Stellar Population Synthesis, a Discriminant Between Gravity Models Akram Hasani Zonoozi Institute for Advanced Studies in Basic Sciences, IASBS Zanjan, Iran In collaboration with: H.Haghi & Y.Sobouti
Introduction Most of alternative gravity models and the DM scenarios simulate the rotation curves of spirals with reasonable details. There is significant disparities in their predictions of mass-tolight ratios, M/L, of the galaxies. This feature are used as a discriminant between different alternative theories, by resorting to stellar population synthesis analysis. The rotation curve for the galaxy NGC3198 from Begeman 1989
Alternative gravity models MOND: Modified Newtonian Dynamics of Milgorom MOG: Modified Gravity of Moffat DM: Newtonian Gravity + Dark matter.
Modified Newtonian Dynamics (MOND) Based on observations of galactic rotation curves, gravity is boosted bellow a certain acceleration. (Milgrom, 1983; Milgrom & Bekenestein 1984; Bekenstein 2004) a0 1.2 10 g µ ( g a ) 0 = mond 10 mond ms 2 g N µ ( x) = x x << 1 µ ( x) = 1 x >> 1 Standard function Simple function Bekenstein function
Modified Gravity of Moffat (MOG) (Moffat 2005) In galactic scale: 1 [ M M ( )] 2 α( r ) = 0 r In larger scales: local group, galaxy clusters: (Brownstein & Moffat 2006, Haghi & Rahvar 2010)
Newtonian Gravity plus Dark Matter (DM) logarithmic halo: (Binney & Tremaine 1987) NFW halo: (Navarro, Frenk & White 1996, 1997) ρ NFW ( r) = ( r / r s ρs )(1 + r / r s 2 )
Constructing rotation curves Rotation speed of a test object is a function of distance from the galactic center and the distribution of the detectable matter. Sanders & McGaugh 2002 In modified gravity: In DM: 2 2 * V = V + V baryonic gas 2 2 V = V + V baryonic dark 2 2 Fitting of the calculated rotation curves to the observed data points is achieved by adjusting the stellar M/L ratio, through a least-square method.
All models trace the observed data with reasonable details. We analyzed 46 galaxies.
MOND3 MOND3
Color - M/L ratio correlation How realistic are the inferred M/L ratios? - Stellar population synthesis (SPS) models are tools for interpreting the integrated light that we observed from the galaxies. - SPS models predict a linear relation between colors and log(m/l) ratios of galaxies. log ( M * / L) = a ( B V ) + (Bell & de Jong (2001, 2003) and Portinari et al. 2004.) b Redder galaxies have larger M/L ratio.
The slope of this linear relation does not depend on exact details of the history of star formation. Different SPS models. B and K refer to different spectral band from Bell & de Jong (2001)
The dominant source of uncertainty in estimating stellar M/L ratios from galaxy luminosities and optical colors is the stellar IMF. Depending on how many stars are present at the low-mass end of the stellar IMF, the color- M/L curve shifts up and down. Different IMFs: Bruzual & Charlot (2001): Salpeter with x=-1.35 Salpeter with x=0 below 0.6 Scalo (1986) IMF The updated PE_GASE models with a steeper x=-1.85 and a flatter x=-0.85. from Bell & de Jong (2001)
Initial Mass Function, IMF Low mass stars contribute significantly to the mass of a population, but not so much to its luminosity and color. An IMF richer in low-mass stars yields a higher stellar M/L ratio at a given color. dn/dlog(m) α =1.3 α = 2.3 Salpeter 1955, Kroupa 2001 0.5 Log(m)
M*/L - Color relation Solid line in each panel is the best-fit to the prediction of the gravity model in question. Other lines denote the theoretical predictions of SPS with different IMFs (Bell & de Jong 2001, Bell et al. 2003). They have almost the same slope but different y-intercepts.
Slopes of MOND are reasonably close to the prediction of SPS. Those of MOG and DM are not.
Results Log(M/L)=a.(B-V) b SPS predictions Salpeter IMF (Scaled) Salpeter IMF Kroupa IMF Bottema IMF Slope 1.74 1.74 1.74 1.74 Y-intercept 0.94 0.79 1.09 1.29 Model MOND1 MOND2 MOND3 MOG DM:NFW DM:Log Slope 1.78 1.81 1.75 1.06 2.33 1.36 (Error) 0.23 0.21 0.26 0.21 0.67 0.40 Y-intercept 0.88 1.06 1.13 0.37 1.58 0.87 (Error) 0.14 0.12 0.15 0.12 0.38 0.23
Concluding Remarks The SPS scheme can differentiate between different gravity models. The slope of MOND, are reasonably close to prediction of SPS model. The y-intercept of MOND with Bekenstein function is in agreement with Kroupa's IMF, while that of MOND with other interpolating functions are somewhere between the standard Salpeter and the scaled Salpeter IMF. The slopes of MOG and DM are different from the predictions of SPS.