Dark Matter. ASTR 333/433 Spring 2018 T R 4:00-5:15pm Sears 552

Transcription

1 Dark Matter ASTR 333/433 Spring 2018 T R 4:00-5:15pm Sears 552 TODAY - Laws of Galactic Rotation - Flat rotation curves - Tully-Fisher - Universal Rotation curve - central Density Relation - Renzo s Rule - Radial acceleration relation

2 <latexit sha1_base64="ialy7qjdqlgolu5hksa9ic51xo8=">aaacbxicbvbps8mwhe39o+e/qkcvwshoy+hecn4gxjxosdtghsxn0i0stuvyq1lg7l78kl4ut4pxv4lfxmzrzzspao/3xkjecxlbntjor7wyura+svnykm7v7o7t2wehtr2nijkxxijw7ybojrhklnaqrj0orqjasfywvjn4ruemni/la2qj60akl3nikqej+fzzs3yppcx7aybkxu/y4zke7hxoa/qhb5ecijmfxibvnjrqjozv/3i9mkyrk0af0bptdrlojogctgubf71us4tqiemz0btggj8aqyfdwjkjau/vuryjtm6iwcqjago96e3e/7xocmgto+iysyfjonsotawgge82wt2ugawrguko4uahma6iihtmckvtvbpydjm4f5xrinn3warx8g0k6bidodkqoitur7eogvxe0qt6q5/oy3q2xq1362mwxbhyo0dodtb3h87zmak=</latexit> <latexit sha1_base64="ialy7qjdqlgolu5hksa9ic51xo8=">aaacbxicbvbps8mwhe39o+e/qkcvwshoy+hecn4gxjxosdtghsxn0i0stuvyq1lg7l78kl4ut4pxv4lfxmzrzzspao/3xkjecxlbntjor7wyura+svnykm7v7o7t2wehtr2nijkxxijw7ybojrhklnaqrj0orqjasfywvjn4ruemni/la2qj60akl3nikqej+fzzs3yppcx7aybkxu/y4zke7hxoa/qhb5ecijmfxibvnjrqjozv/3i9mkyrk0af0bptdrlojogctgubf71us4tqiemz0btggj8aqyfdwjkjau/vuryjtm6iwcqjago96e3e/7xocmgto+iysyfjonsotawgge82wt2ugawrguko4uahma6iihtmckvtvbpydjm4f5xrinn3warx8g0k6bidodkqoitur7eogvxe0qt6q5/oy3q2xq1362mwxbhyo0dodtb3h87zmak=</latexit> <latexit sha1_base64="ialy7qjdqlgolu5hksa9ic51xo8=">aaacbxicbvbps8mwhe39o+e/qkcvwshoy+hecn4gxjxosdtghsxn0i0stuvyq1lg7l78kl4ut4pxv4lfxmzrzzspao/3xkjecxlbntjor7wyura+svnykm7v7o7t2wehtr2nijkxxijw7ybojrhklnaqrj0orqjasfywvjn4ruemni/la2qj60akl3nikqej+fzzs3yppcx7aybkxu/y4zke7hxoa/qhb5ecijmfxibvnjrqjozv/3i9mkyrk0af0bptdrlojogctgubf71us4tqiemz0btggj8aqyfdwjkjau/vuryjtm6iwcqjago96e3e/7xocmgto+iysyfjonsotawgge82wt2ugawrguko4uahma6iihtmckvtvbpydjm4f5xrinn3warx8g0k6bidodkqoitur7eogvxe0qt6q5/oy3q2xq1362mwxbhyo0dodtb3h87zmak=</latexit> <latexit sha1_base64="fvkfok48asfc4kluekq/qcpzca0=">aaacgnicbvbns8mwae39npor6tflcajtw2hfcilcwivh+ve3wetj07qlsz9iuqwu/rqv/huve0+kf/+n2dblnh8ehu+9klznpywkari/2tlyyuraemwjurm1vbor7+0/istjmfg4yqnvekgqrmnissoz6aacomhjpomnbsz+55lwqzp4ueypcsiuxjsggeklufqv/uddclmfn8fd+j20oq37engevedjbf7dofcmthdcx9vrrsoyac4ssyq1uklt6ipbt3awkvhihotomuyqnqjxstejw6qdcziipeahksbdhvbyst4meq5olofencmhsig88lqyqriv5r2x+j/xy2tqdaoap5kkmz4+fgqmygsoh4i+5qrlliucmkfqhxd3eudyqjmrqro5x3srwgeny4zxd15rncsnkuaqhie6mmefaifb0aywwoanjmax+nzetxftq/ucrpe08s4bmih28wfc6z9h</latexit> <latexit