On Quantum-Mechanical Measurements and Processes Of

Difference between Dynamical Masses and Stellar Masses of the Bulge in Spiral Galaxies

Ismaeel A. Al-Baidhany1, Sami Salman Chiad2, Wasmaa A. Jabbar3, Nadir Fadhil Habubi4*, Khalid Haneen Abass5

Abstract This work aims to study the difference between bulge dynamical masses and bulge stellar masses for Spitzer/IRAC 3.6 μm images of 41spiral galaxies. The ratio between the stellar and dynamical masses for the spiral galaxies were studied using the virial relation and mass to light ratio (M*/Lbulge) to find M⋆and Mdyn masses respectively. We found the dynamical mass was found applying the virial relation with the virial coefficient (K = 5). We obtained a stellar velocity dispersion from the literature .We obtained the bulge effective radius (re) using 2Ddecompostion of Spitzer/IRAC at 3.6 µm images. The stellar mass M⋆ of each galaxy measured using the bulge luminosity and (M*/Lbulge) ratio.

Key Words: Dynamical Mass, Stellar Mass, Bulge Luminosity, Mass to Light Ratio. DOI Number: 10.14704/nq.2020.18.1.NQ20110 NeuroQuantology 2020; 18(1):76-82 76 Introduction Several previous studies have found the unphysical history of forming of stars and attenuation of the result that the stellar masses (M⋆) of many galaxy dust. It thought that the uncertainty on host bulges arebigger than their dynamical masses galaxiescouldproduce an error in the measurement (Mdyn). Many of authors have reported the of the masses up to factors of 2–4 [3, 4]. surprising fact that they find stellar masses greater The differentiation with stellar population than dynamical masses for some massive compact synthesis methods can be done applying a band of galaxies both at low and high z [1, 2]. wide range photometric spectral energy To measure the bulge mass, astronomers applied distribution (SED) [5]. This method has the the virial theorem, which show to be quite accurate advantage that can be applied easily at high- [2], and this method needs aaccurate of redshift [6]. spectroscopical measurement of the velocity Several methods used to find dynamical masses. In dispersion. Also, some researchers used different general, the correct techniques are depend on the method for M* by merging Lbulge with a M/L result of the equations of Poisson and Jeans [7], or according to calibrated correlations [2, 3,4]. the charactetion of the system applying an orbit- Stellar masses measurements are depend on the superposition technique [8]. The techniques are ratio ofreal data with synthetic spectra that use the expensive in terms of observing time. A cheaper current information ofspectra of the stars, alternative is to use a simple mass estimation or evolution of the stars, function ofinitial mass (IMF), according on the virial theorem [2, 9]. Corresponding author: Nadir Fadhil Habubi Address: 1Department of Physics, College of Education, Mustansiriyah University, Baghdad, Iraq; 2Department of Physics, College of Education, Mustansiriyah University, Baghdad, Iraq; 3Department of Physics, College of Education, Mustansiriyah University, Baghdad, Iraq; 4*Department of Physics, College of Education, Mustansiriyah University, Baghdad, Iraq; 5Department of Physics College of Education for Pure Sciences, University of Babylon, Iraq. 4*E-mail: [email protected] Relevant conflicts of interest/financial disclosures: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Received: 20 December 2019 Accepted: 15 January 2020

