Tomography of the Ie-Re and L-Sigma Planes
Round 1
Reviewer 1 Report
I have read this review about the properties of the structural parameters of the early-type galaxies. I find the review well written and interesting for readers. For this reason I recommend the paper for publication in the journal. I have only one comment about the notation throughout the paper. The authors use the notation Ie to refer to a quantity with is the effective surface brightness of the galaxies. Usually in the literature is used Ie to refer to the effective intensity. In contrast, the surface brightness of the galaxies is notated by \mu_{e}. I recommend to the authors change the notation in the full paper because it will be more clear.
Author Response
Thank you. You are right. We have changed the name in effective intensity everywhere.
Reviewer 2 Report
Dear Authors,
I read with a lot of interest your manuscript entitled "Tomography of the and Ie-Re and L-sigma planes". In the article you explore the Ie-Re and L-sigma planes for early-type galaxies in the nearby universe using both a large sample of observed and simulated galaxies extracted from the WINGS (+SDSS spectra) survey and Illustrius simulations. From this exploration your extensive and detailed analysis support the idea that the classical FJ relation, valid as an empirical relation fulfilled by ETGs, is the consequence not of a pure reformulation of the VT, but the intersection of this one with a relation with a similar form (L = L_o * sigma^beta), but in which L_o and beta are not universal for all ETGs, but heavely dependent on the Star-formation History, Merging history, and accretion history of each individual galaxy.
I think your results clearly illustrate so, in particular how the distribution in the Ie-Re diagram cannot be explained by the classical FJ relation only, and it is needed to invoke the explored relation (valid for individual galaxies).
I do not have any major comment on your manuscript. It is nicely and clearly presented. If any I have just minor suggestions, essentially details, that I think you can address without iterating any further, if you consider them useful somehow.
1) Although it is not the purpose of the manuscript, I think it would be nice to include more details on the completeness or compatibility between the two explored samples. Fig. 2 show some discrepancies in the distributions (observed galaxies do not expand to the same range of simulated ones in the regime of log_Ie<1.5 and log(Re)<4). I am not sure if is included in some of the references, but I cannot see it clearly explained in the text.
2) Fig.8. When plotting the results of the distribution of galaxies "simulated" using the individual Lo' sigma^beta relation in the Ie-Re diagram you exclude those "galaxies" that enter into de ZoE (pg.20, lines 595-597). However, I think it is very informative to know or estimate the fraction of galaxies that enter in that regime using this simulation. The nature of this test is to demonstrate that using the classical FJ relation (with slope and intercept fixed) does not populate the Ie-Re distribution, but using the new individual relation it is possible to populate it. Thus, to know how many "unreal" galaxies are derived in the this case is relevant. I strongly recommend to include them in Fig.8 using a different symbol (like open-circles with the same colors?). That will illustrate better the way the new relation works in this experiment (something that for instance is better shown in Fig.9)
3) The evolution along the SFR-M* plane shown in Fig.14 has been explored using both cosmological surveys, compilation of data and using the fossil records (e.g., Speagel et al. 2014; Rodrigez-Puebla et al. 2017). In particular, the evolution along this diagram of nowadays Early-type galaxies was presented in Sanchez et al. (2018). I think it is worth to compare the results and cite those studies.
https://ui.adsabs.harvard.edu/abs/2014ApJS..214...15S/abstract
https://ui.adsabs.harvard.edu/abs/2017MNRAS.470..651R/abstract
https://ui.adsabs.harvard.edu/abs/2019MNRAS.482.1557S/abstract
In this latter article it is indeed seen how and when the nowadays ETGs depart from the SFMS.
4) Regarding the new re-formulation of the FJ relation in terms of the individual evolutionary histories of ETGs, I think the authors should depart (or at least discuss) the most recent results regarding the evolution of these objects. It is nowadays clear that a single SSP or a single burst is not enough to explain their evolution. The mass-assambly history is far more complex and change galaxy by galaxy, modulated by their final stellar mass (as a primary proxy of the evolution), but also by the dynamical stage (fast or slow rotators), the environment (central o satellite galaxies, cluster ellipticals...). In this regards you can see the following articles: Garcia-Benito et al. 2018; Sanchez 2020, ARA&A; Lopez-Fernandez et al. 2018; Bluck et al. 2020, and references therein. To codify the evolution by a single parameter as the average Age of the stellar population it is not enough to describe the SF Histories of those galaxies. This like of argument is included along all the article, for instance in the reformulation of Eq 8 to Eq. 9. T_G is just the first moment of the Age Distribution Function, that it is broader and more tailed than what it was assumed before. From the seminal studies by Panter et al. 2003,2007, to my recent review on the topic (Sanchez 2020, ARAA), there is a bulk of literature showing that ETGs present a wide range of SFHs. Some references:
https://ui.adsabs.harvard.edu/abs/2020ARA%26A..58...99S/abstract
https://ui.adsabs.harvard.edu/abs/2021MNRAS.504.3478C/abstract
Thus, even the new formulation of a relation for each galaxy is an approximation. My point is that L'_0 and beta are more complex parameter than what it is indicated in the text. Maybe it is worth noticing it.
