. This is justified by the fact that the optical depth c (ii)4detailedThe LyChatterjee,↵1 atomiccouplinging/cooling physics1 coe Dayal, cient, involved1 duex Choudhury↵,alsoknownasthe to in Compton the scattering & scattering Hutterstrengthen processproduced of residual our conclusions as electrons well as the on spectral the WDM shape. particle Given thesemass quanti- by 1 1 1 TS (z) T (strengthenz) our⌧ conclusions on the1 WDMT particle+ xcTk mass + byx↵T↵ 1 T + xcTk + x↵T↵ Tby(⌫)= three di↵erent channels,1 e namely,, where hydrogen-hydrogen(1) T (Furlanetto= (H- et al. 2006b; Hirata, 2006).(3) Further, J ,the for Ly↵ photons is so high that they undergoT = a large number , b dT(3)k 2Tk 2 ✏iWouthuysen-FieldS couplingwith coe background cient, is essentially photons is deter- givenleading by↵ ties to are a reduction highly uncertain in the atLy high-↵ background,z, they are andalmost hence, impossi- S 1+= z leading to a reduction in the. Ly↵ background,(7) 1+ andxc + hence,x↵ of scatterings – these are su cient to bring the Ly1+↵ radia-xc + x↵ H), hydrogen-electron (H-e) and hydrogen-protonmined bybackground (H-p) the col- background Ly↵ photon Ly↵ flux flux, through is calculated the following using the Del- dz 1+thez coupling3H(z)(1 co-e + z )cient.i kB n 2003) also holds at high-z. We parametrize this correlationthe couplingble to model co-e3EDGESCONSTRAINTSONTHEWDM incient. a self-consistent manner. In this work, taking tion field and the gas intowhere localT equilibriumis the gas kinetic near the temperature centralwhere ⌧ is and theT 21lisions. cmis the optical The color results depth of in the a total di↵use coupling IGMwhere and coeTTk relationSiscient the gasofphi (Furlanetto kineticmodel as temperature et (Ciardi al. 2006b) & Madau and2✏compT↵ 2003)is the color e 8 T u k ↵ X as (Furlanetto et al. 2006b) = a( somewhatT Tk)(8) conservativeMASS and simple approach, we assume and T are theThe neutral first term hydrogen on the (H rightI) handspin temperature side correspondstemperature and to theof the cool- Ly↵ radiation field.3 Further,nkB 1+x and e + fHe 3mec frequency of Ly↵ radiationtemperature (Pritchard of & the Loeb Ly↵ 2012).radiation field. Further, xc and 3 c that the correlation between M˙ and the X-ray luminosity, T H i 11 1 1J↵ ⇤ ing due to the adiabatic expansion⇤ of the Universe while the c (1 + z) dt0 We now discuss howx↵ theare coupling the coupling coe coecients cients andtheCoupling corresponding the background coefficients: radiation to the col- temperature,xc =2.4 The respectively. gas kineticx↵10 TheareTk temperatureop- theni, couplingx↵ =1.81 coe(4) 10cients(1 + correspondingz) S↵ to the˙ 10 col-, (5)0 2.4 The gasWe kinetic now present temperature4 our results for the global 21 cm signal during J↵(z)=where 33=(12 1n ˙ ⌫M0 (z) is) the1 ionizationdz1 , fractionL(6)X , of galaxies ( 10 observed ; in the local Universe (Grimm et al. second term accounts forA10 theT heating and cooling processes ⇥ L =3.4 410⇡ecmf s HzHI ⇤ sr dzJs , (9) e gas kinetic temperaturelisional are calculated. excitations and spin-fliptical due depth to the is usually Ly↵ radiation much less than unity.i=H In, thise,plisional case, for excitations and spin-flipX due to theX Lyz ↵ radiation1 0 cosmic' dawn for the di↵erent dark matter models considered X Bharadwaj⇥ &Z AliM 2004),yr u is the energy density of back- field, respectively. For all practicalthe cosmologicalpurposessummarised one can parameters assume below. used TheThe in quantity next the paper,quantity✏i is the of the interest above energy is injectedthe gas kinetic temperature ✓ ◆ The next quantity of interest is the gas kinetic temperature field, respectively.c 0000 RAS,where For MNRAS all⌫0 practical= ⌫000(1,000–000 + purposesz0)/(1 + onez)with can assume⌫ being the Ly↵ fre- for two scenarios: the first where only X-ray heating is ac- where T =68.5 mKwhich is evolves the temperature as (Furlanetto corresponding et al. 2006b) to ↵ ground photons, T is↵ the Thomson cross-section, fHe = T↵ = Tk. This is justified by theexpression fact that simplifies theinto optical (or taken to depth⇤ out from) the gas per second per unitwhere phys- fX is an unknown normalization factor allowingwhich oneevolves as (Furlanetto et al. 2006b) T↵ = Tk. This isquency, justifiedn ˙ by(z the0) is fact the that production the optical rate depth of photons per unit counted for and the second where we include an excess radio 2.3 The coupling co-e cients icalthe volume 21 cm through transition, processA10i, nisis the the corresponding total number of Einstein- gas ⌫0 0.08 is the helium fraction by number and me is the elec- for Ly↵ photons is so high that they undergo a large number dTk for2T Lyk ↵ photonsH i 2 to is so account high that✏ fori di they↵erences undergo between a large local number and high-z observa- coe cient for spontaneousT (z) emission and isfrequency the spe- per unit comoving volume at redshift z0, c is the dTk background2Tk along2 with the X-ray✏i heating. Gas kineticparticles temperature: and kB is Boltzmann’s constant.= 1/2 The key10 heating . tron˙ (7) mass. of scatterings – these are su cient T tob(⌫ bring) 10 the.1mK Ly↵ radia-HI(z) 1 (1dz + z)1+,z (2)3H(z)(1tions. + z) Giveni kB n the M values yielded by the Delphi model, we = . (7) The coupling coe cients used in this work are calculated as of scatterings – thesespeed are of light su cient and t⇤0 tois bring the cosmic the Ly time↵ radia- corresponding to the dz 1+z 3H(z)(1 + z) i kB n tion field and the gas into local equilibrium⇡ and nearcific cooling the rate central processescoe cient relevantT forS (z spin) at de-excitation high-z include: by collisions with (ii) X-ray heating/cooling: The X-ray photons produced ✓ ◆ tion field and thecalculate gasH Xi into the local star equilibrium formation near rate the density central (SFRD;⇢ ˙ ). The follows: particles of speciesThei with first numberterm on the density right handn .The sideredshift corresponds co-z0. In to this thecool- paper, we assume the spectrum⇤ of pho- X frequency of Ly↵ radiation (Pritchardwhere & Loebis the 2012).(i) neutral Compton hydrogen heating/cooling fraction. : The ratei ofglobally heat-10 averagedby energy early injection sources (e.g., rate per accreting unit volumeThe black first can holes, term miniquasars, on the right hand side corresponds to the cool- (i) The collisional coupling coe cient, xc, is determined HI e cients are calculateding due using to the the adiabaticfrequency fitting expansion functions of Ly↵tons ofradiation given the around Universe in (Pritchard the while Ly↵ thefrequencies & Loeb 2012). to be constant (Furlanetto 3.1 Models with X-ray heating We now discuss how the couplingIn absence coe ing/coolingcients of any and other due the to radiation Compton sources scattering at radio of residual fre- electrons supernova shocks or X-ray binaries)ing due can to heat the upadiabatic gas. The expansion of the Universe while the by three di↵erent channels, namely, hydrogen-hydrogen (H- second term accountsWe for thenow heating discussthenet al. and behow 2006b). cooling expressed the Note coupling processesX-rays as that coe we havecients implicitly and the assumed that all gas kinetic temperature are calculated. withKuhlen background et al. (2006) photons and isCompton given Liszt by (2001). amount of heating depends bothsecond on the term number accounts of photons for the heating and cooling processes H), hydrogen-electron (H-e) and hydrogen-proton (H-p)quencies col- 1420 MHz, the radiationsummarised temperature below.gasT The kinetic(z)is quantity temperature✏i is the are energy calculated. injected In the first case where only X-ray heating is considered, the ⇠ (ii) The Ly↵ coupling coe cient, x↵,alsoknownastheLy↵ photons produced33produced in as the well galaxy⇢˙ as the escape spectral into1 shape. the3 IGM, Given these quanti- given by the CMB temperature2✏ T (z). The8 u spin tem- ✏X =3.4 10 f fX ⇤ Js Mpcsummarised , (10) below.21 cm The di↵ quantityerential brightness✏i is the energy temperatures injected for the four dark lisions. The results in a total coupling coe cient of comp intoCMB (ore taken outT from) the gas peri.e. second a Ly↵ perphoton unit escapeh phys- fraction1 of f =3 1, resulting in our Wouthuysen-Field= coupling coe cient,(T is essentiallyTk)(8) deter- ⇥ ties are highlyM yr uncertainMpc↵ at high-z, they are almost impossi- 2.3 The coupling co-e cientsperature TS can be written3nkB as1+ aical weighted6 volumee +Chatterjee,fHe sum through3me ofc various process Dayal, i, n Choudhuryis the total number & Hutter of gas into (or taken outmatter from) models the gas considered, per second along perwith unit phys-the EDGES observa- T H i mined by the background Ly↵ flux through themodel following overestimating the Ly↵ background. A more reason- ⇤ temperatures (Field 1958) such that 2.3 The coupling co-e cientsble to model in a self-consistent manner.ical volume In this through work,tions, taking process are showni, n inis the Figure total 1. number For each of dark gas matter model, xc = 10 Tkni, (4) particles and kB is Boltzmann’s constant.whereable4 andfh The physicalis thekey heating fraction value corresponding of the X-rays to thatf < contribute1willonly to A10TheT coupling coe cients used in this work arewhererelation calculated e =(1 (Furlanetto as HI) is et the al. ionization 2006b) fraction ( e 10 ; a somewhat conservative and↵ simple approach, we assume i=H,e,p 1 and1ity cooling per unit1 processes comoving relevant volume at' (i.e., high-heating thez include: radio (the emissivity) other part at goes intoexplanation, ionization). however, Weparticles combine are the and quickkBwe transitionis start Boltzmann’s by from showing metal- constant. results The for