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By including the [MATH] photometric samples discussed in 6.1 we can place further constraints on the models. In Fig. we compare the observed size evolution of the available samples, normalized to [MATH] , with the model predictions from Khochfar & Silk ( 2006a . Representing the model predictions by a single line is ju... |
[MATH] with [MATH] is very close to linear. Again, the observed size evolution is stronger than that predicted by the model. It is interesting to note that, in qualitative agreement with the model prediction, we see a hint that size evolution depends on mass in the compilation presented in Fig. . The samples containing... |
with [MATH] 6.3. Size Evolution of Individual Galaxies It appears that the observed size evolution of a factor of [MATH] between [MATH] and the present for early-type galaxies with masses |
[MATH] is similar to the predicted evolution for early-type galaxies that are an order of magnitude more massive (see Figs. and ). This suggests that the mechanism responsible for increasing the average size of early-type galaxies with time may be well understood, but that it is not implemented correctly in the current... |
(see also, e.g., De Lucia et al., 2006 , a prediction that is challenged by various observations (e.g., Cimatti et al., 2006 ; Scarlata et al., 2007 ; Cool et al., 2008 |
It is beyond the scope of this paper to fully discuss these possible discrepancies. Instead we will explore the question whether the proposed physical processes responsible for size evolution are consistent with the observed trends. In the semi-analytic models it is assumed (and this is confirmed by numerical simulatio... |
The question is whether the observed size evolution is dominated by size evolution of individual galaxies or simply by the addition of larger galaxies over time. At [MATH] only about 30–50% of the present-day early-type galaxy evolution had formed (Bell et al., 2004 ; Brown et al., 2007 ; Scarlata et al., 2007 ; Faber ... |
relation implies that the sample-averaged size increases by a factor of 1.3–1.4 between [MATH] and the present. Such evolution is thus expected in the absence of size evolution of individual galaxies and this is less than the observed evolution of a factor of 2. To explain the observed evolution by growth of the early-... |
Similarly, at [MATH] only [MATH] 10% of the galaxies with masses [MATH] had been assembled (Kriek et al., 2008 ; if those galaxies, evolve into the 10% most dense present-day early-type galaxies then an increase in average size by a factor of [MATH] 2 can be accounted for, less than the observed amount of evolution. Th... |
Cimatti et al. ( 2008 , who show that local galaxies with the same sizes and masses as galaxies in the [MATH] samples are so rare in the local universe that it can be confidently ruled out that their structure remains unchanged up until the present day. Note, however, that these arguments may be affected by the aforeme... |
We conclude that size evolution due to the addition of larger galaxies over time contributes at most half of the observed evolution in the |
[MATH] [MATH] relation. The remainder must be due to size evolution of individual galaxies. Numerical simulations have demonstrated that when early-type galaxies accrete neighbors without significant dissipational processes [MATH] does not change by much and that, to first order, [MATH] increases linearly with mass. Th... |
Simulations in a cosmological context show that an increase in size by a factor of 2 between [MATH] and the present is certainly possible |
(Naab et al., 2007 . The strong observed size evolution thus argues in favor of a scenario in which significant mass from low-mass companions is accreted onto existing early-type galaxies over the past [MATH] Gyr, which also explains the broad tidal features that are frequently observed around early-type galaxies (van ... |
Feldmann et al. ( 2008 such features are not necessarily, and are even quite unlikely to be, the result of major merger events and are most likely due to the accretion of low-mass, gas-poor satellites. |
We note that the size evolution of individual galaxies and the evolution of the sample average are inseparable because galaxies evolve in mass as well as in size. Nonetheless, it is important to distinguish this complex scenario from the simple picture in which early-type galaxies that form at different redshifts have ... |
Finally, it is remarkable that the change in the sizes of early-type galaxies is consistent with and differs by less than 15% from the change in the scale factor of the universe, [MATH] . Within the standard cold dark matter scenario this is likely a coincidence since dissipational, strongly non-linear processes that a... |
