Comparison of Dark Matter Proportions Across Types of Spiral Galaxies
A large obstacle on the path to better understanding the evolution of the Universe is knowing the extent to which “nature” and “nurture” affect structures in our Universe. Recent studies have observed that many galactic properties such as luminosity and morphology are dependent on their environment and in particular, their halos, from the galactic cluster scale down to galaxy groups. In this study, we investigate the relationship between dark matter (as a fraction of the total mass of the galaxy) and morphology of individual galaxies to determine if a similar relationship between galaxies and their environment exists at this scale. Our approach differs in the sense that we look at the proportion rather than the actual value of the characteristic we are studying to control for the size of the galaxies. We select the sample from Sa, Sb, and Sc type galaxies, where the spiral arms of Sa galaxies are the tightest and those of Sb, Sc are increasingly more unwound. While unable to statistically prove due to the sample size, an increasing trend in the dark matter fractions was observed between Sa and Sb type galaxies apart from NGC 4594. Little to no trend was discernable in dark matter between Sb and Sc type galaxies. We suggest a larger sample size and controlling for the environment in future experiments.
The current cosmological model of the early formation of stars and galaxies in the Universe involves dark matter, a type of theorized matter that interacts only through the gravitational force and possibly the weak force, that grouped together to form halos that provided a framework for the structure of the Universe. Clouds of baryonic gas converged in these dark matter halos in the early Universe. As more gas was accumulated through mergers and fell into the halos, the gas formed rapidly spinning disks that were the first protogalaxies. Astrophysicists today continue to study dark matter halos and their evolution to better understand their role in forming the different types of galaxies we observe.
Galaxies are sorted by their structure into morphological classes using criteria established by Edwin Hubble and others (Hubble, 1926; van den Bergh, 1960a, 1960b). Studying the shape and structure of galaxies can provide valuable information about their birth and evolution. As advancements have been made over the past decades in the observation techniques and instruments used to study galaxies, astrophysicists have been able to study galaxies in more depth across the electromagnetic spectrum. Identifying galactic structure from multiple wavelengths has brought about a broader and more detailed classification of galaxies in the Universe.
The bottom-up theory of structure formation in the Universe argues that galaxy groups and clusters formed from smaller structures and grew through mergers and other interactions between structures (White, & Rees, 1978). In the past 40 years, it has become more apparent that galactic properties such as morphology and luminosity are linked to their environments (Postman, & Geller, 1983; Zabludoff, & Mulchaey, 1998). Weinmann, van den Bosch, Yang and Mo (2006) found relationships between galaxy properties and halo mass scale smoothly from clusters to groups, providing evidence towards the bottom-up scenario and precedence for studying the relationship between dark matter and galaxy characteristics.
In this study, we investigate the dark matter in a sample of regular spiral galaxies. We are looking to find a trend between dark matter content and morphological type. This could suggest that the influence dark matter has on the structure of the Universe begins on as small a scale as individual galaxies. To test this, we will take light data for seven different galaxies in visible wavelengths. Combined with published rotation curves data and published gas mass data, we will compute dark matter fractions for three Sa, two Sb, and two Sc type galaxies and discuss any trends observed.
Materials and Methods
The aim of this experiment is to test for a trend between morphological type and dark matter content. There are many processes the light data and rotational velocity data go through to produce dark matter fractions, so it is important to be cognizant of the uncertainty present in the calculations. To minimize uncertainties, we control as many factors as possible. Controlled factors are as follows:
Johnson-Cousin Filter Images:
We take all filtered photometric data in Johnson-Cousins B, V, and R filters (Cousins, 1974a, 1974b; Johnson, 1953).
SA Spiral Galaxies:
All galaxies in the sample are unbarred spiral galaxies to eliminate uncertainty in the event that bar structures affect the dark matter fraction (or vice versa).
We adopt a value of H0 = 74.4 (kms-1)Mpc-1 for distances and radii (de Vaucouleurs et al., 1991). We adjust all distance and radii measurements using this number to produce precise and homogenized results.
Kroupa Initial Mass Function:
We calculate mass to light ratios assuming the Kroupa Initial Mass Function (IMF). This is chosen for its modernity and its low uncertainty in higher solar mass values (Kroupa, 2001).
Absolute Magnitude of Sun:
We adopt the value 4.83 for the absolute magnitude of the Sun (Williams) for magnitude and luminosity calculations.
We use the value 1.9885x1030 kg for one solar mass (Williams). This parameter is used for luminosity calculations.
We use a recently published value, 6.67408x10-11m3kg1s-2, for the Gravitational constant in dynamical mass calculations (Mohr, Newell, & Taylor, 2015).
We selected the galaxies with the aim to avoid introducing unwanted variables into the data. The profile of a “normal” spiral galaxy was adopted by looking at galaxies from Zombeck (1990, pp. 83-85). All galaxies chosen fell into the similar ranges that Zombeck observed (Table 1, Table 2):
. Mass of 109 to 1012 Solar masses
. Absolute Magnitude of -18 to -22
. Diameter of ~5 to 40 kpc
NGC 4565 has a diameter outside the range seen in Zombeck (1990) but was still included because it has been in previous studies involving dark matter (Table 1).