key typical heating values of fX =0.2 follows:X BharadwajT &+ Alix 2004),T + ux Tis the energyThe coupling density coeofstrengthen back- cients used our in conclusions this work are on calculated the WDM as particle mass by 1 c k redshift(i) ↵ ↵ Comptonz is then given heating/cooling by : The rate ofthat heat- the correlationfree to between metal-enrichedM˙ andand star cooling the formation X-ray processes luminosity, required relevant as well at as high- the z include: TS = 11 1, (3)J↵ fX and fh into one free parameter fX,h = fX ⇤fh. (Glover & Brand 2003) and fh =0.2 (Furlanetto et al. where T =68.5 mK is the(i) temperatureThe collisional corresponding coupling coe tocient, xgroundc, is determinedx photons,↵ =1.81 T10is the(1 + Thomsonz) S↵ follows: cross-section, fHeleading, = (5) to a reduction in the Ly↵ background, and hence, ⇤ 1+xcing/cooling+ x↵ due to Compton2 1 scattering1 1 of residual electronsLX , of galaxiesfact observed that most in the models⇥ local of Universe(i) PopIII Compton star (Grimm formation heating/cooling et al. predict such: The rate of heat- ⇥ cm s Hz sr Finally, we ignore Ly↵ heating in our work as it is be- 2006b), yielding fX,h =0.04. We then carry out calcula- the 21 cm transition, Aby10 threeis the di↵ correspondingerent channels, Einstein-namely, hydrogen-hydrogen0.08 is the helium (H- fraction by number and 22(i) mThee is collisional⇢ the˙ ( zthe) elec- coupling coupling1 co-e coe1 cient.cient,3 xc, is determined with✏R background(z)=fR photons10 is given⇤ by Js Hz Mpc . a transition at much lower redshifts. Another possibility is H i whereExcessTk is the radio gas background: kinetic temperature and T↵ is the color 1lieved to3 be less important compared to X-ray heatinging/cooling (Chen duetions to Compton varying scatteringfX,h by an of order-of-magnitude residual electrons on either side coe cient for spontaneousH), hydrogen-electron emission and 10 (H-e)is and the hydrogen-proton spe- tron mass. (H-p) col- ⇥by three⇥ M di↵yrerent Mpc channels, namely, hydrogen-hydrogen (H- temperature ofc the0000 Ly RAS,↵ radiation MNRAS field.000,000–000 Further, x and that the productionwith of a background radio signal photons from the is givenfirst stars by cific rate coe cient for spinlisions. de-excitation The results by in acollisions total coupling with coe cient of 2✏comp c e 8& T Miralda-Escud´e2004).u (14) We also ignore the heating and to see how this impacts our results. (ii) X-ray heating/cooling: The X-rayH),= hydrogen-electron photons produced ( (H-e)T T andk)(8) hydrogen-protoncould (H-p) immediately col- be followed by heating of gas by cosmic Hx↵i are the coupling coe cients correspondingThe corresponding3nkB to the1+ 21 col-cme + radiationfHe 3cooling2.4me fluxc The at processes a gas redshift kinetic duringz from temperature the reionization epoch (z 15) We find that, independent of the dark matter model particles of species i with number density ni.TheT 10 co- by early sources (e.g., accreting blacklisions. holes, The miniquasars, results in a total coupling coe cient of . 2✏comp e 8 T u H i rays (Jana et al. 2019). Since the signal= depends only on (T Tk)(8) e cients are calculated using the fittingxc = functions⇤ givenlisional in10 excitationsTkni, and spin-flip(4) duesuch to high- thez Lysources↵ radiation can then be writtensince, by as that(Ciardi time, & Madau the4 IGM is heated up to temperatures used, as fX,h increases, the location of the maximum absorp- A10T supernova shocks orwhere X-ray binaries)e =(1 canHI) heat is the up ionization gas. The fraction ( e 10 ; the ratio T /TS ,thisheatingwillhavethesamee3nkB 1+ e + fHe↵ect3m asec i=Hfield,,e,p respectively. For all practical purposes one can assume The nextT quantity ofH interesti is the gas kinetic temperature Kuhlen et al. (2006) and Liszt (2001). 2003) well above⇤ the CMB,' and hence the 21 cm signal becomes tion shifts to higher redshifts and has a smaller amplitude. X amount of heating dependsBharadwaj both & on Ali the 2004), numberu ofis thephotonsxcwhich energy= evolves density as of (Furlanetto back-10 Tkni, etdecreasing al. 2006b)(4) the radiation temperature. While we cannot pro- 4 T↵ = Tk. This is justified by the fact that the optical depth insensitiveA10T to the exact value of the spin temperature.where e =(1 This HI) is is because the ionization the higher fraction the value ( e of10fX,h ;, the earlier the (ii) The Ly↵ couplingwhere coe Tcient,=68x.5↵,alsoknownasthe mK is the temperature correspondingproduced as well to as theground spectral photons, shape. T Givenis0.7 the these Thomson quanti-3 cross-section,i=H,e,pfHe = vide a fully self-consistent model for the radio background ' ⇤ for Ly↵ photons is so high that they undergo a1420 large number c(1 + z) 1 Xdt0 Bharadwaj & Ali 2004), u is the energy density of back- Wouthuysen-Field couplingthe 21 coe cm cient, transition, is essentiallyA10 is deter-the corresponding Einstein- F (z)= Although✏ (zd0T) k the 21d2zT0k cm, signal relevant2 for comparing✏i with IGM begins heating up, shifting the absorption signal to ties are highly uncertain0.08 atR is high- the heliumz, they fraction are almost by numberimpossi- andR,⌫0 me is= the elec- at the moment, it. is clear that(7) explaining the EDGES data of scatteringsH –i these are su cient to bring the150 Lywhere↵ radia-T =684⇡ .5 mKz is the temperaturedz0 corresponding to ground photons, T is the Thomson cross-section, fHe = mined by the backgroundcoe Lycient↵ flux for through spontaneous the following emission and ble10 tois model the spe- in a self-consistenttron mass. manner.✓ ◆ In this⇤ work, takingtheZ EDGESd dataz is1+ relativelyz 3H( insensitivez(without)(1 + z) incorporating toi thekB n reionization any exotic physics)higher-z requiresas well an as ex- leading to a decrease in its amplitude. the 21 cm transition, A10 is the corresponding(15) Einstein- 0.08 is the helium fraction by number and m is the elec- relation (Furlanetto et al.cific 2006b) rate coe cient for spin de-excitationtion field and by the collisions gas into with local equilibrium(ii) X-ray near heating/cooling the central : Thehistory, X-ray photons we still produced compute it for completeness.cess radioX background We use the during pro- cosmicHowever, dawn that we switches note that o↵ the redshifte at which the absorption a somewhat conservativewhere and✏ simple(z0) approach, is the comoving we assumeThe radio first emissivity term on the at right⌫0 = handH i side corresponds to the cool- frequency of Ly↵ radiationH i (Pritchard & LoebR,⌫0 2012).coe cient for spontaneous emission and 10 is the spe- tron mass. particles of species i with number density nthati.The the10 correlation co- betweenby earlyM sources˙ and the(e.g., X-ray accreting luminosity, blackduction holes, rate miniquasars, of ionizing photonsat producedz 16. per unit time per signature begins to show up corresponds to the formation 11 1 J↵ 150 MHz(1⇤ + zcific0)/(1 rate + z). coe We cient converting duefor thisspin to the flux de-excitation adiabatic into a ra- expansion by collisions of⇠ the with Universe while the x↵ =1.81 10 (1 +e zcients) S↵ are calculated using, the(5) fittingWe now functions discuss given how in the couplingsupernova coe shockscients or and X-ray the binaries)unit can comoving heat up volume, gas. Then ˙ ion, obtainedFinally, from weDelphi show thefor(ii) eachdi↵ X-rayerential heating/coolingof brightness the first temperature galaxies: The X-ray in our photons models produced and is thus independent 2 1 1 1 LX , of galaxies observeddio in brightness the local Universe temperature (GrimmTR. This et al. results in a total back- H i ⇥ cm s Hz sr particles of speciessecondi with term number accounts density for theni.The heating andco- cooling processes Kuhlen et al. (2006) and Lisztgas (2001). kinetic temperature are calculated.amount of heating depends both ongalaxy, the number to compute of photons the evolutionover of10 athe two-dimensional global H byI fraction early grid sources composedof (e.g., the of X-ray the accreting two heating model black e ciency. holes, miniquasars, Given the progressive delay ground temperature given by T summarised(z)=TR(z)+ below.TCMB(z The). quantity ✏i is the energy injected (ii) The Ly↵ coupling coe cient, x↵,alsoknownasthe produced as welle as cients the spectral are calculated shape.as Given using these the quanti- fitting functionsfree given parameters in insupernova Fig. 3. We shocks demarcatein or structure X-ray two regions: binaries) formation the can going heat from up gas.cold The to warm dark mat- c 0000 RAS, MNRAS 000,000–000 We then calculate the 21 cminto di↵erential (or taken brightness out from) tem- the gas per second per unit phys- Wouthuysen-Field coupling coe cient, is essentially deter- ties are highly uncertainKuhlen at et high- al. (2006)z, they and are almostLiszt (2001). impossi-3 11 amount of heating depends both on the number of photons peratures over a two-dimensional grid in f =10 and first (light-shaded; bounded by dot-dashedter models, lines) that this repro- results in the absorption signal appearing mined by the background Ly↵2.3flux The through coupling the following co-e cients icald HI volumeR throughn˙ ion process i, n is the total number3 of gas ble to model0 in7 a self-consistent(ii) The Ly manner.