5) On the same topic , authors should acknowledge that the use of a single parameter for the efficiency of the star-formation for galaxies of different morphology (Table 3, pages 34-35), is not in the line of the recent understanding of this parameter. In Colombo et al. 2018 it is clearly shown that the SFE (depletion time), present a strong dependency with the morphology (and the mass). These results have been confirmed in Sanchez et al. 2021 (RMxAA), and more recently in Sanchez et al. 2021b (A&A Letters), using direct and indirect estimations of the molecular gas content in galaxies and the distribution of alpha/Fe respectively. Authors should revise and acknowledge this dependency, I think.
6) Pg. 34, paragraph starting in line 908: How reasonable is case (i) for ETGs (i.e., the fact that the SF never stops in the course of formation and evolution). In those galaxies, in the last 1-3Gyr the SF activity has dropped to almost zero in the nearby universe. So, this case may be valid for late-type galaxies, but not for early-type ones.
7) Authors do not include in the discussion the fact that part of the scatter in the FJ relation, and most probably in the Ie-Re relation, is due to the fact that a fraction of ETGs present ordered orbits (e.g,. Zhu et al. 2018)
https://ui.adsabs.harvard.edu/abs/2018NatAs...2..233Z/abstract
For this reason the FJ has a dispersion that it is narrower if you introduce an SK parameter, that combines the velocity dispersion and the V_rot (e.g., Aquino-Ortiz et al. 2018;2020)
https://ui.adsabs.harvard.edu/abs/2018MNRAS.479.2133A/abstract
https://ui.adsabs.harvard.edu/abs/2020ApJ...900..109A/abstract
The discovery of the existence of those fast-rotators in the ETG family was a core result from the SAURON and Atlas3D surveys (e.g., Cappellari 2016, for a review on the topic)
https://ui.adsabs.harvard.edu/abs/2016ARA%26A..54..597C/abstract
I think this should be included in the article somehow: i.e., the FJ dispersion and the lack of pure correspondance with the Ie-Re distributions is also partially due to the presence of ordered orbits in ETGs too.
That would be all from my part. It has been a pleasure reading this manuscript, indeed!
Best regards,
Author Response
I read with a lot of interest your manuscript entitled "Tomography of the and Ie-Re and L-sigma planes". In the article you explore the Ie-Re and L-sigma planes for early-type galaxies in the nearby universe using both a large sample of observed and simulated galaxies extracted from the WINGS (+SDSS spectra) survey and Illustrius simulations. From this exploration your extensive and detailed analysis support the idea that the classical FJ relation, valid as an empirical relation fulfilled by ETGs, is the consequence not of a pure reformulation of the VT, but the intersection of this one with a relation with a similar form (L = L_o * sigma^beta), but in which L_o and beta are not universal for all ETGs, but heavely dependent on the Star-formation History, Merging history, and accretion history of each individual galaxy.
I think your results clearly illustrate so, in particular how the distribution in the Ie-Re diagram cannot be explained by the classical FJ relation only, and it is needed to invoke the explored relation (valid for individual galaxies).
I do not have any major comment on your manuscript. It is nicely and clearly presented. If any I have just minor suggestions, essentially details, that I think you can address without iterating any further, if you consider them useful somehow.
1) Although it is not the purpose of the manuscript, I think it would be nice to include more details on the completeness or compatibility between the two explored samples. Fig. 2 show some discrepancies in the distributions (observed galaxies do not expand to the same range of simulated ones in the regime of log_Ie<1.5 and log(Re)<4). I am not sure if is included in some of the references, but I cannot see it clearly explained in the text.