7. SUMMARY In § we construct a large sample of nearby [MATH] ) early-type galaxies extracted from the SDSS (DR6). We use the pipeline velocity dispersion measurements and obtain our own size measurements in order to construct the local dynamical mass-size relation (§ 2.2 ). In addition, we construct a sample of 50 morp... |
[MATH] with measured velocity dispersions (§ ). Sizes are determined from ACS imaging in the same manner as for the galaxies in the nearby sample, and systematic effects are quantified through simulations (§ ). The distant sample contains galaxies in the mass range [MATH] , with a typical mass of [MATH] |
The main result is that the [MATH] [MATH] distributions of the nearby and distant samples are significantly different, even after we correct for the incompleteness of the distant sample at low masses (§ ). The implied size evolution is [MATH] , or a factor of [MATH] between [MATH] |
and the present. Similarly, the projected surface densities of the distant early-type galaxies are a factor of [MATH] 4 higher than those of their local counterparts. The stellar populations of early-type galaxies that already existed at [MATH] may, for the most part, be passively evolving over the past 7–8 Gyr, howeve... |
Our results are in broad agreement (see § 6.1 ) with previously published size-evolution measurements that are based on samples without dynamical mass measurements and, in some cases, without spectroscopic redshifts, high-resolution HST imaging, and/or consistently determined sizes. We therefore conclude that systemati... |
The observed size evolution is in qualitative agreement with predictions from recent semianalytic models. However, the predicted evolution is much slower than the observed evolution. The observed size evolution of early-type galaxies can be understood within the context of the cold dark matter scenario in which galaxie... |
We thank the referee for his helpful review. A. v. d. W. would like to thank Jenny Graves for sharing her SDSS catalog of early-type galaxies, Eric Bell, Hans-Walter Rix, and Pieter van Dokkum for interesting discussions, and Sadegh Khochfar for providing his model predictions. Support from NASA grant NAG5-7697 is also... |
# Source: arxiv 0808.0081 # Title: Towards a realistic axion star # Sections: all # Downloaded: 2026-03-02T07:58:51.760241+00:00 |
Towards a realistic axion star Abstract In this work we estimate the radius and the mass of a self-gravitating system made of axions. The quantum axion field satisfies the Klein-Gordon equation in a curved space-time and the metric components of this space-time are solutions to the Einstein equations with a source term... |
1. Boson stars Boson stars (BS) are gravitationally bounded systems made of scalar particles. They were introduced for the very first time in 1968 by Kaup and later by Ruffini and Bonazzola Ruffini:1969qy . The inclusion of a self-interacting term was done in Colpi:1986ye and the stability under general perturbations w... |
[MATH] is the self-interaction parameter. BS rise as solutions of the Einstein-Klein-Gordon equations [EQUATION] where [MATH] and the energy-momentum tensor is given by |
[EQUATION] Here [MATH] denotes average over the ground state of the system of many particles. The field [MATH] is second quantized. In this formalism, [MATH] is an operator, where we have defined |
[MATH] [MATH] and [MATH] are the creation (annihilation) operators for a particle with angular momentum [MATH] , azimuthal momentum [MATH] and energy [MATH] . From operator [MATH] it is possible to construct the energy-momentum tensor [MATH] by considering an state [MATH] for which all the [MATH] particles are in the g... |
[EQUATION] By demanding regular solution at the origin and flatness at infinity, there exists a family of radial solutions characterized by the number of nodes in the radial coordinate. Those with zero nodes are called ground states. That solutions exhibit a maximum mass for a specific initial central field value |
[MATH] . It is known that boson stars with initial central field value [MATH] are stable and those with [MATH] are unstable. The magnitude of the maximum mass of the boson star depends on the value of the self-interacting coupling. It was shown in Colpi:1986ye that maximum mass scales as [MATH] where [MATH] is the Plan... |
2. The axion An axion is a scalar field originated at the Peccei-Quinn symmetry breaking phase transition Peccei:1977hh . It is one of the favorite candidates to account for the dark matter content of the universe. Its properties have been strongly constrained from astrophysical and cosmological considerations. The axi... |
