Tuning your radio to ���reionization and the cosmic dawn

Andrei Mesinger Scuola Normale Superiore, Pisa

Cosmic History

z  ~  6  tage  ~  1  Gyr  

z~1100  tage  ~  0.4  Myr  

 

Reioniza5on   Dark  Ages   Recombina5on  

HII

z  ~  20  tage  ~  150  Myr  

z  =  0  tage ~ 14 Gyr

HI

Cosmic Dawn and Reionization

z  ~  6  tage  ~  1  Gyr  

z~1100  tage  ~  0.4  Myr  

 

Reioniza5on   Dark  Ages   Recombina5on  

HII

z  ~  20  tage  ~  150  Myr  

z  =  0  tage ~ 14 Gyr

HI

Bulk of our light cone: observational future!

Sources & Sinks Understanding reionization means understanding sources and sinks of ionizing photons. simple analytic model for global evolution (e.g. Barkana & Loeb 2004):

10

Figure 8. The curves correspond to the reionization transitionsof Tvir !> 300 K " 104 K, Tvir !> 300 K " 4.5# 104 K, andTvir !> 300 K " 1.1# 105 K, (left to right). Solid curves cor-respond to no dust obscuration; dashed curves include dust.All curves assume a detection threshold of 1 nJy, analogous totexp = 105 s exposures in the 3.5 µm JWST band. From the fig-ure, one can note that the most optimistic scenario (Tvir !> 300K " 1.1# 105 K), a reionization feature is detectable even ifit occurs over a redshift range !zre ! 4. In other cases, thedetection of the reionization feature requires!zre !< 1 – 3.

3.2.4. Feasibility of a Fairly Sudden Drop in SNe RatesThe details and duration of the reionization epoch, and hence

the shape and width of the drop in SNe rates, are unknown atthis time. Results from WMAP and the SDSS QSOs offer sug-gestive, albeit not conclusive, evidence that reionization wasextended in redshift.4 If reionization is indeed quite extendedin redshift (!z! 10), the associated drop in the SFR and SNRcould be smeared out too much to be detectable. However, evenin the pessimistic (as it pertains to our analysis below) scenariowhere some effective width of the reionization feature is aslarge as !z! 10, the shape of the feature need not be smooth,and could contain “sharp” (!zre ! 1) drops. Such transitionsare probable in reionization histories in which different sourcesdominate different epochs (e.g. Haiman & Holder 2003).The relevant process in determining the width and shape of

the drop in SNRs is the evolution of the volume filling factorof ionized regions and their correlation with the small, vulner-able halos5 whose SFRs are sensitive to the thermal state of theIGM. In other words, the sharpness of the drop in SNRs, in eachepoch during reionization, will depend on:

1. the nature of the dominant ionizing sources

2. the ionizing efficiency of the dominant ionizing sources

3. the level of synchronization of small halo formation withthe formation of dominant ionizing sources

4. the level of synchronization of the dominant ionizingsources

If the small, vulnerable halos themselves are the dominantionizing sources at that particular epoch, then a sharp reioniza-tion feature could result if: (2) is high, and (3) is moderate (inthis case (3) and (4) are the same). If (3) is too high (i.e. theformation of small, vulnerable halos is very clustered in timeand space), then negative feedback from the ionizing radiationcould delay substantial growth of HII bubbles until small halosare no longer forming prodigiously enough to serve as signpostsfor reionization. If (3) is too low, there might not be enough af-fected halos to notice the suppression; or large, isolated patchesmight have to wait a long time for their own ionizing sourcesto form (if (2) is not very high), thus smearing out the signalthrough pure cosmic variance.4Note that there are two, often confused processes and time-scales associatedwith reionization: (i) the increase in intensity of the ionizing background andthe mean free path of ionizing photons and (ii) the increase in the filling factorof ionized regions. For the purposes of this paper, we concern ourselves with(ii).5Note the distinction here between “small halos” and “minihalos”. In the dis-cussion below, we use the term small halos to denote all halos whose SFRs willbe suppressed by reionization. Thus small halos include minihalos as well aslarger halos, depending on their susceptibility to negative photo-heating feed-back.

If the small, vulnerable halos are not the dominant ionizingsources (as would be expected for the later periods of an ex-tended reionization), then a sharp feature could result if (2) ishigh enough to reasonably counter cosmic variance. However,we could relax our fine-tuning on (3) above, since feedback no-longer hinders the growth of HII regions. There merely needto be enough small halos at that epoch to act as signposts forreionization. From Figure 6, we see that this a reasonable as-sumption, especially given the fact that most small halos whichare still forming at such late stages are probably not going to bevery near the large overdensities which were likely to be ion-ized during earlier stages (Furlanetto & Oh 2005; Ricotti et al.2002). We also require (4) to be reasonably high (i.e. that thedominant ionizing sources appear around the same time, with-out too much cosmic scatter). Below, we further quantify sucha scenario.One can get a sense of the possible shapes of the reionization

feature through an estimate of the evolution of the filling factorof ionized regions, FHII(z), (c.f. Barkana & Loeb 2001; Haiman& Holder 2003):dFHII(z)dt

= !! fescNph/b0.76

dFcol(>Mmin(z),z)dt

�"BC$n0H%(1!z)3FHII .(7)

Here fesc is the escape fraction of ionizing photons, Nph/b isthe number of ionizing photons per baryon emitted by a typicalsource, Fcol(>M,z) is the fraction of baryons that reside in col-lapsed halos with a total mass greater thanM at redshift z, "B isthe hydrogen case B recombination coefficient,C& $n2H%/$nH%2is the clumping factor, and $n0H% is the current hydrogen numberdensity. The first term on the right hand side accounts for “new”ionizations contributing to the growth of the HII regions and thelast term on the right hand side accounts for “old” reionizationsdue to recombinations inside the HII region. This equation isa very rough approximation, as it does not include feedbackeffects, light travel time, and it does not accurately model theperiod when bubbles start overlapping (i.e. FHII(z) ! 1). How-ever, it can suffice for the crude estimates we are making here.In Figure 9, we plot FHII(z) for several values ofMmin(z) cor-

responding to redshift–independent values of Tvir = 300 K, 104K, and 105 K, from right to left in the figure. The plot assumesvalues of (!!, fesc, Nph/b, C) = (0.1, 0.1, 4000, 4). From thefigure, it is evident that fairly rapid growth of FHII(z) is possiblefor FHII(z)!> 0.1. For example, the Tvir !> 105 K curve goes fromFHII ! 0.3 to FHII ! 0.8 in a the redshift interval z ! 8.5" 7.So SNe in roughly 50% of small halos could be wiped out ina redshift interval of only !zre ! 1.5. Comparing with Figures4a, 5a or 6, one can see that this could result in a fairly large,easily detectable drop in the SNRs.To summarize, we outline a likely reionization scenario. An

early reionization epoch could be driven by minihalos. Feed-back processes can stall reionization at a constant or even de-creasing filling factor of ionized regions. Then a later popula-tion of more massive halos (Tvir ! 104 – 105 K) could completethe ionization process on time-scales corresponding to!zre ! 1– 2. The research we present here suggests that this later epochis detectable through an accompanying drop in the SNRs.

sources sinks

Even such an overly-simplified model has several unknown, redshift and spatial dependent parameters:

10

Figure 8. The curves correspond to the reionization transitionsof Tvir !> 300 K " 104 K, Tvir !> 300 K " 4.5# 104 K, andTvir !> 300 K " 1.1# 105 K, (left to right). Solid curves cor-respond to no dust obscuration; dashed curves include dust.All curves assume a detection threshold of 1 nJy, analogous totexp = 105 s exposures in the 3.5 µm JWST band. From the fig-ure, one can note that the most optimistic scenario (Tvir !> 300K " 1.1# 105 K), a reionization feature is detectable even ifit occurs over a redshift range !zre ! 4. In other cases, thedetection of the reionization feature requires!zre !< 1 – 3.

