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A Study of Active Galactic Nuclei in Low Surface Brightness Galaxies with Sloan Digital Sky Survey Spectroscopy

Active galactic nuclei (AGN) in low surface brightness galaxies (LSBGs) have received little attention in previous studies. In this paper, we present detailed spectral analysis of 194 LSBGs from the Impey et al. (1996) APM LSBG sample which have been observed spectroscopically by the Sloan Digital Sky Survey Data Release 5 (SDSS DR5). Our elaborate spectral analysis enables us to carry out, for the first time, reliable spectral classification of nuclear activities in LSBGs based on the standard emission line diagnostic diagrams in a rigorous way. Star-forming galaxies are common, as found in about 52% LSBGs. We find, contrary to some of the previous claims, that the fraction of galaxies containing an AGN is significantly lower than that found in nearby normal galaxies of high surface brightness. This is qualitatively in line with the finding of Impey et al. (2001). This result holds true even within each morphological type from Sa to Sc. LSBGs having larger central stellar velocity dispersions, or larger physical sizes, tend to have a higher chance to harbor an AGN. For three AGNs with broad emission lines, the black hole masses estimated from the emission lines are broadly consistent with the well known M-$\sigma_\ast$ relation established for normal galaxies and AGNs.


Introduction
Galaxies with blue central surface brightness significantly fainter than the classical Freeman value of µ B 0 =21.65 mag arcsec −2 are commonly referred to as Low Surface Brightness Galaxies (LS-BGs). The exact defining criterion of µ B 0 , which is the central surface brightness of a galactic disk by convention, varies in the literature, though it falls mostly within µ B 0 =22.0 -23.0 mag arcsec −2 (e.g., O'Neil et al 1998;Bell et al 2000). It has been suggested that LSBGs could account for a significant fraction of all galaxies in the Universe (e.g., Freeman 1970;McGaugh et al. 1995), and thus are an important constituent of galaxies. LSBGs show some extremely different properties from high surface brightness galaxies (HSBGs). The typical value of metallicity in LSBGs is one third of the solar metallicity (Impey & Bothun 1997). Observationally, like Malin 1 (Impey & Bothun 1989), a significant number of LSBGs possess diffuse faint disks with little stellar content but substantial amounts of neutral hydrogen gas. The low surface brightnesses indicates low star formation rates (SFRs) in these systems. Indeed, it has been found that the HI surface mass densities in LSBGs are near or below the critical gas surface density for star formation threshold (Kennicutt 1989;van der Hulst et al. 1993;de Blok et al. 1996;Schaye 2004). These extreme properties imply that LSBGs are less evolved compared to HSBGs. Bulge-dominated LSBGs are redder than disk-dominated LSBGs and both can be well described as exponential surface brightness distribution (Beijersbergen et al. 1999). Bulges of LSBGs were found to be metal-poor compared to those hosted by HSBGs (Galaz et al. 2006). Schombert et al. (1990) found that there is no evidence for heavy dust obscuration in LSBGs. However, a recent study of infrared properties of LSBGs using Spitzer data indicated that modest amounts of dust exist in a fraction of LSBGs, although their metallicity and apparent transparency are low (Hinz et al. 2007).
The low surface brightness, comparable to or fainter than the night sky background (22.5 − 23.0 mag arcsec −2 in the B band), makes the detection of LSBGs difficult. As such, much less optically selected LSBGs samples than normal HSBGs have been cataloged from surveys by ground-based telescopes (e.g., Impey et al. 1996;Monnier Ragaigne et al. 2003). Impey et al. (1996) published a LSBG catalog of 693 LSBGs derived from the Automated Plate Measuring (APM) machine scans of the UK Schmidt Telescope survey plates. A catalog containing 2469 southern-sky LSBGs also from the APM scans of the UK Schmidt photographic plates was given by Morshidi-Esslinger et al (1999).
Unlike HSBGs, which have been the focus of extensive studies in extragalactic astrophysics over many years, nuclear activity in LSBGs has drawn little attention. This may be due partly to lack of large samples of LSBGs. So far, few secured AGNs with reliable detections have been reported in the literature, not mentioning their properties. Potentially, a study of AGNs in LSBGs is as important as in HSBGs for the following reasons. First, it may provide important and complementary clues to uncover the formation and growth of super-massive black holes (SMBH), since LSBGs may have experienced a different route from HSBGs in their formation and evolution. Second, in light of AGN feedback, the evolution and ecology of LSBGs may be affected by the presence of powerful AGNs. Third, a comparison of different host galaxies environments where AGNs reside in, HSBGs and LSBGs, may shed light on the triggering of AGN activity and the dependence of AGN properties on host galaxies.
However, few yet contradicting results have been given in the literature as to the fraction of LSBGs harboring AGNs. When AGN activity was first searched for via optical spectroscopy in small samples of LSBGs, a surprising result was suggested that LSBGs seem to have a higher fraction of AGNs. Among 10 giant LSBGs, Sprayberry et al. (1995) found 4 Seyfert 1 and 1 Seyfert 2 nuclei, indicating a significantly high AGN fraction. In a sample of 34 giant, HI-rich LSBGs, Schombert (1998) found a high fraction (40 − 50%) of low luminosity AGNs, similar to that in the magnitudelimited local galaxy sample studied by Ho et al. (1997a), which are mostly HSBGs. However, such a high AGN fraction could not be confirmed by Impey et al. (2001, hereafter Impey01) in a spectroscopic study of 250 LSBGs drawn from the Impey et al. (1996) LSBG sample; in contrast, they found an AGN fraction as low as less than 5%.
