Rotating Disk Galaxies without Dark Matter Based on Scientific Reasoning
Round 1
Reviewer 1 Report
The paper gives details of a calculation of the mass distribution in spiral galaxies based on the measured rotation curves. In this work, it is not assumed that the mass-to-light ratio is constant across the galaxy. As a result, the dynamics of the galaxy is modeled without the need for dark matter. The 'inverse problem' of finding the surface density from the known rotation curve is solved algebraically for a model of the galaxy consisting of a disk of a uniform thickness. A bulge distribution of matter can be added to the model.
The author refers to work previously done during the last decade, with the addition of newer measurements that have been available since then. The work is very important in the field as it impacts on the amount of non-baryonic dark matter that is required to explain observations. Since no candidate particle for dark matter has yet been detected, a model which does not require any dark matter is a very relevant alternative.
Overall a good paper, but although many references to previous work are given, a number of things can be clarified in this manuscript.
In the abstract, the author writes that a constant mass-to-light ratio is generally assumed and that the "mass determined from rotation curve typically exhibit an exponential-like decline with galactrocentric distance, qualitatively consistent with observed surface brightness." From this sentence, one is inclined to think that the surface brightness is consistent with a 'constant mass-to-light' ratio, but the last sentence of the abstract says the opposite. It seems the wording is not quite right. In the paper it is explained that the inferred mass determined from rotation curves is not consistent with a constant mass-to-light ratio. Please correct the statement in the abstract to reflect this.
Line 245: The arms of the galaxy make the density deviate from an axisymmetric model. How much difference does this make on the final result?
Line 342: The total mass of the galaxy is given as "calculated from the predicted value of A as M_g = V_0^2 R_g / (G A)." This relation with A = 1 is the virial theorem commonly used in astrophysics, and this should be mentioned. Here however, the rotation parameter A is what makes the difference betwen the need of exotic dark matter or not. But A seems to be no larger than 2, so why are the results different compared to other calculations made with the virial theorem?
Only two examples are given, the Milky Way and Andromeda. Could another example be given for a galaxy where a large fraction of dark matter is expected? What I am looking for is an example which shows a big difference between the method of this paper and the usual methods from which dark matter is predicted.
Lines 342 to 350: How is the characteristic rotation velocity V_0 estimated for the calculations? Is it an average velocity weighted by the luminosity?
Line 352: Figure 3 showing the mass density is exponential from r = 0.1 to 0.9, but shows a strong 'cusp' near r = 0. The 'cuspy halo problem' also arises with dark matter models. Could the author comment on this sharp rise in density (over a factor of 100) considering that it is not observed in most galaxies?
In the paragraph lines 378-392, atomic hydrogen and molecular hydrogen are discussed as possible baryonic dark matter. Dust, mentioned at the beginning of the paper, should also be discussed here. A letter written in Physics Today (https://physicstoday.scitation.org/doi/10.1063/1.2743106) describes how dust also has a small optical cross section and can avoid detection. The idea was already discussed over 60 years ago.
The following comments are related to clarifications or style.
Line 52: The author writes "we have been told (mostly by renowned astrophysicists) that about 83% mass of our universe is made up by some type of mysterious “dark matter”..." I fail to see the point of specifying 'mostly by renowned astrophysicists'. Surely the published work of less famous astrophysicists is also just as relevant. There is no need for this comment.
Line 92: "(1 pc = 3.26 light-years = 3.08×10^16 m)" and line 94: "(1 light-year = 9.46×10^15 m, the distance for light to travel in 1 year in vacuum)". This is not necessary in a journal such as 'Galaxies'.
Line 259: "appear to be nearly straight lines with negative slopes, for most part [18 – 21]." It is not clear what the author is trying to say here: 'for the most part'? If so, 'for the most part of the galaxy's radius'?
The comments below highlight some of the typos found in the text.
Line 281: "This kind diagram has become...", this kind 'of' diagram?
Line 60: "sol-called dark matter" typo.
Line 83: "remarks is presented", typo: should be 'are presented".
Line 300: "simply assumed same exponential function", typo: 'assumed the same...'?
Line 437, 451, etc.: "distributed matters", should be 'distributed matter', 'matter ... is expected', etc.
