Astronomy

Correlation between stellar mass and galactocentric distance

Correlation between stellar mass and galactocentric distance


We are searching data for your request:

Forums and discussions:
Manuals and reference books:
Data from registers:
Wait the end of the search in all databases.
Upon completion, a link will appear to access the found materials.

As we move away from the centre of, say, a spiral galaxy, is there a relation between the stellar mass and distance? I know the how the stellar abundance and density varies with the distance but does stellar mass also follow a pattern?


In terms of the distribution of stellar masses when stars form -- the Initial Mass Function (IMF) -- there doesn't seem to be much variation, at least for spirals. (There is evidence that massive elliptical galaxies may have different IMFs as a function of radius, with relatively more low-mass stars formed near their centers. The cause of this is unclear; it might have to do with different conditions for star formation, with very dense, high-pressure gas in what would become the centers of massive elliptical galaxies possibly producing different distributions of stellar masses.)

The current distribution of stellar masses at a given radius in a spiral galaxy will depend almost entirely on the local star-formation history. Since stellar lifetime depends on stellar mass, regions with recent star formation will have more stars that are massive; regions where star formation ceased a long time ago will be dominated by low-mass stars, since all the higher-mass stars there have died.

In most spiral galaxies, the mean age of stars tends to decrease as you move further out in radius (as indicated by optical colors: reddish central regions are mostly old populations dominated by red giants, while the disk further out is blue because there are younger populations dominated by hot, massive stars). This is an example of what's called "inside-out" star formation.

However, a lot of lower-mass spirals seem to show a reversal of this trend at large radii, with redder (older, mostly lower-mass) stars beyond a certain radius. Since this is the same radius at which the density of stars in the disk stars falling off more rapidly (the "break" or "truncation" radius), it's usually thought this is the result of a combination of two effects: 1) A radial threshold/cutoff in star formation, with very few stars being formed beyond a certain radius (possibly because the gas density becomes too low); and 2) Radial scattering of stars over time by spiral arms, which means that older stars tend to be scattered to larger (or smaller) radii simply because they've had more encounters with spiral arms. In this case, the relative fraction of more massive stars would increase with radius out to the truncation radius, and then decrease beyond.


Mind the gap: Scientists use stellar mass to link exoplanets to planet-forming disks

“We found a strong correlation between gaps in protoplanetary disks and stellar mass, which can be linked to the presence of large, gaseous exoplanets,” said Nienke van der Marel, a Banting fellow in the Department of Physics and Astronomy at the University of Victoria in British Columbia, and the primary author on the research. “Higher mass stars have relatively more disks with gaps than lower mass stars, consistent with the already known correlations in exoplanets, where higher mass stars more often host gas-giant exoplanets. These correlations directly tell us that gaps in planet-forming disks are most likely caused by giant planets of Neptune mass and above.”

Gaps in protoplanetary disks have long been considered as overall evidence of planet formation. However, there has been some skepticism due to the observed orbital distance between exoplanets and their stars. “One of the primary reasons that scientists have been skeptical about the link between gaps and planets before is that exoplanets at wide orbits of tens of astronomical units are rare. However, exoplanets at smaller orbits, between one and ten astronomical units, are much more common,” said Gijs Mulders, assistant professor of astronomy at Universidad Adolfo Ibáñez in Santiago, Chile, and co-author on the research. “We believe that planets that clear the gaps will migrate inwards later on.”

The new study is the first to show that the number of gapped disks in these regions matches the number of giant exoplanets in a star system. “Previous studies indicated that there were many more gapped disks than detected giant exoplanets,” said Mulders. “Our study shows that there are enough exoplanets to explain the observed frequency of the gapped disks at different stellar masses.”

The correlation also applies to star systems with low-mass stars, where scientists are more likely to find massive rocky exoplanets, also known as Super-Earths. Van der Marel, who will become an assistant professor at Leiden University in the Netherlands beginning September 2021 said, “Lower mass stars have more rocky Super-Earths — between an Earth mass and a Neptune mass. Disks without gaps, which are more compact, lead to the formation of Super-Earths.”

This link between stellar mass and planetary demographics could help scientists identify which stars to target in the search for rocky planets throughout the Milky Way. “This new understanding of stellar mass dependencies will help to guide the search for small, rocky planets like Earth in the solar neighborhood,” said Mulders, who is also a part of the NASA-funded Alien Earths team. “We can use the stellar mass to connect the planet-forming disks around young stars to exoplanets around mature stars. When an exoplanet is detected, the planet-forming material is usually gone. So the stellar mass is a ‘tag’ that tells us what the planet-forming environment might have looked like for these exoplanets.”

And what it all comes down to is dust. “An important element of planet formation is the influence of dust evolution,” said van der Marel. “Without giant planets, dust will always drift inwards, creating the optimal conditions for the formation of smaller, rocky planets close to the star.”

The current research was conducted using data for more than 500 objects observed in prior studies using ALMA’s high-resolution Band 6 and Band 7 antennas. At present, ALMA is the only telescope that can image the distribution of millimeter-dust at high enough angular resolution to resolve the dust disks and reveal its substructure, or lack thereof. “Over the past five years, ALMA has produced many snapshot surveys of nearby star-forming regions resulting in hundreds of measurements of disk dust mass, size, and morphology,” said van der Marel. “The large number of observed disk properties has allowed us to make a statistical comparison of protoplanetary disks to the thousands of discovered exoplanets. This is the first time that a stellar mass dependency of gapped disks and compact disks has been successfully demonstrated using the ALMA telescope.”

“Our new findings link the beautiful gap structures in disks observed with ALMA directly to the properties of the thousands of exoplanets detected by the NASA Kepler mission and other exoplanet surveys,” said Mulders. “Exoplanets and their formation help us place the origins of the Earth and the Solar System in the context of what we see happening around other stars.”


Mind the gap: Scientists use stellar mass to link exoplanets to planet-forming disks

IMAGE: Protoplanetary disks are classified into three main categories: transition, ring, or extended. These false-color images from the Atacama Large Millimeter/submillimeter Array (ALMA) show these classifications in stark contrast. On left.

Using data for more than 500 young stars observed with the Atacama Large Millimeter/Submillimeter Array (ALMA), scientists have uncovered a direct link between protoplanetary disk structures--the planet-forming disks that surround stars--and planet demographics. The survey proves that higher mass stars are more likely to be surrounded by disks with "gaps" in them and that these gaps directly correlate to the high occurrence of observed giant exoplanets around such stars. These results provide scientists with a window back through time, allowing them to predict what exoplanetary systems looked like through each stage of their formation.