3.2.4. Feasibility of a Fairly Sudden Drop in SNe RatesThe details and duration of the reionization epoch, and hence

the shape and width of the drop in SNe rates, are unknown atthis time. Results from WMAP and the SDSS QSOs offer sug-gestive, albeit not conclusive, evidence that reionization wasextended in redshift.4 If reionization is indeed quite extendedin redshift (!z! 10), the associated drop in the SFR and SNRcould be smeared out too much to be detectable. However, evenin the pessimistic (as it pertains to our analysis below) scenariowhere some effective width of the reionization feature is aslarge as !z! 10, the shape of the feature need not be smooth,and could contain “sharp” (!zre ! 1) drops. Such transitionsare probable in reionization histories in which different sourcesdominate different epochs (e.g. Haiman & Holder 2003).The relevant process in determining the width and shape of

the drop in SNRs is the evolution of the volume filling factorof ionized regions and their correlation with the small, vulner-able halos5 whose SFRs are sensitive to the thermal state of theIGM. In other words, the sharpness of the drop in SNRs, in eachepoch during reionization, will depend on:

1. the nature of the dominant ionizing sources

2. the ionizing efficiency of the dominant ionizing sources

3. the level of synchronization of small halo formation withthe formation of dominant ionizing sources

4. the level of synchronization of the dominant ionizingsources

If the small, vulnerable halos themselves are the dominantionizing sources at that particular epoch, then a sharp reioniza-tion feature could result if: (2) is high, and (3) is moderate (inthis case (3) and (4) are the same). If (3) is too high (i.e. theformation of small, vulnerable halos is very clustered in timeand space), then negative feedback from the ionizing radiationcould delay substantial growth of HII bubbles until small halosare no longer forming prodigiously enough to serve as signpostsfor reionization. If (3) is too low, there might not be enough af-fected halos to notice the suppression; or large, isolated patchesmight have to wait a long time for their own ionizing sourcesto form (if (2) is not very high), thus smearing out the signalthrough pure cosmic variance.4Note that there are two, often confused processes and time-scales associatedwith reionization: (i) the increase in intensity of the ionizing background andthe mean free path of ionizing photons and (ii) the increase in the filling factorof ionized regions. For the purposes of this paper, we concern ourselves with(ii).5Note the distinction here between “small halos” and “minihalos”. In the dis-cussion below, we use the term small halos to denote all halos whose SFRs willbe suppressed by reionization. Thus small halos include minihalos as well aslarger halos, depending on their susceptibility to negative photo-heating feed-back.

If the small, vulnerable halos are not the dominant ionizingsources (as would be expected for the later periods of an ex-tended reionization), then a sharp feature could result if (2) ishigh enough to reasonably counter cosmic variance. However,we could relax our fine-tuning on (3) above, since feedback no-longer hinders the growth of HII regions. There merely needto be enough small halos at that epoch to act as signposts forreionization. From Figure 6, we see that this a reasonable as-sumption, especially given the fact that most small halos whichare still forming at such late stages are probably not going to bevery near the large overdensities which were likely to be ion-ized during earlier stages (Furlanetto & Oh 2005; Ricotti et al.2002). We also require (4) to be reasonably high (i.e. that thedominant ionizing sources appear around the same time, with-out too much cosmic scatter). Below, we further quantify sucha scenario.One can get a sense of the possible shapes of the reionization

feature through an estimate of the evolution of the filling factorof ionized regions, FHII(z), (c.f. Barkana & Loeb 2001; Haiman& Holder 2003):dFHII(z)dt

= !! fescNph/b0.76

dFcol(>Mmin(z),z)dt

�"BC$n0H%(1!z)3FHII .(7)

Here fesc is the escape fraction of ionizing photons, Nph/b isthe number of ionizing photons per baryon emitted by a typicalsource, Fcol(>M,z) is the fraction of baryons that reside in col-lapsed halos with a total mass greater thanM at redshift z, "B isthe hydrogen case B recombination coefficient,C& $n2H%/$nH%2is the clumping factor, and $n0H% is the current hydrogen numberdensity. The first term on the right hand side accounts for “new”ionizations contributing to the growth of the HII regions and thelast term on the right hand side accounts for “old” reionizationsdue to recombinations inside the HII region. This equation isa very rough approximation, as it does not include feedbackeffects, light travel time, and it does not accurately model theperiod when bubbles start overlapping (i.e. FHII(z) ! 1). How-ever, it can suffice for the crude estimates we are making here.In Figure 9, we plot FHII(z) for several values ofMmin(z) cor-

responding to redshift–independent values of Tvir = 300 K, 104K, and 105 K, from right to left in the figure. The plot assumesvalues of (!!, fesc, Nph/b, C) = (0.1, 0.1, 4000, 4). From thefigure, it is evident that fairly rapid growth of FHII(z) is possiblefor FHII(z)!> 0.1. For example, the Tvir !> 105 K curve goes fromFHII ! 0.3 to FHII ! 0.8 in a the redshift interval z ! 8.5" 7.So SNe in roughly 50% of small halos could be wiped out ina redshift interval of only !zre ! 1.5. Comparing with Figures4a, 5a or 6, one can see that this could result in a fairly large,easily detectable drop in the SNRs.To summarize, we outline a likely reionization scenario. An

early reionization epoch could be driven by minihalos. Feed-back processes can stall reionization at a constant or even de-creasing filling factor of ionized regions. Then a later popula-tion of more massive halos (Tvir ! 104 – 105 K) could completethe ionization process on time-scales corresponding to!zre ! 1– 2. The research we present here suggests that this later epochis detectable through an accompanying drop in the SNRs.

