Modelling SFR-M* and M*-Z relations to be observed at
high-redshift with JWST
Emma Curtis-Lake & David Stenning Institute d’Astrophysique de Paris
Stephane Charlot, Jacopo Chevallard, Pratika Dayal, Julia Gutkin,
Michaela Hirschmann
NEOGAL
date 21/06/16
Motivation
Image credit: Harry Fergusonhttp://candels-collaboration.blogspot.fr/2013/02/star-formation-in-mountains.html
Stellar mass
SFR
Motivation
Stark+ 2013
Motivation
Pacifici+ 2014
Salmon+ 2015
Previous work
Kurczynski+ 2016
Previous work
Kurczynski+ 2016
Previous work
Question
How well can recover the intrinsic scatter from simulated, self-consistent star formation and chemical enrichment histories?
CF00 Dust attenuation
SFHs with known input M*-SFR relationshipSAM/Hydrodynamic simulation/toy model
BEAGLEmock catalogue
production
Stellar templates Chosen filter
profiles
Artificial photometry plus noise
BEAGLESED fitting
CF00 Dust attenuation
CF00 Dust attenuation
Charlot & Fall 2000
CF00 Dust attenuation
Charlot & Fall 2000
See Brett Salmon’s poster
BEAGLEmock catalogue
production
SFHs with known input M*-SFR relationshipSAM/Hydrodynamic simulation/toy model
CF00 Dust attenuation
Stellar templates Chosen filter
profiles
Artificial photometry plus noise
BEAGLESED fitting
BEAGLEmock catalogue
production
BEAGLEmock catalogue
production
•Includes self-consistent nebular emission based on wide grid of CLOUDY models - see Julia Gutkin’s poster!
SFHs with known input M*-SFR relationshipSAM/Hydrodynamic simulation/toy model
BEAGLEmock catalogue
productionCF00 Dust attenuation
Stellar templates Chosen filter
profiles
Artificial photometry plus noise
BEAGLESED fitting
BEAGLESED fitting
BEAGLESED fitting
At this stage we get to test impact of different fitting parameters on derivation of individual object physical parameters, as well as the M*-SFR relation as a whole.
Fitting parameters include:•Sampling of SED (different filter sets)•Depth of the data•Dust prescriptions•SFH prescriptions
measuring the M*-SFR relation
Notation
For galaxy i:
• SFRi is log10(SFR/M�yr�1
)
• Mi is log10(M?/M�)
• ⇥i are the remaining parameters (e.g., metallicity, z)
• yi are “observed” photometry, with known errors ⌃i
• µi = G(SFRi,Mi,⇥i) is predicted photometry from
forward-model G
First Level:
yi | SFRi,Mi,⇥i ⇠ N(µi,⌃i)
Second Level:
SFRi|Mi ⇠ �0 + �1Mi +N(0,�)Mi ⇠ Uniform(a, b)
measuring the M*-SFR relation
Multilevel model
First Level:
yi | SFRi,Mi,⇥i ⇠ N(µi,⌃i)
Second Level:
SFRi|Mi ⇠ �0 + �1Mi +N(0,�)Mi ⇠ Uniform(a, b)
P (SFR,M,⇥,�,�0,�1 | Y,⌃)
/ P (�)P (�0,�1)
NY
i=1
P (yi | SFRi,Mi,⇥i,⌃i)
⇥NY
i=1
P (SFRi | Mi,�0,�1,�)P (Mi)P (⇥i),
where SFR = (SFR1, . . . , SFRN ),M = (M1, . . . ,MN ),⇥ = (⇥1, . . . ,⇥N ),Y = (y1, . . . ,yN ),⌃ = (⌃1, . . . ,⌃N ), and N is the number of galaxies.
measuring the M*-SFR relation
Posterior Distribution
P (SFR,M,⇥,�,�0,�1 | Y,⌃)
/ P (�)P (�0,�1)
NY
i=1
P (yi | SFRi,Mi,⇥i,⌃i)
⇥NY
i=1
P (SFRi | Mi,�0,�1,�)P (Mi)P (⇥i),
where SFR = (SFR1, . . . , SFRN ),M = (M1, . . . ,MN ),⇥ = (⇥1, . . . ,⇥N ),Y = (y1, . . . ,yN ),⌃ = (⌃1, . . . ,⌃N ), and N is the number of galaxies.
measuring the M*-SFR relation
Posterior Distribution
Likelihood Function
P (SFR,M,⇥,�,�0,�1 | Y,⌃)
/ P (�)P (�0,�1)
NY
i=1
P (yi | SFRi,Mi,⇥i,⌃i)
⇥NY
i=1
P (SFRi | Mi,�0,�1,�)P (Mi)P (⇥i),
where SFR = (SFR1, . . . , SFRN ),M = (M1, . . . ,MN ),⇥ = (⇥1, . . . ,⇥N ),Y = (y1, . . . ,yN ),⌃ = (⌃1, . . . ,⌃N ), and N is the number of galaxies.
measuring the M*-SFR relation
Posterior Distribution
Likelihood Function
Prior Distribution
P (SFR,M,⇥,�,�0,�1 | Y,⌃)
/ P (�)P (�0,�1)
NY
i=1
P (yi | SFRi,Mi,⇥i,⌃i)
⇥NY
i=1
P (SFRi | Mi,�0,�1,�)P (Mi)P (⇥i),
where SFR = (SFR1, . . . , SFRN ),M = (M1, . . . ,MN ),⇥ = (⇥1, . . . ,⇥N ),Y = (y1, . . . ,yN ),⌃ = (⌃1, . . . ,⌃N ), and N is the number of galaxies.
