An H$\alpha$ Imaging Survey of the Low-surface-brightness Galaxies Selected from the Fall Sky Region of the 40$\%$ ALFALFA \ion{H}{1} Survey

We present the observed H$\alpha$ flux and derived star formation rates (SFRs) for a fall sample of low$-$surface$-$brightness galaxies (LSBGs). The sample is selected from the fall sky region of the 40$\%$ ALFALFA {\ion{H}{1}} survey $-$ SDSS DR7 photometric data, and all the $H\alpha$ images were obtained using the 2.16 m telescope, operated by the National Astronomy Observatories, Chinese Academy of Sciences. A total of 111 LSBGs were observed and $H\alpha$ flux was measured in 92 of them. Though almost all the LSBGs in our sample are {\ion{H}{1}}$-$rich, their SFRs derived from the extinction and filter$-$transmission$-$corrected $H\alpha$ flux, are less than 1$M_{\sun}$$yr^{-1}$. LSBGs and star forming galaxies have similar {\ion{H}{1}} surface densities, but LSBGs have much lower SFRs and SFR surface densities than star$-$forming galaxies. Our results show that LSBGs deviate from the Kennicutt-Schmidt law significantly, which indicate that they have low star formation efficiency. The SFRs of LSBGs are close to average SFRs in Hubble time and support the previous arguments that most of the LSBGs are stable systems and they tend to seldom contain strong interactions or major mergers during their star formation histories.


INTRODUCTION
Low−surface−brightness galaxies (LSBGs) are galaxies whose central surface brightness is at least one magnitude fainter than the level of sky background in the dark night (Freeman 1970;Impey & Bothun 1997). Generally, they are defined as central surface brightness in the B−band µ 0 (B) > 22.0-23.0 mag arcsec −2 (Impey et al. 2001;Ceccarelli et al. 2012). LSBGs account for the bulk of the number of local galaxies, making them an important contributor to the baryon and dark matter mass budget in the local universe (O'Neil & Bothun 2000;Blanton et al. 2005;Boissier et al. 2016). Their morphologies and stellar populations distribute widely, ranging from old, highmetallicity early types to young, low-metallicity latetype galaxies (Bell et al. 2000). Even though the specific procedure of their formation and evolution is still unclear, their lower star formation rate (SFR) is consistent with the hypothesis that they are quiescent galaxies and have different star formation histories from their high surface brightness counterparts (McGaugh et al. 1995;Gerritsen & de Blok 1999;Boissier et al. 2008;Wyder et al. 2009;Schombert et al. 2013).
One of the most important parameters for understanding the evolution of galaxies is SFR. There are many approaches to deriving the SFR, utilizing the luminosity related to young massive stars, such as Hα, UV, or IR luminosities, or fitting the observed spectral energy distribution with a model (Kennicutt 1998a;Silva et al. 1998;Wu et al. 2005;da Cunha et al. 2008;Zhu et al. 2008;Noll et al. 2009;Boselli et al. 2009;Wen et al. 2014;Jimmy et al. 2016). Among those SFR tracers, Hα emission is connected with the photons whose wavelengths are shorter than the 912Å. These ionized photons are produced by young stars with ages of less than ∼10 M yr and masses higher than 17 M ⊙ (Watson et al. 2016). Therefore, compared to the approaches, the star formation timescale traced by Hα emission is shorter.
Recent and ongoing Hα image surveys provide a number of resources to study star formation. The Hα3 survey is an Hα narrow band imaging survey of the Local and Coma Super−clusters selected from ALFALFA (Haynes et al. 2011), which present the complete recent star formation and H I−rich galaxies in the Local Supercluster Fossati et al. 2013). Van Sistine et al. (2016) finished observations and data reduction for a fall sample of 656 galaxies from the H I Arecibo Legacy Fast ALFA Survey (ALFALFA), the galaxies distances between ∼20 and ∼100 Mpc, but there was not focus on LSBGs. There is an ongoing Hα image survey of LSBGs selected from the PSS-II catalog (Schombert et al. 1992). However, only 59 LSBGs have been included in Schombert et al. (2011) ′ s sample. Consequently, up to now, there are only a few Hα surveys of LSBGs, and the total number of LSBGs with available Hα photometry is not large enough to derive confirming results. Therefore, we undertake an Hα survey to follow up H I−selected LSBGs Galaxies from the 40% ALFALFA H I survey (Du et al. 2015), and we aim to study the SFR and star formation efficiency(SFE) of the H I−selected LSBGs.