↵ coupling In= this coef work,esc cient, takingx+(1↵,alsoknownasthe HIduces) ↵B ARCADE-2nH,com (1+produced resultsz) , (11) as wellas well as aas 21 the cm spectral signal in shape. the Given these quanti- fX,h =10 for CDM; increasingly light WDM models re- at progressively later redshifts from CDM to WDM with relation (Furlanetto et al. 2006b) a somewhat conservativeWouthuysen-Field and simpleparticlesd coupling approach,t and coe wekBn H, assumecient,iscom Boltzmann’s is essentially constant.C deter- The key heating The coupling coe cients used in thisquire work increasing are calculated values ofas both these parameters for which redshift range measuredties are by highly EDGES uncertaindecreasing and the at secondm high-x values.z (dark, they Further, are almost the impossi- faster build-up of stel- that the correlationmined between by theM˙ backgroundandand the cooling X-ray Ly processes luminosity,↵ flux through relevant the at high- followingz include: 11 1follows: J↵ the final fine-grid values explored⇤ where are cosmology-dependent.nH,com is the hydrogen comovingshaded; bounded number density, byble solid to modelf lines)esc that,in alar self-consistent additionally, mass (and matcheshence manner. the In SFR) this with work, decreasing taking mx (see e.g. x↵ =1.81 10 (1 + z) S↵ , (5) 2 1 1 1 LX , of galaxies observedrelation in (Furlanetto the local Universe et(i) al. Compton 2006b) (Grimm et heating/cooling al. the :T The= 500 rate75 of mK heat- signal measured by EDGES. As ⇥ cm(i) Thes Hz collisional sr coupling coe Whilecient, usingx , isf determinedcan indeed enhanceis the the escape amplitude fraction of of the ionizing photons,b ↵B is thea (case somewhat B) conservativeDayal et al. and 2015b) simple results approach, in a shorter we assume time interval between c R ing/cooling due to Compton scattering of residual± electrons absorption signal, a redshift independentrecombination value rate leads coe to ancient andshown,is an the increase clumpingthat in f factorX,h thethat correlation increasesthe onset between X-ray of star heatingM˙ formationand of the X-ray and e luminosity,cient X-ray heating - this by three di↵erent channels, namely, hydrogen-hydrogen (H- 11 1 J↵ ⇤ c 0000 RAS, MNRAS 000,000–000 x↵ =1.81 with10 (1 background + z) S↵ photons is givengas byC leading, (5) to a shallower dip, must be compensated by an enhancement that is more extendedof the in IGM. redshift-space than2 1 1 1 LX , of galaxies observed in the local Universe (Grimm et al. H), hydrogen-electron (H-e) and hydrogen-proton (H-p) col- ⇥ cm s Hz sr naturally decreases the amplitude of the absorption profile increasing fR value that increases the radio background, in- lisions. The results in a total couplingthe coeEDGES cient signal. of Inspired by theAt results this2✏ point,comp of Mirocha our model & e has three8 T u free parameters: fX,h, for decreasing mx values as compared to CDM. = creasing the(T depthTk of)(8) the 21 cm signal. As expected, the later Furlanetto (2019),c 0000 we turn RAS, o↵ MNRASthisfesc excessand000,000–000 radio.3nk WhileB background the1+ first e + isf relevantHe 3mec for the cosmic dawn, Finally, it is clear that, irrespective of the underly- T atH zi= 16. In order to ensure numerical stabilityC of the code, emergence of structure in the 5 keV model, as compared to xc = ⇤ 10 Tkni, (4) the latter two are crucial for the reionization history. As4 ing cosmology, none of the models discussed above pro- A10T where e =(1 HI) is the ionizationCDM, requires fraction larger ( e values10 ; of both these parameters to i=H,e,p we model the radio backgroundshown as a tanh in our function previous having works (Dayal et al. 2017), both' the duce an absorption signal with an amplitude larger than X awidth z 1.5; our resultsBharadwaj are insensitive & Ali to the 2004), pre-u isyield the energy a similar density 21 cm of signal. back- where T =68.5 mK is the temperature corresponding⇡ to CMB optical depth ⌧esc =0.055 0.009 (Planck Collabo- about 180 mK which is much smaller than the amplitude cise choice of the width. Further,ground we reject photons, all combinations T is the Thomson± cross-section, fHe = ⇤ ration et al. 2016b) and ionizing emissivity constraints at of 500 200mK measured by the EDGES observations. the 21 cm transition, A10 is thewhich corresponding produce a radioEinstein- background0.08 higher is the than helium that observed fraction by number and me is the elec- H i > 1 ± coe cient for spontaneous emission and is the spe- z 6 can be simultaneously fit, for all four dark matter As noted above, this result is consistent with expectations by ARCADE-210 at z = 0. Notetron that mass. this is a conservative 1.71 models,⇠ using =1+43z 4CONCLUSIONSANDDISCUSSION(Pawlik et al. 2009; Haardt (e.g. Barkana 2018) and requires additional physics to be cific rate coe cient for spin de-excitationchoice as by low- collisionsz galaxies with are expected(ii) to X-ray produceC heating/cooling an addi- : The X-ray photons produced H i &Madau2012)andfesc that evolves as incorporated into models (Barkana 2018; Fraser et al. 2018; particles of species i with number densitytional radioni.The signal10 not co- accountedby for early in this sources work. (e.g., We find accretingThis black work holes, has focused miniquasars, on constraining the warm dark matter Pospelov et al. 2018; Slatyer & Wu 2018). We can also take e cients are calculated using the fittingthat in functions such a formalism given in a varietysupernova of combinations shocks or of X-rayfX,h binaries)1+particlez can↵ mass heat by up comparing gas. The results of our galaxy formation Kuhlen et al. (2006) and Liszt (2001).and f can match the EDGES signal in redshiftfesc(z)=min and ampli-1,f0 model, Delphifor z (Dayal5. et(12) al. 2014, 2015a),a step back with and the globalrelax the constraint on the amplitude, only R amount of heating depends both7 on the number> of photons (ii) The Ly↵ coupling coe cient,tudex↵ as,alsoknownasthe shown in Figure 2. For theproduced CDM and as 5 well keV as models, the spectral✓ 21 shape. cm◆ signal Given recently these detected quanti- by thedemanding EDGES collaboration that the absorption signal is fully contained be- tween 13 < z < 21 so as to be compatible with the EDGES Wouthuysen-Field coupling coe cient,we show is essentially only those deter- models thatHere,ties simultaneously aref0 highly100 uncertain = satisfy 4.5(4 the.1, at3. high-8, 4.(Bowman8)z, and they↵ are=2 et almostal..9(3 2018)..7, impossi-4.3 Our, 6.2) work is based on the fact that ⇥ ⇠ ⇠ mined by the background Ly↵ fluxARCADE-2 through the upper following limits and whereforble the to the model CDM absorption in (5 a keV, self-consistent signal 3 KeV andthe manner. 1.5 frequency keV In WDM) this of work, the model. EDGES taking signalobservations implies the first (e.g. stars Schneider 2018). As shown in (panels a is strictly limited to z > 14. However, as shown in the same to have formed as early as z 18. Theand increasingb of) Figure delay 1, we in find that the CDM and 5keV WDM relation (Furlanetto et al. 2006b) a somewhat conservative and simple approach, we assume⇠ ⇠ galaxy formation in progressively light WDM models could > > figure, there are no combinationsthat of free the parameters correlation that between can M˙ and the X-ray luminosity, models produce such a signal for fX,h 0.04 and fX,h 0.4, 11 1 J↵ ⇤ ⇠ ⇠ x↵ =1.81 10 (1 + z) S↵ reproduce the amplitude, (5) ( 500 175mK), or even a signal in therefore be used to constrain the WDMrespectively. mass at these However, early given the delay in structure forma- 2 1 1 1 ±LXThe, of emissivity galaxies observed is calculated in the using local the Universe approach (Grimm outlined et al. in ⇥ cmthe s required Hz redshiftsr range, for 3 keV and 1.5 keV WDM epochs, inaccessible by any other means. < Kuhlen & Faucher-Gigu`ere(2012), i.e., by combining the obser- tion, mx 3 keV WDM models are unable to produce a models given the delay in galaxy formation in these models. Starting from a scenario wherein the radiation⇠ temper- c vational constraints on the hydrogen photoionization rate from signal in the observed redshift range, irrespective of the fX,h 0000 RAS, MNRAS 000,000–000Based on the EDGES and ARCADE-2 observations, we can ature is solely provided by the CMB and in absence of any Wyithe & Bolton (2011) and the mean free path of ionizing pho- values used. Thus, even with this first estimate, the EDGES therefore rule out WDM model with mX 3 keV. non-standard cooling of the gas, none of our models can < tons from6 Songaila & Cowie (2010). signal can be used to rule out mx 3 keV WDM. While the presence of the additional radio background match the strength of the absorption signal measured by ⇠ during cosmic dawn might be expected because of the for- EDGES. Working with less stringent criteria and only de- c 0000 RAS, MNRAS 000,000–000 mation of the first stars2, the physical reason for this back- manding that the models predict the absorption signal at ground being suppressed at z < 16 is much more di cult to the redshift location demarcated by EDGES, we can essen- < explain. One possible reason could⇠ be the radio background tially rule out mx 3 keV WDM given the delay in galaxy being mostly powered by PopIII stars which tend to die o↵ formation, and hence⇠ the build-up of the Ly↵ background, as the gas gets metal-enriched. The key issues with such an in such models. We also propose a way to reproduce both the red- shift and amplitude of the EDGES signal by introducing 2 However, there are concerns in sustaining the radio background an additional source of radio background radiation which produced by accelerating relativistic electrons because their cool- scales with the SFRD. Some indication of such an excess ex- ing time-scale is much shorter than the Hubble time (see, e.g., ists from local observations with ARCADE-2 (Fixsen et al. Sharma 2018). 2011). However, we find that a redshift-independent scaling
c 0000 RAS, MNRAS 000,000–000 Build-up of cosmic SFRD cosmology-dependent
Galaxies assemble faster in light WDM models compared to CDM. This is because they start off bigger and are less feedback limited as a consequence.
