This doc file outlines plans/tests to compare our empirical results with the simulations (SA as well as N-body+SPH) of Burkert and Kochfar CONTENTS ======== 2-tier approach Details of simulations used for our paper Details on the semi-analytic predictions Details on our samples S1 and S2 Details on the cosmological simulations ************************************************************** 2-tier approach I assume that we will have a 2-tier approach: I) First, we will compare the results from Tim with the semi analytic predictions that you had sent me ealier (B/T figure below) and we can see where the disagreements occur. This can then act as a guide to improving the SA prescriptions. I should mention that our goal is to submit a paper by early/mid April (for Tim's masters thesis) and we could reference your paper or have a joint paper, but these details can be worked out as we move further along in the comparisons. II) Next and on a longer term, start to analyse the cosmological simulations with resolved structural information that Andi is running. ************************************************************** Models from Sadegh 1)mr.sadegh.mar6; model = model.sadegh.fort.6308.mar6-08 # Results of a cosmological simulation in a box of 1E6 Mpc^3. # Major merger is 1/4 < m1/m2 <= 1/1 # Assumes all gas in a major merger get converted to stars # To clarify, when we define spirals we do that using the bulge-to-total fraction of stars in an individual galaxy, i.e. B/T < 0.6. Since you might want to use a different definition for a spiral I send you all galaxies I find with masses above 1.E8 M_sun (please note that we are probably only complete above 1E6 M_sun). It should be straight forward to split this galaxy sample into early type and late type galaxies and look at the distribution of B/T. Please let me know if you have problems with the data. See results in doc2.model.stats 2) model.sadegh.may20-08 # Results of a cosmological simulation in a box of 1E6 Mpc^3. # Major merger is 1/4 < m1/m2 <= 1/1 # Assumes Cox et al prescription for % of gas in a major merger that # gets converted to stars. See results in doc2.model.stats ************************************************************** Details of simulations used for our paper From mr1.sadegh.may14, mr2.sadegh.may14 REFERENCES -- Khochfar & Burkert MNRAS 359 (2005) and -- Khochfar & Silk MNRAS 370 (2006). -- How to plant a merger tree Somerville, R.~S., \& Kolatt, T.~S.\ 1999, \mnras, 305, 1 -- Evaluating approximations for halo merging histories Somerville, R.~S., Lemson, G., Kolatt, T.~S., \& Dekel, A.\ 2000, \mnras, 316, 479 -- Semi-analytic modelling of galaxy formation: the local Universe Somerville, R.~S., \& Primack, J.~R.\ 1999, \mnras, 310, 1087 -- Kauffmann et al 1999 -- Sutherland annd Dopita (1993 ; cooling function -- Springel et al (2001) ; cooling function /prescription -- Kauffmann et al (1999); prescription for SNE feedback 1) The merging history of dark matter haloes is derived by using the extended Press-Schechter formalism to generate merger tress of dark matter halos. This analytical treatment gives results very similar to N-body simulations (see Somerville et al 2000). 2) The semi-analytical treatment are applied for the gas physics See Khochfar & Burkert MNRAS 359 (2005); Khochfar & Silk MNRAS 370 (2006)) In the SAM treatment we follow each individual galaxy and its dark matter halo through time. In that way we try to calculate self-consistently in an evolutionary manner, the amount of cold disc gas, hot halo gas, bulge and disc stars for each individual galaxy. We do not assume ad-hoc scaling relations to 'assign' gas and stellar content that are around during a merger, but take the values we got from our evolutionary calculation. Here are details a) Cosmology (in Khochfar & Silk 2006) Omega_m =0.3 = 1-Omega_Lambda Omega_b/Omega_m = 15% sigma8 = 0.9 h= 0.65 b) Each DM halo has hot primordial gas that was captured by DM potential well. The has is heated to virial temperature of the halo T = 39.5 K * [Vc/ kms-1]^2 (White & Frenk 1991; Kauffmann et al 1999) - The baryonic mass in each halo is set by assumed universal ratio of baryonic fraction Omega_b = 0.024/h^2 or Omega_b/Omega_m = 15% - However, due to reionization (of H background by first luminous objects at z~20), the fraction of baryons captured in low mass halos is reduced (Navarroo and Steimetz 1997; Benson et al 2002). This is implemented via recipe of Somerville et al 2002 - how do we divide the baryonic mass between cold gas, hot gas and stars? The amount of cold gas and stars is set by the cooling rate of hot gas to cold gas and the SF recipe in cold gas. see below c) This gas is allowed to radiatively cool and settle down in a rotationally supported gas disk at center of halo. Cooling function of Sutherland annd Dopita (1993) and prescription of Springel et al (2001) are used t_coo l = ? PN: In general - t_cool = ? - cooling rate per unit volume prop to (rho)^2 - see Fig 9.29 