--------------------------------------------------------------------------------
R. Thanks. We have expanded the section of the data sample to give more info.
Concerning the compatibility of the WINGS and Illustris data they are discussed in many papers of D'Onofrio et al. (2017,2019,2020).
Here we have only discussed the fact that while the sigma and the luminosities of Illustris are in agreement with the data,
the radii are systematically larger. This is a well known feature of the simulations.
The problem is likely linked to the effects of feedback included in the simulation.
Large feedback produces large effective radii in particular for the small massive galaxies.
--------------------------------------------------------------------------------
2) Fig.8. When plotting the results of the distribution of galaxies "simulated" using the individual Lo' sigma^beta relation in the Ie-Re diagram you exclude those "galaxies" that enter into de ZoE (pg.20, lines 595-597). However, I think it is very informative to know or estimate the fraction of galaxies that enter in that regime using this simulation. The nature of this test is to demonstrate that using the classical FJ relation (with slope and intercept fixed) does not populate the Ie-Re distribution, but using the new individual relation it is possible to populate it. Thus, to know how many "unreal" galaxies are derived in the this case is relevant. I strongly recommend to include them in Fig.8 using a different symbol (like open-circles with the same colors?). That will illustrate better the way the new relation works in this experiment (something that for instance is better shown in Fig.9)
--------------------------------------------------------------------------------
R. We have added a new figure showing the behavior of our mathematical exercise. I
The figure shows how the galaxies distribute in the Ie-Re plane according to eq. 11. The trends observed depend
on the chosen Re-sigma relation and on the values adopted for beta and L'_0.
We cannot make any consideration on the statistics of galaxies entering in the forbidden region, simply because
this is only a mathematical exercise and not a true numerical simulation. In other words we use eq. 11
exploring the values of Ie as a function of Re, sigma (through the sigma(Re) depencence), L'0 and beta.
--------------------------------------------------------------------------------
3) The evolution along the SFR-M* plane shown in Fig.14 has been explored using both cosmological surveys, compilation of data and using the fossil records (e.g., Speagel et al. 2014; Rodrigez-Puebla et al. 2017). In particular, the evolution along this diagram of nowadays Early-type galaxies was presented in Sanchez et al. (2018). I think it is worth to compare the results and cite those studies.
https://ui.adsabs.harvard.edu/abs/2014ApJS..214...15S/abstract
https://ui.adsabs.harvard.edu/abs/2017MNRAS.470..651R/abstract
https://ui.adsabs.harvard.edu/abs/2019MNRAS.482.1557S/abstract
In this latter article it is indeed seen how and when the nowadays ETGs depart from the SFMS.
--------------------------------------------------------------------------------
R. We have expanded that section and added the references.
--------------------------------------------------------------------------------
4) Regarding the new re-formulation of the FJ relation in terms of the individual evolutionary histories of ETGs, I think the authors should depart (or at least discuss) the most recent results regarding the evolution of these objects. It is nowadays clear that a single SSP or a single burst is not enough to explain their evolution. The mass-assembly history is far more complex and change galaxy by galaxy, modulated by their final stellar mass (as a primary proxy of the evolution), but also by the dynamical stage (fast or slow rotators), the environment (central o satellite galaxies, cluster ellipticals...). In this regards you can see the following articles: Garcia-Benito et al. 2018; Sanchez 2020, ARA&A; Lopez-Fernandez et al. 2018; Bluck et al. 2020, and references therein. To codify the evolution by a single parameter as the average Age of the stellar population it is not enough to describe the SF Histories of those galaxies. This like of argument is included along all the article, for instance in the reformulation of Eq 8 to Eq. 9. T_G is just the first moment of the Age Distribution Function, that it is broader and more tailed than what it was assumed before. From the seminal studies by Panter et al. 2003,2007, to my recent review on the topic (Sanchez 2020, ARAA), there is a bulk of literature showing that ETGs present a wide range of SFHs. Some references:
https://ui.adsabs.harvard.edu/abs/2020ARA%26A..58...99S/abstract
https://ui.adsabs.harvard.edu/abs/2021MNRAS.504.3478C/abstract
Thus, even the new formulation of a relation for each galaxy is an approximation. My point is that L'_0 and beta are more complex parameter than what it is indicated in the text. Maybe it is worth noticing it.
