A halo model for cosmological neutral hydrogen

Hamsa PadmanabhanETH Zurich, Switzerland

with Alexandre Refregier, Adam Amara, T. Roy Choudhury, Girish Kulkarni

arXiv:1407.6366, 1505.00008, 1607.01021, 1608.00007, 1611.06235

21- cm cosmologyTomography: each

frequency is a different epoch

N ~ 3 × 1016 modes, much smaller scales than

CMB

[Loeb & Zaldariagga (2004)]

MIT

[Loeb (2006)]

Efforts to map the neutral hydrogen distribution

• SKA (South Africa/Australia) • GMRT (Pune, India) • LOFAR (Netherlands) • PAPER,MEERKAT (South Africa) • BINGO, CHIME, TianLai, HIRAX…

….

Predictions for (post-reionization) HI observations,

all scales including nonlinear scales

Efficiently model the astrophysics

The halo model : rationale[e.g. Cooray & Sheth (2002)]

The halo model : rationale❖ Powerful tool in cosmology to discuss non-linear

gravitational clustering❖ Three ingredients: Halo mass function, halo bias and halo

profile❖ Describes abundance and clustering of dark matter, also

used widely for galaxy evolution

Can we develop a halo model framework for neutral hydrogen?

Can we constrain it with the latest observations?

[e.g. Cooray & Sheth (2002)]

Surveying the data

Surveying the data

DLA HIabsorption

z 0 1 2 3 4 5

21 cm emission

21 cm intensity mapping

WHISP column density [Zwaan+ (2005b)]

Surveying the data

DLA HIabsorption

z 0 1 2 3 4 5

21 cm emission

21 cm intensity mapping

ALFALFA clustering, bias [Martin+ (2012)]

HIPASS mass function [Zwaan+ (2005a)]

WHISP column density [Zwaan+ (2005b)]

Surveying the data

GBT/DEEP2 [Switzer+ (2013)]

DLA HIabsorption

z 0 1 2 3 4 5

21 cm emission

21 cm intensity mapping

ALFALFA clustering, bias [Martin+ (2012)]

HIPASS mass function [Zwaan+ (2005a)]

WHISP column density [Zwaan+ (2005b)]

Surveying the data

Mg II selected:z ~ 1

[Rao+ (2006)]

GBT/DEEP2 [Switzer+ (2013)]

DLA HIabsorption

z 0 1 2 3 4 5

21 cm emission

21 cm intensity mapping

z ~ 5 GGG survey [Crighton+ (2015)]

z ~ 0-4 incidence [Zafar+ (2013)]

z ~ 2.3 SDSS [Noterdaeme+ (2012)]

z ~ 2.3 bias [Font-Ribera+ (2012)]

ALFALFA clustering, bias [Martin+ (2012)]

HIPASS mass function [Zwaan+ (2005a)]

The HI halo modelPainting neutral hydrogen on dark matter

The HI halo modelTwo HI ingredients

Painting neutral hydrogen on dark matter

The HI halo model

MHI(M, z)How much HI is associated with a mass M halo?

Two HI ingredientsPainting neutral hydrogen on dark matter

The HI halo model

MHI(M, z)How much HI is associated with a mass M halo?

⇢HI(r,M, z)

How is HI distributed in the halo?

Two HI ingredientsPainting neutral hydrogen on dark matter

The HI halo model

MHI(M, z)How much HI is associated with a mass M halo?

⇢HI(r,M, z)

How is HI distributed in the halo?