10

Figure 8. The curves correspond to the reionization transitionsof Tvir !> 300 K " 104 K, Tvir !> 300 K " 4.5# 104 K, andTvir !> 300 K " 1.1# 105 K, (left to right). Solid curves cor-respond to no dust obscuration; dashed curves include dust.All curves assume a detection threshold of 1 nJy, analogous totexp = 105 s exposures in the 3.5 µm JWST band. From the fig-ure, one can note that the most optimistic scenario (Tvir !> 300K " 1.1# 105 K), a reionization feature is detectable even ifit occurs over a redshift range !zre ! 4. In other cases, thedetection of the reionization feature requires!zre !< 1 – 3.

3.2.4. Feasibility of a Fairly Sudden Drop in SNe RatesThe details and duration of the reionization epoch, and hence

the shape and width of the drop in SNe rates, are unknown atthis time. Results from WMAP and the SDSS QSOs offer sug-gestive, albeit not conclusive, evidence that reionization wasextended in redshift.4 If reionization is indeed quite extendedin redshift (!z! 10), the associated drop in the SFR and SNRcould be smeared out too much to be detectable. However, evenin the pessimistic (as it pertains to our analysis below) scenariowhere some effective width of the reionization feature is aslarge as !z! 10, the shape of the feature need not be smooth,and could contain “sharp” (!zre ! 1) drops. Such transitionsare probable in reionization histories in which different sourcesdominate different epochs (e.g. Haiman & Holder 2003).The relevant process in determining the width and shape of

the drop in SNRs is the evolution of the volume filling factorof ionized regions and their correlation with the small, vulner-able halos5 whose SFRs are sensitive to the thermal state of theIGM. In other words, the sharpness of the drop in SNRs, in eachepoch during reionization, will depend on:

1. the nature of the dominant ionizing sources

2. the ionizing efficiency of the dominant ionizing sources

3. the level of synchronization of small halo formation withthe formation of dominant ionizing sources

4. the level of synchronization of the dominant ionizingsources

If the small, vulnerable halos themselves are the dominantionizing sources at that particular epoch, then a sharp reioniza-tion feature could result if: (2) is high, and (3) is moderate (inthis case (3) and (4) are the same). If (3) is too high (i.e. theformation of small, vulnerable halos is very clustered in timeand space), then negative feedback from the ionizing radiationcould delay substantial growth of HII bubbles until small halosare no longer forming prodigiously enough to serve as signpostsfor reionization. If (3) is too low, there might not be enough af-fected halos to notice the suppression; or large, isolated patchesmight have to wait a long time for their own ionizing sourcesto form (if (2) is not very high), thus smearing out the signalthrough pure cosmic variance.4Note that there are two, often confused processes and time-scales associatedwith reionization: (i) the increase in intensity of the ionizing background andthe mean free path of ionizing photons and (ii) the increase in the filling factorof ionized regions. For the purposes of this paper, we concern ourselves with(ii).5Note the distinction here between “small halos” and “minihalos”. In the dis-cussion below, we use the term small halos to denote all halos whose SFRs willbe suppressed by reionization. Thus small halos include minihalos as well aslarger halos, depending on their susceptibility to negative photo-heating feed-back.

If the small, vulnerable halos are not the dominant ionizingsources (as would be expected for the later periods of an ex-tended reionization), then a sharp feature could result if (2) ishigh enough to reasonably counter cosmic variance. However,we could relax our fine-tuning on (3) above, since feedback no-longer hinders the growth of HII regions. There merely needto be enough small halos at that epoch to act as signposts forreionization. From Figure 6, we see that this a reasonable as-sumption, especially given the fact that most small halos whichare still forming at such late stages are probably not going to bevery near the large overdensities which were likely to be ion-ized during earlier stages (Furlanetto & Oh 2005; Ricotti et al.2002). We also require (4) to be reasonably high (i.e. that thedominant ionizing sources appear around the same time, with-out too much cosmic scatter). Below, we further quantify sucha scenario.One can get a sense of the possible shapes of the reionization

feature through an estimate of the evolution of the filling factorof ionized regions, FHII(z), (c.f. Barkana & Loeb 2001; Haiman& Holder 2003):dFHII(z)dt

= !! fescNph/b0.76

dFcol(>Mmin(z),z)dt

�"BC$n0H%(1!z)3FHII .(7)

Here fesc is the escape fraction of ionizing photons, Nph/b isthe number of ionizing photons per baryon emitted by a typicalsource, Fcol(>M,z) is the fraction of baryons that reside in col-lapsed halos with a total mass greater thanM at redshift z, "B isthe hydrogen case B recombination coefficient,C& $n2H%/$nH%2is the clumping factor, and $n0H% is the current hydrogen numberdensity. The first term on the right hand side accounts for “new”ionizations contributing to the growth of the HII regions and thelast term on the right hand side accounts for “old” reionizationsdue to recombinations inside the HII region. This equation isa very rough approximation, as it does not include feedbackeffects, light travel time, and it does not accurately model theperiod when bubbles start overlapping (i.e. FHII(z) ! 1). How-ever, it can suffice for the crude estimates we are making here.In Figure 9, we plot FHII(z) for several values ofMmin(z) cor-

responding to redshift–independent values of Tvir = 300 K, 104K, and 105 K, from right to left in the figure. The plot assumesvalues of (!!, fesc, Nph/b, C) = (0.1, 0.1, 4000, 4). From thefigure, it is evident that fairly rapid growth of FHII(z) is possiblefor FHII(z)!> 0.1. For example, the Tvir !> 105 K curve goes fromFHII ! 0.3 to FHII ! 0.8 in a the redshift interval z ! 8.5" 7.So SNe in roughly 50% of small halos could be wiped out ina redshift interval of only !zre ! 1.5. Comparing with Figures4a, 5a or 6, one can see that this could result in a fairly large,easily detectable drop in the SNRs.To summarize, we outline a likely reionization scenario. An

early reionization epoch could be driven by minihalos. Feed-back processes can stall reionization at a constant or even de-creasing filling factor of ionized regions. Then a later popula-tion of more massive halos (Tvir ! 104 – 105 K) could completethe ionization process on time-scales corresponding to!zre ! 1– 2. The research we present here suggests that this later epochis detectable through an accompanying drop in the SNRs.

10

Figure 8. The curves correspond to the reionization transitionsof Tvir !> 300 K " 104 K, Tvir !> 300 K " 4.5# 104 K, andTvir !> 300 K " 1.1# 105 K, (left to right). Solid curves cor-respond to no dust obscuration; dashed curves include dust.All curves assume a detection threshold of 1 nJy, analogous totexp = 105 s exposures in the 3.5 µm JWST band. From the fig-ure, one can note that the most optimistic scenario (Tvir !> 300K " 1.1# 105 K), a reionization feature is detectable even ifit occurs over a redshift range !zre ! 4. In other cases, thedetection of the reionization feature requires!zre !< 1 – 3.