There is an empirical relation between the gas surface density(Σ gas = Σ HI+H2 ) and SFR surface density (Σ SF R ), (Σ SF R ∝ Σ 1.4 gas ). Known as the Kennicutt-Schmidt Law, it reflects the relation between the large−scale SFR and the physical conditions in the interstellar medium (Schmidt 1959;Kennicutt 1998b;Bigiel et al. 2008;Leroy et al. 2008;Boissier et al. 2008;Bigiel et al. 2010;Wyder et al. 2009;Leroy et al. 2013;Boissier et al. 2016). However, such an empirical relation, generally derived on the basis of the samples of normal galaxies, might not be suitable for dwarf galaxies or LSBGs (Huang et al. 2012). Shi et al. (2011) proposed an "extended Schmidt Law," which can be suitable for LSBGs.
In this paper, we present an Hα survey for a sample of 111 LSBGs in the fall season in order to explore their SFRs and SFEs. This paper is orgnized as follows. in Section 2, we introduce our sample together with a description of the observations and data reduction. In section 3, we present the catalog of Hα flux and some derived parameters. Results and an analysis are given in section 4, and a summary is provided in section 5. Throughout the paper we adopt a flat ΛCDM cosmology, with H 0 = 70 km s −1 M pc −1 and Ω Λ = 0.7.

Sample
The ALFALFA Survey is a second-generation blind extragalactic H I survey and provides the first full census of H I-bearing objects over a cosmologically significant volume in the local Universe. This extragalactic H I survey is especially useful for studying low-mass, gas-rich objects in the local universe (Giovanelli et al. 2005;Haynes et al. 2011;Huang et al. 2014). This survey covers 7000 deg 2 and intends to detect more than 30,000 extragalactic H I sources. The first release covers 40% of the ALFALFA survey area and is called α.40 (Haynes et al. 2011). Du et al. (2015) constructed an LSBGs sample with µ 0 (B) > 22.5 mag arcsec −2 from ALFALFA α.40 in conjunction with SDSS DR7 photometry data (Abazajian et al. 2009) with an additional constraint on the axis ratio(b/a > 0.3) to prevent the contamination from the edge-on galaxies. Because the SDSS pipeline overestimates the level of sky background and underestimates the total magnitude of galaxies by about 0.2 mag, this value can reach 0.5 mag for LSBGs (Lisker et al. 2007;He et al. 2013). Du et al. (2015) reconstructed the sky background with a better method (Zheng et al. 1999;Wu et al. 2002;He et al. 2013) to get more accurate surface brightness. The galaxy geometric parameters (e.g., disk scale length in pixels, axis ratio) are fitted and obtained by software GALFIT (Peng et al. 2002) and central surface brightness in g-bnd and r-band are calculated by auto-magnitudes from the software Sextractor (Bertin & Arnouts 1996). The central surface brightnesses in B-band are transformed from SDSS gand r-band magnitudes. The final sample includes 1129 H I−rich LSBGs, which are defined as the main LSBG sample; hereafter they are referred to as Du2015.
Our sample contains fall objects (111) from Du2015 (1129) and is located within the region of 21 h < R.A. < 2 h ; 13 • < Dec. < 16 • and 23 • < Dec. < 33 • . To obtain more accurate SFRs of LSBGs, an Hα imaging survey is needed. We observed the Hα images of a sample of 111 LSBGs located in the fall sky. All members of our LSBGs sample are belong to a blue cloud and are in a star formation sequence.