It should be noted that in essentially all those previous studies, the identification of AGNs was subjected to large uncertainties, due to the following limitations. Firstly, the optical spectra taken were mostly of low spectral resolution (a resolution ∼ 20Å used in Impey01) and low signal to noise ratio (S/N), and some of narrow wavelength coverage. As such, the line flux measurements were uncertain, especially those close lines suffering from blending. In most studies above, AGNs were identified as having strong low-ionization features ([NII] and [SII]) combined with [OI], unless a broad Balmer line was present, rather than based on the rigorous line flux ratio diagnostic diagrams. The only case where an emission line ratio diagnostic diagram ([OIII]/Hβ -[SII]/Hα) was invoked to separate AGNs and HII regions was in Impey01. However, there are considerable uncertainties in the line ratios, especially for Hα, which is heavily blended with [NII]λλ6548,6583. Secondly, no subtraction of starlight spectrum of the host galaxy was performed in those studies, which is important for search of AGN signatures, especially for low luminosity AGNs, as discussed in detail in Ho et al. (1997b). The spectra of host galaxy starlight could affect severely the detection and measurement of emission lines, by making some weak emission line invisible (such as Hβ), or distort the line fluxes, or even spuriously mimic weak broad emission lines.
The Sloan Digital Sky Survey (SDSS, Stoughton et al. (2002)) has acquired high quality optical spectra of a million galaxies over a large portion of the sky (Strauss et al. 2002), some of which could be LSBGs. On the other hand, we have developed an algorithm for successful removal of host galaxy starlight and for accurate emission line spectral fit (see Zhou et al. 2006 for details). These two provide us with an opportunity to revisit the above unsolved question of AGNs in LSBGs, with much better spectral S/N and resolution (R = 1800 − 2200), wavelength coverage, and data homogeneity. The high spectral quality of large LSBG samples provided by the SDSS allows us to study not only the AGN demographics, but also, for the first time, the properties of AGNs in LSBGs. This paper presents such a study of nuclear activity in a LSBG sample. We introduce the sample and the data analysis in Section 2. The demographics of nuclear activity in LSBGs are presented in Section 3, followed by a preliminary study of the properties of LSBG AGNs in Section 4. Discussion and a summary of conclusions are given in the last two sections, respectively. A cosmology with H 0 = 70 km s −1 Mpc −1 , Ω M = 0.3, and Ω Λ = 0.7 is adopted.
2. APM-SDSS sample and spectral data analysis 2.1. The APM-SDSS sample In the northern sky, the largest, well-defined optically selected LSBG sample is the catalog compiled by Impey et al. (1996), which was constructed from the Automated Plate Measuring (APM) machine scans of the UK Schmidt Telescope survey plates. It is the most extensive catalog of LSBGs in the northern sky to date, comprising 693 galaxies in the local universe with redshifts < 0.1 selected from a sky region of 786 square degrees centered on the equator. Among them, 513 galaxies have large angular sizes (The major-axis diameter D ≥ 30 ′′ at the limiting isophote of the APM scans of 26mag arcsec −2 ) and 180 have small angular sizes (D < 30 ′′ ). Most LSBGs in this catalog have central surface brightness ranging from µ B 0 =21.5mag arcsec −2 to 26.5mag arcsec −2 in the B band. It should be noted that some of the galaxies with µ B 0 at the bright end may not qualify as LSBG when the µ B 0 =22.0 mag arcsec −2 cutoff is applied. However, a significant fraction of these galaxies is still expected to be LSBGs, since the presence of a galactic bulge residing in a low surface brightness (LSB) disk may apparently result in a bright µ B 0 (Beijersbergen et al. 1999).
We searched for spectral data from the SDSS Data Release 5 (DR5) for the LSBGs in the Impey et al. sample. We found that, out of the 693 LSBGs, 194 have SDSS spectra and were classified as galaxies by the SDSS pipeline. They form our sample of study in this paper. Among them, 95 are also in the spectroscopically observed subsample presented by Impey01. Figure 1 shows the distributions of total B-magnitude and µ B 0 for the whole APM sample and the APM-SDSS subsample. It can be seen that the APM-SDSS subsample spans almost the entire ranges of the total magnitude and µ B 0 , though it drops more quickly at the faint end than the parent sample, due to the magnitude limit of the SDSS spectroscopic survey. It also shows that a large fraction of the APM-SDSS subsample has µ B 0 fainter than 22 mag arcsec −2 , the minimum of the nominal threshold for LSBGs. For the other objects with µ B 0 < 22 mag arcsec −2 , some are likely LSBGs with a (dominating) bulge. Therefore the APM-SDSS subsample can be regarded as being composed of mostly LSBGs, with possible inclusion of some intermediate galaxies in between the typical LSBG and HSBG types. For simplicity, we refer to all the sample objects as LSBGs nominally.