3.2.4. Feasibility of a Fairly Sudden Drop in SNe RatesThe details and duration of the reionization epoch, and hence

the shape and width of the drop in SNe rates, are unknown atthis time. Results from WMAP and the SDSS QSOs offer sug-gestive, albeit not conclusive, evidence that reionization wasextended in redshift.4 If reionization is indeed quite extendedin redshift (!z! 10), the associated drop in the SFR and SNRcould be smeared out too much to be detectable. However, evenin the pessimistic (as it pertains to our analysis below) scenariowhere some effective width of the reionization feature is aslarge as !z! 10, the shape of the feature need not be smooth,and could contain “sharp” (!zre ! 1) drops. Such transitionsare probable in reionization histories in which different sourcesdominate different epochs (e.g. Haiman & Holder 2003).The relevant process in determining the width and shape of

the drop in SNRs is the evolution of the volume filling factorof ionized regions and their correlation with the small, vulner-able halos5 whose SFRs are sensitive to the thermal state of theIGM. In other words, the sharpness of the drop in SNRs, in eachepoch during reionization, will depend on:

1. the nature of the dominant ionizing sources

2. the ionizing efficiency of the dominant ionizing sources

3. the level of synchronization of small halo formation withthe formation of dominant ionizing sources

4. the level of synchronization of the dominant ionizingsources

If the small, vulnerable halos themselves are the dominantionizing sources at that particular epoch, then a sharp reioniza-tion feature could result if: (2) is high, and (3) is moderate (inthis case (3) and (4) are the same). If (3) is too high (i.e. theformation of small, vulnerable halos is very clustered in timeand space), then negative feedback from the ionizing radiationcould delay substantial growth of HII bubbles until small halosare no longer forming prodigiously enough to serve as signpostsfor reionization. If (3) is too low, there might not be enough af-fected halos to notice the suppression; or large, isolated patchesmight have to wait a long time for their own ionizing sourcesto form (if (2) is not very high), thus smearing out the signalthrough pure cosmic variance.4Note that there are two, often confused processes and time-scales associatedwith reionization: (i) the increase in intensity of the ionizing background andthe mean free path of ionizing photons and (ii) the increase in the filling factorof ionized regions. For the purposes of this paper, we concern ourselves with(ii).5Note the distinction here between “small halos” and “minihalos”. In the dis-cussion below, we use the term small halos to denote all halos whose SFRs willbe suppressed by reionization. Thus small halos include minihalos as well aslarger halos, depending on their susceptibility to negative photo-heating feed-back.

If the small, vulnerable halos are not the dominant ionizingsources (as would be expected for the later periods of an ex-tended reionization), then a sharp feature could result if (2) ishigh enough to reasonably counter cosmic variance. However,we could relax our fine-tuning on (3) above, since feedback no-longer hinders the growth of HII regions. There merely needto be enough small halos at that epoch to act as signposts forreionization. From Figure 6, we see that this a reasonable as-sumption, especially given the fact that most small halos whichare still forming at such late stages are probably not going to bevery near the large overdensities which were likely to be ion-ized during earlier stages (Furlanetto & Oh 2005; Ricotti et al.2002). We also require (4) to be reasonably high (i.e. that thedominant ionizing sources appear around the same time, with-out too much cosmic scatter). Below, we further quantify sucha scenario.One can get a sense of the possible shapes of the reionization

feature through an estimate of the evolution of the filling factorof ionized regions, FHII(z), (c.f. Barkana & Loeb 2001; Haiman& Holder 2003):dFHII(z)dt

= !! fescNph/b0.76

dFcol(>Mmin(z),z)dt

�"BC$n0H%(1!z)3FHII .(7)

Here fesc is the escape fraction of ionizing photons, Nph/b isthe number of ionizing photons per baryon emitted by a typicalsource, Fcol(>M,z) is the fraction of baryons that reside in col-lapsed halos with a total mass greater thanM at redshift z, "B isthe hydrogen case B recombination coefficient,C& $n2H%/$nH%2is the clumping factor, and $n0H% is the current hydrogen numberdensity. The first term on the right hand side accounts for “new”ionizations contributing to the growth of the HII regions and thelast term on the right hand side accounts for “old” reionizationsdue to recombinations inside the HII region. This equation isa very rough approximation, as it does not include feedbackeffects, light travel time, and it does not accurately model theperiod when bubbles start overlapping (i.e. FHII(z) ! 1). How-ever, it can suffice for the crude estimates we are making here.In Figure 9, we plot FHII(z) for several values ofMmin(z) cor-

responding to redshift–independent values of Tvir = 300 K, 104K, and 105 K, from right to left in the figure. The plot assumesvalues of (!!, fesc, Nph/b, C) = (0.1, 0.1, 4000, 4). From thefigure, it is evident that fairly rapid growth of FHII(z) is possiblefor FHII(z)!> 0.1. For example, the Tvir !> 105 K curve goes fromFHII ! 0.3 to FHII ! 0.8 in a the redshift interval z ! 8.5" 7.So SNe in roughly 50% of small halos could be wiped out ina redshift interval of only !zre ! 1.5. Comparing with Figures4a, 5a or 6, one can see that this could result in a fairly large,easily detectable drop in the SNRs.To summarize, we outline a likely reionization scenario. An

early reionization epoch could be driven by minihalos. Feed-back processes can stall reionization at a constant or even de-creasing filling factor of ionized regions. Then a later popula-tion of more massive halos (Tvir ! 104 – 105 K) could completethe ionization process on time-scales corresponding to!zre ! 1– 2. The research we present here suggests that this later epochis detectable through an accompanying drop in the SNRs.

10

Figure 8. The curves correspond to the reionization transitionsof Tvir !> 300 K " 104 K, Tvir !> 300 K " 4.5# 104 K, andTvir !> 300 K " 1.1# 105 K, (left to right). Solid curves cor-respond to no dust obscuration; dashed curves include dust.All curves assume a detection threshold of 1 nJy, analogous totexp = 105 s exposures in the 3.5 µm JWST band. From the fig-ure, one can note that the most optimistic scenario (Tvir !> 300K " 1.1# 105 K), a reionization feature is detectable even ifit occurs over a redshift range !zre ! 4. In other cases, thedetection of the reionization feature requires!zre !< 1 – 3.