We show the distributions of some photometric and H I parameters, including central surface brightness, heliocentric velocity, distance, radius containing 50% of Petrosian flux(r 50 ) in the SDSS r-band, H I mass, and stellar mass, of the LSBGs in our fall sample (royal blue) and Du2015(sky blue) in Figure 1. All the H I parameters (heliovelocity, distance, H I mass) are derived from the α.40 catalog, and the heliocentric velocity of the H I source cz ⊙ is in units of km s −1 (Haynes et al. 2011).
Central surface brightness and r 50 and g,r magnitudes are from Du2015. The stellar mass is derived from the r-band magnitude and the g − r color using the formula from Bell et al. (2003).
The distances used in this paper are estimated from two different approaches (Haynes et al. 2011). when the recession velocity (cz ⊙ ) of a galaxy is larger than 6000 km s −1 , the distance is estimated from cz cmb /H 0 ; for those whose cz ⊙ < 6000 km s −1 , a velocity model is used (Haynes et al. 2011) to derive their distances. The peak of the H I mass distribution of our sample is logM HI [M ⊙ ] ∼ 9.7. According to Huang et al. (2014)  7.7). The peak of the stellar mass is around 10 8.5 − 10 9 [M ⊙ ] .

Observation
The observation for this LSBG sample ranged from 2014 to 2016, and the galaxies in our sample were taken in dark night. Both broad R-band and Hα narrow band images were obtained with the BAO Faint Object Spectrograph and Camera (BFOSC) attached to the 2.16 m telescope at Xinglong observatory of the National Astronomical Observatories, Chinese Academy of Sciences (NAOC). The CCD frame of BFOSC is 1152×1274 pixel 2 with the pixel scale of 0.45 arcsec and has a field of view (FOV) of 8.5×9.5 arcmin 2 . The observation was made with a gain mode of 1.08 e − ADU −1 with a readout noise of 3 e − pixel −1 . The FOV is suitable for acquiring the images of galaxies with sizes of less than 3-4 arcmin, owing to the fact that the accurate estimation the of sky background is essential for LSBGs.
Each observation adopts the same R-band filter and a suitable Hα filter. The effective wavelength λ eff of the broad R-band filter is 6407Å .There is a series of narrow band Hα filters whose center wavelengths range from 6533 to 7052Å (6533, 6589, 6631, 6701, 6749, 6804, 6851, 6900Å and 6948, 7000, and 7052Å) with an FWHM of about 55Å. All the central wavelengths and FWHMs of the Hα filters are shown in Table 1. The transmission curves of narrow Hα filters are shown in Figure 2. For each source, the R and Hα images were taken with exposures of 300s (R) and 1800s (Hα narrow band), respectively. The R-band integration time is deep enough to provid continuum subtraction for the narrow band image. The observation information is listed in Table 2.

Image Reduction
Firstly, we check the quality of the images with the naked eye. After that, we reduce the CCD frames, including overscan subtraction, bias subtraction, flat-field correction, and cosmic-ray removal, following the standard image process with IRAF provided by NOAO 1 1 IRAF is the Image Analysis and Reduction Facility made available to the astronomical community by the National Optical Astronomy Observatories, which are operated by AURA, Inc., under contract with the US National Science Foundation. STSDAS is distributed by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under NASA contract NAS 526555. Then, the celestial coordinates are added to each image using Astrometry.net.
The next step is sky background construction, which is the most critical step of data reduction. Sextractor is employed to detect faint or extended objects in the gaussian smoothed image. A mask image is produced after taking all the detected objects off. In order to obtain the large-scale structures of the background, a median filter of 70×70 pixel 2 is applied to the mask image to reduce the random noise and to fill in the mask regions with surrounding sky regions. The constructed sky background image is subtracted from each image. Figure 3 shows an example of the original image, the constructed sky background, and the background-substracted images; all three images are in the same value scale range. We can see that the sky background reflects the vignetting and non-uniformity distribution. We also compare the fluctuation of the original and sky-subtracted images in Figure 4. From Figure 4, the median distribution of the background after being sky-subtracted is more closer to 0. The fluctuation of sky-subtracted image(blue solid line) is much less than that of the original image (black dashed line).