sha1_base64="kplqs2jfrrw7+6xpvkrgfsmy4qi=">aaacsnicbvdns8mwhe3m1dm/qh69bifgxdeowxkqbl48zmg3wtplmqvbwppbkgqj9p/z4swbf4cxxyvpvovtpgg83ntjfr/nxzxjzzrvslrr3tzaruxud/f2dw6no+oujbjbqe0ihom+hyxllks2yortfiwodjxoe970lvd7z1rifowpahbtyydhifmzwuplrsgdakujcnjx5qa/3mmiy9atcnybsdp9aqxywdrj7csi4mrykiy5ctotthb9czuza9tmujkhwidwqwqgqns1xpxrrjkahopwloxammm1tpmhcadz1ukkjtgz4jfn511k6fxli+rhqp9qobm6lmobllpa08l8trnq5ej/3ibrfnoysjbofa3j4im/4uhfkc8wjzigrpgzjpgipidezij1p0rxx9wrw6ulrho7ub+pmw9xtvaz6kactsezuaawuaytca/awayevifpcgejvsip+aw/f9eslo6cgcwuyj++tlpj</latexit> <latexit sha1_base64="/h5zmxgp7dm9rh9xwligt3nlwco=">aaachxicbvdlsgmxfm3uv62vuzdugkwomzijgnuhfgrxwcgxhu4zmmmmdc08sdjcgfivbvwverrxivg3ztpx0cebwogce+49108yfdkyfo3syura+kz5s7k1vbo7z+4fpio45zg4ogyx7/hieeyj4kgqgekknkdqz6ttj25yv/1eukbx9cdhcemfabdrggiktesz126i5jch2ub52t+pfaeuvikzixgdt6q2loqjrtspz1atujubxcr2qaqgqmsz39x+jnoqrbizjetxthlzyxcxfdoikm4qsilwca1inqmn4imw+jciux6rhbn1jodcicahr5p5bmley8vlxjevqaox0shjjynwdfcqmihjmn8k9iknwlkxjghzqjeeeig4wljftkkr2/nff4lzvr+sw/fn1wajueezhifjuam2uabncadawaeyvib38aw+jwfj1fgwpqfrklh8oqqzmh7+acpfo7y=</latexit> <latexit sha1_base64="/h5zmxgp7dm9rh9xwligt3nlwco=">aaachxicbvdlsgmxfm3uv62vuzdugkwomzijgnuhfgrxwcgxhu4zmmmmdc08sdjcgfivbvwverrxivg3ztpx0cebwogce+49108yfdkyfo3syura+kz5s7k1vbo7z+4fpio45zg4ogyx7/hieeyj4kgqgekknkdqz6ttj25yv/1eukbx9cdhcemfabdrggiktesz126i5jch2ub52t+pfaeuvikzixgdt6q2loqjrtspz1atujubxcr2qaqgqmsz39x+jnoqrbizjetxthlzyxcxfdoikm4qsilwca1inqmn4imw+jciux6rhbn1jodcicahr5p5bmley8vlxjevqaox0shjjynwdfcqmihjmn8k9iknwlkxjghzqjeeeig4wljftkkr2/nff4lzvr+sw/fn1wajueezhifjuam2uabncadawaeyvib38aw+jwfj1fgwpqfrklh8oqqzmh7+acpfo7y=</latexit> <latexit sha1_base64="/h5zmxgp7dm9rh9xwligt3nlwco=">aaachxicbvdlsgmxfm3uv62vuzdugkwomzijgnuhfgrxwcgxhu4zmmmmdc08sdjcgfivbvwverrxivg3ztpx0cebwogce+49108yfdkyfo3syura+kz5s7k1vbo7z+4fpio45zg4ogyx7/hieeyj4kgqgekknkdqz6ttj25yv/1eukbx9cdhcemfabdrggiktesz126i5jch2ub52t+pfaeuvikzixgdt6q2loqjrtspz1atujubxcr2qaqgqmsz39x+jnoqrbizjetxthlzyxcxfdoikm4qsilwca1inqmn4imw+jciux6rhbn1jodcicahr5p5bmley8vlxjevqaox0shjjynwdfcqmihjmn8k9iknwlkxjghzqjeeeig4wljftkkr2/nff4lzvr+sw/fn1wajueezhifjuam2uabncadawaeyvib38aw+jwfj1fgwpqfrklh8oqqzmh7+acpfo7y=</latexit> <latexit