PD+ 2015, ApJ, 806, 67 Ruling out light (<3Ruling keV) out WDM 3 keV WDM using using EDGES 21cm7 EDGES data
• Matching to amplitude of EDGES requires an excess radio background. • The dearth of star formation at z>18 in <3 keV WDM modes allows them to be ruled out using EDGES data, even allowing X-ray heating and an excess radio background
Atrideb Chatterjee
Chatterjee, PD+2019, MNRAS, 487, 3560
Figure 2. The global 21 cm di↵erential brightness temperature for the CDM, 5 keV, 3 keV and 1.5 keV WDM models, as marked, including both X-ray heating and an excess radio background (see Sec. 3.2). In each panel the black curve shows the EDGES result. The grey lines in each panel show models that satisfy the ARCADE-2 limits and where the signal is limited to z > 14. The red lines show models consistent with the EDGES result, both in terms of the redshift range of the signal as well as its amplitude⇠ ( T = 500 75mK). b ± As shown, the inclusion of an excess radio background results in free parameter combinations (fR and fX,h)yieldingresultsinagreement < with the EDGES data for the CDM and 5 keV WDM models. However, mx 3keVmodelscane↵ectively be ruled out since they are unable to reproduce either the redshift range or the amplitude of the observed⇠ signal. between the radio background and the SFRD results in an this case too, structure formation is delayed long enough in < absorption that extends much later than conventional mod- mx 3 keV WDM models so that they can be ruled out. els as well as the EDGES signal. Reproducing the EDGES ⇠Although our model contains various simplifying as- data requires such a background be turned o↵ (or equiva- sumptions at di↵erent stages (e.g., the various e ciency pa- lently, the gas be heated up beyond what is predicted by rameters related to X-ray heating are taken to be indepen- X-ray heating) at z 16. As of now, both the sources dent of z), it is clear that WDM models with m < 3 keV ⇠ x (metal free stars or cosmic rays associated with the first simply cannot form stars early enough to satisfy the⇠ EDGES stars and/or black holes) and reasons for the decay of such constraint. We have checked this by varying the free parame- a background at z<16 remain open questions. Despite this ters to their extreme limits, and found our conclusions to be and irrespective of the values of the free parameters used, in robust. Our constraints are thus comparable to constraints c 0000 RAS, MNRAS 000,000–000 GWs from the first billion years The theoretical framework: DELPHI
Galaxies containing gas Galaxies with stars, gas and BH (efficient star formers) Galaxies containing gas and BH Galaxies with stars but no gas IGM smooth accretion (SN feedback limited)
DELPHI; PD et al. 2019 Figure 6: A SAM jointly tracking the (merger and accretion driven) buildup of dark matter halos as well as their baryonic component. SAMs present a powerful tool for capturing the key physics involved in galaxy formation including: the stellar mass growth due to star formation, the merger and accretion driven gas mass growth, the role of SN (and possibly black holes) in ejecting gas from low-mass halos and tracking the resulting impact on the subsequent growth of more massive systems via halo mergers and gas accretion. As shown, galaxies assemble as a result of both wet mergers of “e cient star formers” that do not lose all their gas mass after star formation/black hole accretion and dry mergers of supernova/black hole “feedback limited” systems that lose all their gas resulting in dry mergers. This naturally leads to a variety of galaxy assembly histories and properties for a given halo mass. space around particles. Based on polyhedral cells, this mesh continually de-forms and re-forms as particles move. Despite its obvious advantage in simultaneously tracking both dark matter and gas particles, the enormous computational e↵ort required for hydrodynamic simulations naturally places a limit on the physical volume that can be simulated and the physical parameter space that can be explored for a given mass resolution.
4.2.3. Semi-numerical models As detailed in Sec. 7.3, the past years have seen an increasing realisation of the necessity of coupling galaxy formation - on kiloparsecs scales - with the impact of the radiative feedback generated during reionization - on tens of Megaparsec scales. Indeed, Iliev et al. [134] have shown 1 3 that, while (100h cMpc) boxes are su ciently large for deriving convergent reionization histo- ries, the morphology of the ionized bubbles remains poorly described for box sizes smaller than
32 The key physics explored
DELPHI; PD et al. 2019 The key physics explored
Two types of BH seeds - stellar (PopulationIII) and direct collapse black holes (based on strength of Lyman alpha background)
DELPHI; PD et al. 2019 The key physics explored
Two types of BH seeds - stellar (PopulationIII) and direct collapse black holes (based on strength of Lyman alpha background)
Impact of reionization feedback in photo- evaporating gas from low-mass halos and slowing black hole growth
DELPHI; PD et al. 2019 The key physics explored
Two types of BH seeds - stellar (PopulationIII) and direct collapse black holes (based on strength of Lyman alpha background)
Impact of reionization feedback in photo- evaporating gas from low-mass halos and slowing black hole growth
Black hole growth regulated by both halo mass and gas availability (due to the impact of Supernova and reionization feedback)
DELPHI; PD et al. 2019 The key physics explored
Two types of BH seeds - stellar (PopulationIII) and direct collapse black holes (based on strength of Lyman alpha background)
Impact of reionization feedback in photo- evaporating gas from low-mass halos and slowing black hole growth
Black hole growth regulated by both halo mass and gas availability (due to the impact of Supernova and reionization feedback)
Impact of instantaneous versus (dynamically) delayed galaxy mergers on the black hole merger rate
DELPHI; PD et al. 2019 Baselining the model against all available high-z data
Galaxies containing gas Galaxies with stars, gas and BH (efficient star formers) Galaxies containing gas and BH Galaxies with stars but no gas IGM smooth accretion (SN feedback limited)
Figure 6: A SAM jointly tracking the (merger and accretion driven) buildup of dark matter halos as well as their baryonic component. SAMs present a powerful tool for capturing the key physics involved in galaxy formation including: the stellar mass growth due to star formation, the merger and accretion driven gas mass growth, the role of SN (and possibly black holes) in ejecting gas from low-mass halos and tracking the resulting impact on the subsequent growth of more massive systems via halo mergers and gas accretion. As shown, galaxies assemble as a result of both wet mergers of “e cient star formers” that do not lose all their gas mass after star formation/black hole accretion and dry mergers of supernova/black hole “feedback limited” systems that lose all their gas resulting DELPHI in dry mergers. This naturally leads to a variety of galaxy assembly histories and properties for a given halo mass. PD et al. 2019 space around particles. Based on polyhedral cells, this mesh continually de-forms and re-forms as particles move. Despite its obvious advantage in simultaneously tracking both dark matter and gas particles, the enormous computational e↵ort required for hydrodynamic simulations naturally places a limit on the physical volume that can be simulated and the physical parameter space that can be explored for a given mass resolution.
4.2.3. Semi-numerical models As detailed in Sec. 7.3, the past years have seen an increasing realisation of the necessity of coupling galaxy formation - on kiloparsecs scales - with the impact of the radiative feedback generated during reionization - on tens of Megaparsec scales. Indeed, Iliev et al. [134] have shown 1 3 that, while (100h cMpc) boxes are su ciently large for deriving convergent reionization histo- ries, the morphology of the ionized bubbles remains poorly described for box sizes smaller than
