Analyzing the Upper Mass Boundary of Main Sequence Stars

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The maximum mass of a star is not a fixed value; it fluctuates based on conditions such as stellar winds, metallicity, and the characteristics of the molecular cloud from which the star originates. For decades, the astrophysical community has debated the existence of a maximum mass limit, with estimates typically ranging from 120 to 300 solar masses, contingent upon environmental factors and initial conditions. The formation of massive stars initiates with the gravitational collapse of gas clumps in giant molecular clouds, leading to protostar formation. This phase is characterized by non-homologous collapse, significantly influenced by magnetic fields and accretion dynamics. As material accretes onto the protostar, radiation-driven winds sculpt the surrounding environment, culminating in supernova events. This research reviews several formation mechanisms, including monolithic collapse, competitive accretion, and stellar mergers, each dependent on the initial properties of the interstellar medium (ISM). By analyzing recent simulations and observational data, this work aims to enhance our understanding of the parameters governing massive star formation and their implications for the initial mass function (IMF). Ultimately, this study highlights the complexities of high-mass stars and their vital role in the evolution of the universe. Physical sciences/Astronomy and planetary science Physical sciences/Physics Stellar Mass Limits Main Sequence Maximum Mass Stellar Formatio Stellar Winds Metallicity Molecular Cloud Monolithic Collapse Competitive Accretion Galactic Evolution Supernova Black Hole Formation Initial Mass Function (IMF) Astrophysics Chemical Enrichment Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction When discussing the processes of star creation and propagation, one of the main concerns is the maximum mass limit of a star. Obviously, this is a concern with a complex answer. The maximum mass of a star is dependent on many factors including, stellar winds, metallicity, and the cloud from which it is formed. Another concern is the existence of a maximum mass cut-off. Theorists have proposed such a limit for over 50 years, and the values are dependent on the conditions of the stars creation. Aside from these interests, the study of massive starts offers a wealth of information about our universe. Massive stellar formation can give insight into the evolution of the early universe with understanding of Population III stars. The effects of these stars are also of significant interest to those studying star and planet formation, as well as the composition of the ISM. Currently a mechanism is understood for the creation of massive stars. Gravitational collapse creates optically thick regions of the cloud that can eventually form protostars. It’s important to note that according to Zinnaker and Yorke, this is a nonhomolgous collapse, meaning that the distribution of material changes, as opposed to a homologous self-similar collapse [8]. Material accretes on to the protostellar object, and for lower mass stars, this accretion ends before hydrogen fusion begins. For objects destined to be high mass stars, accretion continues into the hydrogen fusion stage, and radiation driven winds are developed. The winds, outflows, and radiation produced by these objects have a strong influence on their surrounding medium, and will go supernova after ~3 Myr [9] [5]. Statement of Problems The study of the maximum mass limit of stars on the main sequence raises several critical questions that guide our understanding of stellar formation and evolution. These problems include: 1. Understanding Maximum Mass Limits: One of the primary challenges is determining the true maximum mass of a star. While estimates range from 120 to 300 solar masses, the specific factors that influence this limit, such as stellar winds and metallicity, remain poorly understood. What are the precise conditions that lead to these maximum mass estimates? 2. Formation Mechanisms The processes involved in the formation of massive stars are complex and multifaceted. Different mechanisms, such as monolithic collapse, competitive accretion, and stellar mergers, may play distinct roles depending on environmental conditions. How do these mechanisms interact, and what are their relative contributions to the formation of high-mass stars? 3. Role of the Interstellar Medium (ISM) : The initial conditions of the ISM, including its density, temperature, and composition, significantly impact stellar formation. How do variations in the ISM affect the formation process and the resulting mass of stars? 4. Impact of Magnetic Fields : Magnetic fields are known to influence the dynamics of star formation. However, the extent of their impact on the creation of massive stars and their subsequent evolution is still not fully understood. What role do magnetic fields play in regulating mass accretion and the overall formation process? 5. Stellar Winds and Feedback Mechanisms: The outflows and radiation produced by massive stars can significantly affect their surroundings and subsequent star formation. How do these stellar winds influence the mass of the forming stars and the properties of the surrounding medium? 6. Initial Mass Function (IMF): The IMF describes the distribution of stellar masses in a given population. Understanding how the maximum mass limit interacts with the IMF is crucial for comprehending the broader implications for galactic evolution. What are the connections between the maximum mass of stars and the observed characteristics of the IMF? Addressing these problems is essential for unraveling the complexities of star formation and understanding the role of massive stars in the evolution of the universe. Literature review The first step towards the formation of a high-mass star is a core or a clump of molecular gas in a giant molecular cloud. Cold dense filaments can be created by turbulent gas in giant molecular clouds. Turbulent and pressurized clouds may allow sufficient material to be available for this type of formation. An alternate idea suggests that this scenario is more transient due to the random motion within the cloud. Simulations of smoothed particle hydrodynamics have shown this collapse and fragmentation that marks the birth of these high-mass objects. Between the two approaches the only difference is whether or not the protostellar object has to compete for materials or not. The final key element that drives the collapse is the magnetic fields that affect the molecular cloud. Magnetohydrodynamic simulations indicate that without magnetic fields the required cores are not likely to develop. These simulations assume driven turbulence as opposed to decaying turbulence. The outflows of these massive protostars keep the object close to virial equilibrium as opposed to the turbulence. The implications of this work are far reaching in the fact that the IMF may be influenced by the outflows of these objects. Essentially, there are no conclusive observations that indicate whether a