Author Response
Reviewer #1
The paper gives details of a calculation of the mass distribution in spiral galaxies based on the measured rotation curves. In this work, it is not assumed that the mass-to-light ratio is constant across the galaxy. As a result, the dynamics of the galaxy is modeled without the need for dark matter. The 'inverse problem' of finding the surface density from the known rotation curve is solved algebraically for a model of the galaxy consisting of a disk of a uniform thickness. A bulge distribution of matter can be added to the model.
The author refers to work previously done during the last decade, with the addition of newer measurements that have been available since then. The work is very important in the field as it impacts on the amount of non-baryonic dark matter that is required to explain observations. Since no candidate particle for dark matter has yet been detected, a model which does not require any dark matter is a very relevant alternative.
Author: I thank this reviewer for spending the time to read and understand the essence of this manuscript, with a purpose of providing constructive comments and suggestions.
Overall a good paper, but although many references to previous work are given, a number of things can be clarified in this manuscript.
Author: I try my best to make revisions according to the comments and suggestions.
In the abstract, the author writes that a constant mass-to-light ratio is generally assumed and that the "mass determined from rotation curve typically exhibit an exponential-like decline with galactrocentric distance, qualitatively consistent with observed surface brightness." From this sentence, one is inclined to think that the surface brightness is consistent with a 'constant mass-to-light' ratio, but the last sentence of the abstract says the opposite. It seems the wording is not quite right. In the paper it is explained that the inferred mass determined from rotation curves is not consistent with a constant mass-to-light ratio. Please correct the statement in the abstract to reflect this.
Author: A few words “but often with a larger disk radial scale length” have been added in the abstract, to show the quantitative difference which can be removed by a variable mass-to-light ratio. Several sentences were also added at the end of section 3 to discuss and clarify this point. Furthermore, on page 7 I added several sentences to enhance this argument:
But the disk radial scale length, Rd, determined from rotation curve based thin-disk model appears to be larger than that from fitting the brightness data (e.g., 4.5 kpc versus 2.5 kpc for Milky Way [20]). A straightforward interpretation of such a discrepancy would be an indication of increasing mass-to-light ratio with galactocentric distance, namely the (baryonic) matter becomes less luminous in regions further away from the galactic center. This is consistent with typical edge-on views of disk galaxies that often revealing a dark edge against a bright background central bulge (cf. the image of NGC 891 in Figure 1).
Line 245: The arms of the galaxy make the density deviate from an axisymmetric model. How much difference does this make on the final result?
Author: I do not have the first-hand data to quantify this difference, but I’m certain about the existence of density variation from the averaged value provided by the axisymmetric disk model. How much could the difference be depends on how nonuniform the mass is distributed in a ring, which does not seem to have an easily identified upper limit. I don’t think a quantitative value on this is essential for the argument, although it may strengthen it. But this can be highly case-to-case dependent and difficult to generalize. So, I’d rather leave this open for now.
Line 342: The total mass of the galaxy is given as "calculated from the predicted value of A as M_g = V_0^2 R_g / (G A)." This relation with A = 1 is the virial theorem commonly used in astrophysics, and this should be mentioned. Here however, the rotation parameter A is what makes the difference betwen the need of exotic dark matter or not. But A seems to be no larger than 2, so why are the results different compared to other calculations made with the virial theorem?
Author: This is a very interesting suggestion, according to which I added a paragraph after Figure 3 as follows.
Interestingly, the value of A defined in (6) seems to be around 1.70 for various rotation curves, when the characteristic velocity V0 is taken as a representative value of the flat part of rotation curve [18—21]. For Mestel’s disk of constant rotation velocity with available analytical solution, the value of A is determined as p / 2 = 1.5707063 [20]. A proportionality constant from a lognormal density distribution model results of 38 galaxies for Mg versus Vmax 2 Rg [28] indicates a value of A equal to 1.57063 if Vmax and V0 happen to be the same as with Mestel’s disk. Comparing with the scalar virial theorem, Mg = <V2> rg / G with <V2> and rg denoting the mean-square speed of the system’s stars and the gravitational radius [1], this suggests that <V2> rg = V0 2 Rg / A , i.e., rg ~ 0.59 Rg if <V2> = V0 2 is assumed. Given the fact that <V2> also includes the velocity dispersion in addition to the rotational orbital part, it seems that rg = 0.5 Rg (corresponding to <V2> ~ 1.18 V0 2 ) could be a reasonable approximation for rough estimate of the total mass in a disk galaxy from the measured rotational velocity based on the virial theorem.