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Our study distinguished the ratio M⋆/Mdyn at the database. Second; the absolute magnitude at 3.6 µm several of the dynamical parameters of the host was calculated using the standard relation: galaxies (e.g. classical, pseudo bulge, barred, AGN, M3.6µm = m3.6µm + 5.0− 5 log D (4) non-AGN). To the best of our knowledge, this paper Where (D) is the luminosity distance in parsecs. is the first study to show the discrepancy between Third; the bulge luminosity of spiral galaxy was stellar masses and dynamical masses for a sample found using the relation [14]: of 41 spiral galaxies from Spitzer/IRAC at 3.6 µm band by applying two methods. log (L3.6µm/Lʘ) = 0.4(−M3.6µm + 3.24) (5) The resultant of the bulge luminosity of 41 spiral Methods galaxy at 3.6 µm is listed in the column 5in Table In this work, we have studied the discrepancy (1). between stellar masses and dynamical masses in 41 IRAS (3.6μm) spiral galaxies by applying two 2- Stellar mass Measurement (M*) using M/L Ratio methods: Astronomers [2, 16] found in this work a relation between optical colors of the disk of the galaxy (e.g., 1- Measurement of the bulge luminosity (Lbulge) B−V, B−R) and the ratio of stellar mass / light In this method, the mass of SMBH measurement (M*/Lbulge or γ). depend on the bulge luminosity.The value of bulge Previous researches did not find the (M/L) luminosity measured by apply a 2D (bar -bulge - measurement sat 3.6um band. In this study, we disk) decomposition program to model of images used a new correlation to measure (γ). from Spitzer/IRAC at 3.6 µm band [10]. The K 3.6µm luminosity of bulge measured of 41 galaxies images This correlation is related (γ ) and (γ ) which using the 2D multicomponent decomposition found by group of astronomers 2008 [17]: method. 3.6 = B3.6 × k × A3.6 (6) The description of bulge is by a Sersic function: 3.6 3.6 Where A = -0.05 and B = 0.921, and a relation 77 (1) related (γK), and optical colors: Where Iob is the density of central surface, hb is the Log(K ) = bk× Optical Color × ak (7) value of parameter, β=1/n with n=sérsic index. r is b e Where aK and bK are coefficients that related (γK) the effective radius), andwas obtained using: n and optical colors are shownin [2, 16]. re = (bn) hb (2) By adding Equations (6) with (7), and taking on Using the bn ≈ 2.171nb − 0.356; [33], where nbis Sersic index of the bulge. 20% solar metallicity [18], with the data ofoptical The orientation parameter wasfound using 3.6 µm colors [2, 16], and using a scaled Salpeter IMF cutting off the stars less massive than ∼0.36Mʘ, we images of spiral galaxy with MBH measurement [32]. In this work, the imagewere masked out by using measured M/L. the program of S Extractor [11], Second, the profile The resultant of the bulge stellar masses of 41 of surface brightness using the ELLIPSE routine in spiral galaxy at 3.6 µm is listed in the column 7in IRAF1 [10, 12, 13, 14]. By applying the following Table (1). formulato change unitof surface brightness to (mag arcsec-2): 3- Dynamical mass measurement (3) We described the method to measure the bulge Where: mass. The bulges dynamical masses (Mdyn) are −1 S3.6μm: the rateof flux at 3.6 μm (units of MJy sr ), measured by applying the virial theoremis[19, 20, ZP3.6μm: the zero magnitude of flux density, its value 21]: is 280.90 in Jy [15]. 2 Mdyn = K σ re/G (8) To measure the bulge luminosity, First; we used luminosity distance for M31 galaxy using the NED2 Where k is the function of Sérsic index [21, 22], we follow (Cappellari, 2006) [23] to use k=5 that shows that the value of (k) is a constant average 1 IRAF is distributed by the National Optical Astronomy Observatories, value which can measurethe accurate value of Mdyn. which is operated by the Associated Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science σ and re are the dispersion velocity and the Foundation effective radius respectively, and G is the constant 2http://nedwww.ipac.caltech.edu/

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NeuroQuantology | January 2020 | Volume 18 | Issue 1 | Page 76-82 | doi: 10.14704/nq.2020.18.1.NQ20110 Ismaeel A. Al-Baidhany, Difference between Dynamical Masses and Stellar Masses of the Bulge in Spiral Galaxies of gravitation. The resultant of the bulge dynamical masses of 41 spiral galaxy at 3.6 µm is listed in the column 6in Table (1).