3.2.4. Feasibility of a Fairly Sudden Drop in SNe RatesThe details and duration of the reionization epoch, and hence

the shape and width of the drop in SNe rates, are unknown atthis time. Results from WMAP and the SDSS QSOs offer sug-gestive, albeit not conclusive, evidence that reionization wasextended in redshift.4 If reionization is indeed quite extendedin redshift (!z! 10), the associated drop in the SFR and SNRcould be smeared out too much to be detectable. However, evenin the pessimistic (as it pertains to our analysis below) scenariowhere some effective width of the reionization feature is aslarge as !z! 10, the shape of the feature need not be smooth,and could contain “sharp” (!zre ! 1) drops. Such transitionsare probable in reionization histories in which different sourcesdominate different epochs (e.g. Haiman & Holder 2003).The relevant process in determining the width and shape of

the drop in SNRs is the evolution of the volume filling factorof ionized regions and their correlation with the small, vulner-able halos5 whose SFRs are sensitive to the thermal state of theIGM. In other words, the sharpness of the drop in SNRs, in eachepoch during reionization, will depend on:

1. the nature of the dominant ionizing sources

2. the ionizing efficiency of the dominant ionizing sources

3. the level of synchronization of small halo formation withthe formation of dominant ionizing sources

4. the level of synchronization of the dominant ionizingsources

If the small, vulnerable halos themselves are the dominantionizing sources at that particular epoch, then a sharp reioniza-tion feature could result if: (2) is high, and (3) is moderate (inthis case (3) and (4) are the same). If (3) is too high (i.e. theformation of small, vulnerable halos is very clustered in timeand space), then negative feedback from the ionizing radiationcould delay substantial growth of HII bubbles until small halosare no longer forming prodigiously enough to serve as signpostsfor reionization. If (3) is too low, there might not be enough af-fected halos to notice the suppression; or large, isolated patchesmight have to wait a long time for their own ionizing sourcesto form (if (2) is not very high), thus smearing out the signalthrough pure cosmic variance.4Note that there are two, often confused processes and time-scales associatedwith reionization: (i) the increase in intensity of the ionizing background andthe mean free path of ionizing photons and (ii) the increase in the filling factorof ionized regions. For the purposes of this paper, we concern ourselves with(ii).5Note the distinction here between “small halos” and “minihalos”. In the dis-cussion below, we use the term small halos to denote all halos whose SFRs willbe suppressed by reionization. Thus small halos include minihalos as well aslarger halos, depending on their susceptibility to negative photo-heating feed-back.

If the small, vulnerable halos are not the dominant ionizingsources (as would be expected for the later periods of an ex-tended reionization), then a sharp feature could result if (2) ishigh enough to reasonably counter cosmic variance. However,we could relax our fine-tuning on (3) above, since feedback no-longer hinders the growth of HII regions. There merely needto be enough small halos at that epoch to act as signposts forreionization. From Figure 6, we see that this a reasonable as-sumption, especially given the fact that most small halos whichare still forming at such late stages are probably not going to bevery near the large overdensities which were likely to be ion-ized during earlier stages (Furlanetto & Oh 2005; Ricotti et al.2002). We also require (4) to be reasonably high (i.e. that thedominant ionizing sources appear around the same time, with-out too much cosmic scatter). Below, we further quantify sucha scenario.One can get a sense of the possible shapes of the reionization

feature through an estimate of the evolution of the filling factorof ionized regions, FHII(z), (c.f. Barkana & Loeb 2001; Haiman& Holder 2003):dFHII(z)dt

= !! fescNph/b0.76

dFcol(>Mmin(z),z)dt

�"BC$n0H%(1!z)3FHII .(7)

Here fesc is the escape fraction of ionizing photons, Nph/b isthe number of ionizing photons per baryon emitted by a typicalsource, Fcol(>M,z) is the fraction of baryons that reside in col-lapsed halos with a total mass greater thanM at redshift z, "B isthe hydrogen case B recombination coefficient,C& $n2H%/$nH%2is the clumping factor, and $n0H% is the current hydrogen numberdensity. The first term on the right hand side accounts for “new”ionizations contributing to the growth of the HII regions and thelast term on the right hand side accounts for “old” reionizationsdue to recombinations inside the HII region. This equation isa very rough approximation, as it does not include feedbackeffects, light travel time, and it does not accurately model theperiod when bubbles start overlapping (i.e. FHII(z) ! 1). How-ever, it can suffice for the crude estimates we are making here.In Figure 9, we plot FHII(z) for several values ofMmin(z) cor-

responding to redshift–independent values of Tvir = 300 K, 104K, and 105 K, from right to left in the figure. The plot assumesvalues of (!!, fesc, Nph/b, C) = (0.1, 0.1, 4000, 4). From thefigure, it is evident that fairly rapid growth of FHII(z) is possiblefor FHII(z)!> 0.1. For example, the Tvir !> 105 K curve goes fromFHII ! 0.3 to FHII ! 0.8 in a the redshift interval z ! 8.5" 7.So SNe in roughly 50% of small halos could be wiped out ina redshift interval of only !zre ! 1.5. Comparing with Figures4a, 5a or 6, one can see that this could result in a fairly large,easily detectable drop in the SNRs.To summarize, we outline a likely reionization scenario. An

early reionization epoch could be driven by minihalos. Feed-back processes can stall reionization at a constant or even de-creasing filling factor of ionized regions. Then a later popula-tion of more massive halos (Tvir ! 104 – 105 K) could completethe ionization process on time-scales corresponding to!zre ! 1– 2. The research we present here suggests that this later epochis detectable through an accompanying drop in the SNRs.

10

Figure 8. The curves correspond to the reionization transitionsof Tvir !> 300 K " 104 K, Tvir !> 300 K " 4.5# 104 K, andTvir !> 300 K " 1.1# 105 K, (left to right). Solid curves cor-respond to no dust obscuration; dashed curves include dust.All curves assume a detection threshold of 1 nJy, analogous totexp = 105 s exposures in the 3.5 µm JWST band. From the fig-ure, one can note that the most optimistic scenario (Tvir !> 300K " 1.1# 105 K), a reionization feature is detectable even ifit occurs over a redshift range !zre ! 4. In other cases, thedetection of the reionization feature requires!zre !< 1 – 3.

3.2.4. Feasibility of a Fairly Sudden Drop in SNe RatesThe details and duration of the reionization epoch, and hence

the shape and width of the drop in SNe rates, are unknown atthis time. Results from WMAP and the SDSS QSOs offer sug-gestive, albeit not conclusive, evidence that reionization wasextended in redshift.4 If reionization is indeed quite extendedin redshift (!z! 10), the associated drop in the SFR and SNRcould be smeared out too much to be detectable. However, evenin the pessimistic (as it pertains to our analysis below) scenariowhere some effective width of the reionization feature is aslarge as !z! 10, the shape of the feature need not be smooth,and could contain “sharp” (!zre ! 1) drops. Such transitionsare probable in reionization histories in which different sourcesdominate different epochs (e.g. Haiman & Holder 2003).The relevant process in determining the width and shape of

the drop in SNRs is the evolution of the volume filling factorof ionized regions and their correlation with the small, vulner-able halos5 whose SFRs are sensitive to the thermal state of theIGM. In other words, the sharpness of the drop in SNRs, in eachepoch during reionization, will depend on:

1. the nature of the dominant ionizing sources

2. the ionizing efficiency of the dominant ionizing sources

3. the level of synchronization of small halo formation withthe formation of dominant ionizing sources

4. the level of synchronization of the dominant ionizingsources

If the small, vulnerable halos themselves are the dominantionizing sources at that particular epoch, then a sharp reioniza-tion feature could result if: (2) is high, and (3) is moderate (inthis case (3) and (4) are the same). If (3) is too high (i.e. theformation of small, vulnerable halos is very clustered in timeand space), then negative feedback from the ionizing radiationcould delay substantial growth of HII bubbles until small halosare no longer forming prodigiously enough to serve as signpostsfor reionization. If (3) is too low, there might not be enough af-fected halos to notice the suppression; or large, isolated patchesmight have to wait a long time for their own ionizing sourcesto form (if (2) is not very high), thus smearing out the signalthrough pure cosmic variance.4Note that there are two, often confused processes and time-scales associatedwith reionization: (i) the increase in intensity of the ionizing background andthe mean free path of ionizing photons and (ii) the increase in the filling factorof ionized regions. For the purposes of this paper, we concern ourselves with(ii).5Note the distinction here between “small halos” and “minihalos”. In the dis-cussion below, we use the term small halos to denote all halos whose SFRs willbe suppressed by reionization. Thus small halos include minihalos as well aslarger halos, depending on their susceptibility to negative photo-heating feed-back.