Spectral data analysis
The SDSS spectra have a wavelength coverage from 3800 to 9200Å with a resolution of R∼1800-2200. As was demonstrated by Ho et al. (1997a), the vast majority of the AGN population in the local universe is low luminosity AGN (LLAGN). For LLAGNs, the optical spectra taken through either slits or fibers are dominated by host galaxy starlight. The SDSS spectra were taken through a fiber aperture of 3 ′′ in diameter (corresponding to 2.9 kpc at a redshift of 0.05), and thus include large amounts of starlight from the host galaxies for the APM-SDSS sample objects. Careful removal of starlight, especially stellar absorption features, is essential for the detection and measurement of possible nuclear emission lines. For proper modelling of host galaxy starlight spectra, we use the algorithm developed at Center for Astrophysics, University of Science and Technology of China, which is described in detail in Zhou et al. (2006, see also Lu et al. 2006) and is summarized in Appendix A in this paper.
After subtracting modeled stellar spectra and a power-law continuum, the leftover emission line spectra, if any, are fitted using an updated version of the code described in Dong et al (2005), with improvement made for better recovery of weak emission lines. The broad Hα and Hβ lines, if present, are hard to separate from nearby narrow lines. As the narrow Balmer lines and the [N II]λλ6548, 6583 doublet have similar profiles to the [S II]λλ6716, 6731 doublet (Filippenko & Sargent 1988;Ho et al. 1997b;Zhou et al. 2006), we use the [S II]λλ6716, 6731 doublet lines as a template to fit narrow lines. If [S II] is weak, [O III] λ5007 is then used as the template. The [S II] doublet are assumed to have the same profiles and redshifts; and each is fitted with as many Gaussians as is statistically justified, generally with 1-2 Gaussians. Likewise, the [O III] λλ4959, 5007 doublet are fitted in a similar way. Furthermore, the flux ratio of λ5007/λ4959 is fixed to the theoretical value of 3. When a good model of the narrow-line template is achieved, we scale it to fit the narrow Balmer lines and the [N II]λλ6548, 6583 doublet. The flux ratio of the [N II] doublet λ6583/λ6548 is fixed to the theoretical value of 2.96. For the possible broad Hα and Hβ lines, we use multiple Gaussians to fit them, as many as is statistically justified. If a broad emission line is detected at ≥ 5σ confidence level, we regard it as genuine. If the broad Hβ line is too weak to achieve a reliable fit, we then re-fit it assuming that it has the same profile and redshift as the broad Hα line.
Our analysis results in detections of 131 emission line galaxies out of the total 194 LSBGs. This gives a fraction of 68% of emission line galaxies in LSBGs. The objects are list in Table 1, along with the fitted parameters of the important lines. Also listed are the stellar velocity dispersions in the central region of the host galaxies, σ * , which are obtained in the above procedure of modeling the host galaxy starlight spectra. Three out of the 131 galaxies are found to show broad Balmer emission lines and should be broad line AGNs. Their spectra are shown in Figure 2 and the parameters of the broad lines are given in Table 2. It should be noted that the widths of emission line are corrected for the instrumental broadening, which is 55-80 km s −1 for SDSS spectra.
To demonstrate the reliability of our spectral analysis, as well as the spectral quality of the SDSS, we compare our detections of broad line AGNs with those in Impey01. Among the 95 overlapping objects in both the Impey01 spectroscopic subsample and our APM-SDSS subsample, two were claimed to have broad emission lines by the authors. 1226+0105 (SDSS J122912.9+004903.7) is also found in our work with the full width at half maximum (FWHM) of Hα 4750 km s −1 , which is slightly broader than the previous value (4570 km s −1 , Impey01). The narrower FWHM value in Impey01 is likely due to the fact that broad and narrow component deblending could not be performed given the low spectral resolution (20Å). For the second object, 1436+0119 (SDSS J143846.3+010657.7), however, we cannot confirm the presence of a broad Hα line with the starlight subtracted SDSS spectrum ( Figure 3). An inspection of the original spectrum in Impey01 seems to suggest that the previously claimed broad Hα line is likely spurious and just a feature in the stellar spectrum (no starlight subtraction was performed in Impey01) when the resolution and S/N is low. Furthermore, the one with the weakest broad line among the above 3 broad line AGNs in our work (see Figure 2), SDSS J231815.7+001540.2 (NGC 7589), was missed in Impey01. This object is likely a Seyfert 1.9, which was previously found to show strong, highly variable hard X-ray emission (Yuan et al. 2004). We thus conclude that our spectral analysis results are much more accurate and reliable.
It is worth noting that the three LSBGs, J005342.7−010506.6, J111549.4+005137.5 and J133032.0−003613.5 that were classified as type 1 AGNs by Hao et al. (2005), do not show evident broad emission lines in this work. This is likely due to the difference in subtraction of narrow lines. Hao et al. (2005) modeled every narrow line with one single Gaussian. Yet we noticed that the profiles of narrow lines are asymmetric and thus we used 2 Gaussians to model each of the [SII] doublet; the fit is used as a model to subtract the narrow component of Hα and [NII], as described in section 2.2. The asymmetric profiles of the narrow Hα and [NII] components can mimic a broad Hα component (see also Ho et al. 1997b;Greene & Ho 2007). To be conservative, we do not consider these 3 LSBGs as broad line AGNs in this paper.