--------------------------------------------------------------------------------
R. We have expanded that section and added the references.
--------------------------------------------------------------------------------
5) On the same topic , authors should acknowledge that the use of a single parameter for the efficiency of the star-formation for galaxies of different morphology (Table 3, pages 34-35), is not in the line of the recent understanding of this parameter. In Colombo et al. 2018 it is clearly shown that the SFE (depletion time), present a strong dependency with the morphology (and the mass). These results have been confirmed in Sanchez et al. 2021 (RMxAA), and more recently in Sanchez et al. 2021b (A&A Letters), using direct and indirect estimations of the molecular gas content in galaxies and the distribution of alpha/Fe respectively. Authors should revise and acknowledge this dependency, I think.
--------------------------------------------------------------------------------
R. We have added this comment and cited the references.
--------------------------------------------------------------------------------
6) Pg. 34, paragraph starting in line 908: How reasonable is case (i) for ETGs (i.e., the fact that the SF never stops in the course of formation and evolution). In those galaxies, in the last 1-3Gyr the SF activity has dropped to almost zero in the nearby universe. So, this case may be valid for late-type galaxies, but not for early-type ones.
--------------------------------------------------------------------------------
R. You are right. This case is shown here only for a comparative purpose. It is not valid for ETGs. We wanted to see the effects
of a non-stopped SF.
--------------------------------------------------------------------------------
7) Authors do not include in the discussion the fact that part of the scatter in the FJ relation, and most probably in the Ie-Re relation, is due to the fact that a fraction of ETGs present ordered orbits (e.g,. Zhu et al. 2018)
https://ui.adsabs.harvard.edu/abs/2018NatAs...2..233Z/abstract
For this reason the FJ has a dispersion that it is narrower if you introduce an SK parameter, that combines the velocity dispersion and the V_rot (e.g., Aquino-Ortiz et al. 2018;2020)
https://ui.adsabs.harvard.edu/abs/2018MNRAS.479.2133A/abstract
https://ui.adsabs.harvard.edu/abs/2020ApJ...900..109A/abstract
The discovery of the existence of those fast-rotators in the ETG family was a core result from the SAURON and Atlas3D surveys (e.g., Cappellari 2016, for a review on the topic)
https://ui.adsabs.harvard.edu/abs/2016ARA%26A..54..597C/abstract
I think this should be included in the article somehow: i.e., the FJ dispersion and the lack of pure correspondance with the Ie-Re distributions is also partially due to the presence of ordered orbits in ETGs too.
That would be all from my part. It has been a pleasure reading this manuscript, indeed!
--------------------------------------------------------------------------------
R. We have expanded that section and added the references.
Reviewer 3 Report
I would like to apologize for the delay in submitting my report on the manuscript entitled "Tomography of the Ie − Re and L − σ planes" by D'Onofrio and Chiosi. This is a thorough, detailed, and particularly interesting study by two leading researchers in the field of early-type galaxies (ETGs).
The main motivation behind the analysis presented is that the distribution of ETGs on the effective surface brightness I_e vs. effective radius R_e plane and the Faber-Jackson (FJ) relation connecting luminosity L and stellar velocity dispersion σ are incompatible to each other. The authors propose that these two empirical scaling relations can be reconciled into a coherent picture by taking into account the variation of the inverse mass-to-light M/L ratio among ETGs, as previously suggested by D'Onofrio et al. (2017). The proposed functional form L = L0 σ^β encodes in L0 and β the mass assembly history of ETGs (i.e., both the star formation history and the stellar mass growth due to mergers).
As these systems are likely characterized by diversity in their formation history it is to be expected that β deviates from the value of 4 for bright ETGs (and ~2.7 for fainter ones) that is commonly assumed for the FJ relation.
The latter, although primarily reflects the virial theorem, makes the (over)simplifying assumption that luminosity is a good proxy to stellar mass, i.e. that the M/L ratio of ETGs is nearly constant over ~0.5 dex in σ and ~3 dex in I_e.
Prior to testing the L = L_0 σ^β relation, the authors provide in Sect. 1-4 a detailed description of the exiting observational foundation for the I_e vs. R_e and FJ relation, and convincingly argue for the need of taking the luminosity evolution of ETGs into account. On the observational side, the authors use OMEGA-WINGS from which they extract a subset of ~30000 ETGs with photometric/structural determinations (R_e, I_e, Sérsic index, etc.) and, additionally, 1800 ETGs with determinations of σ. This data set allows to study the aforementioned scaling relations over a relevant range in galaxy mass.