Since the Hα images contain contributions from both Hα emission and the underlying stellar continuum, it is also important to remove the stellar continuum to get the real Hα emission. Here, we adopt the R-band image as the stellar continuum, due to the fact that the wavelength coverage of R-band is wide enough to be dominated by the stellar continuum. In order to subtract the continuum from the observed Hα frames, we must scale the continuum flux of Hα to same level as the flux of R-band image. In this process, we assume that field stars have no Hα emission, which means that they should have the same continuum flux ratios between Hα and R-band images. We define the count ratio of the wide R-band and narrow Hα band as WNCR: Here c W,cont and c N,cont are the measured count of the wide R-band and narrow Hα band filters. Statistically, the median WNCR of these field stars could be treated as the scale factor to subtract the continuum from the Hα image. To obtain an accurate WNCR, we adopt aperture photometry, with the radii of 5 times the FWHM ofthe point-spread-function for stars in each image, using Sextractor and selected field stars with S/N greater than 20. To match the continuum, Hα image multiply WNCR and subtract the R-band image. It is tricky to adjust the value around WNCR to get the best scaled one. Finally the continuum is removed from scaled Hα images, when the residual fluxes of most selected field stars reached a minimum.
The scaled values we used are from field stars, However, the scaled value of the object galaxies is somewhat different. The color of the studied galaxy is different from that of the field stars. The color effect of field star would cause errors, leading to underestimates as large as 40% and overestimates as large as 10% when measuring Hα equivalent width (Spector et al. 2012). To quantify the errors, we selected different spectral types (F,G,K) of stars taken from the MILES stellar library.
Because all our sample galaxies are located at high galactic latitude (82 % sample > 30 • ) and M stars are too faint, only F G K stars were considered, the  WNCR error can be under-estimated as large as 7% and overestimated as large as 7%. Figure 5 shows the R-band, Hα narrow band and continuum-subtracted Hα images of LSBG AGC 102243 from left to right, as an example. As Du2015 derived from the SDSS survey, the flux calibrations for the observed broad and narrow band images are undertaken depending on the SDSS photometry. The field stars with S/N > 20 in both SDSS and our R-band image are selected for flux calibration. Here, the aperture magnitudes of the SDSS r-band and i-band are used to calculate the Johnson R-band magnitudes based on the Equation 2 ) as follows. The John-son R-band magnitude is transformed to AB magnitude systems with Equation 3 (Frei & Gunn 1994). Then, the AB magnitude is transformed to flux density with Equation 4.
Based on this formula, we derive the averaged calibration factor (flux density per count) of each image, which is then applied to calibrating the photometric fluxes in both R-band and continuum-subtracted Hα images.

Photometry
An elliptical aperture is adopted to perform photometry on both R-band and Hα band images. Firstly, the broad R-band image is used to determine photometric radius. Helped by the IRAF task ellipse, we can obtain the profile of the total flux counts enclosed by an elliptical aperture, along with the semimajor axis. Then, the flux at which the growth curve reaches 25 magarcsec −2 , the semimajor axis(a) and semimini axis(b) are adopted as the optical photometry radius. Hα flux is total flux enclosed by elliptical area. There are 111 objects in total and 19 objects cannot be detected because of their weak Hα emission.
where T ′ (λ) is the transmission curve, T ′ (Hα) is the direct transmission at galaxy-redshifted Hα wavelength from the transmission curve, T (Hα) is the normalized transmission at the galaxy-redshifted Hα wavelength, and λ1 and λ2 are the starting and ending wavelengths of the transmission curve. FWHM is the full width at half maximum of the Hα filters. The corrected Hα flux is obtained after dividing the normalized transmission T(Hα).
The bandwidth of R-band filter we used is wide enough, which leads to the fact that, apart from the stellar continuum, the observed flux in the R filter still contains the contribution from Hα emission, which will result in the loss of Hα flux during the process of stellar continuum subtraction. Fortunately, such a loss can be estimated (about 4%) and corrected according to the bandwidth of both the R and Hα filters.