[MATH] 3. Towards an axion star By doing and expansion of [MATH] we obtain [EQUATION] The addition of the potential energy density ( ) to the kinetic energy of axions give rise to a energy-momentum tensor of energy similar to eq. except for a sign with the proper identification [MATH] It is natural to investigate if th... |
Ruffini:1969qy with the potential energy eq. ( ). The Einstein-Klein-Gordon equations ( ) obtained with the metric ( ) and [MATH] computed as explained above are |
[EQUATION] where the prime denotes derivative with respect to [MATH] and we have done the definitions [MATH] [MATH] [MATH] and [MATH] |
4. Results We have solved the system ( Towards a realistic axion star ) for different values of [MATH] . As in the [MATH] case, we found a maximum mass for specific [MATH] , but, the switch in the potential sign produces a significant change in the behavior of the maximum mass. The relation [MATH] is not satisfied anym... |
[EQUATION] Plugging the axion values of [MATH] and [MATH] in [MATH] we found [MATH] and using this value in extrapolated [MATH] eq. ( ) we found [MATH] . The value [MATH] , where the maximum mass is reached, depends strongly on [MATH] . Again, by doing an extrapolation, we can estimate the critical density for and axio... |
[MATH] , that is, [MATH] few cm. for axion mass [MATH] eV. Acknowledgments A.B. has been partially supported by SEP-2004-C01-47641. J.B. is partially supported by DGAPA-UNAM. |
# Source: arxiv 0808.0093 # Title: The relationship between gas content and star formation rate in spiral galaxies. Comparing the local field with the Virgo cluster # Sections: all # Downloaded: 2026-03-02T07:58:52.976638+00:00 |
The relationship between gas content and star formation rate in spiral galaxies. Comparing the local field with the Virgo cluster. |
Abstract Context. Despite many studies of star formation in spiral galaxies, a complete and coherent understanding of the physical processes that regulate the birth of stars has not yet been achieved, nor has unanimous consensus been reached, despite the many attempts, on the effects of the environment on the star form... |
Aims. We focus on the local and global Schmidt law and we investigate how cluster galaxies have their star formation activity perturbed. |
Methods. We collect multifrequency imaging for a sample of spiral galaxies, members of the Virgo cluster and of the local field; we compute the surface density profiles for the young and for the bulk of the stellar components, for the molecular and for the atomic gas. |
Results. Our analysis shows that the bulk of the star formation correlates with the molecular gas, but the atomic gas is important or even crucial in supporting the star formation activity in the outer part of the disks. Moreover, we show that cluster members that suffer from a moderate HI removal have their molecular ... |
Conclusions. Our results are consistent with a model in which the atomic hydrogen is the fundamental fuel for the star formation, either directly or indirectly through the molecular phase; therefore galaxies whose HI reservoirs have been depleted suffer from starvation or even from truncation of their star formation ac... |
Key Words.: Galaxies: evolution – galaxies: ISM – galaxies: spiral – galaxies: clusters: individual (Virgo) – stars: formation Introduction |
A satisfactory understanding of the physical processes governing the formation of giant molecular clouds (GMC) from primeval atomic hydrogen (HI) and their instability leading to the formation of stars is still far from achieved. This is not surprising due to the complex mix of hydrodynamical and gravitational physics ... |
[EQUATION] derived for our Galaxy, the validity of this law has been tested also for external galaxies (e.g. Kennicutt 1983 for which a similar relation, usually written in terms of surface densities, holds: |
[EQUATION] Many studies of the global Schmidt law, i.e. the relationship between the disk–averaged star formation rate (SFR) and the total gas content, have been carried out on large samples of galaxies. A milestone paper on this issue is by Kennicutt ( 1998 , who studied the connection between the integrated SFR surfa... |
conversion factor might be responsible for the scatter in the H /SFR correlation. Using seven galaxies from the BIMA survey (Helfer et al. 2003 Wong & Blitz ( 2002 studied the applicability of the Schmidt law on local scales, i.e. through a comparison between the SFR and the gas surface density profiles. They found tha... |