32 Galaxies, BHs & GWs 7 Galaxies, BHs & GWs 7
Baselining the model against all available high-z data
Galaxies, BHs & GWs 7 Ultra Violet Luminosity Function
8 Dayal et al.
limited and bring in gas in mergers (wet mergers), leading Figure 2. The UV LF from z 5 10Figure as marked 2. The in the UV panels. LF from In eachz 5 panel,10 asthe marked violet points in the show panels. the In available each panel, LBG the data violet collected points show the available LBG data collected to a slightly steeper bright end. Finally, including the (max- ' ' both using space- and ground-based observatoriesboth using at: space- (a) z and5(Bouwensetal.2007;McLureetal.2009);(b) ground-based observatories at: (a) z 5(Bouwensetal.2007;McLureetal.2009);(b)z 6(McLureetal.2009; z 6(McLureetal.2009; imal) impact of reionization feedback (ins4 and tdf4), that ' ' ' ' Bouwens et al. 2015; Livermore et al. 2017);Bouwens (c) z et al.7(Bouwensetal.2010;McLureetal.2010;Castellanoetal.2010;McLureetal. 2015;Stellar Livermore et mass al. 2017); (c) z 7(Bouwensetal.2010;McLureetal.2010;Castellanoetal.2010;McLureetal. ' ' photo-evaporates the baryonic content of all galaxies2013; Bowler with et al. 2014; Livermore et al.2013; 2017; Bowler Atek et et al. al. 2014; 2015); Livermore (d) z 8(Bouwensetal.2010;McLureetal.2010;Bradleyetal. et al. 2017; Atek et al. 2015); (d) z 8(Bouwensetal.2010;McLureetal.2010;Bradleyetal. < 1 ' ' Vvir 40 km s ,onlya↵ects the faint-end of2012; the UV McLure LF et al. 2013; Livermore et2012; al. 2017; McLure Atek et et al. al. 2013; 2015);density Livermore (e) z 9(McLureetal.2013;Oeschetal.2013);and(e) et al. 2017; Atek et al. 2015); (e) z 9(McLureetal.2013;Oeschetal.2013);and(e)z 10 z 10 ⇠ ' ' ' ' and leads to a cut-o↵ at brighter magnitudes (M(BouwensUV et14 al. 2014; Oesch et al. 2014).(Bouwens In each panel, et al. 2014; the yellow Oesch points et al. show 2014). the In AGN each panel, data collected the yellow at: pointsz 5(McGreeretal.2013; show the AGN data collected at: z 5(McGreeretal.2013; ⇠ ⇠ ⇠ to 15) as compared to the continued rise excludingParsa et al. this 2018) and z 6 (Willott etParsa al. 2010; et al. Kashikawa 2018) and etz al.6 2015; (Willott Parsa et et al. al. 2010; 2018; Kashikawa Jiang et al. et 2016). al. 2015; In Parsa each panel, et al. lines2018; show Jiang et al. 2016). In each panel, lines show ⇠ ⇠ e↵ect (e.g. in models ins1 and tdf1). In this work,model models UV LFs for galaxies and black holesmodel for UV the LFs following for galaxies models and summarised black holes in for Table the 1, following that bracket models the summarised range of UV in LFs Table allowed 1, that bracket the range of UV LFs allowed ins1 and tdf4, therefore, bracket the plausible UVin theLF presence/absencerange. of a UVB andin for the both presence/absence instantaneous and of a delayed UVB and (by for a merging both instantaneous timescale) merger: and delayedins1 ( (bygalaxies a mergingsolid black timescale) merger: ins1 (galaxies solid black However, it must be cautioned that the theoreticalline; LBGBH solid UV gray line), ins4 (galaxies shortline; BH dashedsolid red gray line; line),BHins4short(galaxies dashedshort light-red dashed line), redtdf1 line;(galaxiesBH shortlong dashed dashed light-red green line; line),BHtdf1 (galaxies long dashed green line; BH long-dashed light green line) and tdf4 (galaxieslong-dasheddot-dashed light green blue line) line; and it BHtdf4 dot-dashed(galaxies purpledot-dashed line). blue line; it BH dot-dashed purple line). Galaxies containing gas LF has, so far, ignoredGalaxies the with impact stars, ofgas dust and enrichmentBH which Figure 2. The UV LF from z 5 10 as marked in the panels. In each panel, the violet points show the available LBG data collected is expected to have(efficient a relevant star formers) e↵ect in decreasing the lumi- ' Galaxies containing gas and BH both using space- and ground-based observatories at: (a) z 5(Bouwensetal.2007;McLureetal.2009);(b)z 6(McLureetal.2009; ' ' nosities at the bright end. Bouwensseen an enormous et al. 2015; increase Livermore in LBG et al. data 2017);seen due an (c) enormous toz a combina-7(Bouwensetal.2010;McLureetal.2010;Castellanoetal.2010;McLureetal. increase in3.1 LBG The data observed due to a combina- UV LF for star3.1 formation The observed and UV LF for star formation and Galaxies with stars but no gas IGM smooth accretion ' 2013;tion of Bowler state-of-the-art et al. 2014; instruments Livermore et suchtion al.2017; as of (the state-of-the-art Atek Wide et al.Field 2015); instruments (d) z black8(Bouwensetal.2010;McLureetal.2010;Bradleyetal. such as holes (the Wide Field black holes (SN feedback limited) ' 2012;Came McLure 3 onboard) et al. the 2013; Hubble Livermore Space etTelescopeCame al. 2017; 3 onboard) (HST Atek)aswell et the al. Hubble2015); (e) Spacez Telescope9(McLureetal.2013;Oeschetal.2013);and(e) (HST)aswell z 10 ' ' 10 Dayal et al. 10 Dayal et al. Focusing on the AGN UV LF, the black hole(Bouwens powered et al. 2014; Oesch et al. 2014). In each panel, the yellow pointsTheobserved show the AGNUV LF data (number collectedGalaxies, density at: Thez of BHs5(McGreeretal.2013; galaxiesobserved & GWs as UV a func- LF (number9 density of galaxies as a func- as refined selection techniques (e.g. Steidelas refined et al. selection 1999). techniques As (e.g. Steidel et al. 1999). As ⇠ Figure 6: A SAM jointly tracking the (merger and accretion driven) buildup of dark matter halos as well as theirParsa et al. 2018) and z 6 (Willott et al. 2010; Kashikawa et al. 2015;tion Parsa of the et absolute al. 2018; magnitude)Jiang et al. 2016). andtion its In ofredshift each the panel, absolute evolution lines magnitude) show and its redshift evolution UV LFs for all four models discussed above arefor AGN,found ato number of⇠ surveys, includingfor AGN, the Sloan a number Digital of surveys, including the Sloan Digital model UV LFs for galaxies and black holes for the following models summarisedo↵er one of in the Table most 1, robust that bracket tests oftheo↵ theoreticaler range one of of UV the models LFs most allowed of robust tests of theoretical models of baryonic component. SAMs present a powerful tool for capturingbe in excellent the key physics agreement involved with in all galaxy available formation AGNSky Survey data at (SDSS)Figure and the 3. Canadian-FrenchThe LBGSky Surveystellar high-z mass (SDSS) quasar density and the (SMD) Canadian-French as a func- high-z quasar z 5 and 6 as shown in Fig. 2. We start byinsurveys, noting the presence/absence that and observationstion of redshift.a with UVB the and Points Subarusurveys, for showboth telescope, and instantaneousthe observational observations have and data with delayedgalaxy collected the (by formation.Subaru a by: merging telescope, We timescale) start have by merger: calculatinggalaxyins1 ( theformation.galaxies UV magni-solid We black start by calculating the UV magni- including: the stellar mass growth due to star formation, the merger⇠ and accretion driven gas> mass11.5 growth, theline; BH solid gray line), ins4 (galaxies short dashed red line; BH short dashed light-red line), tdf1 (galaxies long dashed green line; BH given the large masses (Mh 10 M )associatedwithyielded a statisticalGonz´alezet sample of AGN/QSO al. (2011,yielded red candidates empty a statistical circles), at red- sample Labb´eet oftudes, AGN/QSOal. (2013, separately blue candidates for star at formation red- tudes, and AGN separately activity, for for star formation and AGN activity, for long-dashed light green line) and tdf4 (galaxiesBlackdot-dashed hole blue line; it BH dot-dashed purple line). role of SN (and possibly black holes) in ejecting gas from low-massAGN/QSO halos and host tracking halos, the resulting black⇠ hole impact UV on LF theshifts is only as high rel- as z empty6. In triangles), what follows Starkshifts we et compare as al. high (2013, as 4 purplemodelsz 6. empty In whateach squares), follows theoretical Oesch we compare galaxy 4 models and computingeach the theoretical associated galaxy UV and computing the associated UV < 'et al. (2014, yellow emptymass circles), function Duncan' et al. (2014,LFs, as red shown filled in Fig. 2. We start byLFs, discussing as shown the in LBG Fig. 2. We start by discussing the LBG subsequent growth of more massive systems via halo mergersevant and gas at accretion. MUV As21, shown, corresponding galaxies assemble to number asthat a densities bracket the physically plausiblethat range bracket explored the in physically this plausible range explored in this < 5 1 3 squares), Grazian et al. (2015, purple filled circles)UV and LF: Song firstly, et al. matching to the brightUV end LF: of firstly, the evolving matching to the bright end of the evolving 10 [dex Mpc⇠ ]atz 5 and 6. These resultswork ( areins1, in ins4, tdf1 and tdf4), detailedwork ( inins1, Table ins4, 1, tdf1with and tdf4), detailed in Table 1, with result of both wet mergers of “e cient star formers” that do not lose all their gas mass after⇠ star formation/blackseen an enormous(2016, increase yellow in LBG filled data triangles). due to We a combina-show results for3.1 galaxies The with observed UV LF for star formation and qualitative⇠ agreement with those of Ono et al.anumberofdata-sets,includingtheUVLFs,thestellar (2018) who anumberofdata-sets,includingtheUVLFs,thestellarUV LF requires a maximum star formationUV LF erequires ciency a value maximum star formation e ciency value BH-stellar mass tion of state-of-the-artM instruments< 17.7whichcanbedirectlycomparedtoobservational such as (the Wide Field black holes hole accretion and dry mergers of supernova/black hole “feedback limited” systems that lose all their gas resultingmass density, the blackUV hole mass functionmass density, and the the black black holeof massf function2%. Secondly, and the we blackfind that theof fiducialf 2%. model Secondly, (ins1) we find that the fiducial model (ins1) find 100% of the UV luminosity to come solely fromCame stars 3 onboard) for thedata Hubble points Spacefor the Telescope following models (HST)aswell shown in Table 1:⇤ ins1' (solid ⇤ ' > hole-stellar mass relation. hole-stellar mass relation. is inDELPHI excellent agreement with availableis in LBG excellent observations, agreement with available LBG observations, in dry mergers. This naturally leads to a variety of galaxy assemblygalaxies histories with M andUV properties23 