Stellar mass functions and implications for a variable IMF

Stellar mass functions and implications for a variable IMF

Spatially resolved kinematics of nearby galaxies has shown that the ratio of dynamical to stellar population-based estimates of the mass of a galaxy (
MJAM∗/M∗
) correlates with σe, the light-weighted velocity dispersion within its half-light radius, if M* is estimated using the same initial mass function (IMF) for all galaxies and the stellar mass-to-light ratio within each galaxy is constant. This correlation may indicate that, in fact, the IMF is more bottom-heavy or dwarf-rich for galaxies with large σ. We use this correlation to estimate a dynamical or IMF-corrected stellar mass,
MαJAM∗
, from M* and σe for a sample of 6 × 105 Sloan Digital Sky Survey (SDSS) galaxies for which spatially resolved kinematics is not available. We also compute the ‘virial’ mass estimate
k(n,R)Reσ2R/G
, where n is the Sérsic index, in the SDSS and ATLAS3D samples. We show that an n-dependent correction must be applied to the k(n, R) values provided by Prugniel & Simien. Our analysis also shows that the shape of the velocity dispersion profile in the ATLAS3D sample varies weakly with n: (σR/σe) = (R/Re)−γ(n). The resulting stellar mass functions, based on
MαJAM∗
and the recalibrated virial mass, are in good agreement. Using a Fundamental Plane-based observational proxy for σe produces comparable results. The use of direct measurements for estimating the IMF-dependent stellar mass is prohibitively expensive for a large sample of galaxies. By demonstrating that cheaper proxies are sufficiently accurate, our analysis should enable a more reliable census of the mass in stars, especially at high redshift, at a fraction of the cost. Our results are provided in tabular form.

757-771

Bernardi, M.

8408e06c-ce0c-4052-a938-f42c3ad17627

Sheth, R.K.

94b203a4-bea4-461b-a237-14d548264e15

Fischer, J.-L.

05c5a104-756d-40da-9631-81b07200e593

Meert, A.

acca7405-016e-428c-afd3-711efb79f571

Chae, K.-H.

1e2f9ba7-9642-4449-9bd2-8c35dc7233a8

Dominguez-Sanchez, H.

718e2374-5004-4a73-b95e-77e819f3abea

Huertas-Company, M.

63c10b2f-786c-41dd-9fc1-03b85442468b

Shankar, F.

b10c91e4-85cd-4394-a18a-d4f049fd9cdb

Vikram, V.

5f868b6a-86ba-4fed-8fc4-58384dbf3729

March 2018

Bernardi, M.

8408e06c-ce0c-4052-a938-f42c3ad17627

Sheth, R.K.

94b203a4-bea4-461b-a237-14d548264e15

Fischer, J.-L.

05c5a104-756d-40da-9631-81b07200e593

Meert, A.

acca7405-016e-428c-afd3-711efb79f571

Chae, K.-H.

1e2f9ba7-9642-4449-9bd2-8c35dc7233a8

Dominguez-Sanchez, H.

718e2374-5004-4a73-b95e-77e819f3abea

Huertas-Company, M.

63c10b2f-786c-41dd-9fc1-03b85442468b

Shankar, F.

b10c91e4-85cd-4394-a18a-d4f049fd9cdb

Vikram, V.

5f868b6a-86ba-4fed-8fc4-58384dbf3729

Bernardi, M., Sheth, R.K., Fischer, J.-L., Meert, A., Chae, K.-H., Dominguez-Sanchez, H., Huertas-Company, M., Shankar, F. and Vikram, V.
(2018)
Stellar mass functions and implications for a variable IMF.
*Monthly Notices of the Royal Astronomical Society*, 475 (1), .
(doi:10.1093/mnras/stx3171).

## Abstract

Spatially resolved kinematics of nearby galaxies has shown that the ratio of dynamical to stellar population-based estimates of the mass of a galaxy (
MJAM∗/M∗
) correlates with σe, the light-weighted velocity dispersion within its half-light radius, if M* is estimated using the same initial mass function (IMF) for all galaxies and the stellar mass-to-light ratio within each galaxy is constant. This correlation may indicate that, in fact, the IMF is more bottom-heavy or dwarf-rich for galaxies with large σ. We use this correlation to estimate a dynamical or IMF-corrected stellar mass,
MαJAM∗
, from M* and σe for a sample of 6 × 105 Sloan Digital Sky Survey (SDSS) galaxies for which spatially resolved kinematics is not available. We also compute the ‘virial’ mass estimate
k(n,R)Reσ2R/G
, where n is the Sérsic index, in the SDSS and ATLAS3D samples. We show that an n-dependent correction must be applied to the k(n, R) values provided by Prugniel & Simien. Our analysis also shows that the shape of the velocity dispersion profile in the ATLAS3D sample varies weakly with n: (σR/σe) = (R/Re)−γ(n). The resulting stellar mass functions, based on
MαJAM∗
and the recalibrated virial mass, are in good agreement. Using a Fundamental Plane-based observational proxy for σe produces comparable results. The use of direct measurements for estimating the IMF-dependent stellar mass is prohibitively expensive for a large sample of galaxies. By demonstrating that cheaper proxies are sufficiently accurate, our analysis should enable a more reliable census of the mass in stars, especially at high redshift, at a fraction of the cost. Our results are provided in tabular form.

**Text Stellar mass functions and implications for a variable IMF
- Accepted Manuscript**

## More information

Accepted/In Press date: 5 December 2017

e-pub ahead of print date: 8 December 2017

Published date: March 2018

## Identifiers

Local EPrints ID: 418279

URI: https://eprints.soton.ac.uk/id/eprint/418279

ISSN: 0035-8711

PURE UUID: 59a88cf1-c45f-4c53-ad34-e17ca37eecc1

## Catalogue record

Date deposited: 27 Feb 2018 17:30

Last modified: 05 May 2018 16:30

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## Contributors

Author:
M. Bernardi

Author:
R.K. Sheth

Author:
J.-L. Fischer

Author:
A. Meert

Author:
K.-H. Chae

Author:
H. Dominguez-Sanchez

Author:
M. Huertas-Company

Author:
V. Vikram

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