Two HI ingredients

from which we can derive HI observables

[HP, Choudhury, Refregier, MNRAS (2016)]

Painting neutral hydrogen on dark matter

(NASA/CXC/M.Weiss)

The HI-halo mass relation

Overall normalization; fraction of hydrogen relative to cosmic

Lower cutoff Slope

HP, Refregier, Amara (2016)

[cf. Barnes & Haehnelt (2010, 2014), Villaescusa-Navarro + (2015), …]

The HI-halo mass relation

HI radial profile[HP, Refregier, Amara (2016)]

Exponential:

HI radial profile[HP, Refregier, Amara (2016)]

[Wang + (2014), Bigiel & Blitz (2012) …]

Exponential:

⇢HI(r,M) = ⇢0 exp(�r/rs)

HI radial profile

The viral radius-scale radius relation

[HP, Refregier, Amara (2016)]

[Wang + (2014), Bigiel & Blitz (2012) …]

Exponential:

⇢HI(r,M) = ⇢0 exp(�r/rs)

HI radial profile[HP, Refregier, Amara (2016)]

[Wang + (2014), Bigiel & Blitz (2012) …]

Exponential:

⇢HI(r,M) = ⇢0 exp(�r/rs)

HI radial profile

The concentration parameter and evolution

[HP, Refregier, Amara (2016)]

[Wang + (2014), Bigiel & Blitz (2012) …]

Exponential:

⇢HI(r,M) = ⇢0 exp(�r/rs)

HI radial profile[HP, Refregier, Amara (2016)]

[Wang + (2014), Bigiel & Blitz (2012) …]

[Maccio+ (2007)]

Exponential:

⇢HI(r,M) = ⇢0 exp(�r/rs)

HI radial profile[HP, Refregier, Amara (2016)]

[Wang + (2014), Bigiel & Blitz (2012) …]

[Maccio+ (2007)]

Exponential:

Also considered an altered NFW profile:

⇢HI(r,M) =⇢0r3s

(r + 0.75rs)(r + rs)2

⇢HI(r,M) = ⇢0 exp(�r/rs)

[Maller & Bullock (2004), Barnes & Haehnelt (2010, 2014),HP, Choudhury, Refregier (2016)]

The HI profile

Clustering

P1h,HI =1

⇢2HI

ZdM n(M) M2

HI |uHI(k|M)|2

P2h,HI = Plin(k)

1

⇢HI

ZdM n(M) MHI(M) b(M) |uHI(k|M)|

�2

⇠HI(r) =1

2⇡2

Zk3(P1h,HI + P2h,HI)

sin kr

kr

dk

k

[HP, Refregier, Amara (2016)]

uHI(k|M) =4⇡

MHI(M)

Z Rv

0

⇢HI(r)sin kr

krr2 dr

Constraining the parameters : MCMC

HI abundances and clustering 7

Figure 3. The DLA column density distribution at redshifts z > 0, compared to the model predictions. From left to right: the column density distribution forDLAS at z ⇠ 1, z ⇠ 2.3, and z ⇠ 5 compared with the observations of Rao et al. (2006); Noterdaeme et al. (2012); Crighton et al. (2015) respectively. Theresults from using the Paper I best-fit parameters are indicated in orange.

(iii) The combined set of low-redshift observations likelyfavours an exponential profile for the HI distribution, with evidencefor evolution in the concentration parameter with increasing red-shift, as summarized in Table 4. This form of the profile signifi-cantly reduces the tension (see Fig. 2) between the low-redshift col-umn density distribution and the HI mass function observed (e.g.,Paper I and Padmanabhan & Kulkarni (2016)) with the modifiedNFW profile. Further, this form of the profile is also found to be agood fit to the high-redshift DLA data.

Fig. 6 shows the derived MHI �M relation based on the best-fitparameters. The evolution of the profile ⇢(r) as a function of z isshown in Fig. 7 for a fixed halo mass M = 10

12h

�1M�.

(iv) The model predictions are also in good agreement withthe general trends in the covering fraction and impact parameter-column density relations of high-redshift DLA absorbers, as wellas the surface mass densities observed in low-redshift exponentialdisks.