If the small, vulnerable halos are not the dominant ionizingsources (as would be expected for the later periods of an ex-tended reionization), then a sharp feature could result if (2) ishigh enough to reasonably counter cosmic variance. However,we could relax our fine-tuning on (3) above, since feedback no-longer hinders the growth of HII regions. There merely needto be enough small halos at that epoch to act as signposts forreionization. From Figure 6, we see that this a reasonable as-sumption, especially given the fact that most small halos whichare still forming at such late stages are probably not going to bevery near the large overdensities which were likely to be ion-ized during earlier stages (Furlanetto & Oh 2005; Ricotti et al.2002). We also require (4) to be reasonably high (i.e. that thedominant ionizing sources appear around the same time, with-out too much cosmic scatter). Below, we further quantify sucha scenario.One can get a sense of the possible shapes of the reionization

feature through an estimate of the evolution of the filling factorof ionized regions, FHII(z), (c.f. Barkana & Loeb 2001; Haiman& Holder 2003):dFHII(z)dt

= !! fescNph/b0.76

dFcol(>Mmin(z),z)dt

�"BC$n0H%(1!z)3FHII .(7)

Here fesc is the escape fraction of ionizing photons, Nph/b isthe number of ionizing photons per baryon emitted by a typicalsource, Fcol(>M,z) is the fraction of baryons that reside in col-lapsed halos with a total mass greater thanM at redshift z, "B isthe hydrogen case B recombination coefficient,C& $n2H%/$nH%2is the clumping factor, and $n0H% is the current hydrogen numberdensity. The first term on the right hand side accounts for “new”ionizations contributing to the growth of the HII regions and thelast term on the right hand side accounts for “old” reionizationsdue to recombinations inside the HII region. This equation isa very rough approximation, as it does not include feedbackeffects, light travel time, and it does not accurately model theperiod when bubbles start overlapping (i.e. FHII(z) ! 1). How-ever, it can suffice for the crude estimates we are making here.In Figure 9, we plot FHII(z) for several values ofMmin(z) cor-

responding to redshift–independent values of Tvir = 300 K, 104K, and 105 K, from right to left in the figure. The plot assumesvalues of (!!, fesc, Nph/b, C) = (0.1, 0.1, 4000, 4). From thefigure, it is evident that fairly rapid growth of FHII(z) is possiblefor FHII(z)!> 0.1. For example, the Tvir !> 105 K curve goes fromFHII ! 0.3 to FHII ! 0.8 in a the redshift interval z ! 8.5" 7.So SNe in roughly 50% of small halos could be wiped out ina redshift interval of only !zre ! 1.5. Comparing with Figures4a, 5a or 6, one can see that this could result in a fairly large,easily detectable drop in the SNRs.To summarize, we outline a likely reionization scenario. An

early reionization epoch could be driven by minihalos. Feed-back processes can stall reionization at a constant or even de-creasing filling factor of ionized regions. Then a later popula-tion of more massive halos (Tvir ! 104 – 105 K) could completethe ionization process on time-scales corresponding to!zre ! 1– 2. The research we present here suggests that this later epochis detectable through an accompanying drop in the SNRs.

- escape fraction of ionizing photons

- mass efficiency of conversion of gas to stars

- mean # of ionizing photons per stellar baryon

- minimum halo mass to host ionizing sources

- clumping factor (measurement of the average recombination rate) Many groups are working on modeling such parameters!

Challenges

~ FoV of 21cm interferometers

•  Dynamic range required is enormous: single star --> Universe •  We know next to nothing about high-z --> ENORMOUS parameter space to explore

Morphology of H II regions during reionization 1049

S1 S3 S4S2

z =

7.7

z =

7.3

z =

8.7

Figure 3. Comparison of four radiative transfer simulations post-processed on the same density field, but using different source prescriptions parametrized byN (m) = !(m) m. The white regions are ionized and the black are neutral. The left-hand panel, left centre panel, right centre panel and right-hand panels are,respectively, cuts through Simulations S2 (! ! m"2/3), S1 (! ! m0), S3 (! ! m2/3) and S4 (! ! m0, but only haloes with m > 4 # 1010 M$ host sources). Forthe top panels, the volume-ionized fraction is xi,V % 0.2 (the mass-ionized fraction is xi,M % 0.3) and z = 8.7. For the middle panels, xi,V % 0.5(xi,M % 0.6)and z = 7.7, and for the bottom panels, xi,V % 0.7(xi,M % 0.8) and z = 7.3. Note that the S4 simulation outputs have the same xi,M , but xi,V that are typically0.1 smaller than that of other runs. In S4, the source fluctuations are nearly Poissonian, resulting in the bubbles being uncorrelated with the density field(xi,V % xi,M ). Each panel is 94 Mpc wide and would subtend 0.6 degrees on the sky.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 10

R d

P/dR

R (Mpc/h)

Figure 4. The volume-weighted bubble radius PDF for the S1 (solid curves),S3 (dot–dashed curves) and S4 (dotted curves) simulations. See the text forour definition of the bubble radius R. We do not include curves for theS2 simulation because they are similar to those for S1. The thin curvesare at z = 8.7 and xi,M = 0.3, and the thick curves are at z = 7.3 andxi,M = 0.8. Simulation S4 has the rarest sources and the largest H II regionsof the four models.

0.01

0.1

0.1 1 10

! xx2

k (h Mpc-1)

z = 7.3

0.01

0.1

! xx2

z = 7.7

0.01

0.1

! xx2

z = 8.7

Figure 5. The ionization fraction power spectrum "xx (k)2 = k3 Pxx (k)/2!2

for the S1 (solid curves), S2 (dashed curves), S3 (dot–dashed curves) and S4(dotted curves) simulations. For the top panels, xi,V % 0.2(xi,M % 0.3), forthe middle panels, xi,V % 0.5(xi,M % 0.6) and for the bottom panels, xi,V %0.7(xi,M % 0.8). In all panels, the fluctuations are larger at k ! 1 h Mpc"1

in S3 and S4 than they are in S1 and in S2. As the most massive haloescontribute more of the ionizing photons, the ionization fraction fluctuationsincrease at large scales.