Three of the galaxies included in the study are Seyfert galaxies (NGC 4378, NGC 4565, and NGC 7314). Seyferts have been observed to fluctuate in luminosity over periods as long as years and as short as days because of their active nuclei (that are very luminous). This may affect the stellar mass calculations because these fluctuations come from non-stellar sources.
A summary of the observations is visible in Table 3. The 1m SARA-North Telescope operates at the Kitt Peak National Observatory in Arizona, USA, and the 0.6m SARA-South Telescope operates at the Cerro Tololo Inter-American Observatory in Chile. The galaxies studied were NGC 4378, NGC 4594, NGC 6314, NGC 2841, NGC 4565, NGC 4682, and NGC 7314 (Figure 1, Figure 2, Figure 3).
The 1m SARA-North Telescope operates at the Kitt Peak National Observatory in Arizona, USA, and the 0.6m SARA-South Telescope operates at the Cerro Tololo Inter-American Observatory in Chile. The galaxies studied were NGC 4378, NGC 4594, NGC 6314, NGC 2841, NGC 4565, NGC 4682, and NGC 7314 (Figure 1, Figure 2, Figure 3).
Radii to the 25 mag arcsec-2 surface brightness level measured in the B band were calculated manually from published values of the distance to the galaxies and their apparent size (that use the same blue 25 mag arcsec-2 criterion). The formula,
was used, where r is the radius, D is the distance in megaparsecs and θ is the apparent size of half of the major axis, in arcseconds.
Aperture Photometry Tool (APT) was employed to calculate the apparent magnitude of each galaxy. When available, we manipulate visual band images for calculating apparent magnitude, but empty filter images are used as an alternative when visual band images are unavailable. It is still valid to use empty filter images for visual apparent magnitude calculations because they do not subtract any visual band light out, and all images in APT must be calibrated to nearby stars to produce accurate results anyways. For each galaxy, we select multiple nearby stars to calibrate the apparent magnitude results by measuring their magnitudes in APT and comparing them to published visual apparent magnitude values in the WikiSky database (Wikisky.org). We then use the difference in these values to determine a zero-magnitude constant for APT.
Absolute magnitudes for each galaxy were calculated using the previously measured apparent magnitudes and published distance values. The formula,
is used, with K as the K correction constant, a value that corrects for comparing sources with different redshifts. Blain et al. (2002) addressed the use of the K-correction constant in magnitude calculations and argued that including it does not make a significant difference until redshifts of about 5. Because none of the galaxies in this study have redshifts that exceed 1, we have excluded K correction constants from the calculation of absolute magnitudes.
Since luminosity is directly related to absolute magnitude, it was simple to calculate solar luminosities. The formula reads,
where the absolute visual magnitude of the Sun is Mo.
To calculate stellar mass from luminosity, one needs a stellar mass to light ratio. If no ratio was applied and the luminosity was determined to be equal to the stellar mass, one would be assuming that every star in the galaxy observed is comparable to the Sun in the power of light it emits to the amount of mass it contains. This obviously is not the case, but it is practically impossible to take photometric counts of every star in a galaxy and determine its mass to light ratio, so astronomers have developed other methods of determining mass to light ratios for entire galaxies based on their color. We employ a formula of Bell et al. (2003) with a 0.15 dex adjustment for the Kroupa IMF,
along with published B-V color indices, to calculate stellar mass to light ratios for each galaxy. Included in the Bell et al. (2003) paper are zero point (y-intercept) adjustments for different published initial mass functions. Because we have assumed the Kroupa IMF for the galaxies, we adjusted accordingly. Once we calculated the ratios using the above formula, we multiplied the luminosity by that factor to arrive at the galaxy’s stellar mass.
As mentioned above, dynamical mass can be calculated with rotational velocity and distance from the center of the galaxy using a rearranged version of the circular rotational velocity formula,
Using published rotation curves, we calculated the dynamical mass of the galaxies using the formula,
A linear regression test was performed to test for a relationship between gas mass (by percentage) and morphological type. As the value for NGC 4682 appeared to be an outlier, a second test was performed excluding it (Table 4). An adjusted R-squared value was calculated by,
where p is the total number of explanatory variables in the model (not including the constant term), and n is the sample size. This adjusted value accounts for the small sample size in this study.
From the data, there appears to be a decrease in stellar mass content between Sa and Sb type galaxies, apart from NGC 4594 (Figure 4, Table 2). There also appears to be a slight decrease in stellar mass content between Sb and Sc type galaxies, but because of the size of the sample, the significance of this decrease cannot be tested.
We also present the variation of neutral hydrogen gas content as a function of morphological type (Figure 5). Although there appears to be an increasing trend in gas content in later type galaxies, NGC 4682 seems not to follow this trend. With all conditions met, two linear regression models were calculated: one inclusive of all the data from the sample and one that ignored the data from NGC 4682. The coefficient of determination greatly increased with the exclusion of the data point from NGC 4682. The second model produces an R-squared value of 0.84, thus 84% of the variation in gas content is accounted for by the morphological type (Table 4). While this is an indicative result, the adjusted R-squared value is a more representative number to explain the strength of correlation because it accounts for the size of our small sample. Still, at 0.63, the adjusted R-squared value shows a moderately strong positive correlation between gas content and morphological type.