(v) Although the model has some difficulty fitting the observedbias measurement at z ⇠ 2.3, the model predictions are consis-tent with results from imaging and other DLA surveys that favourDLAs at high-redshift to be hosted by faint dwarf galaxies (e.g.,Cooke et al. 2015; Fumagalli et al. 2014, 2015), and the resultsof hydrodynamical simulations (e.g., Dave et al. 2013; Rahmati &Schaye 2014) and cross-correlations (e.g., Bouche et al. 2005).

We also note that evolving HIHM scenarios, i.e. modified func-tional forms of the MHI � M relation with evolution in one, two,or all of the free parameters ↵, � and vc,0, are not found to be sta-tistically favoured over the base non-evolving scenario when thecomplete set of observations is taken into account (although theymay be favoured by particular subsets of the data).

In future work, it will be useful to use the model results to buildforecasts for upcoming 21-cm observations, to be measured by cur-rent and future experiments. The inclusion of small-scale clusteringenables the calculation of the k-dependence of the HI power spectraand its evolution as a function of redshift. The present framework isfound to be in good agreement with the HI surface density profilesat low redshifts and DLA covering fractions and impact parameterobservations at higher redshifts. It would be worthwhile to explore

Table 4. Summary of the best-fitting HI halo model and the free parameters.

MHI(M) = ↵fH,cM�M/1011h�1M�

��exp

h� (vc0/vc(M))

3i

⇢HI(r) = ⇢0 exp(�r/rs);

cHI(M, z) ⌘ Rv/rs = cHI,0

�M/1011M�

��0.1094/(1 + z)�

cHI,0 = 28.65± 1.76

↵ = 0.09± 0.01

log vc,0 = 1.56± 0.04

� = �0.58± 0.06

� = 1.45± 0.04

these relationships in greater detail in future analyses, by connect-ing the present model to stellar-halo mass relations. This would alsobe useful for comparing to the results of hydrodynamical simula-tions, especially for constraining the stellar-cold gas evolution withredshift.

ACKNOWLEDGEMENTS

We thank Girish Kulkarni and Ali Rahmati for useful discussions,and Joel Akeret for help and support with the COSMOHAMMERpackage. The research of HP is supported by the Tomalla Foun-dation. The simulations used in this work were carried out on theMonch cluster of the Swiss Supercomputing Center CSCS.

MNRAS 000, 000–000 (0000)

[HP, Refregier, Amara (2016)]

Data: low redshifts

7 8 9 10log10 (MHI/M�)

�5

�4

�3

�2

�1

0

log 1

0

� �H

I/cM

pc�

3 dex

�1�

HIPASS (2005)

20.0 20.5 21.0 21.5log10

�NHI/cm�2

��25

�24

�23

�22

log 1

0

� f HI/

cm2�

WHISP (2005)

10�1 100 101

r(h�1 Mpc)

10�3

10�2

10�1

100

101

102

103

⇠ HI(r)

ALFALFA(2012)

• Westerbork Survey — spirals and irregulars (WHISP) [Zwaan+ (2005b)]

HIPASS survey mass function[Zwaan+ (2005a)]

• Clustering of HI-rich galaxies - ALFALFA[Martin+ (2012)]

20.5 21.0 21.5log10

�NHI/cm�2

�

�25

�24

�23

�22

log 1

0

� f HI/

cm2�

z ⇠ 1Rao+ (2006)

20.5 21.0 21.5log10

�NHI/cm�2

�

�25

�24

�23

�22

log 1

0

� f HI/

cm2�

z ⇠ 1This workRao+ (2006)

0.0006

0.0008

⌦H

IbH

I

Data : intermediate redshifts

❖ Intensity mapping measurements with DEEP2/GBT survey [Switzer+ (2013)]

❖ Mg II selected DLA galaxies at redshifts ~ 1 [Rao+ (2006)]

INDEPENDENT MEASUREMENTS, BOTH MATCHED WELL

BY HALO MODEL

0.0006

0.0008

0.0010

⌦H

IbH

I

Data : high redshifts❖ Damped Lyman-alpha systems❖ Column density distributions, incidences (SDSS, UVES,