Only two examples are given, the Milky Way and Andromeda. Could another example be given for a galaxy where a large fraction of dark matter is expected? What I am looking for is an example which shows a big difference between the method of this paper and the usual methods from which dark matter is predicted.
Author: More computational examples were provided in our previous publication [21]. I’m not trying to say that our model can predict the amount of mass exactly matching that from brightness based on mass-to-light ratio. The point I want to make in this paper is that the discrepancy can be explained by inevitable uncertainties in the mass-to-light ratio, among others in the inaccurate astronomical measurements, rather than an indication of nonbaryonic dark matter. I try to give scientific reasons to my best ability for the existence of undetectable baryonic matter in the space at large, and it’s unnecessary to resort to nonbaryonic dark matter in general.
Lines 342 to 350: How is the characteristic rotation velocity V_0 estimated for the calculations? Is it an average velocity weighted by the luminosity?
Author: The characteristic rotation velocity V_0 is taken as a representative value of the flat part of rotation curve (by visual judgement rather than using a rigorous algorithm which can certainly be done such as taking a mean value or so). To clarify this point, a few words were added following V_0 definition after Eq (4).
Line 352: Figure 3 showing the mass density is exponential from r = 0.1 to 0.9, but shows a strong 'cusp' near r = 0. The 'cuspy halo problem' also arises with dark matter models. Could the author comment on this sharp rise in density (over a factor of 100) considering that it is not observed in most galaxies?
Author: I added a paragraph on page 10 to (partially) address the ‘cusp’ near r = 0 as:
Besides the region of 0.1 < r < 0.9 for near-exponential decline of mass distribution, Figure 3 also shows a much sharper increase of mass density toward the galactic center for r < 0.1, which seems to be fairly typical for many galaxies [21]. Rapid increasing luminosity toward the galactic center has also been commonly shown in the surface brightness profiles which some authors would categorize as the “bulge”region [26]. To seriously include the bulge effect in the disk model may introduce more variables to the result, unless the bulge mass distribution is known a priori for uniquely determined mass in disk with a given rotation curve [21].
As elaborated in [21], some rotation curves may even have nonzero velocity at r = 0 that corresponding to infinite local mass density in a disk model (similar to that for Mestel’s disk). This is actually an artifact of thin disk assumption that breaks down in a region near r = 0 where the radial distance becomes comparable or smaller than the disk thickness. This mathematical singularity can be easily removed by adding a small spherical core. But getting into this kind of technical details may be too distractive to the current presentation flow. So, I just point to [21] for seriously interested readers to dig out the details if desired. I do not want to get to the discussion of ‘cuspy halo problem’ with dark matter models, for the same reason because it can be too involved and distractive while generating more heat than light.
In the paragraph lines 378-392, atomic hydrogen and molecular hydrogen are discussed as possible baryonic dark matter. Dust, mentioned at the beginning of the paper, should also be discussed here. A letter written in Physics Today (https://physicstoday.scitation.org/doi/10.1063/1.2743106) describes how dust also has a small optical cross section and can avoid detection. The idea was already discussed over 60 years ago.
Author: This is a great reminder. I added the reference to Meinel’s letter to Physics Today [39], per suggestion.
The following comments are related to clarifications or style.
Line 52: The author writes "we have been told (mostly by renowned astrophysicists) that about 83% mass of our universe is made up by some type of mysterious “dark matter”..." I fail to see the point of specifying 'mostly by renowned astrophysicists'. Surely the published work of less famous astrophysicists is also just as relevant. There is no need for this comment.
Author: Those words “(mostly by renowned astrophysicists)” were eliminated, per suggestion.
Line 92: "(1 pc = 3.26 light-years = 3.08×10^16 m)" and line 94: "(1 light-year = 9.46×10^15 m, the distance for light to travel in 1 year in vacuum)". This is not necessary in a journal such as 'Galaxies'.
