A Novel Technique for the Determination of IMF at Low Masses:

A Few Results for Galaxies withOld Stellar Populations

Nikolay Podorvanyuk1

Igor Chilingarian2,1

Ivan Katkov1

1Sternberg Astronomical Institute, Moscow State University (Russia)2Smithsonian Astrophysical Observatory, Harvard-Smithsonian Center for

Astrophysics (USA)

2008: The first trouble with the IMF• For UCD3 the stellar mass derived using the Salpeter

IMF becomes significantly larger than the dynamical estimate and shows “negative” dark matter fraction (Chilingarian, Cayatte, Bergond, 2008)

2011: UCD and GC dynamicsMassive GCs and UCDs where the dynamical relaxation timescale exceeds tHubble suggest that Salpeter IMF is implausible in certain cases: again, M* > Mdyn

Kroupa IMF

Chilingarian et al. (2011)

How can M* exceed Mdyn?• Big fat black hole – NO (its mass must be negative)

• Dark matter – NO (again, it should be negative)

• Difference caused by IMF - YES

Immediate consequence: if we take a sample of dark matter free objects with (M/L)dyn obtained from internal dynamics, we can reliably determine the IMF shape using full spectral fitting, because the IMF-age degeneracy will be broken

Our technique: in general• We developed a new technique for the determination of

the low-mass slope (α1; M* < 0.5M⊙) of the present day stellar mass function (PDMF) using pixel space fitting of integrated light spectra

• This technique can be used to constrain the IMF of stellar systems with relaxation timescales exceeding the Hubble time (e.g., globular clusters where a mass segregation have not yet finished; UCD)

• It can be used for objects with older stellar populations (t > 4 Gyr; for example, massive elliptical galaxies) where massive stars affecting the potentially variable high-end IMF slope have already evolved into stellar remnants

An extension of NBURSTS• Our technique was developed as an extension of the NBURSTS

package (Chilingarian et al. 2007a,b) -- an approach to determine the parametrized line of-sight velocity distribution (LOSVD) and star formation history (SFH) of unresolved stellar populations by means of the full spectral fitting in the pixel space.

• First attempts made by I. Chilingarian in 2009: computed model grids for a range of a1 values using PEGASE-HR and attempted to fit Galactic GCs from Schiavon et al. (2005).

• The final version of the code presented in:Podorvanyuk N., Chilingarian I., Katkov I.,A new technique for the determination of the initial mass function in unresolved stellar populations. MNRAS, 2013, 432 (4): 2632-2638. arXiv:1303.0897

An extension of NBURST

We provide two versions of the technique:

(1) a fully unconstrained determination of age, metallicity and α1: for high signal-to-noise data

(2) a constrained fitting by imposing the externally determined mass-to-light ratio (M/L) of the stellar population.

Monte-Carlo simulations

(a) age, metallicity and α1 can be precisely determined by applying the unconstrained version of the code to high signal-to-noise datasets (S/N=100, R = 7000 yield α1~0.1);

(b) the M/L constraint significantly improves the precision and reduces the degeneracies, however its systematic errors will cause biased α1 estimates

(c) Lower signal-to-noise ratios are affected by the age-a1 degeneracy

The distribution of α1-sensitive information

IMF-sensitive information is not associated with Lick indices

Most of the IMF-sensitive spectral regions are those containing numerous but relatively faint absorption lines sensitive to the surface gravity in the atmospheres of late type (GKM) stars.

These lines associated with CaI, VI, CoI, NiI and TiI absorption lines

Real data: UCD• (2) high-resolution (R=17000)

intermediate signal-to-noise spectra of UCDs in the Fornax cluster obtained at ESO VLT in narrow wavelength interval, 5120< λ <5450°A (Mieske et al. 2008; Chilingarian et al. 2011) downgraded to R=10000

• Very short wavelength range without any strong IMF sensitive features makes the α1 determination impossible for the unconstrained version of our technique bringing the statistical error to Da1 =0.8 even for the brightest object, UCD 3

Real data: UCD

For UCD 1 and VUCD 5 both, fully unconstrained fitting and the M/L-imposed version of the technique agree well within the statistical uncertainties of the unconstrained fitting.

Intermediate resolution (R=1500–2000) high signal-to-noise ratio spectra (3900< λ <6800 A) of Fornax and Virgo cluster UCDs obtained with Gemini GMOS-N/S (Francis et al. 2012)

Real data: UCD

For UCD 5 having low metallicity and therefore much weaker absorption lines, the unconstrained fitting results in very large uncertainties while the adopted (M/L)V value puts it

close to the edge of the model grid on the MF slope (2.8).

Real data: UCD

For VUCD 3 the situation is inverse, the unconstrained fitting yields α1~2.9, however one has to keep in mind that this object has extremely high value of the [α/Fe] chemical abundance ratio

(Francis et al. 2012) resulting in the significant template mismatch, therefore the unconstrained measurements may get biased.

At present, we do not have empirical stellar population models required to study possible biases that may be introduced to the IMF measurements from integrated light spectra by significantly non-solar abundance ratios.

Another example: 3000 massive ellipticals

We have chosen 3000 ellipticals with highest S/N ratios from Saulder et al. (2013) where ~80k elliptical galaxies from SDSS were used for the calibration of the fundamental plane.

Read data: 3000 massive elliptical galaxies

Determination of the low-mass IMF slope using unconstrain version of our technique for 3000 giant elliptical galaxies form SDSS: the low-mass IMF for the most of objects is bottom-heavy (α1 ~ 3.0-3.5). These estimates have statistical errors Da1 = 0.1-0.3. Systematics (e.g. due to a/Fe and Na abundances) is unknownKEY POINT: We do not see any evidence that the low mass IMF slope in giant ellipticals depends on their mass.

Comparision with MILES models

MILES – Bimodal and Unimodal

PEGASE – α1 as a free parameter (not just 1.3!)

PEGASE / MILES (SDSS)

PEGASE.HR and MILES are both based on empirical stellar libraries with very few late type dwarfs (K, M): a clear source of problems dealing with the bottom-heavy IMF shape

MILES / MILES (SDSS)

The pattern suggests interpolation problems in the population synthesis code: stellar library or evolutionary tracks / isochrones or both

Conclusions• better quality of stellar population models is

required for reliable quantitative IMF studies:– completeness of stellar libraries (K,M dwarfs)– better handling of interpolation in the codes

• a lot of troubles due to degeneracies especially if the wavelength coverage is not optimal: it can become really bad already for 3 parameters (age-[Fe/H]-a1) at moderate S/N=50-70

• non-solar abundance ratios can become a serious problem that has to be studied in detail

Thank you for attention!