Angular Momentum Content in Gas-Rich Dwarf Galaxies

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 |EH | 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 {δi(r)} r 0 Z R M(R) = dr 2πr [Σgas (r) + Σ∗(r)] 0 J(∞) j = M(∞)

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

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 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 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

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

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. (2011); Kimm et al. (2011); Pichon et al. (2011); Danovich et al. (2015)]

10.3 I ”Cold mode” accretion dominates in Mb < 10 M galaxies [Keres et al. (2005)] Summary

I Gas Rich dwarf galaxies have more speciﬁc angular momentum at a given mass than larger spirals.

I Possible Mechanisms include

I Baryon loss due to reheating/reionization or supernovae feedback. I Cold-mode gas accretion from ﬁlaments enhances speciﬁc angular momentum.

I Future HI surveys can further populate the j-M plane leading to distinct regions in the plane that helps us understand galaxy evolution. Angular Momentum Table

Galaxy M∗ Mgas Mb J∗ Jgas Jb jb lg M lg M km/s kpc lg km/s kpc +0.07 +0.06 +0.09 +0.09 +0.08 DDO 154 7.16 8.64−0.08 8.65−0.08 11.90 13.91−0.11 13.92−0.11 2.27−0.10 +0.09 +0.08 +0.11 +0.10 +0.09 DDO 133 7.63 8.48−0.12 8.54−0.10 12.70 13.54−0.15 13.60−0.13 2.06−0.11 +0.08 +0.08 +0.11 +0.11 +0.10 NGC 3741 7.17 8.35−0.10 8.37−0.10 10.75 13.49−0.15 13.49−0.15 2.11−0.13 +0.11 +0.10 +0.15 +0.14 +0.13 UGCA 292 6.32 7.76−0.14 7.78−0.13 10.87 12.08−0.23 12.10−0.21 1.33−0.19 +0.07 +0.07 +0.09 +0.09 +0.07 AND IV 7.39 8.53−0.09 8.56−0.08 11.87 13.72−0.11 13.73−0.11 2.17−0.09 Independent Corroboration

Butler et. al. (2016) Distribution of c0 Distribution of c1 Distribution of c2 Calculation of Psame

1.0

0.8

0.6

0.4 Normalized Counts

0.2

0.0 0 1 2 3 4 5 No of points intersected DDO 154

400 " (a) Moment 0 (Total Intensity) 400 " (b) Moment 1 (Velocity Field) (e) Total Angular Momentum within Radius r gas 1.0 300 " 300 " star

200 " 200 " 0.8

100 " 100 "

0.6

0 " 0 " km/s pc) ⊙ M 14 -100 " -100 " 0.4 10 J ( -200 " -200 " 0.2 -300 " -300 "

-400 " -400 " 0.0 -400 " -300 " -200 " -100 " 0 " 100 " 200 " 300 " 400 " -400 " -300 " -200 " -100 " 0 " 100 " 200 " 300 " 400 " 0 2000 4000 6000 8000 10000 12000 r (pc) (c) Surface Mass Density (d) Rotation Curve (f) Total Mass Within Radius r gas observed velocity gas 8 star 50 50 star ) 2 − pc

⊙ 40 40 ) ⊙ M 6 M 7

30 10 30

20 20 Velocity (km/s) Velocity Total Mass ( 2 10 10 Surface Mass Density (

0 0 0 0 2000 4000 6000 8000 10000 12000 0 2000 4000 6000 8000 10000 12000 0 2000 4000 6000 8000 10000 12000 r (pc) r (pc) r (pc)

The galaxy has a warp and its inclination varies between 50◦ to 70◦. The systematic velocity of the galaxy centre is 352.0 km/s. DDO 133

(a) Moment 0 (Total Intensity) (b) Moment 1 (Velocity Field) (e) Total Angular Momentum within Radius r gas 200 " 200 " star 0.4

100 " 100 "

0.3

0 " 0 " km/s pc) ⊙ M

14 0.2 10

-100 " -100 " J (

0.1

-200 " -200 "

0.0 -200 " -100 " 0 " 100 " 200 " -200 " -100 " 0 " 100 " 200 " 0 1000 2000 3000 4000 5000 r (pc) (c) Surface Mass Density (d) Rotation Curve (f) Total Mass Within Radius r 60 40 gas observed velocity gas star star

) 10 35 2 50 − pc

⊙ 30 )

8 ⊙ M 40 M 7 25 10 6 30 20

15 4 (km/s) Velocity 20 Total Mass ( 10 2 10 Surface Mass Density ( 5

0 0 0 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 r (pc) r (pc) r (pc)

The galaxy has a low inclination of 29◦. The systematic velocity of the galaxy centre is 330.2 km/s. NGC 3741

(a) Moment 0 (Total Intensity) (b) Moment 1 (Velocity Field) (e) Total Angular Momentum within Radius r gas 300 " 300 " 0.40 star 0.35 200 " 200 "

0.30 100 " 100 " 0.25

0 " 0 " km/s pc) ⊙ 0.20 M 14

-100 " -100 " 10 0.15 J (

-200 " -200 " 0.10

0.05 -300 " -300 " 0.00 -300 " -200 " -100 " 0 " 100 " 200 " 300 " -300 " -200 " -100 " 0 " 100 " 200 " 300 " 0 1000 2000 3000 4000 5000 6000 7000 r (pc) (c) Surface Mass Density (d) Rotation Curve (f) Total Mass Within Radius r gas observed velocity gas 25 star 50 star

) 25 2 −

pc 20 ⊙ 40 ) ⊙

M 20 M 7

15 30 10 15

10 20

Velocity (km/s) Velocity 10 Total Mass (

5 10 5 Surface Mass Density (

0 0 0 0 1000 2000 3000 4000 5000 6000 7000 0 1000 2000 3000 4000 5000 6000 7000 0 1000 2000 3000 4000 5000 6000 7000 r (pc) r (pc) r (pc)

The galaxy has a warp and its inclination varies between 65◦ to 75◦. The systematic velocity of the galaxy centre is 223.7 km/s. UGCA 292

100 " (a) Moment 0 (Total Intensity) 100 " (b) Moment 1 (Velocity Field) (e) Total Angular Momentum within Radius r gas star 0.015 50 " 50 "

0.010

0 " 0 " km/s pc) ⊙ M 14 10 J ( -50 " -50 " 0.005

-100 " -100 " 0.000 -100 " -50 " 0 " 50 " 100 " -100 " -50 " 0 " 50 " 100 " 0 500 1000 1500 2000 2500 r (pc) (c) Surface Mass Density (d) Rotation Curve (f) Total Mass Within Radius r 8 30 gas observed velocity gas 40 star 7 star ) 2

− 25 35

pc 6 ⊙ ) ⊙ M 30

20 M

7 5

25 10 15 4 20 3 10 (km/s) Velocity 15 Total Mass ( 2 10 5 Surface Mass Density ( 5 1

0 0 0 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 r (pc) r (pc) r (pc)

The galaxy has a low inclination of 19◦. The systematic velocity of the galaxy centre is 282.4 km/s. 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 "

− 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 galaxy has an inclination of 55◦ with no visible sign of warps. The systematic velocity of the galaxy centre is 256.8 km/s