Result and Discussion The dynamical mass and the stellar mass of the bulge estimated by using the model of isothermal [21], and applyinga new calibration for 3.6µm [17] are consistent within 1σ of two types of methods; no systematic offset is discovered. In addition, the dispersion velocity of the galaxies taken from the literature. Figures (1,2, 3) show two techniques producing Figure 1: Bulge Dynamical Masses as a Function of Bulge Stellar bulge dynamical and stellar masses which used to Masses. The Solid is the fit to all Sprial Galaxies measure and compares dynamical and stellar We found that the systematic difference can be as masses based on the these techniques. high as 0.68and 0.25 times. M⋆/Md is masses ratio There are several explanations which can be used dependent, higher or lower for massive bulges or to explain these figures: (1) We measured and small bulges. In this the cases, pseudo-bulges follow compared the stellar and dynamical masses for 41 a different relation, slope and the intercept spiral galaxies by using equations 1,2,3. (2) comparing with the relation for classical bulges. Measured the masses of dynamical and stellar for However the average M⋆/Md ratio is small, this AGN, non-AGN, barred galaxies. (3) Measured and difference related to the mass contribution from compared the masses of dynamical and stellar for the small bulges and massive bulges. classical bulges and pseudo-bulges galaxies. 78 Fig. (1) Shows a comparison between the bulge dynamical masses and accurate determinations of the bulge stellar masses for the 41 spiral galaxies. We fit the residual systematic difference accounting for errors in both the stellar and dynamical masses applying fitexy. pro in the IDL program. We found that the systematic difference can be as high as 1.2 times.The ratio of stellar to dynamical masses is (M⋆/ Mdyn> 1). This ratio is linked to the compactness of the most spiral galaxies. Thediscrepancy of mass is small to be caused by the accuracy of the stellar mass determination using two techniques producing bulge dynamical and stellar masses. Figure 2: Bulge dynamical masses as a function of bulge stellar masses. Figure 2 illustrates a comparison of different types The linear regression are shown as blue color and red color, of bulge mass estimates for classical bulges and respectively, for pseudo bulges, and bulges galaxies pseudo-bulges galaxies. We noted different M⋆-Mdyn In Fig 3, we shown the distributions of inferred relations obeyed by the two type of bulges Mdyn and M⋆masses for AGN (red), non-AGN (classical bulges and pseudobulges). Pseudobulges (green), and the barred galaxy (blue). These are located below the classical bulges are histograms obviously highlight the emphasized in Figure 2. variousdistributions of Mdyn and M⋆ masses. We found: AGN and non-AGN galaxies have lower Mdynand M⋆ masses than barred galaxies.

The median measurements of the Mdyn and M⋆ masses for AGN and non-AGN galaxies are similar to each other.We found that the systematic

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NeuroQuantology | January 2020 | Volume 18 | Issue 1 | Page 76-82 | doi: 10.14704/nq.2020.18.1.NQ20110 Ismaeel A. Al-Baidhany, Difference between Dynamical Masses and Stellar Masses of the Bulge in Spiral Galaxies difference (M⋆/Md ratio) can be as high as 0.62, 0.26 and 0.23 times for barred, AGN and non-AGN galaxies. In all cases, the average M⋆/Md ratio is small, this differencelinked to the contribution of bulge masses from the dark matter, the baryonic matter, stars, stellar reminants and gas.

In general, M* can be affected by dust extinction, depending on wavebands, and by the assumption of a constant M/L over the entire galaxy.

In this work, It is found that M*is easily measured than Mdyn especially at 3.6um.