Author: I agree that these common unit conversions are not necessary for most of the readers of ‘Galaxies’. But having them there can provide convenient references for some readers like myself, who do not make a living by studying astronomy and astrophysics.
Line 259: "appear to be nearly straight lines with negative slopes, for most part [18 – 21]." It is not clear what the author is trying to say here: 'for the most part'? If so, 'for the most part of the galaxy's radius'?
Author: I added a few words “when the abruptly varying ends at r = 0 and 1 are trimmed out” in that sentence and in the Figure 3 caption, to clarify this point.
The comments below highlight some of the typos found in the text.
Line 281: "This kind diagram has become...", this kind 'of' diagram?
Line 60: "sol-called dark matter" typo.
Line 83: "remarks is presented", typo: should be 'are presented".
Line 300: "simply assumed same exponential function", typo: 'assumed the same...'?
Line 437, 451, etc.: "distributed matters", should be 'distributed matter', 'matter ... is expected', etc.
Author: All those typos are corrected as suggested. I appreciate this reviewer’s careful proof reading of my manuscript.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper deals with dark matter which is rather polemic
There are not only rotation curves with logarithmic decline, but also the bullet cluster which strongly indicates DM,
see E.~W.~Mielke and J. A. V\'elez P\'erez: ``Axion condensate
as a model for dark matter halos,'' Phys.\ Lett. B \textbf{671},
174-178 (2009).
On the other hand there are few galaxies with very liddle DM, cf. P. van Dokkum, Shany Danieli, Roberto Abraham, Charlie Conroy, and Aaron J. Romanowsky:
``A second galaxy missing dark matter in the NGC 1052 group,'' Astrophys.\ J. Letter
The author should discuss his point, more technically, for better "scientific reason".
In the present form, it misses many recent developments, e.g. H.~Y.~Schive, T.~Chiueh, T.~Broadhurst and K.~W.~Huang:
``Contrasting Galaxy formation from quantum wave dark matter, $\psi$DM, with $\Lambda$CDM, using Planck and Hubble data,'' Astrophys.\ J.\ {\bf 818}, no. 1, 89 (2016)
It needs a complete revision, before it can be reconsidered
Author Response
Reviewer #2
The paper deals with dark matter which is rather polemic
Author: As the title indicates, this paper is a review of scientific reasoning for rotating disk galaxies without (nonbaryonic) dark matter. Here I try to focus on the “galactic rotation problem”, often considered as a primary compelling evidence for (nonbaryonic) dark matter. I provide my scientific reasoning to show that rotating disk galaxies can be described by Newtonian dynamics with baryonic matter, luminous and “dark” (or “invisible”), without the need for resorting to mysterious nonbaryonic dark matter. The lack of means for accurate evaluation of amount of matter at different astronomical scales and uncertainties in the value of mass-to-light ratio seems to be sufficient for explaining the apparent “missing mass” in the galactic rotation problem.
There are not only rotation curves with logarithmic decline, but also the bullet cluster which strongly indicates DM,
see E.~W.~Mielke and J. A. V\'elez P\'erez: ``Axion condensate
as a model for dark matter halos,'' Phys.\ Lett. B \textbf{671},
174-178 (2009).
Author: Besides the “galactic rotation problem”, there are various indirect indications of DM also based on observations and measurements with questionable accuracy and poorly examined uncertainties. The bottom line is that so far all direct detections of DM have failed despite decades-long serious efforts. I don’t think getting too deep into a discussion of DM “evidence” or “indicators” can generate much light than heat at current stage.
On the other hand there are few galaxies with very liddle DM, cf. P. van Dokkum, Shany Danieli, Roberto Abraham, Charlie Conroy, and Aaron J. Romanowsky:
``A second galaxy missing dark matter in the NGC 1052 group,'' Astrophys.\ J. Letter
Author: The work of van Dokkum team has been briefly mentioned as Ref [10] in the original version.
The author should discuss his point, more technically, for better "scientific reason".