Spectral classification of nuclear Activity
Generally, there are three types of emission line spectra in galactic nuclei: star-forming (HII) nuclei in which line emitting gas is photoionized by radiation from hot stars, Seyfert nuclei characteristic of photoionization by a power-law continuum powered by black hole accretion, and Low-Ionization Nuclear Emission Regions (LINERs, Heckman 1980) with relatively strong low ionization lines (such as [OI] λ6300 and [NII] λλ6548,6583) and generally lower nuclear luminosities compared to Seyfert galaxies. The nature of LINER is still controversial, though an accretion-powered AGN appears to be preferred in recent studies (see, e.g. Ho et al. 1997a). Following Ho et al., we regard LINERs as a subclass of AGN in this paper.
Classification of galactic nuclei based on optical emission lines has been extensively investigated by various authors. One common and effective method is to compare the flux ratios of close lines with predictions of different photoionization models. It was first shown by Baldwin, Phillips & Terlevich (1981, Ho et al. (1997b). Using a large sample of SDSS emission line galaxies, Kauffmann et al. (2003, hereafter, Ka03) found a clear, empirical separation between star-forming galaxies and AGNs on the BPT diagram of [NII]λ6583/Hα versus [OIII]λ5007/Hβ. This classification scheme was refined recently by Kewley et al. (2006, hereafter, Ke06), by including new criteria to separate Seyferts from LINERs using the [SII]λλ6717,6731/Hα and [OI]λ6300/Hα line ratios. In this scheme, galaxies falling in between the empirical star-forming and AGN dividing line of Ka03 and the theoretical limit (maximum star-formation) of Kewley et al. (2001, hereafter, Ke01) are regarded as composite objects (also referred to as transition objects), which likely contain a metal-rich stellar population plus an AGN, either a Seyfert or a LINER (Ho et al. 1997a;Ke06) In this paper, we adopt the classification scheme of Ke06, since it is the most recent updates and also easy to use. Our careful deblending of the [NII] and [SII] doublets ensure that our spectral classification based on these criteria should be reliable.
The classification scheme of Ke06 is summarized here. First, star-forming galaxies are separated from AGNs using the Ka03 dividing line in the [NII]λ6583/Hα versus [OIII]λ5007/Hβ diagram: star-forming galaxies are those falling below and to the left-hand side of the dividing line, and AGNs are those falling above and to the right-hand side of the dividing line, i.e.
AGNs are further grouped into 3 subclasses: composite galaxies are those falling in between the Ka03 and Ke01 dividing lines in the [NII] The 131 LSB emission-line galaxies are plotted in the [NII] λ6583/Hα-[OIII]λ5007/Hβ diagram in Figure 5 (upper panel), which are marked by different symbols for different categories. It can be seen that the objects reproduce well the 'butterfly'-shaped distribution as shown in Ka03, though with much less objects. The star-forming galaxies (crosses) trace well the Ka03 dividing line, spreading over a large range of metallicity. Further separation between Seyferts and LINERs is demonstrated in Figure 5, in which the line ratios [SII]λλ6717,6731/Hα-[OIII] λ5007/Hβ (middle panel) and [OI]λ6300/Hα-[OIII]λ5007/Hβ (lower panel) are plotted for those with the lines detected with S/N> 3. For the objects with both the [SII] and [OI] lines detected with S/N> 3, these two criteria give mutually consistent classification. Among the three broad line AGN (marked as a filled squares) found in the APM-SDSS sample, two have the narrow line properties as Seyferts and one as composite objects. The resulting classification of each emission line LSBG is given in Table 1. We also overplot in Figure 1 the distributions of the total B magnitudes and µ B 0 for the emission line LSBGs. As demonstrations, in Figure 4 we show example spectra and results of spectral analysis for each of the 3 spectral types. We also list in Table 3 the host galaxy properties of the objects classified as an AGN (Seyfert + LINER + composite), as given in Impey et al. (1996).

