Angular Momentum Content in Gas-rich Dwarf Galaxies Aditya Chowdhury Jayaram N. Chengalur National Centre for Radio Astrophysics February 7, 2017 Origin of Angular Momentum in Galaxies I Tidal torquing in early universe [Hooyle (1949); Peebles 2=3 (1969); Shaya & Tully (1984); etc] : jH = kMH 1=2 jH jEH j 5=3 I λ = 3=2 independent of mass (EH ≈ MH ). Captures GMH details of tidal torquing process via k. 2 aφ I λ ≈ : Measure of rotational support. Collapse of gas ag occurs preserving angular momentum till rotation balances gravitational force. I Dark Matter and Gas mixed up till turnaround when the 0 2=3 galaxy collapses into the halo : jb = jH = k(λ)MH (Oversimplified version:) Evolution of Angular Momentum in Galaxies I From N-body simulations λ follows a log normal distribution independent of mass (as expected!) and environment [Bullock et al. 2001; Macci et al. 2007; Bettet al. 2007] 0 2=3 I At early epochs : jb = jH = k(λ)MH I MH related to baryon mass via : Mb = fbMH I Subsequent evolution of angular momentum via mergers, outflows, etc captured in an angular momentum retention fraction 0 −2=3 2=3 jb = fj jb = fj fb k(λ)Mb The Specific Angular Momentum - Mass Correlation Romanowsky & Fall (2012) Motivation to Study Gas Rich Dwarf Galaxies I Obreschkow & Glazebrook (2014) found a tight correlation between j-M-β for spiral galaxies in the THINGS sample. I They used 3.6 micron, HI, CO maps to measure angular momentum. I Interesting to do similar exercise for dwarfs. I Progenitors to larger galaxies in hierarchical galaxy formation scenario. I Baryonic feedback mechanisms proposed to advert the "angular momentum catastrophe" in N-body simulations. I Feedback more effective in dwarfs with shallower potential wells. I Measurements of gas rich dwarfs more precise because of negligible uncertainty coming from stellar light-to-mass conversion. The Sample Gas rich galaxies in the local group Galaxy Telescope Distance (Mpc) Mgas =M∗ DDO 154 VLA 4.04 ± 0.03 51 DDO 133 VLA 5.11 ± 0.09 23 NGC 3741 WSRT 3.24 ± 0.05 41 UGCA 292 GMRT 3.77 ± 0.06 8 ANDROMEDA IV GMRT 7.18 ± 0.14 14 Distances measurements using fits to the tip of red giant branch (TRGB) from Cosmicflows-2 (Tully et. al. 2013), except DDO 154 which was derived in Jacobs et. al. 2009. Data Analysis I Standard procedures in CASA (Shaw et al. (2007)) : Flagging, calibration, continuum subtraction and clean. I A tilted ring model was fit to each cube using FAT - Fully Automated TiRiFiC, Kamphuis et al. (2015). Rogstad et. al.(1974) Data Analysis I FAT gives as output the variation of rotation velocity, face-on surface brightness profile, inclination and position angle. I It also gives moment 0 map (integrated flux) and moment 1 map (velocity field) generated using SoFiA along with the residual cube (model cube - data cube) Rogstad et. al.(1974) Computation of Angular Momentum Z R J(R) = dr 2πr [Σgas (r) + Σ∗(r)] v(r)cos fδi(r)g r 0 Z R M(R) = dr 2πr [Σgas (r) + Σ∗(r)] 0 J(1) j = M(1) Primary measurements required : I Σgas (r) : Surface mass density of gas I Σ∗(r) : Surface mass density of stars I v(r) : Rotation Velocity I Σgas (r) : Surface mass density of gas I HI mass directly inferred from emission strength I Error on HI mass from error in surface brightness profile q Pr+∆r 2 I σΣgas (r) = cos i(r) r (Σmodel − Σdata) I Helium abundance (Izotov et. al. 2014) : (MHI + MHe )=MHI = 1:342 ± 0:004 I Negligible molecular gas in dwarfs (Taylor et al. 1998; Cormier et al. 2014) I Σ∗(r) : Surface mass density of stars I Exponential disk fits taken from literature, error in parameters ignored. I Error in distance contributes to error in r. Computation of Angular Momentum and Error Budget I v(r) : Rotation Velocity q Pr+∆r 2 I σv (r) = r (vmodel − vdata) = sin i(r) I Σ∗(r) : Surface mass density of stars I Exponential disk fits taken from literature, error in parameters ignored. I Error in distance contributes to error in r. Computation of Angular Momentum and Error Budget I v(r) : Rotation Velocity q Pr+∆r 2 I σv (r) = r (vmodel − vdata) = sin i(r) I Σgas (r) : Surface mass density of gas I HI mass directly inferred from emission strength I Error on HI mass from error in surface brightness profile q Pr+∆r 2 I σΣgas (r) = cos i(r) r (Σmodel − Σdata) I Helium abundance (Izotov et. al. 2014) : (MHI + MHe )=MHI = 1:342 ± 0:004 I Negligible molecular gas in dwarfs (Taylor et al. 1998; Cormier et al. 2014) I Error in distance contributes to error in r. Computation of Angular Momentum and Error Budget I v(r) : Rotation Velocity q Pr+∆r 2 I σv (r) = r (vmodel − vdata) = sin i(r) I Σgas (r) : Surface mass density of gas I HI mass directly inferred from emission strength I Error on HI mass from error in surface brightness profile q Pr+∆r 2 I σΣgas (r) = cos i(r) r (Σmodel − Σdata) I Helium abundance (Izotov et. al. 2014) : (MHI + MHe )=MHI = 1:342 ± 0:004 I Negligible molecular gas in dwarfs (Taylor et al. 1998; Cormier et al. 2014) I Σ∗(r) : Surface mass density of stars I Exponential disk fits taken from literature, error in parameters ignored. Computation of Angular Momentum and Error Budget I v(r) : Rotation Velocity q Pr+∆r 2 I σv (r) = r (vmodel − vdata) = sin i(r) I Σgas (r) : Surface mass density of gas I HI mass directly inferred from emission strength I Error on HI mass from error in surface brightness profile q Pr+∆r 2 I σΣgas (r) = cos i(r) r (Σmodel − Σdata) I Helium abundance (Izotov et. al. 2014) : (MHI + MHe )=MHI = 1:342 ± 0:004 I Negligible molecular gas in dwarfs (Taylor et al. 1998; Cormier et al. 2014) I Σ∗(r) : Surface mass density of stars I Exponential disk fits taken from literature, error in parameters ignored. I Error in distance contributes to error in r. Example Galaxy - ANDROMEDA IV (a) Moment 0 (Total Intensity) (b) Moment 1 (Velocity Field) (e) Total Angular Momentum within Radius r 0.7 gas 200 " 200 " star 0.6 100 " 100 " 0.5 0.4 0 " 0 " km/s pc) ⊙ M 0.3 14 10 -100 " -100 " J ( 0.2 0.1 -200 " -200 " 0.0 -200 " -100 " 0 " 100 " 200 " -200 " -100 " 0 " 100 " 200 " 0 1000 2000 3000 4000 5000 6000 7000 8000 r (pc) (c) Surface Mass Density (d) Rotation Curve (f) Total Mass Within Radius r gas observed velocity gas 50 40 7 star star ) 2 − 35 6 pc 40 ⊙ ) ⊙ 30 M 5 M 7 30 10 25 4 20 3 20 Velocity (km/s) Velocity 15 Total Mass ( 2 10 10 Surface Mass Density ( 1 5 0 0 0 0 1000 2000 3000 4000 5000 6000 7000 8000 0 1000 2000 3000 4000 5000 6000 7000 8000 0 1000 2000 3000 4000 5000 6000 7000 8000 r (pc) r (pc) r (pc) The systematic velocity of the galaxy centre is 256.8 km/s. Moment 1 contours are 10km/s apart. j-M-β Correlation for Spirals h i h i Mb jb β = k1 lg 1010M◦ + k2 lg 103 kpc km s−1 + k3 Obreschkow & Glazebrook (2014) Error in the j-M-β Correlation for Spirals I No errors available on specific angular momentum for spirals 7 I Bootstrap resampling (10 ) to estimate confidence bands. THINGS spirals from Obrescchkow & Glazebrook (2014) Gas rich dwarfs 95% confidence surfaces 1.0 0.8 0.6 0.4 β 0.2 0.0 −0.2 −0.4 3.5 3.0 7.5 2.5 8.0 8.5 j 9.0 2.0lg 9.5 pcKm/s M 10.0 1.5 lg 10.5 M◦ 11.0 11.51.0 A. Chowdhury & J.N. Chengalur (MNRAS, accepted) Gas rich dwarfs have higher specific angular momentum ! A. Chowdhury & J.N. Chengalur (MNRAS, accepted) 5 best fit Obreschow beta<0.05 95% confidence band 4 Gas Rich Dwarfs 3 j kpc km/s lg 2 1 0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 lg M M ⊙ lg jb = c1 lg Mb + c2β + c3 Gas rich dwarfs have higher specific angular momentum ! A. Chowdhury & J.N. Chengalur (MNRAS, accepted) 5 best fit Obreschow beta<0.05 95% confidence band 4 Gas Rich Dwarfs 3 j kpc km/s lg 2 1 0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 lg M M ⊙ −6 Psame < 10 Interpretation - Lower Baryon Mass Fraction and Supernovae Feedback −2=3 2=3 jb = fj fb k(λ)Mb I A decrease in fb that does not affect fj I Escape of baryons from the shallow dwarf potential wells during reheating and reionisation [Gnedin 2000; Crain et al. 2007] I Supernovae feedback biased towards removing low angular momentum material [Governato et al. 2010; Guedes et al. 2011] I Dwarf galaxies have shallow potential wells leading to increased efficiency of feedback. I van den Bosch et al. (2001) found a small fraction of material having low specific angular momentum in dwarf galaxies. (observational evidence!) Interpretation - Cold Mode Accretion −2=3 2=3 jb = fj fb k(λ)Mb I Enhanced fj I Keres et al. (2005) showed that two kinds of accretion operate in the galaxy formation epoch - (i) Hot mode (ii) Cold mode I "Cold mode" anisotropic as compared to "Hot mode" - may lead to an increase in angular momentum [e.g Stewart et al.