sha1_base64="jmyzj3esgpoollcaanjp1vvkvnk=">aaab7xicbvddsgjbgp3w/sx+3oqymyejfej2i8guaigilrowavvqwwznz3vw9oez2ude1+im6krovxqf3qzr90btwmdhndn83/m8hdoplovxyg1sbm3v5hcle/shh0xz6lgl41qq6pcyx6ljyuk5i6ijmok0kwikq4/ttje6m/ntfyoki6nnnu5op8sdiawmykul1yy2ys0kukx35celputxxlnkva050dqxm1kcda3x/on5muldgincszrd20puf4kfyottaagxsppgmsidopmvo0xnwvjreav9ioxm6lioh1koq08nq6ygctwbif953vqftf6erumqaeqwg4kuixwjwxfkm0gj4mnnmbfmb4jieatmll5qqve3v4uue+eyelo1nq5k9vp2gzycwhmuwyzrqmmdnmabaim8wsd8gynxarwbh4tozsj+nmasjo8/eskmtw==</latexit> Empirical Laws of Galactic Rotation Flat rotation curves (Rubin-Bosma Law) Rotation curves tend asymptotically towards a constant rotation velocity that persists to indefinitely large radii: V (R!1)! V f Tully-Fisher relation (Luminous, Stellar Mass, and Baryonic TF relations) The baryonic mass of galaxies scales as the fourth power of the flat rotation velocity: M b = AVf 4 <latexit sha1_base64="n/zqwictykrswvnh8ie/bndvhwm=">aaab6xicbvdlsgnbeoynrxhfuy9ebopgkexkwhgqil68cbhma5j1mz3mjknmh870cihkj7wonhr/xl/wb5wke0liwubrvun3tz9iodg2f63c2vrg5lz+u7czu7d/udw8auo4vyw3wcxj1fap5ljeviecjw8nitpql7zld2+nfuufky3i6bfhcxdd2o9eibhfi7n3nk+uyq1pesftxsuw7li9a1kltkzkkkhufx+6vziliy+qsap1x7etdmduowcstwrdvpoesiht8/fs1qk5m1kpbleyl0iyuxdynnr6fpomgvic6gvvkv7ndvimqu5yremkpglzqueqcczk2pv0hoim5cgqypqwgxi2oioynncpmoroctfv0rgox5xth0qpvs1ukictoivzcoasanahdwgag2d4g0/4sqt1ar1bh/nozsr+hmmcro8/tk6mcq==</latexit> Rotation curve shape varies with luminosity (Persic-Salucci universal rotation curve ) The shape of rotation curves varies systematically with luminosity, declining mildly at high L and rising slowly at low L: V (R) =F (L, R d ) Central density relation (lower surface brightness galaxies exhibit larger mass discrepancies) The central dynamical surface densities of galaxies is related to their central surface brightnesses: dyn (R! 0) = f[ (R! 0)] Renzo s rule (Sancisi s Law) For any feature in the luminosity profile there is a corresponding feature in the rotation curve and vice versa. (Sancisi 2004). Radial acceleration relation (Milgrom s Law) The observed centripetal acceleration is related to that predicted by the observed distribution of baryons: g obs = F(g bar ) g bar = V bar 2 R