Demographics of nuclear activity in LSBGs
Of the 194 LSBGs, there are 131 (68% ± 3%) showing emission lines. Among them, 101 (52% ± 3%) objects are classified as star-forming galaxies and 30 as AGNs (15% ± 2%; 6 Seyferts, 12 LINERs, and 12 composite galaxies). The fraction of broad line AGNs is 2%±1% among LSBGs. This result indicates that the fraction of AGNs is significantly lower than that (>40%) found for the local bright galaxy sample of Ho et al. (1997a), which is predominantly HSBG. The fraction of AGNs is even lower if not all LINERs and composite objects are AGNs.
As discussed in the sample selection above, probably not all the 194 LSBGs are low surface brightness in a strict sense. In fact, 79 (40%) of the 194 LSBGs have µ B 0 from Impey et al. (1996) brighter than 22.0 mag arcsec −2 , which are either LSBGs with (dominating) galactic bulges or simply HSBGs. Among them, there are 25 AGNs, yielding an AGN fraction of 31%. Considering possible contamination of HSBGs in this bright subsample, this fraction is likely overestimated and the actual fraction for genuine LSBGs is likely even lower. The remaining 115 galaxies with µ B 0 > 22.0 mag arcsec −2 should be mostly bona fide LSBGs (Impey01). Among them, there are only 5 AGNs, making a fraction as low as 4% ± 2%. This strengthens the above result that LSBGs have a much lower AGN fraction compared to HSBGs.
The incidence of an AGN has been found to be dependent on the Hubble type of a galaxy, that is higher in early type (E-Sb) than in late type galaxies (Ho, et al. 1997a). Since a LSBG sample has a very different Hubble type distribution from HSBGs (the former tends to consist of more late type than the latter), the above result may be a reflection of the incidence of AGNs on galaxy morphology. To investigate this possibility, we calculate the fraction of both AGNs and star-forming galaxies in each morphological type, using the Hubble type information provided in Impey et al. (1996). The distribution of the objects of each category and their detection rates over the morphological type are shown in Figure.6 (open histograms). Also plotted are the same distributions for the µ B 0 > 22.0 mag arcsec −2 subsample (hatched histograms). The numbers are also given in Table 4. It can be seen that the LSBGs have most morphological types later than Sb and peak at Sc, as expected. The detection rate of AGNs is no more than 20% in LSBs of type Sa, Sb, and Sc, and starts to drop to less than 10% in types later than Sc. This result indicates that the overall low AGN fraction of LSBGs than that of HSBGs is real, rather than a consequence that LSBGs tend to have more of later Hubble types, which have in general low AGN fractions, as known previously. Interestingly, it increases up to 50% in interacting galaxies. When galaxies with µ B 0 > 22.0 mag arcsec −2 are considered only, the detection rates are even lower, though the sample is small.

Comparison with HSBGs
Strictly speaking, an appropriate comparison of AGN detection rate between two samples requires that they should have the same redshift (distance) distributions, and have the same spectral data quality and analysis procedures. To make sure that our above results are not significantly affected by those biases introduced in sample selection and observation, we construct a comparing sample of HSBGs with SDSS spectra. The sample is drawn from the Third Reference Catalogue of Bright Galaxies (RC3) (de Vaucouleurs et al. 1991)-a catalog of typical HSBGs-in such a way that it has the same redshift (distance) distribution as that of the APM-SDSS LSBG sample below z = 0.04 1 . This results in a comparing sample consisting of 142 HSBGs with SDSS spectra. For a comparison, the redshift distribution of the HSBG sample is plotted in Figure 7 (middle panel), which is indistinguishable from that of the LSBGs in the z = 0 − 0.04 range (the K-S test gives a chance probability of 0.1 that the two distributions are drawn from the same population). The HSBG sample is systematically brighter than the LSBG one in total magnitude, as expected. The SDSS spectra of the 142 HSBGs are analyzed using the exactly same procedure as for the LSBGs in Section 2., ensuring the homogeneity in data analysis.
We compare the LSBG and HSBG samples in the range of z < 0.04, and only those with the morphological types of Sa, Sb, and Sc are considered in order to have sufficient objects to ensure statistically meaningful results. The detection rates of AGNs and star-forming galaxies for both the LSBGs and HSBGs are shown in Figure 8. The results for HSBGs (right-hand side panels) are broadly consistent with those obtained by Ho et al. (1997a), suggesting that our results are reliable. Comparisons between the LSBGs (left-hand side panels) and HSBGs show clearly that LSBGs indeed have a low AGN fraction (10-20%) than HSBGs (40-50%), regardless their morphological types. The numbers are also given in Table 5. Thus our above results are confirmed.
Interestingly, the fraction of star-forming galaxies in the LSBGs seems to be comparable to, or even slightly higher than, that in the HSBGs. A surprising difference is found in the distribution of the fraction of star-forming galaxies: in HSBGs, this fraction drops significantly from Sc to earlier types and is the lowest for Sa. While in LSBGs, it keeps a high fraction toward early types and even possible rises for the Sa type.
Summarizing, our results do not apparently support the high AGN fraction reported in Sprayberry et al. (1995) and Schombert (1998), but are consistent qualitatively with that of Impey01.  (Ka03). Therefore, the AGNs in LSBGs are mainly of low luminosity. Interestingly, as inferred from Figure.9, the AGN detection rate becomes higher with higher L[OIII], i.e. increasing gradually from ∼7% at 10 37 ergs s −1 up to ∼78% at 10 41 ergs s −1 .

Narrow line width and stellar velocity dispersion
In AGNs of normal HSBGs, it has been suggested that kinematics of the narrow line region traces well the galactic bulge potential, via the establishment of a tight correlation between the width of the narrow emission lines and the stellar velocity dispersion σ * . Here we test this relationship for AGNs in LSBGs. The value of σ * can be obtained in our modeling of the stellar spectra of the host galaxy starlight (Section 2). For 34 LSBGs (19 AGNs and 15 star-forming galaxies) with both σ * and the [NII] doublet detected at the > 5 σ level, the relation between σ * and the [NII] line width is plotted in Figure 10. Strong correlations are found (For AGNs, σ * = 0.9 × (σ[NII] − 150.0) + 155.3 ; for the whole objects, σ * = 0.97 × (σ[NII] − 150.0) + 151.4. The Spearman correlation test gives a chance probability of 8.6 × 10 −6 for AGNs only and 1.5 × 10 −9 for AGNs and star-forming galaxies.) Thus, the width of the narrow line σ[NII] traces well the stellar velocity dispersion in LSBGs.