measuring the M*-SFR relation
Posterior Distribution
Likelihood Function
Prior Distribution
Hyperprior
measuring the M*-SFR relation
measuring the M*-SFR relation
P (SFR,M,⇥,�,�0,�1 | Y,⌃)
/ P (�)P (�0,�1)
NY
i=1
P (yi | SFRi,Mi,⇥i,⌃i)
⇥NY
i=1
P (SFRi | Mi,�0,�1,�)P (Mi)P (⇥i),
where SFR = (SFR1, . . . , SFRN ),M = (M1, . . . ,MN ),⇥ = (⇥1, . . . ,⇥N ),Y = (y1, . . . ,yN ),⌃ = (⌃1, . . . ,⌃N ), and N is the number of galaxies.
measuring the M*-SFR relation
Posterior Distribution
Test scenario
Test scenarioInput:Constant SFHs drawn from M*-SFR relation with known parameters (intercept, slope and scatter).•No Dust•Single metallicity•Single Redshift•Including nebular emission•CANDELS Deep depths/filters + IRAC CH1 + CH2
SED Fitting:•Constant SFHs•No Dust•Redshift left free•Metallicity left free
Test:•Can we recover the input M*-SFR relation parameters?
Test scenario
6 7 8 9 10 11 12
log(Mass /M�)
�1.0
�0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
log(
SFR
/M�
yr�
1)
6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5
log10 (M⇤ /M�)
�1.0
�0.5
0.0
0.5
1.0
1.5
2.0
2.5
log 1
0(S
FR
/M�
yr�
1)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
log(SFR in)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
log(
SFR
mea
sure
d)
8.0 8.5 9.0 9.5 10.0 10.5
log(Mass in)
7.5
8.0
8.5
9.0
9.5
10.0
10.5
log(
Mas
sm
easu
red)
8.0 8.5 9.0 9.5 10.0 10.5
log(Mass in)
7.5
8.0
8.5
9.0
9.5
10.0
10.5
log(
Mas
sm
easu
red)
6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5
log10 (M⇤ /M�)
�1.0
�0.5
0.0
0.5
1.0
1.5
2.0
2.5
log 1
0(S
FR
/M�
yr�
1)
6 7 8 9 10 11 12
log(Mass /M�)
�1.0
�0.5
0.0
0.5
1.0
1.5
2.0
2.5
log(
SFR
/M�
yr�
1)
8.0 8.5 9.0 9.5 10.0 10.5
0.5
1.0
1.5
2.0
mass
SFR
Test scenario
log10(M* / M☉)
log 1
0(SFR
/ M
☉yr
-1)
8.0 8.5 9.0 9.5 10.0 10.5
0.5
1.0
1.5
2.0
mass
SFR
Test scenario
log10(M* / M☉)
log 1
0(SFR
/ M
☉yr
-1)
8.0 8.5 9.0 9.5 10.0 10.5
0.5
1.0
1.5
2.0
mass
SFR
8.0 8.5 9.0 9.5 10.0 10.5
0.5
1.0
1.5
2.0
mass
SFR
β0 (intercept) β1 (slope) σ (intrinsic scatter)Β0
Density
−6 −4 −2 0 2
0.0
0.1
0.2
0.3
0.4
Β1
Density
0.0 0.2 0.4 0.6
01
23
σ
Density
0.25 0.35 0.45 0.55
02
46
810
Test scenario
log10(M* / M☉)
log 1
0(SFR
/ M
☉yr
-1)
8.0 8.5 9.0 9.5 10.0 10.5
0.5
1.0
1.5
2.0
mass
SFR
8.0 8.5 9.0 9.5 10.0 10.5
0.5
1.0
1.5
2.0
mass
SFR
β0 (intercept) β1 (slope) σ (intrinsic scatter)Β0
Density
−6 −4 −2 0 2
0.0
0.1
0.2
0.3
0.4
Β1
Density
0.0 0.2 0.4 0.6
01
23
σ
Density
0.25 0.35 0.45 0.55
02
46
810
Test scenario
log10(M* / M☉)
log 1
0(SFR
/ M
☉yr
-1)
8.0 8.5 9.0 9.5 10.0 10.5
0.5
1.0
1.5
2.0
mass
SFR
8.0 8.5 9.0 9.5 10.0 10.5
0.5
1.0
1.5
2.0
mass
SFR
β0 (intercept) β1 (slope) σ (intrinsic scatter)Β0
Density
−6 −4 −2 0 2
0.0
0.1
0.2
0.3
0.4
Β1
Density
0.0 0.2 0.4 0.6
01
23
σ
Density
0.25 0.35 0.45 0.55
02
46
810
Test scenario
log10(M* / M☉)
log 1
0(SFR
/ M
☉yr
-1)
8.0 8.5 9.0 9.5 10.0 10.5
0.5
1.0
1.5
2.0
mass
SFR
Summary
BEAGLE allows us to both produce mock photometry with self-consistent SF and chemical enrichment histories and nebular emission as well as performing full Bayesian SED fitting (see Jacopo Chevallard’s talk and Julia Gutkin’s poster).
Our Bayesian Hierarchical modelling can recover and provide the full uncertainties in slope, intercept and intrinsic scatter of the M*-SFR relation.
•No assumption of shape of joint uncertainties in M*-SFR for individual objects.
•Allows us to assess and compare different selection and SED fitting strategies.
For more results - see my talk at the Malta “Signals from the Deep Past” conference