3 Rotation curves tend asymptotically towards a constant rotation velocity that persists to indefinitely large radii: V / const M R R 2 Optical data from Rubin, Thonnard, & Ford 1978, ApJ, 225, L107 Presumably this behavior cannot persist indefinitely, but there are no clear counter-examples.

4 Cases where rotation curves were thought to perhaps be declining have so far turned out to flatten. DDO 154 de Blok et al. (2008 [THINGS]): We do not find steep declines in velocity in the outer rotation curves of NGC 3521, NGC 7793, DDO 154, and NGC Where declines are observed, they are gentler, and (within the uncertainties in rotation velocity and inclination) consistent with flat rotation curves.

5 DDO 154 inclination

6 Mass models van Albada et al. (1985) V 2 tot = V 2 disk + V 2 halo

7 Tully-Fisher: Rotation curve amplitude correlates with observed mass: star dominated HSB gas dominated LSBs Flat rotation curves continue to occur in quite small systems (e.g., Leo P with Vf ~ 15 km/s)

8 Tully & Fisher (1977) Great for distance scale work. But why does it happen? Abs. Mag. line-width

9 Observables Luminosity (must calibrate with known D) Band pass (BVRIJHK) [slope varies with band] Mass - stars, gas, stars+gas Rotation Velocity line-widths; rotation curves W 20, W50; Vflat, V2.2, Vmax inclination corrections 1/ sin(i) turbulence/non-circular motions

10 Luminosity measures Band pass slope becomes steeper from bluer to redder bands (B I H) Worry about internal extinction, especially for blue bands and highly inclined galaxies Mass Can convert luminosity to stellar mass by estimating the stellar M/L via population modeling. IMF biggest systematic uncertainty

11 What we measure Luminosity Stellar Mass Gas: HI, H2 Rotation speed line-width rotation curve NGC 6946 Uncertainties Distance Stellar M*/L HI flux, X-factor velocity dispersion inclination asymmetric drift Vp Rotation curve data from Boomsma et al (2008) [HI] Daigle et al (2006) [Ha] Blais-Ouellette et al (2004) [ Mass model built from 2MASS K-band data (SSM) Vmax Vflat Vp V2.2

12 outer (flat) velocity maximum velocity peak velocity THINGS data (Walter et al 2008)

13 Velocity estimators: Vflat THINGS data (Walter et al 2008) W20 W50 Vp Different velocity measurements correlate but are not identical. TF relations fit using linewidths will differ from those fit using resolved rotation curves. W20 W50 Vmax

14 Tully-Fisher relation H-band Luminosity Bothun et al. (1985) Sakai et al. (2001) Luminosity and line-width are presumably proxies for stellar mass and rotation velocity. line-width

15 Stellar Mass Tully-Fisher relation Bothun et al. (1985) Sakai et al. (2001) nominal M*/L (Kroupa IMF) Stellar Mass M = M L L line-width

16 Stellar Mass Tully-Fisher relation Bothun et al. (1985) Sakai et al. (2001) double M*/L Stellar Mass...but stellar mass is completely dependent on choice of mass-tolight ratio (and degenerate with distance) line-width