Electron density in the narrow line region
Since in the course of our spectral analysis the [SII]λλ6717,6731 doublet is deblended, we can assess the electron density in the narrow line region (NLR) from the flux ratio of these two lines (e.g., Osterbrock & Ferland 2006;Xu et al 2007). We assume an electron temperature of T e = 10 4 K, a typical temperature of the ionized gas in the NLR of AGNs. The electron densities of AGN in both the LSBG and HSBG sample are estimated, whose distributions are shown in Figure.11. For those with [SII]λ6717/[SII] λ6731 flux ratios greater than 1.42, an upper limit of the electron densities is set to be 10 cm −3 . A comparison shows that these two distributions are significantly different (a chance probability of 7 × 10 −5 given by the K-S test), in a way that AGNs in LSBGs on have average lower NLR electron density than AGNs in HSBGs.

Dust extinction
We examine optical extinction in the emission line nuclei of the LSBGs by assuming that the Balmer decrements in excess of the intrinsic value 2.85 for HII region and 3.1 for AGNs (Veilleux & Osterbrock 1987), are caused by dust extinction. The narrow lines Balmer decrements are calculated for star-forming galaxies and AGNs for both the LSBGs and the HSBGs. For the LSBGs, the median Balmer decrement is 3.3 for star-forming nuclei and 4.0 for AGNs, which correspond to an extinction color excess E B−V = 0.16 and 0.24, respectively. For the HSBG comparing sample, the median values are 4.2 for star-forming nuclei and 4.7 for AGNs, which correspond to E B−V = 0.37 and 0.40, respectively. This indicates that dust extinction in LSBGs is relatively weaker compared to that in normal galaxies, for both AGNs and star-forming nuclei. A comparison of the distributions of the Balmer decrement between the HSBGs and the LSBGs shows that they are statistically different, for both AGNs and star-forming nuclei (a chance probability of 2.7 × 10 −7 given by the K-S test for AGNs and star-forming galaxies).

Radio and X-ray detectability of AGNs in LSBGs
Observationally, AGNs emit their power over a wide range of frequencies, from radio, optical, to X−rays or even γ−rays. Among the 30 LSBG AGNs, only one, J231815.7+001540.2 (NGC 7589) was detected in X-rays with XMM-Newton, which exhibits large amplitude variability (Yuan et al. 2004). For the other AGNs, the X-ray flux limits set by the ROSAT All-Sky Survey are comfortably consistent with the distribution of the optical-to-X-ray effective spectral indices α ox found for AGNs. Deeper X-ray observations are needed to detect more such AGNs in X-rays.
Of the 30 AGNs in LSBGs, 8 (26% ± 8%) were detected by the FIRST (Faint Images of the Radio Sky at 20 cm) survey (Becker et al. 1995)), including one with broad emission lines. Among them, 2 are resolved in their radio images. We calculate the radio loudness R, defined as the flux ratio between 1.4 GHz and the optical B-band. Six objects have R > 10 and can be classified as radio-loud. Most of the radio-loud objects of our LSBG AGNs are actually radio-intermediate (R < 100), and there is no very radio loud (R ≥ 100) AGNs. They are all weak radio sources, with 1.4GHz fluxes less than 10 mJy. For the remaining 22 AGNs, 20 were in the FIRST survey field. Assuming an upper flux limit of 1 mJy for the FIRST survey, we found that at least 13 are "radio-quiet" (R ≤ 10). This makes the fraction of radio-loud fraction as 20%-35%,

