Dynamical Imprint of Interstellar Gas on persistence of spiral - - PowerPoint PPT Presentation

Dynamical Imprint of Interstellar Gas

• n persistence of

spiral structure in galaxies

By

Soumavo Ghosh (IISc, India)

In collaboration with

Chanda J. Jog

“The Role of Gas in Galaxy Dynamics” Valletta, Malta

Why Interstellar Gas ?

(Young & Scoville, 1991)

Interstellar gas is ubiquitous in disk galaxies , especially in late-type ones

Sa ~ 5 % Sb ~ 10 % Sc~ 15 % Scd ~25 %

Problem to address

Does the interstellar gas influence the longevity of the spiral arms? —if yes, how strongly ? Where to look for the signature of interstellar gas on spiral arms? How to extract the effect of interstellar gas on spiral arms?

Why should gas make a difference?

Gas makes the system unstable against local, axisymmetric perturbations

(Jog & Solomon 1984; Bertin & Romeo 1988; Rafikov 2001)

For high gas contribution, stellar spiral features get more amplified — explanation for origin of broad stellar spiral arms

(Jog 1992)

Outline of the talk

• Inclusion of gas decreases the group velocity of the wave packet of

density wave , and hence the longevity of the spiral arms are increased to ~ few times 10^9 yrs

Ghosh & Jog, 2015, MNRAS, 434, 56

• At the observed pattern speed value, stars-alone do not give a

stable wave solution – instead one must include gas to get a stable density wave

Ghosh & Jog, 2016, MNRAS, 439, 929

Collisionless stellar disk

Qs = 1.7

(ω − Ω)2 = κ2 − 2πGΣs|k|F(s, χ)

Dispersion relation

s2 = 1 − |x|F(s, χ)

|s|= 1 implies the Lindblad resonances (ILR & OLR) Perturbations exp[i(ωt − kR)] Role of gas in supporting grand-design spiral structure

Radial Group Transport phenomenon

• Any wave packet of density wave

travels radially with its group velocity Information about group velocity can be extracted from the local dispersion relation

(Toomre 1969; Binney & Tremaine 1987)

(cg) = ∂ω/∂k

Group velocity

• can be obtained from the “slope” of the dispersion relation

cg(R) = sgn(ks)(k/kcrit)(ds/dx)

(Toomre 1969)

Lin-Shu theory proposed the ‘grand-design’ spiral arms are density waves in the disk

(Lin & Shu, 1964, 1966)

And then comes the challenge …

• One-component stellar disk
• Targeted region — solar neighbourhood
• Calculated group velocity ~ - 10 km/sec

Sufficient to destroy the spiral structure within few galactic revolutions (Toomre 1969)

Poses a challenge for the “Stationary” picture of the density wave theory !

Two-component Dispersion relation

• Addition of gas decreases the forbidden region, makes the system

more prone to being unstable

• Inclusion of more gas in the system makes the

dispersion relation ‘flat’

|s| = |(ω − mΩ)|/κ

|s| = m|(Ωp − Ω)|/κ

Dimensionless frequency

Ωp =

Pattern speed of the spiral arm

(Ghosh & Jog, 2015, MNRAS)

Group velocity

cg(R) = sgn(ks)(k/kcrit)(ds/dx)

(cg) = ∂ω/∂k

“slope” of the Dispersion relation

Lower slope implies lower group velocity — hence greater longevity of the spiral arms !

Group velocity of such a wave packet of density wave reduces by a factor of few (2 – 3)

It helps to persist the spiral structure for a relatively longer time-scale (several billion years)

(Ghosh & Jog, 2015)

is smaller for star+gas system than the star-alone case

|s|cut−off

• Stars+Gas allows a stable density wave for the observed

pattern speed, whereas stars-alone does not Perturbations exp[i(ωt − kR)]

Parameters :

Qs, Qg, ✏ |s|obs = m|(Ωp − Ω)|/κ

(Ghosh & Jog, 2016, MNARS)

We explore this new idea

Dynamical effect of gas on spiral pattern speed in galaxies

|s|obs ≥ |s|cut−off

Condition for the observed pattern speed to give a ‘stable density wave’

|s|cut−off variation with increasing gas-fraction

steadily decrease with the inclusion of more gas in the system

|s|cut−off

— indicative of the system being more prone to be unstable

Qs = 1.5 Qs = 1.7

Stars + gas allows stable density wave but stars-alone does not Particular Case : NGC 6946

(GJ’16)

(R = 2RD)

(Qg = 1.4 − 1.7)

|s| = |s|obs |s| = |s|obs

Particular Case : M 51

(R = 2RD) Qs = 1.6 Qs = 1.7

Stars + Gas allows a stable density wave but the stars-alone does not

(GJ’16)

A similar trend is shown to hold true for the Galaxy also

(Ghosh & Jog, 2017, IAU Symposium Proceeding)

(Qg = 1.4 − 1.7)

|s| = |s|obs |s| = |s|obs

Take Home

• Inclusion of gas decreases the group velocity by a factor of few

(factor of 2-3)

— helps the spiral arms to survive for relatively longer time (several billion years)

• Addition of gas is necessary to get a stable density wave,

corresponding to the observed pattern speed

(Ghosh & Jog, 2015, MNRAS) (Ghosh & Jog, 2016, MNRAS)