slow or a fast method applies to this type of stellar formation. Regardless of the approach, some of the gas in these filaments can become gravitationally bound and begin the collapse necessary to begin the star formation process. This gravitation must overcome magnetic forces, any rotation, and other form s of pressure to continue stellar formation. The densest portions of the star collapse fastest, while the less dense layers have a greater paucity of matter. This implies that the Jeans mass decreases during the collapse. When the densest parts become optically thick, the gas can heat up and increase the pressure significantly. Rotational forces often increase during the gravitational collapse due to conservation of angular momentum, which creates accretion disks. This phenomenon is not unique to high mass stars, but implies there are significant changes in mass of the object from both influxes and outflows of material. Eventually the temperature reaches critical point where the hydrogen in the cloud fragment dissociates and a second core of material falls on the previous core. The core grows in mass towards hydrogen burning densities and temperatures. The evolution of the star occurs in four components that are effectively ignorant of each other; the central core, accretion of matter onto the disk, material movement inward within the disk, the transportation zone between the disk and the core. Fundamentally the formation process is similar for both high and low mass stellar creation, excluding the assumption that each of the above components is not affecting each other. Due to complex geometry, the exact method for accretion of matter onto the disk is an active theoretical topic. One crucial element in high mass stellar accretion is referred to by Zinnecker as dust destruction, where at a certain temperature dust dissociates and opacity of the material is reduced. Hydrostatic simulations that assume spherically symmetric accretion could create stars of 150M solar [9]. A reduction in effective opacity can also occur by radiation escape through gap areas that have lower density between shocks that are driven by radiation flux of the object. Several prospective methods exist describing the creation of massive stars. Obviously, these methods are dependent on different initial conditions of the molecular cloud and propertied of the ISM. The most prominent are the methods of monolithic collapse, competitive accretion and runaway, and stellar collisions or mergers. Zinnecker notes that the work of Yorke and Sonnhalter has considered the collapse of rotating nonmagnetic massive molecular cores up to 120 M solar using frequency dependent radiation hydrodynamics simulation code. There is an appreciable effect of frequency on opacity and the flux within the disk which lends substance to this approach. Even though this does not represent an upper limit for star mass, scenarios could arise where a denser flow within a filament or fragment could create stars of even greater masses. Speculations have been made in reference to the effect that outflows have on accretion in this method of formation. Magnetized disks are being studied with the intention to understand the flow of vertical radiation within the disk. This can explain super-Eddington accretion in many luminous systems including very massive stars. Efficient angular momentum transfer can also result from weak magnetic fields in the disk, turbulence that comes from gravitational instabilities in both magnetized and nonmagnetized disks. Ultimately, whether a cloud is magnetically sub/supercritical may help determine if massive stars are created in isolated environments or in clusters. Tidal effects of nearby stars can also cause these gravitational instabilities. Methodology of study 1. Research Design This study employs a multi-faceted approach to analyze the upper mass boundary of main sequence stars. The research design integrates theoretical modeling, computational simulations, and observational data analysis. By combining these methods, we aim to provide a comprehensive understanding of the factors influencing the maximum mass limit of stars on the main sequence. 2. Theoretical Framework 2.1 Stellar Evolution Models To establish the theoretical basis for our study, we utilize various stellar evolution models that simulate the life cycles of stars. Key models include: - Standard Stellar Evolution Models: These models follow the evolution of stars from protostar to main sequence and subsequently to post-main-sequence phases. They help identify the mass limits at which stars can sustain hydrogen burning. - Non-Standard Models: We also consider models that incorporate effects such as rotation, magnetic fields, and mass loss due to stellar winds. These factors are crucial in determining the upper mass limit. 2.2 Mass Accretion Theories We explore several mass accretion theories that describe how stars gain mass during formation: - Monolithic Collapse:This theory posits that a single molecular cloud fragment collapses under its own gravity, forming a massive star. We analyze conditions under which this process can yield stars exceeding 100 solar masses. - Competitive Accretion: In this scenario, stars form in clusters and compete for surrounding gas. We investigate how the density and dynamics of the environment affect mass accretion rates. - Stellar Mergers: We examine the effects of stellar collisions and mergers in dense star clusters, assessing their contribution to the formation of supermassive stars. 3. Computational Simulations 3.1 Numerical Methods To simulate stellar formation processes, we implement state-of-the-art numerical techniques: - Hydrodynamic Simulations: We employ smoothed particle hydrodynamics (SPH) to model the collapse of molecular clouds and the birth of stars. This method allows for the study of dynamics, including turbulence and angular momentum transfer. - Magnetohydrodynamic Simulations: To incorporate magnetic fields, we use magnetohydrodynamic (MHD) models. These simulations help us understand the influence of magnetic forces on star formation and mass limits. 3.2 Parameter Space Exploration We systematically vary key parameters such as: - Metallicity: We analyze how different metallicity levels in the initial molecular cloud affect the maximum mass of the resulting stars. - Density and Temperature: By adjusting the initial density and temperature conditions of the gas, we can observe their impact on the star formation process. 4. Observational Data Analysis 4.1 Data Collection We gather observational data from various sources, including: - Telescopic Surveys:** Data from large-scale surveys such as the Sloan Digital Sky Survey (SDSS) and the Hubble Space Telescope (HST) provide information about high-mass stars and their distributions. - Spectroscopic Studies: We analyze spectra from massive stars to determine their mass, luminosity, and chemical composition. This data is crucial for validating our theoretical models. 4.2 Statistical Analysis Using the gathered observational data, we perform statistical analyses to identify trends and correlations: - Initial Mass Function (IMF) Analysis:We examine the IMF of stellar populations to understand the relationship between stellar mass distributions and the upper mass limit. 