AGN fraction in LSBGs
We have shown that LSBGs have a lower AGN detection rate compared to HSBGs in the local Universe. The overall fraction of AGNs in the APM-SDSS LSBG sample is ∼ 15%. Considering that the APM LSBG sample have possible contamination of some HSBGs, the AGN fraction in genuine LSBGs can be even lower. This result holds true within each of the Hubble types from Sa to Sc. We argue that this result is not caused by any selection effects or detecting biases in observations, since it is confirmed by comparisons with the carefully chosen HSBG comparing sample. In fact, AGNs in LSBGs should be more easy to detect spectroscopically compared to those in HSBGs, since the dilution of AGN spectral features by host galaxy starlight spectra is less severe in LSBGs than in HSBGs. To check whether we have missed a substantial amount of AGNs at larger distances, we examine how the AGN detection rate varies with increasing distances. We find that the AGN detection rate keeps nearly a constant at all distances within the largest redshift of th sample (z < 0.1), and thus there is no significant number of faint AGNs missing at large distances.
In general, a low AGN occurrence rate may be possibly due to the inefficiency of fueling gas into the central black holes in galaxies. However, the underlying physical processes responsible for the fueling efficiency is unknown, which is one of the fundamental questions in AGN research. One speculation is that gas in LSBGs may have relative large angular momentum (Dalcanton et al. 1997), even in the inner disk. Alternatively, it may well be possible that this result is just a manifestation of the more fundamental differences between HSBGs and LSBGs in some of the physical properties in the central region of galaxies (such as bulges), which are more directly linked to the onset of nuclear activity.
Motivated by this hypothesis, we search for other potential dependence of the AGN occurrence rate in the LSBG sample. One such dependence is on the physical size of galaxies. Figure 12 shows the distribution of the size of galaxies in the APM-SDSS LSBG sample and the dependence of the AGN fraction on the galaxy scale. The physical scales of the LSBGs are estimated using the angular sizes measured in the SDSS imaging survey by the SDSS pipeline. As can be seen, there exists a clear trend that larger galaxies tend to have a higher fraction of AGNs. This implies that the overall AGN fraction for a sample of LSBGs depends on the distribution of the physical scales of galaxies in the sample. For the current APM-SDSS LSBG sample, the vast majority of the member galaxies are smaller than 50 kpc, which have very low fractions of AGNs. This finding also implies that, when AGN fractions are compared between two LSBG samples, the distributions of the physical scales have to be taken into account. Schombert (1998) reported a high occurrence of AGNs (∼ 50%) in his LSBG sample, which are mostly late-type, HI-massive, and large-size galaxies. In fact, using the data presented in Schombert (1998), we also find a similar strong dependence of the AGN fraction on galaxy size. We compare the distributions of galactic sizes between the Schombert (1998) sample and the APM-SDSS sample; however, no significant difference is found (the K-S test gives a probability of 68%). Thus, we anticipate that the higher AGN fraction found in Schombert (1998) than ours is perhaps due to the small sample size, as well as possibly to the relatively coarse spectral quality, and less rigorous spectral analysis and classification method employed.
A similar trend of increasing AGN fraction with the increase of the size of a galaxy is also found for HSBGs in the comparing sample. Meanwhile, we also find that the HSBG sample has relatively systematically larger galaxies in size (with a median of 42.1 kpc) than the LSBG sample (with a median of 37.4 kpc for z < 0.04); the K-S test shows that the two distributions are significantly different (a probability level 10 −5 ). As such, the observed lower AGN fraction in LSBGs than that in HSBGs in our study is likely a manifestation of the postulation that LSBGs are systematically smaller in size compared to HSBGs, if the proposed AGN dependence on the physical scale of galaxies is the case. However, these postulations need further confirmation in future studies.
We also test the possible dependence of AGN fraction on galactic bulge properties. It has been found that stellar velocity dispersion σ * is well correlated with the bulge mass and luminosity, and is thus a tracer of the gravitational potential of the bulge. Given the spectral resolution of SDSS data, the minimum values of σ * can be measured are around 70 km s −1 . For those objects without measurable σ * , we assume their σ * to be less than 70 km s −1 . Figure 13 shows the distribution of σ * for the APM-SDSS LSBG sample and for their AGNs, as well as the AGN fraction. It can be seen clearly that the AGN fraction increases in higher σ * bins. Similar trend is also found in the HSBG comparing sample, which is a known property that AGNs tend to be found in early type galaxies, where bulges are dominant. Our result in Section 3 shows that even for the same Hubble type (Sa-Sc), LSBGs have a lower AGN fraction than HSBGs. In the context of the AGN fraction dependence on bulge properties, this may imply that within a given morphological type, LSBGs have either relatively smaller bulge mass or lower fraction of galaxies with bulges, compared to HSBGs. Again, this postulation needs confirmation by future studies. The dependence of AGN fraction on both the size of galaxies and galactic bulge property is not surprising, since galaxy sizes and σ * are strongly coupled in the samples studied here. However, we consider the latter relation is perhaps more fundamental, since it has becoming known that the growth of galactic bulges and the growth of central black hole are somehow related (Ferrarese & Merritt 2000;Gebhardt et al. 2000).

Black hole growth in LSBGs
The broad Hα emission lines are well detected in 3 LSBGs. We estimate the masses of central black holes using the linewidth-luminosity mass scaling relation given in Greene & Ho (2007). The values are 2.8 × 10 6 M ⊙ for SDSS J011448.7−002946.1, 2.0 × 10 7 M ⊙ for SDSS J122912.9+004903.7 and 3.4 × 10 6 M ⊙ for SDSS J231815.7+001540.2 respectively. For the two AGNs, SDSS J011448.7−002946.1 and SDSS J122912.9+004903.7, broad components of Hβ are also detected with reliable confidence. It is claimed by Vestergaard & Peterson (2006) that the absolute uncertainties in masses estimated by these mass scaling relationships are about a factor of 4. According to the scaling relationships calibrated by Vestergaard & Peterson (2006) based upon the broad Hβ luminosity, black hole masses are estimated to be 3.6 × 10 6 M ⊙ for SDSS J011448.7−002946.1 and 4.4 × 10 7 M ⊙ for SDSS J122912.9+004903.7 are found, respectively.
For these 3 AGN with central black hole mass estimates, the stellar velocity dispersion σ * can also be measured in our spectral analysis. We are therefore able to, for the first time, test the relationship between black hole mass and stellar velocity dispersion (M−σ * ) relation for LSBGs, though the number of objects is very small. The result is shown in Figure 14. It can be seen that, for LSBG, the observed data are broadly consistent within errors with the known M−σ * established based on local normal galaxies and AGNs (Tremaine et al. 2002, dashed line). However, a statistically meaningful result has to await the availability of a larger sample with both black hole mass and σ * measurements.