In the present form, it misses many recent developments, e.g. H.~Y.~Schive, T.~Chiueh, T.~Broadhurst and K.~W.~Huang:
``Contrasting Galaxy formation from quantum wave dark matter, $\psi$DM, with $\Lambda$CDM, using Planck and Hubble data,'' Astrophys.\ J.\ {\bf 818}, no. 1, 89 (2016)
Author: Without being confirmed by direct detection, the existence of DM remains elusive. Many authors chose to invoke DM in their models seemingly for the convenience of publishing “self-consistent” results, with plenty uncertainties offered by observational “data”. But published results may not guarantee correctness, as Ken Freeman stated in his book [7]:”there is always the possibility that one or all of the estimates could be wrong.” Too much discussion of those DM models can only generate more heat than light. I think it’s better to focus on presenting my scientific reasoning, without commenting on numerous publications of DM models unless they point out defects in my arguments. Therefore, I added a paragraph of generalized comments in the Concluding remarks:
The lack of means for accurate evaluation of amount of matter at different astronomical scales leaves plenty room and freedom for theoretical speculations; “there is always the possibility that one or all of the estimates could be wrong” [7]. Unable to directly and reliably measure the amount of all baryonic matter in the observable universe with the available technology is a scientifically expected and should not be regarded as a mystery. For disk galaxies, the measured rotation curves provide the most reliable information for deriving the mass distribution base on Newtonian dynamics [17, 23]. When the Newtonian dynamics model suggests more mass than that indicated by luminosity based on some value of mass-to-light ratio, there is likely to exist some “invisible” baryonic matter that is “dark” and undetectable to the available instrument. If the mass obtained by other (less reliable) methods, such as that from a mass-to-light ratio, does not match that determined from rotation curve, it should be naturally understandable as a consequence of inevitable uncertainties of inaccurate estimate, instead of being considered as primary evidence for mysterious dark matter. The validity of indirect observational evidence for (nonbaryonic) dark matter remains generally questionable, because of decades-long efforts with again and again failed direct detection. Yet numerous research papers published in scientific literature rather faithfully presumed the existence of nonbaryonic dark matter (for the convenience of obtaining seemingly “self-consistent” results), without serious consideration alternative possibilities. This appears to be a common “snowball” effect in modern astronomy and cosmology for scientists to conform to the mainstream ideas so as to obtain research funds and observing time on major telescopes [49, 50]. But the progress of science generally relies on truth-seeking people who look critically at the contemporary schemes, and continuously overthrow the established, especially unsubstantiated, views based on more reliable evidence. Without inquisitive doubt and skepticism, science cannot thrive and will stagnate.
It needs a complete revision, before it can be reconsidered
Author: I cannot make demanded “complete revision” with comments lack of specific suggestions or critical comments on my reasoning.
Reviewer 3 Report
Referee report of the Manuscript entitled "Rotating Disk Galaxies without Dark Matter Based on Scientific Reasoning" by James Q. Feng ( ID: galaxies-653020)
The author tries to convince the reader that the Newtonian Mechanics is enough to solve the so-called missing mass problem assuming a variable
mass-to-light ratio of baryonic matter in galaxies. Nevertheless, such an assumption is not new in literature (see for example arXiv:0904.4098 ), and it is well established that it cannot replace dark matter. Moreover, the author forgot completely all the other probes supporting the dark matter hypothesis, such as gravitational lensing and CMB power spectrum among the others, that cannot be explained without it or a modified theory of gravity.
Author Response
Reviewer #3
Referee report of the Manuscript entitled "Rotating Disk Galaxies without Dark Matter Based on Scientific Reasoning" by James Q. Feng ( ID: galaxies-653020)
The author tries to convince the reader that the Newtonian Mechanics is enough to solve the so-called missing mass problem assuming a variable
mass-to-light ratio of baryonic matter in galaxies. Nevertheless, such an assumption is not new in literature (see for example arXiv:0904.4098 ), and it is well established that it cannot replace dark matter. Moreover, the author forgot completely all the other probes supporting the dark matter hypothesis, such as gravitational lensing and CMB power spectrum among the others, that cannot be explained without it or a modified theory of gravity.