5. Synthesis of Results 5.1 Comparative Analysis We compare the outcomes of our computational simulations with observational data. This process involves: - Model Validation: We assess the validity of our theoretical models by comparing predicted mass limits with observed data. - Parameter Sensitivity Analysis:We analyze how sensitive our results are to variations in key parameters, helping to identify the most influential factors in determining the upper mass limit. 5.2 Implications for Galactic Evolution The final step involves synthesizing the findings to draw broader conclusions about the implications of massive stars for galactic evolution: - Role in Chemical Enrichment:We discuss how high-mass stars contribute to the chemical enrichment of the interstellar medium through supernova events. - Impact on Star Formation Rates: The influence of massive stars on subsequent star formation rates in their vicinity is analyzed, emphasizing the feedback mechanisms at play. Discussion Having gravitational bodies near by may lead to increased accretion that can aid in massive star formation. Competitive accretion is also a viable method for creation of massive stars. Bonnell presents 3D simulations of stellar mass growth by competitive accretion in small young clusters. In this method, growth is promoted by the size and composition of the stars accretion domain. As mass increases, the gravitational reach increases as well. This implies that stars that are born in the center of a cluster have a greater opportunity to reach higher masses. This is partially due to the fact that gas will settle into the more central parts of the potential in the cloud. Protostars that are off-center are limited by the mass in that specific location in the cloud, where the same object in the center of the cloud can draw on the entire cloud as its supply of accretion material. Competitive accretion comes to the conclusion that eventually these accretion domains will eventually overlap. This eventually means that stars in clouds or in local clumps in clouds will compete for the same material, and the largest stars will be formed in the most ideal conditions and occur very rarely. The lynchpin of this method is the fact simulations were run for strongly gravitationally bound clouds where turbulence was negligible. Arguments have been made by Krumholtz, McKee, and Klein that protostellar masses cannot grow in this type of medium [9]. More recent simulations have corrected and increased the turbulence, and small turbulent velocities were found between protostars and the neighboring medium. The problem suspected above is not as serious as first implied, because protostars are moving with neighboring gas in a similar global motion until they meet with an uncorrelated gas. Omukai and Palla have worked with the mass accretion rate which is a possible catalyst for massive star creation. Their results indicate that the earliest stages are independent of accretion rate [7]. Later in the stars evolution there is a critical mass accretion rate that brings the luminosity to the Eddington Limit before nuclear burning has begun. The M crit is a value near 4x10 -3 M solar yr -1 . This phase is followed by rapid radius expansion, which can possibly lead to reversal of the accretion flow. For time dependent accretion rates, fluctuations in accretion rate can have dramatic effects on the mass of the resulting star. This work uses very small values for Z, and in the Z =0 case, reduced gas temperatures lead to smaller changes in accretion rate. Other critical metallicities exist including Z~0.01 Z solar . This significantly limits the amount of material that can be accreted. Palla and Omukai also note that strong stellar winds have a strong effect, which is blowing off envelope material. Obviously with less stellar material the star can quickly move to the mains sequence as a lower mass star. The notion of a stellar merger is plagued by the concern that massive stars would me packed too tightly into dense clusters, and that there was not a sufficiently large reservoir of gas for a monolithic collapse. This concern is assuaged by the fact that massive stars occur in OB associations that are not a densely populated cluster. Stellar mergers are rare objects and only relevant in the richest youngest clusters. One of the goals of theoretical Astrophysics is to understand the parameters that govern star formation. One of the key elements in star formation is an understanding of the initial mass function (IMF). Since its introduction by Salpeter in 1955, the IMF has been slightly refined by observational studies [1]. Recent modeling has shown that the Salpeter value of -1.35 is an adequate average value for the expression for the IMF [2]. Figure 2 shows that the expectation value of m max has the potential to be greater than generally accepted maximum of 100-120 M solar . It is to be noted that this analysis by Oey et al. is highly dependent on the value used for the Salpeter slope. For the accepted average value of the Salpeter slope, there should be a cutoff at 120-200 M solar . Work done by Elmegreen includes an exponential decrease to the IMF with the intention of simulating the competition for materials in denser turbulent clouds. There should be a turn down for stars of mass greater than 100M solar for several reasons. The main argument for this limit is the apparent structure of the universe on kilo parsec scales. Without this limitation, one could assume that the cloud is only a small part of a larger gas structure that can be used for stellar formation. This observation by Elmegreen suggests that the power-law IMF drops more rapidly than the Salpeter slope at masses near several hundred solar masses [2]. Figure 4 shows a high mass turn-down that would account for the lack of super massive stars under normal star-formation conditions. This data also agrees with the observation of the Salpeter slope to out to a value of approximately 100-130 solar masses in work by Massey et al. [5][2]. Still, concerns are that it is possible to get 130 M solar stars in dense clusters, yet not having any stars of 300 M solar in the entire galaxy. Figure 3 indicates that the summed IMF is very similar to the cluster IMF with the simulations selected parameters. The difference is slope is ~0.1 for masses greater than 10 M solar . The efficiency, ε, contributes minimally in these results. In the upper panel of figure 3, the average maximum stellar follows Elmegreen’s predictions, as does the absolute maximum. The value of absolute maximum mass holds constant with the exception of the lowest mass clusters. Overall, this confirms Elmegreen’s analytical results that the summed IMF of the cluster population is almost indistinguishable from the individual cluster IMF parameters. From this work, the conclusion is that stars form with little apparent physical connection between mass and cluster mass. A statistical connection is made to the sample size effect, with more massive stars created in more