to for24. a given However, halo mass. given that the black line), ins4 (dot-dashed red line), tdf1 (longThe dashed observed green UV LF< (number< density of galaxies as a func-< < as refined selection techniques (e.g. Steidel et al. 1999). As ranging between 22 MUV 13,ranging at all betweenz 5 1022 as MUV 13, at all z 5 10 as AGN number densities⇠ are suppressed due to obscuration line) and tdf4 (dot-dashed blue line). We also show results for the ⇠ ⇠ for AGN, a number of surveys, including the Sloan Digital PDalreadytion et of shownal. the absolute2019 in our previous⇠ magnitude)⇠ works and(e.g.already itsDayal shownredshift et al. in2014). evolution our previous⇠ ⇠ works (e.g. Dayal et al. 2014). (see Sec. 2.3), calculating the fraction of galaxies dominated total SMD obtained by summing over all galaxies at a specific z Sky Survey (SDSS) and the Canadian-French high-z quasar Theo↵er inclusion one of of the a delay most in robust galaxy tests mergersThe of theoreticalinclusion (tdf1)hasnosen- of modelsa delayin of galaxy mergers (tdf1)hasnosen- space around particles. Based on polyhedral cells, thisby mesh AGN continuallyrequires a more de-forms thorough and examination re-forms as which we for the same models noted above: ins1 (solid gray line), ins4 (dot- surveys, and observations with the Subaru telescope, have siblegalaxy impact formation. on the faint-end We start of by the calculating UVsible LF impact - this the on is UV thedue magni- faint-end to of the UV LF - this is due to defer to a future work. Finally, we note that the contribu- dashed light red line), tdf1 (long dashed light green line) and tdf4 yielded a statistical sample of AGN/QSO candidates at red- thetudes, fact that separately the progenitors for star formationof thesethe low-mass and fact AGN that halos the activity, are progenitors SN for of these low-mass halos are SN particles move. Despite its obvious advantage in simultaneouslytion of BH-powered tracking luminosity both coulddark matterbe one explanation and for (dot-dashed purple line). shiftsWe as note high that, as z given6. In their what low follows number weWe densities, compare note that, both 4 models given the theirfeedback loweach number theoretical limited densities, and galaxy hence both and the do computingnot bringfeedback in the any limited associated gas whilst and hence UV do not bring in any gas whilst ' gas particles, the enormous computational e↵ort requiredobserved for UV hydrodynamic LFs that are simulations shallower than naturally the exponentiallythat“light” bracket and “heavy” the physically DCBH seedingplausible cases“light” range yield and explored very “heavy” similar in this DCBH seedingmergingLFs, as cases (dry shown yield mergers) in very Fig. similar as 2. already We start pointedmerging by discussing out (dry previously mergers) the LBG as already pointed out previously declining Schechter function at these high-z (e.g. Ono et al. UV LF: firstly, matching to the bright end of the evolving workresults (ins1, for all ins4, the observational tdf13.2 and The tdf4 LBG data-sets), detailedresults stellar discussed. forin mass Table all the Fordensity 1, observational this with (SMD)(Dayal data-sets et al. discussed. 2014). On For the this other hand,(Dayal the et delay al. 2014). in galaxy On the other hand, the delay in galaxy places a limit on the physical volume that can be simulated2018). and the physical parameter space thatanumberofdata-sets,includingtheUVLFs,thestellarreason, we limit our results to the “lightreason, DCBH we limit seed” our case results tomergersUV the LF “light leads requires DCBH to an a seed”increasing maximum case reduction star formationmergers in the leads e gasciency to masses an increasing value reduction in the gas masses Figure 6. The black hole mass-stellarFigure 6. massThe relation black hole for mass-stellarz 5fortwomodelsthatbrackettheexpectedrange:Instantaneousmerg- mass relation for z 5fortwomodelsthatbrackettheexpectedrange:Instantaneousmerg-Figurein this 4. section.The black holeWe nowmass compare functionin (BHMF)the this theoretical section. at z SMD6. We to thatofof observation- higher-massf 2%. Secondly, halos whose we progenitors find thatof the higher-mass are fiducial not SN model feedback halos ( whoseins1) progenitors are not SN feedback can be explored for a given mass resolution.' ' mass density, the black hole mass function and' the black Figure⇤ ' 5. The black hole occupation fraction as a function of halo ers with/without UV feedbackers (ins1 with/withoutusing black UV points feedback and (ins4ins1usingusing red black points; points left and panel)ins4 andusing mergers red points; after left a merging panel)compare andtimescale mergers observational after aally results merging inferred (gray timescale for line LBGs. with error We start bars) by from comparingis to in observed excellent agreement with available LBG observations, hole-stellar mass relation. mass for z 6(blacklines),z 9(bluelines)andz 12 (red with/without UV feedback (tdf1 using green points and tdf4 using blue points; right panel). In both panels we show two relations derived < < < with/without UV feedback (tdf1 using green pointsWe and findtdf4 thatusing the blue AGN points; UV right LF panel). is extremely InWillott bothc similar panels0000 et al. RAS, we(2010) for show MNRAS to two thoseLBGs000 relations from,000–000 with our derived M modelsUV c 0000 bracketing17 RAS,.7asshowninFig.3.Asseen, MNRAS the plau-000,000–000ranging between⇠ 22 MUV⇠ 13, at all z ⇠5 10 as lines) as marked. The solid lines show the occupation fraction using galaxies in the nearby Universe:using galaxiesMbh =1 in the.4M nearby6.45 Universe: derived forMbh high=1 stellar.4M mass6.45 ellipticals derived for and high bulges stellar and massMbh ellipticals=1sible.05M physical and4 bulges.1 range: and ins1Mbh (solid=1.05 blackM 4 line),.1⇠ ins4 (short-dashed ⇠ ⇠ ⇠ 4.2.3. Semi-numerical models ⇤ heavy⇤ black hole seeds with ↵ varying over an order⇤ of mag- while all four⇤ models (ins1, ins4, tdf1, tdf4)for arealready all in black excel- shown holes; in the our short-dashed previous works and (e.g. dot-dashed Dayal et lines al. 2014). show for moderate luminosity AGNfor in moderatelow-mass halos luminosity (Volonteri AGN & in Reines low-mass 2016), halos as (Volonteri marked. In & each Reines panel 2016), we also as marked. show the In best-fit eachred panel line), relation wetdf1 also(long-dashed show the best-fit green line) relation and tdf4 (dot-dashed blue nitude (for 30 to 300) for the four models discussed above. lent agreement with the data they are o↵setresultsThe in normali- inclusion for Type 1of (stellar a delay black in galaxy holes) mergers and Type (tdf1 2+3)hasnosen- (DCBHs), from our model for high stellarfrom mass our galaxies: model forLogM highbh stellar=1.25 massM galaxies:4.8. As seen,LogM ourbh =1 theoretical.25M model4.8. As yields seen, a our non-linear theoreticalline). scaling model As such shown, yields the a non-linear shape of the scaling BHMF such is independent of the in- As detailed in Sec. 7.3, the past years⇤ have seenThis an is increasing probably⇤ to realisation be expected of given the necessity the extremely low sation from each-other whilst following veryrespectively. similarsible impact slopes on the faint-end of the UV LF - this is due to that black holes in low-mass galaxiesthat black are holes “stuck” in low-mass at their initial galaxies mass; are the “stuck” BH masses at their of initial high-mass mass; hosts, the BH on masses the other of high-masshand,clusion are strongly hosts, of UV on feedback the other and hand, the are merger strongly timescales used. However, number of heavy black hole seeds as compared to the number such that SMD (1 + z)0.42.Asmightbeexpected,modelthe fact that the progenitors of these low-mass halos are SN correlated with the stellar masscorrelated and are within excellent the stellar agreement mass and with are the in results excellent derived agreement for lower- withz thehigh results stellar derived mass galaxies. for lower-the finalz high BH stellar masses mass are galaxies. naturally lower/ when including a delay of coupling galaxy formation - on kiloparsecs scalesof - light with black the holeimpact seeds of as the pointed radiative out in feedback Sec. 2.1; theWe latter note that, givenins1 provides their low the number upper densities, limit to both the the SMD resultsfeedback forob- limited and hence do not bring in any gas whilst in the merger timescales as opposed to instantaneous mergers. generated during reionization - on tens of Megaparsectherefore scales. clearly Indeed, dominate Iliev et al.the [134] UV LF. have As shown for“light” the merger and “heavy”served DCBH galaxies. seeding Including cases yield the very e↵ects similar of delayed galaxymerging merg- (dry mergers) as already pointed out previously timescales, including a delay in the mergers of galaxiesresults for (and all the observationalers (tdf1) results data-sets in a small discussed. decrease For thisin the SMD(Dayal values et byal. 2014). On the other hand, the delay in galaxy lower limit on the DCBH numberlower limit density on the and, DCBH hence, number the densitygalaxies and, and hence, we obtain the a blackgalaxies hole-stellar and we mass obtain relation a black in hole-stellar mass relation in in by merging progenitors halos has a significant contribu- that, while (100h 1 cMpc)3 boxes are su ciently largeblack for holes) deriving results convergent in a smaller reionization black hole histo- growth.reason, This we is limit ourabout results 0.1 to dex. the However, “light DCBH assuming seed” instantaneouscase mergers mergers leads to an increasing reduction in the gas masses Type 2+3 occupation fraction.Type 2+3 occupation fraction. agreement with numerical investigations,agreement with a numericalnon-linearOn investigations, scal- the other hand, a non-linear the impact scal- of reionization feedback tion to the growth of these high-mass systems. On the other reflected in a lower final black hole mass in a givenin this halo section. (also whilst including maximal UVB suppression (ins4of higher-mass) only re- halos whose progenitors are not SN feedback ing where black holes in low-massing where galaxies black holes areand “stuck” in a low-mass delay at in galaxiesthe merging are “stuck” timescale at are much more dra- hand, reionization feedback