Author: The previous publication for variable mass-to-light ratio did not seriously examine the intrinsic uncertainties and lack of reliability in the astronomical measurements, which should be scientifically understandable in view of technical difficulties. I can understand that there is (baryonic) matter that is dark, but disagree with the need for nonbaryonic dark matter to solve the “missing mass” problem. The lack of means for accurate evaluation of amount of matter at different astronomical scales and uncertainties in the value of mass-to-light ratio seems to be sufficient for explaining the apparent “missing mass” in the galactic rotation problem. Over the progressive history of science, what was “well-established” could be later proven wrong. If all the attempts so far for direct DM detection have failed (despite decades-long serious efforts), how well-established can it be? In my opinion, most of the missing mass came from unreliable estimates based on inaccurate measurements with limited means and tremendous technical challenges in astronomical observation. At the current stage, getting too deep into the DM discussion can only generate more heat than light. So, I’d rather keep the focus here on Newtonian dynamics model for disk galaxies and description of rotation curves without invoking the nonbaryonic dark matter. To clarify my point of view, I added a paragraph of generalized comments in the Concluding remarks:
The lack of means for accurate evaluation of amount of matter at different astronomical scales leaves plenty room and freedom for theoretical speculations; “there is always the possibility that one or all of the estimates could be wrong” [7]. Unable to directly and reliably measure the amount of all baryonic matter in the observable universe with the available technology is a scientifically expected and should not be regarded as a mystery. For disk galaxies, the measured rotation curves provide the most reliable information for deriving the mass distribution base on Newtonian dynamics [17, 23]. When the Newtonian dynamics model suggests more mass than that indicated by luminosity based on some value of mass-to-light ratio, there is likely to exist some “invisible” baryonic matter that is “dark” and undetectable to the available instrument. If the mass obtained by other (less reliable) methods, such as that from a mass-to-light ratio, does not match that determined from rotation curve, it should be naturally understandable as a consequence of inevitable uncertainties of inaccurate estimate, instead of being considered as primary evidence for mysterious dark matter. The validity of indirect observational evidence for (nonbaryonic) dark matter remains generally questionable, because of decades-long efforts with again and again failed direct detection. Yet numerous research papers published in scientific literature rather faithfully presumed the existence of nonbaryonic dark matter (for the convenience of obtaining seemingly “self-consistent” results), without serious consideration alternative possibilities. This appears to be a common “snowball” effect in modern astronomy and cosmology for scientists to conform to the mainstream ideas so as to obtain research funds and observing time on major telescopes [49, 50]. But the progress of science generally relies on truth-seeking people who look critically at the contemporary schemes, and continuously overthrow the established, especially unsubstantiated, views based on more reliable evidence. Without inquisitive doubt and skepticism, science cannot thrive and will stagnate.
Round 2
Reviewer 2 Report
The paper should not be published or send to another referee
Author Response
Not allowing publication of scientific reasoning does not make wrong claims right. The progress of science generally relies on truth-seeking people who look critically at the contemporary schemes, and continuously point out flaws in the established, especially unsubstantiated, views based on more reliable evidence. Without inquisitive doubt and skepticism, science cannot thrive and will stagnate.
Reviewer 3 Report
The author confuses the existence of a dark matter particle with the dark matter problem. The latter is a well-established problem in astrophysics and related to numerous observations (not just the rotation curves). Without a doubt, the existence of the dark matter particle and its nature is still actively investigated by the scientific community, but the lack of its direct detection is not proof of its non-existence. Furthermore, Newtonian mechanics and general relativity fail to explain all the astrophysical phenomenology related to dark matter without introducing its contribution or modifying the law of gravity.Author Response
This reviewer might be a firm believer of dark matter. I’ve put forward my scientific reasoning for resolving the so-called galactic rotation problem without dark matter, by pointing out the technical flaws in evidence gathering. If that part of evidence is unreliable and questionable, can those other “well-established” evidences “related to numerous observations (not just the rotation curves)” still be valid without a doubt? Again, as I stated in my concluding remarks, the progress of science generally relies on truth-seeking people who look critically at the contemporary schemes, and continuously point out flaws in the established, especially unsubstantiated, views based on more reliable evidence. Without inquisitive doubt and skepticism, science cannot thrive and will stagnate.