Figure 4: Bulge Dynamical Masses as a Function of Sprial Arm Pitch Angles. The Linear Regression is the Fit to all Spiral Galaxies The correlations is shown in Figure (5). In Figure (5), we found that the Pearson's linear correlation coefficient for this correlation was 0.825. From Pearson's linear correlation coefficient which is 0.825, it can be concluded that most spiral galaxies, which have pseudobulges and classical 79 bulges, have a correlation between M* and P.To the Figure 3: Bulge Dynamical masses as a function of Bulge Stellar Mases. best of our knowledge, this is a new The Linear Regression are shown as Long Dash, Dash Dot Dot Dot, correlationbetween bulge stellar masses and spiral Dash Dot and Dashed, Respectively, for Barred, Nonbarred, and AGN Galaxies. arm pitch angles. In this part, the correlations betweendynamical and The linear fit of the relation is: stellar masses forbulges with spiral arm pitch angle are re-examined. These were initially determined by Al-Baidhany et al. 2017 for 41 spiral galaxies. The correlations are shown in Figures (4), and (5). In Figure (4), we found that Pearson's linear correlation coefficient for this correlation was 0.817, and the fit is a linear relation:

From Figure (4) and Pearson's linear correlation coefficient,this work confirmed the conclusion by Al-Baidhany et al. (2017) that a significant correlation exists between bulge dynamical masses and the spiral arm pitch angles.

Figure 5: Bulge Stellar Masses as a Function of Spiral Arm Pitch Angles. The Linear Regression is the Fit to all Sprial Galaxies