The extinctions for the galaxies in our sample include the contributions from both Galactic and intrinsic extinctions. For nearby galaxies, their Hα emission feature is covered by the SDSS r filter. Therefore, we adopt the extinction value in the SDSS r-band to correct observed Hα Galactic extinction. Generally, intrinsic extinction correction is derived from the Balmer emission line ratio of F Hα /F Hβ . The color excess E(B-V) can be derived from [F Hα /F Hβ ]/[F Hα0 /F Hβ0 ] according to CCM extinction law (Cardelli et al. 1989). Here, we adopt the intrinsic ratio F Hα0 /F Hβ0 as 2.87 for H II galaxies, then the extinction correction of Hα flux is calculated from A Hα = 2.468E(B-V) (Calzetti 2001). However, only 20% of the LSBGs in our fall sample have nuclear fiber spectra from SDSS. Therefore, we have to adopt the same extinction correction and assume that there is no extinction gradient for all sample LSBGs. In total, 510 LSBGs from Du2015 have available SDSS spectra and Balmer ratio F Hα /F Hβ derived from the MPA-JHU catalog of SDSS DR7. Finally, we adopt a median value of F Hα /F Hβ = 3.1493 for the 510 LSBGs as the extinction correction for all sample LSBGs.
Owing to the approximate 60Å FWHM bandwidth of those Hα filters, [N II]λλ6548, 6584 features also contribute to the obtained Hα images. We can remove these [N II] features following equation 6 with the assumption of the a fixed ratio of [N II]/Hα throughout all the galaxies.

Hα Flux and Reliability
After all the corrections above, we get the total Hα flux for each LSBG. In order to compare with previous works, we check eight LSBGs from our spring sample which that also belong to the Hα3 survey (Gavazzi et al. 2015). Figure 6 shows a comparison between the LSBGs fluxes estimated by us and those derived from the Hα3 survey, and the upper panel is the ratio between Hα3 survey flux and ours. The differences between them are around 0.1 dex and less than 0.18 dex. Roughly speaking, these two calibrated Hα fluxes are consistent.
Since 20% of the LSBGs in our fall sample have SDSS fiber spectra, the Hα flux can also be derived directly from the MPA-JHU directly. We firstly measure the Hα flux on the image within the SDSS fiber diameter(3 ′′ ) and then compare with Hα flux from SDSS fiber spectra in Figure 7. Most of the Hα flux is consistent. There are two objects that deviate far away from the SDSS fiber flux. After checking with an Hα image we found that there is no detectable Hα emission where the fiber is located.
We also check the SFR of these LSBGs. Due to the 3 ′′ fiber diameter, an aperture correction is needed to get the total Hα flux of the whole galaxy. Here, we assume that the Hα emission follows the same distribution as the SDSS r-band image. The value of the aperture correction can be calculated from the difference between the fiber and Petrosian magnitudes in r-band as follows: Here, m petro and m fiber are Petrosian and fiber magnitudes in the r-band, respectively. F Fiber represents the Hα flux of a galaxy in the given fiber aperture, whereas F petro is the total Hα flux inside the Petrosian aperture. Hα emission traces the location of the star formation region and also provides a fairly robust quantitative measure of its current SFR. The SFR of the LSBGs in our sample is calculated from the Hα luminosity and using the following calibration (Kennicutt 1998b).  Figure 8 shows the a comparison between the SFRs of LSBGs calculated from an Hα image and Hα spectrum. For most of the LSBGs in our sample, the SFRs derived from SDSS spectra are less than those from Hα images, and there are two LSBGs (AGC 101812, AGC 112503) showing large deviations, probably due to the aperture correction. Checking the SDSS images of AGC 101812 and AGC 112503 shows that there exist several bright blue knots outside of the fiber region. Thus, aperture corrections have largely underestimated the total Hα emission. Therefore, it isinadequate to calculate the total Hα flux for the entire galaxy solely from the fiber spectrum.