C& 2007 The Authors. Journal compilation C& 2007 RAS, MNRAS 377, 1043–1063

!"#$$$% !"#$$%

xHI

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

z = 5.00!xHI"v = 0.10

1"Mpc"

94"Mpc"

2"Gpc"

Wise+ (2010)

McQuinn+ (2007)

Mesinger (2010)

Philosophy… how to approach the problem

scale

Hydrodynamical Numerical Simulations (+RT)

Seminumerical Simulations or lower resolution large-scale numerical simulations

Seminumerical Simulations or Analytic Estimates Strategy #1:

Philosophy… how to approach the problem

Strategy #2: Large scales/analytic models to generate general, robust claims (true for large swaths of parameter space)

make predictions & match observations (caution: interpretation is difficult; watch out for degeneracies..)

DexM & 21cmFAST

•  Combines excursion-set approach with perturbation theory for efficient generation of large-scale density, velocity, halo, ionization, radiation, 21cm brightness fields

•  Portable and FAST! (if it’s in the name, it must be true…) –  A realization can be obtained in ~ minutes on a single CPU –  New parallelized version, optimized for parameter studies

•  Run on arbitrarily large scales •  Vary many independent free parameters; cover wide swaths of parameter space •  Tested against state-of-the-art hydrodynamic cosmological simulations (Trac & Cen

2007; Trac+ 2008) •  Publically available!

semi-numerical simulation (Mesinger & Furlanetto 2007; Mesinger, Furlanetto, Cen 2011)

Tools for modeling large-scale signal:

Density Fields z=7 0.19 Mpc cells

143 Mpc

Halo Finder (DexM)

without adjusting halo locations with adjusting halo locations

Halo Finder (DexM)

z=8.7 N-body halo field from McQuinn et al. (2007)

Ionization fields

Trac & Cen (2007)

21cmFAST (Mesinger+ 2011)

Zahn+ (2010)

DexM (with halos; Mesinger & Furlanetto; 2007)

6

McQ

uin

n e

t al

.T

rac&

Cen

FF

RT

X=0.25 X=0.51 X=0.72z=8.49 z=7.56 z=7.11

Mes

inge

r&F

url

anet

to

Fig. 1.— Comparison of ionization fields generated from four schemes: McQuinn et al., Trac & Cen, MF07, and FFRT. The maps arefrom the same slice (100 Mpc/h by 100 Mpc/h with depth of 0.4 Mpc/h) through the simulation box.

Redshift space distortions (sorry no pics)

nonlinear structure formation creates an asymmetric velocity gradient distribution

21cm comparison (stay tuned…)

hydro+DM+RT DexM (with halos) 21cmFAST (no halos)

~ 1 week on 1536 cores ~ few min on 1 core 100 Mpc/h

Get on board! http://homepage.sns.it/mesinger/Sim

In just over 2 years, 21cmFAST is being used by researchers in 12 countries, and most of the 1st gen. 21cm experiments: LOFAR, MWA, 21CMA

Example:���cosmic 21cm signal

21 cm line from neutral hydrogen Hyperfine transition in the ground state of neutral hydrogen produces 21cm line.

Predicted by van den Hulst when Oort told him to find unknown radio lines to study our galaxy

Now widely used to map the HI content of nearby galaxies

Circinus Galaxy ATCA HI image by B. Koribalski (ATNF, CSIRO), K. Jones, M. Elmouttie (University of Queensland) and R. Haynes (ATNF, CSIRO).

Once upon a time, HI was much more abundant

z  ~  6   z~1100  

Recombina5on  

HII

z  ~  20  

CMB backlight

z  =  0  

HI

υ21~  70  MHz    υ21~  200  MHz    Redshifted 21cm signal. tune radio to:

Once upon a time, HI was much more abundant

z  ~  6   z~1100  

Recombina5on  

HII

CMB backlight

z  ~  20  

HI

υ21~  70  MHz    υ21~  200  MHz    Redshifted 21cm signal. tune radio to:

LOFAR, MWA, PAPER, 21CMA, GMRT 2nd gen: SKA

interferometer

What we learn: Cosmological 21cm Signal

neutral fraction

gas density

LOS velocity gradient

spin temperature

Cosmological 21cm Signal

Powerful probe:

Astrophysics Has something everyone can enjoy! The trick is to disentangle the components: •  separation of epochs and/or •  accurate, efficient modeling (21cmFAST)

Cosmology &

21cm evolution

decoupling (cosmic web)

Lyα pumping (first stars)

X-ray heating (first BHs) Reionization

http://homepage.sns.it/mesinger/21cm_fiducial.mov

Power of the pre-reionization thermal evolution to constrain astro and cosmo

spin temperature:

21cmFAST 11

which is default in 21cmFAST 13. On smaller-scales, MF07 pre-dicts too much power, while 21cmFAST under-predicts the power.It was shown in Zahn et al. (2010) that the FFRT ionization algo-rithm used in 21cmFAST over-predicts the correlation of the ion-ization and density fields on small scales, due to the fact that itoperates directly on the evolved density field. This strong cross-correlation results in an under-prediction of 21-cm power on thesescales. The converse is true of the MF07 scheme, which althoughusing discrete source halos, paints entire filtered regions as ionized,thus under-predicting the cross-correlation of the ionization anddensity fields. The optimal configuration for accurately estimat-ing the 21-cm signal semi-numerically is the FFRT-S scheme dis-cussed in Zahn et al. (2010), set as default in the publicly-availableDexM14.

Most importantly, the model uncertainties of the semi-numerical schemes are smaller than the evolution due to reion-ization over a range !xHI ! 0.2. Therefore, one might naivelypredict that the semi-numerical schemes are accurate enough to es-timate xHI from the power spectra to± !

< 0.1, or even better if thebehavior of the models are understood. However, there are many as-trophysical uncertainties associated with prescriptions for sourcesand sinks of ionizing photons during the epoch of reionization, andit will likely be these which regulate the achievable constraints onxHI. Therefore it is imperative for models to be fast and be ableto span large regions of parameter space. A single 21cmFAST re-alization of the !Tb fields shown in this section (generated from15363 ICs) takes ! 30 minutes to compute on a single-processorcomputer.

3 THE SPIN TEMPERATURE

We now relax the requirement in §2 of TS " T! , and derive the full21-cm brightness temperature offset from eq. (1), including the spintemperature field. As mentioned previously, models predict that theheating epoch concluded well before the bulk of reionization, atz " 10 (Furlanetto 2006; Chen & Miralda-Escude 2008; Santoset al. 2008; Baek et al. 2009). However, the second generation 21-cm interferometers, such as SKA, might be able to peek into thishigh-redshift regime of the dark ages. Furthermore, the astrophys-ical quantities at high-z are uncertain, and we do not really knowhow robust is the assumption of TS " T! even during the earlystages of reionization. Therefore, for many applications, especiallyparameter studies, it is important to compute the spin temperaturefield. Unfortunately, there is currently no numerical simulation thatincludes the computationally expensive radiative transfer of bothX-rays and Ly" photons from atomically or molecularly cooledsources required to compute TS numerically (though see the re-cent work of Baek et al. 2010, who perform RT simulations on asmall subset of sources, withM !