(see the review by Boselli & Gavazzi 2006 or to various hydrodynamical interactions between the ISM and the intergalactic medium (IGM). Tidal interactions between galaxies or between individual galaxies and the cluster potential (Merritt 1984 ; Byrd & Valtonen 1990 produce both the removal of the outer and looser compo... |
can effectively remove the gas components, mainly from the outer part of the disks. Furthermore, a combination of gravitational and hydrodynamic effects can cause galaxy starvation or strangulation (Larson et al. 1980 ; Bekki et al. 2002 According to starvation, the gas that feeds the star formation in the local univer... |
, together with the description of the data reduction procedures; the analysis is given in Sec. , while we discuss our results and conclusions in Sec. and |
Data 2.1 The sample The sample of galaxies chosen for the present analysis is selected primarily according to the availability of high sensitivity, extensive CO mapping, such as in the Nobeyama CO atlas of nearby spiral galaxies by Kuno et al. ( 2007 Secondly we require that reliable H [MATH] imaging exists in the lite... |
(Helfer et al. 2003 that provides images for 44 nearby spiral galaxies. This is mainly to ensure that our flux measurements are unaffected by severe missing flux problems on scales larger than [MATH] at 115 GHz. Even though spectra from the central galaxy regions have been used to recover the missing flux or single dis... |
2.2 [MATH] data We compute the star formation rate from the intensity of the H [MATH] emission line, following the method of Kennicutt ( 1983 1998 . H [MATH] images for the VCC galaxies are retrieved from GOLDMine (Gavazzi et al. 2003 , while for the remaining galaxies we retrieved images from NED Images from GOLDMine ... |
(Kennicutt 1992 Since we consider [NII]/H [MATH] factors averaged over the entire disk, the correction underestimates the [NII] emission from the bulges of galaxies that host active galactic nuclei (AGN), where nuclear [NII] can be even stronger than H [MATH] . This is particularly severe in our sample composed of gian... |
[EQUATION] based on a Salpeter IMF ( [MATH] ) over [MATH] Furthermore we assume that a fraction [MATH] =0.57 of Lyman continuum photons ionizes the hydrogen atoms inside the star forming regions, where dust is mixed with gas (Hirashita et al. 2003 On the contrary, we neglect the correction for the escape fraction of co... |
2.3 data In the absence of a direct tracer of the H molecule, the molecular hydrogen abundance can be inferred from CO observations. We collect flux calibrated maps of the [MATH] transition at 115 GHz from the Nobeyama CO atlas of nearby spiral galaxies taken with the 45–m radiotelescope by Kuno et al. ( 2007 Despite t... |
[EQUATION] With this equation we compute the conversion factor for each galaxies (See Col. 13 in Table for references to metallicity data). For seven galaxies without published 12+log(O/H) we derive the metallicity using (Boselli et al. 2002b |
[EQUATION] calibrated on a sample of nearby and Virgo cluster galaxies. The mean discrepancy between the metallicity directly measured from spectra and derived using ( ) is 0.2 dex in our sample, not much greater than the uncertainties on the measurements themselves and significantly lower than the statistical uncertai... |
[EQUATION] where 1.36 is the helium correction factor, [MATH] is the proton mass and I co is the CO flux in K km/s. 2.4 HI data To study the distribution of the HI mass, we collect images at 21 cm from various sources For seven Virgo galaxies, we obtained moment 0 maps from VIVA, The VLA Imaging of Virgo in Atomic gas |
(Chung et al. 2008, in preparation; Chung et al. 2007 ; VIVA images have a spatial resolution of [MATH] arcsec and they reach a typical sensitivity of [MATH] cm -2 For nine field galaxies, instead, we obtain HI images from THINGS, The HI Nearby Galaxy Survey |
(Walter et al. 2008 ; THINGS images have a spatial resolution of 11 arcsec and a sensitivity of [MATH] cm -2 . For the remaining galaxies, we collect HI data from the literature, either from Cayatte et al. ( 1990 or from Verheijen & Sancisi ( 2001 . These maps have a lower spatial resolution, spanning from 40 to 70 arc... |
[EQUATION] where 1.36 is the correction factor for the helium and I HI is the column density in cm -2 The total HI mass in solar units is computed using: |
[EQUATION] where the total HI flux SintP (Jy km/s) is from ALFALFA, The Arecibo Legacy Fast ALFA Survey (Giovanelli et al. 2005 , or from the HyperLeda database and D is the galaxy distance in Mpc. |
2.5 Optical data The stellar mass distribution is obtained from imaging in the NIR H band from GOLDMine or the [MATH] band from the Sloan Digital Sky Survey |