"We found a strong correlation between gaps in protoplanetary disks and stellar mass, which can be linked to the presence of large, gaseous exoplanets," said Nienke van der Marel, a Banting fellow in the Department of Physics and Astronomy at the University of Victoria in British Columbia, and the primary author on the research. "Higher mass stars have relatively more disks with gaps than lower mass stars, consistent with the already known correlations in exoplanets, where higher mass stars more often host gas-giant exoplanets. These correlations directly tell us that gaps in planet-forming disks are most likely caused by giant planets of Neptune mass and above."

Gaps in protoplanetary disks have long been considered as overall evidence of planet formation. However, there has been some skepticism due to the observed orbital distance between exoplanets and their stars. "One of the primary reasons that scientists have been skeptical about the link between gaps and planets before is that exoplanets at wide orbits of tens of astronomical units are rare. However, exoplanets at smaller orbits, between one and ten astronomical units, are much more common," said Gijs Mulders, assistant professor of astronomy at Universidad Adolfo Ibáñez in Santiago, Chile, and co-author on the research. "We believe that planets that clear the gaps will migrate inwards later on."

The new study is the first to show that the number of gapped disks in these regions matches the number of giant exoplanets in a star system. "Previous studies indicated that there were many more gapped disks than detected giant exoplanets," said Mulders. "Our study shows that there are enough exoplanets to explain the observed frequency of the gapped disks at different stellar masses."

The correlation also applies to star systems with low-mass stars, where scientists are more likely to find massive rocky exoplanets, also known as Super-Earths. Van der Marel, who will become an assistant professor at Leiden University in the Netherlands beginning September 2021 said, "Lower mass stars have more rocky Super-Earths--between an Earth mass and a Neptune mass. Disks without gaps, which are more compact, lead to the formation of Super-Earths."

This link between stellar mass and planetary demographics could help scientists identify which stars to target in the search for rocky planets throughout the Milky Way. "This new understanding of stellar mass dependencies will help to guide the search for small, rocky planets like Earth in the solar neighborhood," said Mulders, who is also a part of the NASA-funded Alien Earths team. "We can use the stellar mass to connect the planet-forming disks around young stars to exoplanets around mature stars. When an exoplanet is detected, the planet-forming material is usually gone. So the stellar mass is a 'tag' that tells us what the planet-forming environment might have looked like for these exoplanets."

And what it all comes down to is dust. "An important element of planet formation is the influence of dust evolution," said van der Marel. "Without giant planets, dust will always drift inwards, creating the optimal conditions for the formation of smaller, rocky planets close to the star."

The current research was conducted using data for more than 500 objects observed in prior studies using ALMA's high-resolution Band 6 and Band 7 antennas. At present, ALMA is the only telescope that can image the distribution of millimeter-dust at high enough angular resolution to resolve the dust disks and reveal its substructure, or lack thereof. "Over the past five years, ALMA has produced many snapshot surveys of nearby star-forming regions resulting in hundreds of measurements of disk dust mass, size, and morphology," said van der Marel. "The large number of observed disk properties has allowed us to make a statistical comparison of protoplanetary disks to the thousands of discovered exoplanets. This is the first time that a stellar mass dependency of gapped disks and compact disks has been successfully demonstrated using the ALMA telescope."

"Our new findings link the beautiful gap structures in disks observed with ALMA directly to the properties of the thousands of exoplanets detected by the NASA Kepler mission and other exoplanet surveys," said Mulders. "Exoplanets and their formation help us place the origins of the Earth and the Solar System in the context of what we see happening around other stars."


Scientists use stellar mass to link exoplanets to planet-forming disks

Using data for more than 500 young stars observed with the Atacama Large Millimeter/Submillimeter Array (ALMA), scientists have uncovered a direct link between protoplanetary disk structures—the planet-forming disks that surround stars—and planet demographics. The survey proves that higher mass stars are more likely to be surrounded by disks with “gaps” in them and that these gaps directly correlate to the high occurrence of observed giant exoplanets around such stars. These results provide scientists with a window back through time, allowing them to predict what exoplanetary systems looked like through each stage of their formation.

“We found a strong correlation between gaps in protoplanetary disks and stellar mass, which can be linked to the presence of large, gaseous exoplanets,” said Nienke van der Marel, a Banting fellow in the Department of Physics and Astronomy at the University of Victoria in British Columbia, and the primary author on the research. “Higher mass stars have relatively more disks with gaps than lower mass stars, consistent with the already known correlations in exoplanets, where higher mass stars more often host gas-giant exoplanets. These correlations directly tell us that gaps in planet-forming disks are most likely caused by giant planets of Neptune mass and above.”

Gaps in protoplanetary disks have long been considered as overall evidence of planet formation. However, there has been some skepticism due to the observed orbital distance between exoplanets and their stars. “One of the primary reasons that scientists have been skeptical about the link between gaps and planets before is that exoplanets at wide orbits of tens of astronomical units are rare. However, exoplanets at smaller orbits, between one and ten astronomical units, are much more common,” said Gijs Mulders, assistant professor of astronomy at Universidad Adolfo Ibáñez in Santiago, Chile, and co-author on the research. “We believe that planets that clear the gaps will migrate inwards later on.”

The new study is the first to show that the number of gapped disks in these regions matches the number of giant exoplanets in a star system. “Previous studies indicated that there were many more gapped disks than detected giant exoplanets,” said Mulders. “Our study shows that there are enough exoplanets to explain the observed frequency of the gapped disks at different stellar masses.”

The correlation also applies to star systems with low-mass stars, where scientists are more likely to find massive rocky exoplanets, also known as Super-Earths. Van der Marel, who will become an assistant professor at Leiden University in the Netherlands beginning September 2021 said, “Lower mass stars have more rocky Super-Earths—between an Earth mass and a Neptune mass. Disks without gaps, which are more compact, lead to the formation of Super-Earths.”

This link between stellar mass and planetary demographics could help scientists identify which stars to target in the search for rocky planets throughout the Milky Way. “This new understanding of stellar mass dependencies will help to guide the search for small, rocky planets like Earth in the solar neighborhood,” said Mulders, who is also a part of the NASA-funded Alien Earths team. “We can use the stellar mass to connect the planet-forming disks around young stars to exoplanets around mature stars. When an exoplanet is detected, the planet-forming material is usually gone. So the stellar mass is a ‘tag’ that tells us what the planet-forming environment might have looked like for these exoplanets.”