massive clusters on average. This statistical connection apparently has no influence on the summed IMF results. Figure 3 shows that, in the Monte Carlo simulation, statistically any number of clusters of a particular mass will produce maximum size stars near the same cutoff value. Ultimately, the only short-coming of this result is that clusters and clouds are not well defined entities and a statistical evaluation is the most reliable work that can be achieved. Conclusion In conclusion, determining the actual maximum mass for a star is an incredibly complex endeavor. The range of maximum stellar masses is determined by the nature of the stars birthplace, including its composition, age, and location with respect to other astrophysical bodies. High-mass stars are the product of a series of conditions being met including the nature of the ISM, the composition of the stars birthplace, and the other objects that exist in its neighborhood. If the initial conditions are met, theoreticians have reasoned that the maximum stellar mass can be between 120-300 M solar . Obviously this range will adjust for the three populations of stars. For Population I stars, the range will be the lowest, because these stars are created from outflow materials of older stars. Population I stars have a higher metallicity, an indicator of age of the material in the stars. Population II stars will have a higher range for the most massive stars due to the nature of their composition, which is from more primal material. Finally, speculated primordial Population III would be the most massive objects, near ~300-600 M solar [7]. Declarations Author Contribution Authers Edit and prepare the main document,Analysis the results,methodology Acknowledgment First and foremost, I want to acknowledge Jesus Christ, whose grace and strength have sustained me throughout this process. Your teachings of perseverance, compassion, and faith have been a source of inspiration, guiding me through moments of doubt and uncertainty. I am grateful for your unwavering presence in my life, providing me with the courage to pursue knowledge and wisdom. References Bonnell IA, Bate MR. 2005. MNRAS 356:1201-1221 Elmegreen BG. 2000. Ap. J. 539: 342-351 Elmegreen BG. 2006. Ap. J. 648:572-579 Garmany CD, Conti PS, Chiosi C. 1982. Ap.J. 263:777-790 Massey P, Johnson KE, Eastwood K. 1995. Ap. J. 454:151-71 Oey MS, Clarke CJ. 2005. Ap. J. Lett. 620:L43-46 Omukai K, Palla F. 2003. Ap.J. 589:677-87 Salpeter EE. 1955. Ap. J. 121:161-67 Zinnecker H, Yorke H. Annu. Rev. Astrophys. 2007. 45:481-563. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5342146","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":370892716,"identity":"896c72a1-6edb-422a-bfa7-e580b7ae4b30","order_by":0,"name":"Diriba Gonfa","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7ElEQVRIie2RsQrCMBCGA4V0Ce16RfEZCoUi6MO0S13S3aG4COIgzu6+QKbOkWJcCl0zCoKDIBQKHauNg2PbUTAfXPgP7oNLgpBG84vwtpZoTrC5VhHGw5QcRRObiEApZKiSec6BuqrvV6ziKK48MUImafWQyZQgMzuzLsWR94XLBQ5Z/kxnVLSLkSiSXYorc39UYhKyS5x6FLcKEL9XAd5AyDi9e7QZohQ7H04b13O21LjFmwGKI3EEp32gHtk34j0Q3HcXq8gE8PqlvvJW0Xo1sc1MdCoIgm/E8Dk7xxU2/0aj7J3WaDSav+QNnxhREUEleTwAAAAASUVORK5CYII=","orcid":"","institution":"Assosa university College of Natural and Computational Science","correspondingAuthor":true,"prefix":"","firstName":"Diriba","middleName":"","lastName":"Gonfa","suffix":""}],"badges":[],"createdAt":"2024-10-27 16:23:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5342146/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5342146/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":68522764,"identity":"5dd5484d-c67e-4913-a9c1-b6ed97551587","added_by":"auto","created_at":"2024-11-08 07:55:54","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":315881,"visible":true,"origin":"","legend":"\u003cp\u003eAn example of a close binary pair and the associated inner accretion disk. An azimuthal cavity is evacuated by both radiation and stellar wind. In this image the disk is shielded by ionized Hydrogen fronts. Size is not to scale.[9].\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5342146/v1/fbd818c39ac0143b7082bc97.png"},{"id":68523112,"identity":"470a2d4f-7cd4-472f-afdf-6f5f4f12cea9","added_by":"auto","created_at":"2024-11-08 08:03:55","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":57217,"visible":true,"origin":"","legend":"\u003cp\u003eGraph of the expectation value of m\u003csub\u003emax\u003c/sub\u003e vs. upper limit mass m\u003csub\u003eup\u003c/sub\u003e for N = 100, 250, and 1000 stars.\u0026nbsp; The Graph assumes a Salpeter IMF and a minimum mass limit of 10M\u003csub\u003esolar \u003c/sub\u003e[1].\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5342146/v1/03fcb5bc1646cb2c03bfefcd.png"},{"id":68522765,"identity":"0e682f1f-e059-4e00-9f8c-9fe5e0b0bfcb","added_by":"auto","created_at":"2024-11-08 07:55:55","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":97318,"visible":true,"origin":"","legend":"\u003cp\u003eData from a Monte Carlo IMF model. The bottom panel shows different star-formation efficiencies, ε, as well as the cluster IMF. The top panel shows average maximum stellar mass in a cluster and the cluster mass. The “x”, “+”, “o” represent the cases ε = 0.1, 0.3, and 0.9 respectively with the theoretical prediction [3].\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5342146/v1/bf86f3b23c7196235c76146b.png"},{"id":68522767,"identity":"1268215d-d68d-4471-a13a-ecfa1884dcfb","added_by":"auto","created_at":"2024-11-08 07:55:55","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":62444,"visible":true,"origin":"","legend":"\u003cp\u003ethe bottom panel shows IMF simulations for two cases; the solid lines the model without timing constraints, and the dotted line is the model with timing constraints. The top panel shows the product of mass with IMF[2].\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5342146/v1/0b6ce7d489cf92160ac303f1.png"},{"id":69418479,"identity":"660fc87a-433f-43a3-8d1c-81358f6b9e9b","added_by":"auto","created_at":"2024-11-20 07:24:26","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":760666,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5342146/v1/961cc52a-ad45-4be7-b958-341fa3341f17.