The formation of_galaxies_disks
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This document summarizes results from simulations of galaxy formation and evolution using hydrodynamical simulations. Higher resolution simulations that include feedback produce galaxies with larger disk scale lengths and smaller bulge-to-disk ratios, in better agreement with observations. Feedback and resolution are necessary to form galaxies with flatter rotation curves and properties matching observed galaxies, like the Tully-Fisher relation. One simulated galaxy has a large disk scale length of 9.2 kpc and small bulge-to-disk ratio of 0.64.
The formation of_galaxies_disks
- 1. Formation and Evolution of Galaxy Disks ASP Conference Series, Vol. 396, c 2008 J. G. Funes, S.J., and E. M. Corsini, eds. The Formation of Galaxy Disks F. Governato,1 L. Mayer,2,3 and C. Brook1 1 Department of Astronomy, University of Washington, Seattle, WA, USA 2 Institute for Theoretical Physics, University of Z¨rich, Z¨rich, u u Switzerland 3 Institute of Astronomy, ETH Z¨rich, Z¨rich, Switzerland u u Abstract. We present a new set of multi-million particle SPH simulations of the formation of disk dominated galaxies in a cosmological context. Some of these galaxies are higher resolution versions of the models already described in Governato et al (2007). To correctly compare simulations with observations we create artificial images of our simulations and from them measure photometric bulge to disk (B/D) ratios and disk scale lengths. We show how feedback and high force and mass resolution are necessary ingredients to form galaxies that have flatter rotation curves, larger I−band disk scale lengths and smaller B/D ratios. A new simulated disk galaxy has an I−band disk scale length of 9.2 kpc and a B/D flux ratio of 0.64 (face on, dust reddened). 1. The Simulation Campaign Here we present results from an ongoing project aimed at simulating a representative sample of galaxies that form in a ΛCDM cosmology. Simulations are run with GASOLINE (Wadsley et al. 2004) and use the ‘blastwave feedback’ described in Stinson et al. (2006). Three of the four models presented here use the same initial conditions as in Governato et al. (2007, hereafter G07) and thus the galaxy halos have the same merging history and form inside the same large scale structure. However, these new simulations use 8 times more resolution elements and a 50% smaller force softening than those presented in G07. To understand the numerical limitations of our work and to better compare with the existing literature, we vary the number of resolution elements and the feedback implementations. In one case (named MW1) we run three models with the number of resolution elements varying from a few tens of thousand to a few million particles and force resolution from 1.2 kpc to 0.3 kpc. To allow a straightforward comparison between simulations and observations, the B/D ratios and disk scale lengths are measured using GALFIT as in on dust reddened, face-on I and K−band artificial images produced using SUNRISE (Jonsson 2006). Recent works by different groups and using different hydrodynamical codes have highlighted the role of feedback in creating galaxies with a dominant stellar component supported by rotation. Significant improvements have been made in reproducing a number of scaling properties of late type galaxies: namely the age – circular velocity, the Tully Fisher, the stellar mass – metallicity relations and the abundance of galaxy satellites (G07; Brooks et al. 2007). However, a well known problem of most galaxies formed 453
- 2. 454 Governato, Mayer, and Brook in cosmological simulations is a massive, centrally concentrated spheroidal component that creates unrealistically declining rotation curves (G07). Low Res, Thermal Feedback Low Res, Blastwave Feedback Average Res, Blastwave Feedback Hi Res, Blastwave Feedback Figure 1. Left panel: The disk, bulge and halo stellar mass fraction (blue, red, and orange) in the MW1-HR, MW1-MR and MW1-MR-TH models. All runs use the ‘blastwave’ feedback, but the one marked ‘TH’, where ‘thermal’ feedback is instead used. MR is the close equivalent of the MW1 galaxy described in G07. Histograms are normalized to 100%. The total stellar masses differ by less than 10%. Right panel: The circular velocity profile from the total mass distribution (Vc = M/r) for the same galaxy halo, run with different resolutions and feedback implementations. The dot marks the radius that contains 85% of the stars. HR, MR and LR runs use a total of 5 million, 600k and 70k dark matter, gas and star particles within the virial radius. Run I−band Rd (kpc) kinematic B/D u−r MW1-HR 3.5 0.83 (0.38) 1.6 MW1-MR 3.3 1.56 1.7 MW1-MR-TH 2.1 1.51 1.6 MW1-LR 2.1 1.35 2.0 Table 1. Summary of the photometric properties of the MW1 run. The value in brackets is the photometric B−band B/D ratio for MW1-HR. MW1 has a total mass of 1012 M⊙ . The explanations proposed in the literature invoke physical and numerical arguments: angular momentum loss due to dynamical friction suffered by gas rich subhalos (Navarro et al. 1996), spurious torques from the grainy potential of a low resolution halo (Kaufmann et al. 2007) or artificial pressure gradients at the cold/hot gas interface (Okamoto et al. 2003). SN feedback is a promising solution as it decouples baryons from the dark matter (DM; Zavala et al. 2008). However, Naab et al. (2007) recently presented results from simulations that did not include feedback from SNe: the resulting circular velocity profile of their simulated galaxies changed significantly with increasing resolution, with the peak velocity dropping from 320 to 220 km s−1 when the number of particles was increased from 403 to 2003 (their Fig. 1). Kaufmann et al. (2007) used simulations of isolated galaxies to show that