And what it all comes down to is dust. “An important element of planet formation is the influence of dust evolution,” said van der Marel. “Without giant planets, dust will always drift inwards, creating the optimal conditions for the formation of smaller, rocky planets close to the star.”

The current research was conducted using data for more than 500 objects observed in prior studies using ALMA’s high-resolution Band 6 and Band 7 antennas. At present, ALMA is the only telescope that can image the distribution of millimeter-dust at high enough angular resolution to resolve the dust disks and reveal its substructure, or lack thereof. “Over the past five years, ALMA has produced many snapshot surveys of nearby star-forming regions resulting in hundreds of measurements of disk dust mass, size, and morphology,” said van der Marel. “The large number of observed disk properties has allowed us to make a statistical comparison of protoplanetary disks to the thousands of discovered exoplanets. This is the first time that a stellar mass dependency of gapped disks and compact disks has been successfully demonstrated using the ALMA telescope.”

“Our new findings link the beautiful gap structures in disks observed with ALMA directly to the properties of the thousands of exoplanets detected by the NASA Kepler mission and other exoplanet surveys,” said Mulders. “Exoplanets and their formation help us place the origins of the Earth and the Solar System in the context of what we see happening around other stars.”


Galactic Outflows: A Stellar Matter?

Galactic images captured by spaced based telescopes, such as Hubble, can be breathtaking. Vibrant hues of stellar light infuse with warm gas and dust emission to illuminate the composition of these stunning structures.

However, despite their ethereal nature, some of the Universe’s most extreme interactions occur near their centers. Here, intense feedback – the mechanism by which outflowing matter and radiation impact their environments – rages on.

The two primary modes of galactic feedback are Active Galactic Nuclei (AGN) feedback and supernova feedback. AGN feedback is fueled by the rapid accretion of material onto a supermassive black hole, which is converted into radiation, jets, and winds. Comparatively, supernova feedback results from the explosion of a massive dying star.

These processes are of great interest to researchers because they may regulate their host galaxy’s evolution. For example, outflowing radiation from a compact source can potentially clear out reservoirs of cold molecular gas in its vicinity and restrict local star formation, potentially suppressing the growth of the host galaxy.

Outflows in Star-Forming Galaxies

The authors of today’s paper explored the properties of galactic stellar feedback. They utilized the Mapping Galaxies at Apache Point Observatory (MaNGA) survey to spatially resolve galactic-scale outflows in a sample of 405 high mass (log M/M ≥ 10) nearby galaxies (z

The authors elected to exclude AGN from their analysis because the elevated cloud velocities (> 1,000 km/s) in the Broad Line Region, the region closest to the AGN, often mimic the presence of outflows. This certainly eliminates potential contamination though, AGN feedback is of great interest to astronomers due to the immense power and physical scale associated with AGN outflows.

Figure 1 showcases a typical MaNGA observation conducted with integral field unit spectroscopy.

To conduct their study, the authors traced the radial extent of the galactic outflows by analyzing the spectra of Sodium absorption and emission lines. To help determine the origin of the outflows, they examined star formation rates, star formation rate densities, dust extinction, and the D(4000) index of the galaxies. In addition, they incorporated a stacking technique that bins spaxels (a pixel with a spectral dimension) to construct high signal to noise composite spectra and determine how outflow properties change as a function of galactocentric distance.

Figure 1. An example of IFU MaNGA galaxy property maps. From left to right, top to bottom: The Sloan Digital Sky Survey image of an example galaxy within the MaNGA field of view, the Hα velocity, Hα flux, Hβ flux, the Balmer decrement (Hα/Hβ), and the D(4000) index. (Figure 2 in the paper.)

Outflow Origins

Their findings reveal strong outflows near the cores of the MaNGA galaxies. Moreover, they identify strong similarities between the evolution of mass outflow rates (M/yr) and star formation rate densities (M/yr/kpc -2 ), as well as stellar densities (M/kpc 2 ) at increasing galactocentric distances (Figure 2). This suggests that elevated star formation activity drives stronger outflows.

Figure 2. The normalized evolution of the mean mass outflow rate compared to several key galaxy properties (i.e., star formation rate density, stellar mass density, dust extinction, and D(4000)), with error bars. The mass outflow rate is most similar to the evolution of star formation density and stellar mass density. (Figure 6 in the paper.)

If outflows are suspected to suppress star formation, why are the strongest outflows found in regions with the highest star formation rates?

Let’s consider a galactic fountain scenario. During this process, a massive star undergoes a brilliant supernova explosion that generates powerful outflows. The energetic streams that emanate from the dying star entrain metal-enriched matter and heat gas several parsecs below or above the plane of the galaxy. The gas eventually cools before falling back down towards the galactic disk, forming the fountain.

The frequency of these events is dependent on the abundance of supernovae, which scales with star formation. The authors’ findings are consistent with this relation. Despite the outflows potentially clearing the cool molecular gas, the star formation density is still found to be the most dominant parameter that scales with the strength of outflows – more stars lead to more supernovae and therefore more outflows.

Furthermore, stellar feedback is generated by more than just supernova activity! Bipolar outflows and stellar winds can also inject energy and momentum into surrounding gas. As star formation increases, the occurrence of these events is likely to increase as well.

The authors also consider a critical “blow out” star formation density that marks the threshold where stellar feedback is strong enough to escape the disk of the galaxy. They equate the weight of the disk gas to the pressure imparted by the feedback and derive a value of

0.02 M/yr/kpc -2 . Above this value, pressure from the feedback exceeds the weight of the gas for nearby galaxies (z

0) – the outflows are liberated.

Missing Link in Galactic Evolution

Today’s paper offers preliminary evidence that star-forming regions strongly influence the presence of outflows. Stellar feedback is also found to be strongest near the center of the observed MaNGA galaxies.

However, to fully unravel the dynamics of the outflows, a thorough analysis of AGN feedback is essential. AGN outflows tend to be more energetic and may be even more critical for understanding the coevolution between feedback and galactic growth. For example, if star formation is determined to be repressed in the presence of AGN outflows, it may suggest that powerful AGN radiation, jets, and winds completely clear the cold molecular gas in their path. Such a result would counter the positive correlation between outflow strength and star formation density found here with stellar feedback. Future MaNGA studies that incorporate both modes of feedback will help determine the true nature of galactic-scale outflows and how they influence galactic growth.

Nonetheless, today’s paper offers us great insight into the properties of outflows and their relation to stellar feedback!