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Analyzing the Upper Mass Boundary of Main Sequence Stars","fulltext":[{"header":"Introduction","content":"\u003cp\u003eWhen discussing the processes of star creation and propagation, one of the main concerns is the maximum mass limit of a star. \u0026nbsp;Obviously, this is a concern with a complex answer. \u0026nbsp;The maximum mass of a star is dependent on many factors including, stellar winds, metallicity, and the cloud from which it is formed. \u0026nbsp;Another concern is the existence of a maximum mass cut-off. \u0026nbsp;Theorists have proposed such a limit for over 50 years, and the values are dependent on the conditions of the stars creation. \u0026nbsp;Aside from these interests, the study of massive starts offers a wealth of information about our universe. \u0026nbsp;Massive stellar formation can give insight into the evolution of the early universe with understanding of Population III stars. The effects of these stars are also of significant interest to those studying star and planet formation, as well as the composition of the ISM. \u0026nbsp; Currently a mechanism is understood for the creation of massive stars. \u0026nbsp;Gravitational collapse creates optically thick regions of the cloud that can eventually form protostars. \u0026nbsp;It’s important to note that according to Zinnaker and Yorke, this is a nonhomolgous collapse, meaning that the distribution of material changes, as opposed to a homologous self-similar collapse [8]. \u0026nbsp;Material accretes on to the protostellar object, and for lower mass stars, this accretion ends before hydrogen fusion begins. \u0026nbsp;For objects destined to be high mass stars, accretion continues into the hydrogen fusion stage, and radiation driven winds are developed. \u0026nbsp;The winds, outflows, and radiation produced by these objects have a strong influence on their surrounding medium, and will go supernova after ~3 Myr [9] [5].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStatement of Problems\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe study of the maximum mass limit of stars on the main sequence raises several critical questions that guide our understanding of stellar formation and evolution. These problems include:\u003c/p\u003e\n\u003cp\u003e1. Understanding Maximum Mass Limits: One of the primary challenges is determining the true maximum mass of a star. While estimates range from 120 to 300 solar masses, the specific factors that influence this limit, such as stellar winds and metallicity, remain poorly understood. What are the precise conditions that lead to these maximum mass estimates?\u003c/p\u003e\n\u003cp\u003e2. Formation Mechanisms \u0026nbsp;The processes involved in the formation of massive stars are complex and multifaceted. Different mechanisms, such as monolithic collapse, competitive accretion, and stellar mergers, may play distinct roles depending on environmental conditions. How do these mechanisms interact, and what are their relative contributions to the formation of high-mass stars?\u003c/p\u003e\n\u003cp\u003e3. Role of the Interstellar Medium (ISM) : The initial conditions of the ISM, including its density, temperature, and composition, significantly impact stellar formation. How do variations in the ISM affect the formation process and the resulting mass of stars?\u003c/p\u003e\n\u003cp\u003e4. Impact of Magnetic Fields : Magnetic fields are known to influence the dynamics of star formation. However, the extent of their impact on the creation of massive stars and their subsequent evolution is still not fully understood. What role do magnetic fields play in regulating mass accretion and the overall formation process?\u003c/p\u003e\n\u003cp\u003e5. Stellar Winds and Feedback Mechanisms: The outflows and radiation produced by massive stars can significantly affect their surroundings and subsequent star formation. How do these stellar winds influence the mass of the forming stars and the properties of the surrounding medium?\u003c/p\u003e\n\u003cp\u003e6. Initial Mass Function (IMF): The IMF describes the distribution of stellar masses in a given population. Understanding how the maximum mass limit interacts with the IMF is crucial for comprehending the broader implications for galactic evolution. What are the connections between the maximum mass of stars and the observed characteristics of the IMF?\u003c/p\u003e\n\u003cp\u003eAddressing these problems is essential for unraveling the complexities of star formation and understanding the role of massive stars in the evolution of the universe.\u003c/p\u003e"},{"header":"Literature review","content":"\u003cp\u003eThe first step towards the formation of a high-mass star is a core or a clump of molecular gas in a giant molecular cloud. \u0026nbsp;Cold dense filaments can be created by turbulent gas in giant molecular clouds. \u0026nbsp;Turbulent and pressurized clouds may allow sufficient material to be available for this type of formation. \u0026nbsp;An alternate idea suggests that this scenario is more transient due to the random motion within the cloud. \u0026nbsp;Simulations of smoothed particle hydrodynamics have shown this collapse and fragmentation that marks the birth of these high-mass objects. \u0026nbsp;Between the two approaches the only difference is whether or not the protostellar object has to compete for materials or not. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe final key element that drives the collapse is the magnetic fields that affect the molecular cloud. \u0026nbsp;Magnetohydrodynamic simulations indicate that without magnetic fields the required cores are not likely to develop. \u0026nbsp;These simulations assume driven turbulence as opposed to decaying turbulence. \u0026nbsp;The outflows of these massive protostars keep the object close to virial equilibrium as opposed to the turbulence. \u0026nbsp;The implications of this work are far reaching in the fact that the IMF may be influenced by the outflows of these objects. \u0026nbsp;Essentially, there are no conclusive observations that indicate whether a slow or a fast method applies to this type of stellar formation.\u003c/p\u003e\n\u003cp\u003eRegardless of the approach, some of the gas in these filaments can become gravitationally bound and begin the collapse necessary to begin the star formation process. \u0026nbsp;This gravitation must overcome magnetic forces, any rotation, and other form s of pressure to continue stellar formation. \u0026nbsp;The densest portions of the star collapse fastest, while the less dense layers have a greater paucity of matter. \u0026nbsp;This implies that the Jeans mass decreases during the collapse. \u0026nbsp;When the densest parts become optically thick, the gas can heat up and increase the pressure significantly. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eRotational forces often increase during the gravitational collapse due to conservation of angular momentum, which creates accretion disks. \u0026nbsp; This phenomenon is not unique to high mass stars, but implies there are significant changes in mass of the object from both influxes and outflows of material. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eEventually the temperature reaches critical point where the hydrogen in the cloud fragment dissociates and a second core of material falls on the previous core. \u0026nbsp;The core grows in mass towards hydrogen burning densities and temperatures. \u0026nbsp;The evolution of the star occurs in four components that are effectively ignorant of each other; the central core, accretion of matter onto the disk, material movement inward within the disk, the transportation zone between the disk and the core. \u0026nbsp;Fundamentally the formation process is similar for both high and low mass stellar creation, excluding the assumption that each of the above components is not affecting each other. \u0026nbsp;Due to complex geometry, the exact method for accretion of matter onto the disk is an active theoretical topic.