Preliminary Exploration of Areal Density of Angular Momentum for Spiral Galaxies

Lan Zhang ,Feilu Wang,2 ,Xiangxiang Xue,3 ,David Salzmann ,Baifei Shen ,Zehao Zhong ,and Gang Zhao,2

1 CAS Key Laboratory of Optical Astronomy,National Astronomical Observatories,Chinese Academy of Sciences,Beijing 100101,China;wfl@bao.ac.cn

2 School of Astronomy and Space Science,University of Chinese Academy of Sciences,Beijing 101408,China

3 Institute for Frontiers in Astronomy and Astrophysics,Beijing Normal University,Beijing 102206,China

4 Department of Physics,Shanghai Normal University,Shanghai 200234,China

Abstract The specific angular momenta (jt) of stars,baryons as a whole and dark matter halos contain clues of vital importance about how galaxies form and evolve.Using a sample of 70 spiral galaxies,we perform a preliminary analysis of jt,and introduce a new quantity,e.g.,areal density of angular momentum(ADAM)(jt M? (2 Rd)2)as anindication for the existence of jet(s) in spiral galaxies.The percentage of spiral galaxies having jet(s) shows a strong correlation with ADAM,although the present sample is incomplete.

Key words: galaxies: jets– galaxies: spiral– galaxies: statistics

1.Introduction

The first evidence of jet-like features emanating from the nuclei of galaxies goes back to the discovery by Curtis (1918)of the optical jet from the elliptical galaxy NGC 4486(M87)in the Virgo cluster.According to the definition of Bridle &Perley (1984) for extragalactic jets,the term “jets” is used to designate collimated ejecta that have opening angles ≤15°.

Jets of matter occur in many astrophysical situations,but can broadly be classified into two types: stellar jets and galactic jets.Stellar jets are generated by a number of different sources,such as T Tauri stars,planetary nebulae,neutron stars and stellar black holes (BHs).Galactic jets,however,are believed to have only a single source,namely,a supermassive black hole(SMBH) at the center of the galaxy.

Many attempts have been made to understand the formation of galactic jets by testing various relations among the physical and observational properties of the host galaxy and its central SMBH.Several options for such relations have been suggested in the literature,

1.correlation between jet properties and central BH mass/spin/accretion rate,e.g.,Laor(2000),Dotti et al.(2013),Narayan &Yi (1995);

2.correlation between jet properties and accretion disk spin,e.g.,Natarajan &Pringle (1998),Ho &Peng (2001),King et al.(2013a);

3.correlation between jet formation and magnetic fields,e.g.,Asada et al.(2002),Takabe et al.(2008).

Fully evolved relativistic jets have traditionally been associated with high-mass elliptical galaxies hosting the most massive BHs,but Vietri et al.(2022) confirmed that also less massive BHs in spiral galaxies could launch and sustain powerful jets,implying that the launching of the jets is governed by factors other than those mentioned previously.

The role that angular momentum in galaxies plays in the jet properties is little understood,although it is believed to control the kinematics of their stars,which on the other hand drives observable quantities such as the apparent radius,the bulge fraction and the alignment with other nearby structures(Cimatti et al.2020).The galactic angular momentum originates from the initial spin,and is lost during mergers.It plays a major role in galaxy formation and evolution and is closely related to the coupling between dark and visible matter (Li et al.2022).The primary goal of this paper is to study the correlation between the presence of jet(s) and various physical quantities.

2.jt ?M?Diagram for Spiral Galaxies

Our sample consists of 67 spiral galaxies in Table 4 of Romanowsky &Fall (2012),whose bulge-to-total mass ratiosB/Trange from 0.0 to 0.6,that correspond to Sc(pure disks)to S0,and three spiral galaxies,in order to extend the stellar mass range of samples in this study.These are the Milky Way,2MASX J23453268-0449256 (hereafter J2345-0449) with large stellar mass and NGC 4395 with small stellar mass,which were added to construct our sample.

Following Romanowsky &Fall (2012),the total specific stellar angular momenta(jt,in the unit of km s?1kpc)of all the samples are calculated by

wherefbis the bulge stellar mass fraction andjbandjdare intrinsic values of specific stellar angular momentum of bulgeand disk components,respectively.Bothjbandjdare calculated from the values along the projected semimajor axis of galaxies(jp,bandjp,d).For the bulge part,

wherevs,bis the observed rotation velocity of the bulge,kn～1–5 is a numerical coefficient that depends on the Sérsic indexnof the galaxy (Equation (A31) in Romanowsky &Fall 2012) andae,bis the effective radius along the semimajor axis.While for the disk component,

whereRdis the intrinsic exponential-disk scale length,vcis the intrinsic circular rotation velocity of the disk,based on the rotation curves over the range (2–3)Rd,andiis the inclination.Then the intrinsic values ofjare converted by the deprojection factorCiwhich are correlated withi,

For the bulge component,

and for the disk component,

For the Milky Way,NGC 4395 and the giant radio source J2345-0449,theirjtare calculated by using Equation (1) and observable data from literature studies,which are listed in Table 1.