EAC for cooling rate as f(T) c) When 2 halos merge it is assumed that all the gas gets heated to the virial temp of the resulting halo. The gas can then cool onto the central new galaxy. - When two halos merge, the central galaxy of the less massive halo becomes a satellite, and the central galaxy of the most massive halo becomes the central galaxy. Thus, a halo can host many satellite galaxies, but only one central most massive galaxy onto which the gas cools. - The cold gas content of a satellite is given by the amount present when they become satellites, and it then decreases with time due to SF and SNe feedback d) Once cooled gas is in a disk, the models allows for gravtitational collapse, fragmentation and subsequent SF according to a parameterized Schmidt-Kennicutt law dM*/dt = alpha M_cold/Tdyn-gal where - alpha = efficiency of conversion of gas to stars - Tdyn-gal = dynamical time of galaxy = taken as 0.1 x Tdyn of DM halo - we allow SF only for DM halo of Vc < 350 kms-1 to prevent too bright central galaxies in clusters e) Feedback from SNE Feedback from SNE important for regulating SF in small mass halos and prevent formation of luminous low mass satellites. SNE feedback implemented via prescription in Kauffmann et al (1999) Delta-M_reheat = 4/3 * e2 * neta_SN * E_SN * Delta_M*/Vc^2 where Delta-M_reheat = ? Delta-M* = ? e2 = unknown efficiency factor with which energy of SN reheats cold gas neta_SN = no of SNe per solar mass of stars formed = depends on IMF = 5 x 10-3 for Scalo IMF E_SN = energy output per SN = 10^51 ergs Vc = circular velocity of the halo in which the galaxy was last present as a central galaxy PN: The idea is that SNe heat the gas increasing the mean thermal speed or sound speed, so that the gas can escape the DM halo, thus quenching further SF in this halo. Example: For gas heated to Te =10^4 K, the mean sound speed is ~10 km/s. This is larger than escape speed for a DM halo of mass 1e8 and R=10 kpc . sound speed in a gas C-s^2 = dP/d_rho where P=nkT, rho= n* m_p C_s = sqrt (K_B T/ mh) = 10 km/s (T/10^4 K)1/2 escape speed 1/2 Ve^2 = GM/R Ve^2 in (km/s)^2 = (M/Msun)/(111 * (R/pc) Ve ~ 10 km/s for M=1e8, R=10 kpc f) Merger rate When 2 DM halos (each with its central galaxy and satellite galaxies) merge, the galaxies merger on a timescale t, which is determined by the timescale it would take the satellite galaxies to reach the center of the DM halo via dynamical friction Different formulae for the dynamical friction timescale are used by diferent groups (see note N1 below). Here they use the prescription of Kauffmann et al 1999, modified to use the Coulomb logarith approximation of Springel et al 2001. -- g) SF during merger - Durong major merger all of the gas is assumed to be funnelled to the center and all of it is converted into stars Neglect possibility that somne of it settles into a residual gas disk. - satellite galaxies in minor mergers M1/M2 > 4 contribute their stars to the bulge of the host. N1: Some studies use a modified formulae for DF, calibrated on N-body simulations, where effects like tidal stripping of galaxies and halos are included K08 stats: within 8 Mpc for galaxies with Vc>150 km/s 7/19 = E or classical buge 1/19 = classical and pseudo 11/19 : no classical bulge ************************************************************************* Possible solutions to discrepancy 1) Decrase no of late mergers B/T = M*_bulge/(M*_bulge + M*_disk + M*_bar) At epoch z_last of last major merger, M*_bulge forms, B/T ~1 or high From z_last to today, M*_disk + M*_bar grow via smooth amd satellite gas accretion, followed by SF --> B/T falls If last major merger occurs at high z, B/T will have time to fall by z=0 (Say : Merger history shows good agreement between data and models at z<1, but between z=1 to 3, detailed checks on models do not exist One possible solution to the discrepancy is that the galaxy merger history in the simulations is not quite right : there are too many late major mergers. This is something I want to add to the discussion. I understand that the DM halo merger history is constrained by the input cosmology, but that there is some uncertainty in the galaxy merger history: is this correct? This is correct. Here the main problem is the dynamical friction time scale estimate which is used by various models. However, as you also showed in your paper the differences are not too large. > However, my recent comparison of galaxy merger fraction and rate > from observations out to z=1, with SAM+ N-body models suggest > that the models (at least those that can get mass function right) > are using reasonable galaxy merger rates + fraction over z=0.2 to > 1.0. > > I have put the paper on > http://www.as.utexas.edu/~sj/temp2/paper.sj.pdf > See fig 12 and 13 on page 38 and 39 > > Can you tell me if the merger fractions & rates in your > models over z~0.2 to 1 are close to the type of values > in the data? (6%-10% and a few x 10-3 Gyr-1 Mpc-3) They are indeed close to what you report. 