\u003c/p\u003e\n\u003cp\u003eOne crucial element in high mass stellar accretion is referred to by Zinnecker as dust destruction, where at a certain temperature dust dissociates and opacity of the material is reduced. \u0026nbsp;Hydrostatic simulations that assume spherically symmetric accretion could create stars of 150M\u003csub\u003esolar\u0026nbsp;\u003c/sub\u003e[9]. \u0026nbsp; \u0026nbsp;A reduction in effective opacity can also occur by radiation escape through gap areas that have lower density between shocks that are driven by radiation flux of the object. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSeveral prospective methods exist describing the creation of massive stars. \u0026nbsp; Obviously, these methods are dependent on different initial conditions of the molecular cloud and propertied of the ISM. \u0026nbsp;The most prominent are the methods of monolithic collapse, competitive accretion and runaway, and stellar collisions or mergers. \u0026nbsp; Zinnecker notes that the work of Yorke and Sonnhalter has considered the collapse of rotating nonmagnetic massive molecular cores up to 120 M\u003csub\u003esolar\u003c/sub\u003e using frequency dependent radiation hydrodynamics simulation code. \u0026nbsp;There is an appreciable effect of frequency on opacity and the flux within the disk which lends substance to this approach. \u0026nbsp;Even though this does not represent an upper limit for star mass, scenarios could arise where a denser flow within a filament or fragment could create stars of even greater masses.\u003c/p\u003e\n\u003cp\u003eSpeculations have been made in reference to the effect that outflows have on accretion in this method of formation. \u0026nbsp;Magnetized disks are being studied with the intention to understand the flow of vertical radiation within the disk. \u0026nbsp;This can explain super-Eddington accretion in many luminous systems including very massive stars. \u0026nbsp;Efficient angular momentum transfer can also result from weak magnetic fields in the disk, turbulence that comes from gravitational instabilities in both magnetized and nonmagnetized disks. \u0026nbsp;Ultimately, whether a cloud is magnetically sub/supercritical may help determine if massive stars are created in isolated environments or in clusters. \u0026nbsp;Tidal effects of nearby stars can also cause these gravitational instabilities. \u0026nbsp;\u003c/p\u003e"},{"header":"Methodology of study","content":"\u003cp\u003e1. Research Design\u003c/p\u003e\n\u003cp\u003eThis study employs a multi-faceted approach to analyze the upper mass boundary of main sequence stars. The research design integrates theoretical modeling, computational simulations, and observational data analysis. By combining these methods, we aim to provide a comprehensive understanding of the factors influencing the maximum mass limit of stars on the main sequence.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;2. Theoretical Framework\u003c/p\u003e\n\u003cp\u003e2.1 Stellar Evolution Models\u003c/p\u003e\n\u003cp\u003eTo establish the theoretical basis for our study, we utilize various stellar evolution models that simulate the life cycles of stars. Key models include:\u003c/p\u003e\n\u003cp\u003e- Standard Stellar Evolution Models: These models follow the evolution of stars from protostar to main sequence and subsequently to post-main-sequence phases. They help identify the mass limits at which stars can sustain hydrogen burning.\u003c/p\u003e\n\u003cp\u003e- Non-Standard Models: We also consider models that incorporate effects such as rotation, magnetic fields, and mass loss due to stellar winds. These factors are crucial in determining the upper mass limit.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;2.2 Mass Accretion Theories\u003c/p\u003e\n\u003cp\u003eWe explore several mass accretion theories that describe how stars gain mass during formation:\u003c/p\u003e\n\u003cp\u003e- Monolithic Collapse:This theory posits that a single molecular cloud fragment collapses under its own gravity, forming a massive star. We analyze conditions under which this process can yield stars exceeding 100 solar masses.\u003c/p\u003e\n\u003cp\u003e- Competitive Accretion: In this scenario, stars form in clusters and compete for surrounding gas. We investigate how the density and dynamics of the environment affect mass accretion rates.\u003c/p\u003e\n\u003cp\u003e- Stellar Mergers: We examine the effects of stellar collisions and mergers in dense star clusters, assessing their contribution to the formation of supermassive stars.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;3. Computational Simulations\u003c/p\u003e\n\u003cp\u003e3.1 Numerical Methods\u003c/p\u003e\n\u003cp\u003eTo simulate stellar formation processes, we implement state-of-the-art numerical techniques:\u003c/p\u003e\n\u003cp\u003e- Hydrodynamic Simulations: We employ smoothed particle hydrodynamics (SPH) to model the collapse of molecular clouds and the birth of stars. This method allows for the study of dynamics, including turbulence and angular momentum transfer.\u003c/p\u003e\n\u003cp\u003e- Magnetohydrodynamic Simulations: To incorporate magnetic fields, we use magnetohydrodynamic (MHD) models. These simulations help us understand the influence of magnetic forces on star formation and mass limits.\u003c/p\u003e\n\u003cp\u003e3.2 Parameter Space Exploration\u003c/p\u003e\n\u003cp\u003eWe systematically vary key parameters such as:\u003c/p\u003e\n\u003cp\u003e- Metallicity: We analyze how different metallicity levels in the initial molecular cloud affect the maximum mass of the resulting stars.\u003c/p\u003e\n\u003cp\u003e- Density and Temperature: By adjusting the initial density and temperature conditions of the gas, we can observe their impact on the star formation process.\u003c/p\u003e\n\u003cp\u003e4. Observational Data Analysis\u003c/p\u003e\n\u003cp\u003e4.1 Data Collection\u003c/p\u003e\n\u003cp\u003eWe gather observational data from various sources, including:\u003c/p\u003e\n\u003cp\u003e- Telescopic Surveys:** Data from large-scale surveys such as the Sloan Digital Sky Survey (SDSS) and the Hubble Space Telescope (HST) provide information about high-mass stars and their distributions.\u003c/p\u003e\n\u003cp\u003e- Spectroscopic Studies: We analyze spectra from massive stars to determine their mass, luminosity, and chemical composition. This data is crucial for validating our theoretical models.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;4.2 Statistical Analysis\u003c/p\u003e\n\u003cp\u003eUsing the gathered observational data, we perform statistical analyses to identify trends and correlations:\u003c/p\u003e\n\u003cp\u003e- Initial Mass Function (IMF) Analysis:We examine the IMF of stellar populations to understand the relationship between stellar mass distributions and the upper mass limit.\u003c/p\u003e\n\u003cp\u003e5. Synthesis of Results\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;5.1 Comparative Analysis\u003c/p\u003e\n\u003cp\u003eWe compare the outcomes of our computational simulations with observational data. This process involves:\u003c/p\u003e\n\u003cp\u003e- Model Validation: We assess the validity of our theoretical models by comparing predicted mass limits with observed data.