Conclusion
We have performed detailed spectral analysis of 194 LSBGs from the Impey et al. (1996) APM LSBG sample which have been observed spectroscopically by the SDSS DR5. Our work improves upon previous spectroscopic studies on LSBGs with high and homogeneous quality SDSS spectra and elaborate spectral analysis, which includes subtraction of host galaxy starlight spectra, and deblending narrow and broad components of the Balmer lines and doublets. These improvements allow us to carry out, for the first time, reliable spectral classification of nuclear activities of LSBGs based on the BPT classification schemes in a rigorous way. We also identified three secured broad line AGNs in LSBGs, and clarified a few spurious ones claimed in previous work. fraction of AGNs depends strongly both on the stellar velocity dispersion of the bulges and on the physical size of the galaxies, the two of which are coupled with each other. We interpret the low AGN fraction in LSBGs in terms of the postulation that, compared to HSBGs, LSBGs possess relatively lower bulge masses, or a lower fraction of galaxies with bulges, even within the same morphological type. This hypothesis can be tested in further observations in the future.
Compared to AGNs of HSBGs, AGNs in LSBGs tend to have relatively lower electron density and lower dust extinction in the NLR. As in HSBGs, the width of narrow emission lines in active nuclei of LSBGs is a good tracer of the stellar velocity dispersion in the galactic bulge. The black hole masses of the 3 broad line AGNs in LSBGs are broadly consistent within errors with the well known M-σ * relation found for nearby galaxies and AGNs.

Acknowledgements
This work is supported by the National Natural Science Foundation of China NSF-10533050 and NSF-10373004. This work has made use of the data products of the SDSS. We thank the anonymous referee for reviewing this paper. We also thank Jianguo Wang and Hongyan Zhou for their checking the SDSS spectra and valuable suggestion. We gratefully thank Poon Helen for her careful English correction.

A. SDSS starlight spectral modeling
The spectra are first corrected for Galactic extinction using the extinction map of Schlegel et al. (1998) and the reddening curve of Fitzpatrick (1999), and transformed into the rest frame using the redshift provided by the SDSS pipeline. Then host-galaxy starlight and AGN continuum, as well as the optical Fe II emission complex are modeled as where S(λ) is the observed spectrum. A(λ) = 6 i=1 a i IC i (λ, σ * ) represents the starlight component modeled by our 6 synthesized galaxy templates, which had been built up from the spectral template library of Simple Stellar Populations (SSPs) of Bruzual & Charlot (2003, hereafter BC03) using our new method based on the Ensemble Learning Independent Component Analysis (EL-ICA) algorithm. The details of the galaxy templates and their applications are presented in . A(λ) was broadened by convolving with a Gaussian of width σ * to match the stellar velocity dispersion of the host galaxy. The un-reddened nuclear continuum is assumed to be B(λ) = λ −1.7 as given in Francis (1996). We modeled the optical Fe II emission, both broad and narrow, using the spectral data of the Fe II multiplets for I Zw I in the λλ 3535-7530Å range provided by Veron-Cetty et al. (2004)[ Table A1,A2]veron04. We assume that the broad F e II lines (C b in Eq.1) have the same profile as the broad Hβ line, and the narrow Fe II lines (C n ), both permitted and forbidden, have the same profile as the that of the narrow Hβ component, or of , λ) are the color excesses due to possible extinction of the host galaxy and the nuclear region, respectively, assuming the extinction curve for the Small Magellanic Cloud of Pei (1992). The fitting is performed by minimizing the χ 2 with E host B−V , E nucleus B−V , a i , σ * , b, c b and c n being free parameters. To account for possible error of the redshifts provided by the SDSS pipeline, in practice we loop possible redshifts near the SDSS redshift, spaced every 5 km s −1 . We fit and subtracted the above model from the SDSS spectra.  3 Surface brightness in B band at the effective radius (mag arcsec −2 ) 4 Total apparent magnitude in Johnson B band (mag) 5 ogarithm of the neutral hydrogen mass in solar masses (M ⊙ ) 6 Effective radius in arcseconds, defined as the radius of a circular aperture that encloses one−half the total intensity received from the galaxy (arcsec)          (upper panel) and in the comparing sample of HSBGs (lower panel). An upper limit of n e = 10 cm −3 is set to those with F [SII]λ6717 / F [SII]λ6731 greater than 1.42, which are shown as hatched histogram. AGNs in LSBGs tend to have lower NLR electron densities than those of HSBGs (the probability that the two samples have the same distribution is P ks = 7.0 × 10 −5 ).  Tremaine et al. (2002) for local normal galaxies and AGNs.