2) Reduce SFE before and during last major merger >> >> Now for the 2> over or minor mergers. These bulges have the additional constraint that >> they need to have low B/T, which will be difficult to achieve in the case >> of major mergers, even if we have lots of residual gas left. All the >> progenitor disk stars will contribute to the bulge, and from our >> simulations in a cosmological context (Khochfar & Silk 2006) we know that >> only 20-30 % of stars in the bulge are made from gas during major >> mergers. The vast majority is made from already existing disk stars. So >> there will be always a dominant bulge component in major mergers. > Now for the 2> over or minor mergers. These bulges have the additional constraint that >> they need to have low B/T, which will be difficult to achieve in the case >> of major mergers, even if we have lots of residual gas left. All the >> progenitor disk stars will contribute to the bulge, and from our >> simulations in a cosmological context (Khochfar & Silk 2006) we know that >> only 20-30 % of stars in the bulge are made from gas during major >> mergers. The vast majority is made from already existing disk stars. So >> there will be always a dominant bulge component in major mergers. > > > > But that has to depend on the assumptions and specifics of the > simulations (e.g., merger history and SF history). For instance, > it would depend on the gas mass fraction vs the stellar mass > fraction at the time of the last major merger: the resulting > B/T could be low if the gas mass fraction was >> the stellar > mass fraction . In the extreme case of very high gas mass > fractions with low SFE (Robertson et al. 2006) the progenitor > of a major merger has very low B/T. Now, I agree that the latter > simulation is probably representative only of the very high z > gas rich mergers, and that as these systems evolve to lower z, > the next major merger will occur at a lower gas fraction and > higher stellar mass fraction, since SF would have converted some > of the gas to disk stars in the meantime. In that case, as you > say a lot of the existing disk stars will contribute to the > bulge, and add to its B/T. One possible workaround to this > would be the following scenario. Suppose > a) the SF efficiency (SFE) was low at times preceding > the last major merger, so that not many disk stars > from before the merger. This is problematic: If one is to reduce the star formation efficiency significantly in SAMs (and I think it is safe to say that the common SAMs agree on this) the number of massive high redshift galaxies will drop strongly, and already the number densities are only just met. Furthermore there is another significant problem right now in the common SAMs. As you might know Daddi et al. showed for his sample of SF BzK galaxies that he finds an order of magnitude more high star forming galaxies at z=2 than is predicted e.g. in the Millennium simulation. This discrepancy would be even worse reducing the star formation deficiency. It also seems to be strong evidence by the work of Genzel and Co, that there are large accretion rates onto disk galaxies at z=2, which would provide enough fuel to make lots of stars. 3) Increase the SFE AFTER the last major merger > b) the SFE became higher at later times after the > last major merger, so that most stars form in the > disk around the bulge . Then one could get low B/T > and 2 and diffuse? But this would only limit SFE and keep J > high at high z....but not work at low z. Also it would be mostly effective in low mass dark halos. Not in the more massive ones. ************************************************************** Details on the semi-analytic predictions =========== mr.sadegh.feb25-08 1) Q from SJ, Answer from Sadegh > First some questions on (I) to make sure we are comparing apples > to apples. > > 1) http://www.as.utexas.edu/~sj/bt/fig-bt.gif > This is the figure you sent me earlier from Burkert, Kochfar, > & D'Onghia in prep. > > a) Can we verify the B/T definition. Is B/T the ratio of the > (bulge stellar mass/total stellar mass)? In other words, T > is NOT a dymamical mass and does not include the DM halo mass. > Correct? This is correct, whenever we talk of B/T we refer to bulge stellar mass to total stellar mass of the galaxy. > > b) How is the fraction F1, labelled on the y-axis of the outer > plot, defined? Below is how I read it. Please confirm whether > this is correct of not. > > I read F1 as being the fraction at z=0 o of ALL galaxies > (Elliptiicals and spirals) with M*>2e10, that end up with > a given B/T at z=0, after running semi-analytical simulations > where you assume that every merger with a stellar mass ratio > below 4:1 (black) or below 5:1 (red) at some early redshift > z>0 gives a triaxial or spheroidal system with B/T =1. This is correct. > This system, can be a bulge or an elliptical galaxy, as > outlined below > > - This system is a bulge if this merger was an early merger > that