\u003c/p\u003e\n\u003cp\u003e- Parameter Sensitivity Analysis:We analyze how sensitive our results are to variations in key parameters, helping to identify the most influential factors in determining the upper mass limit.\u003c/p\u003e\n\u003cp\u003e5.2 Implications for Galactic Evolution\u003c/p\u003e\n\u003cp\u003eThe final step involves synthesizing the findings to draw broader conclusions about the implications of massive stars for galactic evolution:\u003c/p\u003e\n\u003cp\u003e- Role in Chemical Enrichment:We discuss how high-mass stars contribute to the chemical enrichment of the interstellar medium through supernova events.\u003c/p\u003e\n\u003cp\u003e- Impact on Star Formation Rates: The influence of massive stars on subsequent star formation rates in their vicinity is analyzed, emphasizing the feedback mechanisms at play.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eHaving gravitational bodies near by may lead to increased accretion that can aid in massive star formation. \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eCompetitive accretion is also a viable method for creation of massive stars. \u0026nbsp;Bonnell presents 3D simulations of stellar mass growth by competitive accretion in small young clusters. \u0026nbsp;In this method, growth is promoted by the size and composition of the stars accretion domain. \u0026nbsp;As mass increases, the gravitational reach increases as well. \u0026nbsp;This implies that stars that are born in the center of a cluster have a greater opportunity to reach higher masses. \u0026nbsp;This is partially due to the fact that gas will settle into the more central parts of the potential in the cloud. \u0026nbsp;Protostars that are off-center are limited by the mass in that specific location in the cloud, where the same object in the center of the cloud can draw on the entire cloud as its supply of accretion material. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eCompetitive accretion comes to the conclusion that eventually these accretion domains will eventually overlap. \u0026nbsp;This eventually means that stars in clouds or in local clumps in clouds will compete for the same material, and the largest stars will be formed in the most ideal conditions and occur very rarely. \u0026nbsp;The lynchpin of this method is the fact simulations were run for strongly gravitationally bound clouds where turbulence was negligible. \u0026nbsp;Arguments have been made by Krumholtz, McKee, and Klein that protostellar masses cannot grow in this type of medium [9]. \u0026nbsp;More recent simulations have corrected and increased the turbulence, and small turbulent velocities were found between protostars and the neighboring medium. \u0026nbsp; The problem suspected above is not as serious as first implied, because protostars are moving with neighboring gas in a similar global motion until they meet with an uncorrelated gas.\u003c/p\u003e\n\u003cp\u003eOmukai and Palla \u0026nbsp;have worked with the mass accretion rate which is a possible catalyst for massive star creation. \u0026nbsp;Their results indicate that the earliest stages are independent of accretion rate [7]. \u0026nbsp; Later in the stars evolution there is a critical mass accretion rate that brings the luminosity to the Eddington Limit before nuclear burning has begun. \u0026nbsp;The M\u003csub\u003ecrit\u003c/sub\u003e is a value near 4x10\u003csup\u003e-3\u003c/sup\u003e M\u003csub\u003esolar\u003c/sub\u003e yr \u003csup\u003e-1\u003c/sup\u003e. \u0026nbsp;This phase is followed by rapid radius expansion, which can possibly lead to reversal of the accretion flow. \u0026nbsp;For time dependent accretion rates, fluctuations in accretion rate can have dramatic effects on the mass of the resulting star. \u0026nbsp;This work uses very small values for Z, and in the Z =0 case, reduced gas temperatures lead to smaller changes in accretion rate. \u0026nbsp;Other critical metallicities exist including \u0026nbsp; Z~0.01 Z\u003csub\u003esolar\u003c/sub\u003e. \u0026nbsp;This significantly limits the amount of material that can be accreted. \u0026nbsp;Palla and Omukai also note that strong stellar winds have a strong effect, which is blowing off envelope material. \u0026nbsp;Obviously with less stellar material the star can quickly move to the mains sequence as a lower mass star. \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe notion of a stellar merger is plagued by the concern that massive stars would me packed too tightly into dense clusters, and that there was not a sufficiently large reservoir of gas for a monolithic collapse. \u0026nbsp; This concern is assuaged by the fact that massive stars occur in OB associations that are not a densely populated cluster. \u0026nbsp; \u0026nbsp;Stellar mergers are rare objects and only relevant in the richest youngest clusters. \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eOne of the goals of theoretical Astrophysics is to understand the parameters that govern star formation. \u0026nbsp;One of the key elements in star formation is an understanding of the initial mass function (IMF). \u0026nbsp;Since its introduction by Salpeter in 1955, the IMF has been slightly refined by observational studies [1]. \u0026nbsp; Recent modeling has shown that the Salpeter value of -1.35 is an adequate average value for the expression for the IMF [2]. \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigure 2 shows that the expectation value of m\u003csub\u003emax\u003c/sub\u003e has the potential to be greater than generally accepted maximum of 100-120 M\u003csub\u003esolar\u003c/sub\u003e. \u0026nbsp; It is to be noted that this analysis by Oey et al. is highly dependent on the value used for the Salpeter slope. \u0026nbsp; For the accepted average value of the Salpeter slope, there should be a cutoff at 120-200 M\u003csub\u003esolar\u003c/sub\u003e. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWork done by Elmegreen includes an exponential decrease to the IMF with the intention of simulating the competition for materials in denser turbulent clouds. \u0026nbsp;There should be a turn down for stars of mass greater than 100M\u003csub\u003esolar\u003c/sub\u003e for several reasons. \u0026nbsp;The main argument for this limit is the apparent structure of the universe on kilo parsec scales. \u0026nbsp;Without this limitation, one could assume that the cloud is only a small part of a larger gas structure that can be used for stellar formation. \u0026nbsp;This observation by Elmegreen suggests that the power-law IMF drops more rapidly than the Salpeter slope at masses near several hundred solar masses [2]. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigure 4 shows a high mass turn-down that would account for the lack of super massive stars under normal star-formation conditions. \u0026nbsp; This data also agrees with the observation of the Salpeter slope to out to a value of approximately 100-130 solar masses in work by Massey et al. [5][2]. \u0026nbsp;Still, concerns are that it is possible to get 130 M\u003csub\u003esolar\u003c/sub\u003e stars in dense clusters, yet not having any stars of 300 M\u003csub\u003esolar\u003c/sub\u003e in the entire galaxy.