alone (ins4) has a negligible ef- ries, the morphology of the ionized bubbles remainssee poorly Sec. 3.3 described that follows). for box However, sizes thissmaller only than leads to minor sults in a SMD that is di↵erent from the fiducial case by a their initial mass (Habouzittheir et al. initial 2017; mass Bower (Habouzit etmatic al. 2017). when et al. considering 2017; Bower the et entire al. 2017). galaxy population (with- fect on the growth of high-mass halos (as discussed in Sec. changes in the UV LF which are indistinguishablec within0000 RAS, the MNRASnegligible000,000–000 0.03 dex. These results clearly imply that a delay BHs in high-mass hosts, onBHs the in other high-mass hand, can hosts,out be any on above thelimiting other magnitudes hand, can beused). above In this case, the fidu- 3.2 above), yielding a BHMF in close agreement with the 3.4 The black hole-stellar3.4 mass The relation black hole-stellar mass relationscatter shown by the four models considered here. Further, in the merger timescales is more important than the e↵ect the z =0scaling,asshowninFig.6.the z =0scaling,asshowninFig.6.cial model, ins1, shows a slope that evolves with redshift fiducial one. Finally, the model tdf4,includingboththeim- given the large masses of AGN hosts, reionization feedback 0.24of a UVB for these high mass systems. Finally, the lower Constraints on the relationConstraints between BHs on theand relation galaxies between at BHs and galaxies at as SMD (1 + z) .GiventhatinthiscasetheSMDis pact of delayed mergers and the UVB, yields results quite 32 has no relevant e↵ect on the AGN UV LF. Finally, looking/ limit to the SMD results is provided by model tdf4 that is high redshift are scant. In general,high redshift since theare onlyscant. confirmed In general, since the only confirmed dominated by the contribution from low-mass halos, the sit- similar to tdf1 and, provides the lower limit to the BHMF. at the redshift evolution of the AGN UV LF, we find that about 0.13 dex lower than the fiducial results. These slight BHs at these redshifts are thoseBHs poweringat these redshifts powerful are quasars, those powering powerful quasars, uation flips as compared to that discussed above: the merger We recall that our model is not aimed at (re)producing rare it shows a sharper redshift evolution compared to the star- changes in the SMD normalisation shows that most of the the stellar mass of the host cannot be measured (not to timescale has a negligible e↵ect on the SMD of all galaxies the stellar mass of the host cannot be measuredformation (not powered to UV LF given the increasing paucity of stellar mass is assembled in massive progenitorsluminous (see quasars also powered by very massive BH (see Valiante mention the stellar velocity dispersion or bulge mass) be- and shows essentially the same amplitude and slope as the mention the stellar velocity dispersion ortheir bulge high-mass mass) be- hosts. To quantify this e↵ect, let us focus on Dayal et al. 2013) with low-mass progenitorset - al. that 2016; either Pezzulli et al. 2016, and references therein for cause the light from the quasarcause over-shines the light from the host the quasar galaxy. over-shines the host galaxy. fiducial case. However, the UVB suppression of the gas mass models focused on the most massive halos and BHs) but at amagnitudeofMUV = 20: while the star formation driven merge after a dynamical timescale (tdf1), are reionization The best estimates of the host properties for these powerful Quantitatively, we find that the BH mass-stellarof low-mass halos results in both a decrease in the ampli- The best estimates of the host properties forUV these LF only powerful evolves by a factorQuantitatively, of 3 between z we5 findand 7, that the thesuppressed BH mass-stellar (ins4)orincludeboththesee↵ectsthe (tdf4 bulk)-con- of the population of massive BHs. It should there- quasars are obtained throughquasars measures are obtained of the cold through (molec- measuresmass of the relation cold (molec- is strongly correlatedmass relation for high is strongly stellartude⇠ (by correlated mass about 0.23 for dex) high and stellar a, more mass dramatic, steepening fore not be surprising that the BH mass function does not AGN UV LF (negatively) evolves by roughly three orders of tributing only a few percent0.31 to the stellar mass for observed > 9.5 > 9.5 of the SMD slope such that SMD (1 + z) for models ular) gas properties in sub-mmular) observations,gas properties where in sub-mm a dy- observations,(M magnitude19 whereM over) a galaxies dy- the same and(M redshift is best19 range. expressedM ) galaxies by the and re- is best expressedgalaxies. by the/ re- extend to the highest BH masses observed. ⇤ ⇠ ⇤ ⇠ ins4 and tdf4. namical mass, based on thenamical velocity mass, dispersion based ofon the the gas velocitylation dispersionMbh of=1 the.25 gasM 4.8atlationz Mbh5;=1 the. relation25M flattens4.8atz 5; the relation flattens We also show the BH occupation fraction in Fig. 5. As ⇤ ' ⇤ ' > 10.2 and the radius of the emittingand region the radius can be of measured the emitting (e.g., region canbelow be suchmeasured masses. (e.g., Includingbelow the impactsuch masses. of the Including UVB (ins4 the) impact of the UVB (ins4) c 0000 RAS, MNRASshown,000,000–000 galaxies with a halo mass Mh 10 have an oc- Venemans et al. 2016; ShaoVenemans et al. 2017; et Decarli al. 2016; et Shao al. 2018, et al. 2017;has Decarli no impact et al. on 2018, this relationhas atno the impact bright on end. this However,relation at the bright end. However, cupation fraction of 1 by z 6. As expected,⇠ most of these 3.3 The black hole mass function and occupation ⇠ and references therein). Forand these references quasars, therein). the BH For to dy- these quasars,the suppression the BH to of dy- gas massthe in low-mass suppression halos of gas naturally mass in re- low-mass halos naturally re- are stellar black holes except DCBHs that dominate for the fraction namical mass is skewed to valuesnamical much mass larger is skewed than the to values ratio muchsults larger in thanlower the black ratio hole massessults by in as lower much black as two hole orders masses of by as much as two orders of most massive halos. The black hole occupation fraction also of BH to stellar or bulge massof BH in to the stellar local or Universe. bulge mass As in themagnitude local Universe. for a given As stellarmagnitude mass. As for noted a given aboveWe stellar now in Sec. discuss mass. theAs notedblack hole above mass in Sec. function (BHMF) which shifts to progressively lower masses with increasing redshift. discussed in Volonteri & Starkdiscussed (2011) in there Volonteri are reasons & Stark to (2011)3.3, there the are inclusion reasons of to a delay3.3, in the galaxy inclusion merging ofexpresses a timescales delay in the galaxy number merging density timescales of black holes as a function of This is because of two reasons: first in our model, only start- believe that such high massbelieve ratios that should such not high characterize mass ratios shouldresults not in characterize a decrease in theresults mass of in the a decrease most massivetheir in the mass, black mass the of theresults most of massive which at blackz 6 are shown in Fig. ing leaves above z = 13 are seeded with black holes; the in- ' the whole BH population. Beyondthe whole the BH Malmquist population. bias Beyond caus- theholes Malmquist (by about bias 0.8 caus- dex) as seenholes from (by theabout right-hand 0.8 dex)4. As panelas expected, seen of from the right-handnumber density panel of of black holes increase creasing number of starting leaves forming at lower redshifts ing a more frequent selectioning of a moreover-massive frequent BHs selection in low- of over-massivethe same BHs figure in although low- itthe has same no impact figure on although thewith high-mass it decreasing has no impact BH mass on the as high-mass shown in the Figure. The ob- are devoid of any black holes. Secondly, low mass halos con- 7 10 mass hosts (Lauer et al. 2007;mass Salviander hosts (Lauer et al. et 2007), al. 2007; only Salvianderslope. et Further, al. 2007), the only results fromslope.ins4 Further,and tdf4 theare resultsserved quite from BHMF sim-ins4 atandz tdf46 extendsare quite from sim-Mbh 10 M .Our tinually increase in mass with decreasing redshift. We note ⇠ ⇠ under-massive and low-accretionunder-massive BHs can explain and low-accretion the lack of BHs canilar explain as also the expected lack of from theilar discussion as also expected in Sec.theoretical from 3.3 above, the discussion results for in all Sec. four 3.3 models above, discussed above are in that our results are qualitatively in good agreement with widespread AGN detectionswidespread in LBGs. That AGN BHs detections in low-mass in LBGs. Thatyielding BHs the inlow-mass lower-limit to theyieldingMbh theM lower-limitrelation.good toFinally, agreement the Mbh withM therelation. data withinFinally, error bars as seen in those obtained from previous works (e.g. Tanaka & Haiman ⇤ ⇤ galaxies are indeed expectedgalaxies to grow are slowly indeed and expected lag behind to grow slowlythe best-fit and lag relation behind derivedthe for best-fit high stellar relation massthe derived samegalaxies for figure. high Naturally, stellar mass the fiducial galaxies model (ins1), extend- 2009). Finally we stress that the enhancement of the LW 4.8 8.8 the host has now been confirmedthe host in has many now numerical been confirmed inves- in manyfrom numerical our model inves- is in excellentfrom agreement our model with is in theing excellent fromrelationM agreementbh 10 withM the,yieldstheupperlimittothe relation seen by any halos only depends on its bias at that redshift ⇠ tigations (Dubois et al. 2015;tigations Habouzit (Dubois et al. et 2017; al. 2015; Bower HabouzitMbh et=1 al. 2017;.4M Bower6.45 derivedMbh for=1 high.4M stellar6.45 massBHMF. derived ellipti- Including for high a stellardelay in mass the merger ellipti- times for black holes and we have ignored the impact of clustered sources that ⇤ ⇤ et al. 2017; Angl´es-Alc´azaret et al. al. 2017; 2017). Angl´es-Alc´azar Our implementa- et al. 2017).cals Our and bulgesimplementa- in the nearbycals Universe and bulges (Volonteri in the(tdf1 nearby &) Reines leads Universe to a decrease (Volonteri in the & maximum Reines mass attained by could enhance the LW intensity seen by halos in over-dense 8 tion of BH growth includestion a stunted of BH growth includesin low-mass a stunted2016). growth in low-mass 2016). the black holes (Mmax 10 M ) showing that gas brought environments. Our results must therefore be treated as a ⇠ c 0000 RAS, MNRAS 000c 0000,000–000c RAS,0000 RAS, MNRAS MNRAS000,000–000000,000–000 The LISA-detectable GW event rate as functionGalaxies, of BHsmass & GWs 15