involved 2 low mass disks: in this case, the subsequent > accretion of higher angular momentum baryons around this bulge > at later times (modelled semi-analytically) would produce a > disk, leading to a spiral galaxy whose B/T would be < 1 at z=0. > These systems could populate the intermediate B/T values > (e.g 0.4 - On the other hand, if this merger involved 2 massive spirals > then the product would be an Elliptical galaxy whose B/T is > 1 at z=0. These E account for the B/T=1 point on your plot. Our prescription is slightly different to what you laid out. We assume that when a major merger occurs, mass ratio of less than 4:1 or 5:1, the remnant has B/T=1, independent of the mass or morphology of the merging galaxies. After the merger we allow the stellar disc to regrow by gas infall from hot halo gas that cools, just as you described above. The B/T=1 points at z=0 are in general galaxies that had very recently a major merger and could not regrow a substantial disc, and not necessarily massive disc galaxies. > > c) Could you please generate a version of this figure for > the absolute magnitude M_B <= M_B* where M_B*= -20.5? (we > will compare with both Mass and Lum cutoffs) Ok. > d) Could you please generate versions of the figures where > F is the fraction of spirals rather than the fraction of > all galaxies? > Our sample S1 (described in more detail below) only has > spirals and not ellpticals. We could try to correct our > fractions by adding in the relative no of ellipticals, > assuming the local field morphology density relation > (E+S0:Spirals = 10%+10%:80%), but it would still be useful > to see the fraction of spirals from the simulations > directly. I can do that. It would be useful to agree on a definition for the maximum B/T of spirals, i.e. to which extent do you include early-type spirals. I can either stick to a mass criterion or use bulge-to-disc ratios in a given filter band, e.g. B-band. The mass criterion of course is more straight forward. =========== mr.sadegh.feb25-08 please find attached the results of a cosmological simulation in a box of 1E6 Mpc^3. You will find following entries in the ascii table: z of last major merger; stellar mass; bulge stellar mass To clarify, when we define spirals we do that using the bulge-tio-total fraction of stars in an individual galaxy, i.e. B/T < 0.6. Since you might want to use a different definition for a spiral I send you all galaxies I find with masses above 1.E8 M_sun (please note that we are probably only complete above 1E6 M_sun). It should be straight forward to split this galaxy sample into early type and late type galaxies and look at the distribution of B/T. Please let me know if you have problems with the data. Sadegh ************************************************************************* Solutions to discrepancies =========== ms.andi.scenarios.may12 I will send you the full paper in a few hours but for now have attached the summary and 2 key figures. - Note conclusion 4 on distribution of n, and Fig 14 - Note conclusion 6 on distribution of B/T and Fig 27 We need an explanation that explains both the low n and the low B/T of bulges. Below are my thoughts, and I think they are similar to yours, except that I am trying to explain BOTH n and B/T 1) Note conclusion 4 in summary, regarding the large fraction of galaxies whose bulges have n= 2 to 4 (34%) and n<2 (60%). I think this suggests the following a) the group of n=2 to 4 buges is due to dissipative mergers where some fraction of the gas does not form stars before violent relaxation, and this gas settles into a disk, which then builds a disky bulge inside the classical bulge : the resulting hydrib bulge (classical + disky) would have n in range of 2 to 4. Some major merger simullations by Hopkins give a tail of Sersic n less than 3 for dissipative major mergers. b) The large % of of n<2 bulges suggest that galaxies build mostly disky bulges c) The results in (a) and (b) taken together suggest that PURELY classical bulges with n~4 are only built in a RESTRCTIVE range of major mergers: e.g., mass ratio 1:1, moderate gas fraction and high SFE. For other types of major mergers, with lower mass ratios 1:2 to 1:4, high gas fraction and lower SFE during/before violent relaxation, only a fraction of the gas gets converted into stars of a classical bulge. The rest is partly converted by later SF into a compact disky component (disky bulge) inside the classical bulge. This scenario can probably account for the distribution of n. BUT can it also produce lower B/T? If disky bulges are naturally smaller than classical bulges, then YES: we will automatically get lower B/T in lower n bulges. Whether this will reduce B/T ENOUGH is not clear. We may also need a mechanism to remove low angular momentum gas (e.g AGN or other feedback) and thereby cut off gas that makes both disky and classical bulge. I note that this scenario (c) that I come up with, agrees with your email. For the simulation: right