(SDSS-DR6, Adelman-McCarthy et al. 2008 . Exceptions are NGC 5236 and NGC 6951 (not imaged in the SDSS) for which we collect respectively I band and K band images from NED. In Table we show individual references. Due to their large angular dimension, our galaxies are often cut in two or more SDSS fields, thus we retrie... |
(Skrutskie et al. 2006 , thus for these galaxies we adopt the 2MASS standard calibration procedure. For all images, the typical uncertainty is [MATH] 0.05 mag. SDSS images are calibrated (within 1% accuracy) using the zero-points derived from a set of parameters (calibration constant, air mass and extinction coefficien... |
[EQUATION] with [MATH] and [MATH] chosen accordingly to the band used. We use B–V [MATH] from HyperLeda in combination with NIR data and |
[MATH] [MATH] for [MATH] band data. The mean dispersion on M/L is 0.1 dex. 2.6 The surface brightness profiles For each galaxy we derive a calibrated surface brightness profile at four frequencies. All images are firstly astrometrically calibrated using GAIA, then aligned and resampled to 3 arcsec/pixel. Stars near the... |
that fits elliptical isophotes to the galaxy images. Starting from a set of initial parameters given manually for the NIR or [MATH] band imaging, the fit maintains as free parameters the ellipse center, the ellipticity and the position angle; the ellipse semi–major axis is incremented by a fixed fraction of its value a... |
[MATH] [MATH] and [MATH] in [MATH] ; the star formation rate surface density profiles [MATH] are in [MATH] Moreover, we compute the color profiles: [MATH] |
[MATH] and [MATH] Fig. illustrates an example of the imaging material and density profiles for the galaxy NGC 4051. From top-right (anticlockwise): H [MATH] net; [MATH] -band (SDSS); CO image; surface brightness profiles of stars (green), HI (magenta), SFR (red) and H (blue). |
Analysis 3.1 The Schmidt law Following Kennicutt ( 1998 Wong & Blitz ( 2002 and Boissier et al. ( 2003 we test the validity of the Schmidt law on both local and global scales. |
3.1.1 The local Schmidt law Figure (left) shows the correlation between the SFR and the H surface brightness in the individual galaxies belonging to the studied sample; in doing this comparison, we exclude the nuclear regions as previously discussed. Since in each galaxy the profiles do not have exactly the same radial... |
Inspection of the left panel of Figure shows that the faintest points in the SFR/H relation that belong to the outer parts of the disks significantly deviate from the correlation driven by the points associated with the inner part of the galaxy disks. For the remaining 60% of the correlated galaxies, we obtain a reliab... |
Wong & Blitz ( 2002 [MATH] ). Despite this overall agreement, there are slightly differences in the individual indexes [MATH] for the five galaxies we have in common, mainly due to the fact that we exclude the innermost galaxy regions and that Wong & Blitz choose a conversion factor [MATH] that does not vary as a funct... |
We checked that there is no evident correlation between the star formation rate and the atomic hydrogen, especially in the inner part of the galaxy disks where the H [MATH] emission is often strong but usually there is a low abundance of HI. To study the role of the total gas in the Schmidt law we compute the surface d... |
that was suggested by Wong & Blitz, the important difference between our results and theirs is that the addition of HI improves this correlation, significantly reducing the number of galaxies for which the Schmidt law fails in the outer part of the disks. Therefore we cannot agree with the conclusions of Wong & Blitz t... |
3.1.2 The global Schmidt law After having studied the local Schmidt law, we focus on its applicability while considering integrated quantities; therefore, we compute for each galaxy the total SFR and the gas surface density, by integrating along the profiles. In Figure we show the correlation between the SFR and the H ... |
3.2 The environmental effects In the previous section we have shown that the atomic hydrogen seems to play some role in the star formation process, especially at the edge of galaxy disks; moreover, the atomic hydrogen, built up during the cosmological nucleosynthesis, is the primeval constituent of the molecular hydrog... |
[MATH] [MATH] has been found to be linearly correlated to the galaxy linear diameter [MATH] as [MATH] , where [MATH] (kpc) is determined at the [MATH] B–band isophote, and [MATH] and [MATH] are weak functions of the Hubble type. Here we adopt the updated coefficients from Solanes et al. ( 1996 . In the following analys... |