The Link Between Black Holes and Their Galaxies

The size of a supermassive black hole seems to track with the size of its host galaxy. But is this a statistical fluke, or is there a physical reason for the connection? Recent modeling provides new clues.

Growing Together

Composite image of Centaurus A, a galaxy whose appearance is dominated by the large-scale jets emitted by the supermassive black hole at its center. [ESO/WFI (Optical) MPIfR/ESO/APEX/A.Weiss et al. (Submillimetre) NASA/CXC/CfA/R.Kraft et al. (X-ray)]

But why the connection? How can the black hole know about the galaxy size around it, and vice versa? There are a few proposed explanations for the correlation between central-black-hole mass and its host galaxy’s stellar mass:

  1. It’s caused by active galactic nucleus (AGN) feedback.
    In this scenario (recently described here), jets and winds from the accreting black hole can both trigger star formation and quench it by expelling extra gas — star-formation fuel — from the galaxy. This feedback causes the rate of star formation to roughly track the rate of black hole accretion.
  2. It’s caused by black-hole growth and galaxy star formation both relying on the same fuel source.
    If black-hole growth and galactic star formation both arise from the same source of fuel, then these two growths should correlate even if they don’t influence each other. One example of a fuel source that could cause sudden growth is a wet merger — the collision of two galaxies rich in gas.
  3. It’s simply a consequence of statistics, and not caused by a physical mechanism.
    A theorem known as the central limit theorem suggests that the correlation we observe could arise naturally as a statistical consequence of building up galaxies hierarchically from smaller structures over time. In this scenario, there’s no physical connection between the black hole and its host galaxy — it’s all statistics.

It’s a Matter of the Model

To test which of these explanations is most likely, we need to combine models with observations. A new study led by Xuheng Ding (University of California, Los Angeles) recently set out to do so.

Plots showing the correlation between black hole mass (MBH) and stellar mass of the host galaxy (M*. The actual observations are plotted in orange. The blue dots in the top plot show the simulated correlation from the hydrodynamic simulation the green dots in the bottom plot show the simulated correlation from the semianalytic model. The hydro simulation provides a better match to the data. [Adapted from Ding et al. 2020]

The authors then compared these data to the outputs of two state-of-the-art models: a hydrodynamic simulation that focuses on AGN feedback, and a semianalytic model that is especially sensitive to wet galaxy-merger events.

Connecting via Feedback

The results of the authors’ models — in particular, the tightness of the modeled correlation between black-hole and galaxy size across redshifts — strongly support a physical mechanism driving the connection, rather than it being a consequence of statistics.

Of the two models, the hydrodynamic simulation better reproduced the scatter of the correlation, suggesting that AGN feedback may indeed be the driver ensuring that supermassive black holes grow at the same rate as their host galaxies. Observations out to higher redshifts — which may be possible with the upcoming James Webb Space Telescope — will help us further tease out the explanation for this intriguing link.

Citation

“Testing the Fidelity of Simulations of Black Hole–Galaxy Coevolution at z

1.5 with Observations,” Xuheng Ding et al 2020 ApJ 896 159. doi:10.3847/1538-4357/ab91be


Event

A surprisingly tight correlation has been discovered between galaxies’ star formation rates (SFR) and stellar masses (M_*). We show that the evolution of the normalization of the SFR-M_* correlation is driven primarily by the age of the universe. There is an underlying correlation between galaxies’ instantaneous star formation rates and their average star formation rates since the Big Bang. The Dense Basis method of spectral energy distribution fitting allows star formation histories (SFHs) to be reconstructed, along with uncertainties, for 50,000 galaxies in the CANDELS catalogs at 0.5<z<6. For the first time, these SFHs reveal that the SFR-M_* correlation extends to low-mass galaxies at very high redshift. We introduce an improved estimator for burstiness and apply it to 1000 galaxies with 3D-HST H alpha detections at z

1. Our measurements of the correlation between instantaneous, 100 Myr, and past-average star formation rates provide new constraints on the level of stochasticity in galaxy formation.


3. TWO PITFALLS

After the discovery that the presence of Jovian planets is more frequent around metal-rich stars, several studies have explored how the formation of giant planets could be favored in a circumstellar disk enhanced in metals (Ida & Lin 2004 Mordasini et al. 2008). The results of the previous section now leads to the following preliminary question: how do we know that the higher percentage of giant planets detected on metal-rich stars is due to their metallicity and not to some other factor also linked with their origin in the inner disk? The question is relevant, because any measurable property of inner disk stars other than metallicity would be correlated with the presence of planet. The obvious a priori response is that metallicity is a measurable parameter, and intrinsic to the star. But there could be others however, which, although not measurable on the stars, could be no less important, such as, for example, the surface density of molecular hydrogen in the inner galactic disk regions. We now show that there are two cases where the planet–metallicity correlation is not verified, for which radial mixing provides a simple explanation, suggesting that metallicity may not be the relevant parameter. We will show in the following section that a bona fide planet–metallicity correlation can be obtained in the context of radial mixing with no metallicity dependence of any kind.

3.1. The Difference in Giant–Dwarf Metallicity Distributions

The first case where the planet–metallicity correlation breaks down is the metallicity distribution of giant host stars. While the planet–host dwarf metallicity distribution is known to be skewed toward metal-rich objects, giant hosts are known to have a metallicity which is more like the field stars distribution see, in particular, Takeda et al. (2008) and Pasquini et al. (2007).

Figure 2 shows the age–metallicity relation for field dwarfs and giants as derived by Takeda (2007) and Takeda et al. (2008). The progressive enlargement of the metallicity with age is well in accord with the effect of radial mixing, as noted in Haywood (2006, 2008b). The metallicity dispersion is smaller for giants: this is expected given their age distribution, Figure 2 shows that most giants have ages smaller than 1 Gyr. Since radial mixing is a secular process, its effect increases with time: the contamination by stars from the inner and outer disk is proportional to age. Because the sample of giants contains mostly young stars, it is little polluted by old, metal-rich, wanderers of the inner disk. The squares in Figure 2 show the planet host giant stars from Takeda et al. (2008), completed with the few other "massive" (M > 1.4 M) objects available from the exoplanet database. 1 The figure illustrates that these objects, when older than about 2 Gyr, are mostly metal-rich ([Fe/H] > 0.0 dex), while the 14 stars younger than 2 Gyr have a mean metallicity of −0.04 dex. In the sample of Takeda et al., seven host giants (out of 10) are younger than 1 Gyr, and all are younger than 3 Gyr. The explanation for the difference between the dwarf and giant distributions comes out as a natural galactic effect: the giant sample contains a limited bias toward metal-rich objects because it is much younger than the dwarf sample, and then much less contaminated by radial mixing.