We believe that the large deviation seen in the gas content of NGC 4682 is not intrinsic, but rather due to the method used to obtain that value. All other gas mass values were sourced from published papers, but the gas mass value for NGC 4682 was calculated from a proportion given in Young and Scoville (1991). In a survey of 150 galaxies, they also present a positive trend in gas content versus later morphological types. While their proportions do not agree with the data that has been collected with this sample, the similarity of their findings adds validity to this experiment.
Uncertainties were accounted for in the dark matter fractions for both uncertainties found in the published values as well as those calculated from the data taken. We use the absolute uncertainties published alongside the distances from astronomical papers cited. The relative uncertainties of these range from 0.2% to 1.3%. When using APT to calculate apparent magnitudes, an uncertainty of +/- 0.01 mag is adopted because although APT returns values with more than two decimal places, most published values only specify magnitudes to the hundredths place. Therefore, we take 0.01 as an artificial smallest increment for the uncertainty. Lastly, uncertainty in the mass to light ratios was accounted for per the note made in Bell et al. (2003) that “Scatter in the above correlations is ~0.1 dex for all optical M/L ratios...” These uncertainties were propagated through the calculations and are visible as error bars in the figure of the total mass content breakdown (Figure 1).
Considering the abnormality in the gas mass content of NGC 4682, the dark matter fractions seem to have an upwards trend towards later type galaxies, with the exception of NGC 4594 (Table 5). Because the number of galaxies from each morphological type does not exceed 10, the dark matter fractions are neither averaged nor used to conduct a statistical test as the sample size would greatly decrease the power of the test. While NGC 4594 disrupts the trend in the data, it is beneficial to the study because it opens the experiment to further investigation.
In the data that have been presented, a negative trend between stellar mass and morphological type is observed. While this trend is notable in evaluating the possible causes for a trend in dark matter content as a function of galaxy morphology within this sample, it is not universally significant. Calvi, Poggianti, Fasano, & Vulcani (2011) provided evidence that the morphological-mass relation changes with global environment and concluded that galaxy stellar mass cannot be the only factor influencing the morphological distribution of galaxies.
The validity of the luminosity data is supported by comparing the observed apparent magnitudes of the sample with published values. Most observed magnitudes were within a few tenths of a magnitude from published values, with the largest deviation being 0.9 mag (Table 6).
A positive trend in gas mass content with morphological type is observed, and disregarding data from NGC 4682 as a possible outlier, a moderately strong positive correlation is found in a linear regression model. Dark matter fractions appear to increase from Sa galaxies to Sb galaxies, except for NGC 4594. The relationship between Sb and Sc galaxy dark matter fractions is harder to discern if there is a trend at all between them.
The properties of the Seyfert galaxies in the sample appeared similar to the non-active galaxies for the most part. Although NGC 7314’s gas content fraction was less than half that of the other type Sc galaxy, NGC 4682, we have already pointed out above that the method for obtaining the gas mass value for NGC 4682 was different than the rest of the galaxies, so we do not attribute this to its active nuclei characteristics. NGC 4565 (Seyfert 1) had a comparable gas mass proportion to NGC 2841, another type Sb spiral galaxy, but a significantly lower stellar mass percentage. This is puzzling because Seyferts are noted for their luminous nuclei, which would give a larger stellar mass value. On the other hand, the Seyfert 2 galaxy NGC 4378 produced very similar proportions of gas and stellar mass as the regular type Sa galaxy, NGC 6314 (Figure 1, Table 5).
While we are unable to statistically prove that there is an increasing trend in dark matter content in later-type spirals, the results hint that there may be some authenticity to this relationship that would require further experimentation to confirm.
If this study were to be expanded on, a larger sample of galaxies would make any trends in dark matter or otherwise more apparent. As Calvi et al. (2011) found that environment was a confounding variable that affected the stellar mass-morphological distribution of galaxies, and it is also known that there are multiple correlations between galactic properties and environment (Weinmann et al., 2006), we would recommend sampling from a variety of galactic environments to eliminate this variable in the event that dark matter is also tied to environment. Radio astronomy observations could be performed to gather gas mass data from atomic hydrogen lines as well as rotation curves data to add consistency to the variables.
It is thought that in the early universe, dark matter and gas halos clustered and merged to form spiral galaxies (Coil, 2013). This study provides an opportunity to understand more about the role dark matter plays in the evolution of galaxies. As we discover more information about how different types of spiral galaxies are formed, a trend found between dark matter and galaxy morphology could be useful in predicting the life cycles of spiral galaxies.
I would like to thank Dr. Amy Lovell at Agnes Scott College for her help arranging telescope time at both Kitt Peak National Observatory and Cerro Tololo Inter-American Observatory, her training given on using these telescopes and the software necessary to process the images, and her continual support throughout this process.
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