Quite importantly, the authors distinguish between 'ordinary' ETGs with an absolute magnitude that is typically fainter than -19 mag and 'bright' ETGs, and pose the question of why these two ETG sub-populations are discernible in the I_e-R_e plane whereas nearly indistinguishable in the L-σ plane.
Since L0 and β cannot be directly obtained from observations (the WINGS data set), the authors use estimates from Illustris cosmological simulations, and demonstrate that the L = L_0 σ^β law can reproduce the observed scatter of the I_e vs. R_e relation. This is an important new insight that clearly adds physical justification to the proposed ansatz (the L = L_0 σ^β). Moreover, it is to be expected that this study will trigger further observational and theoretical work on the mass- and age-dependence of the exponent β (Δlog(L)/Δlog(σ)), which essentially describes the evolution of the light-to-mass ratio across time, with negative values corresponding to a recent increase of the galaxy luminosity and vice versa. Summarizing, I consider that this study constitutes a solid step forward toward understanding ETG evolution, and I'm glad to recommend its publication without revision.
However, I consider that the value and impact of this study would be enhanced if the authors could briefly comment on the following points:
i) a well-established empirical insight is that lower-luminosity ('ordinary') ETGs are in their majority disky (based on their α4 Fourier coefficient) and show a far higher central luminosity density than 'bright' ETGs, many of which are 'boxy' and exhibit a central flattening (core) in their surface brightness profiles. Additionally, bright ETGs differ from ordinary ETGs in their far higher radio power and X-ray luminosity, which hints at an important role of AGN feedback on their mass assembly history.
This leads to two questions:
a) what is the effect of fitting a Sérsic model to a bright ETG showing a central core? Even though the core is marginally resolvable from ground-based data, could this bias the Sérsic-model-dependent R_e and I_e in such a manner as to mimic a bi-parametric distribution (L proportional to IeRe^2) for ordinary ETGs (without a central core) and a
mono-parametric distribution (Ie depends only on Re; page 2) for bright ETGs?
b) in what manner could negative AGN feedback influence the β exponent for 'bright' ETGs? Could this contribute to the
observed scatter of the I_e vs. R_e relation?
ii) In Eq. 4 the authors compress into the terms L_0 and β, besides the structural and kinematical properties of an ETG, the inverse M/L ratio of its stellar populations. Therefore, in this equation the luminosity L is expressed as the product of 1/(M/L) and the 'kinematical temperature' σ. If ETG formation follows a downsizing trend, then one may expect
their M/L ratio to increase with galaxy mass (or σ), with the brightest ETGs completing their assembly earlier than lower-mass ETGs and showing the highest M/L. If this is the case, then ordinary ETGs should on average be characterized by a lower mass- and light-weighted stellar age than bright ETGs, in other words, the β exponent should follow an inverse relation with the light-weighted stellar age (negative β for bright ETGs having experienced passive photometric evolution since z~1). I'd like to encourage the authors to briefly comment on possibilities for further examining and firming up their scenario using spectral modeling studies of ETGs.
Author Response
I would like to apologize for the delay in submitting my report on the manuscript entitled "Tomography of the Ie − Re and L − σ planes" by D'Onofrio and Chiosi. This is a thorough, detailed, and particularly interesting study by two leading researchers in the field of early-type galaxies (ETGs).
The main motivation behind the analysis presented is that the distribution of ETGs on the effective surface brightness I_e vs. effective radius R_e plane and the Faber-Jackson (FJ) relation connecting luminosity L and stellar velocity dispersion σ are incompatible to each other. The authors propose that these two empirical scaling relations can be reconciled into a coherent picture by taking into account the variation of the inverse mass-to-light M/L ratio among ETGs, as previously suggested by D'Onofrio et al. (2017). The proposed functional form L = L0 σ^β encodes in L0 and β the mass assembly history of ETGs (i.e., both the star formation history and the stellar mass growth due to mergers).
As these systems are likely characterized by diversity in their formation history it is to be expected that β deviates from the value of 4 for bright ETGs (and ~2.7 for fainter ones) that is commonly assumed for the FJ relation.
The latter, although primarily reflects the virial theorem, makes the (over)simplifying assumption that luminosity is a good proxy to stellar mass, i.e. that the M/L ratio of ETGs is nearly constant over ~0.5 dex in σ and ~3 dex in I_e.