Gemini GMOS survey…)

20.5 21.0 21.5 22.0log10

�NHI/cm�2

��26

�25

�24

�23

�22

�21

log 1

0

� f HI/

cm2�

z ⇠ 2.3Noterdaeme+ (2012)

20.5 21.0 21.5 22.0log10

�NHI/cm�2

��26

�25

�24

�23

�22

�21

log 1

0

� f HI/

cm2�

z ⇠ 5

Crighton+ (2015)Noterdaeme+ (2012)

Best fit halo model

1010 1011 1012 1013 1014 1015

M(M�)

106

107

108

109

1010

1011

MH

I(M

�)

z = 0

z = 1

z = 2

z = 3

z = 4

Slope 1

10�1 100 101 102

r (kpc)

102

103

104

105

106

107

108

109

1010

⇢ HI(r)

(M�kp

c�3 )

z = 0.0

z = 1.0

z = 2.0

z = 3.0

z = 4.0

10�1 100 101 102

r (kpc)

10�3

10�2

10�1

100

101

102

103

104

105

106

107

⇢ HI(r)

(M�kp

c�3 )

z = 0.0

z = 1.0

z = 2.0

z = 3.0

z = 4.0

[HP, Refregier, Amara (2016)]

Best fit halo model

1010 1011 1012 1013 1014 1015

M(M�)

106

107

108

109

1010

1011

MH

I(M

�)

z = 0

z = 1

z = 2

z = 3

z = 4

Slope 1

Non - unit slope, exponential profileConsistent with abundance matching, stellar-cold gas relations

10�1 100 101 102

r (kpc)

102

103

104

105

106

107

108

109

1010

⇢ HI(r)

(M�kp

c�3 )

z = 0.0

z = 1.0

z = 2.0

z = 3.0

z = 4.0

10�1 100 101 102

r (kpc)

10�3

10�2

10�1

100

101

102

103

104

105

106

107

⇢ HI(r)

(M�kp

c�3 )

z = 0.0

z = 1.0

z = 2.0

z = 3.0

z = 4.0

[HP, Refregier, Amara (2016)]

[HP & Kulkarni (2016)]

What do we learn?

Insights from the modelling

Insights from the modelling❖ HIHM relations adopted in the

literature [Barnes & Haehnelt 2014; Bagla+ (2010)]

DLA based

21-cm based

7 8 9 10log10 (MHI/M�)

�5

�4

�3

�2

�1

0

log 1

0

� �H

I/cM

pc�

3 dex

�1�

ModelZwaan+ (2005)

Insights from the modelling❖ HIHM relations adopted in the

literature [Barnes & Haehnelt 2014; Bagla+ (2010)]

❖ Combining the relations [HP, Choudhury, Refregier, MNRAS (2016)] does not fit HI mass function well

1010 1011 1012 1013

M(M�)

106

107

108

109

1010

1011

MH

I(M

�)

MHI / M

7 8 9 10log10 (MHI/M�)

�5

�4

�3

�2

�1

0

log 1

0

� �H

I/cM

pc�

3 dex

�1�

ModelZwaan+ (2005)

Insights from the modelling❖ HIHM relations adopted in the

literature [Barnes & Haehnelt 2014; Bagla+ (2010)]

❖ Combining the relations [HP, Choudhury, Refregier, MNRAS (2016)] does not fit HI mass function well

❖ Fitting the mass function requires a non-unit slope of HIHM [HP & Refregier, MNRAS (2017)]

1010 1011 1012 1013

M(M�)

106

107

108

109

1010

1011

MH

I(M

�)

MHI / M

Insights from the modelling❖ HIHM relations adopted in the

literature [Barnes & Haehnelt 2014; Bagla+ (2010)]