All the Hα flux and other basic parameters of LSBGs are listed in Table 3. The table columns can be briefly described as follows: Column 1 : galaxy name in terms of AGC number. Column 2: the semimajor axis from elliptical photometry (kpc), which is the radii at 25 magarcsec −2 . Column 3 : the ellipticity from the elliptical photometry. Column 4 and 5 : logarithm of the Hα flux and error (erg s −1 cm −2 ). Column 6 : the logarithm of the SFR (M ⊙ yr −1 ). Column 7 : the logarithm of the SFR surface density (M ⊙ yr −1 kpc −2 ). Column 8 : the logarithm of the H I mass taken from the α.40 catalog (Haynes et al. 2011). Column 9 : the logarithm of the H I gas surface density (M ⊙ pc −2 ).
We will explore the SFR and SFR surface density, and H I gas and H I gas surface density in the next section.

The Star Formation and Gas Surface Density
For each LSBG in our sample, the enclosed region of elliptical photometry is used as the optical area to calculate the star formation surface density(Σ SF R ). For the majority of the targets, the beam size of ALFALFA H I observation is 3.5 arcmin, which is too large to obtain a suitable H I size. Hence, we have to derive the H I size from the calibrated optical photometry size. r HI /r 25 is almost constant (1.7±0.5) and shows weak dependence on the type from S0 to Im (Broeils & Rhee 1997;Swaters & Balcells 2002;Jaskot et al. 2015). We adopt 1.7 times the optical photometry radii as the H I radii. Hence, the H I surface density Σ HI is calculated from the following Equation: Σ HI = M HI π (1.7 2 ab) Here, M HI is the H I mass derived from the ALFALFA catalog, and a and b are the semimajor and semi-minor radii of photometry ellipticals, respectively. SFE is defined as the ratio of SFR and gas mass. Generally, the gas in a normal galaxy consists of ionized, atomic, and molecular gas. Since our sample is an H I-selected sample and lacks of molecular observations, we just calculate SF E HI as follows: The distributions of the SFR, SF E HI and Σ SF R , Σ HI are shown in Figure 9. For comparison, we also show the distributions for samples of star forming and starburst galaxies. In panels (a) and (b), star-forming galaxies are derived from Young et al. (1996), and star burst galaxies are from Jaskot et al. (2015). In panels (c) and (d), both star forming galaxies and starburst galaxies are derived from Kennicutt (1998b). Compared with star-forming and starburst galaxies, both the SFR and SF E HI of LSBGs are lower than those of star forming galaxies by approximately one order of magnitude, and even far lower than those of starburst galaxies. Furthermore, the SFR surface densities Σ SF R of LSBGs are even about more than one order of magnitudes lower than those of star forming galaxies. Figure 10 shows the relation between SFR surface density and H I surface density (Σ HI ) . The blue symbols are star forming (disk) galaxies from Kennicutt (1998b). The red circles are galaxies belonging to the Local supercluster (Gavazzi et al. 2012) and the black points are LSBGs in our sample. The orange stars are LSBGs from Wyder et al. (2009). Following O'Neil et al. (2003, we plot dotted lines with SFEs of 1%, 10%, and 100% in a timescale of star formation of 10 8 yr, corresponding to typical orbital timescales in galaxies. The Kennicutt-Schmidt law is plotted as a black solid line. The coverage of our LSBGs is similar to that of Wyder et al. (2009) LSBGs, but is toward to even lower star formation surface density. From Figure 10, LSBGs and star forming galaxies are in the same region of the H I surface density, but LSBGs have much lower SFR surface densities than star-forming galaxies. Galaxies in the Local Supercluster have a more diffuse Σ HI distribution.

Kennicutt-Schmidt Law
Several previous works tried to detect CO emission in LSBGs. However, most of them only gave upper limits on CO content, and a few LSBGs detected molecular gas. (Matthews & Gao 2001;O'Neil et al. 2003;Matthews et al. 2005;Das et al. 2010). Cao et al. (2017) observed the CO (2-1) of nine LSBGs from Du2015 with JCMT, but none of them is detected CO (2-1) emission, so only upper limits M H2 are given. The M H2 /M HI ratios are less than 0.02, which indicates a shortage of molecular gas in LSBGs (Cao et al. 2017). Bigiel et al. (2008) derived a correlation between SFR surface brightness density and H 2 surface density,

H2
(11) which helps us to estimate the approximate H 2 surface density from this relation. Even though H 2 gas is not distributed as the H I gas Lisenfeld et al. 2011), Equation 11 can be used as a rough estimation of Σ H2 . To get accurate values, future interferometric H I and CO data are necessary.