Figure 2. Age–metallicity relation for giants (squares) and dwarfs (circles) from Takeda (2007) and Takeda et al. (2008), complemented by "massive" (M > 1.4 M) objects from the exoplanet database. Host planet dwarfs are shown as red large dots, and host planet giants as red filled squares. The mean metallicity of 14 planet host stars with ages <2 Gyr is −0.04 dex.

Pasquini et al. (2007) have suggested that the mass of the convective envelope could play a role. If the excess of metals is due to pollution at the surface of stars, it could be diluted when the dwarf becomes a giant. We propose instead that the excess of metals is intrinsic to the star, and that the age is the determining factor, producing a selective effect on the origin of the stars.

3.2. The Difference between the Thin and Thick Disks

At intermediate metallicities (−0.7< [Fe/H]<−0.3 dex), stellar populations in the solar vicinity can be divided into two groups: the thin and the thick disks, which differentiate both by their α-elements content and their asymmetric drift. At these metallicities, the thin disk is solar in α-elements, but rotates faster than the LSR, while the thick disk is enriched in α-elements ([α/Fe] > 0.1 dex) but lags the LSR. While the local metal-rich stars may be attributed to migration from the inner disk, the metal-poor end can be attributed to stars that came from the outer disk (see Haywood 2008b). It has been shown in Haywood (2008a) that in this metallicity interval, giant planets are found preferentially on thick disk stars. This is illustrated in Figure 3, where 10 stars with giant planets are compatible with being either thick disk or transition objects between the thin and the thick disks. Only one dwarf, HD 171028, and one giant, HD 170693, are compatible with being a member of the metal-poor thin disk with an origin in the outer disk. As commented in Haywood (2008a), this is significant, because the number of thin disk objects at these metallicities is expected to be higher or equal to the number of thick disk stars.

Figure 3. (a) Stars with giant planets at [Fe/H]<−0.2 dex for which α-element abundance is available (the mean of Mg, Si, Ca, Ti, or the last three for some giants). Gray squares are field dwarfs from Reddy et al. (2003, 2006) and Bensby et al. (2005). Large red dots or square symbols are host planet dwarfs or giants in the thick disk regime and transition zone between the thick and thin disks. The black dot and square represent the only dwarf (HD 171028) and giant hosting Jupiters clearly in the metal-poor thin disk regime ([Fe/H] = −0.49, −0.59 dex) and Vrot = (+2, 51.5) km s −1 . The smaller dots below the line are dwarfs clearly in the thin disk regime, with their lag in Vrot suggesting they are not from the outer disk. Plot (b) shows the velocity component in the direction of rotation as a function of metallicity for stars in plot (a). The field stars that make up the branch toward Vrot > 0 and low metallicities ([Fe/H]<−0.3 dex) are the metal-poor objects with a probable origin in the outer disk (at [Fe/H]<−0.3 dex and [α/Fe] < 0.1 dex in plot (a)).

In Figure 3(a), six objects having [Fe/H]<−0.2 dex are thin disk objects (smaller symbols below the line on plot (a)). The rotation lag and α-element content of these stars (plot b) support the view that they are bona fide solar radius objects, with no specific indication that they would come from the outer disk. The search of new giant planet hosts in this metallicity range with no bias in favor or against either the thin disk and the thick disk is highly desirable to confirm this trend, but we think the difference between the two groups is significant.

Finally, it should be noted that the galactocentric radii of origin of thick disk stars (those with [Fe/H]<−0.2 dex and [α/Fe] > 0.15 dex in Figure 3) is not clear. According to Schoenrich & Binney (2008), we should expect the most metal-rich (at [Fe/H] >−0.4, −0.5 dex) and α-elements enhanced thick disk objects to come from the inner disk. This could be the case in particular for HIP 3497, HIP 26381, HIP 58952, HIP 62534, which all have metallicities above [Fe/H] = −0.5, and relatively high level of α abundance. This is an interesting possibility since in this eventuality even thick disk objects could originate from the inner disk.

If metallicity was the determining factor for the presence of giant planet, we should not expect a difference between the number of planet host stars of the thin and thick disks. Since the metal-poor thin disks objects are expected to come from the outer disk, it is again suggested that the distance to the galactic center plays a role.


The Faintest Dwarf Galaxies

Joshua D. Simon
Vol. 57, 2019

Abstract

The lowest luminosity ( L) Milky Way satellite galaxies represent the extreme lower limit of the galaxy luminosity function. These ultra-faint dwarfs are the oldest, most dark matter–dominated, most metal-poor, and least chemically evolved stellar systems . Read More

Supplemental Materials

Figure 1: Census of Milky Way satellite galaxies as a function of time. The objects shown here include all spectroscopically confirmed dwarf galaxies as well as those suspected to be dwarfs based on l.

Figure 2: Distribution of Milky Way satellites in absolute magnitude () and half-light radius. Confirmed dwarf galaxies are displayed as dark blue filled circles, and objects suspected to be dwarf gal.

Figure 3: Line-of-sight velocity dispersions of ultra-faint Milky Way satellites as a function of absolute magnitude. Measurements and uncertainties are shown as blue points with error bars, and 90% c.

Figure 4: (a) Dynamical masses of ultra-faint Milky Way satellites as a function of luminosity. (b) Mass-to-light ratios within the half-light radius for ultra-faint Milky Way satellites as a function.

Figure 5: Mean stellar metallicities of Milky Way satellites as a function of absolute magnitude. Confirmed dwarf galaxies are displayed as dark blue filled circles, and objects suspected to be dwarf .

Figure 6: Metallicity distribution function of stars in ultra-faint dwarfs. References for the metallicities shown here are listed in Supplemental Table 1. We note that these data are quite heterogene.

Figure 7: Chemical abundance patterns of stars in UFDs. Shown here are (a) [C/Fe], (b) [Mg/Fe], and (c) [Ba/Fe] ratios as functions of metallicity, respectively. UFD stars are plotted as colored diamo.

Figure 8: Detectability of faint stellar systems as functions of distance, absolute magnitude, and survey depth. The red curve shows the brightness of the 20th brightest star in an object as a functi.

Figure 9: (a) Color–magnitude diagram of Segue 1 (photometry from Muñoz et al. 2018). The shaded blue and pink magnitude regions indicate the approximate depth that can be reached with existing medium.