\u003c/p\u003e\n\u003cp\u003eFigure 3 indicates that the summed IMF is very similar to the cluster IMF with the simulations selected parameters. \u0026nbsp;The difference is slope is ~0.1 for masses greater than 10 M\u003csub\u003esolar\u003c/sub\u003e. \u0026nbsp;The efficiency, \u0026epsilon;, contributes minimally in these results. \u0026nbsp;In the upper panel of figure 3, the average maximum stellar follows Elmegreen\u0026rsquo;s predictions, as does the absolute maximum. \u0026nbsp;The value of absolute maximum mass holds constant with the exception of the lowest mass clusters. \u0026nbsp;Overall, this confirms Elmegreen\u0026rsquo;s analytical results that the summed IMF of the cluster population is almost indistinguishable from the individual cluster IMF parameters.\u003c/p\u003e\n\u003cp\u003eFrom this work, the conclusion is that stars form with little apparent physical connection between mass and cluster mass. \u0026nbsp;A statistical connection is made to the sample size effect, with more massive stars created in more massive clusters on average. \u0026nbsp;This statistical connection apparently has no influence on the summed IMF results. \u0026nbsp;Figure 3 shows that, in the Monte Carlo simulation, statistically any number of clusters of a particular mass will produce maximum size stars near the same cutoff value. \u0026nbsp; Ultimately, the only short-coming of this result is that clusters and clouds are not well defined entities and a statistical evaluation is the most reliable work that can be achieved.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn conclusion, determining the actual maximum mass for a star is an incredibly complex endeavor. \u0026nbsp;The range of maximum stellar masses is determined by the nature of the stars birthplace, including its composition, age, and location with respect to other astrophysical bodies. \u0026nbsp;High-mass stars are the product of a series of conditions being met including the nature of the ISM, the composition of the stars birthplace, and the other objects that exist in its neighborhood. \u0026nbsp;If the initial conditions are met, theoreticians have reasoned that the maximum stellar mass can be between 120-300 M\u003csub\u003esolar\u003c/sub\u003e. \u0026nbsp;Obviously this range will adjust for the three populations of stars. \u0026nbsp; \u0026nbsp;For Population I stars, the range will be the lowest, because these stars are created from outflow materials of older stars. \u0026nbsp;Population I stars have a higher metallicity, an indicator of age of the material in the stars. \u0026nbsp;Population II stars will have a higher range for the most massive stars due to the nature of their composition, which is from more primal material. \u0026nbsp;Finally, speculated primordial Population III would be the most massive objects, near ~300-600 M\u003csub\u003esolar\u003c/sub\u003e [7]. \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAuthers Edit and prepare the main document,Analysis the results,methodology\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFirst and foremost, I want to acknowledge Jesus Christ, whose grace and strength have\u003c/p\u003e\n\u003cp\u003esustained me throughout this process. Your teachings of perseverance, compassion,\u003c/p\u003e\n\u003cp\u003eand faith have been a source of inspiration, guiding me through moments of doubt\u003c/p\u003e\n\u003cp\u003eand uncertainty. I am grateful for your unwavering presence in my life, providing me\u003c/p\u003e\n\u003cp\u003ewith the courage to pursue knowledge and wisdom.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBonnell IA, Bate MR. 2005. MNRAS 356:1201-1221\u003c/li\u003e\n\u003cli\u003eElmegreen BG. 2000. Ap. J. 539: 342-351\u003c/li\u003e\n\u003cli\u003eElmegreen BG. 2006. Ap. J. 648:572-579\u003c/li\u003e\n\u003cli\u003eGarmany CD, Conti PS, Chiosi C. 1982. Ap.J. 263:777-790\u003c/li\u003e\n\u003cli\u003eMassey P, Johnson KE, Eastwood K. 1995. Ap. J. 454:151-71\u003c/li\u003e\n\u003cli\u003eOey MS, Clarke CJ. 2005. Ap. J. Lett. 620:L43-46\u003c/li\u003e\n\u003cli\u003eOmukai K, Palla F. 2003. Ap.J. 589:677-87\u003c/li\u003e\n\u003cli\u003eSalpeter EE. 1955. Ap. J. 121:161-67\u003c/li\u003e\n\u003cli\u003eZinnecker H, Yorke H. Annu. Rev. Astrophys. 2007. 45:481-563.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Stellar Mass Limits,Main Sequence, Maximum Mass, Stellar Formatio, Stellar Winds, Metallicity, Molecular Cloud, Monolithic Collapse,Competitive Accretion, Galactic Evolution, Supernova, Black Hole Formation, Initial Mass Function (IMF) Astrophysics, Chemical Enrichment ","lastPublishedDoi":"10.21203/rs.3.rs-5342146/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5342146/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study analyzes the upper mass boundary of stars on the main sequence, examining the various factors that influence their formation and evolution. The maximum mass of a star is not a fixed value; it fluctuates based on conditions such as stellar winds, metallicity, and the characteristics of the molecular cloud from which the star originates. For decades, the astrophysical community has debated the existence of a maximum mass limit, with estimates typically ranging from 120 to 300 solar masses, contingent upon environmental factors and initial conditions. The formation of massive stars initiates with the gravitational collapse of gas clumps in giant molecular clouds, leading to protostar formation. This phase is characterized by non-homologous collapse, significantly influenced by magnetic fields and accretion dynamics. As material accretes onto the protostar, radiation-driven winds sculpt the surrounding environment, culminating in supernova events. This research reviews several formation mechanisms, including monolithic collapse, competitive accretion, and stellar mergers, each dependent on the initial properties of the interstellar medium (ISM). By analyzing recent simulations and observational data, this work aims to enhance our understanding of the parameters governing massive star formation and their implications for the initial mass function (IMF). Ultimately, this study highlights the complexities of high-mass stars and their vital role in the evolution of the universe.\u003c/p\u003e","manuscriptTitle":"Analyzing the Upper Mass Boundary of Main Sequence Stars","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-08 07:55:50","doi":"10.21203/rs.3.rs-5342146/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8d8139dc-1b63-48e8-b8cc-6830410137ca","owner":[],"postedDate":"November 8th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":39468933,"name":"Physical sciences/Astronomy and planetary science"},{"id":39468934,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2024-11-20T07:24:10+00:00","versionOfRecord":[],"versionCreatedAt":"2024-11-08 07:55:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5342146","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5342146","identity":"rs-5342146","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}