3.2.1 Global abundances Firstly we focus on the relationship between the global SFR, H mass and stellar mass as a function of the deficiency. Therefore, for each galaxy we compute a mean color along the radial profile between three pairs of quantities: |
[MATH] [MATH] and [MATH] , averaged over the entire disk. Since the color profiles typically exhibit a radial gradient that in some cases can be significant, considering a mean value for each galaxy may sometimes be a too crude assumption. We quantify this effect calculating the standard deviations [MATH] and we obtain... |
[MATH] with a mean of [MATH] dex for [MATH] [MATH] with a mean of [MATH] dex for [MATH] and [MATH] with a mean of [MATH] dex for [MATH] |
these deviations, plotted in Fig. , provide an estimate of the uncertainty in addition to the errors in the profile calibrations. To clarify the physical meaning of these colors we notice that [MATH] is similar to the H [MATH] equivalent width. In fact the [MATH] color and the H [MATH] equivalent width (E.W.) (retrieve... |
(Gavazzi et al. 2008 , the H mass to luminosity ratio M [MATH] /L (Boselli et al. 1997 and the H [MATH] equivalent width (Gavazzi et al. 1996a |
decrease; in other words, the smallest galaxies are, relative to their mass, the richest in gas and the most active in star formation. Before studying if the above three sets of colors display a residual dependence on [MATH] independently of their mass, we need to correct for the primary luminosity dependence. Unpertur... |
[EQUATION] [EQUATION] In Figure we plot, as a function of the HI deficiency, the residuals [MATH] (left panel) and [MATH] (right panel) computed using the previous equations. Inspecting the left panel, we can see a significant correlation ( [MATH] ) between the [MATH] and the deficiency; since environmental processes d... |
[MATH] and the [MATH] , showing that molecular hydrogen, even if well bounded in the galaxy potential well, can be perturbed by the HI removal, at least indirectly. Conversely we find (not shown) that [MATH] and [MATH] are uncorrelated quantities ( [MATH] ), suggesting that the efficiency of molecular gas to star conve... |
3.2.2 Radial behavior After having shown that both the SFR and the molecular abundance are reduced in deficient galaxies on a global scale, a new question arises: is this reduction mainly due to a global quenching or it does take place primarily in the external disk, producing a truncation in the star forming disk? Thi... |
and we compute the mean colors in bins of r/r 25 , averaging over all galaxies in each bin. In Figure we show a comparison between the mean [MATH] profile for deficient (dashed lines) and non deficient (continuous lines) galaxies; from left to right, the deficiency threshold increases, i.e. in the left panel deficient ... |
Increasing the deficiency threshold (middle panel) the gap increases up to 0.6 dex, while for the highest deficient galaxies [MATH] (right panel) the gap increases up to 0.8 dex. Moreover, there are no galaxies with H [MATH] emission beyond r/r [MATH] ; therefore, for extremely deficient galaxies, besides the global qu... |
[MATH] 0.2 dex. The existence of a significant correlation between the extent of the HI disk and the [MATH] parameter is a well known result (e.g. Cayatte et al. 1994 implying that environmental effects, and in particular ram pressure stripping, perturb the ISM distribution outside-in, as also found in the simulations ... |
[MATH] cm -2 , as a suitable measure of the HI disk. This threshold well matches the sensitivity of most of our HI data, except for NGC 3521, 4192, 5055, 5236 and 5457 where the HI column density stays above the threshold at all radii, but their exponential decay can be confidently extrapolated outside; only for NGC 44... |
The results of this analysis are summarized in Figure , where we plot against [MATH] the mean radial gradients for the outer part of the [MATH] (top panel) and [MATH] (bottom panel) color profiles; the mean values are derived averaging in four bins of deficiency (0-0.4, 0.4-0.65, 0.65-0.90, [MATH] 0.90) and the error b... |
[MATH] color profiles are similar for non deficient and moderately deficient galaxies (up to [MATH] ), while when considering highly deficient galaxies the discrepancy becomes significant at [MATH] Finding steeper [MATH] profiles for highly deficient galaxies implies that when the |
[MATH] and thus the HI disk is reduced inside the optical radius, the SFR sharply decreases in the outer part of the disk, consistently with the truncation effect. The second panel shows that the discrepancy between the mean gradients of the |
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