❖ Combining the relations [HP, Choudhury, Refregier, MNRAS (2016)] does not fit HI mass function well

❖ Fitting the mass function requires a non-unit slope of HIHM [HP & Refregier, MNRAS (2017)]

❖ An exponential profile reduces previously observed tension between the HIHM and the column density [HP, Refregier, Amara (2016)]

20.0 20.5 21.0 21.5log10

�NHI/cm�2

�

�25

�24

�23

�22

log 1

0

� f HI/

cm2�

z ⇠ 0

ExponentialAltered NFWWHISP - Zwaan+ (2005)Braun (2012)

7 8 9 10log10 (MHI/M�)

�5

�4

�3

�2

�1

0

log 1

0

� �H

I/cM

pc�

3 dex

�1�

Zwaan+ (2005)

10�1 100 101

r(h�1 Mpc)

10�3

10�2

10�1

100

101

102

103

⇠ HI(r)

Martin+(2012)

Consistency with other observations

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5r/r25

10�1

100

101

102

⌃H

I(r)

(M�pc�

2 )

This work, z = 0.0

Bigiel and Blitz (2012)

102 103

Impact parameter b (kpc)

0.0

0.2

0.4

0.6

0.8

1.0

f cov

(<b)

Covering fraction DLAsM = 1011.5h�1M�M = 1012.1h�1M�M = 1012.5h�1M�Rudie+ (2012)Fumagalli+ (2011)

❖ Low-redshift observations for the HI surface density [Bigiel & Blitz (2012), Leroy+ (2008)]

❖ Anti-correlation between impact parameter - column density of DLAs [Rao+ (2011), Krogager+ (2012), Peroux + (2013)]

❖ Impact parameter - covering fractions of DLAs [Rudie+ (2012)]

Forecasting❖ Observed angular power spectrum constraining cosmological parameters❖ Explored degradation with the astrophysics - SKA 1 MID, z ~ 0.35, 1 Ghz,

observing time 1 year with frequency interval 1 Mhz over 25000 sq. deg❖ Fisher and MCMC forecasts quantitatively similar

100 101 102 103

`

10�8

10�7

10�6

10�5

C`

PRELIMINARY

�C` =

✓2

2`+ 1

◆(f

sky

�`)�1/2(C` +N)

N =

✓�T

pix

¯T

◆2

⌦

pix

W�1

`

W` = exp�`2�2

beam

; Tsys

= Tinst

+ Tsky

2 astrophysical and 2 cosmological parameters

ForecastingPRELIMINARY

ForecastingPRELIMINARY

z = 0.35 z = 0.1

Astrophysical degradation …

ForecastingPRELIMINARY

z = 0.35 z = 0.1 Combined

Astrophysical degradation … alleviated by tomography

To summarize …

Conclusions and outlook

Conclusions and outlook❖ Built a framework for halo model of cosmological HI❖ Two important ingredients : (i) HI-halo mass relation and (ii) HI profile❖ Constrained well by emission line experiments, high redshift DLA

data, intensity mapping data❖ Best fitting HIHM and profile obtained by Bayesian analysis❖ Model predictions consistent with

(i) abundance matching and stellar - cold gas relations (ii) low-redshift observations for the HI surface density (iii) Impact parameter - covering fraction results for DLAsBuild forecasts for the SKA, evaluate astro degradation and alleviation from tomography

Conclusions and outlook❖ Built a framework for halo model of cosmological HI❖ Two important ingredients : (i) HI-halo mass relation and (ii) HI profile❖ Constrained well by emission line experiments, high redshift DLA

data, intensity mapping data❖ Best fitting HIHM and profile obtained by Bayesian analysis❖ Model predictions consistent with

(i) abundance matching and stellar - cold gas relations (ii) low-redshift observations for the HI surface density (iii) Impact parameter - covering fraction results for DLAsBuild forecasts for the SKA, evaluate astro degradation and alleviation from tomography

THANK YOU!