- 3. The Formation of Galaxy Disks 455 Figure 2. Left panel: The rotation curves for the higher resolution version equivalent of the models in G07. The dashed line is the curve for MW1 published in the paper, equivalent to the new ‘MR’ model. The dotted line is the low resolution MW1-LR run. The vertical lines mark the radius at which Vrot is measured: 3.5 I−band Rd ’s. This is a radius were the amount of included mass (dark matter, stars, and gas) is close to converging (Fig. 1, right panel) and gives more reliable results compared to measuring Vrot at 2.2 Rd where numerical effects might still be present. Right panel: The Tully Fisher relation for a sample of four high resolution runs vs. data in Giovanelli et al. (1997). Large and small filled dots correspond to the single stellar population models from Girardi et al. (2000) and Starburst99, respectively. The open square is MW1-LR. the central region of a cold gas disk can lose a large fraction of its initial angular momentum if the number of particles is too low. The literature present encouraging evidence that both a physically motivated description of feedback and a high number of resolution elements help to form galaxies with at least some of the properties of the real ones. However, an analysis of a uniform sample of simulations with techniques directly comparable to those used by observers (who measure the light rather than the underlying mass distribution) has been lacking, making a comparison between observations and theoretical models more open to interpretation. 2. Results from Simulations To show the separate effects of feedback and resolution we focus on a simulation of a Milky way like galaxy (total halo mass 1012 M⊙ ). The disk, halo and bulge components are first identified based on their kinematics (Brook et al. 2008, in preparation). All runs adopted the ‘blastwave’ feedback, but those named ‘TH’, that use the much less effective ‘thermal’ feedback (Katz 1992) which is a lower limit to the possible effects of feedback (the two methods inject the same amount of energy into the intra-cluster medium). All runs include the effects of a uniform cosmic UV background. The kinematically defined stellar disk component becomes more dominant as resolution increases or a physically realistic description of feedback effects is adopted (Fig. 1, left panel). Bulge masses decrease significantly in the high resolution run with feedback (HR vs. MR and MR-TH). Feedback is also particularly effective in reducing the fraction of halo stars, a consequence of a much smaller stellar mass in stripped galaxy satellites (MR vs. MR-TH) (Brook et al. 2004). Fig. 1 (right panel) shows
- 4. 456 Governato, Mayer, and Brook Figure 3. SUNRISE unreddened I−band images of the MW1 model. Upper panel: High to low resolution (with blastwave feedback). Lower panel: The medium resolution model with blastwave feedback, no SN feedback and ‘thermal’ feedback. Galaxies with feedback and high resolution form disks with larger scale lengths and/or less concentrated bulges. The dust reddened, photometrically decomposed B/D ratio in B and I bands is lower than the one measured using the kinematics. the circular velocity profile (Vc (r) = M/r) for the same galaxy as resolution and feedback are varied and shows results consistent with those in Naab et al. (2007) and Kaufmann et al. (2007): higher resolution models are less centrally concentrated. While this plot emphasizes the role of resolution, we have verified that effect of feedback on the mass distribution is larger in less massive halos with a shallower potential well, consistent with Zavala et al. (2008). After a bulge/disk decomposition with GALFIT, photometric, dust reddened I−band disks have larger scale lengths (Rd ) and galaxies have bluer colors in higher resolution runs that include the blastwave feedback (Table 1 and Fig. 3). Fig. 2 (left panel) shows the rotation curves from cold gas or young stars for the high resolution version of the galaxies in G07. Compared with the lower resolution models in G07 rotation curves are flatter, as the very central regions are less dense and the disks dynamically colder in the outer parts. However, they are still not as flat as those of most real galaxies of similar mass. Fig. 2 (right panel) shows the resulting I−band Tully Fisher relation. Vrot is measured at 3.5 Rd . There is good agreement between data and the high resolution models, confirming results in G07, while the low res MW1 model is significantly shifted to the right compared its high resolution equivalent and the observed distribution. We added to the sample a recently simulated large spiral galaxy with an Rd of 9.2, 9.2 and 9.1 kpc in the B, I, and K bands respectively. Its dust reddened I−band B/D is 0.64. References Brook, C. B., Kawata, D., Gibson, B. K., & Freeman, K. C. 2004, ApJ, 612, 894 Brooks, A. M., et al. 2007, ApJ, 655, L17 Girardi, L., Bressan, A., Bertelli, G., & Chioi, C. 2000, A&AS, 141, 371 Giovannelli, R. et al. 1997, AJ, 113, 53 Governato, F., et al. 2007, MNRAS, 374, 1479 (G07) Jonsson, P. 2006, MNRAS, 372, 2 Katz, N. 1992, ApJ, 391, 502
- 5. The Formation of Galaxy Disks 457 Kaufmann, T., Mayer, L., Wadsley, J., Stadel, J., & Moore, B. 2007, MNRAS, 375, 53 Naab, T., Johansson, P. H., Ostriker, J. P., & Efstathiou, G. 2007, ApJ, 658, 710 Navarro, J. F., Frenk, C. S., & White, S. D. M. 1996, ApJ, 462, 563 Okamoto, T., et al. 2003, MNRAS, 345, 429 Stinson, G., et al. 2006, MNRAS, 373, 1074 Wadsley, J., Stadel, J., & Quinn, T. 2004, NewA, 9, 137 Zavala, J., Okamoto, T., & Frenk, C. S. 2008, MNRAS, in press (arXiv:0710.2901)