Prior to testing the L = L_0 σ^β relation, the authors provide in Sect. 1-4 a detailed description of the exiting observational foundation for the I_e vs. R_e and FJ relation, and convincingly argue for the need of taking the luminosity evolution of ETGs into account. On the observational side, the authors use OMEGA-WINGS from which they extract a subset of ~30000 ETGs with photometric/structural determinations (R_e, I_e, Sérsic index, etc.) and, additionally, 1800 ETGs with determinations of σ. This data set allows to study the aforementioned scaling relations over a relevant range in galaxy mass.
Quite importantly, the authors distinguish between 'ordinary' ETGs with an absolute magnitude that is typically fainter than -19 mag and 'bright' ETGs, and pose the question of why these two ETG sub-populations are discernible in the I_e-R_e plane whereas nearly indistinguishable in the L-σ plane.
Since L0 and β cannot be directly obtained from observations (the WINGS data set), the authors use estimates from Illustris cosmological simulations, and demonstrate that the L = L_0 σ^β law can reproduce the observed scatter of the I_e vs. R_e relation. This is an important new insight that clearly adds physical justification to the proposed ansatz (the L = L_0 σ^β). Moreover, it is to be expected that this study will trigger further observational and theoretical work on the mass- and age-dependence of the exponent β (Δlog(L)/Δlog(σ)), which essentially describes the evolution of the light-to-mass ratio across time, with negative values corresponding to a recent increase of the galaxy luminosity and vice versa. Summarizing, I consider that this study constitutes a solid step forward toward understanding ETG evolution, and I'm glad to recommend its publication without revision.
However, I consider that the value and impact of this study would be enhanced if the authors could briefly comment on the following points:
i) a well-established empirical insight is that lower-luminosity ('ordinary') ETGs are in their majority disky (based on their α4 Fourier coefficient) and show a far higher central luminosity density than 'bright' ETGs, many of which are 'boxy' and exhibit a central flattening (core) in their surface brightness profiles. Additionally, bright ETGs differ from ordinary ETGs in their far higher radio power and X-ray luminosity, which hints at an important role of AGN feedback on their mass assembly history.
This leads to two questions:
a) what is the effect of fitting a Sérsic model to a bright ETG showing a central core? Even though the core is marginally resolvable from ground-based data, could this bias the Sérsic-model-dependent R_e and I_e in such a manner as to mimic a bi-parametric distribution (L proportional to IeRe^2) for ordinary ETGs (without a central core) and a
mono-parametric distribution (Ie depends only on Re; page 2) for bright ETGs?
b) in what manner could negative AGN feedback influence the β exponent for 'bright' ETGs? Could this contribute to the
observed scatter of the I_e vs. R_e relation?
--------------------------------------------------------------------------------
R.
a) The values of Re and Ie used here were derived through a fit of the growth curves of the galaxies. This means that no fit
have been made of the light profiles. The effective radius is only the radius of the circle enclosing half the total luminosity.
In this sense no biases are introduced due to the different light profiles of the galaxies. The galaxy position in the Ie-Re plane depends only on the half light radius and the total luminosity. Clearly, the half light radius depends on the viewing angle of the galaxy
with respect to the line of sight and to the presence of dust. As a matter of fact, galaxies of the same luminosity, span a wide range
of Ie and Re in the plane. This interval gives an idea of the influence of such effects.
b) Simulations show that β might take either positive and negative values. However, we do not know what processes
are currently determining the observed β. Certainly AGN feedback might contribute to quench the SF and induce
a negative β, but we do not know how big is this effect with respect to others (e.g. stripping, etc.).
--------------------------------------------------------------------------------
ii) In Eq. 4 the authors compress into the terms L_0 and β, besides the structural and kinematical properties of an ETG, the inverse M/L ratio of its stellar populations. Therefore, in this equation the luminosity L is expressed as the product of 1/(M/L) and the 'kinematical temperature' σ. If ETG formation follows a downsizing trend, then one may expect
their M/L ratio to increase with galaxy mass (or σ), with the brightest ETGs completing their assembly earlier than lower-mass ETGs and showing the highest M/L. If this is the case, then ordinary ETGs should on average be characterized by a lower mass- and light-weighted stellar age than bright ETGs, in other words, the β exponent should follow an inverse relation with the light-weighted stellar age (negative β for bright ETGs having experienced passive photometric evolution since z~1). I'd like to encourage the authors to briefly comment on possibilities for further examining and firming up their scenario using spectral modeling studies of ETGs.
-------------------------------------------------------------------------------------------------
R. We have expanded the discussion of this item adding this consideration.