now, you do not make a distinction between classical vs disky bulge, so you only prediict the B/T distribution, not the n distribution. Could this be expanded? > For example, we could say that 1:1 always leads to a bulge, > 2:1 forms bulges only if the gas fraction is less than 70%, we could say 2:1 with gas fraction less than 70% - converts x% of gas into disky bulge stars with n<3 - converts y% of gas into clasical bulge stars with n~4 > 3:1 forms bulges for a gas fraction below 50% and 4:1 forms we could 3:1 with a gas fraction below 50% - converts x2% of gas into disky bulge stars with n<3 - converts y2% of gas into clasical bulge stars with n~4 etc Sadegh : how long would it take to run these different trial simulations? Shardha ************************************************************************* Details on our samples S1 and S2 1. Our first sample S1 The first sample S1 that Tim is analyzing is the OSU sample of Bright Spirals with B and H images (Eskridge et al 2002, ApJS, 143...73). This sample is widely used at z~0 for studying spirals by many groups. The analysis of disks and bars from ellipse fit was done by my other grad student and I recommend you look at Marinova & Jogee (2007, ApJ, 659, 1176; MJ07) to get an idea of the sample (see Fig 3 in particular). Tim is now pushing this further by doing bar+disk+bar 2D structural decomposition on H-band images (where light traces mass better than B-band), with our main interest being to get the distribution of bulge (B/T, Sersic n). The OSU sample with B+H image has Spiral S0/a or later ; m_B < 12 mag ; D_25 < 6' (189 galaxies) Note a) it only has spirals and no Ellipticals b) Figure 3 of MJ07 shows the Mv and RC3 Hubble type distribution. If I compare M_V with a Schechter LF, it is clear that we are not complete at MV fainter than -20. It also follows that we are not complete for Hubble types later than Sbc. c) We are using the color to generate the stellar mass distribution of the sample shown in Fig. 3 & can send you that. I expect we will not be complete at M<1e10. 2. Our second sample S2 In order to compensate for the lack of late type, low mass galaxies (analogues of Hubble Types Sbc or later) in the sample S1, we are investigating another sample S2 - that is complete dowm to fainter magnitudes, e.g,, -18 - has H or K band image - is high resolution We are looking into SDSS/UKIDDS, but the B+D+Bar decomp for these small bulges might need HST NICMOS or WFC3. ************************************************************** Details on the cosmological simulations We are using the standard zooming method where we first calculate a large cosmological box 128 Mpc with of order 64 Million particles in order to resolve where dark halos, groups and clusters form. The we rezoom the environment of a region we are interested in (typically of order 8 Mpc or so) and add gas particles (several millions), including also star formation and stellar feedback and study the formation, evolution and merger history of the galaxies that form in this region. We compare these results with the semi-analytical predictions by Sadegh and also lateron add chemistry to see the evolution of different stellar population. We can send you the spatial distribution of stars, their ages and metallicities, as well as their kinematical properties. In addition you can get the information about the structure and property of the surrounding dark matter halo. You can then bin this data set adopting some inclination and analyse it like an observed galaxy. > Yes, the B/T plot was generated using Sadegh's semi-analytical > approach. But I now have a graduate student > (Michaela Hirschmann) working on analyses of real cosmological > simulations from which she extracts the merging history. In principle > these simulations could also be used to simulate galaxy evolution in > great details. We are just starting this. So it is too early to > send you some data. > What I had in mind is the following. We have programs that generate > isolated equilibrium disk galaxies with bulges and dark matter halos. > We can also disturb these galaxies to generate bars. It might be > interesting to generate a projected image and projected kinematics > of these models which you could analyse to extract the disk-to-bulge > ratio which we then compare with the real data. Yes. In fact to make things more realistic, you could convolve the projected image with a PSF (to simulate seeing), and send us both the image and PSF as fits files. Tim could try GALFIT on these to derive a B/T, Disk/T, Bar/T. A question: do you know from your simulations what is the "true" B/T of these galaxies? What I mean is that in principle you have orbital information and kinematics (V/sigma) and hence could identify particles that make up the bulge. This would then give you a B/T. It would be interesting to see how this B/T compares with the 'photometric B/T' that we derive above. **************************************************************