Revisiting the Stellar IMF - Dark Matter Halo
Degeneracy in Strong Lens Galaxies
Alessandro Sonnenfeld1 , Alexie Leauthaud1,2 , Matthew Auger3 ,Raphael Gavazzi4 , Tommaso Treu5 , Surhud More1
1 Kavli IPMU, 2 UCSC, 3 Cambridge, 4 IAP, 5 UCLA

November 15, 2017

Alessandro Sonnenfeld

Dark Matter -Stellar IMF Degeneracy

The Stellar Initial Mass Function (IMF)

Stellar mass
Alessandro Sonnenfeld

Dark Matter -Stellar IMF Degeneracy

The stellar IMF - dark matter degeneracy(true)

αIMF ≡M∗(SPS)

IMF mismatch parameter

M∗

Auger et al. 2010
Alessandro Sonnenfeld

Dark Matter -Stellar IMF Degeneracy

Questions
1

Can we break the degeneracy between dark matter profile andstellar IMF using weak lensing data?

Problem
The number of strong lenses available for IMF studies is ∼ 100
The weak lensing signal obtained by combining ∼ 100 such
lenses is very noisy
Need to work with a much larger sample of twin galaxies
2

How does strong lensing selection affect the distribution in
halo mass and stellar initial mass function (∼ stellar
mass-to-light ratio), at fixed stellar mass?

3

What is the simplest possible model that can reproduce bothstrong and weak lensing observations?
Alessandro Sonnenfeld

Dark Matter -Stellar IMF Degeneracy

The galaxy samples

SLACS strong lenses
59 quiescent galaxies from SDSS main spectroscopic sample
Einstein radius, SPS stellar mass, velocity dispersion for eachobject
33 objects with weak lensing measurements from HST ACS
HSC massive galaxies∼ 2, 000 massive (log M∗ > 11.0) quiescent galaxies fromSDSS main spectroscopic sample
SPS stellar mass, velocity dispersion and HSC weak lensing
for each object

Alessandro Sonnenfeld

Dark Matter -Stellar IMF Degeneracy

The Strategy

1

Fit population model to strong lens and HSC sample
separately

2

Apply strong lensing selection correction to HSC sample model

3

Compare results from two samples

4

If models do not match, change model

5

Iterate, until the two inferences match

Alessandro Sonnenfeld

Dark Matter -Stellar IMF Degeneracy

The fit“Vanilla” model
NFW dark matter halo, with mass-concentration relationde Vaucouleurs stellar profile, constant M∗ /LPower-law SHMR, with Gaussian scatter in log Mh
Power-law scaling between stellar mass and stellar IMF, withGaussian scatter in log αIMF

P(log Mh ) ∼ N (µh , σh );µh = log Mh,0 + βh (log M∗ − 11.3)

P(log αIMF ) ∼ N (µIMF , σIMF );µIMF = log αIMF,0 +βIMF (log M∗ −11.3)

Fitting method
Bayesian hierarchical inference approach (Sonnenfeld &Leauthaud 2017, arXiv:1710.00007)
Alessandro Sonnenfeld

Dark Matter -Stellar IMF Degeneracy

Results (1)Vanilla modelσh1.0SLACSHSCSL prediction

0.50.0µIMF,00.3

σIMF

β∗

2.0
1.00.00.1

0.2

βIMF

0.05
0.20.1
12.0

13.0 0.0µh0.5
σh1.0 0.0 1.0 2.0 0.2
β∗Alessandro Sonnenfeld

0.3µIMF,00.05 0.1
σIMF

0.1 0.2
βIMF

Dark Matter -Stellar IMF Degeneracy

Results (2)Adiabatic contraction model

SLACS
HSC
SL prediction

σh1.00.5βh

0.0210µν0.5

σν

-0.5
0.5

µIMF,00.3

σIMF

0.00.10.05

βIMF

0.20.20.0
12 13 0.0
µh,00.5σh

1.0 0 1 2βh-0.5 0.5 0.0µν

Alessandro Sonnenfeld

0.5
σν0.2

0.3
µIMF,00.05 0.1
σIMF

0.0 0.2
βIMF

Dark Matter -Stellar IMF Degeneracy

Results (3)M∗ /L gradient model

SLACS
HSC
SL prediction

σh0.5

βh

1.00.0µγ-0.1-0.2

σγ

0.2
0.1

µIMF,00.2

σIMF

1.00.1
0.05

βIMF

0.00.40.2
13.013.5µh,00.5σh

1.0 0.0 1.0
βh-0.2-0.1µγ

Alessandro Sonnenfeld

0.10.2σγ

0.0 0.2µIMF,00.05 0.1σIMF

0.2 0.4
βIMF

Dark Matter -Stellar IMF Degeneracy

Conclusions
A model in which dark matter halos have an NFW density
profile and the stellar mass follows the light distribution does
not provide a good description of SLACS lenses: the inferred
halo masses are too low.
Allowing for adiabatic contraction or expansion does not solve
the discrepancy between the two samples.
Allowing for a gradient in stellar mass-to-light ratio, results ina good match between the SLACS sample and non-lensgalaxies.
Such a gradient can be interpreted both in terms of a gradientin stellar population properties at fixed IMF, or in terms of agradient in IMF itself.
The main effect of strong lensing selection is to shift themedian stellar mass towards higher values.
Alessandro Sonnenfeld

Dark Matter -Stellar IMF Degeneracy