References

Aaronson, M., Huchra, J., and Mould, J. (1979). The infrared luminosity/H I velocity-width relation and its application to the distance scale. Astrophys. J. 229, 1�. doi: 10.1086/156923

Aaronson, M., and Mould, J. (1983). A distance scale from the infrared magnitude/H I velocity-width relation. IV. The morphological type dependence and scatter in the relation the distances to nearby groups. Astrophys. J. 265, 1�. doi: 10.1086/160648

Abraham, R. (2020). “The dragonfly telephoto array: how it works and where it is going.” in American Astronomical Society meeting 𣈵, Vol. 52 (Bulletin of the American Astronomical Society), 2354401.

Allanson, S., Hudson, M., Smith, R. J., and Lucey, J. R. (2009). The star formation histories of red-sequence galaxies, mass-to-light ratios and the fundamental plane. Astrophys. J. 702, 1275�. doi: 10.1088/0004-637X/702/2/1275

Behroozi, P. S., Conroy, C., and Wechsler, R. (2010). A comprehensive analysis of uncertainties affecting the stellar mass-halo mass relation for 0 < z τ. Astrophys. J. 717, 379�. doi: 10.1088/0004-637X/717/1/379

Binney, J. (1987). Observable consequences of triaxial halos. Proc. IAU Symp. 117:303. doi: 10.1017/S0074180900150405

Braun, R. (1990). The interstellar medium of M31. I. A survey of neutral hydrogen emission. Astrophys. J. Suppl. 72:755. doi: 10.1086/191431

Brooks, A., Papastergis, E., Christensen, C. R., Governato, F., Stilp, A., Quinn, T. R., et al. (2017). How to reconcile the observed velocity function of galaxies with theory. Astrophys. J. 850:97. doi: 10.3847/1538-4357/aa9576

Burkert, A. (2017). The geometry and origin of ultra-diffuse ghost galaxies. Astrophys. J. 838:93. doi: 10.3847/1538-4357/aa671c

Campbell, L., Lucey, J., Colless, M., Jones, D. H., Springob, C., Magoulas, C., et al. (2014). The 6dF galaxy survey: fundamental plane data. Mon. Not. R. Astron. Soc. 443:1231. doi: 10.1093/mnras/stu1198

Cappellari, M., McDermid, R. M., Alatalo, K., Blitz, L., Bois, M., Bournaud, F., et al. (2013b). The ATLAS 3D project–XX. Mass-size and mass- distributions of early-type galaxies: bulge fraction drives kinematics, mass-to-light ratio, molecular gas fraction and stellar initial mass function. Mon. Not. R. Astron. Soc. 432, 1862�. doi: 10.1093/mnras/stt644

Cappellari, M., Scott, N., Alatalo, K., Blitz, L., Bois, M., Bournaud, F., et al. (2013a). The ATLAS 3D project–XV. Benchmark for early-type galaxies scaling relations from 260 dynamical models: mass-to-light ratio, dark matter, fundamental plane and mass plane. Mon. Not. R. Astron. Soc. 432, 1709�. doi: 10.1093/mnras/stt562

Carleton, T., Errani, R., Cooper, M., Kaplinghat, M., Penarrubia, J., Guo, Y., et al. (2019). The formation of ultra-diffuse galaxies in cored dark matter haloes through tidal stripping and heating. Mon. Not. R. Astron. Soc. 485, 382�. doi: 10.1093/mnras/stz383

Cerulo, P., Couch, W. J., Lidman, C., Delaye, L., Demarco, R., Huertas-Company, M., et al. (2014). The morphological transformation of red sequence galaxies in the distant cluster XMMU J1229�. Mon. Not. R. Astron. Soc. 439, 2790�. doi: 10.1093/mnras/stu135

Chabrier, G. (2003). Galactic stellar and substellar initial mass function. Publ. Astron. Soc. Pac. 115, 763�. doi: 10.1086/376392

Ciotti, L., Lanzoni, B., and Renzini, A. (1996). The tilt of the fundamental plane of elliptical galaxies–I. Exploring dynamical and structural effects. Mon. Not. R. Astron. Soc. 282, 1�. doi: 10.1093/mnras/282.1.1

Conroy, C., Dutton, A. A., Graves, G. J., Mendel, J. T., and van Dokkum, P. G. (2013). Dynamical versus stellar masses in compact early-type galaxies: further evidence for systematic variation in the stellar initial mass function. Astrophys. J. Lett., 776, L26. doi: 10.1088/2041-8205/776/2/L26

Conroy, C., and van Dokkum, P. G. (2012). The stellar initial mass function in early-type galaxies from absorption line spectroscopy. ii. results. Astrophys. J. 760, 71. doi: 10.1088/0004-637X/760/1/71

Cortese, L., Fogarty, L. M. R., Ho, I.-T., Bekki, K., Bland-Hawthorn, J., Colless, M., et al. (2014). The SAMI galaxy survey: toward a unified dynamical scaling relation for galaxies of all types. Astrophys. J. Lett. 795:L37. doi: 10.1088/2041-8205/795/2/L37

Croom, S. M., Dawe, J., Bland-Hawthorn, J., Bryant, J. J., Fogarty, L., Richards, S., et al. (2012). The Sydney-AAO multi-object integral field spectrograph. Mon. Not. R. Astron. Soc. 421, 872�. doi: 10.1111/j.1365-2966.2011.20365.x

da Cunha, E., Hopkins, A., Colless, M., Taylor, E. N., Blake, C., Howlett, C., et al. (2017). The Taipan galaxy survey: scientific goals and observing strategy. Publ. Astron. Soc. Aust. 34:47. doi: 10.1017/pasa.2017.41

D'Onofrio, M., Fasano, G., Moretti, A., Marziani, P., Bindoni, D., Fritz, J., et al. (2013). The hybrid solution for the fundamental plane. Mon. Not. R. Astron. Soc. 435, 45�. doi: 10.1093/mnras/stt1278

Dutton, A., and Treu, T. (2014). The bulge-halo conspiracy in massive elliptical galaxies: implications for the stellar initial mass function and halo response to baryonic processes. Mon. Not. R. Astron. Soc. 438, 3594�. doi: 10.1093/mnras/stt2489

Faber, S., and Jackson, R. (1976). Velocity dispersions and mass-to-light ratios for elliptical galaxies. Astrophys. J. 204, 668�. doi: 10.1086/154215

Ferrarese, L., and Merritt, D. (2000). A fundamental relation between supermassive black holes and their host galaxies. Astrophys. J. 539, L9–L12. doi: 10.1086/312838

Fitzpatrick, P., and Graves, G. (2014). Early-type galaxy star formation histories in different environments. Mon. Not. R. Astron. Soc. 447, 1383�. doi: 10.1093/mnras/stu2509

Forbes, D., Alabi, A., Romanowsky, A. J., Brodie, J., and Arimoto, N. (2019). An ultra diffuse galaxy in the NGC 5846 group from the VEGAS survey. Astron. Astrophys. 626:66.