SBH
all
DCBH all; SNR>7
SBH-DCBH
Figure 10. The BH merger event rate (per year) as a function of the redshifted BH mass (Mz = Mbh(1 + z)). The lines show the same models as noted in Fig 9. LISA will preferentially detect BHs with mass 4−7 . In fiducial case (ins1) most • MBH ∼ 10 M⊙ rates fordetectable heavy seeds, mergers compared are to those previous from works, SBH-SBH, is what followedimum by between SBH-DCBH the BH mergers. accreting DCBH-DCBH a certain fraction of the shouldmergers be expected negligible. for a model that predicts extremely rare gas mass left-over after star formation, up to a fraction of seeds. This is the e↵ect of adding the condition on the LW the Eddington limit: while high-mass halos can accrete at background• Although that previous same modelsmass range had not true included. for the tdf4 model,the d Eddingtonue to delayed limit, mergers low-mass halos+ reionization follow a lower e ciency Forfeedback, light (popIII) importance seeds Klein of et DCBH-SBH al. (2016) predict mergers 146.3 decreases.track. We No explore detectable a number DCBH-DCBH of physical scenarios mergers using this mergers/year(with SNR>7). at z>4 (although they extrapolate to 2x this model that include: (i) two types of BH seeds (stellar and rate in their Table 1 and related text) and Sesana et al. those from Direct Collapse BH; DCBH); (ii) the impact of (2007) predict 57.7 mergers/year at z>4. Our model pre- reionization impact; and (iii) the impact of instantaneous dicts between 62.0 and 75.1 mergers/year at z>4asshown versus delayed galaxy mergers on the baryonic growth. in Table 2. When comparing to Ricarte & Natarajan (2018), We show that, using a minimal set of mass and z- again the peak in the rates for light seeds is similarly broad independent free parameters, our model reproduces all avail- and covers a similar range in redshift but the value of the able data-sets for high-z galaxies and BH including the peak rates are lower in our case. In particular, our type 1 evolving (galaxy and AGN) UV LF, the SMD and the peak rate is 0.75 event/yr in the optimistic (ins1)andpes- BHMF. Crucially, our model naturally yields a BH mass- simistic (tdf4) models, while in Fig. 9 their peak rates lie stellar mass relation that is tightly coupled for high stellar between 5 20 events/year. While our merger rate for mass (M > 109.5 M ) halos; lower-mass halos, on the other ⇠ ⇤ light seeds is well within the expectations of the literature, hand, show⇠ a stunted BH growth. Interestingly, while both as we made similar assumptions, the results being on the reionization feedback and delayed mergers have no impact lower side are likely because of the resolution of our merger on the UV LF, the SMD is more a↵ected by reionization trees: for instance, Ricarte & Natarajan (2018) have a mass feedback as compared to delayed mergers. 6 resolution of 10 M , while Klein et al. (2016) follows We then use this model, bench-marked against all avail- ⇠ Barausse (2012) who follows Volonteri et al. (2003) (whose able high-z data, to predict the merger event rate expected trees are used for Sesana et al. 2007) in having a resolution for the LISA mission. We find that LISA-detectable bina- dependent on the halo mass at z=0, reaching 105 M for ries (with SNR > 7) appear in the redshift range z 5 13 halos with mass < 4.1012 M at z=0 and up to 107 M for 3.5 5 ' and range in total mass between M 10 M .While halos with mass 1015 M at z=0. ' type 1 mergers (of two stellar BHs) dominate in all the scenarios studied, type 2 mergers (merger of a stellar BH and a DCBH) can contribute as much as 32% to the cu- mulative event rate by z 4inthefiducial(ins1)model. 5CONCLUSIONSANDDISCUSSION ⇠ However including the impact of reionization feedback and In this work, we have included the impact of BH seeding, delayed mergers (tdf4 model) results in a lower BH growth growth and feedback, into our semi-analytic model, Delphi. with type 2 mergers contributing only 3% to the cumulative Our model now jointly tracks the build-up of the dark matter event rates. Using heavier DCBH seeds results in a larger halo, gas, stellar and BH masses of high-z (z > 5) galaxies. number of type 2 mergers becoming detectable with LISA We remind the reader that our star formation⇠ e ciency is whilst leaving the results e↵ectively unchanged for the tdf4 the minimum between the star formation rate that equals model. the halo binding energy and a saturation e ciency. In the Quantitatively, the model ins1 with “heavy DCBH same flavour, the BH accretion at any time-step is the min- seeds” yields the highest total detection number of 23 ⇠ c 0000 RAS, MNRAS 000,000–000 The LISA-detectable GW event rate as functionGalaxies, of BHsmass & GWs 15
SBH
all
DCBH all; SNR>7
SBH-DCBH
Figure 10. The BH merger event rate (per year) as a function of the redshifted BH mass (Mz = Mbh(1 + z)). The lines show the same models as noted in Fig 9. LISA will preferentially detect BHs with mass 4−7 . In fiducial case (ins1) most • MBH ∼ 10 M⊙ rates fordetectable heavy seeds, mergers compared are to those previous from works, SBH-SBH, is what followedimum by between SBH-DCBH the BH mergers. accreting DCBH-DCBH a certain fraction of the shouldmergers be expected negligible. for a model that predicts extremely rare gas mass left-over after star formation, up to a fraction of seeds. This is the e↵ect of adding the condition on the LW the Eddington limit: while high-mass halos can accrete at background• Although that previous same modelsmass range had not true included. for the tdf4 model,the d Eddingtonue to delayed limit, mergers low-mass halos+ reionization follow a lower e ciency Forfeedback, light (popIII) importance seeds Klein of et DCBH-SBH al. (2016) predict mergers 146.3 decreases.track. We No explore detectable a number DCBH-DCBH of physical scenarios mergers using this mergers/year(with SNR>7). at z>4 (although they extrapolate to 2x this model that include: (i) two types of BH seeds (stellar and rate in their Table 1 and related text) and Sesana et al. those from Direct Collapse BH; DCBH); (ii) the impact of (2007) predict 57.7 mergers/year at z>4. Our model pre- reionization impact; and (iii) the impact of instantaneous dicts between 62.0 and 75.1 mergers/year at z>4asshown versus delayed galaxy mergers on the baryonic growth. in Table 2. When comparing to Ricarte & Natarajan (2018), We show that, using a minimal set of mass and z- again the peak in the rates for light seeds is similarly broad independent free parameters, our model reproduces all avail- and covers a similar range in redshift but the value of the able data-sets for high-z galaxies and BH including the peak rates are lower in our case. In particular, our type 1 evolving (galaxy and AGN) UV LF, the SMD and the peak rate is 0.75 event/yr in the optimistic (ins1)andpes- BHMF. Crucially, our model naturally yields a BH mass- simistic (tdf4) models, while in Fig. 9 their peak rates lie stellar mass relation that is tightly coupled for high stellar between 5 20 events/year. While our merger rate for mass (M > 109.5 M ) halos; lower-mass halos, on the other ⇠ ⇤ light seeds is well within the expectations of the literature, hand, show⇠ a stunted BH growth. Interestingly, while both as we made similar assumptions, the results being on the reionization feedback and delayed mergers have no impact lower side are likely because of the resolution of our merger on the UV LF, the SMD is more a↵ected by reionization trees: for instance, Ricarte & Natarajan (2018) have a mass feedback as compared to delayed mergers. 6 resolution of 10 M , while Klein et al. (2016) follows We then use this model, bench-marked against all avail- ⇠ Barausse (2012) who follows Volonteri et al. (2003) (whose able high-z data, to predict the merger event rate expected trees are used for Sesana et al. 2007) in having a resolution for the LISA mission. We find that LISA-detectable bina- dependent on the halo mass at z=0, reaching 105 M for ries (with SNR > 7) appear in the redshift range z 5 13 halos with mass < 4.1012 M at z=0 and up to 107 M for 3.5 5 ' and range in total mass between M 10 M .While halos with mass 1015 M at z=0. ' type 1 mergers (of two stellar BHs) dominate in all the scenarios studied, type 2 mergers (merger of a stellar BH and a DCBH) can contribute as much as 32% to the cu- mulative event rate by z 4inthefiducial(ins1)model. 5CONCLUSIONSANDDISCUSSION ⇠ However including the impact of reionization feedback and In this work, we have included the impact of BH seeding, delayed mergers (tdf4 model) results in a lower BH growth growth and feedback, into our semi-analytic model, Delphi. with type 2 mergers contributing only 3% to the cumulative Our model now jointly tracks the build-up of the dark matter event rates. Using heavier DCBH seeds results in a larger halo, gas, stellar and BH masses of high-z (z > 5) galaxies. number of type 2 mergers becoming detectable with LISA We remind the reader that our star formation⇠ e ciency is whilst leaving the results e↵ectively unchanged for the tdf4 the minimum between the star formation rate that equals model. the halo binding energy and a saturation e ciency. In the Quantitatively, the model ins1 with “heavy DCBH same flavour, the BH accretion at any time-step is the min- seeds” yields the highest total detection number of 23 ⇠ c 0000 RAS, MNRAS 000,000–000 The emerging picture..
• High-z Universe is being explored to ever greater depths, providing constraints on both global and individual galaxy properties.
• Galaxy assembly delayed in very light WDM models (e.g. 1.5 keV).
• Since halos start of bigger (and hence less feedback limited) in light WDM models, it leads to a change in global quantities (SMD) as well as M/L ratios for individual galaxies - can be constrained with JWST.
• Metal enrichment of the IGM delayed and slightly lower in light WDM models.
• Edges data rules out light (<3 keV) WDM models.
LISA will preferentially detect BHs with mass 4−7 at z>5. • MBH ∼ 10 M⊙