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NeuroQuantology | January 2020 | Volume 18 | Issue 1 | Page 76-82 | doi: 10.14704/nq.2020.18.1.NQ20110 Ismaeel A. Al-Baidhany, Difference between Dynamical Masses and Stellar Masses of the Bulge in Spiral Galaxies Table 1: Column: (1) name of galaxy. (2) Hubble type taken from the catalogue of Hyper-Leda. (3)Dispersion velocity of the bulge, references [1, 11, 19, 21, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]. (4) Spiral arm pitch angle [14, 38, 39, 40, 41]. (5) Logarithmic 3.6µm- luminosities (luminosity of the bulge) in solar units. (6) Bulge dynamical mass. (7) Stellar bulge mass. Name σ (km/sec) L (L ) M (M ) M (M ) Leda Type (2) P (deg.) (4) * ⊙ dyn ⊙ ⋆ ⊙ (1) (3) (5) (6) (7) Circinus Sb 75 26.7 9.81 9.67±0.19 9.72±0.1 IC 2560 SBb 137 16.3 10.7 11±0.4 10.7±0.2 NGC 224 Sb 160±8 8.5±1.3 10.9 10.6±0.5 10.7±0.3 NGC 613 Sbc 125.3±18.9 23.68±1.77 10.5 10.1±0.3 10.4±0.5 NGC 1022 SBa 99 19.83±3.6 10.2 10.1±0.17 10.10.14 NGC 1068 Sb 151±7 17.3±2.2 10.9 10.4±0.11 11.2±0.1 NGC 1097 SBb 150 16.7±2.62 10.8 10.6±0.13 10.8±0.4 NGC 1300 Sbc 145±22 12.7±1.8 10.6 10.5±0.08 10.6±0.1 NGC 1350 Sab 120.91±2.08 20.57±5.38 10.2 10.3±0.13 10.4±0.1 NGC 1353 Sb 83 36.6±5.4 9.62 9.11±0.73 9.43±0.3 NGC 1357 Sab 121±14 16.16±3.48 10.9 10.1±0.02 10.3±0.2 NGC 1365 Sb 151±20 15.4±2.4 10.7 10.3±0.25 10.4±0.2 NGC 1398 SBab 216±20 6.2±2 11.2 10.8±0.23 10.9±0.1 NGC 1433 SBab 84±9 25.82±3.79 9.76 9.5±0.034 10.2±0.4 NGC 1566 SAB 100±10 21.31±4.78 10.2 9.6±0.032 9.77±0.3 NGC 1672 Sb 130.8±2.09 18.22±14.07 10.2 10.1±0.57 9.93±0.3 NGC 1808 Sa 148 23.65±7.77 10.5 9.89±0.3 10.2±0.1 NGC 2442 Sbc 140.74±2.18 14.95±4.2 10.6 10.5±0. 32 10.4±0.4 NGC 3031 Sab 143±7 15.4±8.6 10.9 10.7±0.14 10.9±0.1 NGC 3227 SABa 128±13 12.9±9 10.4 10.9±0.06 10.7±0.4 NGC 3368 SABa 122±(28,24) 14±1.4 10.8 10.5±0.03 10.8±0.3 80 NGC 3511 SABc 93.56±2.04 28.21±2.27 9.81 9.51±0.13 9.58±0.1 NGC 3521 SABb 130.5±7.1 21.86±6.34 10.5 10.3±0.07 10.4±0.4 NGC 3673 Sb 117.45±2.07 19.34±4.38 10.7 10.3±0.08 10.3±0.1 NGC 3783 SBab 95±10 22.73±2.58 9.84 9.31±0.03 9.42±0.2 NGC 3887 Sbc 102.01±2.05 24.4±2.6 10.3 9.75±0.08 9.63±0.3 NGC 4030 Sbc 122.43±2.1 19.8±3.2 10.6 10.7±0.08 10.9±0.3 NGC 4151 SABa 156±8 11.8±1.8 10.7 10.3±0.07 10.5±0.3 NGC 4258 SABb 146±15 7.7±4.2 10.9 10.8±0.18 11.2±0.7 NGC 4462 SBab 146±8 17.2±5.42 10.7 10.6±0.07 10.7±0.2 NGC 4594 Sa 240±12 6.1 11.3 11.4±0.09 11.3±0,4 NGC 4699 SABb 215±10 6.2±2.2 11.4 10.7±0.06 10.8±0.2 NGC 5054 Sbc 104.48±2.05 25.57±3.73 10.4 9.9±0.13 10.2±0.3 NGC 5055 Sbc 101±5 14.9±6.9 10.5 9.84±0.37 9.95±0.5 NGC 6300 SBb 94±5 24.3±3.8 9.82 9.82±0.04 10±0.053 NGC 6744 SABb 112±25 21.28±3.8 10.86 10.3±0.19 10.3±0.5 NGC 6902 SBab 145.86±2.1 13.71±2.3 10.9 10.6±0.84 10.6±0.5 NGC 7213 Sa 185±20 7.05±0.28 11.2 11±0.048 10.9±0.4 NGC 7531 SABb 108.7±5.6 18.31±9.09 10 10.2±0.08 10.2±0.5 NGC 7582 SBab 137±20 14.7±7.44 11 10.7±0.08 10.9±0.5 NGC 7727 SABa 181±10 15.94±6.39 11.5 10.9±0.06 11.1±0.4 dynamical masses (M⋆/Mdyn> 1) is linked to the Conclusion compactness of the bulges of spiral galaxies,the mass discrepancy for most spiral galaxies is small We studied the difference between dynamical to be caused by the accuracy of the stellar mass masses and stellar masses for bulges of determination, where the stellar mass Spitzer/IRAC 3.6 μm images of 41 spiral galaxies. In determination can be both mass estimators, and the this work, we concluded that the ratio of stellar to

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NeuroQuantology | January 2020 | Volume 18 | Issue 1 | Page 76-82 | doi: 10.14704/nq.2020.18.1.NQ20110 Ismaeel A. Al-Baidhany, Difference between Dynamical Masses and Stellar Masses of the Bulge in Spiral Galaxies discrepancy ratio of stellar to dynamical masses pattern speed, stellar and dark matter mass distribution, can be explained by a variation in the compactness MNRAS, 2017; 465(2): 1621–1644. of the bulges of spiral galaxies. In general, ratio of Laurikainen E, Salo H, Buta R. Multicomponent decompositions for a sample of S0 galaxies. Monthly Notices of the Royal dark matter for spiral galaxies is small, and the Astronomical Society, 2005; 362(4): 1319-1347. variation in the dark matter fraction is a different Davies B, Origlia L, Kudritzki RP, Figer DF, Rich RM, Najarro F, with the type of galaxy or its morphology. In Negueruela I, Clark JS. 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