17 Stellar Mass Tully-Fisher relation Bothun et al. (1985) Sakai et al. (2001) nominal M*/L Stellar Mass...but stellar mass is completely dependent on choice of mass-tolight ratio (and degenerate with distance) line-width

18 Stellar Mass Tully-Fisher relation Bothun et al. (1985) Sakai et al. (2001) half M*/L Stellar Mass...but stellar mass is completely dependent on choice of mass-tolight ratio (and degenerate with distance) line-width

19 Stark, McGaugh, & Swaters et al. (2009) If you want to use Vflat, you have to observe far enough out to measure it. log log R < 0.1 OK works well as a criterion. Scatter in TF increases as threshold weakened. marginal

20 Scatter in TF relation reduced with resolved rotation curves (Verheijen 2001) Stellar Mass TF Stellar Mass Stellar Mass line-width outer (flat) velocity

21 Stellar Mass TF Low mass galaxies tend to fall below extrapolation of linear fit to fast rotators (Matthews, van Driel, & Gallagher 1998; Freeman 1999) M = M L L Stellar Mass outer (flat) velocity

22 Gas Mass TF Gas mass by itself does NOT produce a good TF relation, at least for fast rotators. M g =1.4M HI Gas Mass outer (flat) velocity

23 Stellar Mass TF M = M L L Stellar Mass outer (flat) velocity

24 Baryonic TF Adding gas to stellar mass restores a single continuous relation for all rotators. M b = M + M g Baryonic Mass Baryonic mass is the important physical quantity. It doesn t matter whether the mass is in stars or in gas. outer (flat) velocity

25 Baryonic TF Twice Nominal M*/L Now instead of a translation, the slope pivots as we vary M*/L. Baryonic Mass Scatter increases as we diverge from the nominal M*/L. outer (flat) velocity

26 Baryonic TF Nominal M*/L Now instead of a translation, the slope pivots as we vary M*/L. Baryonic Mass Scatter increases as we diverge from the nominal M*/L. outer (flat) velocity

27 Baryonic TF Half Nominal M*/L Now instead of a translation, the slope pivots as we vary M*/L. Baryonic Mass Scatter increases as we diverge from the nominal M*/L. outer (flat) velocity

28 Baryonic TF Quarter Nominal M*/L Now instead of a translation, the slope pivots as we vary M*/L. Baryonic Mass Scatter increases as we diverge from the nominal M*/L. outer (flat) velocity

29 Baryonic TF Zero M*/L Now instead of a translation, the slope pivots as we vary M*/L. Baryonic Mass Scatter increases as we diverge from the nominal M*/L. outer (flat) velocity

30 Low mass galaxies considerably expand range of the TF relation. Gas dominated galaxies can provide absolute calibration of mass scale.

31 Gotta believe the data. Biggest challenge for low mass systems is the inclination e.g., Begum et al. (2008) estimate inclinations from both optical and HI morphology. Only half agree to within 12% in sin(i).

32 Trachternach et al. (2009) Example low line-width, gas dominated galaxies with M <M g optical HI

33 D500-3 Trachternach et al. (2009) D631-7 D512-2 D575-2

34 D646-7 D575-5 Trachternach et al. (2009) D575-1 D NO SIGNAL Note that you can measure a line-width even if there is no evidence of rotation.

35 Trachternach et al. (2009) rotation curves Systematic inclination errors bias data to left of the BTFR. (A galaxy can be face-on without looking perfectly circular.) line-widths

36 Stellar Mass Tully-Fisher relation X McGaugh et al. (2000) Begum et al. (2008) Trachternach et al. (2009) Gurovich et al. (2010) McGaugh (2005) Stark et al. (2009) Begum et al. (2008) Trachternach et al. (2009) gas dominated star dominated line-width outer (flat) velocity

37 HI Tully-Fisher relation X McGaugh et al. (2000) Begum et al. (2008) Trachternach et al. (2009) Gurovich et al. (2010) McGaugh (2005) Stark et al. (2009) Begum et al. (2008) Trachternach et al. (2009) gas dominated star dominated line-width outer (flat) velocity