Forbes, D., Martin, C., Matuszewski, M., Romanowsky, A. J., and Villaume, A. (2020). The formation of ultradiffuse galaxies in clusters. Mon. Not. R. Astron. Soc. 492, 4874�. doi: 10.1093/mnras/staa180

Graham, A. (2012). Extending the MBH, diagram with dense nuclear clusters. Mon. Not. R. Astron. Soc. 422, 1586. doi: 10.1111/j.1365-2966.2012.20734.x

Graves, G., and Faber, S. (2010). Dissecting the red sequence. III. Mass-to-light variations in three dimensional fundamental plane space. Astrophys. J. 717, 803�. doi: 10.1088/0004-637X/717/2/803

Grillo, C., and Gobat, R. (2010). On the initial mass function and tilt of the fundamental plane of massive early-type galaxies. Mon. Not. R. Astron. Soc. 402, L67–L71. doi: 10.1111/j.1745-3933.2009.00803.x

Jiang, F., Dekel, A., Freundlich, J., and Romanowsky, A. (2019). Formation of ultra-diffuse galaxies in the field and in galaxy groups. Mon. Not. R. Astron. Soc. 487, 5272�. doi: 10.1093/mnras/stz1499

Jones, D. H., Read, M., Saunders, W., Colless, M., Jarrett, T., Parker, Q., et al. (2009). The 6dF galaxy survey: final redshift release (DR3) and southern large-scale structures. Mon. Not. R. Astron. Soc. 399, 683�. doi: 10.1111/j.1365-2966.2009.15338.x

Kim, S., and Park, C. (2007). Topology of H I gas distribution in the large magellanic cloud. Astrophys. J. 663:244. doi: 10.1086/518470

Koribalski, B., Staveley-Smith, L., Westmeier, T., Serra, P., Spekkens, K., Wong, O. I., et al. (2020). WALLABY𠄺n SKA pathfinder HI survey. arXiv[Preprint].arXiv:2002.07311.

Kormendy, J., and Ho, L. (2013). Coevolution (or not) of supermassive black holes and host galaxies. Annu. Rev. Astron. Astrophys. 51, 511�. doi: 10.1146/annurev-astro-082708-101811

Kormendy, J., and Kennicutt, R. (2004). Secular evolution and the formation of pseudobulges in disk galaxies. Annu. Rev. Astron. Astrophys. 42, 603�. doi: 10.1146/annurev.astro.42.053102.134024

Lagattuta, D., Mould, J., Forbes, D., Monson, P.astorello, and Persson, S. E. (2017). Evidence of a bottom-heavy initial mass function in massive early-type galaxies from near-infrared metal lines. Astrophys. J. 846:166. doi: 10.3847/1538-4357/aa8563

Lagos, C., Obreschkow, D., Ryan-Weber, E., Zwaan, M., Kilborn, V., Bekiaris, G., et al. (2016). The fundamental plane of star formation in galaxies revealed by the EAGLE hydrodynamical simulations. Mon. Not. R. Astron. Soc. 459, 2632�. doi: 10.1093/mnras/stw717

Lu, S., Xu, D., Wang, Y., Mao, S., and Ge, J. (2020). SDSS-IV MaNGA: Stellar population correlates with stellar root-mean-square velocity gradients or total-density-profile slopes at fixed effective velocity dispersion 㰾. Mon. Not. R. Astron. Soc. 492, 5930�.

Magorrian, J., Tremaine, S., Richstone, D., Bender, R., Bower, G., Dressler, A., et al. (1998). The demography of massive dark objects in galaxy centers. Astron. J. 115, 2285�. doi: 10.1086/300353

Magoulas, L. J., Lagos, C., Kuehn, K. G., Barat, D., and Bian, F. (2012). The 6dF galaxy survey: the near infrared fundamental plane of early type galaxies. Mon. Not. R. Astron. Soc. 427:245. doi: 10.1111/j.1365-2966.2012.21421.x

Maraston, C. (2005). Evolutionary population synthesis: models, analysis of the ingredients and application to high-z galaxies. Mon. Not. R. Astron. Soc. 362, 799�. doi: 10.1111/j.1365-2966.2005.09270.x

Masci, F., Cutri, R., Francis, P., Nelson, B., and Huchra, J. (2010). The southern 2MASS active galactic nuclei survey: spectroscopic follow-up with six degree field. Publ. Astron. Soc. Aust. 27, 302�. doi: 10.1071/AS10001

Masters, K., Springob, C., and Huchra, J. (2008) 2MTF. I. The Tully-Fisher relation in the two micron all sky survey J, H, K Bands. Astron. J. 135, 1738�. doi: 10.1088/0004-6256/135/5/1738

Moster, B., Somerville, R., Maulbetsch, C., van den Bosch, F., Maccio, A., Thorsten, N., et al. (2010). Constraints on the relationship between stellar mass and halo mass at low and high redshift. Astrophys. J. 710:903. doi: 10.1088/0004-637X/710/2/903

Mould, J. (2014). What are we missing in elliptical galaxies? arXiv[Preprint].arXiv:1403.1623.

Mould, J. (2017). Modified gravity and large scale flows, a review. Astrophys. Space Sci. 362:25. doi: 10.1007/s10509-017-3005-3

Mould, J., and Sakai, S. (2008). The extragalactic distance scale without cepheids. Astrophys. J. Lett. 686:L75. doi: 10.1086/592964

Naab, T., Oosterloo, T., Sarzi, M., Serra, P., Weijmans, A., and Young, L. (2009). Minor mergers and the size evolution of elliptical galaxies. Astrophys. J. 699, L178–L182. doi: 10.1088/0004-637X/699/2/L178

Nelan, J., Smith, R., Hudson, M., and Wegner, G. (2005). NOAO fundamental plane survey. II. Age and metallicity along the red sequence from line-strength data. Astrophys. J. 632, 137�. doi: 10.1086/431962

Papovich, C., Bassett, R., Lotz, J., van der Wel, A., Tran, K. V., Finkelstein, S., et al. (2012). CANDELS observations of the structural properties of cluster galaxies at z = 1.62. Astrophys. J. 750:93. doi: 10.1088/0004-637X/750/2/93