From Figure 11, gas surface density Σ HI+H2 (red circles) is very close to Σ HI (black dots), which is consistent with our previous assumption: H I dominates the gas content of our LSBGs. All LSBGs are located at the cutoff region, deviating from the kennicutt-Schmidt law (black line), which is derived from the star-forming (blue dots) and starburst galaxies (green dots).
According to the dashed line (SFE), starburst galaxies have SFEs that are higher than 10%, and star forming galaxies have SFEs a little lower than 10%, but still much higher than 1%. Though a small number of LS-BGs are blended with star forming galaxies, LSBGs have SFEs far below those of star forming galaxies and of around 1% for most of them. In some extreme cases, SFE can even be lower than 0.1%. There is a special LSBG, AGC 748765, whose SFE is far above 10%. It has an extremely luminous H II region in its disk. Kennicutt & Evans (2012) pointed out that the gas surface density can crudely be divided into three regions: low density (Σ gas < 10M ⊙ pc −2 ), intermediate density(10M ⊙ pc −2 < Σ gas < 100 − 300M ⊙ pc −2 ), and high density (Σ gas > 100 − 300M ⊙ pc −2 ). Although the SFR surface density of LSBGs can spread more than three orders of magnitudes, their gas surface densities are in a narrow region within one order of magnitude from 1 to 10 M ⊙ pc −2 . The SFR surface density of LS-BGs does not show any dependence on gas or H I surface density. The brown line is the upper limit for the low-density region in Figure 11. The mean gas surface density for LSBGs in our sample (Σ gas = 4.1M ⊙ pc −2 ) is shown as a pink line in Figure 11. As expected, LSBGs are located in the low-density region. However, many star forming galaxies are also located in the low-density region, but with higher SFR density. The tight relation between SFR and molecular gas (Gao & Solomon 2004;Bigiel et al. 2008) demonstrates that the molecular gas could still dominate the gas in star forming galaxies. From Figure 11, the turnff point of the K-S Law is at around Σ gas = 4M ⊙ pc −2 , which is almost the lowest gas density of star forming galaxies, and also a the similar value to the mean gas surface density of LSBGs. What causes that the SFR surface density to be widely distributed in such low-density regions is worth exploring in the future work.

Star Formation History
To characterize the evolutionary status of the star formation in galaxies, we follow specific (sSF R = SF R/M * ) and HI depletion time(t dep (HI) = M HI /SF R) to study the star formation history of LSBGs. Stellar mass is derived from g-and r-band magnitudes from Du2015 follows the equation log(M * /M ⊙ ) = −0.306 + 1.097 * (g − r) + logL r /L ⊙ (Bell et al. 2003). H I depletion time and sSFR relation are shown in Figure 12. The red circles are galaxies from the Local Supercluster (Gavazzi et al. 2012) and the black solid circles are our LSBGs. The dashed line representing the sSFR value is -10.1367, which means a galaxy can gain current stellar mass in current SFR throughout the Hubble time. Here, Hubble time is adopted with 13.7 Gyr (Spergel et al. 2007). The dashed line is the boundary between the active phase of galaxies and the quiescent phase.