38 Baryonic Tully-Fisher relation: slope & scatter depend on Velocity estimator slope: x = 3.5 slope: x = 4 X McGaugh et al. (2000) Begum et al. (2008) Trachternach et al. (2009) Gurovich et al. (2010) McGaugh (2005) Stark et al. (2009) Begum et al. (2008) Trachternach et al. (2009) gas dominated star dominated M,intrinsic 0.2 M,intrinsic < 0.15 finite intrinsic scatter negligible intrinsic scatter line-width outer (flat) velocity

39 Gas dominated galaxies can provide absolute calibration of mass scale. Gas Mass gas dominated star dominated Fraction of error budget due to systematics in M*/L Stellar Mass Baryonic Mass Systematic errors in M*/L no longer dominate the error budget for galaxies with Mg > M*.

40 Gas Rich Galaxy Baryonic Tully-Fisher relation (Stark et al 2009; Trachternach et al 2009; McGaugh 2011, 2012)

41 select M g >M try fits with many different combinations of IMF and populations synthesis models M b = A V f x slope x =3.94 ± 0.07 (random) ± 0.08 (systematic) Stark, McGaugh, & Swaters (2009, AJ, 138, 392) Fixing the slope to 4 gives A = 47 ± 6M km 4 s 4

42 <latexit sha1_base64="ljejr+f9sppxtmqjguxgru6z23q=">aaacanicbvdlssnafl2pr1pfuzdubqvgqqrssc6eggvdcbvmw2hqmewn7ddjg5mjuekwbvwvn4orxq/wf/wbj203bb0wcdjndpee48wcswvzv0zhzxvtfao4wdra3tndm/cpwjjkbke2ixgkoh6wlloq2ooptjuxodjwog17o+tcbz9rivkupqhxthsbhotmzwqrtbnmirngnrrbijn0haxkhtm+wcrtuf5jlutv0j3rza5ztirwznayqm5agwbtdm0fpx+rjkchihxl2a1aseqlwchgom1ktijpjmkid2g6yzchu031kr8j/ukfjuycdwdsjgnpo/ol5akwk/9p3ut59v7kwjhrncttrx7ckypqxgjqm0gj4mmnmbfmx4jieosolk6tpknxf4mua/u8clmx7mvlrn3wqrgo4bjooaox0ibbaiinbf7gdt7hy3g2xo1342nqlrizp4cwn8b3h1+xlgi=</latexit> <latexit sha1_base64="yg5pcubjlezfmhgevhlmsm5swnk=">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</latexit> a=0.8 V f 4 Slope 4 corresponds to an acceleration: hai =1.24 ± ms 2 GM b McGaugh (2011, 2012) selected gas rich galaxies histogram: data line: distribution expected from observational uncertainties. The data are consistent with zero intrinsic scatter. M < 0.15 dex

43 NGC 2403 UGC 128 Size/surface brightness variations from TF

44 No residuals from TF with size or surface density Same (M,V) but very different size and surface density which is strange, since V 2 = GM R

45 No residuals from TF with size or surface brightness (Zwaan et al 1995; Sprayberry et al 1995; McGaugh & de Blok 1998)

46 TF already edge-on projection of disk fundamental plane No residuals from TF with size or surface density for disks V 2 = GM R log(v ) log(r) = 1 2 expected slope (dotted line) Note: large range in size at a given mass or velocity

47 Baryonic TF Relation Fundamentally a relation between the baryonic mass of a galaxy and its rotation velocity M b = M* + Mg = 47 Vf 4 (McGaugh 2012) doesn t matter if it is stars or gas Intrinsic scatter negligibly small Can mostly be accounted for by the expected variation in stellar M*/L Physical basis of the relation remains unclear Relation has real physical units if slope has integer value - Slope appears to be 4 if Vflat is used.