Pina, M., Fraternali, F., Adams, E., Marasco, A., Oosterloo, T., Oman, K., et al. (2019). Off the Baryonic Tully-Fisher relation: a population of Baryon-dominated ultra-diffuse galaxies. Astrophys. J. 883:L33. doi: 10.3847/2041-8213/ab40c7

Proctor, R., Colless, M., Jones, D. H., Kobayashi, C., Campbell, L., Lucey, J., et al. (2008). The effects of stellar populations on galaxy scaling relations in the 6dF galaxy survey. Mon. Not. R. Astron. Soc. 386, 1781�. doi: 10.1111/j.1365-2966.2008.13208.x

Sakai, S., Mould, J., Hughes, S., Huchra, J., Macri, L., Kennicutt, R., et al. (2000). The Hubble space telescope key project on the extragalactic distance scale. XXIV. The calibration of Tully-Fisher relations and the value of the Hubble constant. Astrophys. J. 529, 698�. doi: 10.1086/308305

Sales, L., Navarro, J., Penaafiel, L., Peng, E., Lim, S., and Hernquist, L. (2019). The formation of ultradiffuse galaxies in clusters. Mon. Not. R. Astron. Soc. 494, 1848�. doi: 10.1093/mnras/staa854

Silk, J. (2019). Ultra-diffuse galaxies without dark matter. Mon. Not. R. Astron. Soc. 488, L24–L28. doi: 10.1093/mnrasl/slz090

Skrutskie, M., Cutri, R., Stiening, R., Weinberg, M., Schneider, S., Carpenter, J., et al. (2006). The two micron all sky survey (2MASS). Astron. J. 131, 1163�. doi: 10.1086/498708

Smith, R. (2014). Variations in the initial mass function in early-type galaxies: a critical comparison between dynamical and spectroscopic results. Mon. Not. R. Astron. Soc. 443, L69–L73. doi: 10.1093/mnrasl/slu082

Smith, R., and Lucey, J. (2013). A giant elliptical galaxy with a lightweight initial mass function. Mon. Not. R. Astron. Soc. 434, 1964�. doi: 10.1093/mnras/stt1141

Spiniello, C., Trager, S., Koopmans, L., and Conroy, C. (2014). The stellar IMF in early-type galaxies from a non-degenerate set of optical line indices. Mon. Not. R. Astron. Soc. 438, 1483�. doi: 10.1093/mnras/stt2282

Springel, V., Wang, Y., Vogelsberger, M., Naiman, J., and Hernquist, S. L. (2018). Redshift evolution of the fundamental plane relation in the IllustrisTNG simulation. Mon. Not. R. Astron. Soc. 475, 676�. doi: 10.1093/mnras/stx3304

Springob, C., Magoulas, C., Mould, J., Proctor, R., Colless, M., Heath Jones, D., et al. (2012). The 6dF galaxy survey: stellar 351 population trends across and through the fundamental plane. Mon. Not. R. Astron. Soc. 420, 2773�. doi: 10.1111/j.1365-2966.2011.19900.x

Teerikorpi, P., Bottinelli, L., Gouguenheim, L., and Paturel, G. (1992). Investigations ofthe local supercluster velocity field. I. Observations close to Virgo, using Tully-Fisher distances and the Tolman-Bondi expanding sphere. Astron. Astrophys. 260, 17�.

Tonini, C., Jones, D. H., Mould, J., Webster, R., Danilovich, T., and Ozbilgen, S. (2014). The fundamental manifold of spiral galaxies: ordered versus random motions and the morphology dependence of the Tully-Fisher relation. Mon. Not. R. Astron. Soc. 438, 3332�. doi: 10.1093/mnras/stt2442

Tortora, C., La Barbera, F., Napolitano, N. R., de Carvalho, R. R., and Romanowsky, A. J. (2013). SPIDER–VI. The central dark matter content of luminous early-type galaxies: benchmark correlations with mass, structural parameters and environment. Mon. Not. R. Astron. Soc. 425, 577�. doi: 10.1111/j.1365-2966.2012.21506.x

Tully, R. B., and Fisher, R. (1977). A new method of determining distance to galaxies. Astron. Astrophys. 54:661.

van Dokkum, P., Romanowsky, A., Abraham, R., Brodie, J., Conroy, C., Geha, M., et al. (2015). Spectroscopic confirmation of the existence of large, diffuse galaxies in the Coma cluster. Astrophys. J. 804:26. doi: 10.1088/2041-8205/804/1/L26

van Dokkum, P., Wasserman, A., Danieli, S., Abraham, R., and Brodie, J. (2019). Spatially resolved stellar kinematics of the ultra-diffuse galaxy dragonfly 44. I. Observations, kinematics, and cold dark matter halo fits. Astrophys. J. 880:91. doi: 10.3847/1538-4357/ab2914

Walker, M., Mateo, M., Olszewski, E., Penarrubia, J., Evans, N., Gilmore, G., et al. (2009). A universal mass profile for dwarf spheroidal galaxies? Astrophys. J. 704, 1274�. doi: 10.1088/0004-637X/704/2/1274

Wolf, J. (2010). Modeling mass independent of anisotropy: a comparison between Andromeda and Milky Way satellites. Highlights Astron. 15:79. doi: 10.1017/S174392131000832X

Keywords: galaxies: distances and redshifts, galaxies: elliptical and lenticular, galaxies: stellar content, galaxies: spiral, stars: luminosity function, mass function

Citation: Mould J (2020) Understanding the Fundamental Plane and the Tully Fisher Relation. Front. Astron. Space Sci. 7:21. doi: 10.3389/fspas.2020.00021

Received: 14 February 2020 Accepted: 24 April 2020
Published: 26 May 2020.

Didier Fraix-Burnet, UMR5274 Institut de Planétologie et dɺstrophysique de Grenoble (IPAG), France
Alessandro Pizzella, University of Padova, Italy

Copyright © 2020 Mould. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.



Comments:

  1. Poni

    Many thanks for the help in this question.

  2. Stearn

    I believe that you are wrong. Let's discuss. Email me at PM.

  3. Marleigh

    Creatively!

  4. Laurian

    You are making a mistake. Let's discuss this. Email me at PM, we'll talk.

  5. Benjiro

    I apologize, but I think you are wrong. I offer to discuss it. Write to me in PM.

  6. Kazram

    Agrees, very useful room

  7. Arashikasa

    and can you paraphrase it?



Write a message