On average, the current SFRs in the Local Supercluster cannot account for their current masses, though they present higher SFRs than those of LSBGs. Galaxies in the Local Supercluster should experience intensive star formation events once or several times in their star formation histories. Most LSBGs are around the dashed line and some LSBGs are active phase galaxies. Even Figure 9. Distributions of (a) star formation rate; (b) star formation efficiency, SFE=SFR/mass(H I); (c) star formation surface density; (d) gas (H I) surface density. Blue represents the LSBGs in this paper. The black and red colors in (a) and (b) represent star forming galaxies from Young et al. (1996) and starburst galaxies from Jaskot et al. (2015). The green (c) and purple (d) represent star forming galaxies and starburst galaxies from Kennicutt (1998b), respectively. with such a low current SFRs, most LSBGs can still obtain the current stellar mass over the timescale of universe. They do not need a strong interacting or major merging process to occur. A stochastic and sporadic star formation scenario could explain such a low and stable star formation histories (de Blok et al. 1995;Lam et al. 2015). The lower number density environment of LS-BGs may indicate that they seldom experience galactic interacting or merging (Du et al. 2015). This is supported by the stellar populations with ages around 2 Gyr in LSBGs ). The higher t dep (HI) of our LSBGs suggest that they will have an abundant supply of H I in the future.

SUMMARY
We performed a narrow band Hα imaging survey for LSBGs selected from the 40% ALFALFA extragalactic H I survey. A sample of 111 LSBGs in the fall sky has been observed with the Xinglong 2.16m telescope. The LSBGs in this sample have recession velocities ranging from 1012 to 9889 Km s −1 and H I masses from log 10 M HI = 7.73 to log 10 M HI = 10.14. Hα fluxes of 92 objects are measured using IRAF ellipse photometry. The derived total Hα fluxes and corresponding SFRs are listed in Table 3. All the LSBGs in our sample have blue features that are similar to those of other LSBG Figure 10. Relation between SFR surface density and H I surface density. The black dots are from this paper, the yellow diamonds are LSBGs from Wyder et al. (2009), and the blue dots are star forming galaxies from Kennicutt (1998b). The red circles are galaxies in the Local Supercluster in the Hα3 survey from Gavazzi et al. (2012). The black solid line is the Kennicutt-Schmidt Law, and the three dotted lines show the H I SFEs of 100%,10%,1% in a timescale of star formation of 10 8 yr.
samples. They have lower SFRs, lower SFEs, lower star formation surface densities, lower gas surface densities and similar H I surface densities compared with normal star forming galaxies.
Most of LSBGs are in low surface density regions and are below the Kennicutt−Schmidt relation. Their SFR surface densities spread about three orders of magnitude and their SFE efficiencies are around 1% or even lower. To characterize the star formation histories of LSGBs, we adopt parameters of t dep (H I) and sSFR. From the distribution of both parameters, LSBGs tend to be gas-rich and their star formation histories tend to be stable, rarely suffering from intensive interaction or major mergers.

ACKNOWLEDGMENTS
We thank the referee for constructive comments and suggestions. This project is supported by the National Key R&D Program of China (No.2017YFA0402704), and the National Natural Science Foundation of China (grant No. 11733006,11403037, 11225316, 11173030, 11303038, 11403061 and U1531245)  . Relation between SFR surface density and H I surface density. our LSBG sample is the black solid circle (H I gas surface density) and red circles (gas surface density). The blue dots are star forming galaxies and the green dots are starburst galaxies; both are from Kennicutt (1998b). The black solid line is the Kennicutt-Schmidt Law, and the three dotted lines show the H I SFEs of 100%,10%,1% on a timescale of star formation of 10 8 yr. The pink line is the mean value of the LSBG gas surface density and the brown dashed line is the upper boundary of the low gas surface density of 10 M⊙pc −2 .
We acknowledge the support of the staff of the Xinglong 2.16m telescope. This work is partially supported by the Open Project Program of the Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences. We also thank the ALFALFA team and the SDSS team for the released data. The Arecibo Observatory is part of the National Astronomy and Ionosphere Center, which is operated by Cornell University under a cooperative agreement with the National Science Foundation. The authors acknowledge the work of the entire ALFALFA collaboration team in observing, flagging, and extracting the catalog of galaxies used in this work. The ALFALFA team at Cornell is supported by NSF grant AST-0607007 and AST-1107390 and by grants from the Brinson Founda-tion. The authors are thankfull for the useful SDSS database and the MPA/JHU catalogs. Funding for the SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England.     Table 3 continued  Table 3 continued