> 1010M!). Therefore we cannotdirectly compare our spin temperature fields to numerical simula-tions.

Our derivations in this section are similar to other semi-analytic models (Furlanetto 2006; Pritchard & Furlanetto 2007;

generated directly on the same scale 2563 grids show similar shot noiseupturns in power on these scales (see Fig. 7 in Zahn et al. 2010).13 Note that the FFRT results shown here are not precisely analogous tothose in Zahn et al. (2010), since there the evolved density field was takenfrom an N-body simulation, where in 21cmFAST, we self-consistently gen-erate the density field according to §2.1.14 http://www.astro.princeton.edu/ mesinger/DexM.html

Santos et al. 2008). However, unlike Santos et al. (2008) and Santoset al. (2009), we do not explicitly resolve the halo field as an inter-mediary step. Instead we operate directly on the evolved densityfields, using excursion set formalism to estimate the mean num-ber of sources inside spherical shells corresponding to some higherredshift. As discussed above, bypassing the halo field allows thecode to be faster, with modest memory requirements. Below we gothrough our formalism in detail.

The spin temperature can be written as (e.g. Furlanetto et al.2006):

T"1S =

T"1! + x"T"1

" + xcT"1K

1 + x" + xc(5)

where TK is the kinetic temperature of the gas, and T" is the colortemperature, which is closely coupled to the kinetic gas tempera-ture, T" # TK (Field 1959). There are two coupling coefficientsin the above equation. The collisional coupling coefficient can bewritten as:

xc =0.0628 KA10T!

h

nHI#HH1"0(TK) + ne#

eH1"0(TK) + np#pH

1"0(TK)i

,

(6)whereA10 = 2.85$10"15 s"1 is the spontaneous emission coeffi-cient, nHI, ne, and np are the number density of neutral hydrogen,free electrons, and protons respectively, and #HH

1"0(TK), #eH1"0(TK),

and #pH1"0(TK) are taken from Zygelman (2005), Furlanetto &

Furlanetto (2007), and Furlanetto & Furlanetto (2007), respec-tively. The Wouthuysen-Field (Wouthuysen 1952; Field 1958; WF)coupling coefficient can be written as:

x" = 1.7 $ 1011(1 + z)"1S"J" , (7)

where S" is a correction factor of order unity involving detailedatomic physics, and J" is the Lyman " background flux in unitsof pcm"2 s"1 Hz"1 sr"1. We compute T" and S" according toHirata (2006).

According to the above equations, there are two main fieldsgoverning the spin temperature: (1) the kinetic temperature of thegas, TK(x, z), and (2) the Ly" background, J"(x, z). We addressthese in §3.1 and §3.2, respectively.

3.1 The Kinetic Temperature

3.1.1 Evolution Equations

To calculate the kinetic temperature, one must keep track of the in-homogeneous heating history of the gas. We begin by writing downthe evolution equation for TK(x, z) and the local ionized fraction inthe “neutral” (i.e. outside of the ionized regions discussed in § 2.2)IGM, xe(x, z):

dxe(x, z#)dz#

=dtdz#

ˆ

"ion % "ACx2enbfH

˜

, (8)

dTK(x, z#)dz#

=2

3kB(1 + xe)dtdz#

X

p

$p

+2TK

3nb

dnb

dz#%

TK

1 + xe

dxe

dz#, (9)

where nb = nb,0(1 + z#)3[1 + !nl(x, z#)] is the total (H +

c! 0000 RAS, MNRAS 000, 000–000

Tγ – temperature of the CMB TK – gas kinetic temperature Tα – color temperature ~ TK

the spin temperature interpolates between Tγ and TK Any source of heat could leave an imprint: -X-rays, shocks, DM annihilation, cosmic strings…

Fiducial heating: X-rays (HMXBs)

Mesinger & Ewall-Wice, in prep

Fiducial heating: X-rays (HMXBs)

Mesinger & Ewall-Wice, in prep

But 21cm also probes cosmology 1) “clean” epochs where cosmo signal dominates à Dark Ages z > 40

!"#$%&'($)*+,-.$/0,.$1,12-3$

45,$

But 21cm also probes cosmology 2) Models which suppress small-scale power, like WDM result in a dearth of low mass galaxies

But 21cm also probes cosmology 3) Heat input (e.g. DM annihilations) 5

FIG. 3: Evolution of the 21cm power at k = 0.1 h Mpc!1.

21cmFAST to generate the reionization and heating sce-nario. We vary astrophysical parameters, looking for gen-eral trends and physical insight. summarize our resultsas follows.Acknowledgments CE acknowledges a visiting grant

from SNS where part of this work has been carried out,and support from the “Helmholtz Alliance for Astroparti-cle Physics HAP” funded by the Initiative and Network-ing Fund of the Helmholtz Association.

" Electronic address: carmelo.evoli@desy.de[1] E. Komatsu, J. Dunkley, M. R. Nolta, C. L. Bennett,

B. Gold, G. Hinshaw, N. Jarosik, D. Larson, M. Limon,L. Page, et al., ApJS 180, 330 (2009), 0803.0547.

[2] S. A. Wouthuysen, AJ 57, 31 (1952).[3] G. B. Field, ApJ 129, 536 (1959).[4] C. M. Hirata, MNRAS 367, 259 (2006), arXiv:astro-

ph/0507102.[5] S. R. Furlanetto, S. P. Oh, and F. H. Briggs, Phys. Rep.

433, 181 (2006), arXiv:astro-ph/0608032.[6] M. Valdes and A. Ferrara, MNRAS 387, L8 (2008),

0803.0370.[7] X. Chen and M. Kamionkowski, Phys. Rev. D 70, 043502

(2004), arXiv:astro-ph/0310473.[8] A. Mesinger, S. Furlanetto, and R. Cen, MNRAS 411,

955 (2011), 1003.3878.[9] C. Evoli, M. Valdes, A. Ferrara, and N. Yoshida, MNRAS

422, 420 (2012).[10] P. Madau, A. Meiksin, and M. J. Rees, ApJ 475, 429

(1997), arXiv:astro-ph/9608010.[11] M. Valdes, A. Ferrara, M. Mapelli, and E. Ripamonti,

MNRAS 377, 245 (2007), arXiv:astro-ph/0701301.

Evoli+, in prep

Conclusions •  Cosmological 21cm signal is very rich in information, containing both

cosmological and astrophysical components.

•  The range of scales and unknown parameter space is enormous! We need (i) bottom-up modeling; (ii) parameter space explorations

•  SKA is great!

!"#$%&'($)*+,-.$/0,.$1,12-3$

45,$