Table 1Observations used in jt Calculation

The stellar specific angular momentum-mass relation was first studied by Fall (1983).Follow-up studies confirmed the relation with more and better data (e.g.,Romanowsky &Fall 2012;Posti et al.2018;Fall &Romanowsky 2018).However,no previous literature studies explore whether the jets can effect the relation or not.For better understanding the role of jets in the stellar specific angular momentum-mass relation,especially for spiral galaxies with jets,we modeledjt(jt,mod)as a function ofM?in log ?log space for samples both with and without jets

We carried out a Markov chain Monte Carlo (MCMC)calculation to explore the relation and the uncertainties of the fitted parameters α and β,for three groups of our sample,that is,(a) all the sample galaxies;(b) all possible jetted galaxies;(c) all possible jetted galaxies excluding NGC 3898,NGC 4258,NGC 4736 and NGC 5033,because the jets of these four galaxies are still in doubt (Baldi et al.2021).

The fitting also does not include NGC 4395 since its mass is much lower than the others and is an irregular galaxy whose gas component seems to dominate (Repetto et al.2017).Our fitting results for three groups are shown in Figure 1 and Table 2.

Figure 1.The total angular momenta of our sample vs.their stellar mass.For all plots,black dots are observation data,while galaxies with jets are marked with red circles.Thick lines are best fits of log jt ? log relations.Star symbols indicate NGC 4395,which was excluded during the fittings.Red,blue and green represent that its jt is calculated with stellar mass and velocity,gas mass and velocity,and total baryonic mass and velocity,respectively.The shaded area of each line indicates 1σ fitting error range.(a) features the fitting results of all spiral galaxies in the present study;(b) displays the fittings for all possible spiral galaxies with jets;(c) is similar to (b),but with the assumption that NGC 3898,NGC 4358,NGC 4736 and NGC 5033 are spiral galaxies without jets.

Table 2Fits to Stellar Mass and Specific Angular Momenta

3.Percentage of Galaxies with Observed Jet(s)

After cross-matching the samples with recent radio-and X-ray observation studies (e.g.,King et al.2013b;Baldi et al.2021),13 galaxies are labeled as ones with jets.Among them,there are nine galaxies with the presence of a jet or jets in the observations,i.e.,NGC 2639 (Sebastian et al.2019),NGC 3031(M81)(Baek et al.2019),NGC 4395(King et al.2013b),NGC 4594(M104)(Hada et al.2013),NGC 2841(Baldi et al.2018),NGC 3198 (Baldi et al.2018),NGC 7217 (Baldi et al.2018),J2345-0449 (Bagchi et al.2014) and the Milky Way(Cecil et al.2021).For the other four galaxies,NGC 4258(M106)was identified as a galaxy with jet in Cecil et al.(2000),however,in the recent study of Baldi et al.(2021),the jet morphology of NGC 4258 (M106),as well as those of NGC 3898,NGC 4736 and NGC 5033,were uncertain.Therefore,NGC 3898,NGC 4258,NGC 4736 and NGC 5033 may not be galaxies with jets (Baldi et al.2021).

Figure 2 gives the percentage of galaxies with jet(s) in our sample to find a better indication for the existence of a jet in spiral galaxies.Here we introduce a new quantity,e.g.,the areal density of angular momentum(ADAM),which is defined byjtM?(Reff)2,whereReffis the effective radius of the stellar mass.For the present samples,we take 2Rdas the effective radius.Therefore,the ADAM adopted in this work isjtM?(2Rd)2.In order to ensure the percentage is statistically significant,the number of samples in eachjtor ADAM bin is more than or equal to 3.Comparingjtwith ADAM,the latter seems to be a better indicator of the presence of a jet,since the percentage is lower than 20% when ADAM is less than 1012km s?1M⊙kpc.What makesjta quantity of great astrophysical importance is not only its relation to the baryonic matter content of galaxies,but also its connection with galactic jet(s).

Figure 2.The percentage of galaxies having jet(s) in the sample as a function of the specific angular momenta jt (in red,upper scale) and those having ADAM (in blue,lower scale).

The present results are preliminary.First,our samples are limited to spiral galaxies.As far as we know,more jets are launched in elliptical galaxies.However,spiral galaxies have,on average,higher angular momentum than elliptical ones for a given stellar mass(Fall 1983;Cadiou et al.2022).Second,our galaxy sample is neither statistically complete nor the average distribution of the parameters,e.g.,stellar mass,BH mass andjt.In addition,the scale of jets is not taken into account,which is from several pc to 102–103kpc.It may matter,since the relation of accretion mass with the jet luminosity seems to be valid for kpc-scale jets,but not for pc-scale cases (Panessa &Giroletti 2013).

As to the possible relation between the ADAM and the jet,it is well known that a tornado can suck matter on Earth and a solar storm is related to magnetic helicity.We carried out a numerical simulation by putting plasma in an axial magnetic field and a radial electrical field which could be formed by a quick shrink.In the real case the electric field could be replaced with the gravitational force.In simulation,we find the particles rotate around the axis and jets are emitted along the axis (Qiu et al.2018).The rotation of the particles can also be driven by a twist in a laser pulse.In that case,jets are also observed in simulation (Wang et al.2019).

Acknowledgments

We thank Dr.Lin Zhu and Dr.Dawei Xu for useful suggestions and discussions,and the anonymous referee for helpful comments.This work is supported by the National Natural Science Foundation of China (NSFC,grant Nos.11988101 and 12073043) and National Key Research and Development Program of China No.2019YFA0405500.L.Z.and X-X.X.acknowledge the support from CAS Project for Young Scientists in Basic Research grant No.YSBR-062.